Eric plays basketball and volleyball for a total of 95 minutes every day. he plays basketball 25 minutes more than he plays volleyball. part a: write a pair of linear equations to show the relationship between the number of minutes eric plays basketball (x) and the number of minutes he plays volleyball (y) every day. (5 points) part b: how much time does eric spend playing volleyball every day? (3 points) part c: is it possible for eric to have spent 35 minutes playing basketball every day? explain your reasoning. (2 points) (10 points)

Solution:

The equation in standard form with center (h,k) and radius r is given by the following formula:

In this case, note that we have the following data:

(h, k) = (8, 10)

r = 2/5 = 0.4

Replacing this data into the standard equation of a circle, we obtain:

So that, we can conclude that the correct answer is:

Hello !

\(y=3+x\\y = 3x + 8\)

\(\boxed{y=}3+x\\\boxed{y=} 3x + 8\)

We know that y = y, so :

\(3 + x = 3x + 8\)

3.1 Solve x

\(\\\\\\\\3+x = 3x + 8\\\\3 + x - x = 3x + 8 -x\\\\3 = 2x + 8\\\\3 - 8 = 2x + 8 - 8\\\\-5=2x\\\\x = -\frac{5}{2}\\\\\boxed{x = -2,5}\)

3.2 Solve y

\(y = 3 + x\\\\y = 3 + (-2,5)\\\\y = 3 - 2,5\\\\\boxed{y = 0,5}\)

x = -2,5

y = 0,5

The rate at which length of shadow of person changing is 3 ft /sec.

H = Height of streetlight; 16 ft

h = Height of man; 6 ft

x = Length of man's shadow.

s = Distance from streetlight to man.

Using the similarities of the triangles.

H/h = (s + x)/x

Hx = h(s + x)

Differentiate with respect to 't' on both sides.

H(dx/dt) = h(ds/dt + dx/dt)

Put the values.

16(dx/dt) = 6(5 + dx/dt)

16(dx/dt) = 30 + 5dx/dt

10dx/dt = 30

dx/dt = 3 ft /sec

Thus, the rate at which length of shadow of person changing is 3 ft /sec.

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The system of equations that models the situation is as follows:

7t +  3w = 438

4t + 9w = 336

Mai bought seven Christmas trees and three Christmas wreaths for a total of $438.  Samantha Bought 4 Christmas trees and nine Christmas wreaths for a total of $336 from the same store.

The system of equations modelling the situation is represented as follows:

let

Therefore,

Mai total cost:

7t +  3w = 438

Samantha total cost:

4t + 9w = 336

Hence,

7t +  3w = 438

4t + 9w = 336

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Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

----------------------------------------------------------------------------------------------------------------

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

----------------------------------------------------------------------------------------------------------------

Hope this helps! <3

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14

Answer:

What is the average time it took the car to travel 0.25 meters?

What is the average time it took the car to travel 0.50 meters?

I hope is work you!!

(1) The first velocity of the car with two washers at the 0.25 meter mark is 0.125 m/s.

(2) The second velocity of the car with two washers at the 0.5 meter mark is 0.25 m/s.

Velocity is the rate of change of displacement with time. The velocity of the  cars depends on displacement and time of motion.

The first velocity is calculated as follows;

v1 = 0.25 m / t1

let t₁ = 2 s

v₁ = 0.25/2

v₁ = 0.125 m/s

v2 = 0.25 m / (t2 – t1)

let t₂ = 3 s

v₂ = 0.25(3 - 2)

v₂ = 0.25 m/s

The complete question is below:

Calculate the first and second velocities of the car with two washers attached to the pulley, using the formulas

v1 = 0.25 m / t1, and

v2 = 0.25 m / (t2 – t1)

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The inequality that represents the graph is: y ≥ -2x - 5

Using two points on the line, (-1, -3) and (0, -5), find the slope (m):

Slope (m) = change in y / change in x = -5 - (- 3) / 0 -(-1)

m = -2/1

m = -2

The y-intercept (b) is -5, because the line intercepts the y-axis at -5.

The line is a solid line and the shaded region is above it, therefore the inequality sign to use is "≥". To write the inequality, substitute m = -2 and b = -5 into y ≥ mx + b:

y ≥ -2x - 5

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Answer:

it's D

Step-by-step explanation:

12x-12x would give us 0, so x would be eliminated

The calculated length of the container is 70.11 inches

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

Shape = triangular prism

Height = 3 inches

Base = 8 inches

Surface area = 956 square inches

The slant lengths of the triangular sides are calculated using

a² = (8/2)² - 3²

a = √7

The surface area of a triangular prism is calculated as

SA = bh + (a + a + c) * l

So, we have

3 * 8 + (8 + √7 + √7) * l = 956

So, we have

(8 + √7 + √7) * l = 932

Divide

l = 70.11

Hence, the length of the container is 70.11 inches

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Answer:

Step-by-step explanation:

To find the length of the container, we need to determine the area of the two triangular bases.

