All categories

3 years ago

An angle measures 16.4° less than the measure of its supplementary angle. What is the measure of each angle?

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

3 0

Answer:

Step-by-step explanation:

Let one angle = A

Let the other angle = B

A + B = 180

A = B - 16.4 Substitute for A in the top equation

B - 16.4 + B = 180 Combine the left

2B - 16.4 = 180 Add 16.4 to both sides

2B = 180 + 16.4

2B = 196.4 Divide by 2

B = 196.4/2

B = 98.2

A = B - 16.4

A = 98.2 - 16.4

A = 81.8

You might be interested in

Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).

Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0

3 years ago

A forest covers 37 comma 000 acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth

miss Akunina [59]

74 acres of old-growth are there in the forest

Step-by-step explanation:

To answer the question, we need to calculate the 0.2% of 37,000.We can calculate this stating that exists a linear relationship between the percentage and the number of acres. We also need to state that 37,000 acres are the 100% of the acres.

$=\frac{0.2}{100} \times 37000\\ =0.002 \times 37000\\=74$

We find that if 37,000 acres are the 100% of the acres ⇒ The 0.2% of the acres are 74 acres (in which there are old-growth trees).

6 0

3 years ago

Senior classes high school A and high school B planned separate trips to New York City. The senior class at high school A rented

ICE Princess25 [194]

Let van =v and bus=b
V+6B=324
9V+3B=264×2 this will become
18V+6B=528 minus equ 1 from equ 2
-17V=-204 divide both side by -17
V=-204/-17=12
if V is 12 put it in equ 1
12+6B=324,6B=324-12=312 divide both side by 6
B=312/6=52
therefore the van and bus will take 12 and 52 persons respectively

3 0

3 years ago

What is the independent variable. T=2h+5

likoan [24]

Answer:

Step-by-step explanation:

H does not depend on a number.

5 0

3 years ago

Is a ratio a rate always?

Pavlova-9 [17]

No a rate is a special type of ratio

"A ratio is a comparison of two numbers or measurements. The numbers or measurements being compared are called the terms of the ratio. A rate is a special ratio in which the two terms are in different units."

4 0

3 years ago