Find the volume of the triangular prism as pictured below with a = 7 cm, b = 4
cm, c = 3 cm, and d = 8 cm. Do not include units in your answer.

Answer:

D

Step-by-step explanation:

I took Edgy 2021 test

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

answer is first option,,,

The coach can select 3 people to swim in the relay in 120 ways.

'In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.'

According to the given problem,

Number of players = 10

Number of people to be selected = 3

We know,

[tex]^{n}C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex] where, n = Total number of players

                                 r = Number of players to be selected

Number of ways to select 3 people out of 10 = [tex]^{10} C_{3}[/tex]

                                                                           = [tex]\frac{10!}{3!*7!}[/tex]

                                                                            = 120 ways

Hence, we can conclude, the coach can select 3 people out of 10 in 120 ways.

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First, we have to understand the slope-intercept form.

[tex] \large \boxed{y = mx + b}[/tex]

A linear function/equation has three forms and the slope-intercept is one of the form. It is also commonly used in Function topic while the other two forms are commonly used in Analytic Geometry.

In the slope-intercept form, the m-term represents the slope while b-term represents the y-intercept of a graph.

Which equation represents a linear function that has a slope of 5 and a y-intercept of -6.

As you notice the bold, italic and underlined words in the question that I quoted or rewrote. I've just explained that the slope is m-term and y-intercept is b-term.

Therefore, substitute m = 5 and b = -6 in the equation.

[tex] \large{y = mx + b \longrightarrow \bold{y = 5x + ( - 6)}} \\ \large \boxed{ \tt{ \purple{y = 5x - 6}}}[/tex]

I hope this helps! Let me know if you have any questions regarding the linear function, don't hestitate to ask. Good luck with your assignment and have a nice day!

Answer:

I can't understand number 6 sorry :(

7. The DO side is the hypotenuese8.

8. 107.62

Step-by-step explanation:

The formula for this is:

[tex]a^2+ b^2 = c^2[/tex]

66 × 66 = 4,356

85 × 85 = 7,225

4356 + 7225 = 11,581

[tex]\sqrt{11,581}[/tex] ≈ 107.62

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Have a great summer :)

Answer: conjecture

Step-by-step explanation:

A conjecture is a statement or an opinion based on logical reasoning or trivial facts that are always true. It does not require any proof.

Thus, A conjecture is a statement that you conclude to be true based on logical reasoning.

Note:

Answer:

Subtraction property of equality

Step-by-step explanation:

In the equation, 5 is subtracted from both the sides

Solution :

Sales Revenue

Sales                                                                                   $ 2,400,000

Less:

Sales discount                                $ 8,500

Sales returns and allowances       $ 41,000

                                                                                             $ 48,500

Net Sales                                                                              $ 2,350,500

Cost of goods sold                                                               $ 1,085,000

Gross profit                                                                            $ 1,265,500

Operating expense :

Salaries expenses                         $ 675,000

Advertising expenses                    $ 55,000

Depreciation expense                  $ 125,000

Freight expense                             $ 25000

Insurance expense                        $ 15,000

Total operating expenses                                                 $ 895,000

Operating income                                                              $ 370,500

Non operating income

Interest revenue                            $ 30,000

Rent revenue                                  $ 24,000

                                                                                           $ 54,000

Non Operating expenses  :

Interest expense                                                                 $ 70,000

Income before income tax                                                 $ 354,500

Income tax expense                                                            $ 70,000

Net income                                                                            $ 284,500

Answer:

(a) 3

(b) 3+5÷2 =4

Step-by-step explanation:

(a) you look at which number appears the most on the data in this case it's 3 it appeares three times in the data compared to other numbers.

(b) arrange the data in ascending order divide the data equally to find the number in the middle if the are two numbers you simply add them and divide by 2 to get your median.

Answer:

[tex] y = 6 \sqrt{3} \: units[/tex]

Step-by-step explanation:

In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.

By geometric mean theorem:

Length of the perpendicular

[tex] =\sqrt{9\times 3}[/tex]

[tex] =\sqrt{27}\: units [/tex]

Next, by Pythagoras theorem:

[tex] {y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units[/tex]

Answer:

the answer is c

Step-by-step explanation:

juice would be 1 variable and magazines would be another. u would put each variable next the things that they represent, so j for juice would be put with 3.25 because that's how much 1 bottle costs. The variable m would be with 8.5 because that's how much the magazines cost.

Answer:

f⁻¹(x) = (x+1)/2

Step-by-step explanation:

Given the function f(x) = 2x - 1, we are to find its inverse;

Let y = f(x)

y = 2x - 1

Replace y with x

x = 2y - 1

Make y the subject of the formula

2y = x + 1

Divide both sides by 2

2y/2 = (x+1)/2

y = (x+1)/2

Replace y with f⁻¹(x)

f⁻¹(x) = (x+1)/2

Hence the required inverse is (x+1)/2

Answer:

---

Step-by-step explanation:

Start at -3. Then subtract 5 from it(or go backwards 5).