The formula for the area of a triangle is: Area = (base * height) / 2.

Let's calculate the area of one triangular base:

Base = 8 inches

Height = 3 inches

Area of one triangular base = (8 * 3) / 2 = 12 square inches.

Since there are two triangular bases, the total area of the bases is 2 * 12 = 24 square inches.

We are given that the total area of the container is 956 square inches.

Total area of the container = 2 * Area of one triangular base + Lateral surface area

Lateral surface area = Total area of the container - 2 * Area of one triangular base

Lateral surface area = 956 - 24 = 932 square inches.

The lateral surface area of a triangular prism is given by the formula: Lateral surface area = perimeter of the base * height.

The perimeter of a triangular base is the sum of the lengths of its sides. Since it is an isosceles triangle with a base of 8 inches, the two equal sides will have a length of 8 inches as well.

Perimeter of the base = 8 + 8 + 8 = 24 inches.

Now, we can find the length of the container by rearranging the formula for the lateral surface area:

Lateral surface area = perimeter of the base * height

932 = 24 * length

length = 932 / 24

length ≈ 38.83 inches (rounded to two decimal places)

Therefore, the length of the container is approximately 38.83 inches.

Answer:

24 - 6 = 2(12 - 3)

24 - 6 = 24 - 6

Subtract 24 from both sides of the equation

24 - 24 - 6 = 24 - 6 - 24

-6 = -6

Add 6 to both sides of the equation

6 - 6 = -6 + 6

0 = 0

The input is an identity: it is true for all values

-TheUnknownScientist

The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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The expression is equivalent to this expression is  \(2x^2+3x\).

The correct option is A.

Given

The expression is;

= x(2x + 3)

Algebraic expressions consist of numbers and variables along with operational signs.

The equivalent expression is found by multiplying x and simplifying.

Therefore,

The expression is equivalent to this expression is;

\(\rm = x(2x + 3) \\\\= 2x\times x+ 3 \times x\\\\= 2x^2+3x\)

Hence, the expression is equivalent to this expression is  \(2x^2+3x\).

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Answer:

it is 1275.6ft3

Among the given options, the "Success/Failure Condition" is not a requirement for testing means. The other three options—Randomization, Nearly Normal Condition, and 10% Condition—are necessary conditions to be considered when conducting hypothesis tests on means.

Randomization: Randomization is essential to ensure that the samples being compared are representative of the population and to minimize bias. Random assignment of individuals to treatment groups helps control for confounding variables and increases the validity of the statistical analysis.

Nearly Normal Condition: The Nearly Normal Condition assumes that the data follows a roughly normal distribution within each group being compared. This condition is important because many statistical tests, such as t-tests, rely on the assumption of normality to provide accurate results.

10% Condition: The 10% Condition is relevant when sampling from a finite population. It states that the sample size should be no more than 10% of the population size to ensure that the sampling process does not significantly affect the population distribution.

Success/Failure Condition: The Success/Failure Condition is not directly related to testing means. It is typically associated with tests involving proportions, where the condition specifies that both the number of successes and the number of failures should be at least 10 in each sample or category being compared.

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Given:

The two functions are

\(f(x)=5x+1\)

\(g(x)=\dfrac{x}{5}-\dfrac{1}{5}\)

To find:

The presentation which establishes that the functions are inverse functions.

Solution:

Two functions f(x) and g(x) are inverse of each other, if

\(f(g(x))=g(f(x))=x\)

We have,

\(f(x)=5x+1\)

\(g(x)=\dfrac{x}{5}-\dfrac{1}{5}\)

Now,

\(g(f(x))=\dfrac{5x+1}{5}-\dfrac{1}{5}\)

\(g(f(x))=\dfrac{5x}{5}+\dfrac{1}{5}-\dfrac{1}{5}\)

\(g(f(x))=x\)

Similarly,

\(f(g(x))=5\left(\dfrac{x}{5}-\dfrac{1}{5}\right)+1\)

\(f(g(x))=x-1+1\)

\(f(g(x))=x\)

Since, \(f(g(x))=g(f(x))=x\), therefore, the given functions are inverse of each other.

Hence, the correct option is C.

