The table represents a bicycle rental cost in dollars as a function of time in hours.

which explains weather or not the function represents a direct variation ?

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-6}{-5-1}\implies \cfrac{-13}{-6}\implies \cfrac{13}{6}[/tex]

The slope of the line is [tex]\frac{13}{6}[/tex].

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

If [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] are the two points on a straight line, then the slope formula is given by:

Slope, m = Change in y-coordinates/Change in x-coordinates

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

According to the given question.

We have a two points (1, 6) and (-5,-7).

Therefore, the slope of the line from these points is given by

[tex]slope = \frac{-7-6}{-5-1} = \frac{-13}{-6} =\frac{13}{6}[/tex]

Hence, the slope of the line is [tex]\frac{13}{6}[/tex].

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Answer:

3 times 10

Step-by-step explanation:

x=4.80989686

by simplifying both sides of the equation, then isolating the variable.

Answer:

x= - 9

Step-by-step explanation:

This problem bothers on the law of indices

Given the expression

3^4x=27^x-3

We can also simplify it using the law

3^4x= 3^3(x-3)

Equating the powers we have

4x= 3(x-3)

Opening bracket

4x= 3x-9

Collecting like terms we have

4x-3x=-9

x=-9

Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.

Original measurements:

L = 4; W = 6; H = 7

surface area = 2(LW + LH + HW)

surface area = 2(4 * 6 + 4 * 7 + 6 * 7)

surface area = 2(24 + 28 + 42)

surface area = 2(94)

surface area = 188

Doubled measurements:

L = 8; W = 12; H = 14

surface area = 2(LW + LH + HW)

surface area = 2(8 * 12 + 8 * 14 + 12 * 14)

surface area = 2(96 + 112 + 168)

surface area = 2(376)

surface area = 752

The surface area was 188 square inches and it became 752 square inches.

752/188 = 4

As the side lengths increased by a factor of 2, the surface area increased by a factor of 4.

Answer:

You can make 11 recipes with 7 1/2 cups of walnuts

Answer:

Step-by-step explanation:

11 1/4 but it says the number of full recipes so it would be 11

first off, let's solve the "given" line for "y", that way we can put it in slope-intercept form to see what its slope might be.

[tex]\bf 10x+2y=-2\implies 2y=-10x-2\implies y=\cfrac{-10x-2}{2} \\\\\\ y=\cfrac{-10x}{2}-\cfrac{2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-5}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

well, a parallel line to that one, will have the same exact slope, so then, we're really looking for the equation of a line whose slope is -5 and runs through (0 , 12)

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{12})~\hspace{10em} slope = m\implies -5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-12=-5(x-0) \\\\\\ y-12=-5x\implies y=-5x+12[/tex]

this is the answer to your equation

The solutions to the equation x² = -63 in simplified, rationalized form are:

x = 3√7 * i

x = -3√7 * i

Isolate x²: In this case, x² is already isolated on one side of the equation.

Apply the Square Root Property: Take the square root of both sides of the equation to eliminate the exponent on x²:

√(x²) = √(-63)

Simplify and Introduce Imaginary Unit: Recall that the square root of a negative number is an imaginary number. We introduce the imaginary unit 'i,' defined as √(-1):

x = ±√(63) * √(-1)

x = ±√63 * i

Simplify and Rationalize: √63 cannot be simplified further, but we can rationalize it by multiplying both the numerator and denominator by √3:

x = ±√63 * i * √3 / √3

x = ±3√7 * i

The unit rate in the equation 64t = 384 is 64.

The unit rate in the equation 64t = 384 is 64.

To find the unit rate, we divide the total value by the number of units. In this case, the total value is 384 and the number of units is 64. When we divide 384 by 64, we get the unit rate of 6.

Therefore, the unit rate in the equation is 64.

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The unit rate in the equation 64t = 384 is 6.

The unit rate in the equation 64t = 384 is 6.

To find the unit rate, divide both sides of the equation by 64:

t = 384/64 = 6.

Therefore, the unit rate is 6, which means that Steve drove at a constant rate of 6 hours to reach the beach.

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Answer:

0 has multiplicity 1

-2 has multiplicity 3

-4 has multiplicity 2

5 has multiplicity 4

Step-by-step explanation:

The multiplicity of the root of a polynomial function, refers to the number of time the root repeats itself.

The given function is

[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]

To find the roots of this function, we equate the function to zero.

