Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′.

Answer:

Step-by-step explanation:

Vertices of ΔABC are,

A(-3, 6), B(2, 1) and C(9, 5)

Use the formula to get the distance between two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

By using the formula,

AB = [tex]\sqrt{(1-6)^2+(2+3)^2}[/tex]

     = [tex]\sqrt{50}[/tex] units

BC = [tex]\sqrt{(5-1)^2+(9-2)^2}[/tex]

     = [tex]\sqrt{65}[/tex] units

AC = [tex]\sqrt{(6-5)^2+(-3-9)^2}[/tex]

     = [tex]\sqrt{145}[/tex]

Use cosine rule to find the measure of ∠ABC.

AC² = AB² + BC²- 2(AB)(BC)cos(B)

[tex](\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}[/tex]

145 = 50 + 65 - 2(√3250)cosB

cos(B) = [tex]-(\frac{145-115}{2\sqrt{3250}})[/tex]

          = -0.26312

B = [tex]\text{cos}^{-1}(-0.26312)[/tex]

B = 105.26°

Answer:

5/3 or 0.666666666667

Step-by-step explanation:

2/3*(-2)+3

5/3 or 0.666666666667 (Solved by calculator)

Answer:

Multiples of 120 are 120, 240, 360, 480, 600, 720, 840 etc; Multiples of 150 are 150, 300, 450, 600, 750, 900 etc; Therefore, the least common multiple of 120 and 150 is 600.

Least common multiple (LCM) of 19600 and 19619 is 384532400.

Answer: 19600

Step-by-step explanation:

19600/120 = 160

Answer:

110°

Step-by-step explanation:

Answer:

44 kg, and since both sold the same amount so did A.

Let me know if this method doesn't make sense though and I should be able to explain it.

Step-by-step explanation:

Both shops sold the same amount, let's call it x.

At the end, let's say shop B had y left, this means A would have 4y left, since the question says "After each shop sold the same quantity of rice, the amount of rice left in Shop A was 4 times that of Shop B"

So this means A started with 156, sold x and was left with 4y, or in math 156 - x = 4y

B you could write 72 - x = y

Now you have a system of equations.

156 - x = 4y

72 - x = y

There are a number o ways to look at this.  If you graph them you want the (x, y) coordinates where they intersect, or in other words the x and y values that work for both of these equaions.  

The methods all wing up making you solve for one variable and plugging it into the other equation to solve for the other.  The easiest method is probably canceling out.

156 - x = 4y

72 - x = y

Now, for these two the goal is to make one of the variables go away by adding or subtracting one equation from the other.  You could also multiply one by something.  In fact here are all possibilities.  

If you subtract one from the other here is what would happen.

156 - x = 4y

-(72 - x = y)

_________

156 - x = 4y

-72 + x = -y because you distribute the minus sign

_________

84 = 3y because 156-72 = 84, -x + x = 0 so they canceled out and 4y - y = 3y

28 = y because you divide both sides by 3.

It's all just algebra after the addition/ subtraction.  You could also do it the other way subtracting 156 - x = 4y from 72 - x = y.  Either way would cancel the xs.  But now that you know y = 28 you can plug that into either of the equations again to find x.

156 - x = 4y

156 - x = 4(28)

156 - x = 112

156 = 112 + x

44 = x

72 - x = y

72 - x = 28

72 = 28 + x

44 = x

Now, if you wanted to cancel the ys initially you would have to multiply.

156 - x = 4y

72 - x = y

Normally subtracting just got rid of the xs.  You would need to multiply the bottom one by 4 to get rid of ys.

156 - x = 4y

288 - 4x = 4y

Now if you subtracted one from the other the 4ys would cancel.  You could also divide the top one by 4 and get

39 - x/4 = y

72 - x = y

here you have a fraction though and that's gonna make things a little more difficult.

Let me know if this method doesn't make sense though and I should be able to explain it.

well, let's take a look at two independent events

A)  the potato is hot

B) it's raining

now, the potato could be hot whether is raining or not, A is totally independent of B, so what's the probability of "the potato being hot, GIVEN that it's raining" P(A | B)  is the same as if it wasn't raining, or P(A), the fact that B occurred, doesn't affect A at all, the potato is hot regardless, rain or not.  So P(A | B) = P(A).