---

hope it helps

Answer:

The machine can make 24 bottles of soda per minute

Step-by-step explanation:

Looking at the graph of the relationship, we can see that the number of bottles per minute simply represent the slope of the line

Thus, by calculating the slope using the given points, we can have the number of bottles per minute

We have the formula as;

m = (y2-y1)/(x2-x1)

(x1,y1) = (4,96)

(x2,y2) = (6,144)

m = (144-96)/(6-4) = 48/2 = 24

Answer:

Perimeter = 6s + 9 units

Step-by-step explanation:

Perimeter = 2s + 4 + 4s + 2 + 3

                = 2s + 4s + 4 +  2 + 3

                = 6s + 9 units

Answer:

b=77

c = 103

Step-by-step explanation:

b and 77 are vertical angles and vertical angles are equal

b= 77

c and 77 are supplemental angles and supplemental angles add to 180

c+77 =180

c = 180-77

c =103

[tex] \large \sf \star \: \blue{Answer} \: \star[/tex]

[tex] \small \sf \mapsto\: b = \fbox{77 °} [/tex]

[tex] \small \sf \mapsto \: c = \fbox{ 103 °}[/tex]

Here,

And,

So, b + c = 180 °

77° + c = 180 ° ... { b = 77 -( vertical angle )}

subtract 77 from each sides

77 - 77 + c = 180 ° - 77 °

c = 103 °

Answer:

yes this is true helpful answer

Answer:

Decreasing linear

Step-by-step explanation:

An arithmetic sequence decreases by a set amount every time through subtraction, so that means it's linear

Answer:

x² + 7x + 10 = 0

Subtract 10 from both sides

x² + 7x = -10

Use half the x coefficent (7/2) as the complete the square term

(x + 7/2)² = -10 + (7/2)²

   note: the number added to "complete the square" is (7/2)² = 49/4

(x + 7/2)² = -10 + 49/4

(x + 7/2)² = 9/4

Take the square root of both sides

x + 7/2 = ±3/2

Subtract 7/2 from both sides

x = -7/2 ± 3/2

x = {-5, -2}

=======================================================

There are a few ways to do this.

One way is to slice horizontally to break up the L shape into two separate rectangular blocks. Refer to the diagram below to see what I mean.

The block on top has length 80-60 = 20 mm (horizontal), width 10 mm, and height 40 mm.

The volume of this block on top is L*W*H = 20*10*40 = 8000 mm^3, where mm^3 means "cubic millimeters"

The block down below has a length of 80 mm, width of 10 mm, and height of 60-40 = 20 mm (vertical). Its volume is L*W*H = 80*10*20 = 16000 mm^3

Add up the two volumes to get the overall volume: 8000+16000 = 24000 mm^3

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

Another approach you could take is to do a vertical slice to form two separate blocks. You would follow similar steps mentioned in the section above to find the two volumes, and add up the smaller pieces.

Yet another way to find the answer is to find the area of the L shape, and then multiply that by the depth of 10 mm.

answer is :59/3-2x^10/3

Step-by-step explanation:

Answer:

0.01666666666

Answer:

60

Step-by-step explanation:

if you flip it around from "0.15 divided by 9" and turn it into "9 divided by 0.15" you will the answer 60.

(hopes this helps )

Answer:

3570

Step-by-step explanation:

the current monthly rent is 4200.

now, decreasing it by 15% means to reduce it, to subtract 15% from it.

4200 = 100%

42 = 1%

15% = 42 × 15 = 630

so, the new rent is 4200 - 630 = 3570

Answer:

Total distance cover by car = 253.45 km (Approx.)

Step-by-step explanation:

Given:

Speed of car = 45 km/h for 3¾ hour

Distance cover in next 2 hour = 84.7 km

Find:

Total distance cover by car

Computation:

Distance = Speed x time

Distance cover by car = 45 x 3¾

Distance cover by car = 168.75 km

Total distance cover by car = Distance cover by car + Distance cover in next 2 hour

Total distance cover by car = 168.75 + 84.7

Total distance cover by car = 253.45 km (Approx.)

Your answer would be y=4sin(x+1)-2. That would be A.

The required function is y = 3 sin (x -2) + 1.

A relation between a collection of inputs and outputs is known as a function.

A mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).

From the graph that is provided to us we observe that,

when x=2

then f(x)=1

Here, from the function y = 3 sin (x -2) + 1

So, when x=2

we get: y=1

Also,  all the other points are satisfied.

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Answer:

with?

Step-by-step explanation:

Answer:

scale factor = 2

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, fig. B to fig. A

Consider the horizontal lengths, then

scale factor = [tex]\frac{8}{4}[/tex] = 2