A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.

The constant of proportionality is
.
The equation that represents this proportional relationship is
.

The value of f[ -4 ] and g°f[-2] are [tex]\frac{14}{3}[/tex] and 13 respectively.

Given the function;

For f[ -4 ], we substitute -4 for every variable x in the function.

[tex]f(x) = \frac{3x-2}{x+1}\\\\f(-4) = \frac{3(-4)-2}{(-4)+1}\\\\f(-4) = \frac{-12-2}{-4+1}\\\\f(-4) = \frac{-14}{-3}\\\\f(-4) = \frac{14}{3}[/tex]

For g°f[-2]

g°f[-2] is expressed as g(f(-2))

[tex]g(\frac{3x-2}{x+1}) = (\frac{3x-2}{x+1}) + 5\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2}{x+1} + \frac{5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2+5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{8x+3}{x+1}\\\\We\ substitute \ in \ [-2] \\\\g(\frac{3x-2}{x+1}) = \frac{8(-2)+3}{(-2)+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-16+3}{-2+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-13}{-1}\\\\g(\frac{3x-2}{x+1}) = 13[/tex]

Therefore, the value of f[ -4 ] and g°f[-2] are [tex]\frac{14}{3}[/tex] and 13 respectively.

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Answer:

3/16 pounds more.

Step-by-step explanation:

It is 1 1/8 - 15/16

= 9/8 - 15/16

= 18/16 - 15/16

=  3/16.

Hello,

[tex]34 = p + 19[/tex]

[tex]34 - 19 = p + 19 - 19[/tex]

[tex]15 = p[/tex]

[tex]p = 15[/tex]

The equation that could be used to solve for the length of XY is XY = 22/sin(41)

An equation is an expression that shows the relationship between two or more variables and numbers.

Sine rule is used to show the relationship between the sides and angles of a trinagles.

Using sine rule on triangle XYZ:

XY / sin(Z) = XZ / sin(Y)

XY / sin(90) = 22/sin(41)

XY = 22/sin(41)

The equation that could be used to solve for the length of XY is XY = 22/sin(41)

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Answer:

D

Step-by-step explanation:

If ages are normally distributed then using a significance level of 0.05 , we can claim that the population mean is greater than 24.

Given sample mean of 25 years , sample size of 16 ,standard deviation of 2 years.

We have to find whether the population average is greater than 24.

We have to use t test because n is less than 30. It is right tailed.

We have to first form Hypothesis.

[tex]H_{0}[/tex]:μ>24,

[tex]H_{1}[/tex]:μ<24.

t=X-μ/S/[tex]\sqrt{n}[/tex]

t critical at 5% significance level and degree of freedom=15    (16-1)=1.7531

t=24-25/2/[tex]\sqrt{16}[/tex]

=-1/0.5

=-2

Because 1.7531 is greater than -2 so we will accept the null hypothesis.

Hence we can say that the average of population is greater than 24.

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Using a linear function, we have that:

a) The fixed cost is of $10.

b) The equation is: C = 10 + 12d.

c) The cost of an 18 km trip is $226.

d) The distance traveled is of 20 km.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:

C(d) = 12d + b

70 = 60 + b

b = 10.

Hence the equation is:

C(d) = 12d + 10.

For a trip of 18 km, d = 18, hence the cost is:

C(12) = 12 x 18 + 10 = $226.

When the cost is of $250, the distance is found as follows:

250 = 12d + 10

12d = 240

d = 240/12

d = 20 km.

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Answer:

Step-by-step explanation:

The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.

Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.

Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."

When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:

  [tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

This quadratic formula tells you the solutions based on the coefficients of the original equation, so does not require rearranging the equation in any way.

The answer which are true about the two rectangular pyramids are;

It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.

On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.

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The mean height of plants is 44.07cm.

Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.

The mean is defined as the mean value equal to the ratio of the total number of a given set of values ​​to the total number of values ​​contained in that set.

Firstly, we will find the midpoint of the height by using the formula

(upper limit +lower limit)/2

When h is 10<h<20 then the midpoint is

x₁=(10+20)/2

x₁=15

When h is 20<h<0 then the midpoint is

x₂=(20+40)/2

x₂=30

When h is 40<h<50 then the midpoint is

x₃(40+50)/2

x₃=45

When h is 50<h<60 then the midpoint is

x₄=(50+60)/2

x₄=55

When h is 60<h<90 then the midpoint is

x₅=(60+90)/2

x₅=75

Now, we will find the mean height by using the formula

x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)

Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8

and Σfi=7+15+27+12+8=70

Substitute these values in the formula, we get

x=(7×15+15×30+27×45+12×55+8×75)/70

x=(105+450+1215+715+600)/70

x=(3085)/70

x=44.07

Hence,  the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.

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Answer:

Step-by-step explanation:

Well first you have:

$15.95 for one sweater
$9.00 each for two shirts

You would double the amount $9.00 which would be:

9 + 9 = 18 or Multiply 9 x 2 = 18

So this would total to 15 + 18 = $33

If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .

Distance travels= 175 miles

time is taken to cover 175 miles = 2.5 hours

We have to find out the speed in mph.

We know that,

Distance = speed x time

⇒speed = distance / time

Putting the value of distance and time, we get:

speed = 175 / 2.5 = 70 mph

Hence the final answer is 70 mph.

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Answer:

7

Step-by-step explanation:

frist simplfying

3x-6=15

addind six to both side

3x-6+6=15+6

3x=21 dividing by 3

x=7

Answer:

x = 42

Step-by-step explanation:

Cross multiplying is done as follows:

the denominator of the second fraction is multiplied with the numerator of the first equation and denominator of the first fraction is multiplied with the numerator of the second equation

5(3x+6) = 4(4x-3) multiply inside the parenthesis

15x + 30 = 16x - 12 transfer like terms to same side of the equation

30 + 12 = 16x - 15x

42 = x

Answer:

y=x^2-10

Step-by-step explanation:

The contribution margin per unit is $ 1.50

The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.

