Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units
down on the parent function f(x)=x^2

The price of one chair Ben bought is $80 and he bought 6 chairs in total.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.

Assuming each chair costs $x and his total cost is $720.

∴ 240 + 6x = 720.

6x = 720 - 240.

6x = 480.

x = 80

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2nd X..

I hope that this is correct

Answer:

L = 40

w = 36

Step-by-step explanation:

P = 2*L + 2*w

L = w + 4

w = w

P = 152

P = 2*(w + 4) + 2*w             Remove the brackets

P = 2w + 8 + 2w                  Combine and switch sides Use P = 152

4w + 8 = P

4w + 8 = 152                        Subtract 8 from both sides.

4w = 152 - 8

4w = 144                               Divide by 4

4w/w = 144/4                  

w = 36

L = w + 4

L = 36 + 4

L = 40

Answer:

zero point zero three six

Answer:

F(x) = 4+ 1/x + 6 = 10x + 1

                                    x

Answer:

The first number is 24.08 and the second number is 34.17

Using the power and chain rules, the derivative of

y = sin²(x) - cos²(x)

is

dy/dx = 2 sin(x) cos(x) - 2 cos(x) (-sin(x))

dy/dx = 2 sin(x) cos(x) + 2 sin(x) cos(x)

dy/dx = 4 sin(x) cos(x)

and using the double angle identity for sine, this is equivalent to

dy/dx = 2 sin(2x)

Alternatively, we can first simplify y using the double angle identity for cosine:

cos(2x)= cos²(x) - sin²(x)

so that

y = -cos(2x)

and the derivative is

dy/dx = sin(2x) • 2

dy/dx = 2 sin(2x)

Answer:

See below

Step-by-step explanation:

(-4,0) is the solution to x+4=0

(0,0) is the solution to x=0

(2,0) is the solution to x-2=0

Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes

Answer:

C.24

Step-by-step explanation:

First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40

Answer:

x=7

Step-by-step explanation:

1/2(x-6)=1/2

(1/2)(x)+(1/2)(−6)=1/2

1/2x+−3=1/2

1/2x−3=1/2

1/2x−3+3=1/2+3

1/2x=7/2

2*(1/2x)=2*(7/2)

x=7

tada!

Answer:

Step-by-step explanation:108 divided by 12 equals 9 so nine feet next to 108 inches.

and nine divided by 3 is 3 so nine yards in the row with 108 inches.

360 divided by 12 which is 30 so 30 feet in the row with 360 inches.

90 feet divided by three so 30 so 30 yards in the row with 360 inches.

24 inches equals 2 feet

double this length is 48 inches or 4 feet

so in all he cut 6 yards and since he only had three yards you will still have  3 yards left over.

Answer:

Step-by-step explanation:

6x + 10 + 2x + 26 = 180

8x + 36 = 180

8x = 144

x = 18

Answer:

(9d+3)

Step-by-step explanation:

(6d+5)-(2-3d)

>(6d+5)+(-2+3d)

>{(6d+3d)+(5-2)}

=(9d+3)

Answer:

Step-by-step explanation:

Both the given points have x- coordinate of -1.

The first three of the answer options have same -1  as the x-coordinate, this means all three points are on the same line.

It is therefore impossible to have those as vertices of a triangle.

Correct option is D

Plotting the graph using geogebra online graphing tool and attaching.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let P represent the pressure in pounds and d represent the depth in feet.

Given the equation:

P = 0.455d + 14.3

Plotting the graph using geogebra online graphing tool and attaching.

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Answer:

im pretty sure it's A thx

Answer:

There is no solution to this equation.

Hope this helps :)

Answer:

no solution.

Step-by-step explanation:

carry the -5 and - sign and multiply the numbers within the () signs. so - 5×x and -5×6. which is -5x + -30. the other side will be -5x + 9. so then if you take away the -5x your left with -30 = 9 which is impossible.

Answer:

the answer is B

Step-by-step explanation:

on the Cartesian plane u have to think of the distance from both the positive and negative side

so 3 is 3 units from the origin and -6 is 6 units from the origin

Therefore the total length is 9 (3+6)

And B is the only answer which will give 9

Answer:

Step-by-step explanation:

Done

Answer:

if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)

The equilibrium price of the commodity at the given demand and supply is 1,000.

The given parameters:

The equilibrium price of the commodity is calculated as follows;

At equilibrium price, the demand curve and supply curve cross each other.

[tex]QS= QD\\\\15,000 +2P = 20,000 - 3P\\\\2P+3P = 20,000 - 15,000\\\\5P = 5,000[/tex]

[tex]P = \frac{5,000}{5} \\\\P = 1,000[/tex]

Thus, the equilibrium price of the commodity is 1,000.

The complete question is below;

Determine the equilibrium price, if QD = 20000 -3P  and QS = 15000 +2P.

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Answer:

87/103

Step-by-step explanation:

Answer:

indeed

Step-by-step explanation:

3+3=6

Answer:

Try setting up a proportion: [tex]\frac{5}{15}=\frac{3}{x}[/tex] then cross multiply to solve for x which will try you how many boys are in the class.  Then add the number of boys and girls together.

Step-by-step explanation:

Answer:

Slope: 7/5 , Y-int: 1/5

Step-by-step explanation:

To find the slope, lets use the points (-3,-4) and (2,3)

The slope formula is (y2-y1)/(x2-x1) so we will plug in the numbers.

(3-(-4))/(2-(-3))=7/5. 7/5 is the slope (you can also do rise over run)

We find the y-int in many ways but i will show two.

We can make an equation in point-slope form. The formula is: y-y1=m(x-x1) and we use the point (-3,-4).

y-(-4)=7/5(x-(-3))

y+4=7/5x+21/5 (then move the 4 to the other side)

y=7/5x+1/5

The 1/5 is our y-int since we now have it in slope intercept form!

The other method we can use is putting it into slope intercept form first and using (-3,-4) to find the missing variable.

Slope intercept form is y=mx+b, let m be slope, b is y int, and (x,y) is our point

-4=(7/5)(-3)+b

-4=-21/5+b (move -15/7 to other side)

1/5=b !

we get the same answer I hope this helps sorry its long

Answer:

[tex]g(x)=x+8[/tex]

Step-by-step explanation:

Translating a function up is very simple, all you need to do here is add 8.

If you want to think of it logically,

[tex]f(x)=x[/tex]

the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.

Hey there!

(5 * 6) * 4

= 30 * 4

= 120

So you’re basically looking for something that’s equivalent to 120

CHOICE A.

5 * (5 * 6)

= 5 * 30

= 150

So, Choice A is probably NOT the answer you’re looking for!

CHOICE B.

4 * (5 * 6)

= 4 * 30

= 120

Choice B. is probably the answer you’re probably looking for.

So, I recommend you to color it apricot. :)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

If

f(x) = x⁶ (x - 8)⁷ / (x² + 2)²

then taking the logarithm of both sides lets us expand the right side as

ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)

ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)

using the property ln(ab) = ln(a) + ln(b).

We can also use the property ln(aⁿ) = n ln(a), so that

ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)

Then differentiating both sides using the chain rule gives

f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)

f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)

f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)

Solve for f'(x) :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)

and replace f(x) with the given function :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²

We can expand the product :

f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³

then simplify by factoring :

f'(x) = x⁵ (x - 8)⁶/(x² + 2)³  • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))

Simplify the rest :

f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³

Answer:

0.5 > 0.25

Step-by-step explanation:

2/8 = 1/4 = 0.25

1/2 = 0.5

Answer:

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Step-by-step explanation:

1/2 equals more than 2/8.

Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.