The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
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Two cars start moving from the same point. One travels south at 50 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.
The rate at which the distance between the cars is increasing 2 hours later is 0 mi/h, by using the Pythagorean theorem.
To find the rate at which the distance between the cars is increasing, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Let's assume that after 2 hours, the distance traveled by the southbound car is d_south and the distance traveled by the westbound car is d_west.
Since the southbound car travels at a speed of 50 mi/h for 2 hours, we have d_south = 50 mi/h [tex]\times[/tex] 2 h = 100 mi.
Similarly, the westbound car travels at a speed of 20 mi/h for 2 hours, so d_west = 20 mi/h [tex]\times[/tex] 2 h = 40 mi.
Now, we can use the Pythagorean theorem to find the distance between the two cars:
[tex]distance^2 = d_south^2 + d_west^2distance^2 = 100^2 + 40^2distance^2 = 10000 + 1600distance^2 = 11600[/tex]
distance ≈ sqrt(11600) ≈ 107.68 mi
To find the rate at which the distance between the cars is increasing, we differentiate the equation with respect to time:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 2 [tex]\times[/tex] d_south [tex]\times[/tex] [tex]\(\frac{{d(d_{\text{{south}}})}}{{dt}}\)[/tex] + 2 [tex]\times[/tex] d_west [tex]\times[/tex] (d(d_west)/dt)
Since d_south and d_west are constant (no mention of their rates of change), we can simplify the equation to:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 0
Therefore, the rate at which the distance between the cars is increasing 2 hours later is 0 mi/h.
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How are triangleABC and triangle ADE related? How do you know pls explain.
Triangle ABC and ADE are similar triangles
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.
It has been shown that angles in ABC and ADE are equal.
To show that the ratio of corresponding sides are equal
6/12 = 8/16 = 10/20
The ratios all give a value of 1/2
Therefore we can say that the triangles ABC and ADE are similar.
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What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
16
Find X.
25
X
Pythagorean Theorem
Answer:
3√41
Step-by-step explanation:
a^2+b^2=c^2
rearrange this to make x (a or b it doesn't matter) the subject
√b=c^2-a^2
now substitute this in:
√b=25^2-16^2
=369
then simple do the square root
√369
=3√41
Hope this helps!
a) angle of line of From a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three figure bearings? A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point. (b) How far is the boy now from the start- ing point? A boy runs 200 m on a bearing of 230°.
a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$
\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}
100 sin 35° = 80 sin 55°=57.73 mT
herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.
Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.
To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.
Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.
Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.
To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.
(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus
:$$c^2 = a^2 + b^2$$
where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$
c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$
Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.
Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$
Therefore, the bearing of the boy's current position from the starting point is N51°E.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The value of x is equal to 15 units.
What is the triangle midpoint theorem?In Mathematics and Geometry, the Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
In Mathematics and Geometry, a midsegment is a type of line segment that is used for connecting the midpoints of two sides of a triangle.
By applying the triangle midpoint theorem, we can determine the value of x as follows:
JH = 1/2(LM)
JH = 1/2 × 30
JH = x = 15 units.
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what is the solution to the system of equations graphed below
The solutions to the system of equations is (a) (1, 5)
Selecting the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The graph
This point of intersection of the lines of the graph represent the solution to the system graphed
From the graph, we have the intersection point to be
(x, y) = (1, 5)
Hence, the solutions to the system is (1, 5)
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if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
[tex]b(x) = \sqrt{x-4}[/tex]
Therefore, the composite function (boa)(x) is given by;
[tex]b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}[/tex]
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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Mamá compra una caja de cubitos de azúcar. María se come la capa superior (S), que tiene 77 cubitos; después se come la cara lateral (L), que consta de 55 cubitos; y finalmente se come la cara frontal (F) también. ¿Cuántos cubitos quedan en la caja
Si mamá compra una caja de cubitos de azúcar y María se come la capa superior (S) de 77 cubitos, luego se come la cara lateral (L) de 55 cubitos y finalmente se come la cara frontal (F) también, podemos determinar cuántos cubitos quedan en la caja sumando todas las partes que María ha consumido.
En total, María se ha comido 77 cubitos de la capa superior, 55 cubitos de la cara lateral y otros cubitos de la cara frontal. Como no se proporciona el número exacto de cubitos de la cara frontal, no podemos calcular el número total de cubitos que quedan en la caja.
Para obtener la cantidad final de cubitos que quedan en la caja, necesitaríamos saber cuántos cubitos hay en la cara frontal y luego restar la suma de los cubitos que María se ha comido. Sin esa información adicional, no podemos determinar cuántos cubitos quedan en la caja.
