Find the volume of the triangular prism

Answer:

4 = 22

Step-by-step explanation:

Factor 40 into its prime factors

          40 = 23 • 5

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          4 = 22

Factors which will remain inside the root are :

          10 = 2 • 5

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          2 = 2

At the end of this step the partly simplified SQRT looks like this:

        2 • sqrt (10x4)  

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(x4) = x2

  sqrt (40x4) =

       2 x2 • sqrt(10)

Simplified Root :

2 x2 • sqrt(10)

Answer:

x > 2

Graph in picture

Step-by-step explanation:

Given:

7x + 10 < 11x + 2

To Find:

Solve and graph on a number line. Show your work in the box below.

Solve:

Subtract 10 from both sides

7x + 10 -10 < 11x + 2-10

Simplify

-4x < - 8

Multiply both sides by -1 which reverse the inequality

Simplify

4x > 8

Now, Divide both sides by 4

4x ÷ 4 > 8 ÷ 4

Simplify

x > 2

Solution: x > 2

Now graphing:

> means greater than

that means x is greater than 2

Thus, the line is going to the right.

Graph below:

Answer: x > 2

Step-by-step explanation:

7x+ 10 < 11x + 2

7x+10-10 < 11x + 2 -10

subtract the numbers

7x < 11x -8

7x < 11x -8

7x - 11x < 11x -8 - 11x

-4x < -8

-4x < -8

-4x/-4 > -8/-4

x > 2

Answer:

Step-by-step explanation:

[tex]\begin{cases}9x-9y=-9&\left(1 \right) \\ 3x+9y=-15&\left( 2\right) \end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9x-9y=-9&\left( 1\right) \\ 12x=-24&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}x-y=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=x+1=-2+1=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]

Answer:

  (b)  $1450

Step-by-step explanation:

For her debt-to-credit ratio to be 25%, Gwen must reduce her credit accounts balance to 25% of her limits of $6740. That balance will be ...

  0.25 × $6740 = $1685

__

To get her balance down to that amount, she must reduce it by ...

  $3135 -1685 = $1,450.00

Answer:

0.7

Step-by-step explanation:

1+3+3+2+3+3 = 15/6 = 2.5

2+4+4+2+4 = 16/5 = 3.2

3.2-2.5 = 0.7

Answer:

See below ~

Step-by-step explanation:

The given polynomial : -2x + 1 + 2x² needs to be written in the form :

On rewriting in this asked format,

Answer: B

Step-by-step explanation:

Step-by-step explanation:

thats the answer i think

Answer:

y=-4/3x-4

Step-by-step explanation:

The equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex]

" Equation of line is defined as the equation which represents the set of points using slope."

Formula used

[tex]y=mx+c[/tex]

m = slope of the line

c = y-intercept

Product of the Slopes of perpendicular lines  = -1

According to the question,

Slope of the given line = [tex]\frac{3}{4}[/tex]

Using condition for slope of perpendicular lines we have,

Slope of the line perpendicular to the given line 'm' = [tex]\frac{-4}{3}[/tex]

From given point (0, -4)

Y- intercept 'c' = -4

Substitute the value in the formula to get equation of required line,

[tex]y= \frac{-4}{3} x-4[/tex]

Hence,  equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex].

Learn more about equation of line here

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[tex]~~~~~~\cos B = \dfrac{\text{Base}}{\text{hypotenuse}}\\\\\\\implies \cos B = \dfrac{BC}{AB}\\\\\\\implies \cos B = \dfrac{12}{13}[/tex]

Answer:

After adding the numbers the result obtained is called the sum.

Answer:

792 cm²

Step-by-step explanation:

Surface Area (Cylinder)

⇒ 2πrh + 2πr²

⇒ 2πr (h + r)

Here, r = 9 cm and h = 5 cm.

⇒ 2π × 9 (5 + 9)

⇒ 18π × 14

⇒ 252 x 22/7

⇒ 36 x 22

⇒ 792 cm²

The amount of money which is expected to lose if the game of spinner is played 1000 times is $111.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

You spin the spinner two times.

Let suppose there are total 12 outcomes on a spinner which has 12 blocks. In this block, 4 is blue. The probability of getting blue twice in this spinner and earning $15 is,

[tex]P=\dfrac{4}{12}\times\dfrac{4}{12}\\P=\dfrac{1}{9}[/tex]

The probability of not getting two blue in two spun and losing $2 is,

[tex]P^{-1}=1-\dfrac{1}{9}\\P^{-1}=\dfrac{8}{9}[/tex]

The money to expect to win or lose if you play this is,

[tex]E(X)=15\times\dfrac{1}{9}-2\times\dfrac{8}{9}\\E(X)=-0.111[/tex]

For 1000 games,

[tex]E(X)=-0.111\times1000\\E(X)=-111[/tex]

Thus, the amount of money which is expected to lose if the game of spinner is played 1000 times is $111.

