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2 years ago

Use absolute value notation to represent the distance between x and 8 is no more than 4

1 answer:

3 0

The distance: use absolute value
Between x and 8: x-8

The distance between x and 8: | x-8 |

“is no more than” means it can be that or be less than that, so use ≤

The distance between x and 8 is no more than 4

| x-8 | ≤ 4

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Directions: Find the indicated trigonometric ratio as a fraction in simplest form. 1. Sin L =

Rainbow [258]

Answer:

$\sin L = 0.60$

$tan\ N = 1.33$

$\cos L = 0.80$

$\sin N = 0.80$

Step-by-step explanation:

Given

See attachment

From the attachment, we have:

$MN = 6$

$LN = 10$

First, we need to calculate length LM,

Using Pythagoras theorem:

$LN^2 = MN^2 + LM^2$

$10^2 = 6^2 + LM^2$

$100 = 36 + LM^2$

Collect Like Terms

$LM^2 = 100 - 36$

$LM^2 = 64$

$LM = 8$

Solving (a): $\sin L$

$\sin L = \frac{Opposite}{Hypotenuse}$

$\sin L = \frac{MN}{LN}$

Substitute values for MN and LN

$\sin L = \frac{6}{10}$

$\sin L = 0.60$

Solving (b): $tan\ N$

$tan\ N = \frac{Opposite}{Adjacent}$

$tan\ N = \frac{LM}{MN}$

Substitute values for LM and MN

$tan\ N = \frac{8}{6}$

$tan\ N = 1.33$

Solving (c): $\cos L$

$\cos L = \frac{Adjacent}{Hypotenuse}$

$\cos L = \frac{LM}{LN}$

Substitute values for LN and LM

$\cos L = \frac{8}{10}$

$\cos L = 0.80$

Solving (d): $\sin N$

$\sin N = \frac{Opposite}{Hypotenuse}$

$\sin N = \frac{LM}{LN}$

Substitute values for LM and LN

$\sin N = \frac{8}{10}$

$\sin N = 0.80$

7 0

3 years ago

A box of cereal states that there are 99 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many cal

Otrada [13]

The unit rate for one serving would be 132 calories, and the total calories in 3 cups would be 396 calories.

Step-by-step explanation:

You solve you the unit rate by multiplying 99 calories by 4 then dividing the amount by 3 and get 132 calories. Finally, you multiple by 3 and get 396 caloriesm

6 0

3 years ago

Read 2 more answers

What is the equation of the line passing through ( -5, -3 ) and perpendicular

Artist 52 [7]

Answer:

y = 7/5x + 4

Step-by-step explanation:

use the slope from the equation -5/7 and take the negative reciprocal to get the perpendicular slope = 7/5. Then use the equation y=mx+b. Plug in x and y from the point given and the new slope and solve for b.

(-3) = (7/5)(-5) + b, (-3) = -7 + b, add 7 to both sides. b = 4. Rewrite the equation now to be y = 7/5x + 4

4 0

3 years ago

Mike compared the y-intercept of the graph of the function

aleksklad [387]

Answer:

-4

Step-by-step explanation:

Given function

f(x) = 5x + 12

From the table we get the function g(x), use pairs (1, 10) and (3, 14)

The slope:

m = (14 - 10)/(3 - 1) = 4/2 = 2

The y-intercept:

10 = 2(1) + b
b = 10 - 2
b = 8

The function g(x) is found as:

g(x) = 2x + 8

The y- intercept of f (x) is subtracted from the y-intercept of g (x):

8 - 12 = -4

4 0

2 years ago

Read 2 more answers

Which graph represents f(x)=−2cos(4πx)?

algol [13]

Answer:

the last one (bottom right)

Step-by-step explanation:

4×pi is the same as twice around the whole circle to the beginning. it is the same as 0°, and cos(0) = 1, and then -2×cos(0) = -2

so, we only need to look, where the function reaches -2.

it should be at x = 0, x = 0.5 and x = 1.

3 0

1 year ago