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3 years ago

Find the values of p and q such that 4x^2+12x=4(x+p)^2-q

Mathematics

1 answer:

-Dominant- [34]3 years ago

7 0

Answer:

p = 1.5 and q = 9

Step-by-step explanation:

Expand the right side then compare the coefficients of like terms on both sides, that is

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

= 4(x² + 2px + p²) - q ← distribute parenthesis

= 4x² + 8px + 4p² - q

Comparing coefficients of like terms on both sides

8p = 12 ( coefficients of x- terms ) ← divide both sides by 8

p = 1.5

4p² - q = 0 ( constant terms ), that is

4(1.5)² - q = 0

9 - q = 0 ( subtract 9 from both sides )

- q = - 9 ( multiply both sides by - 1 )

q = 9

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Step-by-step explanation:

Let's say there are 17 girls and 8 boys. So there is 25 people in total.

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3 years ago

What is the value of x in the equation (StartFraction one-half EndFractionx + 12) = StartFraction one-half EndFraction(StartFrac

anastassius [24]

Answer:

$x =-24$

Step-by-step explanation:

Given

$(\frac{2}{3})(\frac{1}{2}x + 12) = (\frac{1}{2})(\frac{1}{3}x + 14) - 3$

Required

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Open all brackets

$\frac{2}{3}*\frac{1}{2}x + \frac{2}{3}*12 = \frac{1}{2}*\frac{1}{3}x + \frac{1}{2}*14 - 3$

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$\frac{1}{3}x + \frac{24}{3}= \frac{1}{6}x + \frac{14}{2} - 3$

$\frac{1}{3}x +8= \frac{1}{6}x + 7 - 3$

Collect like terms

$\frac{1}{3}x - \frac{1}{6}x =7 - 3 -8$

$\frac{1}{3}x - \frac{1}{6}x =-4$

Solve fraction

$\frac{2-1}{6}x =-4$

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3 years ago

NEEDED NOW

stealth61 [152]

Answer:

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Step-by-step explanation:

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8 0

3 years ago

Read 2 more answers

Does anyone know? Can anyone help me throughout these type of questions?

ozzi

Your answer would be D you would add up all the days together then just put the clear days together to get 17/30 that then reduces to .57

4 0

3 years ago

1 2 3 4 5 6 7 8 9 10 11 12 13

Rina8888 [55]

Answer:

The mean will increase more than the median, but both will increase.

[third option listed]

Step-by-step explanation:

the median of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

the mean of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

[91 ÷ 13 = 7]

because our number is greater than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by more than the median [as to be expected]

you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]

hope this helps!! :)

3 0

2 years ago