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Markshisand
Which steps should be used to compare the fractions and
O Find a common numerator.
O Add the numerators and denominators to determine which sum is larger.
O Use the "greater than" symbol to show which denominator is larger.
O Multiply the first fraction by 2 and the second fraction by 3
For the following equations find 1) the general form for all solutions 2) the solutions on the interval (pi/2)<=θ<3pi in terms of pi.
cscθ=2
For the following equations:
1) In general, the solutions can be expressed as θ = π/6 + 2πn or θ = 5π/6 + 2πn, where n is an integer.
2) The solutions within the interval (π/2) ≤ θ < 3π can be represented as θ = 7π/6 or θ = 11π/6, both in terms of π.
To solve the equation cscθ = 2, we need to find the values of θ that satisfy the equation.
1) General Form for All Solutions:
The reciprocal of sine is cosecant (csc), so we can rewrite the equation as 1/sinθ = 2. To solve for θ, we can take the reciprocal of both sides:
sinθ = 1/2
Now, we need to determine the values of θ where the sine function equals 1/2. The sine function is positive in the first and second quadrants, so we'll focus on those quadrants.
In the first quadrant (0 ≤ θ < π), the reference angle with a sine of 1/2 is π/6.
In the second quadrant (π < θ < 2π), the reference angle with a sine of 1/2 is also π/6.
To account for all solutions, we can add multiples of the period of sine (2π) to the reference angles. Therefore, the general form for all solutions is:
θ = π/6 + 2πn or θ = 5π/6 + 2πn
where n is an integer representing the number of periods of sine added.
2) Solutions on the Interval (π/2) ≤ θ < 3π in Terms of π:
For the given interval, we need to find the values of θ that satisfy the equation and lie within the interval (π/2) ≤ θ < 3π.
From the general form, we can see that the solutions that satisfy the interval are:
θ = π/6 + 2π or θ = 5π/6 + 2π
Simplifying these expressions gives us:
θ = 7π/6 or θ = 11π/6
Therefore, the solutions on the interval (π/2) ≤ θ < 3π in terms of π are:
θ = 7π/6π or θ = 11π/6π.
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What is the solution to this system of equations? 10 y = x - 2; y = - 0.5x + 7 10 (3, 2); (6, 4); (4, 6); (2, 3)
Answer:x=bx2 is the answer
Step-by-step explanation:
What did Amy do wrong
What Amy did wrong was not moving the pointer to the arc intersection with the horizontal side
What is an angle bisector?An angle bisector is defined in geometry as a line that splits an angle into two equal angles.
The steps involved in constructing an angle bisector are;
Draw an angle on your paper. Make sure one side is horizontal.Place the pointer on the vertex. Draw an arc that intersects both sides.Move the pointer to the arc intersection with the horizontal side.Connect the arc intersections from with the vertex of the angle.Learn more about angle bisectors at: https://brainly.com/question/24334771
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You can make $ when you activate a prepaid device with equipment
When you activate a prepaid device with equipment, you may have the opportunity to earn money through various means.
Firstly, as a retailer or reseller, you can make a profit by selling the prepaid device and associated equipment at a higher price than your purchase cost. This markup allows you to earn a margin on each sale.
Additionally, some service providers or retailers offer commission-based programs where you earn a commission or referral fee for each prepaid device activation. By promoting and selling these devices, you can earn a percentage of the total sale value or a fixed amount per activation.
Furthermore, you might have the chance to upsell customers on additional accessories or services during the activation process. By offering relevant accessories like cases, screen protectors, or headphones, you can increase the overall sale value and earn extra income.
It's worth noting that the specific earning potential can vary depending on factors such as the popularity of the device, the commission structure, and the competitiveness of the market. It's advisable to research and understand the terms and conditions of any commission or referral programs before engaging in such activities.
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What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
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What are 2 equations/ratios you could write to sovle for a? Do NOT SOLVE just write the equations
you would use to solve.
AN
The two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
The bigger triangle with sides t, u, v and the smaller triangle with sides q, r , s are both right triangle so we can use the ratio of sine for their angle α to get the two equations as:
sin α = u/t {opposite/hypotenuse} for the bigger triangle.
sin α = r/s {opposite/hypotenuse} for the smaller triangle.
