Proportion question
y is directly proportional to the cube of x
y = 20h when x = h

The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer: 50% of her average running speed is her average walking speed

Step-by-step explanation:

60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.

Answer: x+5

Step-by-step explanation:

Because we don't have a number so we call it x. And to increase by 5 just need to +5. So x+5

If one of the brightest stars in the sky is Sirius ​, which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. The distance is 5.29 x 10^13 miles.

Distance can be defined as the length of an object or how far an object is from another object.

Given data:

9 light years

5.88 x 10^12 miles

Now let find the how far, in​ miles, is Sirius ​

Distance = 5.88 x 10^ 12 miles× 9  light year

Distance = 52,920,000,000,000

Distance = 5.29 x 10^13 miles

Therefore we can conclude that the distance is  5.29 x 10^13 miles.

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The ordered pair is (3, 1) which is the intersecting point of these two equations.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.

Now the solution to this system is the common intersecting point of these equations.

With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.

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The spring is compressed to 95.5 cm to the right if 129 N of force are used.

In this question, we have been given the spring constant k = 283 N/m

if 129 N of force are used then we need to find distance  that the spring compressed to the right.

Let the spring stretch from the equilibrium position x.

An equation for the spring's potential energy is,

PE = 1/2 ​kx^2

129 = 1/2 * 283 * x^2

2 * 129 = 283 * x^2

258/283 = x^2

x^2 = 0.9117

x = 0.9548 m

x = 95.5 cm

Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.

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The rate of change of the function is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the function are 3 and 5

The inputs of the function are 1 and 2.

We have,

We will find two points on the graph.

The points on the graph are:

(0, 5), (1, 3), and (2, 1)

We can choose any two points.

(0, 5) and (1, 3)

The rate of change of the function.

= (3 - 5) / (1 - 0)

= -2/1

= -2

Thus,

The rate of change of the function is -2.

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Step-by-step explanation:

the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).

the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).

y = 10 - 2x

when x = 0, that means y = 10 - 2×0 = 10.

when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5

x-intercept = (5, 0)

y-intercept = (0, 10)

4y + 9x = 18

x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5

y = 0, 9x = 18, x = 18/9 = 2

x-intercept = (2, 0)

y-intercept = (0, 4.5)

6x - 2y = 44

3x - y = 22

x = 0, -y = 22, y = -22

y = 0, 3x = 22, x = 22/3 = 7 1/3

x-intercept = ( 7 1/3, 0)

y-intercept = (0, -22)

2x = 4 + 12y

x = 2 + 6y

x = 0, 6y = -2, y = -2/6 = -1/3

y = 0, x = 2 + 6×0 = 2

x-intercept = (2, 0)

y-intercept = (0, -1/3)

When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.

We have,

55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.

jam content of each container.

= 55 cups / 4 container

= 13.75 cups / 1 container

This indicates that there are 13.75 cups of jam in each container.

55 cups of jam are divided into 4 equal containers in this manner.

13.75 cups / 1 container

The amount of jam in each container is 13.75 cups of jams.

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Answer:

3

Step-by-step explanation:

The length of the photo having a width to length ratio of 2:3  is 6.9 cm.

Length is the distance between two points.

To calculate the length of the photo, use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the length of the photo is 6.9 cm.

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Answer:

C

Step-by-step explanation:

If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.

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The value  of x and y is  3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Let the equations be

x + 3y = 8    ..............(1)

x + y = 2    ..............(2)

substracting equation 1 from 2

(x + 3y) - (x + y ) = 8 - 2

x + 3y - x + y = 6

3y - y = 6

2y =6

y = 6/2

y = 3

multiply the equation 2  with value of 3

x + y=2*3

x+y =6

x+3 = 6

x = 6 - 3

x = 3

Therefore the value of x and y is both are 3

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Tracy need 5 weeks to save enough money to buy a new guitar.

Given that,

Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).

Tracy has already saved $136. 27.

Now she needs = 253. 77- 136. 27

                          = $117.50

she can save each week = $23. 50

Tracy will take weeks to save enough money

     = [tex]\frac{117.50}{23.50}[/tex]

     = 5 weeks.

Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.

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Answer:

Step-by-step explanation:

Ok:

If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price

2. 28.45-7.44=$21.01

3. Answer: The cost of the other one is $21.01

The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.

Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:

(x - h)² / a² + (y - k)² / b² = 1, b > a

Where:

If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:

(x - 3)² / 12² + (y - 5)² / 14² = 1

(x - 3)² / 144 + (y - 5)² / 196 = 1

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The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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The value of car after 6 years is £498.53

Define Modeling Exponential Decay

Given that,

Dan buys a car =  £700

Depreciates at a rate of = 5.5% per year

The value after 6 years = 700 (1 - 5.5 / 100) ^6

                                       = 498.527 or 498.53

Therefore, the value of car after 6 years is £498.53

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Answer:

4

Step-by-step explanation:

use slope formula y2-y1/x2-x1

6-2/2-1

4/1

4 is the slope

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if we take 360 to be the 100%, what's 18 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 360 & 100\\ 18& x \end{array} \implies \cfrac{360}{18}~~=~~\cfrac{100}{x}\implies 20=\cfrac{100}{x} \\\\\\ 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]

Answer: log2-log6=-log3

Step-by-step explanation:

[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]

Answer: (0, -3)

Step-by-step explanation:

You start from the x axis which is zero and then u go to the y axis and look for -3

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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The temperature decrease for every meter that the mountain climber's altitude increases is given by:

-100 ºF.

The function that models this situation is a linear function, which has the format defined as follows:

y = mx + b.

In which the coefficients are given as follows:

In the context of this problem, the function is defined as follows:

f(a) = -100a + 75.

Hence the slope of the function is of:

-100.

Representing the temperature decrease for each meter of altitude increase of the climber.

The function is defined as:

f(a) = -100a + 75.

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There is exactly one more real solution or there is exactly one more complex solution

Given,

One solution to a quadratic equation is x = -5/3

We have to find the correct statements from the given ones;

A polynomial of degree two is a quadratic equation.

This implies that a polynomial has two solutions.

We already have an answer to the query, which is a true root.

Then, the additional response that we lack can appear in the form of two responses.

It may be a real root or a complicated root, depending on the situation.

The following is the response to this query:

There is exactly one more real solution or there is exactly one more complex solution

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The half-life of vanadium-48 is 16 days.

What is half life?

The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.

According to law of radio active decay, IN=N

N-- amount of sample present

N1--- initial amount of sample

Decay 0 constant

Half life = 16 days

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Answer:

37

Step-by-step explanation:

4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37

The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and XY ≅ FE .

The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.

The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.

From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.

Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .

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Answer:

AB = 8cm ; BC = 6.5 cm

Step-by-step explanation:

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm