What is the surface area of the right rectangular prism shown?

Answer:

x² (x^n + 1)

Step-by-step explanation:

factor x^(n+2) + x²

= x^(n+2) + x²

= x^n • x² + x² (using law of indices)

= x²(x^n + 1)

Answer:

7, 10, 15, 22, .... 106

3, 12, 27, 48, .... 300

Step-by-step explanation:

Plug n as 1, 2, 3, 4, and 10 to find the terms.

(a)

1² + 6

1 + 6 = 7

2² + 6

4 + 6 = 10

3² + 6

9 + 6 = 15

4² + 6

16 + 6 = 22

10² + 6

100 + 6 = 106

(b)

3(1)²

3(1) = 3

3(2)²

3(4) = 12

3(3)²

3(9) = 27

3(4)²

3(16) = 48

3(10)²

3(100) = 300

Answer:

a) n²+6

U1 = 1²+6 = 1+6=7

U2= 2²+6 = 4+6 = 10

U3= 3³+6= 9+6= 15

U4= 4²+6= 16+6 = 22

U10= 10²+6 = 100+6= 106

So= 7, 10, 15, 22,... 106

b) 3n²

U1= 3(1)²= 3(1)= 3

U2= 3(2)²= 3(4) = 12

U3= 3(3)²= 3(9)= 27

U4= 3(4)²= 3(16)= 48

U10= 3(10)²= 3(100)= 300

So= 3, 12, 27, 48,..., 300

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

Work Shown:

T = tens digit of the original number

U = units digit of the original number

U+T = 10 since the digits add to 10. Solve for U to get U = 10-T

10T+U = original number

10U+T = new number where digits are reversed

-----------

new number = (old number) + 36

10U+T = (10T+U)+36

10U+T = 10T+U+36

10(10-T)+T = 10T+10-T+36 ... plug in U = 10-T

100-10T+T = 10T+10-T+36

-9T+100 = 9T+46

100-46 = 9T+9T

54 = 18T

18T = 54

T = 54/18

T = 3 is the tens digit of the original number

U = 10-T

U = 10-3

U = 7 is the units digit of the original number

10T+U = 10*3+7 = 30+7 = 37 is the original number

73 is the reversed number.

73-37 = 36 is the difference, showing that 37 increased by 36 leads to 73. The answer is confirmed.

Answer:

37

Step-by-step explanation:

Answer:

4)12(n+4)

    =12n+48

Step-by-step explanation:

Answer:

4) 12(n + 4) = 12n + 48

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rigid motions are the transformations that produce congruent images.

There are three main kinds of rigid motions  :

But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.

So, the options having dilation and term "stretch" cannot produce congruent figures.

Hence, the correct options are :

Answer:

461.02

Step-by-step explanation:

2 × ( (12.3 × 4.3) + (12.3 × 10.7) + (4.3 × 10.7)) = 461.02 m^2

Answer:

461.02 M^2

Step-by-step explanation:

A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

SA = 2lw+2lh+2hw

2LW = 105.78 M^2        (  52.89* 2 )

L= 12.3 M^2 , W = 4.3 M^2

LW = 52.89 M^2

2LH =  263.22       ( 131.61 * 2 )

L = 12.3 M^2 , H = 10.7 M^2

LH = 131.61 M^2

2HW = 92.02       ( 46.01 * 2 )

H = 10.7 M^2 , W = 4.3 M^2

HW = 46.01 M^2

SA = 2lw+2lh+2hw

SA = 105.78 M^2+ 263.22 M^2  + 92.02 M^2

SA = 461.02 M^2

Answer:

16a^2+5

Step-by-step explanation:

Answer:

39.5

Step-by-step explanation:

Let's figure out the equations of l and m first.

For line l, we see that the coordinates (0, 5) and (3, 0) are on the line. The equation of a line is y = mx + b where m is the slope and b is the y-intercept.

We can find the slope, which is the difference in the y-coordinates divided by the difference in the x-coordinates:

m = slope = (5 - 0) / (0 - 3) = 5/-3 = -5/3

The y-intercept of a line is the place where the line crosses the y-axis. For line l, it is at (0, 5), so b = 5. Our equation is thus: y = (-5/3)x + 5.

For line m, we see that the coordinates (0, 2) and (7, 0) are on the line. The slope is:

m = slope = (2 - 0) / (0 - 7) = 2/-7 = -2/7

The y-intercept is at (0, 2), so b = 2. Our equation is hence: y = (-2/7)x + 2.

Taking the two equations, let's set 15 equal to y and solve for x:

y = (-5/3)x + 5  ⇒  15 = (-5/3)x + 5  ⇒  10 = (-5/3)x  ⇒  x = -6

y = (-2/7)x + 2  ⇒  15 = (-2/7)x + 2  ⇒  13 = (-2/7)x  ⇒  x = -91/2

Let's find the difference:

-6 - (-91/2) = 39.5

The answer is thus 39.5.

~ an aesthetics lover

Answer:

Option A. π

Step-by-step explanation:

The period of a simple harmonic motion is the time taken to make one complete circle or oscillation.

