Which sequence of transformations proves that shape I is similar to shape II?
Answers
The sequence of transformations that proves that the shapes are similar is given as follows:
B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5
How to obtain the transformations?First, we have that the orientation of the figure, hence it was reflected.
The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.
The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:
3/2 = 1.5.
Hence option B is the correct option for this problem.
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Related Questions
John is a furniture maker. The graph shows the number of chairs John makes and the time it takes to make those chairs. Based on the graph, how many chairs can John make in 5 hours?
A.
55
B.
50
C.
45
D.
40
Answers
The correct answer is Option B. 50 chairs can John make in 5 hours from the graph.
John is a furniture maker and the graph shows the number of chairs John makes and the time it takes to make those chairs.
Based on the graph, the number of chairs John can make in 5 hours can be found by following the given steps:
Step 1: Look for the point on the graph where the line intersects the vertical line marking 5 hours.
Step 2: From the point on the graph found in step 1, read the horizontal line and find the point at which it intersects the y-axis.
This point will give us the number of chairs John can make in 5 hours.
According to the graph, John makes 50 chairs in 5 hours.
Therefore, the correct answer is option (B) 50.
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Geometry
Show work and if you’re a slow kid then don’t answer
Answers
Answer:
x = 26
Step-by-step explanation:
Since s║t and r is a transversal, consecutive interior angles add to 180
⇒ 2(x + 15) + (3x + 20) = 180
⇒ 2x + 30 + 3x + 20 = 180
⇒ 5x + 50 = 180
⇒ 5x = 180 - 50
⇒ 5x = 130
⇒ x = 130/5
⇒ x = 26
Answer:
x=26
Step-by-step explanation:
Given:
s || t
2(x+15) + (3x+20) = 180°
Since the sum of co interior angle is 180°
Opening bracket
2x + 30 + 3x + 20 =180
Solving like terms
5x+50= 180
subtracting both side by 50
5x=180-50
5x = 130
dividing both side by 5.
[tex]\tt x=\frac{130}{5}[/tex]
x = 26
Therefore value of x is 26.
in your view support the method that you find important to enhance the strong number sense. Provides appropriate examples for chosen method
Answers
The method that you find important to enhance the strong number sense is the use of manipulatives and hands-on activities.
Example:
Illustrating numbers and executing mathematical operations through block representations can assist students in visualizing addition, subtraction, and multiplication.
How to determine the methodUsing manipulatives and interactive activities, numerical concepts can be grasped more tangibly, as learners physically engage with these objects, thereby developing a concrete understanding of mathematics.
Students can enhance their comprehension of measurement and units by employing measurement instruments such as rulers and measuring tapes.
Through participation in these tasks, students cultivate a profound sense of intuition in regard to numbers, operations, and their interconnections, thereby establishing a firm groundwork.
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Evaluate the following improper integral. If the integral diverges, enter "DIV".
[₁
IH
Te dx=
Answers
The calculated value of the integral [tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex] is 0.7358
How to evaluate the integralFrom the question, we have the following parameters that can be used in our computation:
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex]
The above expression can be integrated using integration by parts method
When integrated, we have
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(x+1\right)\mathrm{e}^{-x}[/tex]
Recall that the x values are from 1 to ∝
This means that
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(\infty +1\right)\mathrm{e}^{-\infty} + \left(1+1\right)\mathrm{e}^{-1}[/tex]
So, we have
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + \frac{2}{e}[/tex]
Solving further, we get
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + 0.7358[/tex]
Evaluate
[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0.7358[/tex]
Hence, the value of the integral is 0.7358
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in general, the y intercept of the function F(x) = (a) (b^x) is the point _____.
Answers
Answer:
(0,a)
Step-by-step explanation:
The y-intercept of a function is the point where the graph of the function intersects the y-axis.
To find the y-intercept of the function F(x) = (a)(b^x), we can substitute x = 0 into the equation and solve for F(0).
When x = 0, we have:
=> F(0) = (a)(b^0)
=> F(0) = (a)(1)
=> F(0) = a
Therefore, the y-intercept of the function F(x) = a * b^x is the point (0, a).
Mitch is buying candy bars for his friends.
