Find the volume of this Triangular Prism

Answer:

The solution to the given expression is -x³ + 9x + 6

Step-by-step explanation:

(9x - 4x² + 9) + (-x³ + 4x² - 3)

Since there is a positive sign in front of the second parentheses, then the terms inside will stay the same.

9x - 4x² + 9 - x³ + 4x² - 3

Group terms together that are alike. Also known as like terms.

-x³ + (-4x² + 4x²) + 9x + (9 - 3)'

Combine like terms.

-x³ + 9x + 6

Answer:

- [tex]x^{3\\}[/tex] + 9x + 6

Step-by-step explanation:

First, you need to combine like terms. Like terms, when dealing with exponents can be categorized by their powers.

hIn this case, 9x stands alone, because there is no other coefficient with the power of just x.

9x

Next, we can look at the -4x^2. The other similar coefficient is + 4x^2. We can combine both of those, which will equal out to 0.

Next, you have 9. It can be combined with -3, since none of them have an exponent attached. It will equal 6

9x + 6

We also have a -x^3 left over. There is no like term to combine with it, so we can leave it as is.

Our problem now looks like

9x + 6 - [tex]x^{3}[/tex]

You can rearrange them in the proper order, so it will look like,

- [tex]x^{3}[/tex] + 9x + 6.

And there you have it!

Step-by-step explanation:

Let the rate of boarding a dog and a cat be x and y respectively.

Now,

Further solving the two equations :

Y = $ 18.75

X = $ 28.25

Answer:

adjacent / hypotenuse cos x° = g divided by h is right

Step-by-step explanation:

If   [tex]tanx^{o} = \frac{6}{g}[/tex] and [tex]sinx^{o} = \frac{6}{h}[/tex]  then  [tex]cosx^{o} = \frac{g}{h}[/tex] .

By right angled triangle we have,

  Trigonometric ratios as

 Given  [tex]sinx^{o} = \frac{6}{h}[/tex]  and [tex]tanx^{o} = \frac{6}{g}[/tex]

              opposite = 6, hypotenuse = h, adjacent = g

                  [tex]cosx^{o}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]  [tex]=\frac{g}{h}[/tex]

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Answer: 9 to 4

Step-by-step explanation:

Using the grids you can count them to see what the width is.

The width is 9 units and the height is 4 units so the ration will be  9 to 4

The ratio of width of the rectangle to the height of the rectangle is 9 to 4.

A rectangle is a quadrilateral with four sides and four angles. It is a type of geometric shape characterized by its properties, including having opposite sides that are equal in length and all angles measuring 90 degrees (right angles).

In the given rectangle, there are 4 units or boxes in the height.

There are 9 units or boxes which makes width of the rectangle.

Hence, the ratio of width of the rectangle to the height of the rectangle is 9 to 4.

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Answer:

$24.35

Step-by-step explanation:

sale price⇒ total price-discount price

s.p=$24.60-25/100                              ∴25%⇒25/100

s.p⇒$2460/100-25/100                           ∴24.60⇒2460/100

s.p⇒$24.35

           ⇒$24.35

Answer: A

Step-by-step explanation:

There are 2 ways to solve this problem.

Solution 1:

Since we are given two equations, we set them equal to each other to find where they intersect, the solution.

3x+3=-2x+3                              [combine like terms]

5x=0                                         [divide both sides by 5]

x=0

Now that we have x=0, we can plug it into either equation to find the point of intersection.

y=3(0)+3

y=3

We know that the point of intersection is (0,3).

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Solution 2:

This way of solving the problem doesn't require any calculations. All it requires is an understanding of slope-intercept form equation. From the two equations given, we know that they are linear lines. Linear lines can only intersect once. Knowing this, we know that there can only be exactly one solution.

Step-by-step explanation:

given data:

total marbles = 75

red marble = 10

white marble = 30

blue marble = 20

orange marble = 15

solution:

a. Probability of drawing an orange or red

= 15/75 + 10/75

= 1/3

b. probability of not drawing a red or blue

= 1 - 20+10/ 75

= 3/5

c. Not blue

= 1 - p

= 1 - 20/75

= 11/5

d. Probability of drawing a white

= 30/75

= 2/5

e = red, white or blue

= 10/75 + 30/75 + 20/75

= 4/5

Answer:

Step-by-step explanation:4/5

Answer:  x= y

Step-by-step explanation:

3x + y =5x -y         Subtract 5x from both sides

-5x         -5x

-2x + y = -y         Now subtract  y from both sides

       -y    -y

-2x = -2y      Now divide both sides by -2

x = y

Answer:

false

Step-by-step explanation:

hope this helps✨

Answer:

y = (ln x) / (ln 6)

Step-by-step explanation:

1.  Exchange x and y:  x = 6^y

2. Solve for y:  Take the natural log of both sides:

                         ln x = y ln 6

             Then:  y = (ln x) / (ln 6)

Note:                 y = (log x) / (log 6) is also correct

Answer:

6:2 or 1:3

Step-by-step explanation:

Not really sure how to explain this, but I hoped this helped!

Answer:

x = -2i and 2i (or ±2i)

Step-by-step explanation:

Solve for x:

2x² - 4 = -12

2x² = -8

x² = -4

x = √(-4) = ±2i

Answer:

i tried to answer but the question made no sense

Step-by-step explanation:

Answer:

$26

Step-by-step explanation:

Divide 78 by 3, which will get you 26 dollars per bouquet!

Answer:

Cost per bouquet is $26.

Step-by-step explanation:

You take the total cost of all three bouquets and divide them by the number of bouquets. 78/3 = 26.

Answer:

Hey there!

3^-8(3^4)=3^-4

The second option is correct.

Hope this helps :)

Answer:

Option A

Step-by-step explanation:

z-score = (value - mean)/std = (65-62)/2.4 = 1.25

Answer: INDEPENDENT SAMPLES T-TEST

Step-by-step explanation:

Given that;

sample size n₁ = 40, sample size n₂ = 40

sample mean x₁ = 32.9, sample mean x₂ = 30.6

Standard deviation S₁ = 4.4, Standard deviation S₂ = 5.1

Now

NULL hypothesis H₀ : u₁ = u₂

and Alternative hypothesis H₁ : u₁ > u₂

Therefore based on the information provided above, the type of test that should be used to determine whether the level of nicotine are now lower than what they were 10 years ago is the INDEPENDENT SAMPLES T-TEST

Answer:

y = 5/4x -11

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b

where m is the slope and b is the y intercept

y = 5/4 x + b

Substitute the point into the line

-1 = 5/4(8) +b

-1 =10 +b

Subtract 10 from each side

-11 = b

y = 5/4x -11

Answer:

[tex]\huge \boxed{y=\frac{5}{4} x-11}[/tex]

Step-by-step explanation:

The slope-intercept form of a line is written as,

[tex]y=mx+b \\ \\ \\ \sf m= slope \\ \\ b=y -intercept[/tex]

The slope is given.

[tex]\displaystyle y=\frac{5}{4} x+b[/tex]

The line passes through the point (8, -1).

[tex]x=8 \\ \\ y=-1[/tex]

Plugging in the values.

[tex]\displaystyle -1=\frac{5}{4} (8)+b[/tex]

Solving for b or y-intercept of the line.

[tex]\displaystyle -1=\frac{40}{4} +b[/tex]

[tex]-1=10+b[/tex]

[tex]-11=b[/tex]

The y-intercept of the line is -11.

[tex]\displaystyle y=\frac{5}{4} x-11[/tex]

Answer:

Option (A)

Step-by-step explanation:

If a function 'f' is an odd function,

f(-x) = -f(x)

If a function 'f' is an even function,

f(-x) = f(x)

In this question given function is,

f(x) = [tex]\frac{220}{x^3}[/tex]

To check the given function is odd or even,

f(-x) = [tex]\frac{220}{(-x)^{3} }[/tex]

      = [tex]-\frac{200}{x^{3}}[/tex]

Therefore, from the definition of even and odd functions,

Function 'f' is an odd function.

Option (A) will be the correct option.

Answer:

30

Step-by-step explanation:

Formula is 1/2bh

6 times 10 = 60

60 divided by 2 equals 30

Answer:

⇒30 in²

Step-by-step explanation:

area ofΔ⇒1/2×length×width

              ⇒ 1/2×6 in×10 in

              ⇒1/2×60in²

               ⇒30 in²

Question:

At the beginning of the months, a consumer had $437.52 of in his bank account. During which he made deposits of $80, $256 and $217.14 and write checks of $115.98 and $108.90 - What balance left?

Answer:

The customer's balance is $765.78

Step-by-step explanation:

Given

Start Amount = $437.52

Deposits = $80, $256 and $217.14

Withdrawals (Checks) = $115.98 and $108.90

Required

Determine his balance

We start by calculating the total deposits made by the customer

[tex]Total\ Deposits = \$80 + \$256 + \$217.14[/tex]

[tex]Total\ Deposits = \$553.14[/tex]

Next, we calculate the total withdrawals (checks)

[tex]Total\ Withdrawals = \$115.98 + \$108.90[/tex]

[tex]Total\ Withdrawals = \$224.88[/tex]

At this point, we can now calculate the customer's balance as follows;

[tex]Balance =Start\ Amount + Total\ Deposits - Total\ Withdrawals[/tex]

[tex]Balance = \$437.52+ \$553.14 -\$224.88[/tex]

[tex]Balance = \$765.78[/tex]

Hence, the customer's balance is $765.78

The balance left in the consumer's account is $765.78.

The amount of money in the consumer's account increases with the deposits made and reduces when she writes checks.

The total value of the deposits have to be determined first.

Total value of the deposits = $256 + $217.14 + $80 = $553.14

The value of the checks written has to be determined

$115.98 + $108.90 = $224.88

Add the value of deposit, subtract the value of checks from the beginning balance

$437.52 + $553.14 - $224.88 = $765.78

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Answer:

Hey there!

a/3=-18

a=-54

Let me know if this helps :)

Answer:

The probability that a student owns a laptop or a desktop is 92%.

Step-by-step explanation:

We are given that the probability that an online student owns a laptop is 0.82 and the probability that a student owns a desktop is 0.65. The probability that a student owns both is 0.55 .

And we have to find the probability that a student owns a laptop or a desktop.

Let the probability that a student owns a laptop = P(L) = 0.82  

The probability that a student owns a desktop = P(D) = 0.65

The probability that a student owns both laptop and desktop = P(L [tex]\bigcap[/tex] D) = 0.55

Now, the probability that a student owns a laptop or a desktop is given by = P(L [tex]\bigcup[/tex] D)

         P(L [tex]\bigcup[/tex] D) = P(L) + P(D) - P(L [tex]\bigcap[/tex] D)

                        = 0.82 + 0.65 - 0.55

                        = 0.92 or 92%

So, the probability that a student owns a laptop or a desktop is 92%.

Answer:  10) 40°      11) 9.9

Step-by-step explanation:

[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

10) Given: a = 31,  b = 20, A = 84°

[tex]\dfrac{\sin 84^o}{31}=\dfrac{\sin B}{20}\\\\\\\dfrac{20\sin 84^o}{31}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{20\sin 84^o}{31}\bigg)=B\\\\\\39.9^o=B[/tex]

11) Given: a = 18,  A = 105°, B = 32°

[tex]\dfrac{\sin 105^o}{18}=\dfrac{\sin 32^o}{b}\\\\\\b=\dfrac{18\sin 32^o}{\sin 105^o}\\\\\\b=9.87[/tex]

Answer:

B. 40 ≤ e ≤ 100

Step-by-step explanation:

In a function, the domain values are the independent variables, and are always plotted on the x-axis, while the range values the dependent variables, which are always plotted on the y-axis on a graph.

From the graph given, it shows that f is a function of e. Which is, [tex] e(f) [/tex].

Therefore, the range of the function would be: B. 40 ≤ e ≤ 100

Answer:

a) Cost of a chicken shawarma wrap?

$10.99

b) Cost of one order of spiced potatoes?

$4.99

Step-by-step explanation:

Cost of a chicken sharwarma wrap = a

Cost of an order of spiced potatoes = b

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3a + 2b = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5a + 4b = $74.91 ................Equation 2

So we have:

3a + 2b = $42.95 .............Equation 1

5a + 4b = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of b in Equation 2

Equation 2 by coefficient of b in Equation 1

3a + 2b= $42.95 .............Equation 1 × 4

5a + 4b = $74.91 ................Equation 2 × 2

12a + 8b = 171.80..............Equation 3

10a + 8b = 149.82..............Equation 4

Subtract Equation 3 from Equation 4

2a = 21.98

a = 21.98/2

a = 10.99

Therefore, a = Cost of Chicken sharwarma wrap = $10.99

Subtitute 10.99 for 9in Equation 1

3a + 2b = $42.95 .............Equation 1

3(10.99) + 2b = 42.95

32.97 + 2b = 42.95

2b = 42.95 - 32.97

2b = 9.98

b = 9.98/2

b = 4.99

b = Cost of an order of spiced potatoes = $4.99

Hence,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

Widths are 2, 4, 5

Border or the perimeter of all these rectangles = 16

Perimeter of a rectangle

=> 2 ( L + W)

W = Width

L = Length

Area of a rectangle

=> L x W

First rectangle

Perimeter =  2(L+W)

=> 2 (L + 2) = 16

=> 2L + 4 = 16

=> 2L + 4 - 4 = 16 - 4

=> 2L = 12

=> 2L/2 = 12/2

=> L = 6

Length of the First Rectangle = 6

Area = L x W

=> 6 x 2 = 12

Area of the First Rectangle = 12

Second rectangle

Perimeter =  2( L + W)

=> 2 (L + 4) = 16

=> 2L + 8 = 16

=> 2L + 8 - 8 = 16 - 8

=> 2L = 8

=> 2L/2 = 8/4

=> L = 4

Length of the Second Rectangle = 4

Area = L x W

=> 4 x 4

=> 16

Area of the Second Rectangle = 16

Third Rectangle

Perimeter = 2 (L + W)

=> 2 (L + 5) = 16

=> 2L + 10 = 16

=> 2L + 10 - 10 = 16 - 10

=> 2L = 6

=> 2L / 2 = 6/2

=> L = 3

Length of the Third Rectangle = 3

Area = L x W

=> 3 x 5

=> 15

Area of the Third Rectangle = 15

To find which figure covers more spaces, we need to which figure has more area.

=> Rectangle 2 has the largest area = 16

Answer:

Step-by-step explanation:

Units = 30

Thousands = 2,000

Hundreds of Thousands = 400,000

Tens = 60

Hundreds = 100

HTHHTU

400,000

    2,000

       100

         60

         30

402,190

The value of each digit in a number is known as the place value. The number is 412,630.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

As per the given statement, the part of the numbers can be written as,

Now, summing up all, we will get the number,

Number = 30 + 2,000 + 400,000 + 600 + 10,000

              = 412,630

Hence, the number is 412,630.

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Answer:

5

Step-by-step explanation:

Hi,

f(12)= 12/2 -1 = 6 -1 = 5

Thanks

Answer:

5

Step-by-step explanation:

f(x) = x/2 - 1

Let x = 12

f(12) = 12/2  -1

       = 6-1

       = 5