Considering the graph given above, we can see that at the completion of one circle, the angle θ, has value as pi (π).

This value is equivalent to the period of the graph.

Therefore, the period of the graph shown above is π.

Answer:

Step-by-step explanation:

The exterior of angle XWY is 74 degrees, so the angle XWY itself is 180-74 = 106 degrees. The two angles form a 180 degree straight line or angle.

Answer:

the answer is 74

Step-by-step explanation:

i did the cumulative test

Answer:

Step-by-step explanation:

Garden roller is in the shape of cylinder.

So, one revolution =  Curved surface area of the cylinder

diameter  = 70 cm

radius = 70/2 = 35 cm

h = 100 cm

Curved surface area of the cylinder = 2πrh

                                                           = [tex]2*\frac{22}{7}*35*100[/tex]

                                                           = 22000 square cm

Area covered in 15 revolutions = 15 * 22000

                                                    = 330000 square cm

2) Coin

diameter = 22 mm

r = 22/2 = 11 mm

Volume of coin = 66 mm

πr²h = 66

[tex]\frac{22}{7}*11*11*h=66\\\\\\h=\frac{66*7}{11*11*22}\\h=0.17 mm[/tex]

Answer:

√13

Step-by-step explanation:

(-3, -2) (0, 0)

distance √(9 + 4) = √13

The distance from the origin to the point A is [tex]\sqrt{13}[/tex] unit.

Let, the co-ordinates of two points in 2D plane are [tex](x_{1} ,y_{1} )[/tex] & [tex](x_{2}, y_{2} )[/tex]

Then the distance between this two points be d (say)

Therefore, [tex]d=\sqrt{(x_{2}- x_{1}) ^{2}+ (y_{2} -y_{1} )^{2} }[/tex]

The co-ordinate of point A in the graph is (-3, -2)

The co-ordinate of origin is (0, 0)

∴ The distance between (0, 0) & (-3, -2) is = [tex]\sqrt{((-3)-0) ^{2}+ ((-2) -0 )^{2} }[/tex]

                                                                    = [tex]\sqrt{(-3)^{2}+(-2)^{2} }[/tex]

                                                                    = [tex]\sqrt{9+4}[/tex]

                                                                    = [tex]\sqrt{13}[/tex]

Learn more about distance of two points here :

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Answer:

The x-axis.

Step-by-step explanation:

This is an ellipse.

In standard form it s  x^2/36 + y^2/9 = 0.

When y = 0, x = +/- 6 and when x = 0, y = +/- 3  so the minor axis has length 6 and the major axis has length 12 and runs along the x-axis.

Answer:

D

Step-by-step explanation:

Well scanning the road for mileage wouldn't be the correct formula for "scanning" but looking for a gas station sounds more right.

Answer: d

Step-by-step explanation: i did it and got it right

Answer:Answer: THE ANSWER IS

A)

Answer:

The answer is D.

Answer: D) (-2)*2 - (-8) +1

Step-by-step explanation:

w = -2.

so the w2 is equal to -2*2

v = -8

so -v + 1 = -(-8) + 1

Put it together and you get (-2)*2-(-8)+1

the parentheses are needed for the first -2 because other wise it'd be -(2*2) instead of (-2)*2

Answer:

The Inter Quartile Range is 20.

Step-by-step explanation:

The interquartile range is Q3 - Q1. So first let's find the median (Q2) so we can find Q1 and Q3. Since there is an even amount of numbers, we need to find the average of the middle to numbers. My work is in the attached image.

If this helps, I would appreciate it if you gave me brainliest :)

Answer:

They are right

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]4 {x}^{2} + 8x - 7 - (3 {x}^{2} - x + 9)[/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression:

[tex]4 {x}^{2} + 8x - 7 - 3 {x}^{2} + x - 9[/tex]

Collect like terms

[tex]4 {x}^{2} - 3 {x}^{2} + 8x + x - 7 - 9[/tex]

[tex] {x}^{2} + 9x - 7 - 9[/tex]

Calculate

[tex] {x}^{2} + 9x - 16[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

i think its the first one-

Step-by-step explanation:

Answer:

the answer is the second one to the right on the top.

Step-by-step explanation:

i got it right on the quiz

Answer:

y -1 = -3(x+1)

Step-by-step explanation:

First find the slope

(-1,1) and (1,-5)

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

   = (-5-1)/(1--1)

   =-6/ (1+1)

   = -6/2

   = -3

We are using point slope form

y-y1 = m(x-x1)  where m is the slope

y - 1 = -3( x - -1)

y -1 = -3(x+1)

Answer:

The answer is option D.

Step-by-step explanation:

Equation of a line is y= mx + c

where m is the slope

Slope of the line using points

(-1,1) and (1,-5) is

[tex] \frac{ - 5 - 1}{ 1 + 1} = \frac{ - 6}{2} = - 3[/tex]

Therefore the equation of the line using point (-1,1) is

Hope this helps you

Answer:

86 square miles

Step-by-step explanation:

To answer this question you have to separate the shape into smaller ones. In this case, you can separate the shape into one larger rectangle on top and one smaller rectangle on bottom.