He wants to give 2 bars to each friend, and he wants to have 10 spare bars. He can afford to buy 20 candy bars.
Answers
Its the second one.
2f+10=20
(5.8 x 10)+(8.2×10⁹) in standard form
Answers
5.8 x 10 + 8.2 x 10^9 = 5.8 x 10^1 + 8.2 x 10^9
To add these numbers, we'll need to convert 5.8 x 10^1 to the same exponent as 10^9, which is 10^9.
5.8 x 10^1 can be written as 0.58 x 10^2 since 10^1 equals 10.
Now we can add:
0.58 x 10^2 + 8.2 x 10^9 = 8.2 x 10^9 + 0.58 x 10^2
Performing the addition:
8.2 x 10^9 + 0.58 x 10^2 = 8.200000058 x 10^9
Therefore, (5.8 x 10) + (8.2 x 10^9) in standard form is approximately 8.200000058 x 10^9.
O
Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5
Answers
The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.
To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.
Step 1: Apply De Morgan's laws
NOT (R AND NOT P) can be simplified as (NOT R) OR P.
Step 2: Distributive property
F5 = (P AND Q) OR ((NOT R) OR P)
Step 3: Apply associative property
F5 = (P AND Q) OR (P OR (NOT R))
Step 4: Apply absorption law
F5 = P OR (P OR (NOT R))
Step 5: Apply idempotent law
F5 = P OR (NOT R)
By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.
Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.
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The question probable may be:
Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:
F5 = (P AND Q) OR (R AND NOT P)
Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?
From the diagram below: pls help
Answers
The correct option is C, ON is the normal to the surface.
What is the segment ON?Remember that when we have an incident ray on a surface, a reflected ray will be emmited such that the angle with respect to the normal is the same one for the incident ray.
For any plane surface, this normal is perpendicular to the surface.
Here, we can see that ON is normal to the sruface of reflection, thus, the correct option is C, segment ON is the normal.
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solve the exponential equation for x. 2^9x+2 = 16^5x-2
Answers
The value of is 2/11
How to determine the valueTo determine the value, we have;
Index forms are mathematical forms used to represent numbers or values that are too large or too small in more convenient forms.
From the information given, we have the expression written as;
2⁹ˣ+2 = 16⁵ˣ -2
Put all the terms in one base form, we have;
2⁹ˣ + 2¹ = 2²⁰ˣ - 2¹
equate the exponents, we have;
9x + 1 = 20x - 1
collect the like terms, we have;
9x - 20x = -2
-11x = -2
Make 'x' the subject of formula, we have;
x = 2/11
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A driver's distance D in miles from a rest stop after x hours is given by D(x) = 72x.
a) How far is the driver from the rest stop
after 3 hours?
b) Find the slope of the graph of D. Interpret
this slope as a rate of change.
Answers
the slop is 72 (x is always slope)
Answer & Step By Step Explanation:
a) The function D(x) = 72x represents the distance traveled by the driver after x hours. To find out how far the driver is from the rest stop after 3 hours, we simply substitute x = 3 into the function:
[tex]D(3) = 72 * 3 = 216 miles[/tex]
So, the driver is 216 miles away from the rest stop after 3 hours.
b) The slope of the graph of D(x) = 72x is 72. In the context of this problem, the slope represents the rate of change of the distance with respect to time. This is essentially the speed of the driver. So, the driver is traveling at a constant speed of 72 miles per hour.
in need of help
use the formula to find the hypotenuse of the right triangle below. Make sure you show your work. Round to the nearest tenth if needed.
Answers
The hypotenuse of the right triangle is 25
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem
h² = sum of squares of the legs
Using the above as a guide, we have the following:
h² = 15² + 20²
Evaluate
h² = 625
Take the square roots
h = 25
Hence, the hypotenuse of the right triangle is 25
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In the diagram below, which distance represents the distance from point Qto RS?
Answers
The distance that represents the distance from point Q to RS is: QT.
How to find the line distance?The distance between a point and a line, is usually defined as the shortest distance that exists between a fixed point and any point on the line. It is the length of the line segment that is perpendicular to the line and passes through the point.
