EFGH is a square with diagonals EG and HF that intersects at O. What is the measure of m angle HOG

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:

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

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:

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:

[tex]y = 7.3[/tex]

Step-by-step explanation:

Answer:

3x-1

Step-by-step explanation:

Let the area of the mint section = Length * Width

Given

Area = 6x²-2x

Length

Required

Width

A = LW

Substitute

6x²-2x = 2x(W)

2x(3x-1) = 2xW

Divide both sides by 2x

2x(3x-1)/2x = 2xW/2x

3x-1 = W

W = 3x-1

Hence the width of the mint section is 3x-1

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:

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:

Multiplication

Step-by-step explanation:

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

Answer:

78qt= 19.5 U.S. gallons

Step-by-step explanation:

Answer: £45

Step-by-step explanation:

First find the amount of simple interest in on year:

= Amount * simple interest rate

= 300 * 5%

= £15

Now that you have the annual interest, the 3 year interest is:

= 15 * 3 years

= £45

Answer:

y=180-63-63/2=27degree...in triangle mln

x=180-27-63=90....in triangle mon

Answer:

y=27, x=80

Step-by-step explanation:

∠N= 63°(angles opposite to equal sides)

2∠y+63+63=180°(angle sum property)

2∠y=54°

∠y=27°

27°+63°+∠x=180°(ASP)

∠x=180°-90°=90°

Hope it helps, mark me brainliest pls

9514 1404 393

Answer:

  vertex: (2, -3.2)

  axis of symmetry: x = 2

  zeros: x=0, x=4

  formula for axis of symmetry:

Step-by-step explanation:

a) The vertex x-coordinate is halfway between the zeros, so is x = (0+4)/2 = 2. It is where the graph has a turning point.

The vertex y-coordinate is the low point of this graph. It is not on a grid line, so we can only guess at its value. I choose to call it -3.2.

The vertex is (2, -3.2).

__

b) The axis of symmetry is the vertical line through the vertex. The constant in its equation is the x-coordinate of the vertex:

  x = 2

__

c) The zeros of the function are where the function crosses the x-axis. These are marked on the graph with red dots. The zeros are x=0 and x=4.

__

d) When the quadratic is written in standard form, ax^2 +bx +c, the equation of the axis of symmetry is ...

  x = -b/(2a) . . . . . perhaps this is the formula you're being asked for (?)

When there is no equation, the axis of symmetry can be found from the graph a couple of ways. One is to identify the x-coordinate of the vertex.

  x = <x-coordinate of the vertex>

Another is to average the zeros, since they are symmetrical about the axis of symmetry.

  x = average of zeros = (z1 +z2)/2

If the quadratic is written in vertex form, the vertex coordinate is the constant in the equation for the axis of symmetry.

  y = a(x -h)^2 +k . . . . . quadratic with vertex (h, k)

  x = h . . . . . . equation of axis of symmetry

Answer:

Length of fencing: 4, 6, 7, 9, 10

Cost: 36, 54, 63, 81, 90

Step-by-step explanation: I hope this gave you your answer!!

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:

ANSWER IS x = 2.6

[tex]5x + 13 = \: 2.6\times 6[/tex]

Step-by-step explanation:

[tex]5x + 13 \\ x = 13 \div 5 \\ x = 2.6[/tex]

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:

2.35

Step-by-step explanation:

Answer:

2.35

Step-by-step explanation:

move decimal point left 2

Answer:

I only know where da first one goes lol

Step-by-step explanation:

8.333333333333.... can be denoted using a fraction, therefore it's a rational number. It turns out that irrational numbers cannot be denoted using simple fractions.

Answer:

y=2x

Step-by-step explanation:

as y goes up 2 x goes up 1

Answer:

341

Step-by-step explanation:

l=

sin52/320sin123

​ ≈340.572≈341

Answer:

8 tickets

Step-by-step explanation:

To find how many she can buy, divide 36 by 4.5

36/4.5

= 8

So, Mai can buy 8 movie tickets

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:

52.8

Step-by-step explanation: