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2 years ago

HELP!!! 31) Find the measure of line segment DF. A) 12 B) 13 C) 14 D) 15

Mathematics

1 answer:

oksian1 [2.3K]2 years ago

6 0

Step-by-step explanation:

for the relationship of lengths of internal chords the product of both segments of a chord is equal for all intersecting chords.

in our case

(x+8)×8 = 7×16 = 112

8x + 64 = 112

8x = 48

x = 6

so, D-F = x + 8 = 6 + 8 = 14

so, C is correct

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PLEASE HELP IM STUCK PLS

QveST [7]

Answer:

<u>The slope is -3.</u>

Step-by-step explanation:

The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

3 0

2 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Why can you use Linear Pairs and Vertical Angles to prove lines are parallel?

natta225 [31]

Answer:

The reason why linear pairs and vertical angles are used to prove lines are parallel is because they area transversal drawn through the parallel lines will form angles on each of the two parallel lines including;

1) Supplementary linear pairs and

2) Vertical angles

3) Alternate angles

Given that either;

a) The corresponding angles that form the linear pairs are congruent

b) The corresponding vertically opposite angles are congruent

c) The corresponding alternate angles are congruent, we have;

The two lines are said to be parallel.

Step-by-step explanation:

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3 years ago

Monique made several batches of soup for a potluck supper. Each batch required 3/4 of a pound of potatoes, and she used a total

Rina8888 [55]

Answer:

B and E

Step-by-step explanation:

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3 years ago

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I don’t know how to do these I need help

Citrus2011 [14]

k = 15 is the answer!!!!!!

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3 years ago