Analyze the diagram below and complete the instructions that follow.


Find the unknown side length, x. Write your answer in simplest radical form.


A.24
B.4// 37
C.2 // 154
D.5 // 117 I posted the pictures below

Answer:

To find f(-3), substitute -3 for x in the equation for f(x):

f(-3) = 2(-3) + 5 = -6 + 5 = -1

Answer:

f(-3) = -1

To find g(x) - h(x), first substitute x into both g(x) and h(x) and then subtract h(x) from g(x):

g(x) - h(x) = -3x^2 + 2x - 6 - (-4 - x) = -3x^2 + 3x - 2

Answer:

g(x) - h(x) = -3x^2 + 3x - 2

To solve for x when f(x) = h(x), first substitute x into both f(x) and h(x), and then solve for x:

2x + 5 = -4 - x

3x = -9

x = -3

Answer:

x = -3

To determine which of the functions are linear, we need to look at the degree of the polynomials in each function. Linear functions have a degree of 1, while non-linear functions have a degree greater than 1.

f(x) = 2x + 5 is linear because it has a degree of 1

g(x) = -3x^2 + 2x - 6 is non-linear because it has a degree of 2

h(x) = -4 - x is linear because it has a degree of 1

Answer:

f(x) and h(x) are linear, while g(x) is non-linear.

Answer:

Step-by-step explanation:

What are the possible combinations of three-digit numbers that could add up to a four-digit number?

There are many possible combinations of three-digit numbers that can add up to a four-digit number. Here are some examples:

1. 100 + 900 = 1000

2. 200 + 800 = 1000

3. 300 + 700 = 1000

4. 400 + 600 = 1000

5. 500 + 500 = 1000

6. 600 + 400 = 1000

7. 700 + 300 = 1000

8. 800 + 200 = 1000

9. 900 + 100 = 1000

10. 111 + 889 = 1000

11. 222 + 778 = 1000

12. 333 + 667 = 1000

13. 444 + 556 = 1000

14. 555 + 445 = 1000

15. 666 + 334 = 1000

16. 777 + 223 = 1000

17. 888 + 112 = 1000

18. 999 + 001 = 1000

19. 123 + 877 = 1000

20. 234 + 766 = 1000

The scale factor for each of the dilation is given as -

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y}, greater than {x}.

Given is a line segment and its dilated image.

The scale factor is given by -

K = y/x

[1] -

K₁ = 18/12 = 3/2

[2] -

K₂ = 8/12 = 2/3

[3] -

K₃ = 12/12 = 1

[4] -

K₄ = 6/12 = 1/2

Therefore, the scale factor for each of the dilation is given as -

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The correct solution set for the given graph include the following: D. {infinite set of points on the line}.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.

In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].

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The number of people that uses exactly one of gym, swimming pool and track is 49people

A set is the mathematical model for a collection of different things. A set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

The number of people that uses gym= 73- ( 32-14+ 36-14 + 14)

73-(18+22+14)

73 - (54) = 19 people

The number of people that use pool only = 73-(36-14+35-14+14)

= 73-(22+21+14)

= 73-(57)

= 16people

The number of people that use track only = 67-(32-14+35-14+14)

= 67-(18+21+14)

= 67-53

= 14people

therefore the number of people that use one of the facility is 19+16+14 = 49people

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Answer: The fractional increase in Gershon's broccoli sprouts is 7/4 and the percent increase in Gershon's broccoli sprouts is 175%.

Step-by-step explanation:

The fractional increase in Gershon's broccoli sprouts is the difference between the final amount and the initial amount divided by the initial amount.

So in this case, it would be (11 - 4) / 4 = 7 / 4.

The percent increase in Gershon's broccoli sprouts is the fractional increase multiplied by 100.

So, it would be (7 / 4) * 100 = 175%.

It means Gershon's broccoli sprouts increased by 175% from 4 pounds to 11 pounds.

Value of g(x) with given values of x:

                      x -5 -4 -3 -2 -1

                   g(x) 7 1 -1 1 7

Given: the functional equation:

                          g(x) = 2(x + 3)^2 – 1

Solution:

Value of g(x), when x= -5

g(x) = 2 (-5 +3)^2 – 1

      = 2 (-2)^2 – 1

      = 2* (-2)* (-2) – 1

      = 8 – 1

      = 7

Value of g(x), when x= -4

g(x) = 2 (-4 +3)^2 – 1

      = 2 (-1)^2 – 1

      = 2* (-1)* (-1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -3

g(x) = 2 (-3 +3)^2 – 1

      = 2 (0)^2 – 1

      = 2* 0  – 1

      = 0 – 1

      = - 1

Value of g(x), when x= -2

g(x) = 2 (-2 +3)^2 – 1

      = 2 (1)^2 – 1

      = 2* (1)* (1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -1

g(x) = 2 (-1 +3)^2 – 1

      = 2 (2)^2 – 1

      = 2* (2)* (2) – 1

      = 8 – 1

      = 7

The coordinates of the triangle before and after dilation is

preimage        image

R (6, 9)             R' (2, 3)

S (3, -9)            S' (1, -3)

T (-6, -3)           T' (-2, -1)

The rule that best describes the transformation is

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                             image

R (6, 9)  → (1/3 * 6, 1/3 * 9) → R' (2, 3)

S (3, -9) → (1/3 * 3, 1/3 * -9) → S' (1, -3)

T (-6, -3) → (1/3 * -6, 1/3 * -3) → T' (-2, -1)

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Answer:

00088n886668hb76u8y687440

Answer:

12

Let X be the unknown number we are supposed to find.

Given information from the question, we can form up an equation:

2X + 7 = 3X - 5

3X - 2X = 7 + 5

X = 12

Therefore the unknown number is 12

The sketch for slope is attached below.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Point               Slopes

(1, 1)                     (a) 3

_                        (b) -3

_                        (c) -5/2

_                         (d) Undefined

a) Now, using slope intercept form

y - 1= 3 (x-1)

y- 1= 3x- 3

y= 3x - 2

(b) Equation of a line has a slope -3 is given by

y - 1= (-3) (x-1)

y-1 = 3- 3x

y = -3x + 4

(c) Equation of a line has a slope -5/2 is given by

y - 1= (-5/2) (x-1)

y-1 = -5/2x + 5/2

y= -5/2x + 7/2

(d) The line parallel to y axis and passes through given point : x=1

"undefined" means the line is vertical.

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The use of internal rhyme affect the poem by: C. It helps create and maintain the poem's playful tone

Internal rhyme tend to occurs when words that are in the same line of a poem rhyme with one another.

The use of internal rhyme can tend to  add  more musical quality to a poem and it as well help to create cohesion within a line or stanza. Internal rhyme also help to a sense of playfulness in the poem.

Therefore we can conclude that the correct option is C.

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Answer:

(x+1)(x-2)

Step-by-step explanation:

[tex](x+1)(x-2)=x^{2} -x-2[/tex]

Hope this helps

The diameter of the circle would be given as = 10

Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.

The diameter of the circle can be found through finding first the radius of the circle.

The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.

Using the Pythagorean formula c² = a² + b²

The lines that represents ;

a= DG

b= EI/2 = 4.8

C= DI = ?

C² = DI

a² = 1.8²

b² = (9.5/2)² = 4.8²

c² = 2.24 + 23.04 = 25.28

C =√25.28

C = 5

Therefore the diameter of the circle = 5×2 = 10

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The new equation is y=-1/2x+5.  An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

Our first line in this equation is y=2x-1. By applying the equation y=mx+b, where "m" stands for the slope, we can see that our "m" in this instance is 2. then negate 2. It turns into -2.

Change the denominator and numerator after that. Since -2 is actually -2/1, let's change it to -1/2. The perpendicular line's slope is that.