One of the main components of break-even analysis is the idea of contribution margin.

Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.

According to the question,

Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)

                                        = $ 20

Selling Price per unit = $ 21.50

Thus, contribution margin per unit = $ (21.50 - 20)

                                                         = $ 1.50

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The slope of the parallel line is undefined and the slope of the perpendicular line is 0

The equation is given as:

x = 1

The above do not have any y value.

This means that the slope of the line is undefined

i.e.

m = undefined

The slope of the parallel line is:

Slope = m

This gives

Slope = undefined

The slope of the perpendicular line is:

Slope =-1/m

This gives

Slope = -1/undefined

Slope = 0

Hence, the slope of the parallel line is undefined and the slope of the perpendicular line is 0

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Using translation concepts, the equation of g(x) is:

D) [tex]\log_5{x + 3}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Researching this problem on the internet, g(x) is a shift left of 3 units of [tex]f(x) = \log_5{x}[/tex], hence:

[tex]g(x) = f(x + 3) = \log_5{x + 3}[/tex], which means that option D is correct.

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To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.

Option C is the correct answer.

There are ways to prove that two triangles are congruent.

- Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

- Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

- Angle-Side-Angle (ASA) Congruence.

The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

- Angle-Angle-Side (AAS) Congruence.

We have,

AD is parallel to BC

From the figure and the given information,

We have,

∠DAC ≅ ∠BCA

This means,

Angle-Side-Angle (ASA) Congruence

ΔDAC ≅ ΔBCA

Thus,

To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.

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Answer: 30.

Step-by-step explanation:

[tex]7\frac{1}{2} =\frac{7*2+1}{2} \\\frac{14+1}{2}=\frac{15}{2}\\ \frac{15*2}{2*2}=\frac{30}{4} \\ \frac{30}{4}=30*\frac{1}{4} .[/tex]

There are total 30 quarters in [tex]7\frac{1}{2}[/tex].

A quarter is one out of four equal parts. One quarter is the same as the fraction ¼.

A fraction represented with its quotient and remainder is a mixed fraction.

To change a mixed fraction to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.

According to the given question.

We have a mixed fraction [tex]7\frac{1}{2}[/tex].

So, the improper fraction of the given mixed fraction is given by

[tex]7 \frac{1}{2} = \frac{15}{2}[/tex]

To find the number of quarters in the given mixed fraction, we will divide [tex]7\frac{1}{2}[/tex]  by  [tex]\frac{1}{4}[/tex].

Therefore,

[tex]\frac{7\frac{1}{2} }{\frac{1}{4} }[/tex]

= [tex]\frac{\frac{15}{2} }{\frac{1}{4} }[/tex]

[tex]= \frac{15\times 4}{2}[/tex]

[tex]= 15\times 2[/tex]

[tex]= 30[/tex]

Hence, there are total 30 quarters in [tex]7\frac{1}{2}[/tex].

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The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of kite = (product of diagonals)/2

Area of kite = (10 * 14) / 2 = 70 in²

The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

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The tree is 23.54 feet tall.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.

According to the question,

Height of tree= 22*tan [tex]47^{o}[/tex]

                       = 22* 1.07

                       = 23.54 ft.

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Answer:

B 4 1/3

Step-by-step explanation:

The graph of the inverse of the function is shown in the image attached below.

In this question we must apply the following transformation rule to the three points to determine the points of the inverse function:

(x, y) → (y, x)

Now we proceed to find the points:

(- 7, 3) → (3, - 7)

(-3, 0) → (0, -3)

(-2, -2) → (-2, -2)

Lastly, we proceed to construct the graph of the inverse of the function.  

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The function that could be a stretch of the exponential decay function shown on the graph is B. f(x) = One-half(6)x.

From the information given, it can be seen that function A is a monotonically increasing function.

Also, it can be seen that C and D don't pass through (0, 1).

Therefore, the function could be a stretch of the exponential decay function shown on the graph is B.

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Answer:

b

Step-by-step explanation:

Answer:b

Step-by-step explanation:goooooooo

The slope of the line through the points is -3

The points are given as:

(-1, 8) and (3, -4)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

So, we have:

m = (-4 - 8)/(3 + 1)

Evaluate the expression

m = -3

Hence, the slope of the line through the points is -3

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The slope of the line that passes through (-1, 8) and (3, -4) is: -3.

Slope of a line (m) = change in y / change in x.

Given the points, (-1, 8) and (3, -4):

Slope (m) = (-4 - 8)/(3 - (-1))

Slope (m) = (-12)/(4)

Slope (m) = -3

Thus, the slope that passes through the given points is: -3.

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The number of different 4 digit numbers that can be formed using only digits 1,2,3 and 4 if they are repeated is; 256 possible numbers

Since the numbers can be used as many times as we want, then it means they can be repeated.

Thus, if we are looking at the number of 4 digit numbers we can create using the numbers 1, 2, 3, and 4, we can calculate that the following way:

For each digit (thousands, hundreds, tens, ones), we have 4 possible choices of numbers. And so we can create;

4 × 4 × 4 × 4 = 256 numbers

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Hey there!

12(w - 3)

= 12(10 - 3)

= 12(10) + 12(-3)

= 120 - 36

= 84

OR

12(w - 3)

= 12(10 - 3)

= 12(7)

= 84

Therefore, your answer should be:

84

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

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The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3

The expression is given as:

6 to the power of 5/6to the power of 2.

Rewrite properly as:

6^5/6^2

Apply the law of indices

6^(5-2)

Evaluate the difference

6^3

Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3

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