Express the square root of -80 in its simplest terms.

A- cannot be determined
B- 8i sqrt 10
C- 4i sqrt 5
D- 2i sqrt 20

Answers

Answer 1

Answer:

C

Step-by-step explanation:

noting that [tex]\sqrt{-1}[/tex] = i

Given

[tex]\sqrt{-80}[/tex]

= [tex]\sqrt{16(-1)(5)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] × [tex]\sqrt{5}[/tex]

= 4i[tex]\sqrt{5}[/tex] → C

Answer 2

The square root of -80, expressed in simplest terms, is 4i sqrt 5, where 'i' is the imaginary unit.So,option C is correct.

To express the square root of -80 in its simplest terms, we need to use the imaginary unit i, which is defined as the square root of -1. We can rewrite -80 as -1  imes 80, and thus the square root of -80 as the square root of -1 times the square root of 80. We know that the square root of -1 is i, and the square root of 80 can be simplified to the square root of 16 times the square root of 5, which is 4 times the square root of 5. Combining these, we get:
√-80 = √(-1 times 80)
      = √-1 times √80
      = i times 4√5
      = 4i√5.

The correct answer is C- 4i sqrt 5.


Related Questions

What is the sine cosine and tangent of 120 degrees

Answers

The sin of 120 is the square root of 3 over 2.

The cos of 120 is -1/2

The tan of 120 is negative square root of 3

Use cast rule

120 degrees is in the Quadrant 2 meaning it is in the “S” quadrant AKA where Sin is positive, Cos is negative, & Tan is negative.

I found the angle of the coterminal by subtracting 120° from 180° -> 180-120=60°

Then I used the 30°-60°-90° triangle rule to find my lengths and ratios for sin, cos and tan!




suppose that F(x)=x^3 and G(x)=-2x^3

Answers

Answer:

A

Step-by-step explanation:

Given a function f(x) = x^2, we can say:

g(x) = -(x^2) is the reflection of f(x) in the x-axish(x) = ax^2 is a vertical stretch if a > 1 and a vertical compression if 0 < a < 1

The negative sign in front says that G(x) is flipped over the x-axis with respect to F(x). Also, the 2 in front tells us that it is a vertical stretch of the function F(x), since a > 1.

Hence, answer choice A is right.

Answer:

it is answer A

Step-by-step explanation:

Ap*x

What is the vertex of the parabola

Answers

Answer:

(1,-4) the vertex will always be the lowest point

Step-by-step explanation:

lowest point my dude

Answer: (1,-4)

Step-by-step explanation: The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.

In this case, since the parabola opens upward, we can see that

the vertex is the lowest point on the parabola which is (1,-4).

Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus two.

Answers

Answer:

[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]

Step-by-step explanation:

We have the following limit

[tex]\lim_{x \to 0}\ x^2 -2[/tex]

To solve this limit using direct substitution to substitute the value that tends x into f(x) and simplify.

In this case x tends to zero, then we substitute x = 0 in the function and simplify

[tex]\lim_{x \to 0}\ x^2 -2= (0)^2 -2= -2[/tex]

Therefore

[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]

When x approaches 0 then f(x) it tends to -2

An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.

To summarize the situation, a worker writes the inequality:

10c + 20s ≤ 4,000, where c is the number of ounces of copper material and s is the number of ounces of silver material.

Which graph's shaded region shows the possible combinations of raw materials the company can buy?

Answers

Answer:

Option B is the correct answer.

Step-by-step explanation:

The function y=3.75 + 1.5(x-1) can be used to determine cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

Answers

Answer:

1.5 dollars/miles

Step-by-step explanation:

Given function [tex]y=3.75 + 1.5(x-1)[/tex] can be used to determine cost in dollars for a taxi ride of x miles.

Now we need to find about what is the rate of change of the cost in dollars with respect to the number of miles.