Learn more about the probability here;

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Answer:

=> 7√3

Step-by-step explanation:

Given :

∠ Q = 30°

RS/QR = tan 30°

7/QR = 1/√3

QR = 7√3

Answer:

2/3.

Step-by-step explanation:

Full revolution = 12 hours

11 - 3 = 8 hors

So it is 8/12 = 2/3 of a revolution.

Answer:

Fraction: 23/18

Radians: 23π/ 18

Step-by-step explanation:

A semi circle is 180 degrees, so 230 degrees of a semi circle would be 230/180, or 23/18.

To convert degrees to radians, do the degree times π/180, so the answer is 23π/18

Answer:

It's technically the same thing, because if we solve both of these the answer would be same.

First one says 70 percent part of 7 and the other one says 7 percent part of 70. However, if we solve both of these the answer will be same:

i) 70% of 7

= (70/100) × 7

= 4.9 answer

ii) 7% of 70

= (7/100) × 70

= 4.9 answer

So, here as you can see, through both the equations we get the same answer, which is 4.9 .

This is one of the basic principles of multiplication actually, where:

a × b = c

b × a = c

Therefore,

a × b = b × a

Hope that helps...

Answer:

There are 4 third grade classes

Step-by-step explanation:

12 packs of pencils

3 packs to each class so you are making groups of 3.  

12 ÷ 3 = 4

There are 4 third grade classes

3 packs × 4 classes = 12 packs of pencils

Deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.

A box plot has 5 data description.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

We're specified here that:

Total 440 crates is being shipped by company.

The box plot is defined by the points 84, 99.5, 113, 143, 170

The point 99.5 is the first quartile.

There are 75% observations on its right, so 75% of 440 is the number of crates which weigh greater than 99.5 pounds.

We get this value as:

[tex]\dfrac{440}{100} \times 75=330[/tex]

Thus, deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.

Learn more about quartiles here:

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Answer:

19

Step-by-step explanation:

100, 121, 144, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841 . are perfect squares in between 90 and 890, all together there are : 19

Answer:

Another method to graph a line in the xy-axis or xy-plane is to use its intercepts. What are intercepts? These are points of the line that are found on the xx and yy axes. There are two kinds of intercepts.

The first one is called the x-intercept because it is the point of the line located on the horizontal axis (x-axis).

The second is the y-intercept which is the point of the line located on the vertical axis (y-axis).

Step-by-step explanation:

Hey there!

3 * 2/3

= 3/1 * 2/3

= 3(2) / 1(3)

= 6 / 3

= 6 ÷ 3 / 3 ÷ 3

= 2 / 1

= 2 ÷ 1

= 2

Therefore, your answer is: 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

1/4

Step-by-step explanation:

There are 8 sections and skating is on 2 of the 8;  the probability is 2/8 = 1/4. It does not matter how many times it has appeared on previous spins.

Answer:

180/19

Step-by-step explanation:

(10x)/15+(9x)/15＝5+7

19x＝12(15)

x＝180/19

Answer:

See below ~

Step-by-step explanation:

Using PEMDAS

Our equation

1. Simplifying Parentheses

2. Simplifying Exponents

3. Multiplying

4. Adding (As division without simplifying isn't correct)

5. Subtracting

6. Dividing

Answer:

The amount y is depends on what x's value is. It is helpful to make a table or graph so we can see how the y value changes like the x value :)

Have an amazing day!!

Please rate and mark brainliest!!

If you want the type of relationship between 'x' and 'y'

  ⇒ they are a linear relationship as in they form a straight line together

If you want to describe how the value of x correlates to y

 ⇒ as x increases, y increases thus it is a direct variation.

Hope that helps!

The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

A regular octagon has 8 sides, and a triangle has 3 sides

Assume that there is a point on the triangle.

Then we select (3 - 1) points from the (8 - 1) sides.

8 - 1 = 7

3 - 1 = 2

So, the total number of selection is:

Selection = 7C2

Evaluate the combination expression

Selection = 21

Adjacent triangles have 5 lines (one line in common).

So, we have:'

n = 5 - 1

n = 4

The number of ways this points can be selected is:

Selection = 4C2

Evaluate

Selection = 6

The probability that the triangle and the octagon do noth have the same side is:

P= 6/21

The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule

P = 1 - 6/21

Evaluate the difference

P = (21 -6)/21

P = 15/21

Reduce fraction

P = 5/7

Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

Read more about probability at:

https://brainly.com/question/251701

Answer:

C.

Step-by-step explanation:

when you put it in a graphing calculator it would show the standard graph of an exponential decay function.