[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]

We now use the zero product principle, to obtain;

[tex]x=0[/tex], with multiplicity 1

[tex](x+2)^3=0[/tex]

[tex]\Rightarrow x=-2[/tex], with multiplicity 3

[tex](x+4)^2=0[/tex]

[tex]\Rightarrow x=-4[/tex], with multiplicity 2

[tex](x-5)^4=0[/tex]

[tex]\Rightarrow x=5[/tex], with multiplicity 5.

Answer:

The roots of the function;

[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]

Step-by-step explanation:

Given information:

The function;

[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]

As, we know that multiplicity of any function is defined as the number of times the roots repeats in the solution.

Hence, we need to find the roots of the function

So, equating the function to [tex]0[/tex]

[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]

As, [tex]x=0[/tex] , is having multiplicity [tex]1[/tex].

[tex](x+2)^3=0\\x=-2[/tex]

Having a multiplicity  3.

Now,

[tex](x+4)^2=0\\x=-4[/tex]

Having a multiplicity  2.

And,

[tex](x-5)^4=0\\x=5[/tex]

Having multiplicity  4.

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Answer:

its A i just took the test

Step-by-step explanation:

Answer: The correct answer is 24 square units.

Step-by-step explanation:

ANSWER

0

EXPLANATION

Given :

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

We solve for 'a' to obtain,

[tex]2a + 2 = 4a[/tex]

This implies that,

[tex]2 = 4a - 2a[/tex]

[tex]2 = 2a[/tex]

This implies that,

[tex]a = 1[/tex]

We substitute a=1 into

[tex] \frac{ 2{a}^{2} - 2}{ {a}^{2} } [/tex]

This gives us,

[tex]\frac{ 2{(1)}^{2} - 2}{ {(1)}^{2} } = \frac{2 - 2}{2} = \frac{0}{2} = 0[/tex]

have a good day!!!!!!!!!

The total cost of the regular price for a group of x people is represented by the equation C = 22x, while the total cost of the group special is represented by C = 18x + 24.

Equations for Total Cost

1. Total Cost of Regular Price: Ms. Chen can calculate the total cost for x people with the regular price by using the equation C = 22x. Here, C represents the total cost, and x is the number of people in the group.

2. Total Cost of Group Special: To calculate the total cost for x people with the group special, Ms. Chen would use the equation C = 18x + 24. C is still the total cost, x is the number of people, and 24 represents the additional fee for the private room.

By comparing the results of both equations for a specific number of people, Ms. Chen can determine which option is more cost-effective.

Answer:

number 16 is correct nice job!  number 17 is J=PM/300

Step-by-step explanation:

For 16 the answer is option D

For 17 the correct option is D

See the attached figure

you would multiply by 4 because if there are 4 cups in a quart then u have 1 quart or 4 cups . thats the only explanation even possible for this problem

No, they do not represent the same quantity. Explained in attached sheet.

Part A: You can add the time in hours to find the total. 1/3 + 3/4 + 4/6 + 1/2 = 2 1/4 hours which can also be expressed as 2 hours and 15 minutes (1/4 of an hour is 15 minutes.)

Part B: It takes him 3/4 hr to do homework, 4/6 hr to play soccer, and 1/2 hr to play piano. 3/4 + 4/6 + 1/2 = 1 11/12 hrs or 1 hour and 55 minutes (11/12 of an hour is 55 minutes.) Therefore Kevin is wrong.

the answer is negative 168

Answer:

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

you need to divide 89 by 8 then round and you get 11

Answer:

19.32

Step-by-step explanation:

To find the missing number, we need to solve for the total of the left side of the equation.

Total = 8.4(1.5 + 2.3)

Total = 8.4(3.8)

Total = 31.92

Now we subtract the total to the only value on the right side.

Missing number = 31.9-12.6

Missing number = 19.32

8.4(1.5+2.3) = 12.6 + 19.32

this is an example, but it's not drawn accurately and not to scale

use a protractor and ruler for yours

Answer:

A. $24.11

Step-by-step explanation:

Take $210 out of the $250 he gave the cashier

250 - 210 = 40

So you have his exact change without the tax though. so take what he RECIVED away from what he was suppose to recive which is 40. So.....

40 - 15.89 = 24.11

$24.11

Hope this helps!

Answer: there are 360 degrees in a circle, that there are 90 degrees in a right angle, and that the angle of an equilateral triangle contains 60 degrees.

Step-by-step explanation:

There are 360 degrees in a circle

Answer:

7.25

Step-by-step explanation:

2 7/8 + 3 2/8 * 1 1/8 = 7.25

Answer:

7 1/4

Step-by-step explanation:

exact form is 29/4 but if you wanted to simplify it the mixed number form is 7 1/4

Answer:

-3/4 g =x

Step-by-step explanation:

g=-4x/3

Multiply each side by 3

3g = -4/3 x *3

3g = -4x

Divide each side by -4

3/-4 g = -4x/-4

-3/4 g =x

Answer:

[tex]\large\boxed{b)\ y=\dfrac{3}{4}x-1}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b = y-intercpt → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (4, 2) and (0, -1) - y-intercept → b = -1.

(we see this already which equation. Only in b) y-intercept is b = -1).

Anyway, calculate the slope:

[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]

Finally we have the equation:

[tex]y=\dfrac{3}{4}x-1[/tex]

Bred has a total of 771 ways to paint the wall, taking into account that he can use at most two colors for the stripes or just one.

The subject matter pertains to the field of combinatorics, a branch of mathematics dealing with combinations and permutations. The task requires finding the number of ways to paint 8 stripes on a wall using up to 2 colors from a selection of 3 colors, namely: blue, red, and white. Since we have more paint than stripes, the limiting factor in this problem is the number of stripes, not the quantity of paint.

As Bred can use at most two colors for the stripes, the combinations we can have with two colors are: blue and red, blue and white, red and white. In each of these combinations, there are 2^8 (or 256) ways to paint 8 stripes (exploration of all binary possibilities). So, for three combinations, it will be 3*256 = 768 ways.

Now, let's look at the single color options. He can also paint the stripes all in one color, but since he has only three colors, he has three ways for this.

Hence, in total, Bred has 768 (from two-color combinations) + 3 (from single color option) = 771 ways to paint a wall.

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Answer:

(x - 7)(x + 6)

Step-by-step explanation:

Consider the factors of the constant term ( - 42) which sum to give the coefficient of the x- term ( - 1)

The factors are - 7 and + 6, since

- 7 × 6 = - 42 and - 7 + 6 = - 1

x² - x - 42 = (x - 7)(x + 6)

Answer:

Factor x²−x−42 using the AC method.

Step-by-step explanation:

What is the factored form of the following expression?

x^2 - x - 42

STEPS:

x²-x-42

Break the expression into groups:

=(x²+6x)+(-7x-42)

Factor out x from x²+6x: x(x+6)

Factor out -7 from -7-42: -7(x+6)

=x(x+6)-7(x+6)

Factor out common term x+6

Option B is correct since both the lines given in option B have same slope so both the lines do not intersect each other and hence have no common solution.

The given equations are of the form

ax + by = c ......(1)

Slope for the equation of line is given by [tex](\dfrac{-a}{b} )[/tex]

We can  clearly see that in option B the lines given are

4x + 2y = 12 .......(2)

20x + 10y = 30....... (3)

Slope of equation (2)

[tex](\dfrac{-4}{2} )= -2[/tex]

Similarly slope of equation (3)

[tex](\dfrac{-20}{10} )= -2[/tex]

Which concludes that both are parallel to each other.

Since parallel lines can not have any common solution so  they never intersect each other. Hence option B is correct.

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Answer: 1 3/4 gallons

Step-by-step explanation: In order to determine the total number of gallons in the recipe you need to convert 8 cups to gallons. There are 16 cups in 1 gallon. In order to determine how many gallons 8 cups is you need to divide 8/16 = 1/2 gallon.

The total number of gallons is 1 1/4 + 1/2.

1 1/4 + 1/2 = 1 3/4 gallons.

Answer: OPTION C

Step-by-step explanation:

By definition you know that:

[tex]\sqrt[n]{a^n}=a[/tex]

and by the exponents properties you also know that:

[tex]a^n*a^m=a^{(n+m)}[/tex]

Now, descompose 18 into its prime factors:

18=2*3*3=2*3²

Rewrite the expression and simplify (Keep on mind that: [tex]\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}[/tex]). Then, you obtain:

[tex]\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}[/tex]

Answer:

C. [tex]3x^2y\sqrt{2y}[/tex].

Step-by-step explanation:

The given radical expression is  [tex]\sqrt{18x^4y^3}[/tex].

We can rewrite this radical expression to obtain;

[tex]\sqrt{2\times9 \times (x^2)^2\times y^2\times y}[/tex].

This will give us;

[tex]\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}[/tex].

[tex]3x^2y\sqrt{2y}[/tex].

The correct choice is C