First we need to rewrite [tex]y=3.75 + 1.5(x-1)[/tex] in y=mx+b form

[tex]y=3.75 + 1.5(x-1)[/tex]

[tex]y=3.75 + 1.5x-1.5[/tex]

[tex]y=2.25 + 1.5x[/tex]

[tex]y=1.5x + 2.25[/tex]

comparing with y=mx+b, we get m=1.5

Hence rate of change of the cost in dollars with respect to the number of miles is 1.5.

Identify the following as exponential or linear and growth or decay

Answers

This would be linear growth because the y values are increasing, but not at an exponential rate.

Find the lateral area and surface area of cone

Answers

Answer:

[tex]\large\boxed{L.A.=168\pi\ in^2}\\\boxed{S.A.=232\pi\ in^2}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - slant height

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

We have r= 8in and l = 21in. Substitute:

[tex]L.A.=\pi(8)(21)=168\pi\ in^2[/tex]

[tex]S.A.=\pi(8^2)+168\pi=232\pi\ in^2[/tex]

Need help with b and c

Answers

Answer:

Step-by-step explanation:

the formula is:

[tex]a_n = \frac{n+1}{n+2}[/tex]

[tex]a_100 = \frac{101}{103}[\tex]

Answer:

see explanation

Step-by-step explanation:

We note that for each term, the numerator increases by 1 and the denominator increases by 1 from the previous term, that is

term 1 = [tex]\frac{1+1}{1+2}[/tex] = [tex]\frac{2}{3}[/tex]

term 2 = [tex]\frac{2+1}{2+2}[/tex] = [tex]\frac{3}{4}[/tex]

term 3 = [tex]\frac{3+1}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]

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

term 100 = [tex]\frac{100+1}{100+2}[/tex] = [tex]\frac{101}{102}[/tex]

If we let n be the term value, then the n th term is

[tex]a_{n}[/tex] = [tex]\frac{n+1}{n+2}[/tex]

Find the length of the missing side. The triangle is not drawn to scale. Show your work. (Will give brainliest)

Answers

A^2 + b^2 = c^2

C is your hypotenuse or the longest side of the triangle; you plug in your values and solve for the missing side:

15^2 + b^2 = 17^2

225 + b^2 = 289

*-225 on both sides to get b by itself*

B^2 = 64

*to get rid of the ^2; you take the square root*

B = sqrt 64

B= 8 <— final answer

We can use the Pythagorean Theorem to solve for the missing side length (a).

Pythagorean Theorem:

a² + b² = c²

a and b are the legs (shorter sides) of the triangle and c is the hypotenuse (the longer side of the triangle).

1. Substitute in the known values.

a = ?

b = 15

c = 17

a² + 15² = 17²

2. Solve for a.

a² + 15² = 17²

a² + 225 = 289

a² + 225 - 225 = 289 - 225

a² = 64

√a² = √64

a = 8

Hope this helps!

Use the elimination method to solve the system of equations

Answers

Answer:

D- (3, 1).

Step-by-step explanation: Add the first equation so you can figure out what x equals. Then, plug the value into your next equation in order to find y. Hope this helps. :)

For this case we have the following system of equations:

[tex]2x + 4y = 10\\3x-4y = 5[/tex]

We solve by the method of elimination, then:

We add both equations:

[tex]2x + 3x = 10 + 5\\5x = 15\\x = \frac {15} {5}\\x = 3[/tex]

We find the value of y:

[tex]3 (3) -4y = 5\\9-4y = 5\\9-5 = 4y\\4 = 4y\\y = \frac {4} {4}\\y = 1[/tex]

Answer:

(3,1)

Option D

kate has 2/3 yards of fabric to make small flags each flag requires 1/6 yards of fabric how many flags cane kate make​

Answers

Answer:

THE ANSWER IS 7

Step-by-step explanation:

CAUSE UR MOM IS A TRASHIE                 i'm sorry i meant YO MAMA

Final answer:

Kate can make 4 small flags from 2/3 yards of fabric since each flag requires 1/6 yards of fabric.

