Mathematics High School

simplest form of the expression
3sqrt750+3sqrt2058-3sqrt48
can someone explain

Answers

Answer 1
First, you have to decompose the numbers under the square root:
750 = 2·3·5²
2058 = 2·3·7³
48 = 2⁴·3

Then, enlight all the exponents multiple of 2 (which is the index of the root):
3·√(2·3·5²) + 3·√(2·3·7²·7) + 3·√(2⁴·3)

At this point, you can take outside the square root everything that has an even number, and doing so you have to halve the exponent; you'll get:
3·5·√(2·3) + 3·7·√(2·3·7) + 3·2²·√3

You can now multiply:
15√6 + 21√42 + 12√3
which is the simplest form of your expression.

Related Questions

Translate shapes , pls help me with this

Answers

A. (-4,-2)
B. (-3,-4)
C. (0,2)
D. (-2,-1)
Try this

Answer:

A: (-4,-2)

B: (-3,-4)

C: (0,2)

D: (-2,-1)

Hope this helps! I'm not the best at math though, so it could be incorrect.

What happens when you square a cubed root or cube a square root and problems like these. Please tell me how to do it!

Answers

You would do the innermost operation first, so for your first example: squaring a cubed root- you would first take the cubed root, get your answer, and square that answer. For example what's the square of the cubed root of 8? Well, the cubed root of 8 is 2. (Because multiplying 2, three times will give me 8). Since the cubed root of 8 is 2, I need to square 2 and I'll get 4.

Number 11 please....

Answers

This is pretty easy
(39 + x) / 2 = 44
39 + x = 88
x = 49

The other number would be 5
Here is how I solved it all you have to do is 44-39= and you get 5 
pretty simple if you have any other questions feel free to ask.

I hope this helps! ❤️

Suppose that 1% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive?,

Answers

Answer: There is a 2.9% chance that a person has head lice given that the test is positive. (I know that sounds very low, but watch the math)

Imagine there are 10,000 students in the school. If 1% have lice, that makes 100 students that have it and 9,900 that don't.

Assume the test was given to all students. Out of the 100 that have lice, only 75 would get a positive test because it is only 75% accurate.

Now, out of the 9,900 student who don't have lice, 25% of them would get a positive test, because the test is only 75% accurate. That is 2,475 false positive tests!!!

So we had a total of 2,550 positive tests, but only 75 of those students actually have lice. 75 out of 2550 is 2.9%.


If the test is positive, there is a 2.9% chance that the subject has head lice.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Assume that the school has 100 students. If 1 student has lice and 99 others don't, that means one student has lice.

Suppose that all students took the test. Only 0.75 of 1 people with lice would have a positive test result because it is only 75% accurate.

Because the test is only 75% accurate, out of the 99 students who do not have lice, 25% would test positive. 24.75 false positive tests are involved here!

So far, 25.50 of our students have had positive tests, although only 0.75 of them truly have lice. 2.9% is 0.75 out of 25.5.

learn more about conditional probability here :

https://brainly.com/question/30144287

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What is the period for the graph of y

Answers

The period of cosine is 2pi radians or 360 degrees. Think of a full circle. To do a full revolution, you must rotate 360 degrees. Afterward, things start to repeat over again.

The answer is choice C. 

Simplify the expression.

Answers

= (x +3)(x -2)*(x -3)(x +3)/((x -2)(x +2)*(x +3)^2)
= (x -3)/(x +2) . . . . . matches selection A
The answer is A because I did he math in my head so fast

35 points!

What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answers

Have you worked with the law of sines and cosines? I will explain this using the law of sines.

Here is the formula for area: ¹⁄₂ • c • b • sin(A)

¹⁄₂ • 11 • 9 • sin63
¹⁄₂ • 99 • sin63
49.5 • sin63
49.5 • .8910065242...
≈44.1

That should be the area of the triangle. The other way to do this is to just start by using the law of cosines, and then finding the height of the triangle, and then using the area formula. I believe the way I showed you is the easier way though. Message me if you have any questions.

Also make sure to include units : 44.1cm²

The amount of grass seed needed to cover a lawn is proportional to its area. The lawn is rectangular and has an area of 2c^2 + 2c square meters. Factor this polynomial to find possible expressions for the length and width of the lawn. (Assume the factors are polynomials.) HELP ASAP!!

Answers

2c is a factor of both terms.
.. area = 2c(c+1)

Possible expressions for length and width are
  1, 2, c, 2c, c+1, 2(c+1), c(c+1), 2c(c+1).

NEED HELP ASAP!

to find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit of 8 feet tall, measures the angle of elevation to the top of the pole to be 36°. to the nearest foot, what is the height of the pole?


a. 87 feet
b. 95 feet
c. 71 feet
d. 79 feet

Answers

The ratio of height above the transit to the distance to the transit is the tangent of the angle.
.. height = 8 ft +(120 ft)*tan(36°) = 95 ft . . . . . . matches selection B

Answer:

95 feet

Step-by-step explanation:

Refer the attached figure.

A surveyor moves 120 feet away from the base of the pole i.e. BC = 120 feet.

BC= ED = 120 feet (refer the figure)

Height of transit i.e. DC = 8 feet

DC = EB = 8 feet (refer the figure)

The angle of elevation to the top of the pole to be 36° i.e. ∠ADE = 36°

Height of pole = AE+EB

To find AE use trigonometric ratio

[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]

[tex]tan36^{\circ}= \frac{AE}{ED}[/tex]

[tex]0.726= \frac{AE}{120}[/tex]

[tex]0.726*120= AE[/tex]

[tex]87.12 = AE[/tex]

Height of pole = AE+EB = 87.12+8 = 95.12 feet≈95 feet

Hence the height of pole is 95 feet

In ∆TUV, Y is the centroid. If TW = 30, what is YW?

Answers

the complete question in the attached figure

we know that
the centroid is always 2/3 the distance of each median to each vertex
TW=30
TW=TY+YW
TY=(2/3)*30---------> TY=20
then
YW=TW-TY-----------> YW=30-20-----------> YW=10

the answer is 
YW=10

Answer:

answer is 10

Step-by-step explanation:

Line segment AC has endpoints A (-1,-3.5) and C (5,-1). Point B is on line segment AC and is located at (0.2,-3). What is the ratio of AB/BC

Answers

The first thing you should do in this case is find the distance between the points.
 The distance between two points can be thought of as a line.
 To find the length of this line, you can use the distance formula:
 d = √ (x2 - x1) ^ 2 + (y2 - y1) ^ 2
 We have then:
 AC distance:
 AC = root ((5 - (-1)) ^ 2 + (-1 - (-3.5)) ^ 2) = 6.5 units
 AB distance:
 AB = root ((0.2 - (-1)) ^ 2 + (-3 - (-3.5)) ^ 2) = 1.3 units
 BC distance: 
 BC = 6.5-1.3 = 5.2 units
 
 Answer:
 The ratio is:
 AB / BC = (1.3) / (5.2)

Answer:

AB/BC = (1.3) / (5.2). Hope this helps :)

Step-by-step explanation:

A pair of jeans originally cost $80, but is on sale for 30% off. there is a coupon available for an additional 10% off of the sale price. how much do the jeans cost with the coupon?

Answers

30% = 0.3. 

0.3*80 = 24, so we know that 30% of 80 is 24. 

80 - 24 = 56, so after the sale, the price for a pair of jeans is $56.

10% = 0.1

0.1*56 = 5.6, so with the coupon, we get $5.60 off. 

56 - 5.60 = 50.40

The jeans cost $50.40 after the sale and the coupon. 

A parallelogram has vertices E(−8, 3), F(2, −2), G(−1, 3), and H(−5, −2). What are the coordinates of the midpoint of each diagonal?

(3, −0.5)
(−4.5, 3)
(−3, 0.5)
(0.5, −1.5)

Answers

The first thing we must do in this case is to draw the ordered pairs given in a Cartesian plane.
 Then, join the points to find the parallelogram sought.
 We observe that the half point of both diagonals is the same.
 Therefore, it is enough to calculate the half point of only one of the diagonals.
 The half point is calculated according to the expression:
 (((x1 + x2) / 2), ((y1 + y2) / 2))
 Substituting values of one of the diagonals:
 (((-1-5) / 2), ((3-2) / 2))
 (-3, 0.5)
 Answer: 
 (-3, 0.5)

Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.

Answers

3- The number of tickets each game requires.
18 - The number of tickets bought.
g - The number of games played.

The "3g" represents the number of games we can determine Zhi and Diego went to. Both equations have values and variables that mean the same thing, however Diego chose to use the distributive property in setting up his equation. 

Yes, Zhi's expression multiplies the tickets per game by the number of games to get the number of tickets used and then subtracts this amount from the total tickets.

Val rented a bicycle while she was on vacation. A paid a flat rental fee of $55 plus $8.50 each day the total cost was 123 dollars write an equation you can use to find the number of days when she rented to bicycle

Answers

Total $= $123
Flat fee= $55
Daily cost= $8.50
d= number of days rented

Total cost equals (the daily cost times the number of days rented) plus the flat fee.

T= (Daily cost)(# Days) + Flat fee
$123= $8.50d + $55


ANSWER: $123= $8.50d + $55

Hope this helps! :)



The first term of a sequence is -12. The recursive formula for the sequence is an = an-1 + 9. What are the next 3 terms in the sequence?

Answers

The next three terms are: -3, 6, and 15

To get each new term, we simply add 9 to the last term. So we add 9 to -12 to get -3. Then we add 9 to -3 to get 6. Finally we add 9 to 6 to get 15

In other words,
first term = -12
second term = first term+9 = -12+9 = -3
third term = second term + 9 = -3+9 = 6
fourth term = third term + 9 = 6+9 = 15

This process repeats forever though we only need three terms in this case.

So that's why the answer is the three values -3, 6 and 15

Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property

Answers

The subtracton property of equality allows you to subtract the same amount from both sides of an equation without changing the truth of the equation.

Answer:

subtraction property

Step-by-step explanation:

The DIAMETER of a sphere is doubled. What is the new volume of the sphere?
A)
8/3πr3
B)
16/3πr3
C)
32/3πr3
D)
64/3πr3

Answers

we  know that
[volume of a sphere]=(4/3)*pi*r³
if the diameter is doubled 
then 
the radius also is doubled

the new volume=(4/3)*pi*(2r)³------> 8*[(4/3)*pi*r³]-------> (32/3)*pi*r³

the answer is C)
32/3πr3 

plz help "geometry"

the intersection of roads M and N creat a 71.4 degrees what are the complumentry and suplumentry angels of this intersection
A 161.4' ; 18.6'
B 18.6'; 161.4'
C 108.6' ; 18.6'
D 18.6' ; 108.6',

Answers

Complementary angles sum up to 90 degrees and supplementary angles sum up to 180 (I remember that because they are alphabetical). 90 - 71.4 = 18.6 180 - 71.4 = 108.6 Therefore, D. is the answer.

What is the value of x in the equation 1/5x-2/3y=30,when y =15?

Answers

1/5x + 2/3(15) = 30

1/5x +10 = 30

1/5x = 20

x = 20 * 5

x = 100

If mAD=85 degrees and mBC=31 degrees find the value

Answers

Answer: x = 11

To start, we know that a whole circle equals 360 degrees. If we subtract the 2 arcs we know, 85 and 31, we have 244 degrees left for the 2 congruent arcs. Dividing that by 2 gives us 122 for each arc.

Now, write the equation:  122 = 13x - 21

Solve this, to find the x = 11.

By the properties of angles on a circle, the degree measure of x in the circle is 11 degrees

Calculating the degree measure of x

From the question, we have the following parameters that can be used in our computation:

The circle

The angle in a circle is 360 degrees.

So, we have

Unused arcs = 360 - 85 - 31

Unused arcs = 244

This means that

2(13x - 21) = 244

So, we have

13x - 21 = 122

This gives

13x = 143

Evaluate

x = 11

Hence, the degree measure of x is 11 degrees

Read more about angles at

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At the pet store, 3 cats are brown with stripes, 2 cats are orange with stripes, and 5 cats are solid brown. What is the probability of a cat being brown or having stripes?

Answers

Answer:

Its 1 or 100%

Step-by-step explanation:

what does X equal to ?

Answers

Answer:

x= 15

Step-by-step explanation:

We can use cross products to solve this problem

7     2x+5

-- = --------

3       x

7x = 3(2x+5)

Distribute

7x = 6x +15

Subtract 6x from each side

7x-6x = 6x-6x+15

x = 15

if she can read 22 pages in 1 hour how many hours did she read in 114.5 hours

Answers

We already know that 22 = 1, but we need to find how many pages she'd read if it were 114.5 hours: 114.5 x 22 = 2519.

Hope this helps,
♥A.W.E.S.W.A.N.♥

Angle A is a right angle in △ABC.

Which side is opposite to angle A?


side BC

side AB

side AC

Answers

side BC is opposite to angle A

Option 1 is correct. The side opposite to angle A is side BC, which is the hypotenuse.

In a triangle, the side opposite the right angle is known as the hypotenuse. Since angle A is given as a right angle in △ABC, the side opposite this right angle will be the hypotenuse.

In △ABC:

Side AB is adjacent to angle A, forming one leg of the right triangle.

Side AC is also adjacent to angle A, forming the other leg of the right triangle.

Side BC is opposite angle A and is the longest side of the triangle, making it the hypotenuse.

Therefore, side BC is opposite to angle A in △ABC.

Complete question:

Angle A is a right angle in △ABC.

Which side is opposite to angle A?

1. side BC

2. side AB

3. side AC

If the train that Megan is riding covers 60 miles in 2 hours, how fast is the train traveling?

Answers

Speed= Distance/Time

60 miles/ 2 hours = 30 miles per hour

PLEASE HELP ASAP!!!

Max is running the concession stand at the local football game. He is selling popcorn and water. Each bag of popcorn costs $1.25 and each bottle of water costs $. 75.

He sold a total of 108 items for a total of $105.00. He needs to report the number of bags of popcorn and bottles of water that were sold.

Determine how many of each item he sold. Be sure to plug your solution back into the equation to verify that it is correct.


Having variables represent the popcorn and the water, so p for popcorn and w for water... I think the equation would be


p + w = 108

and

1.25p + .75w = 105


but after that I get kind of confused...

Answers

take both equations and write a new one incorporating both.
Solve the new equation for p.
Use your p solution to plug back into an original equation and solve for w.
Check your solutions by checking them in both original equations.
p= # of popcorn
w= # of waters

QUANTITY EQUATION
p + w= 108

COST EQUATION
$1.25p + $0.75w= $105

STEP 1:
solve for one variable in cost equation

p + w= 108
subtract w from both sides
p= 108 - w

STEP 2:
substitute p=108-w in for p in cost equation

$1.25p + $0.75w= $105
1.25(108-w) + 0.75w= 105
multiply 1.25 by all in parentheses
(1.25*108)+(1.25*-w)+0.75w= 105
135 - 1.25w + 0.75w= 105
combine like terms
135 - 0.5w= 105
subtract 135 from both sides
-0.5w= -30
divide both sides by -0.5
w= 60 water bottles

STEP 3:
substitute w=60 in either equation to find p

1.25p + $0.75w= $105
1.25p + 0.75(60)= 105
1.25p + 45= 105
subtract 45 from both sides
1.25p= 60
divide both sides by 1.25
p= 48 popcorn

CHECK:
p + w= 108
60 + 48= 108
108= 108

ANSWER: There were 60 popcorn sold and 48 waters sold.

