Determine the lateral area and surface area of the given prism. Round answers to the nearest whole number.

Answer:

opposite=8.402402490459  ,adjacent is already given=12, hypotenuse=14.64929507

Step-by-step explanation:

to do this you will have to use the law of sines. the first thing you need to do is solve for the unknown angle by subtracting 90+35 from 180. so you get the equation 180-(90+35)=55. now that you know all your angles, you can use the law of sines to solve for the unknown sides. the law of sines state that a/sin(A)=b/sin(B). if you substitute the values of 12 and 55 into the equation, since you know those sides, you can then find a ration that you can use to find the other sides, 12/sin(55)=b/sin(B), which is equal to, 14.649... Next you pick whichever side you want to solve for next, and plug in its opposite angle (i would solve for the other leg, because then you can use pythagorean theorem to solve for the hypotenuse, so i will demonstrate that way) plug in the angle 35, since it is opposite the leg and then finish for the variable, 14.649...=b/sin(35). once you have the sin, you can multiply it by the 14.649 to get your side, 14.649...*.5736...=8.402...=b. now you have your two legs, so you can use a^2+b^2=c^2 to solve for the hypotenuse. once you plug in your values it should look like this, 12^2+8.402...^2=c^2. which simplifies down to 214.602...=c^2. so you take the square root of both sides to find c, which equals 14.649. you can check that by seeing if 14.649 is bigger then the other two sides, which it is. This number should look familiar because it was the ratio we got when we divided 12 by the sin(55). the reason that happened is because the sin(90) is 1, the 14.649*1=14.649.

If you have any questions, leave them in the comments and will try to answer them, if this helped, pls give brainliest.

Answer:

range = 9

Step-by-step explanation:

The range is the difference between the largest and smallest values

largest value = 12

smallest value = 3

range = 12 - 3 = 9

Answer:12-3=9

Step-by-step explanation:To find the range,you have to subtract the highest number and the lowest number which in this case the highest number is 12 and the lowest number is 3 so the answer is 9.

Answer:

[tex]4m ^{2} = 4 \times 5 \times 5 = 100[/tex]

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step explanation:

Given

See attachment for M and N

Required

Which maps M to N

The coordinates of the radius of the circles are:

[tex]M = (5,5)[/tex]

[tex]N = (5,-5)[/tex]

And the radius of circles are:

[tex]r_M=2[/tex]

[tex]r_N=3[/tex]

The first transformation from M to M' is:

- Reflect across the x-axis

The rule is:

[tex](x,y) \to (x,-y)[/tex]

[tex]M(5,5) \to M'(5,-5)[/tex]

At this point, M' and N now have the same center but different radius.

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

[tex]k =\frac{r_N}{r_M}[/tex]

[tex]k =\frac{3}{2}[/tex]

At this point, M has been completely mapped to N.

Answer:

C

Step-by-step explanation:

The transitive property states that a line is congruent to itself.

Answer:

The answer is, (C) transitive property.

Step-by-step explanation:

The (interior) bisector of an angle, also called the internal angle bisector  is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter. , which has trilinear coordinates.

Then, For angle bisector construction, a statement column proof is given.

Justification for Statement.

CPCTC and MBP have the same angle.

NBP angle

Since SSS established congruence for the two triangles in the preceding sentence,

The next step is to ensure that matching angles are identical and that congruent triangle portions are congruent.

A line is congruent to itself if it has the transitive attribute.

To know more angle bisector here, https://brainly.com/question/24334771

#SPJ2

Answer:

960 cm³ I think it may be correct

I think the first one c and the second one a

Answer:

open bracket

7j - 35 = 14

7j = 14 + 35

7j = 49

divide thru by 7

7j / 7 = 49 / 7

j = 7

Answer: 114

Step-by-step explanation:

Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114

Answer:95

Step-by-step explanation:

Answer: 60 holes

Step-by-step explanation:

Nate made par or better 34 out of 85 holes. You need to use this to find the rate at which he makes par or better holes:

= 34 / 85 * 100%

= 40%

40% of the time he makes par or better holes.

If there are 150 holes left, he will make par or better of:

= 40% * 150

= 60 holes

Answer:

[tex]10f - 5-5f +2 =5f -3= -3+5f[/tex]

last option

Answer:

C

Step-by-step explanation:

If we solve 10f-5f+8+69+4, We get 5f+81 (put in comments if you want a step by step explanation on how i solved this).  

Let's try to solve each of the options.  

A) 15f + 14g + 4  

It would not be option A because there isn't a variable such as g in the expression.  

B) 15f + 8 + 10g

C) 5f + 69 + 12

5f+ 81  

This one is correct because the expression also equals 5f+81  

D) 5f + 149 +4​

5f+ 153  

D would be wrong as well

Hope this helps! <3

Answer:

∠A= 80°

Step-by-step explanation:

if they are supplementary then put them equal to 180

7x + 3 +7x + 23 = 180

14x + 26 = 180

14x = 154

x= 11

now plug in

7(11)+3

77+3= 80

Answer:

A) One Solution

Step-by-step explanation:

3x + 4 = -x

4 = -4x

x = -1

y = 3(-1)+4

y = 1

One Solution

Answer:

30%

Step-by-step explanation:

Think of this as converting a fraction. 28/40 to x/100. You do this because in the situation, 40 is 100 percent of the price. So 28 is x percent of 100.

You multiply 40 by 2.5 to get to 100, so multiply 28 by the same number to get x. 28 * 2.5 = 70.

