Simplify the following expression (3i+4-i+4(6+2i)

Use SOHCAHTOA.  You must use sine or cosine since the hypotenuse is involved, but since you are given both angles, it does not matter which one of them you choose.  We'll use sine:

sinx=O/H

sin60=O/14

√3/2=O/14

*Cross multiply*

(14√3)=2O

*Divide both sides by 2*

7√3=O

Hope this helps!!

Answer:

B

Step-by-step explanation:

Since the triangle is right we can use the sine ratio to find TI along with

the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{TI}{TR}[/tex] = [tex]\frac{TI}{14}[/tex]

Multiply both sides by 14

TI = 14 × sin60° = 14 ×[tex]\frac{\sqrt{3} }{2}[/tex] = 7[tex]\sqrt{3}[/tex]

Answer:

Nvm about those questions the answer is 1440 degrees

Step-by-step explanation:

Answer:

Final factor is [tex](x + 3)(x+5)(x-5)[/tex].

Step-by-step explanation:

Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]

Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.

[tex]x^3 + 3x^2 - 25x -75[/tex]

[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]

factor each group

[tex]=x^2(x + 3)-25(x +3)[/tex]

[tex]=(x + 3)(x^2-25)[/tex]

[tex]=(x + 3)(x+5)(x-5)[/tex]

Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].

I got the Same answer

Answer:

$9259.26

Step-by-step explanation:

The school receives $20 on $75.

We can calculate the percentage by using the values.

20/75 = 0.27%

The school recieved 0.27% of the payment.

Now we know the target amount and percentage, we can calculate the principal amount here.

Let x dennote the worth on which the school will recieve 2500 dollars. [tex]2500 = x * 0.27\\x = \frac{2500}{0.27}\\ x = 9259.26[/tex]

$9259.26 worth of ribbon has to be sold for the school to get $2500 ..

Answer:

False.

Step-by-step explanation:

The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.

Answer:

True

Step-by-step explanation:flip it and reverse it its esrever dna ti pilf

For this case we have the following functions:

[tex]f (x) = - x ^ 2 + 3x + 5\\g (x) = x ^ 2 + 2x[/tex]

We must find (f + g) (x), by definition we have to:

[tex](f + g) (x) = f (x) + g (x)[/tex]

So:

[tex](f + g) (x) = - x ^ 2 + 3x + 5 + (x ^ 2 + 2x)\\(f + g) (x) = - x ^ 2 + 3x + 5 + x ^ 2 + 2x\\(f + g) (x) = 5x + 5[/tex]

ANswer:

See attached image

Answer:

Step-by-step explanation:

see graph below

The diameter of the sphere is approximately 19.82 units.

To calculate the diameter of a sphere given its volume, we'll use the formula for the volume of a sphere:

[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]

Where:

- [tex]\( V \)[/tex] is the volume of the sphere,

- [tex]\( \pi \)[/tex] is a mathematical constant (approximately equal to 3.14159),

- [tex]\( r \)[/tex] is the radius of the sphere.

Since we have the volume, we rearrange the formula to solve for the radius:

[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]

Substituting the given volume [tex]\( V = 3052.08 \)[/tex], and the value of[tex]\( \pi \)[/tex], we can find the radius:

[tex]\[ r = \sqrt[3]{\frac{3 \times 3052.08}{4 \times 3.14159}} \][/tex]

[tex]\[ r \approx \sqrt[3]{\frac{9156.24}{12.56636}} \][/tex]

[tex]\[ r \approx \sqrt[3]{729.128} \][/tex]

[tex]\[ r \approx 9.85 \][/tex]

Now, to find the diameter, we double the radius:

[tex]\[ \text{Diameter} = 2 \times r \][/tex]

[tex]\[ \text{Diameter} = 2 \times 9.85 \][/tex]

[tex]\[ \text{Diameter} \approx 19.82 \][/tex]

So, the diameter of the sphere is approximately 19.82 units.

To recap, we first found the radius of the sphere using the formula for volume, then we doubled the radius to find the diameter.

Complete question:

The volume of a sphere is 3052.08 units cubed what is its diameter?

