Three students were given the expression shown to simplify.

Given: m arc IV =140°, m arc VK =30°, m∠ISV=135° Find: m∠VPL

Blizzard [7]

Answer:

$m$

Step-by-step explanation:

step 1

Find the measure of arc PK

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

Let

x------> the measure of arc IV

y ------> the measure of arc PK

$m$

substitute the values and solve for y

$135\°=\frac{1}{2}(140\°+y)$

$270\°=(140\°+y)$

$y=270\°-140\°=130\°$

The measure of arc PK is $130\°$

step 2

Find the measure of angle VPL

we know that

The inscribed angle measures half that of the arc comprising

Let

z------> the measure of arc VK

y ------> the measure of arc PK

$m$

substitute the values

$m$

5 0

3 years ago

Ari bought a car with a loan. She owes $3000 in interest after 6 years. The rate was 3.75%. How much money did she borrow?

Grace [21]

Answer:

she borrowed $800

Step-by-step explanation:

$800 x 3.75% =$3,000

6 0

3 years ago

What is the shape of the cross section taken parallel to the base of a square pyramid

horsena [70]

Answer:

A square

Step-by-step explanation:

A parallel cross section will be the same shape of the base. Since it's a square base, all parallel cross sections will also be parallel. Think of it as a different floor of a pyramid shaped building.

4 0

3 years ago

Read 2 more answers

Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.

Mariulka [41]

Answer:

$2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))$

$2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)$

Step-by-step explanation:

The original expression given in the text is

$2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)$ (1)

And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:

$\frac{3}{2}x+14-\frac{3}{2}x+15$ (2)

Let's verify each of the other expressions separately. For the first one:

$2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))$

We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get

$2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)$

Which is equivalent to (1).

For the 2nd one:

$2(\frac{3}{4}x)+2(7)+3(\frac{1}{2}x)+3(-5)$

This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.

If we write it explicitely in fact, we get

$\frac{3}{2}x+14+\frac{3}{2}x-15$