triangle A'B'C is created by dilating triangle ABC by a scale factor of 4. what is the length of AB? The length of A'B'

Triangle A'B'C Is Created By Dilating Triangle ABC By A Scale Factor Of 4. What Is The Length Of AB?

Answers

Answer 1

Answer:

The length of AB is 20 units

Step-by-step explanation:

The given parameters from the graph for coordinates A and B are;

The coordinates of the point A = (1, 4)

The coordinates of the point B = (4, 8)

The length of segment AB is given by the equation for finding the distance, d between two points given their coordinates as follows;

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

Where;

(x₁, y₁) = (1, 4)

(x₂, y₂) = (4, 8)

Substituting gives;

[tex]d_{AB} = \sqrt{\left (8-4 \right )^{2}+\left (4-1 \right )^{2}} = \sqrt{25} = 5[/tex]

The length of [tex]\overline {AB}[/tex] = 5

Therefore, given that ΔA'B'C is created by dilating ΔABC by a scale factor of 4, the length of A'B' = 4 × The length of AB

Therefore, the length of [tex]\overline {A'B'}[/tex] = 4 × The length of [tex]\overline {AB}[/tex] = 4 × 5 = 20

The length of [tex]\overline {A'B'}[/tex] = 20 units.


Related Questions

Paige ran 3 miles on Monday, walked 8 miles Tuesday
and ran a combined 11 miles on Wednesday and
Thursday. How many total miles did Paige exercise in
four days?

Answers

Answer:

22

Step-by-step explanation:

add 11 + 8+ 3


Identify all segments that are parallel to XY

A. ST
B. VZ, VW, ST
C. QR, QU
D. VW

Answers

The answer is AAAAAAASS

Answer:

a. ST

Step-by-step explanation:

Which shows the equation below written in the from ax^2 + bx + c = 0? x + 9 = 2(x - 1) ^2

Answers

Answer:

i may be wrong but i thinks its A

Step-by-step explanation:

What is the exponential expression for the numerical expression ​14⋅14⋅14⋅14​?


​144​

4⋅144

​564​

414

Answers

Answer:

144

Step-by-step explanation:

i just did the test

If l, m, and n are parallel, solve for x. Type in numerical values only, do not type in x=

Answers

Answer:

x = 11

Step-by-step explanation:

According to proportionality theorem, the transversal is divided proportionally as it cuts across parallel lines l, m, and n.

Therefore:

[tex] \frac{12.8}{x + 5} = \frac{x - 3}{10} [/tex]

Cross multiply

[tex] (12.8)(10) = (x + 5)(x - 3) [/tex]

[tex] 128 = x^2 - 3x + 5x - 15 [/tex]

[tex] 128 = x^2 + 2x - 15 [/tex]

[tex] 0 = x^2 + 2x - 15 - 128 [/tex]

[tex] 0 = x^2 + 2x - 143 [/tex]

Factorise:

[tex] 0 = x^2 - 11x + 13x - 143 [/tex]

[tex] 0 = x(x - 11) +13(x - 11) [/tex]

[tex] 0 = (x - 11)(x + 13) [/tex]

x = 11 or x = -13

We'd take the positive value.

Therefore, the value of x is 11.

Zack delivers mail for the post office.everyday he walks a seven mile route.How many miles does Zack walk in one month if he works 22 days a month

Answers

If im right give me brainliest

Answer: 154

Step-by-step explanation: 22 represents days 7 represents miles he walks a day i think you to have to multiply. 22 times 7 is 154  

What is the measure of AX, in degrees?
N
6
Х
6
70
у

Answers

Answer:

C

Step-by-step explanation:

Since XY = XZ = 6, then the triangle is isosceles.

The base angles are therefore congruent, that is

∠ Y = ∠ Z = 70°

The sum of the 3 angles in the triangle = 180°, thus

∠ X = 180° - (70 + 70)° = 180° - 140° = 40° → C

mx - y = 7
How do I solve for x

Answers

Explanation and Awnser:

y=mx−7

Swap sides so that all variable terms are on the left hand side.

mx−7=y

Add 7 to both sides.

mx=y+7

Divide both sides by m.

m

mx

=

m

y+7

Dividing by m undoes the multiplication by m.

x=

m

y+7

Barry wants to take out a loan from his bank for $1000 to buy bicycle the interest rate on the loan from the bank is 9% he wants to pay the toll amount in three monthly payments what is the amount that vary with pay in interest rate loan

Answers

Answer:

22.50

Step-by-step explanation:

formula I=prt

I=1000x0.09x.25

I=22.50

The required interest paid by Barry is given as, $22.5.