Explanation:

Kate has 2/3 yards of fabric and each small flag requires 1/6 yards of fabric. To find out how many flags Kate can make, you divide the total amount of fabric by the amount needed for one flag:

2/3 yards \/ 1/6 yards = 4 flags.

Here's the step-by-step calculation:

First, recall that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/6 is 6/1.

So, multiply 2/3 by the reciprocal of 1/6:

2/3 × 6/1 = 12/3 = 4.

Thus, Kate can make 4 small flags from the fabric she has.

Find the value of y . 13/9 = y/18 y = ___. HELP ME IMMEDIATELYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY PLZ

Answers

Answer: 9 :)

Step-by-step explanation:

Answer:

[tex]y=26[/tex]

Step-by-step explanation:

[tex]\frac{13}{9}=\frac{y}{18}[/tex]

Cross multiply, isolate the variable, and divide by the coefficient to solve.

[tex]\frac{13}{9}=\frac{y}{18} \\ \\ 9y=234 \\ \\ y=26[/tex]

Plug back in to check.

[tex]\frac{13}{9}=1.4... \\ \\ \frac{26}{18}=1.4...[/tex]

This table shows the length, in inches, of several nails.
Length (in.)

1
2


1
8



3
8



5
16



5
16



5
16



1
2



5
16



3
16



1
8



Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.

Answers

A construction of the line plot for the length, in inches, of several nails is shown in the image attached below.

In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given length (in yards) of several nails on a line plot as shown in the image attached below;

Length        Frequency

1/2                     2

5/16                   4

1/8                     2

3/8                     1

3/16                    1

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5/16 because it has the highest frequency of 4.

Complete Question;

This table shows the length, in inches, of several nails.

Length (in) 1/2, 5/16, 1/8, 1/2, 3/8, 5/16, 5/16, 3/16, 5/16, 1/8.

Create a line plot to display this data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.

Type the correct answer in the box. Round your answer to the nearest hundredth.
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º.
Scarlett's height is 1.65 meters, so the height of the dam is meters.

Answers

Answer:

top question is not correct

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

(17 points)
Determine if line AB is tangent to the circle

Answers

1. If AB is tangent to the circle, then

[tex]18^2=(2\cdot7.2)^2+10.8^2[/tex]

We have

[tex]18^2=324[/tex]

[tex](2\cdot7.2)^2+10.8^2=324[/tex]

so AB is indeed tangent to the circle.

2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,

[tex](10+8)^2=8^2+15^2[/tex]

but we have

[tex](10+8)^2=324[/tex]

[tex]8^2+15^2=289[/tex]

so that cannot be a right triangle and AB is not tangent to the circle.

What is the total perimeter of this figure? Express your answer in feet.

Answers

Answer:

i need to see the figure

Step-by-step explanation:

Answer:

i cant get the figure to go thru

Step-by-step explanation:


The volume of a cube is 85.184 cubic inches. What is the length of each side of the cube?

Answers

Answer:

4.4 inches

Step-by-step explanation:

To work out the length of each side of the cube you would need to cube root of the volume as seen below:

[tex] \sqrt[3]{85.184} [/tex]

And this gives the answer 4.4 inches.

Answer:

Volume = Length * Width * Height

A cube has equal length, width, and height values.

[tex]\sqrt[3]{85.184}[/tex] is 4.4

So the length of each side is 4.4 units

125.663 in terms of pi

Answers

Just divide by pi, so it would be about 39.999(Pi)

Which of the following is an outlier in the set of data below? I think it’s 12 but I’m not so sure.

Answers

I think the answer might be 2

because

in the data given above all the numbers are between 12-19 they are all bigger than 10

and then there's 2 which is very far from 12 or any other numbers there and it is also less than 10

which makes more sense for it to be an outlier.

