Find the number of terms in the series for the series given below.

QUICK !! What is the image point of (-9,5) after a translation right 3 units and down 2 units ?

klemol [59]

Answer:

(-6,3)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5660 and his st

disa [49]

8,160.. but rounding would be 8170 sooo both increased by 5 and 9 percent would be 1270 and 1507 !

6 0

3 years ago

]Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the le

Murrr4er [49]

The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C

<h3>How to determine the value</h3>

It is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.

Thus, we have

RT/TQ = RV/VS

RT = x + 10

TQ = x - 3

RV = x + 10

VS = x

Substitute the value

$\frac{x + 4}{x-3} = \frac{x + 10}{x}$
Cross multiply

(x+ 4) × x = (x + 10) × (x-3)

x² + 4x = x² -3x + 10x -30

Divide through by x²

4x = -3x + 10x - 30

Collect like terms

4x + 3x - 10x = - 30

-3x = -30

x = -30/ -3

x = 10

Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C

Learn more about triangles here:

https://brainly.in/question/1399334

#SPJ1

4 0

2 years ago

What is the exact value of sin(theta + beta)?

NISA [10]

Answer: $\frac{-3\sqrt{13}+4\sqrt{3}}{20}$

This is the single fraction of -3*sqrt(13)+4*sqrt(3) up top all over 20.

sqrt = square root

=======================================================

Explanation:

Angle theta is between pi and 3pi/2. This places the angle in quadrant Q3 where both cosine and sine are negative

Use the pythagorean trig identity to get the following:

$\sin^2 \theta + \cos^2 \theta = 1\\\\\sin^2 \theta + \left(-\frac{\sqrt{3}}{4}\right)^2 = 1\\\\\sin^2 \theta + \frac{3}{16} = 1\\\\\sin^2 \theta = 1 - \frac{3}{16}\\\\\sin^2 \theta = \frac{16}{16} - \frac{3}{16}\\\\\sin^2 \theta = \frac{16-3}{16}\\\\\sin^2 \theta = \frac{13}{16}\\\\\sin \theta = -\sqrt{\frac{13}{16}} \ \text{ ... sine is negative in Q3}\\\\\sin \theta = -\frac{\sqrt{13}}{\sqrt{16}}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\$

Angle beta is in Q1 where sine and cosine are positive.

Draw a right triangle with legs 3 and 4. The hypotenuse is 5 through the pythagorean theorem. In other words, we have a 3-4-5 right triangle.

Since $\tan \beta = \frac{3}{4}$ , this means $\sin \beta = \frac{3}{5} \ \text{ and } \ \cos \beta = \frac{4}{5}$

Use these ideas:

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

In this case we have: opposite = 3, adjacent = 4, hypotenuse = 5.

-------------------------------------

To recap:

$\cos \theta = -\frac{\sqrt{3}}{4}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\\cos \beta = \frac{3}{5}\\\\\sin \beta = \frac{4}{5}\\\\$

They lead to this

$\sin\left(\theta + \beta\right) = \sin \theta * \cos \beta - \cos \theta * \sin \beta\\\\\sin\left(\theta + \beta\right) = -\frac{\sqrt{13}}{4} * \frac{3}{5} - \left(-\frac{\sqrt{3}}{4}\right) * \frac{4}{5}\\\\\sin\left(\theta + \beta\right) = -\frac{3\sqrt{13}}{20}+\frac{4\sqrt{3}}{20}\\\\\sin\left(\theta + \beta\right) = \frac{-3\sqrt{13}+4\sqrt{3}}{20}\\\\$

6 0

3 years ago

The sum of 2 and three times a number equals 11. Find the number.

Illusion [34]

Answer:

-5

Step-by-step explanation:

x = first number

y = second number

From the first sentence

11 = 2x + 3y

From the second sentence (I'm assuming the word "dust" should be "first"

y = 2-x

rewritten as

x + y = 2

So your system of equations is

2x + 3y = 11

x + y = 2

Multiply the 2nd equation by -2

2x + 3y = 11

-2x - 2y = -4

Add the two equations together

y = 7

Use y=7 to solve for x

x = 2-y = 2-7 = -5

7 0

3 years ago

Read 2 more answers