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antiseptic1488 [7]

3 years ago

10

hELP!!! PLEASE?! BRAINLIEST ANSWER INCLUDED!!! A cashier has a total of 98 bills, made up of fives and fifties. The total value

of the money is $2425. How much of each kind does he have?

1 answer:

Yanka [14]3 years ago

8 0

Answer:

84 5$ bills and 42 $10 bills

Step-by-step explanation:

The problem has two variables, let:

F=number of $5 bills

T=number of $10 bills

Translate:

"a total of 126 bills, made up of fives and tens" means

126 = F + T (the number of each)

"total value of the money is $800" means

5F + 10T = 800 [use $10 and $5 times the number of bills]

Now, solve for either T or F in the first equation and put that into the second equation:

T = 126 - F

5F + 10(126-F) = 800 [now, all expressed in terms of F so we can solve for F]

5F + 1260 -10F = 800 [distribute]

-5F = -460 [subtract 1260 from both sides]

F = 92 [divide both sides by -1]

Now, put that value into either of the equations to solve for T (the second equation looks easy):

T = 126 - F

T = 126 - 92

T = 34

Checking (very important):

Is 126 = 92 + 34 ?

126 = 126 ? yes

Is 5(92) + 10(34) = 800 ?

460 + 340 = 800 ?

800 = 800 ? yes

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Verify in the following whether g(x) is a factor of p(x)

notsponge [240]

$\red{\large\underline{\sf{Solution-i}}}$

Given that,

$\rm \longmapsto\: p(x) = {x}^{4} - {x}^{3} - {x}^{2} - x - 2$

and

$\rm \longmapsto\:g(x) = x - 2$

<em>We know, </em>

Factor theorem states that if g(x) = x - a is a factor of polynomial f(x), then remainder f(a) = 0.

So, using Factor theorem, Consider

$\rm \longmapsto\:p(2)$

$\rm \: = \: {2}^{4} - {2}^{3} - {2}^{2} - 2 - 2$

$\rm \: = \: 16 - 8 - 4 - 4$

$\rm \: = \: 16 - (8 + 4 + 4)$

$\rm \: = \: 16 - 16$

$\rm \: = \: 0$

$\rm\implies \:p(2) \: = \: 0$

<u>So, </u>

$\bf\implies \:g(x) \: is \: factor \: of \: p(x)$

$\red{\large\underline{\sf{Solution-ii}}}$

$\rm \longmapsto\: p(x) = 2{x}^{3} + {x}^{2} - 2x + 1$

and

$\rm :\longmapsto\: g(x) = x + 1$

Now, By using Factor Theorem, Consider

$\rm \longmapsto\:p( - 1)$

$\rm \: = \: 2 {( - 1)}^{3} + {( - 1)}^{2} - 2( - 1) + 1$

$\rm \: = \: - 2 + 1 + 2 + 1$

$\rm \: = \: 2$

$\rm\implies \:p( - 1) \: \ne \: 0$

<u>So, </u>

$\bf\implies \:g(x) \: is \: not \: a\: factor \: of \: p(x)$

8 0

3 years ago

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ryzh [129]

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C

Step-by-step explanation:

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x = 199/10 = 19 (round to 20)

x = 20

<A= 20

<B= 80-19= 61

<C=. 59

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saw5 [17]

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3 years ago

The product of nine and a number is added to six the result is 24 what is the number

Andru [333]

Hello!

We can make an equation based on what we know

The product of 9 and a number is

9 * x

Added to six

9 * x + 6

Gives the result of 24

9 * x + 6 = 24

Now you solve it algebraically

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8 0

3 years ago

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Fofino [41]

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So, these two equations equal to the same thing.
Glad I could help and gave a fantastic day!

8 0

3 years ago