Answer: 312 balcony seats and 396 ground seats

Step-by-step explanation:

Multiplying the second equation by 10, we get 10b+10g=7080.

Subtracting this from the first equation, we get that 5b = 1560, and thus b=312.

Thus, g=396.

Answer:

34, and if 55 was replaced with 33, the new median would be 33.

Step-by-step explanation:

The median is the number that is in the middle of a data set, once the numbers are organized from least to greatest. If we put the numbers in order (18, 22, 24, 32, 34, 39, 55, 57, 59), the number in the middle is 34. If we do the same, but replace 55 with 33, (18, 22, 24, 32, 33, 34, 39, 57, 59), we get 33 as the median.

Answer:

93.53m.

Step-by-step explanation:

.

Answer: -24x^7

Step-by-step explanation:

pemdas so you do parentheses first therefore getting  (2x^2)^3x3x

remove the parentheses

do -8x^6x3x

after that you end up with -24x^7

Simplify (-2x^2) ^3 by raising each term by 3:

-2^3x^6

Now you have

-2^3 x^6 times 3x

-2^3 = -8

x^6 tomes x = x ^7

-8 x 3 = -24

Answer is -24x^7

Answer:

y=(-ax+c)/b

Step-by-step explanation:

ax+by=c

by=c-ax

by=-ax+c

y=(-ax+c)/b

Answer:

the answer is probably complicated but this is POSSIBLY similar to your problem

Step-by-step explanation:

x^2 - 1x - 3x + 3

x^2 - 4x + 3

Answer:

6 because why not

Step-by-step explanation:

うsじょうぉじょあそlざ

ありおdごうおの

Answer:

First drop box: 40x + 18(x - 3) = 468

Second drop box: $6

Step-by-step explanation:

Explanation in progress! Enjoy your answer first then come back for the explanation once you've done it (●'◡'●)

Answer:

isoceles

Step-by-step explanation:

The vertices are not equal

Answer:

The probability that the average score of a group of n = 4 people is between 70 and 75=0.13591

Step-by-step explanation:

We are given that

[tex]\mu=65[/tex]

[tex]\sigma=10[/tex]

n=4

We have to find the probability that the average score of a group of n = 4 people is between 70 and 75.

[tex]P(70<\bar{x}<75)=P(\frac{70-65}{\frac{10}{\sqrt{4}}}<\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{75-65}{\frac{10}{\sqrt{4}}})[/tex]

[tex]=P(\frac{5}{5}<Z<\frac{10}{5})[/tex]

[tex]=P(1<Z<2)[/tex]

[tex]=P(Z<2)-P(Z<1)[/tex]

[tex]=0.97725-0.84134[/tex]

[tex]=0.13591[/tex]

Hence,  the probability that the average score of a group of n = 4 people is between 70 and 75=0.13591

Answer:

94.8

Step-by-step explanation:

sin 45 = 67/x

x = 67/sin 45

x = 94.8

Answer:

TFY

Step-by-step explanation:

let's start with the 90 degrees angle.

this is C in the first, and T in the second triangle.

so, C and T must be aligned.

and the we go around.

F ~ H

and then

Y ~ S

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

[tex]\large\boxed{ \sf{Answer}} [/tex]

[tex]4x - ( - 2) = 18 \\ 4x + 2 = 18 \\ 4x = 18 - 2 \\ 4x = 16 \\ x = \frac{16}{4} \\ x = 4[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

4x-1-2=18

4x+2=18

4x=18-2

4x=16

x=16/4

x=4

Hello,

We have :

27 = 3³ = 3 × 3 × 3

[tex]x[/tex]³ = [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex]

So :

The cube root of 27[tex]x[/tex]³ is :

3 × [tex]x[/tex] = 3[tex]x[/tex]

(  because : (3[tex]x[/tex])³ = 27[tex]x[/tex]³ )

We have :

8 = 2³ = 2 × 2 × 2

So :

The cube root of 8 is : 2

[tex]a^{3} +b^{3} = (a+b)(a^{2} -ab+b^{2} )[/tex] with [tex]a=3x[/tex] and [tex]b=2[/tex]

We have :

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

Have a nice day :)

Answer:

4.15, or 1.32pi

Step-by-step explanation:

arclength is circumference(34/360)

so pi x d (34/360)

3.14 x 14 x (34/360) = 4.15, or 1.32pi

The arc length PR is 4.151 cm.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Moreover, every angle has rotational symmetry around the centre.A section of a line that runs from a circle's centre to any point on the circle itself. "R" or "r" stand for the circle's radius.

As per the given data:

The diameter of circle Q = 14 cm

From the given diagram:

∠PQR = 34°

For finding out the arc length PR:

arc length = angle in radian × radius

radius = diameter / 2 = 14 / 2 = 7 cm

angle in radian = 34° × (π / 180°) = 0.593 radians

arc length PR = 0.593 × 7 = 4.151 cm

Hence, the arc length PR is 4.151 cm.

To learn more about circle, click:

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Answer:

12

Step-by-step explanation:

45-33 is 12

And I guess to check, make sure 12 < 18

Answer: 70

Step-by-step explanation:

We are required to calculate the total distance Cecilia travelled in 5 days

The total distance Cecilia travelled for 5 days is 99 kilometers

Day 1 = 27 kilometers

Day 2 to day 5 = 2/3 of 27

= 2/3 × 27

= 2 × 9

= 18 kilometers each day

Total distance = day 1 + day 2 + day 3 + day 4 + day 5

= (27 + 18 + 18 + 18 + 18) kilometers

= 99 kilometers

Therefore, the total distance Cecilia travelled for 5 days = 99 kilometers

Read more:

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Answer:

2x-4+14=26    add -4+14 this will give you +10

2x+10=26       subtract 10 on both side this will give you 16

2x=16        divide by 2 on both side this will give you 8

x=8

Step-by-step explanation:

Answer:

12y+x = -20

Step-by-step explanation:

Question restructured

Identify the equation of the line that is perpendicular to y =12x−7 and runs through the point (4,−2).

The equation of a line in point-slope form is expressed as;

y-y0 = m(x-x0)

m is the slope

(x0,y0) is a point on the line

Given the equation y = 12x - 7

Slope = 12

Since the required line is perpendicular to this line, the slope of the required line will be;

m = -1/12

Get the required equation

y-(-2) = -1/12 (x - 4)

y+2= -1/12(x-4)

Cross multiply

12(y+2) = -(x-4)

12y+24 = -x+4

12y + x = 4-24

12y+x = -20

Hence the required equation is 12y+x = -20

NB: The equation of the line used in question was assumed

Point A is located at (1,-3)

The ordered pair (–2, 4) is located at T

The point A is located at (1,-3). The ordered pair (-2,4) is located at point T.

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent and study geometric figures and their properties using algebraic equations and coordinates.

In coordinate geometry, points in a plane are represented by ordered pairs of numbers called coordinates. The most common coordinate system is the Cartesian coordinate system, which uses two perpendicular lines, the x-axis and the y-axis, to locate points.

The location of point A is at (1,-3) from the graph. The ordered pair (-2,4) is representing point T on the graph.

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Answer:

34.4

Step-by-step explanation:

Using Triangle Sum Theory, you see that the triangles are similar. They have the same angle measurements. That means their corresponding sides are proportional.

[tex]\frac{MN}{NO}[/tex] = [tex]\frac{PQ}{QR}[/tex]

[tex]\frac{14}{11}[/tex] = [tex]\frac{PQ}{27}[/tex]

Cross multiply

14(27) = 11(PQ)

378 = 11(PQ)

[tex]\frac{378}{11}[/tex] = PQ

PQ = 34.4

Answer:

(2, 0) and (6, 0)

Step-by-step explanation:

[tex]y = x^2 - 8 x + 12[/tex]

To get the x intersept put y = 0

[tex]x^2 - 8 x + 12 = 0 \\\\x^2 - 6 x - 2 x + 12 = 0 \\\\x(x- 6) - 2(x - 6) = 0 \\\\(x - 2) (x - 6) = 0 \\\\x = 2 and x = 6[/tex]

So, the intersepts are

(2, 0) and (6, 0)

Answer:

There are 16 pink jelly beans.

There are 16+34+24+26=100 jelly beans in total.

The probability is 4/25, or 16%.

Step-by-step explanation: hope this helps and gl :)

Answer:

The answer is 4/25

Step-by-step explanation:

Hope this helps