Answer:

The equation is y = -x + 2.5

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the equation of a line is y = mx + c , where m is the slope

  of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)

- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)

∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5

∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]

∴ The slope of the line is -1

∵ y = mx + c

∴ y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  one of the two points

∵ Point (5 , -2.5) lies on the line

∴ x = 5 at y = -2.5

∵ y = -x + c

∴ -2.5 = -(5) + c

∴ -2.5 = -5 + c

- Add 5 to both sides

∴ c = 2.5

∴ y = -x + 2.5

* The equation is y = -x + 2.5

The slope and y-intercept to get y = -x + 2.5.

The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.

Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.

Therefore, the equation of the line is y = -x + 2.5.

For this case we must find the sum of the given series. For this we must expand the series for each value of k.

[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]

Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.

[tex]-1-3-5-7 =\\-16[/tex]

The value of the series is -16

ANswer:

-16

Heya!

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

Things to know before we solve:

The "6" at the top means that the the sequence only goes to the 6th term.

k = 3 represents that the sequence starts with the 1st term.

(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.

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

Solving for each term:

3rd term:

-2(3) + 5

-6 + 5

-1

4th term:

-2(4) + 5

-8 + 5

-3

5th term:

-2(5) + 5

-10 + 5

-5

6th term:

-2(6) + 5

-12 + 5

-7

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

Simplifying:

Write these terms in expanded form:

(-1) + (-3) + (-5) + (-7)

Find the sum of the series:

(-1) + (-3) + (-5) + (-7) = -16

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

Answer:

The sum of the series is -16

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

Best of Luck!

Answer:

C

Step-by-step explanation:

x(x2 + 5) – 9(x2 + 5)

= x³ + 5x - 9x² - 45

(try to expand one by one of the answer given)

Answer:

x(x2 + 5) – 9(x2 + 5)

Step-by-step explanation:

Answer:

3.4594

Step-by-step explanation:

To change the base of a logarithm

• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]

where c represents the new base

Changing the base from 2 to 10

[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594

notice, the x-coordinate is the same for both points, thus is a vertical line.

Check the picture below.

To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.

To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.

The distance formula in a two-dimensional Cartesian coordinate system is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Since the x-coordinates are identical, the formula simplifies to:

d = |y₂ - y₁|

Applying this to the points given:

d = |-18 - (-9)|

d = |-18 + 9|

d = |-9|

Therefore, the distance is 9 units.

Answer:

y = -1/4 x + 15.

Step-by-step explanation:

y = 4x - 2 has a slope of 4 ( = the coefficient of x).

The line  at right angles to it will therefore of a slope of -1/4.

Using the point-slope form of a line the line t which passes through (4, 14) is found as follows:

y - 14 = -1/4(x - 4)

y = -1/4x + 1 + 14

y = -1/4x + 15

The percentage increase from yesterday's gas price to today's price is 1.8%.

To find the percentage increase from yesterday's price to today's price, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100.

The difference between $2.88 and $2.83 is $0.05. Dividing $0.05 by $2.83 gives us 0.0176. Multiplying by 100 gives us 1.76%. Rounding to the nearest tenth of a percent, the percentage increase is 1.8%.

it's the first one !!! so it's A

It will take Steve's friend 6.5 hours to catch up to Steve.

The correct answer is:

e) 6.5 hours.

To calculate this, let's first determine the time it takes for Steve's friend to catch up to him after he starts driving.

Steve's speed = 55 mph

Steve's friend's speed = 65 mph

Relative speed = Speed of Steve's friend - Speed of Steve

Relative speed = 65 mph - 55 mph = 10 mph

Now, since Steve's friend starts one hour later, Steve has already traveled for one hour at 55 mph before his friend starts.

Distance traveled by Steve in one hour = Speed × Time

Distance = 55 mph × 1 hour = 55 miles

Now, when Steve's friend starts driving, he needs to catch up this initial distance of 55 miles.

Time = Distance / Relative speed

Time = 55 miles / 10 mph = 5.5 hours

But we must remember that Steve's friend started driving one hour later than Steve. So, we add this one hour to the time calculated above to find the total time it takes for Steve's friend to catch up to Steve.

Total time = 5.5 hours + 1 hour = 6.5 hours

Therefore, it will take Steve's friend 6.5 hours to catch up to Steve.

