What function is
graphed below?

That is a question about spatial geometry.

In our problem, we have to calculate lateral surface area of a triangular prism. Let's see how to solve this.

A triangular prism has 5 faces: 3 equals rectangles and 2 equals triangles. If we can find a way to calculate those areas, we can solve the problem.

The first thing that we should note is that we know the dimensions of the rectangular faces. The dimesions of the rectangular are 5cm and 8cm. To calculate the are of a rectangle, we multiplicate the dimensios of it. Therefore, each rectangle (in our problem) has [tex]5 \times 8 = 40cm^2[/tex] of area. There are 3 rectangles, so, the sum of the 3 rectangular area is [tex]40 + 40 + 40 = 120cm^2[/tex].

Now, we need to know the area of the triangular areas. To calculate the area of a triangle, we need to know the value of the base and the value of the height.

In the image, we know the value of the base, but we do not know the value of the height. To calculate the height, we can use the Pythagorean Theorem because we have a right triangle. (Please find attached the document.)

The Pythagorean theorem says that:

[tex]\boxed{a^2 = b^2 + c^2}[/tex]

a is the hypotenuse and b and c are cathetus.

In this right triangle, the value of the hypotenuse is 5cm and the value of one cathetus is the half of 6cm (that is 3cm). Let's replace the values in the expression:

[tex]a^2=b^2+c^2\\5^2= 3^2 +c^2\\25 = 9 + c^2\\c^2 = 25 - 9\\c^2 = 16\\c = \sqrt{16} \\c = 4cm[/tex]

Now, we know the bases and the height of the triangular areas. To calculate the area of a triangle, we multiply the base and the height and we divided the result by 2. See the expression:

[tex]\boxed{A_t=\frac{b\times h} {2}}[/tex]

b is the base and h is the height. Let's replace the values in the expression:

[tex]A_t = \frac{b\times h}{2} \\A_t = \frac{6\times4}{2} \\A_t = \frac{24}{2} \\A_t = 12cm^2[/tex]

So, each triangular area has 12cm² of area. Therefore, the sum of the triangular areas is [tex]12 + 12 = 24cm^2[/tex].

Finally, we know that the sum of the rectangular area is 120cm², and the sum of the triangular area is 24cm², so, the lateral surface area is [tex]120 + 24 = 144cm^2[/tex].

In other words, they didn't choose the correct answer because the correct answer is J) 144 cm².

I hope I've helped. :D

Enjoy your studies. \o/

Answer:

Step-by-step explanation:

5 km/h or 6 km/h

Step-by-step explanation:

Let the speed of the boat be x

Speed against the current in the river is x - 2

Time in the river:

6/(x - 2)

Time in the lake:

15/x

The difference:

6/(x - 2) = 15/x - 1

Solve for x to find the speed of the boat

Multiply both sides by x(x - 2) to clear the fraction:

6x = 15(x - 2) - x(x - 2)

6x = 15x - 30 - x² + 2x

x² - 11x + 30 = 0

(x - 5)(x - 6) =0

x -5 = 0, x - 6 = 0

x = 5 km/h, x = 6 km/h

Answer:

Step-by-step explanation:

16c(7g/4c)=28g

Answer:

The volume of the metal is:

[tex]V_{t}=548\: cm^{3}[/tex]

Step-by-step explanation:

First, let's find the volume of the front face of the square:

[tex]V_{1}=12*7*1=84\: cm^{3}[/tex]

The back face is the same, so we have:  

[tex]V_{2}=84\: cm^{3}[/tex]

The volume of the side faces will be:

[tex]V_{3}=7*10*1=70\: cm^{3}[/tex]

[tex]V_{4}=70\: cm^{3}[/tex]

And finally, the volume of the top and bottom side faces of the box will be:

[tex]V_{5}=12*10*1=120\: cm^{3}[/tex]

[tex]V_{6}=120\: cm^{3}[/tex]

The total volume of the metal will be:

[tex]V_{t}=V_{1}+V_{2}+V_{3}+V_{4}+V_{5}+V_{6}[/tex]

[tex]V_{t}=2(84)+2(70)+2(120)[/tex]

[tex]V_{t}=548\: cm^{3}[/tex]

I hope it helps you!

Answer:

The answer is 76.97

Step-by-step explanation:

The formula that I used

V=πr^2h

Volume = π·3.52·2 ≈ 76.96902

Answer:76.93

Step-by-step explanation:

Answer:

341

Step-by-step explanation:

l=

sin52/320sin123

​ ≈340.572≈341

Answer:

Yep your very smart

Step-by-step explanation:

Answer:

yep

Step-by-step explanation:

since a triangle's total angle is 180 degrees,

(5x + 18) + (3x + 2) + (x + 16) = 180

9x + 36 = 180

9x = 144

x = 16

m<D = (3x + 2)

m<D = 3(16) + 2

m<D = 48 + 2

m<D = 50 (your answer)

Answer:

B and D

Step-by-step explanation:

a. 5t+4t =9t

b. t+5+4= t+9

c. 9t

d. 4×5×t= 20t

e. t(5+4)- do the inside the parenthesis first. =9t

the answer would me B and A because the answer isn't 9t so it would be those!! also the boxes on the right you multiply t×5 and t×4 and that would be 5t + 4t =9t

Answer:

158cm squared

Step-by-step explanation:

Area of triangle=1/2×b×h

Area of rectangular base of prism=l×w

Area of 2 rectangular sides of the prism=l×w

So Total surface area= 1/2×6×5×2)+(8×6)+(8×5×2)=158cm squared

Answer:

[tex]y = 7.3[/tex]

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

this isnt my answer it is someone named baylee in the comments, i tried it and it was right .