Therefore, the two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine
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Kubin Company's relevant range of production is 13,000 to 18,000 units. When it produces and sells 15,500 units, its average costs per
unit are as follows:
Direct materials
Direct labor
Variable manufacturing overhead
Fixed manufacturing overhead
Fixed selling expense
Fixed administrative expense
Sales commissions
Variable administrative expense
Average
Cost per
Unit
$7.40
$ 4.40
$ 1.90
$ 5.40
$ 3.90
$ 2.90
$ 1.40
$0.90
Required:
1 Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 15,500 units?
b. What is the total indirect manufacturing cost incurred to make 15,500 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of
its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the
company's sales representatives' compensation.
a. When the company sells 15,500 units, what is the total direct selling expense that can be readily traced to individual sales
representatives?
b. When the company sells 15,500 units, what is the total indirect selling expense that cannot be readily traced to individual sales
representatives?
1. a. The Total direct manufacturing cost is $212,350. b. The Total indirect manufacturing cost is -$128,650. 2. a. the total manufacturing cost directly traceable to the Manufacturing Department is $212,350. b. the total manufacturing cost that is an indirect cost is $83,700. 3. a. the total direct selling expense that can be readily traced to individual sales representatives is $21,700. b. the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
1. Assume the cost object is units of production:
a. The total direct manufacturing cost incurred to make 15,500 units can be calculated by multiplying the average cost per unit for each cost component by the number of units produced:
Total direct manufacturing cost = (Direct materials cost + Direct labor cost + Variable manufacturing overhead cost) × Number of units produced
Direct materials cost = $7.40/unit × 15,500 units = $114,700
Direct labor cost = $4.40/unit × 15,500 units = $68,200
Variable manufacturing overhead cost = $1.90/unit × 15,500 units = $29,450
Total direct manufacturing cost = ($114,700 + $68,200 + $29,450) = $212,350
b. The total indirect manufacturing cost incurred to make 15,500 units can be calculated by subtracting the total direct manufacturing cost from the average cost per unit for fixed manufacturing overhead:
Total indirect manufacturing cost = Fixed manufacturing overhead cost × Number of units produced
Fixed manufacturing overhead cost = $5.40/unit × 15,500 units = $83,700
Total indirect manufacturing cost = $83,700 - $212,350 = -$128,650
Note: The negative value indicates that the fixed manufacturing overhead cost is not fully utilized within the relevant range of production. It suggests that there may be unused capacity or fixed costs that are not being allocated to the production of 15,500 units.
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units:
a. The total manufacturing cost directly traceable to the Manufacturing Department is the sum of the direct manufacturing costs:
Total manufacturing cost directly traceable to the Manufacturing Department = Total direct manufacturing cost
Using the values calculated in part 1a, the total manufacturing cost directly traceable to the Manufacturing Department is $212,350.
b. The total manufacturing cost that is an indirect cost and cannot be easily traced to the Manufacturing Department is the fixed manufacturing overhead cost:
Total manufacturing cost that is an indirect cost = Fixed manufacturing overhead cost
Using the value calculated in part 1b, the total manufacturing cost that is an indirect cost is $83,700.
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of its total fixed selling expense on advertising, and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives' compensation:
a. When the company sells 15,500 units, the total direct selling expense that can be readily traced to individual sales representatives is the sales commissions:
Total direct selling expense = Sales commissions × Number of units sold
Sales commissions = $1.40/unit × 15,500 units = $21,700
Therefore, the total direct selling expense that can be readily traced to individual sales representatives is $21,700.
b. When the company sells 15,500 units, the total indirect selling expense that cannot be readily traced to individual sales representatives is the fixed portion of the company's sales representatives' compensation:
Total indirect selling expense = Total fixed selling expense - Total direct selling expense
Total fixed selling expense = $3.90/unit × 15,500 units = $60,450
Total indirect selling expense = $60,450 - $21,700 = $38,750
Therefore, the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
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Sunita performed a transformation on trapezoid LMNQ to create L'M'N'Q', as shown
in the figure below:
What transformation did Sunita perform to create LMMQ?
1 rotation of 90 counterclockwise of the origin
2rotation of 270 counterclockwise of the origin
3 reflection across the xaxis
4reflection across the line of symmetry of the figure
Answer: rotation of 90 counter clockwise about the origin
Step-by-step explanation:
What is the area of this rectangle? Rectangle with width 5.1 cm and height 11.2 cm. Responses 16.3 cm2 16.3 cm, 2 32.6 cm2 32.6 cm, 2 57.12 cm2 57.12 cm, 2 571.2 cm2
The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.
Area = length × width
Area = 11.2 cm × 5.1 cm
Calculating the product, we get:
Area = 57.12 cm²
Therefore, the area of the rectangle is 57.12 cm².
The correct answer is: 57.12 cm².
It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.
So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
[tex]\textsf{(C)} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
To find the probability of a point chosen at random being in the shaded area of the given diagram, we first need to calculate the areas of the larger circle and the shaded circle.
The formula for the area of a circle is A = πr², where r is the radius.
Given the radius of the larger circle is 8 units:
[tex]\begin{aligned}\sf Area\;of\;the\;larger\;circle&=\pi (8)^2\\&=64 \pi \end{aligned}[/tex]
Given the radius of the shaded circle is 4 units:
[tex]\begin{aligned}\sf Area\;of\;the\;shaded\;circle&=\pi (4)^2\\&=16 \pi \end{aligned}[/tex]
Probability formula[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
To find the probability that a point chosen at random is in the shaded area, divide the area of the shaded circle by the area of the larger circle:
[tex]\sf Probability= \dfrac{16 \pi}{64 \pi}=\dfrac{1}{4}[/tex]
Therefore, the probability of a point chosen at random being in the shaded area is 1/4.
Answer:
[tex]\frac{x}{y}[/tex] 1 over 4 (one-fourth)
Step-by-step explanation:
Let f(x)
f'(x) =
-
=
1
v2x2+5x+3
Question Help:
(Use sqrt(N) to write √N)
Video Written Example
The derivative of the function [tex]f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}[/tex] is [tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
How to calculate the derivative of the functionFrom the question, we have the following parameters that can be used in our computation:
[tex]f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}[/tex]
Factor the expression
So, we ave
[tex]f(x) = \frac{1}{\sqrt{(x + 1)(2x + 3)}}[/tex]
The derivative of the function can be calculated using as follows:
[tex]f'(x) = (-\frac{1}{2})((x + 1)(2x + 3))^{-\frac{1}{2} - 1} \cdot \frac{d}{dx}[(x + 1)(2x + 3)][/tex]
Next, we have
[tex]f'(x) = -\frac{\frac{d}{dx}(x + 1) \cdot (2x + 3) + (x + 1) \cdot \frac{d}{dx}(2x + 3)}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Differentiate
[tex]f'(x) = -\frac{1 \cdot (2x + 3) + (x + 1) \cdot 2}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
This gives
[tex]f'(x) = -\frac{2x + 3 + 2x + 2}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Evaluate the like terms
[tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Hence, the derivative of the function is [tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The volume of the pyramid is 357.7 inches³.
The volume of the cone is 1230.9 yard³.
How to find the volume of a cone/pyramid?The volume of a pyramid can be represented as follows;
volume of the pyramid = 1 / 3 Bh
where
B =base areah = heightTherefore,
B = 10 × 8 = 80 inches²
Hence,
h² = 14² - 4²
h = √196 - 16
h = √180
h = √180 inches
volume of the pyramid = 1 / 3 × 80 × √180
volume of the pyramid = 357.7 inches³
Therefore, let's find the volume of the cone.
volume of the cone = 1 / 3 πr²h
h = √25² - 7²
h = √576
h = 24 yards
volume of the cone = 1 / 3 × 3.14 × 7² × 24
volume of the cone = 1230.9 yard³
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Factor using the GCMF.
6x4 + 12x³ + 15x²
2x^3 + 4x^2 + 5x
3(2x^4 +4x³+5x²)
3x² (2x² + 4x + 5)
3x^2
Answer:
3x² (2x² + 4x + 5)
Step-by-step explanation:
Step 1: Identify the coefficients.
In the given expression, the coefficients are 6, 12, and 15.
Step 2: Find the GCMF of the coefficients.
The GCMF is the largest number that can divide each coefficient evenly. In this case, the GCMF of 6, 12, and 15 is 3.
Step 3: Identify the variables.
The variables in the expression are x^4, x^3, and x^2.
Step 4: Find the GCMF of the variables.
The GCMF of the variables is the highest power of x that appears in each term. Here, it is x^2.
Step 5: Combine the GCMF of the coefficients and variables.
The GCMF of the coefficients (3) and the GCMF of the variables (x^2) can be multiplied together to get the overall GCMF: 3x^2.
Step 6: Factor out the GCMF from the expression.
To factor out the GCMF 3x^2, divide each term of the expression by 3x^2:
(6x^4 + 12x^3 + 15x^2) / (3x^2) = 2x^2 + 4x + 5
Step 7: Write the factored form.
The factored form of 6x^4 + 12x^3 + 15x^2 is 3x^2(2x^2 + 4x + 5).
