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IrinaK [193]
2 years ago
5

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = –8x + x2 + 7 ?

Mathematics
2 answers:
hjlf2 years ago
8 0
Vertex of x^2 = (0,0)

Vertex of x^2 - 8x + 7

     Find the roots by factoring
         (x - 7)( x -1 )=0
           x= 7, x = 1
           middle: [7+1]/2 = 8/2 = 4
           g(4) = 4^2 -8(4) + 7 = 16 - 32 + 7 = -9
           Vertex = (4,-9)

Then the translation is right 4, down 9. This is the first option.

 
Leya [2.2K]2 years ago
8 0
The vertex form of the function:
g ( x ) = x² - 8 x + 7 = ( x² - 8 x + 16 ) - 16 + 7 =
= ( x - 4 )² - 9
Answer:
C )  right 4, down 9.
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Alan is loading a pallet with boxes that each weighs 55 pounds. The pallet can safely support no more than 1595 pounds. How many
Ne4ueva [31]

Answer:

At most 29 boxes can be safely loaded onto the pallet.

Step-by-step explanation:

Given:

Weight of each box = 55 pound

Weight pallet can support \leq 1595 pounds.

We need to find the number of boxes .

Solution:

Let the number of boxes loaded safely onto the pallet be 'x'.

So we can say that;

Weight of each box Multiplied by number of boxes should be less than or equal to Weight pallet can support.

framing in equation form we get;

55x\leq 1595

Dividing both side by 55 we get;

\frac{55x}{55}\leq \frac{1595}{55}\\\\x\leq 29

Hence At most 29 boxes can be safely loaded onto the pallet.

4 0
3 years ago
The price of an item decreased by 20% to $200. Then later the price decreased again from $200 to $150. What is the percent of de
cricket20 [7]

Answer:

40%

Step-by-step explanation:

ok so first find the og price:

100% - 20% = 80%

so 80% = 200

let the 100% be x:

x * 0.8 = 200

x= 250

100% = 250

(difference/ og price) * 100% = the percentage decrease/ increase

(250-150/250)* 100% = 40%

OR

((the final price/ og price) * 100%) - 100%

((150/250)*100%) - 100% = 40%

There was a 40% decrease from the og price to the final price of 150.

3 0
3 years ago
The back yard at Mr. Smith's house is 16 ft. wide 10 ft. long. What is the perimeter of his back yard?
KonstantinChe [14]

Answer:

1.6?

Step-by-step explanation:

4 0
2 years ago
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For the purpose of purchasing new baseboard and​ carpet, complete parts a and b below.
Phantasy [73]

Answer:

(a)i. Area=72 square feet

ii. Perimeter =34 feet

(b) Baseboard - perimeter

Carpet - area

Step-by-step explanation:

The room is 9ft x 8ft, therefore it is rectangular shaped.

Length=9ft; Breadth=8ft

(a)i. Area of a Rectangle= Length X Breadth

Area of the room=8X9=72 square feet

ii. Perimeter of a Rectangle=2(Length+Breadth)

Perimeter of the room=2(8+9)=2 X 17 =34 feet

(b) A baseboard goes around the edge or boundary of the room, so it has to do with perimeter

A carpet covers the entire floor so it has to do with the area of the room.

3 0
3 years ago
Consider the differential equation: y′′−8y′=7x+1. Find the general solution to the corresponding homogeneous equation. In your a
Margaret [11]

Answer:

yp = -x/8

Step-by-step explanation:

Given the differential equation: y′′−8y′=7x+1,

The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)

First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;

y′′−8y′=0

The auxiliary equation will give us;

m²-8m = 0

m(m-8) = 0

m = 0 and m-8 = 0

m1 = 0 and m2 = 8

Since the value of the roots are real and different, the complementary solution (yc) will give us

yc = Ae^m1x + Be^m2x

yc = Ae^0+Be^8x

yc = A+Be^8x

To get yp we will differentiate yc twice and substitute the answers into the original DE

yp = Ax+B (using the method of undetermined coefficients

y'p = A

y"p = 0

Substituting the differentials into the general DE to get the constants we have;

0-8A = 7x+1

Comparing coefficients

-8A = 1

A = -1/8

B = 0

yp = -1/8x+0

yp = -x/8 (particular integral)

y = yc+yp

y = A+Be^8x-x/8

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2 years ago
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