Which theorem would be used to write 15x + 12 + 117 = 180 in the diagram below?
a. Alternate Interior Angles Theorem
b. Corresponding Angles Theorem
c. Consecutive Exterior Angles Theorem
d. Vertical Angles Theorem

The answer for the following question is 12i.

Answer:

t + u = 10 + 2i

Step-by-step explanation:

t + u

= 4 + 6 + 2i ← collect like terms

= 10 + 2i

Answer:82

Step-by-step explanation:

Answer:

∠ 7 = 82°

Step-by-step explanation:

∠ 2 and ∠ 7 are Alternate exterior angles and are congruent, then

∠ 7 = ∠ 2 = 82°

Answer:

The length of the missing side is 18yd

Step-by-step explanation:

Sq30 - Sq 24 = Sq (x)

Answer:

The true statements are;

1) The center of the ellipse is at (-2, -5)

3) The covertices are at (-2, -4) and (-2, -6)

4) The distance between the center and each focus is 2·√6 units

Step-by-step explanation:

The given graph of the ellipse gives;

1) The location of the center of the ellipse = (-2, -5)

2) The location of the vertices of the ellipse = (-7, -5) and (3, -5)

The distance between the center (-2, -5) and each vertex, d, is given as follows;

d = -2 - (-7) = 5 and d = 3 - (-2) = 5

Therefore, the distance between the center (-2, -5) and each vertex is 5 units

3) The location of the covertices, given in the diagram are (-2, -4), and (-2, -6)

4) The coordinates of the focus of an ellipse = h - c, k

c = √(a² + b²)

Where, for the given ellipse, h = -2, k = -5, c = √(5² - 1²) = √(24) = 2·√6

∴ The location of the focus of the ellipse = (-2 - 2·√6, -5)

The distance between the center and each focus, d = -2 - (-2 - 2·√6) = 2·√6

5) The x-coordinate of the directrices of the ellipse = ± a/e

Where; a = 5

b² = a²·(1 - e²)

∴ e² = 1 - b²/a² = 1 - 1/25 = 24/25

e = 2·√6/5

The directrices = -2 ± 5/(2·√6/5) ≈ -2 ± 5.1

The distance between the center and the directrices ≈ 5.1 units

Therefore, the directrices are vertical lines approximately 5.1 units from the center

Answer:

45 Tokens

Step-by-step explanation:

3:5:7

Anya = 3

Daniel = 5

Victoria = 7

Daniel + Victoria = 36

5 + 7 = 36

12 = 36

1 = 3

(1 ratio is 3 tokens)

(3 + 5 + 7) × 3 = 45

Answer:

Step-by-step explanation:

I think its A

Answer:

0.9999

Step-by-step explanation:

One way to calculate the probability that at least one of them need repairs is that we can calculate the opposite (none need repairs) and subtract that from 1 (100%).

The probability that a car does not need repairs is 0.2. To find the probability that six cars all fulfill this 0.2 probability, we can get [tex]0.2^{6} =0.000064[/tex] . This is the probability that none require repairs. The opposite of this is that at least one needs repairs, so 1-0.000064 - 0.999936. Rounded to 4 decimal places, the probability is 0.9999

Answer:

5940 rupees

Step-by-step explanation:

99 multiplied by 29×5 is 5940

Answer:

[tex]\text{(b) }[/tex] ₹[tex]5,940[/tex]

Step-by-step explanation:

Each pair of scissors on the chart represents 5 haircuts, as indicated by the key. There are 2 scissors on Saturday and 10 scissors on Sunday, hence a total of 12 scissors over the weekend. Therefore, there were [tex]12\cdot 5=60[/tex] haircuts over the weekend.

Since the salon charges 99 rupees per cut, they made a total of [tex]99\cdot 60=\boxed{5,940}[/tex] rupees over the weekend.

Answer:

20 girls

Step-by-step explanation:

boys : girls  : total

3           5        3+5 = 8

There are 32 students

32/8 = 4

Multiply each term by 4

boys : girls  : total

3*4       5*4     8*4

12        20         32

There are 20 girls

Answer: 20 girls

Step-by-step explanation:

So boys to girls is 3 to 5

It asks for girls in class

Suppose there were 8 people in class, 5/8 of the people would be girls

It states that 32 people are in the class, so do 32 x 5/8 to get 20 girls

Answer:

101°

Step-by-step explanation:

Using translation concepts, it is found that the domain of g(x) = f(x) - 12 is the same domain of f(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) - 12, that is, g(x) is a shift down of 12 units of f(x).

The domain of a function is the set that contains all possible input values for the function. A shift down does not add any restriction to the function, hence the domain of f(x) and g(x) are the same.

More can be learned about translation concepts at https://brainly.com/question/4521517

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Answer : B

Step-by-step explanation:

Ape

The statement which is true is  KM = 2 .JM, the correct option is C.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

AJKL is an equilateral triangle

Now,

Using these properties, we can eliminate some of the options.

