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1 year ago

Solve for x* (17x - 8)

Mathematics

1 answer:

djyliett [7]1 year ago

3 0

Answer:x=4

Step-by-step explanation:

This triangle is an equilateral triangle with all angles equal.

Sum of angles in a triangle=180

17x-8+17x-8+17x-8=180

Collect like terms

17x+17x+17x-8-8-8=180

51x-24=180

51x=180+24

51x=204

Divide both sides by 51

51x/51=204/51

x=4

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A submarine is 730 m below sea level. An airplane that is directly over the submarine is 9,144 m above sea level. What is the ve

Rina8888 [55]

Submarine: -730
Airplane: 9,144
|-730-9,144|=|-9,874|=9,874
|d|: absolute value
The vertical distance between the submarine and airplane is 9,874 meters.

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2 years ago

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What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

uysha [10]

Answer:

The perimeter of the trapezoid is $38.25\ units$

Step-by-step explanation:

we know that

The perimeter of the trapezoid is the sum of its four side lengths

In this problem

$P=QR+RS+ST+QT$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$Q(8, 8), R(14, 16), S(20, 16),T(22, 8)$

step 1

Find the distance QR

$Q(8, 8), R(14, 16)$

substitute the values in the formula

$d=\sqrt{(16-8)^{2}+(14-8)^{2}}$

$d=\sqrt{(8)^{2}+(6)^{2}}$

$d=\sqrt{100}$

$QR=10\ units$

step 2

Find the distance RS

$R(14, 16), S(20, 16)$

substitute the values in the formula

$d=\sqrt{(16-16)^{2}+(20-14)^{2}}$

$d=\sqrt{(0)^{2}+(6)^{2}}$

$d=\sqrt{36}$

$RS=6\ units$

step 3

Find the distance ST

$S(20, 16),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-16)^{2}+(22-20)^{2}}$

$d=\sqrt{(-8)^{2}+(2)^{2}}$

$d=\sqrt{68}$

$ST=8.25\ units$

step 4

Find the distance QT

$Q(8, 8),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-8)^{2}+(22-8)^{2}}$

$d=\sqrt{(0)^{2}+(14)^{2}}$

$d=\sqrt{196}$

$QT=14\ units$

step 5

Find the perimeter

$P=10+6+8.25+14=38.25\ units$

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2 years ago

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Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know t

Ber [7]

Answer:

The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

Step-by-step explanation:

The random variable X is defined as the amount of time until the next student will arrive in the library parking lot at the university.

The random variable X follows an Exponential distribution with mean, μ = 4 minutes.

The probability density function of X is:

$f_{X}(x)=\lambda e^{\lambda x};\ x\geq 0, \lambda >0$

The parameter of the exponential distribution is:

$\lambda=\frac{1}{\mu}=\frac{1}{4}=0.25$

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10}{0.25e^{-0.25x}}\, dx$

$=0.25\times \int\limits^{\infty}_{10}{e^{-0.25x}}\, dx\\=0.25\times |\frac{e^{0.25x}}{-0.25}|^{\infty}_{10}\\=(e^{-0.25\times \infty})-(e^{-0.25\times 10})\\=0.0821$

Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

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2 years ago

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777dan777 [17]

Answer with explanation:

Theorem : The diagonal of a parallelogram divides it into two congruent triangles.

Properties of parallelogram

1. Opposite sides are equal and parallel.

2. Diagonal bisect each other.

3. Opposite Angles are equal.

If you will look at the first three options

A: Diagonals of a parallelogram bisect opposite angles.→→False(Alternate angles are equal)

B: Consecutive sides of a parallelogram are congruent.→→→False(Opposite sides are congruent)

C: Consecutive angles of a parallelogram are congruent.→→→False(Opposite angles are congruent)

D: Consecutive angles of a parallelogram are supplementary.→→→→True

For,any parallelogram, having vertices , A, B and C and D

Opposite sides are parallel, so

1.∠A + ∠B=180°

2.∠C + ∠B=180°

3.∠C+ ∠D=180°

4. ∠A + ∠D=180°

Option D

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2 years ago

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adell [148]

Their sum would be of odd number....

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