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4 years ago

Missing side length

Mathematics

1 answer:

ratelena [41]4 years ago

6 0

Answer:

Since ΔABC ~ ΔQRS, we know that:

=> AB/QR = BC/RS

=> 2/n = 6/15

=> n = (2 × 15)/6 = 5

*You can also use AB/QR = AC/ QS to calculate n

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Solve the equations for all values of x by completing the square x^2+62=-16x

lorasvet [3.4K]

Answer:

$x = \sqrt{2} - 8\\x = -\sqrt{2} - 8$

Step-by-step explanation:

To complete the square, we first have to get our equation into $ax^2 + bx = c$ form.

First we add 16x to both sides:

$x^2 + 16x + 62 = 0$

And now we subtract 62 from both sides.

$x^2 + 16x = -62$

We now have to add $(\frac{b}{2})^2$ to both sides of the equation. b is 16, so this value becomes $(16\div2)^2 = 8^2 = 64$ .

$x^2 + 16x + 64 = -62+64$

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because $8\cdot8=64$ and $8+8=16$ .

$(x+8)^2 = -62 + 64$

We can now take the square root of both sides.

$x+8 = \sqrt{-62+64}\\\\ x+8 = \pm \sqrt{2}$

We can now isolate x on one side by subtracting 8 from both sides.

$x = \pm\sqrt{2} - 8$

So our solutions are

$x = \sqrt{2} - 8\\x = -\sqrt{2} - 8$

Hope this helped!

4 0

3 years ago

In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014,

DochEvi [55]

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

7 0

3 years ago

Read 2 more answers

What is the volume of a right circular cone if the circumference of the base is 125.6 ft and the height is 75 ft.? Use π=3.14 an

Alex_Xolod [135]

Answer:

The volume of a right circular cone is $31400\ \text{feet}^3$ .

Step-by-step explanation:

The circumference of the base of a right circular cone is 125.6 ft.

Height of cone is 75 ft.

Circumference of base is :

$C=2\pi r$ , r is radius

$r=\dfrac{C}{2\pi}\\\\r=\dfrac{125.6}{2\times 3.14}\\\\r=20\ ft$

The volume of a cone is given by :

$V=\dfrac{1}{3}\pi r^2 h\\\\V=\dfrac{1}{3}\times 3.14\times (20)^2\times 75\\\\V=31400\ \text{feet}^3$

So, the volume of a right circular cone is $31400\ \text{feet}^3$ .

5 0

3 years ago

What is the arc measure of D C in degrees

Mashutka [201]

Hello there!

Sense this is a 360 degree angle, it is divide by 2. This would then be considered 180. If you (noticed) on the other side, it shows us that . . .

$AB=19 \\ and \ AB=CD$

We then do (180-19)

$DC= \ \boxed{161}$

4 0

3 years ago

Help me with the question of o.math

Lelu [443]

Answer:

Hello,

Answer 163

Step-by-step explanation:

1,7,16,28,43,..., 10th term=?

$u_1=1,u_2=7,u_2-u_1=7-1=6=2*3\\u_3=16, u_3-u_2=16-7=9=3*3\\u_4=28, u_4-u_3=28-16=12=4*3\\u_5=43, u_5-u_4=43-28=15=5*3\\\\\boxed{ u_1=1, \ u_{n+1}-u_{n}=(n+1)*3}\\\\u_{10}=163\\$

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7 0

3 years ago

Read 2 more answers