which transformation could have taken place to map ABC to ABC

a reflection and a dilation

a rotation and a dilation

a translation and a dilation

a reflection and a translation​

Check the picture below.

[tex]\bf \stackrel{\measuredangle DAC}{4y+2x}~~=~~\stackrel{\measuredangle BCA}{9y-x}\implies 2x=5y-x\implies 3x=5y\implies \boxed{x=\cfrac{5y}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle DAB}{[(4y+2x)+35]}~~+~~\stackrel{\measuredangle ADC}{5x+4}~~=~~180\implies 4y+2x+5x+39 = 180 \\\\\\ 4y+7x+39=180\implies 4y+7x=141\implies \stackrel{\textit{substituting "x"}}{4y+7\left( \boxed{\cfrac{5y}{3}} \right)} = 141[/tex]

[tex]\bf 4y+\cfrac{35y}{3}=141\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 4y+\cfrac{35y}{3} \right)=3(141)}\implies 12y+35y=423 \\\\\\ 47y=423\implies y=\cfrac{423}{47}\implies \blacktriangleright y = 9 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=\cfrac{5y}{3}}\implies x = \cfrac{5(9)}{3}\implies \blacktriangleright x = 15 \blacktriangleleft[/tex]

To solve the equation a = 2x + 6xz for x, isolate x on one side of the equation by following the steps: subtract 6xz from both sides, factor out x, and divide both sides by (2 + 6z).

To solve the equation a = 2x + 6xz for x, we need to isolate x on one side of the equation. Here are the steps:

Start with the equation: a = 2x + 6xz

Subtract 6xz from both sides: a - 6xz = 2x

Factor out x on the right side: a - 6xz = x(2 + 6z)

Divide both sides by (2 + 6z): (a - 6xz) / (2 + 6z) = x

Therefore, the solution for x is x = (a - 6xz) / (2 + 6z).

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Answer:

[tex]y = \frac{3}{2}x + 1[/tex]

Step-by-step explanation:

-2 = 1½[-2] + b

-3

1 = b

y = 1½x + 1

** 1½ = 3⁄2

Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:

-⅔ → 1½

I am joyous to assist you anytime.

Answer:

y=3/2x+1

Step-by-step explanation:

You’re trying to find the perpendicular like equation of y=-2/3x+4 that passes through (-2,-2). Use reciprocal of slope -2/3= 3/2. use y=mx+b and plug in info, (-2,-2) will be plugged in for both y and x and 3/2 will be plugged in for m making -2=(3/2)(-2)+b. Multiply the () to get -2=-3+b, add 3 to both sides of the equation to get 1=b. Use your info to make the finished equation y=3/2x+1

Answer:

58

Step-by-step explanation:

1392/24=58

Answer: 24 goes into the number 1,392, 58 times

Answer:

The slope of the line is 3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a line that passes through the origin,

so

The graph shows a proportional relation ship

[tex]k=y/x[/tex]

For (1,3) ------> [tex]k=3/1=3[/tex]

For (2,6) ------> [tex]k=6/2=3[/tex]

For (3,9) ------> [tex]k=9/3=3[/tex]

The equation is

[tex]y=3x[/tex]

The slope of the line is 3

Answer:

The slope of the line is 3.

Step-by-step explanation:

In the graph x-axis shows Pyramid Volume in cubic units and the y-axis shows Prism Volume in cubic units.

The line starts at (0, 0) and passes through (1, 3), (2, 6) and (3, 9).

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Consider any two points of the line: (0, 0) and (1, 3). So, the slope of the given line is

[tex]m=\frac{3-0}{1-0}[/tex]

[tex]m=3[/tex]

Therefore, the slope of the line is 3.

Answer:

10,000

Step-by-step explanation:

Hope this helps!

Hey!

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

Solution and Answer:

2 = hundred thousands

1 = ten thousands

3 = thousands

6 = hundreds

6 = tens

9 = ones

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

Hope This Helped! Good Luck!

Answer:

12x < 200

Step-by-step explanation:

Substitute x = 12 into the left side of the inequality and compare with right side, that is

12 ÷ 12 = 1 < 12 ← not a solution

12 - 12 = 0 < 4 ← not a solution

12 × 12 = 144 < 200 ← this is a solution

Answer:

9.257

Step-by-step explanation:

7 goes into 64 nine times with the remainder of 1. Bring the decimal point up and the 8 down. 7 goes into 18 two times with the remainder of 4. 7 goes into 40 5 times with the remainder of 5. 7 goes into 50 7 times. That equals 9.257.