Given that,
Barry wants to take out a loan from his bank for $1000 to buy a bicycle the interest rate on the loan from the bank is 9% he wants to pay the toll amount in three monthly payments what is the amount that varies with pay in interest rate loan is to be determined.

What is interest?

Simple interest is defined as the percentage of earnings on the lending for a period of time

Here,
Principal = 1000
Rate = 9%
Time = 3 / 12 = 0.25 years
So,
Interest = Principal × rate × time
interest = 1000 × 0.09 × 0.25
Interest = $22.5

Thus, the required interest paid by Barry is given as, $22.5.

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Angie uses the equation E=0.03s + 25,000 to find her yearly earning E based on her total sales s. What is the independent variable

Answers

Answer:

25000

Step-by-step explanation:

it's independent because it's not related with her total sales s

Solve for a.
1/2a - 4 = 6

Answers

a=20, you simplify both sides of the equation and then isolate the variable to find a

Which graph is the solution to the inequality below?

Answers

Answer:

it the third answer

Step-by-step explanation:

3(x-5)< 5x+7

x>-11

Equations and Inequalities One-Pager

Answers

Could I see a picture cause not sure

SOLVE FOR X. HELP ME NOW PLEASE!

Answers

Answer:

For number 2, its A. For number 1, its C.

Step-by-step explanation:

For both equations, you just set it equal to to each other because alternate interior angles are equivalent.

2) The equation would be

     7x+3=6x+12

   Then solve.

1) The equation would be

     14x-3=95

   Then solve.

I love geometry! If you have questions, just comment.

In the souvenir shop, Gary finds a shirt and a key chain he would like to buy. The shirt costs $13.75 and the key chain costs $2.33. What will be the total of Gary's souvenirs?

Answers

Answer:

$16.08

Step-by-step explanation:

13.75+2.33=16.08

ANSWER ASAP!! THIS IS GEOMETRY SCALE FACTORS. ONLY ANSWER IF YOU KNOW FOR SURE!

Answers

Answer:

45

Step-by-step explanation:

The scale is 3:1 so multiply 15 by 3 just like 12 to 36.

Answer:

30

Step-by-step explanation:

HELP ILL GIVE BRAINLIEST FOR RIGHT ANSWER
Which expression represents each mathematical phrase? Drag the answer into the box to match each phrase. subtract 9 from z add 9 and z divide 9 by z multiply 9 by z

Answers

1. z-9 2. 9+z 3. I THINK 9/z 4. 9z

Answer:

subtract 9 from z = z - 9

add 9 and z = 9 + z

divide 9 by z = 9/z

multiply 9 by z = 9z

Step-by-step explanation:

It's tricky but if you pay attention it's pretty easy dude.

PLEASE HELP!!! GIVING BRAINLIST

If x + 2y = 8 and x/2 -y= 10, then x = ?
A)-3
B) 0
C) 10
D) 14

Answers

Answer:

D. 14

make y the subject of the formula in equation 1 and then substitute it in equation 2

Nathaniel invested $37,000 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $70,900?

Answers

Answer:

11

Step-by-step explanation:

\text{Compounded Daily:}

Compounded Daily:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

 

Compound interest formula

A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365

A=70900P=37000r=0.057n=365

Given values

70900=

70900=

\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}

37000(1+  

365

0.057

​  

)  

365t

 

Plug in values

70900=

70900=

\,\,37000(1.0001562)^{365t}

37000(1.0001562)  

365t

 

Simplify

\frac{70900}{37000}=

37000

70900

​  

=

\,\,\frac{37000(1.0001562)^{365t}}{37000}

37000

37000(1.0001562)  

365t

 

​  

 

Divide by 37000

1.9162162=

1.9162162=

\,\,1.0001562^{365t}

1.0001562  

365t

 

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)

log(1.0001562  

365t

)

Take the log of both sides

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\color{blue}{365t}\log\left(1.0001562\right)

365tlog(1.0001562)

Bring exponent to the front

\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=

log(1.0001562)

log(1.9162162)

​  

=

\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}

log(1.0001562)

365tlog(1.0001562)

​  

 

Divide both sides by log(1.0001562)

4164.8632402=

4164.8632402=

\,\,365t

365t

Use calculator

\frac{4164.8632402}{365}=

365

4164.8632402

​  

=

\,\,\frac{365t}{365}

365

365t

​  

 

Divide by 365

11.4105842=

11.4105842=

\,\,t

t

t\approx

t≈

\,\,11

11

Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.

