If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96

Answer:  I suggest using desmos, since I can't help!! I can't see the function!!

Answer:

I'm sorry but there is no graph if you could take a picture I could try to help.

Answer:

your answer is 19,683 in^3

Step-by-step explanation:

i don't know what the heck an exercise cube is, but hey, it's the world of real world problems

volume of a cube = side length ^ 3

= 27*27*27

=19,683 in^3

If the side of cube is 27 inches then the volume of cube is 19683 [tex]inches^{3}[/tex].

The volume is the amount of substance a container can hold in its capacity. Substance can be liquid or solid. Volume of cube is side*side*side which can be written as [tex]side^{3}[/tex].

We have been given that the side of cube is 27 inches and we are required to find the volume of cube.

Volume=[tex]side^{3}[/tex]

Putting side=27.

Volume=[tex](27)^{3}[/tex]

=19683 cubic inches.

Hence if the side of cube is 27 inches then the volume of cube is 19683 [tex]inches^{3}[/tex].

Learn more about volume at https://brainly.com/question/463363

#SPJ2

Answer:

y+5 = -3(x-1)  point slope form

y = -3x-2 slope intercept form

Step-by-step explanation:

First we need to find the slope

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

m = (7--5)/(-3-1)

   = (7+5)/(-3-1)

   = 12/-4

   = -3

The slope is -3

Then we can use point slope form to write an equation

y-y1 = m(x-x1)

y--5 = -3(x-1)

y+5 = -3(x-1)

This is in point slope form

Distribute

y+5 = -3x+3

Subtract 5 from each side

y+5-5 = -3x +3-5

y = -3x-2

This is in slope intercept form

Answer:

A

Step-by-step explanation:

A function maps one member in the domain ( x values ) to exactly one member in the range (y values ).

A is the only diagram representing this characteristic.

Answer: [tex]x=-5\\y=-7[/tex]

Step-by-step explanation:

Given the system of equations:

[tex]\left \{ {{y=\frac{4}{5}x-3 } \atop {y=-7}} \right.[/tex]

You can apply the Substitution method.

You need to substitute the second equation which gives the value of the variable "y" into the first equation and solve for the variable "x", then:

[tex]y=\frac{4}{5}x-3\\\\-7=\frac{4}{5}x-3\\\\-7+3=\frac{4}{5}x\\\\-4=\frac{4}{5}x\\\\(-4)(5)=4x\\\\x=\frac{-20}{4}\\\\x=-5[/tex]

Answer:

[tex]H'(-3,-18)\\\\J'(3,-9)\\\\K'(-15,-3)\\\\L'(15,-15)[/tex]

Step-by-step explanation:

We know the coordinates of the polygon HJKL:

H(-1,-6), J(1,-3), K(-5,-1), and L(5,-5)

We know that the polygon HJKL is dilated using the scale factor 3. This means that, to find the coordinates of the vertices of polygon H'J'K'L', we need to multiply the x-coordinate and the y-coordinate of each vertex by this scale factor.

Then:

[tex]H'=(-1(3),-6(3))=(-3,-18)\\\\J'=(1(3),-3(3))=(3,-9)\\\\K'=(-5(3),-1(3))=(-15,-3)\\\\L'=(5(3),-5(3))=(15,-15)[/tex]

Konichiwa~! My name is Zalgo and I am here to help you out on this amazing day. I believe the answer that you would be looking for is (x-1)  (6x-1).

I hope that this answer helps! :3

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Arigato~! XP)

Answer:

[tex]f(x) = (4\sqrt{5})^{x}[/tex]

Step-by-step explanation:

The exponential function looks like the following: [tex]f(x) = b^{x}[/tex].

If the function passes through the point (2, 80), then:

[tex]f(x) = b^{x}[/tex] → [tex]80 = b^{2}[/tex]

Solving for 'b':

[tex]b = \sqrt{80}[/tex] →[tex]b=4\sqrt{5}[/tex]

Then, the equation of exponential function that passes through the point (2, 80) is: [tex]f(x) = (4\sqrt{5})^{x}[/tex]

[tex]\bf x(2x+4x^2-5-3x)\implies x(\stackrel{\textit{like-terms}}{2x-3x}+4x^2-5)\implies x(-x+4x^2-5) \\\\\\ -x^2+4x^3-5x\implies \stackrel{\textit{general form}}{4x^3-x^2-5x}[/tex]

Answer:

Here's what I get.

Step-by-step explanation:

x(2x + 4x² - 5 – 3x)

1. Distribute the x

2x² + 4x³ - 5x - 3x²

2. Combine like terms

4x³ - 5x – x²

3. Write the expression in order of descending powers of x

[tex]\boxed{\mathbf{4x^{3} - x^{2} - 5x}}[/tex]

Answer: c. area ≈ 5 units²

Step-by-step explanation:

Step 1: Use Law of Sines to find b:

[tex]\dfrac{sinC}{c}=\dfrac{sinB}{b}\\\\\\\dfrac{sin44.9}{4}=\dfrac{sin107.3}{b}\\\\\\b=\dfrac{4sin107.3}{sin44.9}\\\\\\b=5.4[/tex]

Step 2: Use SAS formula to find the area of the triangle:

[tex]Area = \dfrac{1}{2}bcsinA\\\\\\Area=\dfrac{1}{2}(5.4)(4)sin27.8\\\\\\Area = 5.05[/tex]

Answer:

156 square inches

Step-by-step explanation:

We are given the two quantities

Let

length = l = 13 inches

and

Width = w = 12 inches

The formula for the area of rectangle is:

[tex]Area=l*w[/tex]

where l is length and w is width

Putting the values of both that are given

[tex]Area = 13*12\\=156[/tex]

so the area is 156 square inches ..

Answer:

(x+7) is not a factor

Step-by-step explanation:

we know that

If (x+7) is a factor of f(x)

then

For [tex]x=-7, f(-7)=0[/tex]

Verify

we have

[tex]f(x)=x^{3}-3x^{2} +2x-8[/tex]

Substitute x=-7

[tex]f(-7)=(-7)^{3}-3(-7)^{2} +2(-7)-8[/tex]

[tex]f(-7)=-343-147 -14-8[/tex]

[tex]f(-7)=--512[/tex]

[tex]-512\neq 0[/tex]

therefore

(x+7) is not a factor

Answer:

Part a) The elevation of the road is [tex]6\°[/tex]

Part b) The rise is [tex]0.2\ km[/tex]

Step-by-step explanation:

Part a) What is the elevation of the road to the nearest degree?

Let

y-----> the rise of the road ( vertical distance)

x ----> the run of the road (horizontal distance)

we have

y/x=1/10

we know that

The ratio y/x is equal to the tangent of the angle of the elevation of the road

Let

[tex]\theta[/tex] ---->  angle of the elevation of the road

[tex]tan(\theta)=y/x[/tex]

[tex]tan(\theta)=1/10[/tex]

[tex]\theta=arctan(1/10)=6\°[/tex]

Part b)  If the road is two km long, how much does it rise?

using proportion

[tex]1/10=y/2[/tex]

[tex]y=2/10=0.2\ km[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]g(x)=\left|x+3\right|[/tex]

we know that

The graph is V-shaped

The vertex of the function is the point (-3,0)

The y-intercept is the point (0,3)

The graph in the attached figure

Answer:

172.5 mg/dl

Step-by-step explanation:

Given the equation y= -2.5x + 222.5, where 'x' is the time spent exercising in minutes. If we want to know the amount of cholesteron for a person exercising 20 minutes a day, we just have to subtitute 20 into the equation for x.

So we have: y= -2x + 222.5 → y= -2.5(20 minutes) + 222.5 = 172.5 mg/dl

Answer:

172.5

Step-by-step explanation:

Confirmed on test

Answer:

[tex]x^{2}+y^{2}=25[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

(h,k)=(0,0)

r=5 in

substitute

[tex](x-0)^{2}+(y-0)^{2}=5^{2}[/tex]

[tex]x^{2}+y^{2}=25[/tex]

Answer:

16

Step-by-step explanation:

6+8+10+20=44+16= 60 divided by 5 is 12

Reading from top to bottom. Answers are as follows:

1. 7(2)^t

2. 3000(0.93)^t

3. 300(1.015)^t

4. 300(0.985)^t

We know that the exponential function is given by:

             [tex]f(x)=ab^x[/tex]

where a is the initial amount.

and b is the change in the amount and is given by:

[tex]b=1+r[/tex] if the function is increasing by a rate of r

and [tex]b=1-r[/tex] if the function is decreasing by a rate of r.

a)

The initial amount of fish in the trout are: 7

i.e. a=7

Also, the population doubles every year.

This means that that b=2

Hence, the population after t years is given by the function P(t) as:

[tex]P(t)=7(2)^t[/tex]

b)

The original amount of the machine is: $ 3,000

i.e. a=3,000

Also, the value of machine decreases by a rate of 7%

i.e.

[tex]r=7\%\\\\i.e.\\\\r=0.07[/tex]

Hence, we have:

[tex]b=1-r\\\\i.e\\\\b=1-0.07\\\\i.e.\\\\b=0.93[/tex]

Hence, the function which represent the price of the machine after t years i.e. P(t) is given by:

[tex]P(t)=3000(0.93)^t[/tex]

c)

The initial population of colony of ants i.e. a=300.

The number of ants increases at a rate of 1.5% every month.

i.e. [tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]

i.e.

[tex]b=1+r\\\\i.e.\\\\b=1+0.015\\\\i.e.\\\\b=1.015[/tex]

Hence, the function P(t) which represents the population of ants after t months is given by:

[tex]P(t)=300(1.015)^t[/tex]

d)

The initial infected cells i.e. a=300

The infected cells are decaying at a rate of 1.5% per minute.

i.e.

[tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]

Since, there is a decay hence,

[tex]b=1-r\\\\i.e.\\\\b=1-0.015\\\\i.e.\\\\b=0.985[/tex]

Hence, the function P(t) which represents the number of infected cells after t minutes is given by:

[tex]P(t)=300(0.985)^t[/tex]

Answer:

[tex]4h> 14\ cm^{2}[/tex]

Step-by-step explanation:

Let

b -----> the base of parallelogram

h ----> the height of parallelogram

we know that

The area of parallelogram is equal to

[tex]A=bh[/tex]

[tex]A> 14\ cm^{2}[/tex]

so

[tex]bh> 14\ cm^{2}[/tex]

substitute the value of b

[tex]4h> 14\ cm^{2}[/tex] ---->inequality that represents all possible values of h

Answer:

The answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5x+31+3x=3

move everthing to one side

-5+31+3x-3=0

add and subtract common terms

-2x+28=0

divide across by common denominator

-x+14=0

Solve for x

x=14

Let the number of hours driven equal x.

You would multiply the number of hours by his speed, so you would have 50x

You would then want to subtract that from the total miles to see how many more miles he needs to drive.

The answer would be E. y = 470 - 50x

first off, we know the angles at vertices C and F are right-angles, meaning both triangles are right-triangles.

we also know that sides AC = DF and BC = EF.

now, for right-triangles, if the two shorter legs are congruent in both triangles, the triangles are congruent by the Leg Leg theorem, namely LL.

Answer:

6 units

Step-by-step explanation:

We require to calculate the absolute value so as to consider the measure both ways, that is

AB = | 1 - (- 5) | = | 1 + 5 | = 6

BA = | - 5 - 1 | = | - 6 | = 6

Answer:

The division was completed in the wrong order

Step-by-step explanation:

To convert [tex]\frac{5}{8}[/tex] to a percent

The numerator is divided by the denominator, that is

    0.625

8 | 5.0

Multiply 0.625 × 100% = 62.5%

Answer:

[tex]{\huge \boxed{X<-2}}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

Expand.

4(1-3x)-14=-12x-10

4(2x+3)-9x=-x+12

-12x-10>-x+12

Add by 10 from both sides of equation.

-12x-10+10>-x+12+10

Simplify.

-12x>-x+22

Add by x from both sides of equation.

-12x+x>-x+22+x

Simplify.

-11x>22

Multiply by -1 from both sides of equation.

(-11x)(-1)<22(-1)

Simplify.

11x<-22

Divide by 11 from both sides of equation.

11x/11<-22/11

Simplify, to find the answer.

-22/11=-2

x<-2 is the correct answer.

I hope this helps you, and have a wonderful day!

For this case we have that a quadratic equation is of the form:[tex]ax ^ 2 + bx + c = 0[/tex]

Where:

a: is the main coefficient because it accompanies the quadratic variable.

b: It is the linear coefficient

c: It is the constant term.

Then, a quadratic function with a main coefficient of "3" and a constant term of "-12" is:

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

Option B

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

It is B. f(x) = 3x2 + 11x – 12

Step-by-step explanation:

If this question is on Edg, then it is B, & B is Correct.

Answer:

The distance between both points would be 14.

Step-by-step explanation:

The y coordinate or -8 stays the same for both points on a coordinate grid. However the x coordinate changes from -4 to 10, which is 14 places away on a coordinate grid. Therefore the distance between these two points is 14.

Answer:

14

Step-by-step explanation:

Use the distance equation:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (10 − -4)² + (-8 − -8)²

d² = 14² + 0²

d = 14

Answer:

A.

Only function g is even

Option: A is the correct answer.

  A.   Only function g is even.

Here by looking at the graph we observe that the graph of function g satisfies the condition of even function.

( whereas the graph of function f is not symmetric about the y-axis and hence function f is not even )

     Hence,  the function g is an even function.

Answer: A is correct (x+2)/(x-1)

Step-by-step explanation:

Divide the top and bottom by 2, to simplify

[2(x^2+x-2)]/[2(x^2+2x+1)]

The 2's cancel each other out, since 2/2 would be 1.

Now factor (x^2+x-2)/(x^2+2x+1)

[(x+2)(x-1)]/[(x-1)(x-1)]

Now you can cancel out one of the (x-1) on top and bottom. All that's left is (x+2)/(x-1) which is your answer. Hope this helps!

Answer:

Step-by-step explanation:

We have:

two squares 10ft × 10ft

three rectangles 14ft × 10ft

two rectangles 9ft × 14ft

two triangles with base 10ft and height 8ft

The formula of an area of a reactangle l × w  (square s × s) :

[tex]A=lw\qquad(s^2)[/tex]

Substitute:

[tex]A_1=10^2=100\ ft^2\\\\A_2=(14)(10)=140\ ft^2\\\\A_3=(9)(14)=126\ ft^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{(base)(height)}{2}[/tex]

Substitute:

[tex]A_4=\dfrac{(10)(8)}{2}=40\ ft^2[/tex]

The Surface Area:

[tex]SA=2A_1+3A_2+2A_3+2A_4[/tex]

Substitute:

[tex]SA=(2)(100)+(3)(140)+(2)(126)+(2)(40)=952\ ft^2[/tex]