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2 years ago

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Olga has $40 in her wallet. She has one more $5 bill than $10 bills, and two more $1 bills than $5 bills. If Olga has only three

types of bills, how many bills of each denomination does she have?

1 answer:

Scrat [10]2 years ago

5 0

Answer:

Number of $10 bills = 2

Number of $5 bills = 3

Number of $1 bills = 5

Step-by-step explanation:

Given:

Total amount = $40

Number of $10 bills = x

Number of $5 bills = x + 1

Number of $1 bills = x + 1 + 2 = x + 3

Find:

Number of each bills

Computation:

10(x) + 5(x+1) + 1(x+3) = 40

10x + 5x + 5 + x + 3 = 40

16x = 32

x = 2

Number of $10 bills = x = 2

Number of $5 bills = x + 1 = 3

Number of $1 bills = x + 3 = 5

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The length of a rectangle is 6 cm longer than its width.

oksian1 [2.3K]

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12+2w+2w=40
12+4w=40
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w=7
Now we know that the width is 7; abd the length is 7+6 which is 13.
To find the area we multiply 13x7
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2 years ago

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

2 years ago

Find the missing side or angle.

bonufazy [111]

Answer:

c = 6.1

Step-by-step explanation:

Given that: B = 18° , C = 152°, and b = 4.

The missing side, c, can be determined by applying the sine rule which states that:

$\frac{b}{Sin B}$ = $\frac{c}{Sin C}$

$\frac{4}{Sin 18^{o} }$ = $\frac{c}{Sin 152^{o} }$

c = $\frac{4* Sin 152^{o} }{Sin 18^{o} }$

= $\frac{1.8779}{0.3090}$

= 6.0773

c = 6.1

Therefore, the value of the missing side, c, is 6.1

3 0

2 years ago

Using the order of operations rule, solve the following: 12 ÷ 2 + 4 – 2 × 3 = ? A. 36 B. 0 C. 4 D. 24 Mark for review

AlexFokin [52]

<h2>Answer:</h2>

<u>The answer is </u><u>(C) 4</u>

<h2>Step-by-step explanation:</h2>

According to the rule of BODMAS

We will first do division then Multiplication then addition and in the last we do subtraction

So

12 ÷ 2 + 4 – 2 × 3 will be done as

= (12 ÷ 2) + 4( – 2 × 3)

= 6+4-6

= 4

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Pie

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