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3 years ago

If (4x−7)2=ax2+bx+c for all values of x, what is the value of c(b+a)?

Mathematics

1 answer:

ollegr [7]3 years ago

8 0

Answer:

-1960

Step-by-step explanation:

The expression on the left expands to ...

(4x -7)² = (4x)² +2(4x)(-7) +(-7)² = 16x² -56x +49

Matching coefficients, you have ...

a = 16
b = -56
c = 49

Then the expression c(b+a) evaluates to ...

49(-56+16) = 49(-40) = -1960

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3 years ago

Abraham has visited country somebody he has a cold or visiting at least 50 countries he plans to choose a school by visiting fiv

Ipatiy [6.2K]

Question:

Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.

Answer:

$Countries \geq 50 + 5y$

$y \leq 29$

Step-by-step explanation:

Given

$Countries = 50$ ------ at least

$Yearly =5$

Required

Represent as an inequality

"at least" means $\geq$

So the countries he has visited can be represented as thus;

$Countries \geq 50$

1 year = 5 countries

y years would be 5y countries

So, in y years; he'd have visited

$Countries \geq 50 + 5y$

To determine the value of y.

We have that

$Countries = 195$ in the world

Substitute 195 for Countries

$195 \geq 50 + 5y$

Collect Like Terms

$195 - 50 \geq 5y$

$145 \geq 5y$

Divide through by 5

$145/5 \geq y$

$29 \geq y$

Reorder

$y \leq 29$

This means that; he'll visit all countries in at most 29 years' time

3 0

2 years ago

Ella collects 50 bottles to recycle. Of the bottles she collects, 19 are plastic and the rest are glass.

nekit [7.7K]

QUESTION A

The total number of bottles Ella collected is
$50$

The number of bottles that are plastic is

$19$

The percentage of bottles that are plastic is

$= \frac{number \: of \: plastic \: bottles}{total \: number \: of \: bottes} \times 100\%$

$= \frac{19}{50} \times 100\%$

$= 19 \times 2\%$
$= 38\%$

Therefore 38% of the bottles are plastic.

QUESTION B

The total number of bottles that are glass is
$50 - 19 = 31$

The total number of bottles Ella collected is
$50$

The percentage of bottles that is glass is
$= \frac{number \: of \: glass \: bottles}{total \: number \: of \: bottles} \times 100\%$

$= \frac{31}{50} \times 100\%$

$= 31 \times 2\%$
$= 62\%$

Therefore 62% of the bottles are glass

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2 years ago

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