So 28 is 70 percent of 40. But the question is asking by what percentage it is discounted. If it's now selling for 70%, it has been discounted 30%. So the answer is 30%

Answer:

14.379

Step-by-step explanation:

1. Line up from left to right

2. Make sure that the decimals are lined up

3. Add the thousandths and hundredths with 0

4. Add 3 in the tenths place

5. Add up 9 and 5 to make 14

*IF YOU DID THE STEPS RIGHT, THEN YOU SHOULD HAVE 14.379 AS YOUR ANSWER*

Answer:

9.079

+5.300

_______

14.379

Step-by-step explanation:

Just line the decimals up and add zeros for 5.3 to 5.300 because you can't do 9.079

   +5.3   because your decimal will be in the wrong spot and your answer will come out wrong

Answer:

ok hiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

Option C, No real solutions

Hope this helps!

Answer:

[tex]P(2)=(32,46)[/tex]

Step-by-step explanation:

From the question we are told that:

Height of robot [tex]h=12 inches[/tex]

Weight of robot [tex]W=4[/tex]

Start position [tex]P(1)=(4,4)[/tex]

Per minute distance [tex]d=(4,6)[/tex]

Total time [tex]T=7min[/tex]

Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by

 [tex]d_T=d*T[/tex]

 [tex]d_T=(4.6)*7[/tex]

 [tex]d_T=(28,42)[/tex]

Generally the position of the robot after 7 minutes is  mathematically given by

 [tex]P(2)=P(1)+d_T[/tex]

 [tex]P(2)=(4,4)+(28,42)[/tex]

 [tex]P(2)=(32,46)[/tex]

Therefore the position of the robot after 7 minutes is

 [tex]P(2)=(32,46)[/tex]

Step-by-step explanation:

idek but Goodluck and I hope you figure it our bye.

Answer:

x=16√3 units

y=8√3 units

z=24 units

Step-by-step explanation:

z=(24√2)/√2=24 which means the height is also 24 following 45-45-90 triangle rules

y=24/√3=24√3/3=8√3 (remember 30-60-90 triangles rules and to rationalize the denominator)

x=2y=2(8√3)=16√3 (remember 30-60-90 triangle rules)

Answer:

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Step-by-step explanation:ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Answer:

24

Step-by-step explanation:

8 correct for every 2 wrong

multiply both sides by 3

24 correct and 6 wrong

which adds up to 30

9514 1404 393

Answer:

  ±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

  |x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

  sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

  A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

  A·cos(c) = 3   and   A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

  (A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

  x = A·sin(θ +c) . . . . for some angle c

  x = (√58)sin(θ +c)

This has the bounds ±√58.

Answer:

5.x^8.y^3

Step-by-step explanation:

15.x^10.y^5.z^2 ÷ 3.x^2.y^2.z^2

= 15/3. x^(10-2). y^(5-2). z^(2-2)

= 5.x^8.y^3.z^0

= 5.x^8.y^3

[tex]\\ \rm\hookrightarrow \dfrac{15x^{10}y^5z^2}{3x^2y^2z^2}[/tex]

[tex]\\ \rm\hookrightarrow 5x^{10-2}y^{5-2}z^{2-2}[/tex]

[tex]\\ \rm\hookrightarrow 5x^8y^3[/tex]

Option B has type error or none of the above

Answer:

А.The system has two solutions, but only one is viable because the other results in a negative width.

Step-by-step explanation:

Given

Let:

[tex]L_A \to[/tex] length of play area A

[tex]W_A \to[/tex] width of play area A

[tex]L_B \to[/tex] length of play area B

[tex]W_B \to[/tex] width of play area B

[tex]x \to[/tex] Area of A

[tex]y \to[/tex] Area of B

From the question, we have the following:

[tex]L_A = 1 + 4W_A[/tex]

[tex]W_B = 2 + W_A[/tex]

[tex]L_B = 2 + 3W_B[/tex]

[tex]x = y[/tex]

The area of A is:

[tex]x = L_A * W_A[/tex]

This gives:

[tex]x = (1 + 4W_A) * W_A[/tex]

Open bracket

[tex]x = W_A + 4W_A^2[/tex]

The area of B is:

[tex]y = L_B * W_B[/tex]

[tex]y = (2 + 3W_B) * ( 2 + W_A)[/tex]

Substitute: [tex]W_B = 2 + W_A[/tex]

[tex]y = (2 + 3(2 + W_A)) * ( 2 + W_A)[/tex]

Open brackets

[tex]y = (2 + 6 + 3W_A) * ( 2 + W_A)[/tex]

[tex]y = (8 + 3W_A) * ( 2 + W_A)[/tex]

Expand

[tex]y = 16 + 8W_A + 6W_A + 3W_A^2[/tex]

[tex]y = 16 + 14W_A + 3W_A^2[/tex]

We have that:

[tex]x = y[/tex]

This gives:

[tex]W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2[/tex]

Collect like terms

[tex]4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0[/tex]

[tex]W_A^2 -13W_A - 16 =0[/tex]

Using quadratic calculator, we have:

[tex]W_A = -14.1[/tex] or [tex]W = 1.13[/tex] --- approximated

But the width can not be negative; So:

[tex]W = 1.19[/tex]

Answer:x = 1.2

Step-by-step explanation:

Answer:

[tex]{\huge\pink{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]

[tex]6x + 1 = x - 5 \\ 6x - x = - 5 - 1 \\ 5x = - 6 \\ x = \frac{ - 6}{5} \\ x = - 1.2[/tex]

Answer:

Divide the area by pi. Then, square root the answer.

Step-by-step explanation:

Area of a cirlce= pi r^2

Answer:

You have to divide by pi (3.14) APROXIMATELY and then divide what you get by the square root.

Answer:

y=-3x-4

Step-by-step explanation:

i solved it by the two points