Answer:

Step-by-step explanation:

ima a braintlest

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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\((4d)(6d)(0.25d)=d^3[(4)(6)(0.25)]=\boxed{6d^3}\)

The scale factor of triangle PQR to triangle ABC is equal to 2/3.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation of the triangle PQR implies it is expanded to the bigger triangle ABC, we shall evaluate for the scale factor as follows:

side PR corresponds to side AC and we derive the scale factor as follows:

scale factor = 12/18

by simplification;

scale factor = 2/3

Therefore, the scale factor of triangle PQR to triangle ABC is equal to 2/3.

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Answer:

Step-by-step explanation:

You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.

Angles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.

  x + y + z = 290°

  x + 180° = 290°

  x = 110°

Angles x and y are vertical angles, so are congruent.

  y = x = 110°

Then z is found from ...

  y + z = 180°

  110° + z = 180°

  z = 70°

The measures of x, y, and z are 110°, 110°, and 70°, respectively.

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Answer:

12 17 19 =48

Step-by-step explanation:

The transformations include a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, a translation 1 unit to the right, and a vertical shift of 4 units upward. The graph of f(x) will be steeper, narrower, shifted to the right, and shifted upward compared to the graph of y = log(x).

1. For the function f(x) = 3log[2(x-1)] + 4:

(a) Describe the transformations of the function when compared to the function y = log(x).

The function f(x) is a transformation of the logarithmic function y = log(x). The transformation includes a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, a translation 1 unit to the right, and a vertical shift of 4 units upward.

(b) Sketch the graph of the given function and y = log(x) on the same set of axes.

To sketch the graph, start with the graph of y = log(x) and apply the transformations.

The vertical stretch by a factor of 3 will make the graph steeper, the horizontal compression by a factor of 2 will make it narrower, the translation 1 unit to the right will shift it to the right, and the vertical shift of 4 units upward will move it vertically.

Plot key points and draw the curve to reflect these transformations.

A visual representation of the graph would be more helpful to understand the transformations.

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The C-intercept at (0, 180) and r- intercepts at (6, 0), (-6, 0), and (5, 0).

The points on each axis where the function crosses will be the intercepts. Therefore, the p-intercept will be at the point where r = 0, and the r-intercepts will be at the point where C = 0.

We have been given the function as

C(r) = (r-6)(r+6)(r-5)

We have to determine the C-intercept and r- intercepts.

We should plug in 0 for r and solve.

Solving for the C-intercept

Plug in 0 for r.

C(0) = (0-6)(0+6)(0-5)

C(0) = 180

The C-intercept is (0, 180)

Solving for the r-intercepts, we get

Set the function equal to 0.

0 = (r-6)(r+6)(r-5)

Solve for the zeros.

(r-6) = 0 ⇒ r = 6

(r+6) = 0 ⇒ r = -6

(r-5) = 0 ⇒ r = 5

The r-intercepts are (6, 0), (-6, 0), and (5, 0)

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The idea that two variables are unrelated in the population is referred to as statistical independence. Therefore, option d is correct.

Statistical independence is a term used in probability theory and statistics to describe the independence of two random variables. If two random variables are independent, the occurrence of one does not have any impact on the probability distribution of the other.Therefore, if we have two random variables X and Y, and they are statistically independent, the occurrence of X has no effect on the likelihood of Y occurring. In other words, the occurrence of X does not affect the occurrence of Y in any way.So, we can say that two variables are said to be statistically independent when the occurrence of one variable does not have any influence on the probability of occurrence of the other variable. We can also say that there is no association between the two variables.In conclusion, we can say that statistical independence is a fundamental concept in probability theory and statistics, which helps to understand the relationship between two random variables and the probability of their occurrence.

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The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x.

Part a:

The value of the integral from 0 to 6 of f(x)dx is 16. This can be calculated using the Fundamental Theorem of Calculus (FTC) which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫f(x)dx = F(6) - F(0)

The anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫f(x)dx = (62 + 2*6) - (02 + 2*0) = 36 - 0 = 16.

Part b:

The value of the integral from 4 to 9 of g(x)dx is 20. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫g(x)dx = G(9) - G(4)

The anti-derivative of g(x) is G(x) = x3 + 3x2, so the value of the integral is:

∫g(x)dx = (93 + 3*9) - (43 + 3*4) = 729 - 168 = 20.

Part c:

The value of the integral from 4 to 9 of 2*g(x) - f(x)dx is 68. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫(2*g(x) - f(x))dx = 2*G(9) - F(9) - [2*G(4) - F(4)]

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫(2*g(x) - f(x))dx = (2*(93 + 3*9) - (92 + 2*9)) - [2*(43 + 3*4) - (42 + 2*4)]

= (1854 - 19) - (544 - 16) = 1735 - 528 = 68.

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