Have a nice day!!!!!! :-)

KA

To divide 64.8 by 7 using long division, calculate how many times 7 can be subtracted from each part of the number 64.8 in sequence. This results in the final answer of 9.25.

To find 64.8 divided by 7 using long division, first write down 64.8 with a division bar over it and 7 on the left side of the bar. You would write:

7 | 64.8

Next, ask: How many times does 7 go into 64? This is 9 times since 7 times 9 is 63. Record the 9 above the line and record the product (63) below 64. Subtract 63 from 64 to get 1.

Bring down the 8 (from 64.8) to the right of the 1. Now you have 18. Ask how many times does 7 go into 18? This is 2 times. So you add the digit 2 next to 9 on top of the bar. 7 times 2 is 14.

Subtract 14 from 18 to get 4. As the decimal point should be straight up from where it is in the 64.8, record a decimal point.

Now, since there's no more numbers to bring down, you can add a 0 to 40. 7 goes into 40, 5 times. Therefore, we add 5 next to the 2 after the decimal point. So, 64.8 divided by 7 is 9.25.

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Answer:

x-2

x decreased by 2 equals x-2.

Have a nice day!!!!!!!!!! :-)

KA

Answer:

q≤7

Step-by-step explanation:

q+8≤15

1) Subtract 8 from both sides:

q≤7

Answer:

[tex]\displaystyle 7 ≥ q; q + 8 ≤ 15[/tex]

Step-by-step explanation:

q + 8 ≤ 15

- 8 - 8

_______

[tex]\displaystyle q ≤ 7[/tex]

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

Answer:

1.5

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

30 cannot be multiplied to give a power of 10, so to find the decimal you have to divide: 2/3 = 2/3 + 2 ÷ 3

2 divided by 3 is 0.6666666... It is a recurring decimal.

However it is not practical to use recurring decimals in calculations, so the decimal is usually rounded off to 2 or 3 decimal places depending on the accuracy required for the answer.

Answer:$14.35

Step-by-step explanation:

The shop will charge $14.352 as markup price.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Cask’n’Cork wine shop that has a markup rate of 15%. A bottle of zinfandel wine costs $12.48 wholesale.

Assume that the shop charges $x. Then, we can write -

x = 12.48 + 15% of 12.48

x = 12.48 + (15/100) x 12.48

x = 12.48 + (3/20) x 12.48

x = 12.48 + 1.872

x = 14.352

Therefore, the shop will charge $14.352 as markup price.

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Answer:

x < 3

Step-by-step explanation:

Apply distributive property on the left of the inequality to get rid of the parenthesis:

8+4x > 5x+5

subtract 4x from both sides to group all terms with x on the right:

8 > 5x-4x+5

8 > x +5

Now subtract 5 from both sides to collect all numerical terms on the left:

8 - 5 > x

3 > x

Therefore the solution to the inequality are of those real numbers strictly smaller than 3.

The inequality can be written as x < 3 or also as we had it initially: 3 > x

Notice that the opening of the angle symbol is always facing the number 3 , meaning that 3 is the larger of the two numerical objects that are compared.

Answer:

The value of x = 0.5, y = 0.8 and z = 0.9

Step-by-step explanation:

From the given figure. Let's form the equations

50z + 13 + 45x + [tex]\frac{19}{2}[/tex] = 90°

45x + 50z + 13 + 9.5 = 90

45x + 50z + 22.5 = 90

45x + 50z = 90 - 22.5

45x + 50z = 67.5  --------------------------(1)

[tex]\frac{225y}{2} = 90[/tex]° Because it is a right angle.

225y = 180

y = [tex]\frac{180}{225}[/tex]

y = 0.8   --------------------(2)

44x + 125y + 80z -14 = 180° because they are supplementary angles add upto 180 degrees.

44x + 125y + 80z = 180 + 14

44x +125y + 80z = 194  ------------(3)

Now plug in y = 0.8 in the above equation (3), we get

44x + 125 times 0.8 + 80z = 194

44x + 100 + 80z = 194

44x + 80z = 194 - 100

44x + 80z = 94 ---------------------(4)

Now let's solve the equation (1) and (4) using elimination method.

x = 0.5

Now plug in x = 0.5 in the equation (4) and find the value of z

44(0.5) + 80z = 94

22 + 80z = 94

80z = 94 - 22

80z = 72

z = [tex]\frac{72}{80}[/tex]

z = 0.9

Therefore, the value of x = 0.5, y = 0.8 and z = 0.9

Answer:

[tex]B.-240[/tex]

Bob got that by calculating the change amount of money in Imamu's account after [tex]\frac{1}{3}[/tex] of a year (4 months).

