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navik [9.2K]
3 years ago
15

at the cafe, Rebecca can choose to earn $10 per hour plus a $60 starting bonus or earn $12 per hour with no starting bonus. afte

r how many hours of work will she earn the same amount of both payment options? write an equation to solve the problem. solve.
Mathematics
1 answer:
qwelly [4]3 years ago
8 0
Hi there! The answer is 30 hours.

Let the number of worked hours be represented by X.

The total earn of option 1, would then be 10X + 60
The total earn of option 2, would then be 12X

We end up with the following equation:
10x + 60 = 12x
Subtract 10X from both sides.

60 = 2x
Divide both sides by 2.

x = 30
Therefore, after 30 hours of work Rebecca will earn the same amount of money.
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The length of a rectangle is 5 m greater than the width. The perimeter is 150 m. find the width
Elza [17]

P = perimeter

Perimeter of a rectangle = l + l + w + w

or  P = 2l + 2w

You know:

P = 150 m

l = w + 5     [length is 5 m greater than the width]

P = 2l + 2w        Plug in what you know

150 = 2(w + 5) + 2w     Simplify, distribute/multiply 2 into (w + 5)

150 = 2w + 10 + 2w

150 = 4w + 10     Subtract 10 to both sides of the equation

140 = 4w       Divide 4 on both sides

35 = w

PROOF               l = w + 5 --->  l = 40

P = 2l + 2w

150 = 2(40) + 2(35)

150 = 80 + 70

150 = 150

4 0
3 years ago
Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their an
densk [106]

Answer:

see the explanation

Step-by-step explanation:

we have

<em>Felicia</em>

-5(3x+2)+10x

Apply distributive property

-5(3x)-5(2)+10x

-15x-10+10x

Combine like terms

-5x-10

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant  term in Gregory's expression

so

-12-4x+ax+b

equate Gregory's expression to Felicia's expression

-12-4x+ax+b=-5x-10

so

-12+b=-10 ----->b=2

-4x+ax=-5x ------> a=-1

so

Gregory's expression is

-12-4x+2-x

therefore

The missing terms are 2 and -x

7 0
3 years ago
To calculate the cost of painting his silo, a farmer must find its height. The farmer uses a cardboard square to line up the top
tankabanditka [31]

Answer:

Height of the silo = 18 feet.

Step-by-step explanation:

From the figure attached BC is the length of the silo and the height of the farmer is 5 ft.

Farmer is standing at 8 ft distance from the silo.

From triangle AEC,

tan(∠CAE) = \frac{CE}{AE}

                 = \frac{5}{8}

m(∠CAE) = tan^{-1}(\frac{5}{8})

               = 32°

m∠BAE = 90° - 32° = 58°

From the triangle ABE,

tan58° = \frac{BE}{AE}

BE = 8tan58°

BE = 12.8 ft

Total height of the silo = BE + EC

                                         = 12.8 + 5

                                         = 17.8

                                         ≈ 18 ft          

Therefore, total height of the silo is 18 ft.

3 0
2 years ago
Find the slope of a line which goes through the points (2,5) and (−4,3)
natka813 [3]

Answer:

slope (m) = 0.75

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

=

1

3

= 0.33333333333333

θ =

arctan( ΔY ) + 180°

ΔX

= 198.43494882292°

ΔX = -4 – 2 = -6

ΔY = 3 – 5 = -2

Distance (d) = √ΔX2 + ΔY2 = √40 = 6.3245553203368

Equation of the line:

y = 0.33333333333333x + 4.3333333333333

or

y =  

1 x

3

+  13

3

When x=0, y = 4.3333333333333

When y=0, x = -13

please mark brainliest

3 0
2 years ago
Read 2 more answers
Anthropologists can estimate the height of a woman by measuring the length of her radius bone (from the wrist to the elbow). The
zloy xaker [14]
B = 0.26 h - 18.85,
where b is the length of the radius bone and h is the height.
To find the equation for height of a woman, you can solve the equation for h.
0.26 h = b + 18.85
h = ( b + 18.85 ) / 0.26
h = ( 100 b + 1,885 ) / 26
Then you can plug in the length of the radius bone in this equation.
4 0
2 years ago
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