We must now make it pass through (-2,6). We just have a line like this to work with at the moment: y=-1/2x

Plugging in the x-coordinate of our target location, -2, yields y=-1/2(-2), or 1. But hold on, because the y-coordinate we were given is 6, shouldn't y be equal to 6 as well? Yes! The only thing left to do is to add 5 to get from 1 to 6!

The complete question  is,

Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (-2,6)

Write an equation for a line perpendicular to y=2x−1 and passing through the point (-2,6)

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The acccceleration will be 1m/s² and the average speed is 47m/s.

For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.

Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.

Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.

If we estimate the speed at 5 seconds intervals, then we have

Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7

Average speed = 331/7 = 47.29 m/s

Average speed = 47 m/s

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The digit that occurs in the 2023rd place after the decimal point is; 1

A repeating decimal has another name called a recurring decimal, and it is defined as a number whose decimal representation eventually becomes periodic

Now, we are given the fraction as 1/7 which is a repeating decimal because its decimal representation is periodic for every 6 decimal units as shown below; 1/7 = 0.142857142857...

Now, the digits are repeated after every 6 digits and as such to get the digit in the 2023rd place;

2023/7 = 337 remainder 1

Thus, the sequence 142857 would be repeated 337 times after which the next digit which is the 2023rd digit will be 1.

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Answer:

Step-by-step explanation:

The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:

Balance = Principal + Interest

where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.

Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:

Interest = Principal * Interest Rate * Time

Substituting the given values:

Interest = m * 0.03 * 1

So the expression that represents Arianys balance after a year is:

Balance = m + (m*0.03)

= m + 0.03m

= 1.03m

This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.

Answer:

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all its sides. To find the perimeter of MNPQ, we need to add up the lengths of MN, NP, PQ and PM.

Given that:

MW=-2+37 = 35

QP= y+14

NP= x-5

MN=4y+5

The perimeter can be calculated by adding up the above expressions:

Perimeter = MN + NP + QP + MW

= (4y + 5) + (x - 5) + (y + 14) + 35

= 4y + x + y + 54

= (4y + y) + (x + 54)

= 5y + x + 54

So the perimeter of MNPQ is 5y + x + 54 units.

Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:

x^2 - 8x + 15 = 0

To solve this equation we should factor it or use the quadratic formula.

(x - 5)(x - 3) = 0

x = 5, x = 3

This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.

The solution of the inequality is x < 3 or x > 5.

Step-by-step explanation:

The height of the cuboid is 4 cm  

What is a cuboid?

A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.

volume of a cuboid = l *w*h

where, l= length, w=width, h= height

=> 364 = 7*13*h

=> h=364/(7*13) = 364/91

=> h= 4 cm

Thus, the height of the cuboid is 4 cm  

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{5}{x}[/tex] - [tex]\frac{2}{x^2}[/tex] = 2

multiply through by x² ( x ≠ 0 ) to clear the fractions

5x - 2 = 2x² , that is

2x² = 5x - 2 ( subtract 5x - 2 from both sides )

2x² - 5x + 2 = 0 ← in standard form

(2x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 2 = 0 ⇒ x = 2

since x₁ < x₂ , then

x₁ = [tex]\frac{1}{2}[/tex] and x₂ = 2

Then

3x₁ + x₂

= 3 × [tex]\frac{1}{2}[/tex] + 2

= [tex]\frac{3}{2}[/tex] + 2

= [tex]\frac{3}{2}[/tex] + [tex]\frac{4}{2}[/tex]

= [tex]\frac{7}{2}[/tex]

Using scientific notation, the number of gallons of water saved in two years by the wireless soil monitors is 1.2 x 10^12.

Scientific notation is a shorthand way of writing very large numbers or very small numbers in a simpler form.

The parts of a scientific notation are coefficient, base, and exponent.

We state that a number is written in standard notation when the number is between 1 and 10 and it is multiplied by a power of 10.

The number of gallons of water per year saved by wireless soil monitors = 6 trillion

The number of gallons of water saved by wireless soil monitors in 2 years = 12 trillion

In scientific notation, 12 trillion = 1.2 x 10^12.

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The measure of the apothem is 1.75cm.

What is a regular octagon?

Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.

Here, we have

Given: The area of the regular octagon is 10.15 cm².

We have to find the measure of the apothem.

The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.

Area (triangle AOB) = 10.15/8 = 1.27cm².

Area(triangle AOB) is also 1/2*MO*AB

 1.27 =  1/2*MO*1.45

MO = 1.75cm

Hence, the measure of the apothem is 1.75cm.

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The area of triangle MNB, MNC and ABC 6 in.², 60 in.², and 30 in.² respectively

The ratio of the base of the triangles ΔMNB and ΔCBM, that shares a common vertex, is the ratio of their areas.

M is the midpoint of side AB in ΔABC

NB:CB = 1:5

Area of ΔCAM = 30 in.²

The area of ΔMNB and ΔABC

Area = 1/2 * base * height

Height of ΔCAM = Height of ΔCBM = Altitude of point C above line AB

MA = MB by definition of midpoint

MA is the base of ΔCAM, and MB is the base of ΔCBM

Therefore; Area of ΔCAM = 1/2 AM * Height of ΔCAM

= 1/2 * AM* height of ΔCAM

Which gives;

Area of ΔCAM = Area of ΔCBM = 30 in.²

Area of ΔABC = Area of ΔCAM + Area of ΔCBM = 30 + 30 = 60

Area of ΔABC = 60 in.²

Taking CB as the base of ΔCBM, we have;

Height of ΔMNB = Height of ΔCBM from line CB

Base length of ΔCBM = 5 × Base length of ΔMNB

Therefore; Area of ΔMNB = 30/5 = 6 in²

Area of ΔCBM = 30 in.² = 5 × The area of ΔMNB

Conclusively, the Area of ΔMNB = 6 in.²

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Correct question:

In a triangle ABC, M is the mid point of the side AB and N is the mid point of the side AC.  Find the lenght of the segment MN if AB =18, BC = 10 and AC = 20

Answer:

Let's call the amount Erica earned from her job at the college "x". We know that:

Total income = $67,160

Income from store = 3x + 1,550

Total income = Income from store + Income from college

67,160 = 3x + 1,550 + x

67,160 = 4x + 1,550

Now we can solve for x:

67,160 - 1,550 = 4x

65,610 = 4x

x = 16,402.5

Erica earned $16,402.50 from her job at the college.

The given triangles are not similar because the sides given are not proportional.

Similar triangles are those triangles which has the same shape but different size.

The length of sides and angles are proportional in similar triangles.

Given are two triangles QRS and TUV.

Also given the measure of two sides of each triangle and an included angle of these sides of each triangle.

From the figure, given angles are equal.

If we prove that the sides including these angles are proportional, we can say the given triangles are similar by SAS similarity theorem.

7 / 35 = 1/5

But 13/55 ≠ 1/5

So they are not proportional.

Hence the given triangles are not similar.

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if im not wrong

4+3(2x+2) multiply since its in parenthesis first

property of mulitplication i think

4+6x+6

property of addition

6x+10

(this should be right)

Plan A has the majority of votes.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given this,  the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.

thus we can say the total number of members who voted is 7.

Therefore, 4 votes are required for the majority.

Therefore, there is no plan that receives a majority of votes.

1st choice votes to A=3

1 choice votes to B=3 1st choice votes to C=1

So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)

First choice vote to A = 3 + 1 = 4

First choice vote to B = 3

Since A gets the majority of votes A is the winner

Thus, Plan A has the majority of votes.

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Complete question:

The solutions for the given function are (-2, 0) and (2, 0).

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

The given function is f(x)=√(x²-4).

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,−2]∪[2,∞),{x|x≤−2,x≥2}

Range: [0,∞),{y|y≥0}

Therefore, the solutions for the given function are (-2, 0) and (2, 0).

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