All categories

2 years ago

The drawing shown contains the intersection of two lines.

Mathematics

1 answer:

Phantasy [73]2 years ago

3 0

Answer:

$\Huge \boxed{x=5}$

$\Huge \boxed{121\°}$

Step-by-step explanation:

∠1 and ∠2 are vertical angles.

∠1 = ∠2

Part A:

Create an equation and solve for x.

20x + 21 = 30x - 29

Add 29 and -20x on both sides.

20x + 21 + 29 - 20x = 30x - 29 + 29 - 20x

Simplify the equation.

50 = 10x

Divide both sides by 10.

$\frac{50}{10}$ = $\frac{10x}{10}$

Simplify the equation.

5 = x

Switch sides.

x = 5

Part B:

Let x = 5

20(5) + 21

Distribute.

100 + 21

Add.

= 121

Since both angles are vertical angles, they are equal.

∠1 = 121°

∠2 = 121°

You might be interested in

Skylar Sutherland earns a salary of $80,000 per year. How much is Skylar paid per month? *

Nataliya [291]

Answer:

6,666$

Step-by-step explanation:

Because there are 12 months in a year u just have to divide 80,000 by 12.

Got chu :)

7 0

2 years ago

the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.

laila [671]

The perimeter of a rectangle is length + length + width + width.

We know that the length of a rectangle is 3cm more than its width, which gives us the equation: (l for length and w for width)

l = 3 + w

We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

98 = 2l + 2w (equation for perimeter of a rectangle as noted above)

We can divide both sides of this equation by 2 to get:

49 = l + w

Now we'll stick l = 3 + w into the above equation, which gives us:

49 = 3 + w + w

which simplifies to 49 = 3 + 2w.

Now we'll subtract 3 from both sides:

49 - 3 = 46

3 + 2w - 3 = 2w

which gives us 46 = 2w.

Dividing both sides by 2 gives us 23 = w.

Substituting w = 23 into the equation l = 3 + w gives us:

l = 3 + 23

l = 26cm.

Let's check our answer. 26cm is 3cm more than 23cm. 26cm + 26cm + 23cm + 23cm gives us 98cm. The length is 26cm and the width is 23cm.

7 0

2 years ago

What kind of number does distance always represent?

Sliva [168]

Answer:

Step-by-step explanation:There are other kinds of numbers that can be graphed on the number line, too. ... which are natural numbers and which are whole numbers is to think of a “hole,” which can be represented by 0. ... Notice that distance is always positive or 0.

8 0

3 years ago

What term is used to describe the graphical representation of the change in microbial population over time?

ruslelena [56]

Answer:

The term exponential is often used.

Step-by-step explanation:

The term exponential is used to represent changes in population over time. The idea of (positive) exponential is that the higher the number, the higher the growth. You can relate this with a population, because the higher the population, the more opportunities for it to multiply, thus, the higher it grows.

Usually the way to meassure the population of an species after certain number of years x, you use an exponential function of the form

$f(x) = K_0 * a^x$

For certain constants K₀ and a. K₀ is the initial population at the start of the experiment and a number of exponential growth. Essentially, the population of the species is multiplied by a during each year.

For example, if K₀ = 1000 and a = 2, then the population at the start of the experiment is 1000. After the first year is 1000*2 = 2000 and after the second year it is 2000*2 = 4000. Note that, not only the population grow during the years, but also the amount that the population increases also grow: in the first year it grows 1000, and between the first and second year it grows 2000.

7 0

2 years ago

An organic farm has been growing an heirloom variety of summer squash. A sample of the weights of 40 summer squash revealed that

natta225 [31]

Answer:

b. 0.0228

Step-by-step explanation:

We are given that

n=40

Mean, $\mu=402.7 g$