Area of large rectangle on top:

13 miles x 5 miles = 65 square miles

Area of smaller rectangle on bottom:

3 miles x 7 miles = 21 square miles

65 + 21 = 86 square miles

Answer:

The answer is 86 square miles

Step-by-step explanation:

First of all you can seperate this shape into shapes that you already know how to solve. Then the rest is easy...You can see how I solved it in more detail  by looking at the image below. I hoped it was helpful!

Answer:

The answer to the union of the two sets is: [tex]x\leq -3[/tex]

Step-by-step explanation:

Since they are asking for an "OR" condition, we need to find the set of solutions for each inequality, and then use the union of those two sets.

First inequality:

[tex]-7x+1\geq 22\\1-22\geq 7x\\-21\geq 7x\\-3\geq x\\x\leq -3[/tex]

so this is the set of all real numbers smaller than or equal to -3 (visualize the numbers on the number line to the left of -3 and including -3 itself)

Second inequality:

[tex]-10x+41\geq 81\\41-81\geq 10x\\-40\geq 10x\\-4\geq x\\x\leq -4[/tex]

So, this sets consists of all real numbers smaller than or equal to -4 (visualize the numbers on the number line to the left of -4 and including -4 itself.

Then, when we do the union of these two sets, we get:

[tex]x\leq -3[/tex]

since the number -4 is located to the left of -3 on the number line, so the set defined by the second inequality is in fact a subset of the one defined by the first inequality.

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

Explanation:

x = time it takes for the bell to ring, time is in minutes

d = distance from his house to the school, in meters

distance = rate*time

If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late. This means he took x+3 minutes to get to class. The x represents the amount of time it takes if he arrived on time, then the +3 is those 3 minutes he is late. We then write

d = 50(x+3)

d = 50x+150

If he runs to school, then he's 3 minutes early. So he took (x-3) minutes to get to class. His rate is 80 meters per minute

d = 80(x-3)

d = 80x-240

We're referring to the same distance (d) value, which allows us to perform substitution to solve the two equations we formed

80x-240 = 50x+150

80x-50x = 150+240

30x = 390

x = 390/30

x = 13

Andrew has 13 minutes to get to class.

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

Checking the answer:

If he walks at a speed of 50 m per minute, then he'll be 3 minutes late. So he really took 13+3 = 16 minutes to arrive. His distance traveled is d = r*t = 50*16 = 800 meters.

If he ran 80 m per minute, and is 3 minutes early, then he took 13-3 = 10 minutes to get to class. His distance is the same as before d = r*t = 80*10 = 800 meters. The fact we get 800 both times helps confirm we have the right answer.

Andrew has 13 minutes to get to class.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.

Now, let x be the time it takes for the bell to ring.

let d be the distance from his house to the school, in meters

distance = speed*time

If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late.

So, Andrew took x+3 minutes to get to class.

Here in the expression +3 shows that she is late.

So,

d = 50(x+3)

d = 50x+150

Now, If he runs to school, then he reached 3 minutes early.

So, toe get in class he will take (x-3) minutes

Here -3 show the child reached early

d = 80(x-3)

d = 80x-240

Since the distance is same.

So, the two equations are equal.

80x-240 = 50x+150

80x-50x = 150+240

30x = 390

x = 390/30

x = 13

Hence, Andrew has 13 minutes to get to class.

Learn more about algebra here:

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Answer:c

Step-by-step explanation:

becuase it minus so we can get rid of a and b, and since d is not the equation to find absolute value, it is not correct

Answer:

Yes

Step-by-step explanation:

You can take 1/2 and find a common denominator if this helps you.

We will multiply 1/2 by 25/25 because 25/25 equals 1 so you get the same amount just with a different numerator and denominator. So you get 25/50 and then you compare. 31/50 > 25/50

Let the total weight of the candy = x

We know the total weight is:

X = 3/20x + 1.2 + 3/5x+ 0.3

Simplify:

X= 3/20x + 1.2 + 12/20x + 0.3

X = 15/20x + 1.5

Subtract 15/20x from both sides:

5/20x = 1.5

Divide both sides by 5/20:

X = 1.5 / 5/20

X = 6

Total = 6 pounds.

Answer: she needs to work 8 hours

Step-by-step explanation:

Answer:

y = -x + 17

Step-by-step explanation:

A(-10,-3)

B(7,14)

C(5,12)

Need line CD perpendicular to AB through C.

Solution:

slope of AB, m1 = (yb-ya) / (xb-xa) = (14- -3) / (7- -10) = 17/17 = 1

Slope of CD, m2 = -1/m1 = -1 / 1 = -1

Line CD through C, using the point slope form

y-yc = m2(x-xc)

y-12 = -1 (x-5)

rearrange

y = -x + 5 + 12

y = -x + 17

Answer:

x intercept of CD is (17, 0)

Point (-2, 19) lies on CD

Step-by-step explanation: