Triangle ABC is translated to create triangle DFG, as shown below.
2y + 12 cm
212y - 3) cm
312x + 10) cm
12x + 12 cm
G
In these triangles, side AB is congruent to side DF, and side BC is congruent to side FG. Determine the values of x
andy
Show your work
Answers
Answer:
[tex]x=3[/tex]
[tex]y = 9[/tex]
Step-by-step explanation:
Given
The translated triangles
Required
Find x and y
We have:
[tex]AB = DF[/tex]
[tex]BC = FG[/tex]
[tex]AB = DF[/tex] means:
[tex]3(2x + 10) = 12x + 12[/tex]
Open bracket
[tex]6x + 30 = 12x + 12[/tex]
Collect like terms
[tex]12x - 6x = 30 -12[/tex]
[tex]6x = 18[/tex]
Divide by 6
[tex]x=3[/tex]
[tex]BC = FG[/tex] means
[tex]2y + 12 = 2(2y - 3)[/tex]
Open bracket
[tex]2y + 12 = 4y - 6[/tex]
Collect like terms
[tex]4y - 2y = 12+6[/tex]
[tex]2y = 18[/tex]
Divide by 2
[tex]y = 9[/tex]
Related Questions
One number is 8 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1090, find the numbers.
Answers
Answer:
Number one: x
Number two:8x
Number three: x+ 100
They added together equal to 1090:
x + 8x + x+ 100 = 1090
10x= 1090-100
10x=990
x=99
Number one: 99
Number two: 792
Number three: 199
Sum: 1090
What is f(-2) for f(x)=(1/2)x^2
Answers
Answer:
[tex]{ \bf{f(x) = \frac{1}{2} {x}^{2} }} \\ \\ { \tt{f( - 2) = \frac{1}{2} {( - 2)}^{2} }} \\ = 2[/tex]
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 30 months at 8% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
$
Answers
Answer:
13.33
Step-by-step explanation:
Because it's only payment one we can easily figure out the interest portion
we first need the effective rate
.08/12= .006666667
We the just mulitply this by loan amount
2000*.006666667= 13.33
Step-by-step explanation:
its your answer
I hope it's help you
Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
2) Phủ định hai phán đoán ở phần 1) (viết dưới dạng câu văn hoàn chỉnh).
Answers
Answer:
Step-by-step explanation:
Shen started to run on a treadmill after setting its timer for 93 minutes. The display says that he has finished 69% of his run. How many minutes have gone by?
Round your answer to the nearest tenth.
Answers
Answer:
64.2 minutes
Step-by-step explanation:
We are given that
Shen set timer to run=93 minutes
He has finished his run=69%
We have to find total number of minutes have gone by.
69% of 93
=[tex]\frac{69}{100}\times 93[/tex]
By using
a%[tex]=\frac{a}{100}[/tex]
69% of 93=[tex]\frac{6417}{100}[/tex]
69% of 93=64.17 min
69% of 93[tex]\approx 64.2min[/tex]
Hence, 64.2 minutes have gone by.
Consider random samples of size 86 drawn from population A with proportion 0.43 and random samples of size 60 drawn from population B with proportion 0.15
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
(b) Are the sample sizes large enough for the Central Limit Theorem toa
Yes or No?
Answers
Answer:
a) The standard error is s = 0.071.
b) Yes, as both sample sizes are above 30.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of size 86 drawn from population A with proportion 0.43
This means that [tex]n = 86, p = 0.43[/tex]. So:
[tex]s_A = \sqrt{\frac{0.43*0.57}{86}} = 0.0534[/tex]
Samples of size 60 drawn from population B with proportion 0.15:
This means that [tex]n = 60, p = 0.15[/tex]. So:
[tex]s_B = \sqrt{\frac{0.15*0.85}{60}} = 0.0461[/tex]
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
This is:
[tex]s = \sqrt{s_A^2 + s_B^2}[/tex]
[tex]s = \sqrt{(0.0534)^2 + (0.0461)^2}[/tex]
[tex]s = 0.071[/tex]
The standard error is s = 0.071.
(b) Are the sample sizes large enough for the Central Limit Theorem. Yes or No?
Yes, as both sample sizes are above 30.
HELP MATH ANSWER QUESTION
Answers
Answer:
Last one.
Step-by-step explanation:
[tex]\sqrt{3}[/tex] is used in 30-60-90 triangles
[tex]\sqrt{2}[/tex] is used in 45-45-90 triangles
Base is x, leg is x[tex]\sqrt{3}[/tex], hypotenuse is 2x
Answer:
x = 20 ; y= 10√3
Step-by-step explanation:
30, 60 , 90 triangle ratio is
Side opposite to 30 is a
a = AC = 10
Side opposite to 60 is a[tex]\sqrt{3}[/tex]
AB = a[tex]\sqrt{3}[/tex] = 10√3
Side opposite to 90 is 2a
BC = 2a = 2* 10 = 20
what is a proof
PLS PLS PLS HELP GELP HELPPPPPPPP
Answers
A. Definition = (the third meaning.)
B. Postulate (axiom) = (the first meaning.)
C. Common notion = (the last meaning.)
D. Theorem = (The second meaning.)
E. Corollary = (the fourth meaning.)
Proof is evidence or an argument that helps to establish a fact or the truth of a statement. For example, most people won't accept new concepts or ideas without proof of its existence.
Peter Piper picked a pickled pepper out of a pepper jar. If the probability of drawing a pickled pepper was 2/5,
how many total peppers could be in the jar (psst. you can't have a half of a pepper)?
Answers
Answer:
5
Step-by-step explanation:
2/5 pickled peppers means that there are 2 pickled peppers out of 5 total peppers.
Mô hình quy hồi tuyến tính và ứng dụng
Answers
Answer:
where are you from Korea or not
Hope it helps you!
-miraculousfanx-
What is the system of equations represented by the tables?
O A. y=2x-1
y = -x + 3
B. y = x + 2
y = x-1
O c. y=-3x-1
y = 3x + 2
O D. y = 2x-3
y = -x + 2
Answers
Answer:
C.
y = -3x - 1
y = 3x + 2
Step-by-step explanation:
Find the slope (m) and y-intercept (b) of each table to write an equation for each.
✔️First table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, -1) and (1, -4),
Slope (m) = (-4 - (-1))/(1 - 0) = -3/1
m = -3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = -1 when x = 0. Therefore,
y-intercept (b) = -1
To write an equation for table 1, substitute m = -3 and b = -1 into y = mx + b
Equation for table 1:
y = -3x - 1
✔️ Second table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, 2) and (1, 5),
Slope (m) = (5 - 2)/(1 - 0) = 3/1
m = 3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = 2 when x = 0. Therefore,
y-intercept (b) = 2
To write an equation for table 1, substitute m = 3 and b = 2 into y = mx + b
Equation for table 1:
y = 3x + 2
Anna's electricity bill costs $21.59 per month plus $4.66 per kilowatt hour. How many kilowatt hours can she use and keep
her bill to no more than $51?
Round your answer to a whole number
Answers
Answer:
6 kwh
Step-by-step explanation:
(51 - 21.9)/4.66 = 6.24 => 6 kwh
simplify 7^1
4^0
6^-1
Answers
1. [tex] \: {7}^{1} [/tex]
➺ [tex]\boxed{\: 7 }[/tex]
2. [tex] \: {4}^{0} [/tex]
➺ [tex]\boxed{ \: 1 }[/tex]
( ∵ any number to the power of 0 is 1. )
3. [tex] \: {6}^{ - 1} [/tex]
➺ [tex] \: \frac{1}{6} [/tex]
[tex]( \: ∵ {a}^{ - 1} = \frac{1}{a} )[/tex]
➺ [tex]\boxed{ \: 0.1667 }[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?
To maximize his income, Dr. Lum should teach_______classes for Hilltop College and __________classes for Serra College. His maximum income would be________.
Answers
Answer:
z (max) = 34500 $
x₁ = 2
x₂ = 3
Step-by-step explanation:
Hilltop College
3 hours per week preparing lessons and grading papers
Serra College
4 hours per week preparing lessons and grading papers
Total hours to spend per week preparing lessons 18
Let´s call x₁ numbers of class at Hilltop College
and x₂ numbers of class at Serra College then:
Objective function
z = 6000*x₁ + 7500*x₂
Constraints:
1.- x₁ + x₂ ≤ 5 the total number of class
2.- 3*x₁ + 4*x₂ ≤ 18
3. General constraints x₁ ≥ 0 x₂ ≥ 0 integers
After 6 iteration optimal solution is: From on-line solver
z (max) = 34500 $
x₁ = 2
x₂ = 3
What does it mean to the rise over run when the slope is an integer? a. the rise number is one c. the run part of the slope is going to be one b. the run number is always negative d. there will be no slope Please select the best answer from the choices provided A B C D
Answers
Answer: integer is a whole number
Eg
10/2 = 5/1 = 5 = integer
But 12/8 = 3/2 = 1.5 = not an integer
So really, slope = integer
Means rise greater than run
And run is a factor of rise
Or run = 1 will satisfy the above too :)
Answer:
C. The run part of the slope is going to be one
Step-by-step explanation:
.
Dennis collected a total of 1712 stamps over the past 16 years At this rate how many stamps would he collect in 21 years
Answers
2,247
Step-by-step explanation:
you take 1712 and divide that by 16 which is 107 and then you multiply 107 by 21 thus you get 2,247.
The list price on slacks is $22, and the list price on jumpers is $37. If Petit’s Clothing Store orders 30 pairs of slacks and 40 jumpers at a discount rate of 11%, what is the trade discount on the purchase?
