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3 years ago

X + y = 21 3y + x = 19 Which value of x is part of a solution to this system of equations?

Mathematics

1 answer:

Yanka [14]3 years ago

3 0

We have that
<span>x + y = 21
3y + x = 19

using a graph tool
see the attached figure

the solution is the point (22,-1)

the answer is
the value of x is 22
</span><span>
</span>

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A central angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your

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Answer:

$\theta=71.6\°$

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

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we have

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substitute the values

$C=2\pi (4)=8 \pi\ m$

step 2

Remember that

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3 years ago

Velida took out a 5/1 variable-rate mortgage for $150,000. The interest rate

Afina-wow [57]

Answer:

Step-by-step explanation:

The amortization period in months is:

30 years * 12 = 360 months

The monthly interest rate would be 5.25%/12 = 0.004375

The payment for monthly mortgage formula would be:

$E=\frac{C*r}{1-(1+r)^{-n}}$

Where

E is the monthly mortgage payment

C is the cost of mortgage, cost is $150,000

r is the monthly rate of interest, which is 0.004375

n is the period, in months, which is 360

Substituting, we get our answer:

$E=\frac{C*r}{1-(1+r)^{-n}}\\E=\frac{150,000*0.004375}{1-(1+0.004375)^{-360}}\\E=\frac{656.25}{1-(1.004375)^{-360}}\\E=\frac{656.25}{0.7923}\\E=828.31$

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3 years ago

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lesantik [10]

For this case we use the following formula
Area of Sector = Area * radians of sector / 2 * pi radians
Where,
Area: it is the area of the complete circle.
We have then:
Area = pi * r ^ 2
Area = pi * (6) ^ 2
Area = 36pi
Substituting values:
5pi = 36pi * radians of sector / 2 * pi
Clearing:
radians of sector = ((5pi) * (2pi)) / (36pi)
radians of sector = (10pi ^ 2) / (36pi)
radians of sector = (10pi) / (36)
radians of sector = (10/36) pi
radians of sector = (5/18) pi
in degrees:
(5/18) pi * (180 / pi) = 50 degrees
Answer:
The measure of the central angle is:
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