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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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In a city the record monthly high temperature for july is 88. The record monthly low temperature is 30.
Zinaida [17]

Answer:

 58 degrees    or   [30, 88]

Step-by-step explanation:

In such a context, the word "range" can have different meanings. On the one hand it is the difference between high and low:

  88 -30 = 58 . . . . range of temperatures

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On the other hand, it is the interval between (and including) the high and low:

  [30, 88] . . . . temperature range

3 0
3 years ago
The probability of an event is 1. What do you know about the event?
Harrizon [31]

Answer:  A probability of 1 means the event is certain to happen.  A probably of zero means the event is certain not to happen.

3 0
3 years ago
A family is planning a three-week vacation for which they will drive across the country. They have a van that gets 12 miles per
svetoff [14.1K]

Answer:

The family will pay 34722 cents more if they take the van

Step-by-step explanation:

Given

Van = 12 miles per gallon

Sedan = 36 miles per gallon

Distance = 2500 miles

Gas = $2.50 per gallon

First, we need to determine the number of gallons that'll be used by both vehicles

This  is done by dividing total distance by number of miles per gallon

Van = \frac{2500}{12} \ gallon

Sedan = \frac{2500}{36}\ gallon

Next, is to multiply this by the cost of gas per gallon;

This gives the total spendable amount on both vehicles

Van = \frac{2500}{12} * \$2.50

Van = \frac{\$6250}{12}

Van = \$520.833

Sedan = \frac{2500}{36}* \$2.50

Sedan = \frac{\$6250}{36}

Sedan = \$173.611

Next is to get the difference between these amounts

Difference = \$520.833 - \$173.611

Difference = \$347.222

Multiply by 100 to convert to cents

Difference = 347.222 * 100 cents

Difference = 34722.2 \ cents

Difference = 34722\ cents (Approximated)

Hence;

<em>The family will pay 34722 cents more if they take the van</em>

8 0
3 years ago
PLS ASAP ANSWER ONE MATH QUESTION CORRECTLY
Shtirlitz [24]
Hey there!
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Now, we multiply that by three to get the total volume of the three cubes, to get 648 cubic units- so A.
Hope this helps!
3 0
3 years ago
What is the solution to the liner equation That -12+3b-1=-5-b
andrew11 [14]
-13+3b = -5-b

4b -13 = -5
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b= 2
4 0
3 years ago
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