In the given figure attached, we can see that among the lines drawn from point Q to line RS ,the line QT is perpendicular to RS and as such, it means that is represents the distance between the point and the line.
Therefore, we conclude that the distance that represents the distance from point Q to RS is: QT.
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k(t)=13t−2k, left parenthesis, t, right parenthesis, equals, 13, t, minus, 2
�
(
3
)
=
k(3)=k, left parenthesis, 3, right parenthesis, equals
Answers
The value of k(3) in the function given is 37
Given the function :
k(t) = 13t - 2To find k(3) ; substitute t = 3 into the equation
k(3) = 13(3) - 2
k(3) = 39 - 2
k(3) = 37
Therefore, the value of k(3) would be 37.
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The following cost estimates were provided for your project: Cost of soil: $80.00 per cubic yard Cost of sand: $100.00 per cubic yard Cost of Sod: $100.00 per roll that is 3’ by 30’ Tree and shrubbery installation: $2500.00 You are at the final phase of your project and are doing final grading and landscaping. The estimates are 8 cubic yards of soil, 3 cubic yards of sand, 3600 square feet of sod, and tree/shrubbery installation. Including a 3 percent contingency, what is the estimated total cost?
Answers
The estimated total cost of the project is $7,663.20.
What is the estimated total cost?We need to add up the costs of soil, sand, sod, and tree/shrubbery installation, including the contingency.
Soil: 8 cubic yards x $80/cubic yard = $640
Sand: 3 cubic yards x $100/cubic yard = $300
Sod: 3600 square feet / 30 square feet/roll x $100/roll = $1200
Tree and shrubbery installation: $2500
Contingency: 3% x $4640 = $139.20
Total cost: $640 + $300 + $1200 + $2500 + $139.20 = $7,663.20
Therefore, The estimated total cost of the project is $7,663.20
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Which graph represents h(x)?
5
T
3-
2
3-2-1₁
hoo
2.
hou
M
32
론
Answers
The graph that represents the piecewise function, h(x) is the second option
Please find attached the graph that represents h(x) created with MS Excel
What is a piecewise function?A piecewise function comprises of two or more functions, which are defined based on specified intervals of the input variable.
The possible piecewise function that is represented by h(x), obtained from a similar question on the site can be presented as follows;
[tex]h(x) \begin{cases} \frac{1}{4}\cdot x-4, & \text{ } x\leq0 \\\frac{1}{3}\cdot x - 3, & \text{ } 0 < x \leq 3 \\\frac{1}{2}\cdot x-2, & \text{ } x\geq4\end{cases}[/tex]
Therefore, at x ≤ 0, the y-intercept is -4, for h(x) = (1/4)·x - 4, which corresponds to the second graph.
The range for h(x) at 0 < x ≤ 3 is; h(0) = (1/3)×0 - 3 < h(x) ≤ (1/3)×3 - 3, which can be expressed as; (-3, -2], also corresponding to the second graph
The value of x-intercept of h(x) in the interval x ≥ 4 can be found from the equation; h(x) = (1/2)·x - 2 = 0
(1/2)·x = 2
x = 2 × 2 = 4
The x-intercept, (4, 0), corresponds to the second graph, therefore, the graph that represents h(x) is the second graph
Please find attached the graph that represents the piecewise function, h(x), created with MS Excel
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the shortest side of a right triangle measures 7m. The lengths of the other two sides are Consecutive integers. What is the length of the other two sides?
Answers
The lengths of the other two sides of the right triangle are 24m and 25m, respectively.
Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we have the equation:
[tex]7^2 + x^2 = (x + 1)^2[/tex]
Expanding and simplifying this equation, we get:
[tex]49 + x^2 = x^2 + 2x + 1[/tex]
Now, we can cancel out [tex]x^2[/tex] from both sides of the equation:
49 = 2x + 1
Next, we can isolate 2x:
2x = 49 - 1
2x = 48
Dividing both sides by 2, we find:
x = 24
Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.
Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.
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In the space provided below,
1) Write an example of a closed declarative statement.
2) Write an example of an open declarative statement.
Answers
Declarative sentences are those which state a fact, describe something, or make a statement. A declarative sentence is a simple statement that gives some information. It ends with a period and always has a subject and a predicate.
