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Rotation 90 degrees counterclockwise about the origin.

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Explanation:

Plot a point at the origin. Let's call it point D.

Form segments AD and A'D.

Use the slope formula to note that those segments have negative reciprocal slopes, which leads to the segments being perpendicular.

This proves we have a 90 degree rotation. The direction is counterclockwise when going from A to A'.

The same idea applies when going from B to B', and also C to C'.

The transformation that changes triangle ABC to triangle A'B'C' is a reflection of the y-axis followed by a translation up by 8 units.

Option B is the correct answer.

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

To determine the transformation that changes triangle ABC to triangle A'B'C', we need to find the transformation that maps each vertex of triangle ABC to the corresponding vertex of triangle A'B'C'.

To map A to A', we need to move 10 units to the right (from x = -5 to x = 5) and stay at the same y-coordinate (y = -6).

This is a horizontal translation of +10 units.

To map B to B', we need to move 1 unit to the left (from x = -3 to x = 2) and 1 unit up (from y = -2 to y = -3).

This is a horizontal translation of -1 units followed by a vertical translation of +1 units.

To map C to C', we need to move 2 units to the right (from x = -4 to x = 6), and 2 units up (from y = -6 to y = -4).

This is a horizontal translation of +10 units followed by a vertical translation of +2 units.

Therefore,

The transformation that changes triangle ABC to triangle A'B'C' is a reflection of the y-axis followed by a translation up by 8 units.

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Step-by-step explanation:

the first thing we notice is : there are always 2 "extra" squares (1 added to the bottom left, and 1 added to the top right).

and then we see that we have a "core" of n+1 squares that are added n-1 times.

e.g. for n=2 we get (2+1)(2-1) = 3×1 = 3 squares in the middle.

for n=3 we get (3+1)(3-1) = 4×2 = 8 squares in the middle.

just to verify for n=1 : that would be (1+1)(1-1) = 2×0 = 0. meaning no middle squares, which is correct.

so, the formula for n is

squares(n) = (n+1)(n-1) + 2 = n² - 1 + 2 = n² + 1

The number of squares that it takes to make the nth figure in this pattern will be n² + 1.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The growing pattern will be

⇒ (n+1)(n-1) + 2

⇒ n² - 1 + 2

⇒ n² + 1

Where n is the integer number.

More about the Algebra link is given below.

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Answer:

5 miles

Step-by-step explanation:

Let's first break down the question.

Suzie has a total of 32 minutes for her run. She runs 1 mile in 5 minutes and then after running she cools down for 7 minutes.

So then, now for the math...

5 + 5 + 5 + 5 + 5 + 7 = 32 minutes

5 * 5 = 25

25 + 7 = 32

During her time limit she will run a total she will run 5 miles.

Answer:

t= 2

Explanation:

[tex] 64 = 16{t}^{2} [/tex]

[tex] \frac{64}{16} = \frac{16 {t}^{2} }{16} [/tex]

[tex]4 = {t}^{2} [/tex]

[tex]t = \sqrt{4} \\ t = 2[/tex]

Answer:

d

Step-by-step explanation:

Answer:

22.5%

Step-by-step explanation:

Find new values:

124(1−0.25)=93

125(1−0.2)=100

Last Year: Boys 124 & Girls 125

This Year: Boys 93 & Girls 100

Total: Last Year 249 & This Year 193

249(1−r)=193

249(1−r)/249=193/249

1−r=0.7751

−r=−0.2249(Subtracted 1)

r=0.2249(Divided by -1)

Final Answer: 22.5%(Multiply by 100 and round to nearest 10th)

Polynomials are equations that uses variables and several terms

The polynomial in standard form is f(x) = x^2 - x -20

The polynomial has 2 zeros.

So, the form of the polynomial is:

f(x) = a(x - x1)(x - x2)

The zeros of the polynomial are 5 and -4.

So, the equation becomes

f(x) = a(x - 5)(x + 4)

The value of a = 1.

