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Vedmedyk [2.9K]
2 years ago
8

Y= (x-1)^2 + 2 change this equation into standard form

Mathematics
1 answer:
BaLLatris [955]2 years ago
8 0

Answer:

x² - 2x + 3

Step-by-step explanation:

y = (x - 1)² + 2

= (x - 1)² + 2 [a - b]² = <em><u>a²- 2ab + b²</u></em>

= x²- 2x + 1 + 2

= x² - 2x + 3

Thus, the standard form of the equation is x² - 2x + 3

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1. Which of the following measurements could be the three side lengths of a right triangle? a. 4 cm, 5 cm, 9 cm b. 12 cm, 20 cm,
HACTEHA [7]

Answer:

b and c

Step-by-step explanation:

The Triangle Inequality Theorem lets us know that the sum of the two shortest sides of the triangle must be greater than the third side of the triangle.

In both A and D, the sum of the shortest two sides are equal to, not greater than the third side, so they will not form a triangle.

In B, 12+20 is 32, which is greater than 25. And in C, 18+24 is 42, which is greater than 30, so they both will form a triangle.

8 0
3 years ago
5. Mai attempted 40 free throws and was successful 25% of them. How many free throws did
Kipish [7]

Answer:

10 were successful

Step-by-step explanation:

40x25%=10

4 0
2 years ago
Read 2 more answers
Amanda went to the store to purchase ink pens. She found three kinds of pens. The first cost $4 each; the price of the second ki
KonstantinChe [14]

Answer:

Amanda buy first kind of pen = 3

Amanda buy second kind of pen = 2

Amanda buy third kind of pen = 15

Step-by-step explanation:

Given - Amanda went to the store to purchase ink pens. She found three    

            kinds of pens. The first cost $4 each; the price of the second kind

            was 4 for $1; and the cost for the third kind was 2 for $1. She bought

            20 pens and she bought at least one of each kind. (It is possible to

            buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was

            $20.

To find - When she got back to her office, Amanda decided to turn this into

              a math problem for me. She asked: how many of each kind did I

              buy?

Proof -

Let Amanda buy first kind of pen = x

                      second kind of pen = y

                           third kind of pen = z

As given,

She bought total pen = 20

⇒x + y + z = 20          ...............(1)

Now,

As given,

cost for first kind pen = $4 for 1 pen

As she bought x pens of first kind , so

Cost of x pens of first kind = $4x

Now,

The price of the second kind was 4 for $1

⇒Cost of second kind = $\frac{1}{4} for 1 pen

As she bought y pens of send kind , so

Cost of y pens of second kind = $\frac{1}{4}y

Now,

The price of the third kind was 2 for $1

⇒Cost of third kind = $\frac{1}{2} for 1 pen

As she bought z pens of send kind , so

Cost of z pens of third kind = $\frac{1}{2}z

Now,

As given, The cost was $20

⇒4x + \frac{1}{4}y + \frac{1}{2}z = 20

⇒16x + y + 2z = 80             .....................(2)

∴ we get 2 equations

x + y + z = 20                   .....................(1)

16x + y + 2z = 80             .....................(2)

Now,

Subtract equation (1) from equation (2) , we get

16x + y + 2z  - ( x+ y + z )= 80 - 20

⇒16x + y + 2z - x - y - z = 60

⇒15x + z = 60

⇒z = 60 - 15x

Now,

Put the value of z in equation (1) , we get

x + y + 60 - 15 x = 20

⇒ y - 14x = 20 - 60

⇒y - 14x = -40

⇒14x - y = 40

⇒y = 14x - 40

Now,

we get

z = 60 - 15x

y = 14x - 40

As given

she bought at least one of each kind

it means x > 1, y > 1, z > 1

Now,

If x = 1, then y = 14 - 40 = -26

Not possible

If x = 2 , then y = 14(2) - 40 = -12

Not possible

If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15

Possible.

If x = 4,  then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0

Not Possible.

If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15

Not Possible.

∴ we get

x = 3, y = 2, z = 15

Amanda buy first kind of pen = x = 3

Amanda buy second kind of pen = y = 2

Amanda buy third kind of pen = z = 15

7 0
2 years ago
The graph of this system of equations is used to solve 4x2-3+6=2x4-9x3+2x What represents the solution set?
Vilka [71]

ANSWER

x coordinates of the intersection points

EXPLANATION

The given system of equations is:

y = 4 {x}^{2}  - 3x + 6

y = 2 {x}^{4}  - 9 {x}^{3}  + 2x

We want to use the graph of these functions to solve

4 {x}^{2}  - 3x + 6 =  2 {x}^{4}  - 9 {x}^{3}  + 2x

The point of the intersection of the graph gives the solution to the simultaneous equation above.

Hence the x-coordinates of the intersection points gives the solution set of

4 {x}^{2}  - 3x + 6 =  2 {x}^{4}  - 9 {x}^{3}  + 2x

The last choice is correct.

3 0
2 years ago
Read 2 more answers
What is the surface area of the triangular prism?
Fofino [41]

Answer:

116.33

Step-by-step explanation:

6 0
2 years ago
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