Steve travels for one hour at 55 mph before his friend starts driving. By then, Steve's friend needs to catch up the initial distance of 55 miles at a relative speed of 10 mph. This gives us a time of 5.5 hours. However, since Steve's friend started one hour later, we add this one hour to the calculated time, resulting in a total time of 6.5 hours. Therefore, the correct answer is 6.5 hours.

Complete question:

Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.

How many hours will it take his friend to catch up to Steve?

a.10 hours

b.5.5 hours

c.8.5 hours

d.55 hours

e. 6.5 hours.

Answer:

First option

b = (8) * Tan (30)

Step-by-step explanation:

Tan (B) = Oppo. / Adj.

Tan (B) = AC/BC

Tan (30) = b / 8

b = (8) * Tan (30)

Answer

First option

b = (8) * Tan (30)

Answer:

The height of the water is [tex]60.5\ ft[/tex]

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=16\ ft[/tex]

[tex]h=96\ ft[/tex]

substitute

[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]

[tex]V=8,192\pi\ ft^{3}[/tex]

step 2

Find the 25% of the tank’s capacity

[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

[tex]\frac{R}{H}=\frac{r}{h}[/tex]

substitute

[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone

substitute

[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]

Simplify

[tex]221,184=h^{3}[/tex]

[tex]h=60.5\ ft[/tex]

Answer: 84

Step-by-step explanation:

7 x 3 x 4 = 84

It would be 84.

Hope this helps!

Pls tell me if it is inncorrect and i will revise my answer.

7•3•4=84

Hello There!

Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.

First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.

Next, we multiply pi*radius^2 * height because a cylinder has a height too.

HOW TO SOLVE

First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.

Once we multiply, we get a product of 471.

Our final answer is 471.units^3

30 ≥ g [keyword - "no more than"

4 ≤ i [keyword - "at least"]

Answer:

348

Step-by-step explanation:

The answer is 1/9 or about 11%.

Answer:8

Step-by-step explanation: it’s right

Answer:

well how many tables are there?

Step-by-step explanation:

Winona's bowling scores have a mean of 204.6, a median and mode both of 195.

To find the mean, median, and mode of Winona's bowling scores, we follow these steps:

The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.

Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6

The mean score is 204.6.

To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.

The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.

The mode is the number that appears most often, which is also 195.

Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.

Answer:

B) Angle G is smaller than angle P.

Step-by-step explanation:

It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.

I know that's a mouthful and probably sounds really weird but just trust me.

Would appreciate brainliest, new to brainly! good luck!

The correct option is, (B) Angle G is smaller than angle P.

Learn more about triangle here:

brainly.com/question/1058720

#SPJ2

Answer:

A. Median

Step-by-step explanation:

Mean and median both are used to measure the central tendency of a given data while range gives us the spread of the data roughly.

Mean is even affected by a single extreme value in the data while median gives us the central value of data even when there are extreme values.

The given set of five prices has one extreme value which will affect the mean. While median is a better option to measure the central tendency of data.

So Daniel will use median to measure the central tendency to describe the prices..

Step-by-step explanation:

Answer is A. Median by jesse

Answer:

• zero: -4, -4/3, 7

• positive: -4 < x < -4/3 . . . or 7 < x

• negative: x < -4 . . . or -4/3 < x < 7

Step-by-step explanation:

Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.

The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)

Answer:

405.80

Step-by-step explanation:

So, we know Carlos ran 21 miles per week, for 12 weeks....

That makes 21 mi/wk x 12 weeks = 252 miles.

Then we know each km is 0.621 mile.

So, we divide 252 miles by 0.621 mile/km to get= 405.80 km

Dividing miles by miles/km gives us the unit we want (km).

There was a trap in this question, because if instead of dividing the 252 miles by 0.621 you would have multiplied it, you would have gotten another answer listed... just not the right one. :-)

Answer:

-60.75

Step-by-step explanation:

-12 / 8 = -3/2

18 / -12 = -3/2

-27 / 18 = -3/2

This is a geometric sequence with a common ratio of -3/2.

an = 8 (-3/2)^(n-1)

The sixth term is:

a₆ = 8 (-3/2)^(6-1)

a₆ = 8 (-3/2)^5

a₆ = -60.75