Step-by-step explanation:

You know that Imamu pays $30 each month for his gym membership.

Since there are 12 months in a year, you can find the the number of months that [tex]\frac{2}{3}[/tex] of a year represents:

[tex](12\ months)(\frac{2}{3})=\frac{24\ months}{3}=8\ months[/tex]

Now, in order to find the change amount of money in his account after [tex]\frac{2}{3}[/tex] (8 months), you must solve the following multiplication:

[tex](-30)(8)=-240[/tex]

Bob chose [tex]-120[/tex] (Option A) as the correct answer, but that is incorrect, because he got it by calculating the change amount of money in Imamu's account after [tex]\frac{1}{3}[/tex] of a year (4 months).

Answer:

7 groups, 3 boys and 8 girls

Step-by-step explanation:

Let total number of groups be [tex]x[/tex]

and total hikers in one group be [tex]y[/tex]

if number of girls and boys in every group is same, then

[tex]\frac{21}{x} + \frac{56}{x} = y[/tex]

[tex]\frac{21 + 56}{x} = y\\x*y = 77[/tex] ....(1)

from (1) [tex]x[/tex] will either be 11 or 7

for [tex]x = 11[/tex] the values won't be real.

For [tex]x = 7\\y = \frac{77}{7} \\y = 11[/tex]

so there will be 7 groups with 11 hikers in each groups and every group will have [tex]\frac{21}{7} = 3[/tex] boys and [tex]\frac{56}{7} = 8[/tex] girls

A) The total for the plants she buys is 8.50, so the change in her checking account would be -8.50, because they will take 8.50 out of her account when the check is cashed, the amount in her account is lowered.

B) Mr. Clark's total is 11.25. If he pays with a 20, subtract the plant total from 20:

20 - 11.25 = 8.75 is the amount of change Jeremy owes him.

The amount of money Jeremy collects would be that amount higher than what he needs.

C)  Suzie owed 2.50, divide the amount she borrowed by the number of weeks her mom is keeping money:

2.50 / 5 = 0.50

Her allowance will be 0.50 less than what she normally would get.

D) Grandparents original amount = $15.00

3 daises = 3 x 3.75 = 11.25

1 geranium = 2.25

Total for new order = 11.25 + 2.25 = 13.50

Difference = 15 - 13.50 = 1.50

The new order would be $1.50 less.

E) Divide the total amount of the donation by the number of people:

14.40 / 3 = $4.80

F) Divide total amount by total people:

270 / 22 = $12.27 average

Covert the ratios so they are all the same measurement type.

A. 5 feet = 5 x 12 = 60 inches.

The scale becomes 1:60

B. 1:30

C. 12 yards = 12 x 3 = 36 feet x 12 = 432 inches.

The scale is 12:432  = 1:36

D. 1 meter = 39.37 inches.

1 inch = 2.54 cm

39.37 x 2.54 = 99.99 inches

The scale converted to inches becomes 1 :100 inches.

The first number would be the size of the drawing, the second number is the size of the actual object

If you use all 4 scale factors for a real object that is 100 inches:

A would need 100/60 = 1.67 inches.

B would need 100/30 = 3.3 inches.

C would need 100/36 = 2.78 inches.

D would need 100/100 = 1 inch.

The larger scaled drawing would be B.

Answer:

Option B.

Step-by-step explanation:

We need to find which scale would produce the largest scale drawing of an object when compared to the actual object.

First of all cover all units in inches.

In option 1,

1 inch : 5 feet

We know that

1 feet = 12 inch → 5 feet = 60 inch

So the ratio in inches is 1:60. It means the scale factor is 60.

In option 2,

1 inch : 30 inches

So the ratio in inches is 1:30. It means the scale factor is 30.

In option 3,

1 foot : 12 yards

12 inches : 12 yards                     (1 feet = 12 inch)

1 inch : 1 yards

1 inch : 36 inch                     (1 yard = 36 inch)

So the ratio in inches is 1:36. It means the scale factor is 36.

In option 4,

1 centimeter : 1 meter

1 centimeter : 100 centimeter         (1 m = 100 cm)

1 inch : 100 inch

So the ratio in inches is 1:100. It means the scale factor is 100.

Option B has smallest scale factor, so it will produce the largest scale drawing of an object when compared to the actual object.

Therefore, the correct option is B.