Hence, the parameters are given as follows:

[tex]A(t) = 70900, P = 37000, n = 365, r = 0.057[/tex]

We have to solve for t, then:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}[/tex]

[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}[/tex]

[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622[/tex]

[tex](1.00015616)^{365t} = 1.91621622[/tex]

[tex]\log{(1.00015616)^{365t}} = \log{1.91621622}[/tex]

[tex]365t\log{1.00015616} = \log{1.91621622}[/tex]

[tex]t = \frac{\log{1.91621622}}{365\log{1.00015616}}[/tex]

t = 11.41

Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.

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A computer company offers a special discount to college students of 15% off. Find the discounted price of a computer that costs $1265.

Answers

Answer:

1075.25

Step-by-step explanation:

subtract the 15 percent using freindly percents

NEED ANSWER ASAP PLEASE HELP!!!
What composition of transformations is equivalent to a rotation of 180°?
Open-ended question

Answers

I think it’s 90 because 180 divided by 2 is 90

Answer:

90 is correct good job

Step-by-step explanation:

Find the ratios x:y:z if x:y=9:10 and y:z=5:3

Answers

Answer:

Step-by-step explanation:

Answer:

x : y : z = 9 : 10 : 6

Step-by-step explanation:

Expressing the ratio y : z = 5 : 3 in fractional form, that is

[tex]\frac{y}{z}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )

5z = 3y ( divide both sides by 5 )

z = [tex]\frac{3}{5}[/tex] y = [tex]\frac{3}{5}[/tex] × 10 = 3 × 2 = 6

Thus

x : y : z = 9 : 10 : 6

At Gloria’s Restaurant, the average diner tips 18% of their total bill. Carter’s bill was $66.50. How much money should Carter tip?

Answers

Answer:

$11.97

Step-by-step explanation:

If Carter were to tip that 18%, then he should give a $11.97 tip.

0.6650 x 18 = 11.97

The amount Carter should tip at the restaurant is $11.97.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, At Gloria’s Restaurant, the average diner tips 18% of their total bill.

Therefore, The amount Carter must tip should be 18% of 66.50 which can be numerically expressed as,

(18/100)×66.50.

= $11.97.

So, Carter should tip $11.97.

learn more about percentages here :

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True or False
If an acute angle is 80o then we add the obtuse angle of 110o to equal 180o?

Answers

Answer:

true

Step-by-step explanation:

24% of what number is 16.08

Answers

Answer:

67

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

16.08*100/24 is the formula

what is 2/3 divided by 1/2 in fractions

Answers

Answer:

4/3

Step-by-step explanation:

Answer:

the answer is 4/3

Step-by-step explanation:

Hope that helps!

Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: ∠1 ≅ ∠4.

Answers

Answer:

∠1 ≅ ∠4 because yeah

Step-by-step explanation:

A person can pay $9 for a membership to the history museum and then go to the museum for just $1 per visit. For a member of the history museum, what is the total cost of 23 visits?

Answers

Answer:

$32

Step-by-step explanation:

  Step one:

Given that membership is $9 and the cost per visit is $1

let the number of visits be x

and the total cost be y

the total cost  for the situation is modeled as

y=mx+c-----equation of a line

   Step two:

given that x=23, we can solve for the totals cost as

by substituting we have

y=1*23+9

y=23+9

y=32

The total cost for 23 visits is $32

James bought 6 2/3 cups of raising to use in a recipe for oatmeal raisin cookies. If he plans on making three separate batches of cookies, how many cups of raisins will go to each batch?

Answers

eu não sei

espero ter ajudado muito

espero ter ajudado muito

You form a company with two other partners. You own 40%, partner two owns 35% and partner three owns 25%. The company makes $950,000 in the first year and distributes profits in proportion to each partners ownership share. How much does partner two get?

Answers

Answer:$332,500

Step-by-step explanation:

I used a percent calculator and got it correct

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