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3 years ago

Rewrite in simplest terms: 3(2p - 5) - 6p

Mathematics

1 answer:

mylen [45]3 years ago

7 0

-15

Reason:

First, use the distributive property

3(2p - 5) - 6p = 6p - 15 - 6p = -15

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Consider the following incomplete deposit ticket: what was art’s total deposit? a. $1,701.23 b. $1,545.83 c. $1,856.63 d. $1516.

34kurt

Step-by-step explanation:

the answer is $1,145.39

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2 years ago

Which is a correct two-column proof? Given: <H and <X are supplementary. prove: l || n

andriy [413]

Answer:

option-B

Step-by-step explanation:

we are given

<H and <X are supplementary angles

so,

<H+<X=180

we know that

<H and <E are vertically opposite angles

so, they must be equal

<H=<E

we can plug it

<E+<X=180

It means that angle(E) and angle(X) are supplementary angles

and these two angles are same side interior angles

By using same side interior angles converse

so, line(l) and line(n) must be parallel

so, option-B

8 0

3 years ago

Read 2 more answers

Write an expression that can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds

aivan3 [116]

Answer:

3.25g + 0.74f = t

5 0

3 years ago

Given that sec (x) = 2 and cosec (x) is negative,

weeeeeb [17]

Answer:

i) sin(2x) = $-\frac{\sqrt{3}}{2}$

ii) cot(x+360) = $-\frac{\sqrt{3}}{3}$

iii) sin(x-180) = $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = $\frac{1}{2}$

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

$sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}$

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

$sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}$

So,

$sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}$

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

$cot(x) = \frac{cos(x)}{sin(x)}\\$

Using the values, we get:

$cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}$

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = $-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

6 0

3 years ago

Brittany has 50 beads. 70% of the beads are gold. <br>How many beads are gold?

tankabanditka [31]

The number of beads that are gold is 35.

<h3>How many gold beads are there?</h3>

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Number of gold beads = percentage of gold beads x total number of beads

70% x 50

0.7 x 50 = 35

To learn more about percentages, please check: brainly.com/question/25764815

#SPJ1

6 0

1 year ago