Which linear equation is represented in the graph?

A. y = x – 1

B.y = 2x – 1

C. y = x + 1

D. y = 3x – 1

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

The ratio that could also be included in this table is (c) 18 : 30

From the question, we have the following parameters that can be used in our computation:

Games won   Games played

6                    10

24                  40

36                60

42                70

From the above, we have the ratio of the number of games won to the number of games played to be

Ratio = 6 : 10

Simplify

Ratio = 3 : 5

From the options, we have

(c) 18 : 30

Simplify

Ratio = 3 : 5

Hence, the ratio that could also be included in this table is (c) 18 : 30

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Answer:  B, C, D

Step-by-step explanation:

Looking at the parabola, this is a width vs area graph.

A)    Incorrect.  the greatest possible area is not 10.  Area goes higher

B) True.  The highest possible area, highest point for area is 100

C) True.  The area is 0 when width is 0

D)True.  The area is also 0 when the width is 20

The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

Center = (a, b) = (-4, -5)

Radius, r = 4 units

The equation of the circle graphed is represented as

(x - a)^2 + (y - b)^2 = r^2

So, we have

(x + 4)^2 + (y + 5)^2 = 4^2

Evaluate

(x + 4)^2 + (y + 5)^2 = 16

Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16

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i Got u Bro!

Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.

Answer:

figure A = square ( All sides are equal)

figure B = Rectangle (Two sides are equal)

Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)

Answer:

A

Step-by-step explanation:

the domain is the values of x covered by the graph

on the left the graph → - ∞

on the right the graph tends to + ∞

there are no excluded values of x on the domain , so

domain is - ∞ < x < ∞

Answer:

19π/6 radians and 31π/6 radians

Step-by-step explanation:

To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:

The angle of point B = angle of point A + 7π/6 radians

= 0 radians + 7π/6 radians

= 7π/6 radians

Angle of point B in degrees = (7π/6) * (180/π) degrees

= 210 degrees

To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:

angle of rotation 1 = angle of point B + 2π radians

= 7π/6 radians + 2π radians

= 19π/6 radians

angle of rotation 1 in degrees = (19π/6) * (180/π) degrees

= 285 degrees

angle of rotation 2 = angle of point B + 4π radians

= 7π/6 radians + 4π radians

= 31π/6 radians

angle of rotation 2 in degrees = (31π/6) * (180/π) degrees

= 465 degrees

So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.

Note:

To convert the angles from radians to degrees, we can use the conversion factor:

1 radian = 180/π degrees

Answer:

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The expression is:

1234 - 4566 / 45.44 + 67 * 755.34

First, we need to perform the division operation since it comes before addition and multiplication.

4566 / 45.44 = 100.50

Now, we can substitute that into the expression:

1234 - 100.50 + 67 * 755.34

Next, we need to perform the multiplication operation:

67 * 755.34 = 50,548.78

Now, we can substitute that into the expression:

1234 - 100.50 + 50,548.78

Next, we can perform the addition and subtraction operations:

1234 + 50,448.28 = 51,682.28

Therefore, the result of the expression is 51,682.28.

Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,

8x-10 =6x

8x-6x = 10

2x =10

x= 5.

Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.

Answer:

The answer is C

Step-by-step explanation:

The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.

Answer:3/2

Step-by-step explanation:

1/3 ÷ 2/9=

1/3 ×9/2=3/2

Answer:

3/2 u can also do 1 1/2 their equivalent fractions

Step-by-step explanation:

sorry about the handwriting :) not the best

Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.

To calculate the interest Marcus will earn, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.

In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.

So we can plug in these values into the formula:

I = 500 * 0.068 * 5

I = $170

This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.

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Answer:

C = 45

AC = 1

BC = 2

Step-by-step explanation:

C: 180 - (90 + 45) = 45

AC: Because the angles are the same, it is equal to the other leg, 1 cm

BC: a^2 + b^2 = c^2, so 1 + 1 = 2

Answer:

1. 30; 2. 6.25.

Step-by-step explanation:

1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;

2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.

The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.

To find the sum of two expressions, we simply add their like terms.

The given expressions are x+9 and 7x²-2x+1.

The first expression has two terms - x and 9.

The second expression has three terms - 7x², -2x, and 1.

We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.

First, we can simplify the second expression by combining the like terms -2x and 1.

7x² - 2x + 1 = 7x² - (2x - 1)

Now, we can add the like terms from both expressions.

(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9

= 7x² - x + 10

Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.

(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1

= 7x² - x + 10

In either case, the final answer is 7x² - x + 10.

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Answer: Given b=2√14 and c=9,

a = 5

Step-by-step explanation:

The scale factor used is 1/4.

We have,

Length of sides of triangle D 24, 32, and 40.

Length of sides of triangle D' 6, 8, and 10.

So, scale factor

= length of corresponding side in D' / length of corresponding side in D

= 6/24

= 1/4

Thus, the scale factor used is 1/4.

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The area of a sector is 8.75 [tex]m^{2}[/tex].

A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

where r is the radius, and θ is the central angle.

Given a circle whose area is 45 sq. m.; then;

area of a circle = π[tex]r^{2}[/tex]

45 = π[tex]r^{2}[/tex]

r = [tex]\sqrt{\frac{45}{\pi } }[/tex]

Then,

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

                  = ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]

                  = [tex]\frac{7}{36}[/tex]*π*45/π

                  = [tex]\frac{7}{36}[/tex]*45

                  = 8.75 sq. m.

The area of the sector is 8.75 [tex]m^{2}[/tex].

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Answer:

34.83/.9 = 38.7 g mass (after one hour)

38.7/.9 = 43 g (starting mass)

The starting mass of the ice cube was 43 grams.

The required experimental probability that a team will consist entirely of boys is 0.04. Option B is correct.

To find the experimental probability that a team will consist entirely of boys, we need to count the number of trials in which all three coin tosses resulted in tails (which represents a team consisting entirely of boys), and divide by the total number of trials (which is 50).

From the data, we can see that there are only 2 trials where all three coin tosses resulted in tails, so the experimental probability of a team consisting entirely of boys is:

2/50 = 0.04

Therefore, the experimental probability that a team will consist entirely of boys is 0.04.

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The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).

To compute the margin of error for the proportion, we use the formula:

Margin of error = z*√((P(1-P))/n)

where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have

P = 0.52 (sample proportion)

n = 900 (sample size)

z = 1.96 (for 95% confidence level)

Substituting these values into the formula, we get

Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344

Therefore, the margin of error is approximately 0.0344, or 3.44%.

To compute the confidence interval, we use the formula:

Confidence interval = P ± z*(√((P(1-P))/n))

where P, z, and n are the same as in part 1. Substituting these values into the formula, we get

Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)

Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.

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The number of cars that pass through the intersection between 6 am and 10 am is 4800.

To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].

Integrating r(t) with respect to t, we get:

∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C

where C is the constant of integration.

Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:

(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars

In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.

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The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1

From the question, we have the following parameters that can be used in our computation:

The exponential expressions a to f

The general rule is that

a^b = a * a * a..... in b places

Using the above as a guide, we have the following:

a. 7⁴ = 7 * 7 * 7 * 7 = 2401

b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000

c. 5¹ = 5

d. 0⁴ = 0 * 0 * 0 * 0

e. –6² = -6 * -6 = 36

f. –3⁰ =  1

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Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,

a + b = < 3, -5 >

The graph of the vector sum is given below.

The addition of vectors suggests the addition of the corresponding components of the involving vectors.

Given the vectors are:

a = < 4, - 3 >

b = < - 1, - 2 >

So doing vector addition we get,

a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>

Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.

Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,

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Answer: Look at the image below

Step-by-step explanation: I took the test.

Step 1: Select Vector

Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)

Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)

Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)

Your answer should now look like mine, now go get that A.

Answer:

16

Step-by-step explanation:

To find the median, we find the middle of the data set.

7, 9, 11, 14, 18, 20, 30, 35

There are 8 values

7, 9, 11,    14, 18,     20, 30, 35

The median is between the 4th and 5th numbers

We need to find the mean of the middle two numbers

(14+18)/2 =32/2= 16

Answer:

16

Step-by-step explanation:

             [tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]

       Here,

             n ⇒ number of terms

Let us find it now.

7, 9, 11, 14, 18, 20, 30, 35

[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]

In this case, add 4th and 5th data and divide it by 2.

[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]

The volume of this rectangular prism is equal to: B. 8 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;

Dimensions = 16 × (1/2)³ = 2inches.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 2 × 2 ×  2

Volume of rectangular prism = 8 cubic inches.

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Complete Question:

A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?

A. 2 in³

B. 8 in³

C. 16 in³

D. 32 in³

Answer:

The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.

For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.