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2 years ago

Mathematics challenge

Mathematics

1 answer:

kari74 [83]2 years ago

6 0

Get the equation of the line containing PQ using the point-slope formula:

y - (-2) = 3/2 (x - (-6))

Solve for y to get it in slope-intercept form:

y = 3/2 x + 7

so the y-intercept is (0, 7).

The line containing QR is then

y - 7 = -3/4 (x - 0)

y = -3/4 x + 7

The point R is on the x-axis, so its y-coordinate is 0. Plug in y = 0 and solve for x to get the other coordinate:

0 = -3/4 x + 7

3/4 x = 7

x = 4/3×7 = 28/3

So the point R has coordinates (28/3, 0).

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2 years ago

Read 2 more answers

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the me

mel-nik [20]

Answer:

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

The complete question is

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

$x+y=180^o$ ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

$x=2y$ ----> equation B

substitute equation B in equation A

$2y+y=180$

$y=60^o$

$x=120^o$

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

$b=12/2=6\ units$

The perimeter of the hexagon is given by the formula

$P=6b$

substitute

$P=6(6)=36\ units$

3 0

3 years ago

Find sin D sin E cos D and cos E

Andrew [12]

9514 1404 393

Answer:

sin(D) = cos(E) = (√3)/2

cos(D) = sin(E) = 1/2

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and right triangle sides.

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

For this diagram, this means ...

sin(D) = cos(E) = (13√3)/26 = (√3)/2

cos(D) = sin(E) = 13/26 = 1/2

5 0

2 years ago

QUESTION 2 21 Write THREE equivalent actions for the following traction 25/50

MrMuchimi

The three equivalent fractions for $\frac{25}{50}$ are, $\frac{1}{2},\frac{5}{10},$ and $\frac{50}{100}$ .

<h3>What are equivalent fractions</h3>

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, $\frac{2}{4}$ and $\frac{3}6}$ are equivalent fractions, because they both are equal to the $\frac{1}{2}$ . A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.