21/5 is the additive inverse of a)-4.2 b)-5/21 c)-4.5 d)5/21

Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and

motikmotik

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that n ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

YZ = 2n ≥ 2 × 5 = 10

ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

6 0

4 years ago

Help, Help, Please

Lesechka [4]

Answer:

θ = $\frac{\pi }{3}$ (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1

2cosθ - 1 = 0

cosθ = $\frac{1}{2}$ , so

θ = $cos^{-1}$ ( $\frac{1}{2}$ ) = $\frac{\pi }{3}$ ( or 60° )

8 0

3 years ago

Read 2 more answers

Collin worked at the ice cream parlor over the summer. On his last 7 shifts, he scooped:

zlopas [31]

Answer:

add up the numbers and divide by the counting of the numbers. so the answer will be 56/7 equal to 8

6 0

4 years ago

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bott

Andreyy89

Answer:

(15.8495,16.2505)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 16.05 ounces

Standard Deviation, σ = 0.2005 ounces

We are given that the distribution of amount poured into the bottles is a bell shaped distribution that is a normal distribution.

Empirical rule:

It states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ).

It shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Confidence interval:

$\mu \pm 2\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$16.05 \pm 2(\frac{0.2005}{\sqrt{4}} ) = 16.05 \pm 0.2005 = (15.8495,16.2505)$

4 0

3 years ago

WILL MARK BRAINLIEST IF CORRECT!

kotykmax [81]

Answer:

$\lim_{x \to -\infty} f(x)= - \infty \\ \lim_{x \to \infty} f(x)= -\infty$

Step-by-step explanation:

$f(x)=-x^4-x^3+3x^2+1$

The question wants you to determine the end behavior of this polynomial function.

In order to determine the end behavior of polynomial functions, you want to look at the polynomial in its general form. This means that the variables have powers that are in descending order.

Look at the leading term of the polynomial in general form. Here, the function $f(x)=-x^4-x^3+3x^2+1$ is in general form, so we can look at the first term (term with the highest power).

The leading term for this polynomial function is $-x^4$ . The leading term has the highest power; therefore, its behavior will dominate the graph shape.

When graphed, this function will behave similarly to an upside down parabola.

Based on the leading term, we can see that the leading coefficient is -1 and the degree is 4.

Look to see if the degree is even/odd, and if the leading coefficient is negative/positive.

The degree of 4 is even, and the leading coefficient of -1 is negative.

When the degree is even and the LC is negative, the graph of the polynomial function falls to the left and falls to the right.

Therefore, if the end behavior falls to the left and falls to the right, that means that as x approaches negative infinity and positive infinity, the y-values will approach negative infinity and negative infinity on either side of the graph.

The answer is the rightmost option:

$\lim_{x \to -\infty} f(x)= - \infty \\ \lim_{x \to \infty} f(x)= -\infty$

4 0

3 years ago

21/5 is the additive inverse ofa)-4.2b)-5/21c)-4.5d)5/21​

21/5 is the additive inverse ofa)-4.2b)-5/21c)-4.5d)5/21