The correct answer is (B) Only (-3, 3).

To determine which ordered pair is a solution of the equation, you need to substitute the values of \( x \) and \( y \) into the equation and see if it holds true. Let's check:

For option A: (-4, 4)
Substituting into the equation: \( -3(-4) - 4 - 6 = 12 - 4 - 6 = 2 \) which is not equal to 0, so it's not a solution.

For option B: (-3, 3)
Substituting into the equation: \( -3(-3) - 3 - 6 = 9 - 3 - 6 = 0 \) which is equal to 0, so it is a solution.

Thus, the correct answer is (B) Only (-3, 3).

Complete question :

Which ordered pair is a solution of the equation?

-3x-y-6

Choose 1 answer:

A Only (-4, 4)

B Only (-3, 3)

C Both (-4, 4) and (-3,3)

D Neither.

Answer:

Step-by-step explanation:

subtract 8

-5b=-15

divide negative 5

b=3

Answer the answer to your question is b=3

Answer:

Undefined or No solution

Step-by-step explanation:

Because this line is a straight, vertical line, it means that the slope is undefined, or no solution. Any time you see a straight line going up and down, this will be true. However, if you see a horizonal line, this will not be true.

Answer:

5

Step-by-step explanation: Mind/Bamboozling question

Answer:

Bob has 5 apples still

Step-by-step explanation:

All by the amazing scientific reasoning of

when you have 5 of something

you go away and you still have 5

YOU WILL ALWAYS HAVE 5

Answer:

The input is -5 when the output is -8

Step-by-step explanation:

Let

y-----> the output

x ----> the input

we know that

The linear equation that represent this problem is

[tex]y=3x+7[/tex]

so

For y=-8

substitute in the equation and solve for x

[tex]-8=3x+7[/tex]

Subtract 7 both sides

[tex]-8-7=3x\\-15=3x[/tex]

Divide by 3 both sides

[tex]x=-5[/tex]

therefore

The input is -5 when the output is -8

Answer: $127

Step-by-step explanation:

5th day: 8 * 2 = 16

6th day: 16 * 2 = 32

7th day: 32 * 2 = 64

Then add all the money he got throughout the week,

1 + 2 + 4 + 8 + 16 + 32 + 64

= 127

Answer: Last option.

Step-by-step explanation:

In order to estimate the percent "n" of a number"x", you need easy numbers to work with, therefore you can round  "n" and "x" up or down; but it is important to remember that this estimation does not give you an exact value.

You can observe that Sergei's first step was to round 149% and 67 up, getting this result:

[tex]=105[/tex]

To verify if this estimate is less or greater than the actual answer, we can find the actual answer. This is:

[tex]\frac{67*149}{100}=99.83[/tex]

Therefore, we can conclude that the estimate is greater than the actual answer because the percent and the number were both rounded up.

Answer:

D

Step-by-step explanation:

I did it on Edgen 2020

we'll first off put the two points in component form, then we'll multiply that by the fraction 3/10 and those coordinates we'll simply add to the first point, anyhow, let's proceed,

[tex]\bf \textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{9}~,~\stackrel{y_2}{4})~\hspace{8em} \frac{3}{10}\textit{ of the way from }A\to B \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \textit{component form of segment AB}}{ (\stackrel{x_2}{9}-\stackrel{x_1}{(-3)}, \stackrel{y_2}{4}-\stackrel{y_1}{(-6)})\implies (9+3~,~4+6)\qquad \implies \qquad (12,10)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{~\hfill \textit{values to be added to Point A coordinates}} {\cfrac{3}{10}(12,10)\implies \cfrac{3}{10}(12)~,~\cfrac{3}{10}(10)\qquad \implies \qquad \left(\frac{18}{5}~,~3\right)} \\\\\\ \stackrel{\textit{addition of Point A coordinates and values}} {A(-3,-6)+\left( \frac{18}{5},3\right)\implies \left( -3+\frac{18}{5}~~,~~-6+3 \right)\qquad \implies \left( \frac{3}{5}~,~-3\right)}[/tex]

Hello!

your answer is: 4

2 cubed is also written as: 2³

2 squared is also written as: 2²

so the re-written equation is: 2³ - 2²

To solve, simplify by doing the exponents.

2³ = 8

2² = 4

8 - 4 = 4

I hope this helps, and have a nice day!

Answer:

5.4 m/s2

Step-by-step explanation:

Answer: 216 meters per 8th second

Step-by-step explanation:

do 27 times 8 it will give you 216