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'
Answers
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
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
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.
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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
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:
$32Step-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
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.
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 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
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
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
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!
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:
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
Solve for a.
1/2a - 4 = 6
Answers
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>-11Find 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
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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Equations and Inequalities One-Pager
Answers
NEED ANSWER ASAP PLEASE HELP!!!
What composition of transformations is equivalent to a rotation of 180°?
Open-ended question
Answers
Answer:
90 is correct good job
Step-by-step explanation:
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
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
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
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.
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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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:
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
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.
Identify all segments that are parallel to XY
A. ST
B. VZ, VW, ST
C. QR, QU
D. VW
Answers
Answer:
a. ST
Step-by-step explanation:
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:
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
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
Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: ∠1 ≅ ∠4.
Answers
Answer:
∠1 ≅ ∠4 because yeah
Step-by-step explanation:
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.