Four friends want to book a three-

We can imagine the parallel line to the left as a shifted version of the one on the right. As we move it further left along the line the in middle (called a transversal), ∠B will slide closer and closer to ∠A. Eventually, the two will totally coincide, showing that ∠B ≅ ∠A. We call ∠A and ∠B corresponding angles, because they can be made to perfectly overlap in that way.

Since corresponding angles are congruent, their measures must be equal, so in this example, we can say that

$\angle A =\angle B$ , and since $\angle A = 7x+40^{\circ}$ and $\angle B=3x+112^{\circ}$ ,

$7x+40^{\circ}=3x+112^{\circ}$

To solve for x, we can subtract 3x and 40° from both sides:

$4x=72^{\circ}$

and divide both sides by 4:

$x=18^{\circ}$

We can now replace x with 18° in our expression for ∠A to find

$\angle A = 7(18^{\circ})+40^{\circ}\\\angle A=126^{\circ}+40^{\circ}\\\angle A=166^{\circ}$

3 0

3 years ago

A skateboarder is practicing in the city park. He is skating up and down the steepest straight-line ramp. If the highest point o

dalvyx [7]

C is the answer to your problem have a good day

3 0

3 years ago

Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8

vredina [299]

Question:

Consider the sequence of numbers: $\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

$f(n + 1) = f(n) + \frac{3}{8} .$

Explanation:

A sequence of numbers are

$\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Let us first change mixed fraction into improper fraction.

$\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}$

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

$\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}$

$\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}$

$\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}$

$\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}$

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding $\frac{3}{8}$ to the previous term.

Hence, the sequence is recursive and can be represented by the function $f(n + 1) = f(n) + \frac{3}{8} .$

3 0

3 years ago