Option A is false because JK and KM are not equal. JK is half of JL, which is one side of the equilateral triangle AJKL, while KM is a perpendicular bisector of JL.

Option B is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 90 degrees.

Option D is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 45 degrees.

Option C must be true because KM bisects JL into two equal parts JM and ML. Since JL is one side of the equilateral triangle AJKL, we have JL = AK = AL. Therefore, JM = ML = JL/2 = AK/2 = AL/2. By Pythagoras’ theorem, we have:

KM^2 = AK^2 - AM^2

KM^2 = (AK/2)^2 - (AL/4)^2

KM^2 = (AK/4)^2 + (AL/4)^2

KM^2 = ((AK + AL)/4)^2

Since AK + AL = 2 * JL,

KM^2 = (JL/4)^2 * 4

KM^2 = (JL/4)^2 * 4

KM = JL/4 * 2

KM = JL/2

Therefore, the answer of the triangle will be KM = 2 * JM.

Learn more about a right triangle;

https://brainly.com/question/7116550

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Answer:

your answer would be B. -5 +3i✓3

Answer:

1

Step-by-step explanation:

An equilateral triangle is a triangle with all three sides of equal length, so there's only one option, a triangle with all three sides 7 centimeters.

Answer:

b = 8 in

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here A = 12 and h = 3 , then

[tex]\frac{1}{2}[/tex] b × 3 = 12 , that is

1.5b = 12 ( divide both sides by 1.5 )

b = 8

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the triangles CAP and HIT are not given. The general explanation to solve sides of similar triangles is as follows;

[tex]\triangle CAP \sim \triangle HIT[/tex] implies that the following sides are similar:

[tex]CA \to HI[/tex]

[tex]AP \to IT[/tex]

[tex]PC \to TH[/tex]

Take for instance:

[tex]CA = y[/tex]     [tex]HI = b[/tex]

[tex]AP = 20[/tex]    [tex]IT = 38[/tex]

Then the solution is:

[tex]CA : HI = AP : IT[/tex]

Substitute values for CA, HI, AP and IT

[tex]y : b= 20 : 38[/tex]

Express as fraction

[tex]\frac{y }{ b}= \frac{20 }{ 38}[/tex]

Multiply both sides by b

[tex]y= \frac{20 }{ 38}*b[/tex]

Substitute 19 for b

[tex]y= \frac{20 }{ 38}*19[/tex]

[tex]y= \frac{20 }{ 2}[/tex]

[tex]y=10[/tex]

Answer:

49

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Linear are the one with straight line

Answer:

16days

Step-by-step explanation:

1 man =4days

4men=4men/1man×4days

=4×4days

=16days

Answer:

1

Step-by-step explanation:

averaging

Given:

The inequalities are:

[tex]2x-3<7[/tex]

[tex]2x+1>-3x-4[/tex]

To find:

The range of values of [tex]x[/tex] for the given inequalities.

Solution:

We have,

[tex]2x-3<7[/tex]

Adding 3 on both sides, we get

[tex]2x-3+3<7+3[/tex]

[tex]2x<10[/tex]

Divide both sides by 2.

[tex]\dfrac{2x}{2}<\dfrac{10}{2}[/tex]

[tex]x<5[/tex]                      ...(i)

The second inequality is:

[tex]2x+1>-3x-4[/tex]

Subtracting 1 from both sides, we get

[tex]2x+1-1>-3x-4-1[/tex]

[tex]2x>-3x-5[/tex]

Adding [tex]3x[/tex] on both sides, we get

[tex]2x+3x>-3x-5+3x[/tex]

[tex]5x>-5[/tex]

Divide both sides by 5.

[tex]\dfrac{5x}{5}>\dfrac{-5}{5}[/tex]

[tex]x>-1[/tex]            ...(ii)

Using (i) and (ii), we get

[tex]-1<x<5[/tex]

Therefore, the required range is [tex]-1<x<5[/tex].

Answer:

Alice: 82, 84, 86

Pat: 103, 105, 107

Step-by-step explanation:

Alice:

x + (x+2) + (x+4) = 252

3x + 6 = 252

3x = 246

x = 82 so Alice's last term is 82+4 = 86

Pat:

y + (y+2) + (y+4) = Pat's Total

Pat's last term is (y+4) so

Alice's last term + 25 = Pat's last trem

86 + 25 = 111 = y+4

y = 107

Answer:

x = 308 feet

Step-by-step explanation:

tan = opp/adj

tan72 = x/100

multiply both sides by 100

100 * tan72 = x

Use calculator

x = 307.76835371752534

Rounded

x = 308 feet

Answer:

Angle EBF is the alternate interior angle of BEA.

Step-by-step explanation:

We are taking AE parallel to BF and EB as the transversal.

Hope it helps you.^_^

Answer:

3. first make Y the subject, then x^2 will become negative which will make the the parabola open up