So, we have;

f(x) = 1(x - 5)(x + 4)

This gives

f(x) = (x - 5)(x + 4)

Expand

f(x) = x^2 - x -20

Hence, the polynomial in standard form is f(x) = x^2 - x -20

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Answer:

SA = 280 in²

Step-by-step explanation:

The net comprises:

To calculate the surface area (SA), calculate the area of each rectangle and add them together.

Area of a rectangle = width x length

Therefore, SA of net = 2(5 x 10) + 2(6 x 10) + 2(5 x 6)

⇒ SA = 100 + 120 + 60

⇒ SA = 280 in²

Answer:

-5, -2/3, 7, 3/4

Step-by-step explanation:

The solutions of S(x) = 0 satisfy one of the equations:

3x^2 + 17x + 10 = 0, x - 7 = 0, 4x - 3 = 0

The latter two are straightforward to solve:

x = 7 and x = 3/4

We now factor 3x^2 + 17x + 10 = 0

Note 10 = 5 * 2, 3 = 3 * 1 and 3 * 5 + 2 - 17.

So, we can factor it as (3x + 2) (x + 5) = 0

Thus, we also have solutions -2/3, -5.

Answer:

A

Step-by-step explanation:

[tex]7n + \frac{1}{5} [/tex]

[tex] \frac{35n + 1}{5} [/tex]

And

[tex] \frac{1}{5} + 7n[/tex]

[tex] \frac{1 + 35n}{5} [/tex]

Answer:

A, because they switched around the order of the expression but it still equals the same thing.

Step-by-step explanation:

Answer:

no she won't but my answer is an estimate

Step-by-step explanation:

16 X 118 is like 1900 and 20 percent of 1900 is like 380

1900 add 380 is 2280 not enough money.

Answer:

x = 70

Step-by-step explanation:

The Left base angle is also = x. that's because both angles are opposite = lines

x + x + 40 = 180                     All triangles have 180 degrees.

2x + 40 = 180                        Combine left angles. Subtract 40 from left and right sides.

2x+40 - 40 = 180 - 40           Combine

2x = 140                                 Divide by 2

2x/2 = 140/2

x = 70

Answer:

The total surface area of the prism

=Lateral surface area of prism +

area of the two bases = (2 ×

Base Area ) + Lateral surface

area or (2 × Base Area) + (Base

perimeter × height) .

Step-by-step explanation:

hope it helps

Answer:

472 in²

Step-by-step explanation:

This net is made up of 3 identical rectangles and 2 identical triangles.

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Rectangle

Triangle

Surface Area

SA = 3(8 x 19) + 2(0.5 x 8 x 2)

⇒ SA = 456 + 16

⇒ SA = 472 in²

Answer:

n + 6

Step-by-step explanation:

5n - 3 ( n - 2 ) - n

4n - 3 ( n -2 )

4n - 3n - 3 x (2)

4n - 3n - 3 x 2

4n - 3n + 6

n + 6

1. Observe problem

Degree of three, so

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

x^3-4x^2+3x

Answer:

100% for the conditions given.

Step-by-step explanation:

P(out) = .34 + .18 + .13= 0.65

This is the probability for going out. The 4th person is the one not going out. We are to assume that he wants to watch Monday Night Football or something like it

So the probability of not going out for 1 person is 0.35

You can justify this in two ways.

Either you can rely on the given (P(stay at home) = 0.35)

or you can take the probability of the 3 given who do go out and subtract it from certainty (or 1)

1 - 0.65 = 0.35

Answer:

A 109

Step-by-step explanation:

Pentagram's angles add up to 540. After subtracting all the other angles, you are left with 109.

Answer:

A

Step-by-step explanation:

add all the angles, answer should be 431, then subtract it from 540 (sum of interior angles for a pentagon), this gives u the answer of 109

cosA:-

[tex]\\ \rm\longmapsto \sqrt{1-sin^2A}=\sqrt{1-(1/4)^2}=\sqrt{1-1/16}=\sqrt{15/16}=\dfrac{3\sqrt{5}}{4}[/tex]

Now

[tex]\\ \rm\longmapsto sinA+cos^2A[/tex]

[tex]\\ \rm\longmapsto 1/4+15/16[/tex]

[tex]\\ \rm\longmapsto 4+15/16=19/16[/tex]

Answer:

996

Step-by-step explanation:

Although that's the exact answer

Answer:

Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3.

This system of inequalities models the scenario:

2x + 3y < or equal to sign 15

x + y > or equal to sign 3

Answer:

-When (2×-5) intersects at ×-axis the value of × will be zero.

=>F(×)=× 0=2×-5

hence,

0,=2×-5

5=2×

=>×=5/2

Step-by-step explanation:

hpe it hlps

Answer:

#1= 24.23

#2= 57.91

#3= 35.84

#4= 48.59

Step-by-step explanation:

soh cah toa

sin=opposite/hypotenuse

cos=adjacent/hypotenuse

tan= opposite/adjacent

use inverse sin cos and tan to find angles!

Answer:

Example 1 tan-1(9/20)=24.23°

Example 2 cos-1(17/32)=57.91°

Example 3tan-1(13/18)=35.84°

Example 3 sin-1(21/28)=48.59°

Step-by-step explanation:

I assume they intersect at a right angle (90°).

then the intersection is a rectangle with one side being 12 m, and the diagonal being 13 m long.

the diagonal is the Hypotenuse (baseline) of a right-angled triangle with the length and the width of the rectangle as legs.

so, by using Pythagoras we have

diagonal² = length² + width²

13² = 12² + width²

169 = 144 + width²

25 = width²

width = 5 m

so, Oakdale Avenue is 5 m wide.

Answer:

Domain: [-2,5)

Range: (2,-2]

Step by step explanation:

a open circle , means a parenthesis. a close Circle means a bracket . the domain is X . The range is y . for the range you start from the top of the graph and go all the way to the bottom of the graph . then for the domain, you go from the beginning of the graph to the end of the graph, side to side. and that's how I got this answer

Answer: 5/8 > 1/2

Use L.C.M:

The L.C.M is 8:  1 x 5  5       1 x 4

                            1 x 8  8       2 x 4

                                      5 ---  4 = 5 is more than 4

                                          8

Answer:

162 [m²].

Step-by-step explanation:

required surface is:

A=(3*7+6*7+3*6)*2=162 [m²].

Answer:

So surface area is calculated by
2lw + 2lh + 2hw = SA
L is length
W is width
H is Height

SA is surface area.

So plug it in, (reminder this equation only works for cubes, rectangular prisms)

2(3)(6) + 2(3)(7) + 2(7)(6) = ?

So now follow order of operations to solve.
36 + 42 + 84 = 162

So 162m^2 is the surface area.

Answer: 106

Step-by-step explanation: 12x10=120 7x2=14 120-14=106

Answer:

[tex]A_{shaded} = 106\ m^2[/tex]

Step-by-step explanation:

Step 1:  Get the area of the inside box

[tex]A=l*w[/tex]

[tex]A_{inside\ box} = 7\ m* 2\ m[/tex]

[tex]A_{inside\ box} = 14\ m^2[/tex]

Step 2:  Get the area of the outside box

[tex]A = l * w[/tex]

[tex]A_{outside\ box} = 12\ m * 10\ m[/tex]

[tex]A_{outside\ box} = 120\ m^2[/tex]

Step 3:  Subtract the inside box from the outside box

[tex]A_{shaded} = A_{outside\ box} - A_{inside\ box}[/tex]

[tex]A_{shaded} = 120\ m^2 - 14\ m^2[/tex]

[tex]A_{shaded} = 106\ m^2[/tex]

Answer:  [tex]A_{shaded} = 106\ m^2[/tex]