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Novay_Z [31]
3 years ago
15

an angle whose measure is –102° is in standard position. in which quadrant does the terminal side of the angle fall? quadrant i

quadrant ii quadrant iii quadrant iv

Mathematics
2 answers:
swat323 years ago
5 0

Answer: Quadrant iii.


Step-by-step explanation:  Given, the measurement of the angle in standard position is -102°. When we are considering negative angles, we will in the clockwise direction. Angles with measurement 0° to -90° will fall in the quadrant iv. Angles measuring -90° to -180° will fall in the quadrant iii. Since -102° lies between -90° and -180°, so, it will be lying in quadrant iii. Please see the attached figure.

Thus, the correct answer is quadrant iii.


DENIUS [597]3 years ago
3 0

it will be the third quadrent

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The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent
Rzqust [24]

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.

<h3>What is a quadratic equation?</h3>

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given expression is 8x² − 144x + 864

Let y = 8x² − 144x + 864

also,  y - 864 = 8x² - 144x

by Extracting common factor 8 on the right side

y - 864 = 8(x² - 18x)

Add (18/2)² on both sides, we get

y - 864 + 8(18/2)² = 8 (x² - 18x + 81²)

y - 864 + 648 = 8 (x² - 8x + 9)

on simplification

y - 216 = 8 (x - 9)²

y = 8(x - 9)² + 216

therefore, y = 8 (x - 9)² + 216

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Learn more about a quadratic equation here:

brainly.com/question/2263981

8 0
2 years ago
Use digits to write each number. 5. Twelve thousand, three hundred forty-five 6. Fifty-three million, eighty-nine thousand, seve
postnew [5]

Answer:

5. Twelve thousand, three hundred forty-five can be written as 12,345.

6. Fifty-three million, eighty-nine thousand, seven hundred two can be written as 53,089,702.

7. Two hundred fifty-six thousand, seven hundred eighty can be written as 256,780.

8. Eighty-five thousand, nine can be written as 85,009.

9. Two hundred thirty-eight thousand, eight hundred fifty-seven miles can be written as 238,857.

Step-by-step explanation:

According to the place value chart:

Millions     Hundred Th. Ten Th     Thousands   hundreds   Tens   Ones

1,000,000    100,000       10,000       1,000             100            10        1

We can write any number with the help of place value chart:

For example:

8 thousand, seven hundred seventy-five.

8,000+700+75 = 8,775

Now consider the provided information.

5. Twelve thousand, three hundred forty-five

This can be written as:

12,000+300+45 = 12,345

Twelve thousand, three hundred forty-five can be written as 12,345.

6. Fifty-three million, eighty-nine thousand, seven hundred two

This can be written as:

53,000,000+89,000+700+2 = 53,089,702

Fifty-three million, eighty-nine thousand, seven hundred two can be written as 53,089,702.

7. Two hundred fifty-six thousand, seven hundred eighty

This can be written as:

256,000+780 = 256,780

Two hundred fifty-six thousand, seven hundred eighty can be written as 256,780.

8. Eighty-five thousand, nine

This can be written as:

85,000+9 = 85,009

Eighty-five thousand, nine can be written as 85,009.

9. Two hundred thirty-eight thousand, eight hundred fifty-seven miles

This can be written as:

238,000+800+57 = 238,857

Two hundred thirty-eight thousand, eight hundred fifty-seven miles can be written as 238,857.

8 0
3 years ago
. Marco has $100 in a savings account. He
vlabodo [156]
15x+100
x-number of weeks
100-starting amount
3 0
3 years ago
Back Next
emmasim [6.3K]

Answer:

C

Step-by-step explanation:

✔️First, solve for r:

r/2 ≤ 3

Multiply both sides by 2

r/2 × 2 ≤ 3 × 2

r ≤ 6

This implies that possible value of r is equal to 6 or less than 6.

Graphing this on a number line, the line with a shaded circle, indicating that 6 is included, starts at 6 and points to the left.

This indicates that value of r ranges from 6 and below.

The graph is C.

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=integration%20%5C%3A%20of%20%5Cfrac%7B1%7D%7B2%7D%20%20ln%282x%20%7B%5E%7B2%7D%20%29%20" id="T
In-s [12.5K]

Using properties of the logarithm, you can rearrange the integrand as

\dfrac12\ln(2x^2)=\dfrac{\ln2+\ln x^2}2=\dfrac{\ln2+2\ln x}2=\ln\sqrt2+\ln x

Then recall that the integral of \ln x is

\displaystyle\int\ln x\,\mathrm dx=x(\ln x-1)+C

(or you can find that out by integrating by parts) and so

\displaystyle\int\frac12\ln(2x^2)\,\mathrm dx=(\ln\sqrt2)x+x(\ln x-1)+C

5 0
3 years ago
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