Hope this helps! :)

2. The triangles are similar. write a similarity statement for the triangles.

A. Triangle JKL ~ Triangle NPM

B. Triangle JKL~ Triagle PNM

C. Triangle JKL~ Triangle MNP

D. Triangle JKL~ Triangle PMN

Answers

C. Triangle JKL~Triangle MNP because since when you wrote the first part of the solution you began with the corner that had an arc so you have to begin with the corner that has an arc in the second part of the solution.

Answer:

The correct option is C.

Step-by-step explanation:

In triangle JKL and MNP,

[tex]\angle J=\angle M[/tex]                    (Given)

[tex]\angle L=\angle P=90^{\circ}[/tex]                    (Given)

According to AA property of similar triangle, two triangles are similar if their two corresponding angles are same.

Here, J is corresponding angle of M,  K is corresponding angle of N and L is corresponding angle of P.

Using AA property of similar triangles,

[tex]\triangle JKL\sim \triangle MNP[/tex]

Therefore the correct option is C.

PLEASE HELP ON THIS AND EXPLAIN
THX

Answers

n=1→f(1)=-5.25

f(n)=f(n-1)+1.75, for n=2, 3, 4, ...
n=2→f(2)=f(2-1)+1.75=f(1)+1.75=-5.25+1.75→f(2)=-3.5
n=3→f(3)=f(3-1)+1.75=f(2)+1.75=-3.5+1.75→f(3)=-1.75
n=4→f(4)=f(4-1)+1.75=f(3)+1.75=-1.75+1.75→f(4)=0
n=5→f(5)=f(5-1)+1.75=f(4)+1.75=0+1.75→f(5)=1.75

Answer:
Sequence
-5.25, -3.5, -1.75, 0, 1.75

1400 principal earning 7% compounded monthly after 22 years

Answers

The future value of a $1,400 investment at a 7% interest rate compounded monthly over 22 years using the compound interest formula is $44,923.

The question regards a principal amount of $1,400 earning a 7% interest rate compounded monthly over 22 years. To calculate the future value of this investment, one would typically use the compound interest formula:

[tex]A = P(1 +rn)^n[/tex]

Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($1,400 in this case).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.

To calculate the future value using our example, you can substitute the given values into the formula:

A = [tex]1400(1+(0.07){12})^{12*22}[/tex] = 44923

After 22 years, the balance in the account with a $1,400 principal earning 7% interest compounded monthly would be approximately $3,808.39. This is calculated using the compound interest formula with the given parameters: principal, interest rate, compounding frequency, and time.

To find the balance in the account after 22 years with a $1,400 principal earning 7% interest compounded monthly, we use the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

[tex]- \( A \) is the amount of money accumulated after \( t \) years,- \( P \) is the principal amount (the initial amount of money),- \( r \) is the annual interest rate (in decimal),- \( n \) is the number of times interest is compounded per year, and- \( t \) is the time the money is invested for in years.[/tex]

Given:

[tex]- \( P = $1,400 \),- \( r = 0.07 \) (7% interest rate converted to decimal),- \( n = 12 \) (compounded monthly),- \( t = 22 \) years.[/tex]

Plugging in the values:

[tex]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{(12)(22)} \]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{264} \]\[ A = 1400 \left(1 + \frac{0.005833}{1}\right)^{264} \]\[ A = 1400 \left(1.005833\right)^{264} \][/tex]

Now, we calculate:

[tex]\[ A \approx 1400 \times 2.72028 \]\[ A \approx $3,808.39 \][/tex]

So, the balance in the account after 22 years would be approximately $3,808.39.

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