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Stolb23 [73]
3 years ago
12

1. Given that 4x²- 16x + 15 = a(x-p)²+ q for all values of x.

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

a = 4, p = 2, q = - 1

Step-by-step explanation:

Expand the right side of the identity, then compare the coefficients of like terms with those on the left side.

a(x - p)² + q ← expand (x - p)² using FOIL

= a(x² - 2px + p²) + q  ← distribute parenthesis

= ax² - 2apx + ap² + q

Compare coefficients of x² term

a = 4

Compare coefficients of x- term

- 2ap = - 16, that is

- 2(4)p = - 16

- 8p = - 16 ( divide both sides by - 8 )

p = 2

Compare constant terms

ap² + q = 15 , that is

4(2)² + q = 15

16 + q = 15 ( subtract 16 from both sides )

q = - 1

Thus a = 4, p = 2, q = - 1

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lana [24]

I think it’s six because 3n=6-5 3 n=6-5 then subtract 5 5 from 6 6

7 0
3 years ago
What is the y-intercept of the function, represented by the table of values
AleksandrR [38]

Answer:

9

Step-by-step explanation:

The table is given below

\left|\begin{array}{c|cc}x&y\\--&--\\-2&15\\1&6\\2&3\\4&-3\\7&-12\end{array}\right|

We can see that the table represents a linear function since by checking its slope.

Using:

  1. Points (-2,15) and (1,6)
  2. Points (1,6) and (2,3)

Slope =\dfrac{6-15}{1-(-2)} =\dfrac{3-6}{2-1}=-3

Therefore, the values represent a linear function.

A linear equation is of the form y=mx+b

Therefore:

y=-3x+b

Using the points (7,-12)

-12=-3(7)+b\\-12=-21+b\\b=-12+21\\b=9

Therefore, the y-intercept of the function, represented by the table of values is 9.

6 0
3 years ago
Bessie bought 10 gallons of Bush's Sweet Tea for a family reunion. How many liters did Bessie buy?
RUDIKE [14]

1 gallon = 3.78541 liters.

Multiply the number of gallons by 3.78541:

10 x 3.78541 = 37.8541 liters (round the answer as needed)

8 0
3 years ago
5 more than the product of 4 and some number is equal to 33
gregori [183]

Answer:

33 = 4x + 5

Step-by-step explanation:

If you convert this expression into numbers, it would be 4 times the number x plus 5 is equal to 33.

Hopefully this helps! Let me know if you have any questions!

8 0
3 years ago
Read 2 more answers
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svp [43]
2 inches = 50 miles
1 inch = 25miles
0.5 inches = 12.5 miles
0.25 inches = 6.25
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4 0
3 years ago
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