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Natasha2012 [34]
2 years ago
5

Marie will earn $15 per hour at a new job. During training, she will earn $10 per hour. What percent of Marie’s regular hourly r

ate will she earn during training?
Mathematics
1 answer:
Hitman42 [59]2 years ago
4 0

Answer: 66.67%

Step-by-step explanation:

Given: The amount Marie will earn at a new job = $15 per hour

The amount she will earn during the training = $10 per hour

The percent of Marie’s regular hourly rate she will earn during training is given by :-

P=\frac{\text{Rate of amount she earn in training }}{\text{Rate of amount she earn at new job }}\times100\\\\\Rightarrow\ P=\frac{10}{15}\times100\\\\\Rightarrow\ P=66.66666\%\approx66.67\%

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In the diagram, . To prove that △VWZ ~ △YXZ by the SAS similarity theorem, which other sides or angles should be used? WV and XY
My name is Ann [436]

Step-by-step explanation:

To prove that △VWZ ~ △YXZ by SAS theorem, we must prove that two of the sides for each triangle is congruent, and the angle inbetween the sides are congruent. Depending on which side is given to you, choose the one that conforming to it. For example:

Figure 1:

Side HJ is congruent with side ML, Angle J is congruent with angle M, Side IJ is congruent with side KM (SAS)

~

5 0
2 years ago
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A log splitter uses a pump with hydraulic oil to push a piston, attached to which is a chisel. The pump can generate a pressure
faust18 [17]

we are given

The pump can generate a pressure of 2.3x107 pa

so,

p=2.3*10^7

a radius of 0.041 m

so,

r=0.041m

a stroke lasting 29 s, the piston moves 0.57 m

so,

h=0.57m

t=29s

Firstly, we will find area

A=\pi r^2

A=\pi (0.041)^2

A=0.00528

now, we can use power formula

P=\frac{W}{t}

F=pA

W=Fh

so, W=pAh

we can plug it

P=\frac{p*A*h}{t}

now, we can plug values

P=\frac{2.3*10^7*0.00528*0.57}{29}

now, we can simplify it

Power=2386.92414 watt.........Answer

6 0
2 years ago
Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
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2 years ago
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Anit [1.1K]

Answer:

The lengths of the sides are 2.2 ft and 4.5 ft

Step-by-step explanation:

Let

a -----> the length of one side of the mosaic

b ----> the length of the other side of the mosaic

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we know that

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substitute equation B and equation C in equation A and solve for b

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b=\sqrt{5}=2.2\ ft

Find the value of a

a=2b ------> a=2\sqrt{5}=4.5\ ft

therefore

The lengths of the sides are 2.2 ft and 4.5 ft

6 0
2 years ago
If the sin 90º = 1, then which statement is true?
Natali [406]

in a right-triangle, like in the 1st Quadrant, cosine and sine are complements, so then

sin(x) = cos(90° - x)

cos(x) = sin(90° - x)

for this case, sin(<u>90°</u>)  = cos(90° - <u>90°</u>), or just cos(0°) = 1.

6 0
2 years ago
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