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makvit [3.9K]
2 years ago
3

Which of the following equations is equivalent to 4[x + 2(3x – 7)] = 22x – 65?

Mathematics
2 answers:
fgiga [73]2 years ago
5 0
4[x + 2(3x - 7)] = 22x - 65

4[x + 6x - 14] = 22x - 65

4x + 24x - 56 = 22x - 65

28x - 56 = 22x - 65

umka2103 [35]2 years ago
4 0

Answer: 28x-56= 22x - 65

Step-by-step explanation:

The given expression: 4[x + 2(3x - 7)] = 22x - 65

Consider L.H.S. 4[x + 2(3x -7)]

Solving the bracket present inside by using distributive property, we get

4[x + 6x -14]=4[7x-14]

Now, Multiplying 4 inside the bracket by using distributive property:-

28x-56

Hence, the given function is equivalent to 28x-56= 22x -65

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A bacteria culture begins with 13 bacteria which triple in amount at the end of every hour. How many bacteria are grown during t
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The end of first hour = 13*3 = 39

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The end of third hour = 117*3 = 351

The end of fourth hour = 351*3 = 1,053

The end of fourth hour = 1053*3 = 3,159

The end of fifth hour = 3159*3 = 9,477

The end of sixth hour = 9477*3 = 28,431

The end of seventh hour = 28341*3 = 85,293

The end of eighth hour = 85293*3 = 255,879

The end of ninth hour = 255879*3 = 767,637

The end of tenth hour = 767637*3 = 2,302,911

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

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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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