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Answer:
(x + 3)(5x + 2) , (2x - 1)(3x + 5)
Step-by-step explanation:
given
A = 5x² + 12x + 6
consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 5 × 6 = 30 and sum = 17
the factors are + 15 and + 2
use these factors to split the x- term
5x² + 15x + 2x + 6 ( factor the first/second and third/fourth terms )
= 5x(x + 3) + 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(5x + 2)
then
length = x + 3 , breadth = 5x + 2 or indeed the other way round
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given
A = 6x² + 7x - 5
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 5 = - 30 and sum = + 7
the factors are - 3 and + 10
use these factors to split the x- term
6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )
= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term
= (2x - 1()3x + 5)
then
length = 2x - 1 , breadth = 3x + 5 or the other way round
Find each value given the following function:
Answer:
Step-by-step explanation:
1) f(-4) --> if x < or equal to 3
2) 1/(-4)-4
3) The answer is - 1/8
Solve for x.
OA. 9
OB. 1
OC. 4
OD.7
The value of x in the secant intersection is 4.
How to find the length in a secant?If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
Therefore, let's find the value of x using the secant intersection theorem as follows;
4(4+x + 2) = 5(5 + x - 1)
4(6 + x) = 5(4 + x)
24 + 4x = 20 + 5x
24 - 20 = 5x - 4x
x = 4
Therefore,
x = 4
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Is the following infinite sum defined?
0.69+1.38+2.76+5.52+…
Select the correct answer below:
The given infinite sum 0.16 + 0.4 + 0.1 + 0.25 + ... is defined as it converges to a finite value. Option A is the correct answer.
To determine whether the given infinite sum is defined, let's examine its pattern.
If we observe the terms in the sum, we can see that each term is obtained by dividing the previous term by 4. Specifically, each term is one-fourth the value of the previous term.
Let's verify this pattern:
Term 1: 0.16
Term 2: Term 1 / 4 = 0.16 / 4 = 0.04
Term 3: Term 2 / 4 = 0.04 / 4 = 0.01
Term 4: Term 3 / 4 = 0.01 / 4 = 0.0025
It appears that each term is one-fourth the value of the previous term. If this pattern continues, we can write the nth term as:
Term n = (1/4)^(n-1) * 0.16
To determine whether the sum is defined, we need to check whether the terms approach a finite value or converge to a specific value.
As n approaches infinity, the term (1/4)^(n-1) * 0.16 will approach zero since (1/4)^(n-1) approaches zero exponentially. Therefore, the sum of the infinite terms in this sequence will converge to a finite value. Hence, Option A is the correct answer.
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Which description is paired with its correct expression?
four less than the quotient of a number cubed and seven, increased by three; 4-2+3
five times the difference of a number squared and six; 5(6-n²)
nine more than the quotient of six and a number cubed, decreased by four; 8+²-4
9+
O twice the difference of nine and a number squared; 2(9-n²)
The correct pairings are:
a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
b) Five times the difference of a number squared and six: 5(n² - 6)
c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
d) O twice the difference of nine and a number squared: 2(9 - n²)
The correct pairings of descriptions and expressions are as follows:
Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.
Five times the difference of a number squared and six: 5(n² - 6)
This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.
Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.
O twice the difference of nine and a number squared: 2(9 - n²)
This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.
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The slope of a parabola
�
=
3
�
2
−
11
�
+
10
y=3x
2
−11x+10 at a point
�
P is 7. Find the
�
−
y− coordinate of the point
�
P
The y-coordinate of point P is 1.To find the y-coordinate of the point P on the parabola y = 3x^2 - 11x + 10 where the slope is 7, we can differentiate the equation to find the derivative. The derivative of y = 3x^2 - 11x + 10 is y' = 6x - 11.
To find the x-coordinate of point P, we can set the derivative equal to the given slope: 6x - 11 = 7. Solving for x, we get x = 3.
To find the y-coordinate of point P, we substitute the x-coordinate back into the original equation: y = 3(3^2) - 11(3) + 10. Simplifying, we find y = 1.
Therefore, the y-coordinate of point P is 1.
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State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
The triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
How to determine if triangles ∆UTS and ∆UBA are similarTo determine if triangles ∆UTS and ∆UBA are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are proportional.
If ∆UTS is similar to ∆UBA, the following conditions must be true, then each angle in ∆UTS must have a corresponding congruent angle in ∆UBA. Also, the ratio of the lengths of corresponding sides in ∆UTS and ∆UBA must be equal.
AB/ST = 984/1271 = 0.7742
UB/UT = 768/994 = 0.7742
UA/US = 648/837 = 0.7742
AB/ST = UB/UT = UA/US
Therefore triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
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