Question 8 of 10

Mathematics

2 answers:

Fofino [41]2 years ago

8 0

Answer:

a) x - 3

Step-by-step explanation:

Given:

a) (f)(x) = 3x - 2

b) (g)(x) = 2x + 1

Find (f - g)(x):

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (3x - 2) - (2x + 1) [subtract]

(f - g)(x) = 3x - 2x - 2 - 1 [combine like terms]

(f - g)(x) = x - 3

Learn more about subtracting functions here:

brainly.com/question/27846660

brainly.com/question/16287318

Andrew [12]2 years ago

5 0

Answer:

Step-by-step explanation:

when adding or subtracting (or multiplying or dividing) functions, we do this by applying the same operation to the functional expressions.

(f-g)(x) = (3x - 2) - (2x + 1) = 3x - 2 - 2x - 1 = x - 3

so, A is the correct answer.

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Rama09 [41]

Answer: x=15

Explanation: you can set 2x+100 = 5x+55 because they are corresponding interior angles.

Work:
2x+100 = 5x+55
2x+100-5x = 55
2x-5x = 55-100
-3x = -45
divide by -3 to cancel the negative and get x by itself
x = 15

Hope this helped! :)

5 0

3 years ago

How would I do this? Please explain instead of just giving me the answer.

djverab [1.8K]

According to the Pythagorean theorem, the square of the hypotenuse (the longest side) of a right-angled triangle equals to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, which equals to the distance between the bottom of the ladder and the tree + the distance we want to find (x):
5² + x² = 13²
25 + x² = 169
x² = 144
x = √144 = 12.
The distance between the ground and the top of the ladder is 12 ft.

4 0

3 years ago

What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters