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2 years ago

In ΔSTU, the measure of ∠U=90°, ST = 9.7 feet, and US = 4 feet. Find the measure of ∠T to the nearest degree.

Mathematics

1 answer:

BaLLatris [955]2 years ago

5 0

Answer:

Around 24 degrees

Step-by-step explanation:

*Make sure calculator is on degree mode*

Try to draw out triangle--it helps

Need to use law of sines... this is where an angle and the side that opposes it are equal to each other. For example, Angle U is equal to 9.7

$\frac{sin\alpha }{4} = \frac{sin90}{9.7}$

Multiply 4 and sin90 and then divide the product by 9.7

Use $sin^{-1}$ on calculator to convert the answer into degrees

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Abbey gets paid a flat rate of $10.00 to mow her neighbor's lawn plus an additional $5 per hour to rake the leaves.

sp2606 [1]

Answer:

Since you didn't provide any choices, a possible equations would be h = (m - 10) / 5

Step-by-step Solution:

Since we know that the flat-rate 10 doesn't have anything to do with the hourly rate, we first subtract that. Then, we divide that number by 5 to get rid of it, so we're only left with h.

This process of removing things from the equation by reversing their methods can be applied all over math and is a strategy vary commonly used.

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2 years ago

The following indicates the number of hours that Johnny spent playing video games the week before each exam in his classes along

dedylja [7]

Answer: idk sorry :(

Step-by-step explanation:

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2 years ago

In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, AE=x2−16 , and CE=6x .

MAXImum [283]

Answer:

<h3>AC=96 units.</h3>

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

$AE=x^2-16.$ , and CE=6x .

<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

$x^2-16=6x.$

Subtracting 6x from both sides, we get

$x^2-16-6x=6x-6x$

$x^2-6x-16=0$

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of $x^2-6x-16=0$ quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0 => x=8

x+2=0 => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

<h3>AC = AE + EC = 48+48 =96 units.</h3>

5 0

2 years ago

Which statements are true about circle Q? Select three options. The ratio of the measure of central angle PQR to the measure of

kkurt [141]

Answer:

<h3>- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. </h3><h3>- The area of the shaded sector depends on the length of the radius. </h3><h3>- The area of the shaded sector depends on the area of the circle</h3>

Step-by-step explanation:

Given central angle PQR = 45°

Total angle in a circle = 360°

Ratio of the measure of central angle PQR to the measure of the entire circle is $\frac{45}{360} = \frac{1}{8}$ . This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.

Area of a sector = $\frac{\theta}{360}*\pi r^{2}$

$\theta$ = central angle (in degree) = 45°

r = radius of the circle = 6

Area of the sector

$= \frac{45}{360}*\pi (6)^{2}\\ = \frac{1}{8}*36 \pi\\ = 4.5\pi units^{2}$

<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>

From the formula, it can be seen that the ratio of the central angle to that of the circle is multiplied by area of the circle, this shows <u>that area of the shaded sector depends on the length of the radius and the area of the circle.</u>

Since Area of the circle = πr²

Area of the circle = 36πunits²

The ratio of the area of the shaded sector to the area of the circle = $\frac{4.5\pi }{36 \pi } = \frac{1}{8}$

For length of an arc

$= \frac{45}{360}*2\pi r\\= \frac{45}{360}*2\pi (6)\\= \frac{45}{360}*12 \pi \\= \frac{12\pi }{8} \\= \frac{3\pi }{2} units$

ratio of the length of the arc to the area of the circle = $\frac{\frac{3\pi}{2} }{36\pi} = \frac{3}{72} =\frac{1}{24}$

It is therefore seen that the ratio of the area of the shaded sector to the area of the circle IS NOT equal to the ratio of the length of the arc to the area of the circle

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2 years ago

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Which pairs of rectangles are similar polygons?<br><br> Select each correct answer.

oee [108]

The corrects answers are B and D for this one.

Since you divide the same side for both the the rectangles on both parts and if the division statements are equaled, then they are similar.

For example;

Answer B.
50 / 10 = 5
and
30 / 6 = 5

Answer D.
7.5 / 2.5 = 3
and
4.5 / 1.5 = 3

Since they both equal the same for both of the rectangles for the answers individually, they are similar polygon rectangles.

Hope this helps!

<em>~ ShadowXReaper069</em><em />

8 0

2 years ago

Read 2 more answers