1. Example of a closed declarative statement: A closed declarative sentence is one that has only one answer and cannot be disputed.
An example of a closed declarative statement would be: The capital of France is Paris. This is a closed declarative statement because there is no other city that is the capital of France other than Paris.
2. Example of an open declarative statement: An open declarative sentence is one that may have many possible answers and may be disputed.
An example of an open declarative statement would be: The best pizza topping is pepperoni. This is an open declarative statement because some people may disagree and have their own preferences about pizza toppings.
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Find the value of 9u-9 given that 2u-5=3 plsss help
Answers
Answer:
27
Step-by-step explanation:
[tex]2u-5=3\\2u=8\\u=4\\\\9u-9=9(4)-9=36-9=27[/tex]
HELP PLSSS!!!!!!!!!!!!!
Answers
Answer:
84
Step-by-step explanation:
A= [tex]\frac{1}{2}[/tex]b*h
A= [tex]\frac{1}{2}[/tex]14*12
A=84
Select the correct answer from each drop-down menu.
The figure shown is made up of a cone and a cylinder. The height of the cone is 5 ft and its diameter is 12 ft. The height of the cylinder is 20 ft.
12 ft.
5 ft
4
20 ft
Find the lateral surface area of the cone and the surface area of the sides and bottom of the cylinder.
The lateral surface area of the cone is about
The total surface area of the figure is about
². The surface area of the sides and the bottom of the cylinder is about
1².
n².
Answers
Answer:
The lateral surface area of the cone is about 147.2 ft².
The surface area of the sides and the bottom of the cylinder is about 867.1 ft².
The total surface area of the figure is about 1014.3 ft².
Step-by-step explanation:
The formula for the lateral surface area of a cone is:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Lateral Surface Area of a Cone}\\\\$L.S.A.=\pi r \sqrt{r^2 + h^2}$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius of the circular base. \\ \phantom{ww}$\bullet$ $h$ is the perpendicular height of the cone.\\\end{minipage}}[/tex]
From inspection of the given diagram (attached), we can see that the diameter of the base of the cone is 12 ft.
As the radius of a circle is half its diameter, the radius of the base of the cone is r = 6.
The height of the cone is 5 ft, so h = 5.
Substitute the values of r and h into the formula to calculate the lateral surface area of the cone:
[tex]\begin{aligned}\textsf{Lateral Surface Area of the Cone}&=\pi (6) \sqrt{6^2 + 5^2}\\&=6\pi \sqrt{36 +25}\\&=6\pi \sqrt{61}\\&=6\sqrt{61}\pi \\&=147.219738...\\&=147.2\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
The surface area of the cylinder part of the figure is made up of the lateral surface area of the cylinder and the area of one circular base.
Therefore the formula to use to calculate the area of the sides and bottom of the cylinder is:
[tex]\boxed{L.S.A.=2\pi r h+\pi r^2}[/tex]
where r is the radius and h is the height of the cylinder.
From inspection of the given diagram, we can see that the radius of the cylinder is r = 6 and the height is h = 20. Substitute these into the formula to find the area of the sides and bottom of the cylinder:
[tex]\begin{aligned}\textsf{S.A. side and bottom of cylinder}&=2 \pi (6)(20)+\pi (6)^2\\&=2 \pi (120)+\pi (36)\\&=240 \pi +36\pi\\&=276 \pi \\&=867.079572...\\&=867.1\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
The total surface area of the figure is the sum of the lateral surface area of the cone and the sides and bottom of the cylinder. Therefore:
[tex]\begin{aligned}\textsf{Total Surface Area}&=147.219738...+867.079572...\\&=1014.29931...\\&=1014.3\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
In conclusion:
The lateral surface area of the cone is about 147.2 ft².The surface area of the sides and the bottom of the cylinder is about 867.1 ft².The total surface area of the figure is about 1014.3 ft².Leon has two boxes with coloured pencils. Boxed A contained 3/8 of all his coloured pencils. Leon removes 2/5 of the pencils from box B to colour a picture. If 15 pencils are used to colour his picture, how many pencils are there in box A?
Answers
Answer:
Step-by-step explanation:
Let's assume that Leon has 'x' number of coloured pencils. According to the question, Box A contains 3/8 of all his coloured pencils.So, Box B contains (1-3/8) = 5/8 of all his coloured pencils. Therefore, number of pencils in Box A = (3/8) * x Also, number of pencils in Box B = (5/8) * x According to the question, Leon removes 2/5 of the pencils from Box B to colour a picture. So, pencils used from Box B = (2/5) * (5/8) * x = (1/4) * x And the total number of pencils used for the picture = 15. So, pencils used from Box A = 15 - (1/4) * x Now, the total pencils used in the picture = pencils used from Box A + pencils used from Box B Therefore, 15 = 15 - (1/4) * x + (1/4) * x Thus, x = 60 Therefore, number of pencils in Box A = (3/8) * 60 = 22.5. Hence, there are 22.5 pencils in Box A.
What the degree of the polynomial!
2x^2y-8xy^3+5xy
Answers
The degree of the given polynomial is 4.The given polynomial is 2x²y - 8xy³ + 5xy. Let us count the number of terms in this polynomial. We have 3 terms.Let us now calculate the degree of each of these terms.
The degree of the first term is (2 + 1) = 3, as there are two variables x and y, and both are raised to the power 2 and 1 respectively.The degree of the second term is (1 + 3) = 4, as there are two variables x and y, and x is raised to the power 1 and y to the power 3.
The degree of the third term is (1 + 1) = 2, as there are two variables x and y, and both are raised to the power 1 each. So the degree of this polynomial will be the highest degree among these 3 terms.
The highest degree is 4. Therefore, the degree of the given polynomial is 4.
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The product of two whole numbers is 50
and their sum is 15
. What are the two numbers?
Answers
this system of equations represents the scenario given:
x(y) = 50
x+y=15
isolate x:
x+y=15… x=15-y
plug in 15-y for x:
(15-y)(y)=50
15y-y^2=50
y^2 - 15y + 50 = 0
(y-10)(y-5) = 0
y = 10 or 5
therefore…
x+10=15
x+5=15
x=5 or 10
the numbers are 5 and 10 :)
in how many ways can first, second, and third prizes be awarded in a contestant with 375 contestants? assume there are no ties
Answers
There are 52,406,250 ways to award the first, second, and third prizes in a contest with 375 contestants, assuming there are no ties.
To solve this problem, we will use permutations.
A permutation is a way of arranging objects or elements in a specific order.
In this case, we want to find the number of permutations of 375 objects taken 3 at a time, because we are selecting three prize winners.
The formula for permutations is: P(n, r) = n!/(n-r)!where n is the total number of objects and r is the number of objects we are selecting.
So in our case, we want to find the number of ways to select 3 prize winners out of 375 contestants:
P(375, 3) = 375!/(375-3)!P(375, 3) = 375!/372!P(375, 3) = 375*374*373P(375, 3) = 52,406,250
Therefore, there are 52,406,250 ways to award the first, second, and third prizes in a contest with 375 contestants, assuming there are no ties.
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which value of x makes this inequality true? x+9<4x
Answers
Answer:
Step-by-step explanation:
x+9
Let x, be 4
4+9=13
given condition,
x+9<4x
4+9<4(4)
13<16
The answer is:
x > 3Work/explanation:
Our inequality is:
[tex]\sf{x+9 < 4x}[/tex]
Flip it
[tex]\sf{4x > x+9}[/tex]
Solve
[tex]\sf{4x-x > 9}[/tex]
Combine like terms
[tex]\sf{3x > 9}[/tex]
Divide each side by 3
[tex]\sf{x > 3}[/tex]
Hence, x > 35. (03.01 MC)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. (1 point)
Answers
Using this property on the given expression, we get:
[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]
Now, we can rewrite the expression in radical form as √x which is the required answer.
The given expression to rewrite with rational exponents as a radical expression by extending the properties of integer exponents is:
[tex]{(x^3/4)^2/3}[/tex]
To rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, the general formula of the power rule of exponents can be used, which states that [tex](a^m)^n = a^(mn)[/tex].
