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1 year ago

9

How do you evaluate 1.5x + 120 ≥ 270

1 answer:

Y_Kistochka [10]1 year ago

5 0

1.5x + 120 ≥ 270

1.5x ≥ 150

x ≥ 100

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A triangle with exterior angles is shown. A triangle sits on a line and forms 2 exterior angles on the left and right of the tri

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Answer:

Option 3.

Step-by-step explanation:

It is given that a triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2h) degrees.

The top interior angle of the triangle is 40 degrees.

$\angle BAC=40$

From the given figure it is clear that

$\angle ABC+2h=180$ (Supplementary angle)

$\angle ABC=180-2h$

$\angle ACB+2h=180$ (Supplementary angle)

$\angle ACB=180-2h$

According to the angle sum property of triangle, the sum of all interior angles of a triangle is 180 degree.

$\angle ABC+\angle ACB+\angle BAC=180$

$(180-2h)+(180-2h)+40=180$

Combine like terms.

$(180+180+40)+(-2h-2h)=180$

$400-4h=180$

$-4h=180-400$

$-4h=-220$

Divide both sides by -4.

$h=\frac{-220}{-4}$

$h=55$

The value of h is 55.

Therefore, the correct option is 3.

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"A consultant compiled the following data set that shows" the number of visits made to the National Museum of American History f

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Step-by-step explanation:

The best option is for the consultant to remove these data points because they are outliers. Unusual data points which are located far from rest of the data points are known as outliers.

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A company’s equipment manager buys $7,000 worth of equipment. This equipment depreciates 19% each year. The manager can replace

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Graph the equation 7000(1-0.19)^x and then the inequality y<500, the point of intersection should be 12.524, so the answer will be rounded up to 13 i think

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Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly

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Answer:

The balance be after he has made exactly half of his monthly payments is $56881.4.

Step-by-step explanation:

Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.

To find : What will his balance be after he has made exactly half of his monthly payments?

Solution :

Formula of monthly payment ,

$M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $40,000

Rate r= 4% compounded monthly

$i=\frac{4}{100}=0.04$

Time = 10 years

$n=10\times12=120$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.04)^{-120}}{0.04}$

$D=\frac{1-(1.04)^{-120}}{0.04}$

$D=\frac{1-0.00903}{0.04}$

$D=\frac{0.9909}{0.04}$

$D=24.7725$

$M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{40000}{24.7725}$

$M=1614.69$

Half of the monthly payment is $807.345

Payment for 10 years is $807.345\times 120=96881.4$

The balance is $96881.4-$40000=$56881.4

Therefore, The balance be after he has made exactly half of his monthly payments is $56881.4.

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15u + 11u - 9d - 19d = -2d
It went up 26, down 28, a net change of down 2.

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