Hope this helps

Which statement about these rectangles is true ?

Answers

the answer for this question is the dilation is reduction

Answer:

The statement which is true about these rectangles is:

          The dilation is an enlargement.

Step-by-step explanation:

Dilation Transformation--

It is the translation which changes the size of the original figure.The shape of the figure is conserved.Also, in dilation either the size increases (i.e. the figure enlarges) or it decreases( i.e. the figure reduces).Also, in a polygon if there is a dilation then there is a scalar multiplication in each of the sides of the polygon.If the scalar multiple is greater than 1 then there is a enlargement.and if the scalar multiple is less than 1 but greater than 0 then there is a reduction.

Here we see that each of the sides of the original figure is multiplied by "1.5" to obtain a larger rectangle.

This means that the dilation is a enlargement.

( since the scalar is strictly greater than one )

PLEASE SOLVE THIS ASAP

Answers

OK..

So first you need to divide it into two shapes, rectangle and square

Then u find the area for rectangle and add it with the area of square..

Answer:

I think the answer is 23. Please tell me if I am wrong.

Step-by-step explanation: 8 + 4 = 12   4 + 5 + 2 = 11  12 + 11 = 23


What value of y makes
the equation below true?
y + 2.9 = 11
A 8.1
B 8.9
C 9.1
D 13.9

Answers

Answer is “A”

Because since we know if we need to find the y is so we need to subtract 11-2.9=8.1

which mean y mean 8.1

The answer would be A

That is because you can not add unlike terms, so you would have to subtract 2.9 - 11 to find your answer. Therefore, the answer is 8.1

Hope you found this useful.

Find the area of the following polygon

Answers

Answer:

84 m^2

Step-by-step explanation:

We can break the polygon into a rectangle and a triangle

The rectangle at the bottom is 12 by 4

A = 12*4 = 48

The triangle at the top has a base of 12 and a height of (10-4) = 6

A = 1/2 (12) *6 = 36

The total is the sum of the two areas

A = 48+36 =84 m^2

you find a triangle that has an area of 10 sq ft. the height of the triangle is 10 feet. what is the length of the base of the triangle?​

Answers

Solution:

Given :

Area of triangle = 10 ft² Height of triangle = 10 ft

So, We have to find the Base of Triangle .

Area of triangle = 1/2*b×h, Where represents

B represent Base H represent Height

Step : Substitute those value in Formula;

Area of triangle = 1/2 × b × h

10 = 1/2 × b × 11

20 = 11 × b

b = 20/11

b = 1.81 ft

Therefore, Base of Triangle is 1.81 ft

Final answer:

To find the base of a triangle with an area of 10 sq ft and a height of 10 ft, use the formula 1/2 × base × height. By rearranging the formula and substituting the known values, the base is calculated to be 2 feet.

Explanation:

The question is asking to find the length of the base of a triangle when the area is 10 square feet and the height is 10 feet. The formula for the area of a triangle is 1/2 × base × height. In this case, we know the area (10 sq ft) and the height (10 ft), and we need to solve for the base.

Inserting the known values into the formula gives us:

Area = 1/2 × base × height
10 = 1/2 × base × 10

To solve for the base, we rearrange the formula:

base = 2 × Area / height
base = 2 × 10 / 10
base = 2 feet

Therefore, the length of the base of the triangle is 2 feet.

answer this fast
will mark brainlist for sure
answer the question whichever u know
:)

Answers

Answer:

[tex]\large\boxed{1.\ 38\ and\ 22}\\\boxed{1'.\ 42\ and\ 30}[/tex]

Step-by-step explanation:

[tex]1.\\x,\ y-the\ numbers\ (x>y)\\\\\text{We have the system of equations:}\\\\\underline{\left\{\begin{array}{ccc}x-y=16\\x+y=60\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=76\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=38}\\\\\text{Put the value of x to the second equation.}\\\\38+y=60\qquad\text{subtract 38 from both sides}\\\boxed{y=22}[/tex]

[tex]1'.\\x-larger\ part\\x-12-smaller\ page\\\\x+(x-12)=72\\x+x-12=72\qquad\text{add 12 to both sides}\\2x=84\qquad\text{divide both sides by 2}\\\boxed{x=42}\\\boxed{x-12=30}[/tex]

Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product?

Answers

Final answer:

Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.

Explanation:

To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.

Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.

Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).

Next, we can simplify the expression by combining like terms and further distributing where necessary:

3x2 – 36x2 + 3x2 – 2x2 + 8x – 8

Combine like terms:

– 35x2 + 8x – 8

Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.

Match the description to the best example so that all terms have a matching example.
1. A set of decimal fractions

2. A set of whole numbers

3. A set of integers

4. A set of natural numbers

5. A set of rational numbers

here are the options

{3,4,5}

{¼,½, ¾ }

{0.1, 0.2, 0.3}

{0,1,2,3 }

{-2, -1, 0, +1}

Answers

Answer:  1. A- (0.1 0.2 0.3)

2.a-(3,4,5)

3.A-(-2,-1,0,+1)

4.a-(0123)

5.a-( 1/4 1/2 3/4

Step-by-step explanation:

I'm sorry you had to wait a whole year to get your answer :)

Final answer:

The exercise involves matching the terms decimal fractions, whole numbers, integers, natural numbers, and rational numbers to their respective sets of numbers. The correct matches are: decimal fractions {0.1, 0.2, 0.3}, whole numbers {0,1,2,3}, integers {-2, -1, 0, +1}, natural numbers {3,4,5}, and rational numbers {1/4,1/2, 3/4}.

Explanation:

The goal here is to

match

the given

description

or term to the given sets of numbers according to their properties. Let's start.

A set of decimal fractions would be {0.1, 0.2, 0.3} as these are fractions written in decimal format. A set of whole numbers would be {0,1,2,3}. Whole numbers include all natural numbers and zero. A set of integers would be {-2, -1, 0, +1}. Integers are numbers that do not have fractional or decimal parts and they include both positive and negative numbers, and the number zero. A set of natural numbers would be {3,4,5} as these are numbers naturally counted starting from 1. Finally, a set of rational numbers would be {1/4,1/2, 3/4}. Rational numbers are numbers that can be expressed as fractions or ratios.

So, we have successfully made a

matching

for each description.

Learn more about matching here:

https://brainly.com/question/36757679

#SPJ2

Answer #6 and tell the steps of how u did it

Answers

Answer:

3131x+1

Step-by-step explanation:

Make equation simple

5x times 5x times 5x times 5x times 5x +x+1

Solve

5 times 5 times 5 times 5 times 5 = 3125

x times x times x times x times x times x = 5x

3125+5x=3130x

Now you might be thinking you cant add x but here your can because it is just broken apart

now add x+1

3131x+1

An engineer estimated the weight of a steel beam to be 600 pounds. The actual weight of the beam was 639 pounds. Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.

Answers

Answer:

Absolute error = 39

Percent Error = 6.10%

Step-by-step explanation:

Actual value = 639 pounds

Observed Value = 600 pounds

The formula to find absolute error is:

Absolute Error = Actual value - Observed Value

                        = 639 - 600

                        = 39

The formula to find Percent error is:

Percent Error = (Actual value - Observed Value / Actual value)*100

                       = (639 - 600/639)*100

                       = 6.10%

                 

Answer:

Absolute error = 39 pounds

Percent error = 6.10%

Step-by-step explanation:

We know that the estimated weight was 600 pounds while the actual weight of the beam was 639 pounds.

So we will find their difference to get the absolute error.

Absolute error = 639 - 600 = 39 pounds

We will use the following formula to find the percent error.

Percent error = (Estimated value - actual value / actual value) * 100

Percent error = 639 - 600 / 600 * 100 = 6.10%

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