As per the given data, the slope-intercept form of the first equation is y = x - 5, which is represented by option A.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

The equation that represents the first equation written in slope-intercept form is:

y = x - 5

To convert the equation 5x - 2y = 10 into slope-intercept form, we need to isolate y on one side of the equation.

Starting with 5x - 2y = 10:

Subtract 5x from both sides: -2y = -5x + 10

Divide both sides by -2: y = (5/2)x - 5

Now, we can simplify the expression (5/2)x - 5 to the form y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the correct option is A.

For more details regarding slope-intercept, visit:

https://brainly.com/question/30216543

#SPJ7

Answer:

78qt= 19.5 U.S. gallons

Step-by-step explanation:

The answer is [tex] 5 \sqrt{3} [/tex]

[tex] \frac{ {m}^{2} }{15} - 3 = 2[/tex]

[tex] \frac{ {m}^{2} }{15} = 2 + 3[/tex]

[tex] \frac{ {m}^{2} }{15} = 5[/tex]

[tex] {m}^{2} = 5 \times 15[/tex]

[tex] {m}^{2} = 75[/tex]

[tex]m = \sqrt{75} [/tex]

[tex]m = \sqrt{25 \times 3} [/tex]

[tex]m = \sqrt{25} \times \sqrt{3} [/tex]

[tex]m = 5 \sqrt{3} [/tex]

CMIIW

Answer:

17/6

Step-by-step explanation:

Answer:

2 5/6

Step-by-step explanation:

4 1/3= 13/3

1 1/2= 3/2

lowest common denominator of 3 and 2 is 6 so:

13/3*2/2=26/6

3/2*3/3=9/6

26/6-9/6=17/6

17/6= 2 5/6

Answer:

-8/16 or -1/2

Step-by-step explanation:

Hi, use the slope-intercept formula (rise over run)

(y₂-y₁)/(x2-x1)

(-9--1)/(9--7)

(-9+1)/(9+7)

-8/16

-1/2

Answer: It is false

Step-by-step explanation:

2/4x3/5=3.14

1/2 x 3/5=3.14

3/10=3.14

0.3=3.14

This is false

Answer:

Hey mat its me haylee id k if you remember me cuz its been a long while and im sorry about that but id like to talk again sometime soon.

Step-by-step explanation:

Answer:

Oi tudo bem?

meu nome é Ana Kesia, e qual é o seu nome também?

Desculpe-me eu Nn consegui responder sua pergunta.

Mas mesmo assim, agradeço pelos pontos estava precisando.

tchau, tenha uma Ótima tarde!

Bons estudos nas suas atividades! ❤♥

Answer:

The months in which the income was greater than the expenses are;

June, July, and August

Step-by-step explanation:

The recorded income and expenses for the bakery are given as follows;

[tex]\begin{array}{cccc}Month&Income \ (\$)&Expense \ (\$)& Difference \ (\$)\\January&1,606&1,664.75 & (58.75)\\February&1,378&1,432.62 & (54.62)\\March&1,225&1,225.00&0.00\\June&2,381&1,995.55&385.45\\July&2,391&2,083.68&307.32\\August&2,187&1,802.63&384.37\end{array}[/tex]

From the difference values obtained in the table above, the months in which the income was greater than the expenses are;

June, July, and August

Answer:

2.35

Step-by-step explanation:

Answer:

2.35

Step-by-step explanation:

move decimal point left 2

Answer:

The group of line segments that could form the other 2 sides of the triangle is;

B. 7 cm and 8 cm

Step-by-step explanation:

The triangle inequality theorem states that the sum of the length of any two sides of a triangle is larger than the length of the third side

The given parameter of the triangle is that the length of the longest side of the triangle = 10 cm

Let, 'a', and 'b', represent the remaining two sides of the triangle

Therefore, by the triangle inequality theorem, we have;

(1) a + b > 10 cm

(2) 10 cm + a > b

(3) 10 cm + b > a

The option that satisfies condition (1), (2), and (3) are options 'B' and 'D', for which we have;

7 cm + 8 cm = 15 cm > 10 cm

10 cm + 7 cm = 17 cm > 8 cm

10 cm + 8 cm = 18 cm > 7 cm

9 cm + 10 cm = 19 cm > 10 cm

10 cm + 9 cm = 19 cm > 10 cm

10 cm + 10 cm = 20 cm > 9 cm

Therefore, the possible combination of the other two sides are;

7 cm and 8 cm or 9 cm and 10 cm

However, a side of option 'D' is 10 cm and given that the longest side of the triangle = 10 cm, the length of each of the other two side should be less than 10 cm and the only given possible combination of the other two side should be option 'B', 7 cm and 8 cm.

Answer:

B 7cm and 8cm

Step-by-step explanation:

Answer:

what is the question? please write a question.

Based on how the graph turns out 15 years into the business is when the company made its minimal profit.

Answer:

Multiplication

Step-by-step explanation:

7y means 7 times the value of y. So 7 times y = 7y