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Otrada [13]
2 years ago
8

Cole earns $12.50 per hour and will receive a $0.75 per hour raise every year. Adam earns $10.50 per hour and will receive a $2

per hour raise every other year. The chart shows the expected hourly pay rates for Cole and Adam for the first six years.
Math item stem image



Assuming the pattern continues, which hourly pay rate will each earn in the year when they are making the same amount per hour?
Mathematics
1 answer:
Ugo [173]2 years ago
4 0
The equation for Cole's earnings per hour is
y = 12.5 + 0.75x
for Amad's:
y = 10.50 + 2x/2

When we equate them
12.5 + 0.75x = 10.50 + 2x/2
Solving for x
x = 2
They will have the same earning rate after 2 years
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Here it is given that AB || CD

< EIA = <GJB

Now

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA  ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180° and ∠DLH +  ∠JLD =180° (Linear Pair Theorem)

So

m∠IKL + m∠IKC = 180°       ....(1)

But ∠IKC  ≅ ∠JLD

m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)

So we have

m∠IKL + m∠JLD = 180°

∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)

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2 years ago
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A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of
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So, we're finding ratios first okay, for every 4ft:12in and 6ft:18in so for every one foot there is 3 inches which is your rate of incline 1:3 or every one foot  there are 3 inches of incline hope this helped you have an amazing day

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El caño de una fuente está inclinado 60° sobre la horizontal. Si el agua sale del caño con una velocidad inicial de 10 m/s: a) ¿
jeka94

Answer:

A) Parabola; B) 3.83 m; C) 8.84 m; D) 10 m/s

Step-by-step explanation:

A) Shape of water jet

The water jet has the shape of a parabola.

B) Maximum height

Data:

θ = 60°

u = 10 m/s

a = 9.8 m·s⁻²

Calculations:

1. Calculate the horizontal and vertical components of the velocity

u_{\text{h}} = u \cos \theta = \text{10 m/s} \times \cos 60 ^{\circ} = \text{10 m/s} \times 0.5 = \text{5 m/s}\\u_{\text{v}} = u \sin \theta = \text{10 m/s} \times \sin 60 ^{\circ} = \text{10 m/s} \times 0.866 = \text{8.66 m/s}

2. Maximum height

H = \dfrac{(u_{\text{v}})^{2}}{2a} = \dfrac{8.66^{2}}{2\times 9.8} =\textbf{3.83 m}

C) Range

1. Calculate the time of flight

Use the vertical component of velocity to calculate the time to the maximum height of the stream.

u_{\text{v}} = at\\t = \dfrac{ u_{\text{v}}}{a} = \dfrac{\text{8.66 m$\cdot$s}^{-1}}{\text{9.8 m$\cdot$s}^{-2}}= \text{0.884 s}

It will take the same time to reach the ground.

Thus,

Time of flight = 2t = 2 × 0.884 s  = 1.77 s

2. Calculate the horizontal distance

s = vt = 5 m·s⁻¹ × 1.77 s = 8.84 m  

You should place the drain 8.84 m from the pipe.}

D) Modulus of velocity

The stream of water will hit the drain with the same velocity as when it left the pipe.

Thus, the modulus of the velocity is 10 m/s.

The graph below shows the trajectory of the water stream.

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Answer:

The result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

Step-by-step explanation:

Consider the provided equation.

\left(x+\dfrac{b}{2a}\right)^2=\dfrac{-4ac+b^2}{4a^2}

As the above equation is formed by perfect square trinomial so simply applying the square root property as shown:

\sqrt{(x+\dfrac{b}{2a})^2}=\pm \dfrac{\sqrt{-4ac+b^2}}{\sqrt{4a^2}}\\x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}

Isolate the variable x.

x=-\dfrac{b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}\\x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Hence, the result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

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2 years ago
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Rudiy27

Answer:

Area of the base of the prism = 48cm²

Step-by-step explanation:

A rectangular prism has a rectangular base

Area of a rectangular base, A = length x width

A = 6cm x 8cm = 48cm²

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