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mojhsa [17]
3 years ago
9

Jackie and Rachel both worked during last summer and made $960 each. Rachel worked 16 hours more than Jackie, but Rachel earned

$2 less per hour. How many hours did Jackie work?
Mathematics
1 answer:
Pavel [41]3 years ago
7 0

Answer:

The number of hours Jackie worked  = 80hours

Step-by-step explanation:

Last summer:

Jackie made $960

Rachel made $960

let number of hours Jackie worked = x

Rachel worked 16 hours more than Jackie:

Number of hours Rachel worked = x + 16

if Jackie earned $y  per hour

Rachel earned $2 less per hour = y-2

Jackie: 960 = x × y = xy

Rachel: 960 = (x+16)(y-2)

960 = xy -2x +16y -32

recall xy = 960, insert the value for xy

960 = 960 - 2x +16y -32

- 2x +16y -32 = 0

2x -16y = -32

x-8y = -16

x = 8y-16

recall xy = 960, insert the expression for x

(8y-16)y = 960

8y² -16y = 960

y² -2y - 120 = 0

y²+10y-12y -120 = 0

y(y+10) -12(y+10) = 0

(y-12) = 0 or (y+10) = 0

y = 12 or -10

since y can't be negative, y = 12

x = 8y-16

x = 8(12) -16 = 80

The number of hours Jackie worked = x = 80 hours

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Step-by-step explanation:

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F(x){3/4x+2 If x≠2<br> {-4. If x=2 <br> Whats f(-5), f(2),f(4)
satela [25.4K]

The values of the functions are -1/ 4, 3/ 16 and 3/ 8 respectively.

<h3>What is a function?</h3>

A function is a rule or expression showing the relationship between a dependent and independent variable.

We have the function to be;

f(x) = 3/ 4(x + 2)

Let's find f(-5), substitute the value of x as -5

f(-5) = 3/ 4 ( -5 + 2)

f(-5) = 3/ 4 × -3

f(-5)  = -1/ 4

f(2), substitute the value of x as  2

f(2) = 3/ 4(2 + 2)

f(2) = 3/ 4 (4)

f(2) = 3/ 16

f(4) = 3/ 4 ( 4 + 2)

f(4) = 3/ 4(6)

f(4)  = 3/ 8

Thus, the values of the functions are -1/ 4, 3/ 16 and 3/ 8 respectively.

Learn more about functions here:

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7 0
1 year ago
What is the arc length of the arc sub tended in a circle with radius 6 and an angle of 7 pi/ 8
KengaRu [80]

Answer:

Formula for the Arc length is given by:

\text{Arc length} = 2 \pi r \cdot \frac{\theta}{360^{\circ}}

As per the statement:

radius of circle(r) = 6 units

Angle (\theta) = \frac{7 \pi}{8} radian

Use conversion:

1 rad = \frac{180}{\pi}

\frac{7 \pi}{8} = \frac{180}{\pi} \cdot \frac{7 \pi}{8} = \frac{1260}{8} = 157.5^{\circ}

then;

substitute these given values we have;

Use value of \pi = 3.14

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot \frac{157.5^{\circ}}{360^{\circ}}

or

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot 0.4375

Simplify:

\text{Arc length}=16.485

Therefore, the arc length of the arc substended in a circle with radius 6 units an angle of 7 pi/8 is 16.485 units

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3 years ago
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Answer:

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Step-by-step explanation:

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