Now applying this power rule of exponents on the given expression:
[tex]{(x^3/4)^2/3}={x^(3/4*2/3)}={x^(1/2)}[/tex]= √x
Hence, the required expression, when rewritten with rational exponents as a radical expression by extending the properties of integer exponents, is √x.
To understand the solution, let's understand the concepts and formulas used in it.
The given expression is {(x^3/4)^2/3}. Now, to rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, we need to use the power rule of exponents.
The power rule of exponents is an important property of the exponents that states that when we raise a power to another power, we need to multiply the exponents.
That is (a^m)^n = a^(mn).
Using this property on the given expression, we get:
[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]
Now, we can rewrite the expression in radical form as √x which is the required answer. Hence, the given expression rewritten with rational exponents as a radical expression by extending the properties of integer exponents is √x.
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Find BE, if DC is equal to 27 and FA is equal to 46.
Answers
Considering the triangles, the value of BE is 27
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
In the figure, BE is solved using the following ratio
FD / FA = DC / AE
1 / 2 = 27 / AE
AE = 27 * 2
AE = 54
BE = 1/2 AE
BE = 27
hence BE = 27
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Jack's father has recorded the amount of time his son has played video games for the last 7 days. The corresponding scatterplot is shown below. Using the best-fit line, which of the following predictions is TRUE? a.) Jack devoted 38 minutes to playing video games after 1 day. b.) Jack devoted 50 minutes to playing video games after 6 days. c.) Jack devoted 64 minutes to playing video games after 8 days. d.) Jack devoted 41 minutes to playing video games after 2 days.
Answers
Based on the best-fit line, the prediction that is TRUE is option d.) Jack devoted 41 minutes to playing video games after 2 days.
1. Look at the scatterplot and identify the best-fit line, which represents the trend or pattern in the data points.
2. Locate the point on the x-axis corresponding to 2 days.
3. Follow the vertical line from that point until it intersects with the best-fit line.
4. From that intersection, move horizontally to the y-axis to find the predicted value for the amount of time Jack devoted to playing video games after 2 days.
5. Based on the best-fit line, the predicted value is approximately 41 minutes.
6. Compare the predicted value with the given options.
7. Among the options, option d.) states that Jack devoted 41 minutes to playing video games after 2 days, which matches the prediction from the best-fit line.
8. Therefore, the TRUE prediction is option d.) Jack devoted 41 minutes to playing video games after 2 days.
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Answer:
Step-by-step explanation:
The line of best fit can be used to get predictions. So if we look at a particular day, we can get a predicted time based on the corresponding value on the best-fit line. If we look at Day 8, then the predicted time looks to be about 64 minutes.
For a certain company, the cost function for producing x items is C(x) = 40 x + 150 and the
revenue function for selling x items is R(x) = -0.5(x - 100)2 +5,000. The maximum capacity
of the company is 160 items.
Answers
The company should produce and sell 60 items to maximize its profit. The profit at this level of production will be $2,350.
For a certain company, the cost function for producing x items is C(x) = 40 x + 150 and the revenue function for selling x items is R(x) = -0.5(x - 100)2 + 5,000. The maximum capacity of the company is 160 items.To find the optimal number of items that the company should produce and sell, we need to maximize the revenue function R(x) while also taking into account the cost function C(x).
The profit function P(x) can be expressed as:P(x) = R(x) - C(x).
Substituting the given equations, we get:P(x) = (-0.5(x - 100)2 + 5,000) - (40x + 150)P(x) = -0.5(x - 100)2 - 40x + 4,850.
To maximize the profit, we need to find the value of x that gives the maximum value for P(x). The maximum capacity of the company is 160 items, so we only need to consider the values of x from 0 to 160.
To find the optimal value of x, we can take the derivative of P(x) and set it equal to zero: d P(x)/dx = -x + 100 - 40 = 0.
Solving for x, we get: x = 60. This means that the optimal number of items that the company should produce and sell is 60. At this level of production, the profit will be:P(60) = -0.5(60 - 100)2 - 40(60) + 4,850 P(60) = $2,350.
Therefore, the company should produce and sell 60 items to maximize its profit. The profit at this level of production will be $2,350.
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