Answers
Answer: $235.4
Step-by-step explanation:
Given
Price list on slacks is $22
Price list on jumpers is $37
Store ordered 30 pairs of slacks and 40 Jumpers
Total price becomes
[tex]\Rightarrow 22\times 30+37\times 40\\\Rightarrow \$2140[/tex]
for a discount of 11%
Trade discount is [tex]2140\times 11\%[/tex]
[tex]\Rightarrow 2140\times 0.11\\\Rightarrow \$235.4[/tex]
What is the domain of the function y=3 sqrt x?
Answers
Answer:
Step-by-step explanation:
y=3√x
domain : all real values≥0
Pls I’ve been stuck on this
Answers
Area of a circle is pi x radius^2
Area = pi x 22 ^2
Area = pi x 484
Area = 1,519.8 mm^2
Answer:
1520.5mm²
Step-by-step explanation:
Area of a circle=πr²
π(22mm)²
π484mm²
1520.5308443374599mm²
to one decimal place
1520.5mm²
What is MS Word?
O It is a computerized tool.
O It is a calculating tool
O It is a graphic design tool.
O Its is a typing tool.
Answers
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Round your answer to nearest tenth if necessary,
Answers
Answer:
JK ≈ 12.3
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{FI}{JM}[/tex] = [tex]\frac{FG}{JK}[/tex] , substitute values
[tex]\frac{59}{26}[/tex] = [tex]\frac{28}{JK}[/tex] ( cross- multiply )
59 JK = 728 ( divide both sides by 59 )
JK ≈ 12.3 ( to the nearest tenth )
find the square root of 20 1/4
Answers
Answer:
Step-by-step explanation:
[tex]20 \frac{1}{4} =\frac{80+1}{4} =\frac{81}{4} \\\sqrt{\frac{81}{4} } =\frac{9}{2} =4.5[/tex]
Please help me solve this. I keep getting the answer weong
Answers
Answer:
21 is the answer I think sike I lied ik its not im just trying get this over with
You can use this formula to work out the area of a triangle when you know two sides and the angle inbwtween them :
1/2 x a x b x sin(C)
where a and b are the two sides you know and C is the angle in between them.
So here a = 7, b = 14, C = 125.
Area = 1/2 x 7 x 14 x sin(125) = 40.138...
= 40.1 (nearest 10th)
Choose the equation of the line that is parallel to the x-axis.
x = 4
x + y = 0
x = y
y = 4
Answers
When y = 0 the line falls on the x axis, so when y = 4, it will move up 4 spaces and be parallel to the x axis.
Hope this helps!!
Can someone please help me out?
The difference between two numbers is 16. The first number is three times the other number. What are the numbers?
A. 8 and 25
B. 8 and 24
C. 9 and 24
D. 9 and 25
No links or fake answers pls
Answers
24 is three times the value of 8 and when you subtract 8 from 24 you receive a total of 16.
9514 1404 393
Answer:
B. 8 and 24
Step-by-step explanation:
There are a number of approaches you can use here. One of them is to choose the only answer that makes any sense in the problem.
The problem tells you the numbers have a ratio of 3, so numbers like 8 and 25, 9 and 24, 9 and 25 cannot be the answer.
The only answer choice that makes any sense is B: 8 and 24.
__
If you want to work the problem, there are different ways you can do that. One of my favorite is to consider ratio units. The ratio of the two numbers is 3:1. The difference of the two numbers is 3-1 = 2 ratio units, which we are told is 16. Then each ratio unit represents 16/2 = 8. Then the numbers are ...
3×8 and 1×8 = 24 and 8.
Or, you can let a variable represent one of the numbers. If x is the first number, then the other number is 1/3x, and their difference is ...
x -1/3x = 16
2/3x = 16
x = 16(3/2) = 24
The numbers are 24 and 24/3 = 8.
__
Additional comment
You need to talk to your teacher about this question. The answer choices list the smaller number first, but the problem statement tells you the first number is 3 times the second number. The correct answer would be 24 and 8.
The function is f(x) is shown on the graph.
What is f(0)
•12 only
•2 and 3 only
•-2, -1, 1, and 2 only
•-2, -1, 1, 2 and 12
Answers
Answer:
12 only
Step-by-step explanation:
The function is given on the graph.
What is f(0)?
This is the value of y when x = 0.
Looking at the horizontal axis, when x = 0, the vertical axis is at y = 12, and at no other point the horizontal axis is at x = 0, which means that the correct answer is given by:
12 only
Suppose the mean height for men is 70 inches with a standard deviation of 2
inches. What percentage of men are between 68 and 74 inches tall? Enter
the value of the percentage without the percent sign.
Answers
Answer:
81.85.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose the mean height for men is 70 inches with a standard deviation of 2 inches.
This means that [tex]\mu = 70, \sigma = 2[/tex]
What percentage of men are between 68 and 74 inches tall?
The proportion is the p-value of Z when X = 74 subtracted by the p-value of Z when X = 68.
X = 74
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74 - 70}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 68
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 70}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.9772 - 0.1587 = 0.8185
0.8185*100% = 81.85%.
Thus the percentage is 81.85%, and the answer is 81.85.
What is 2+2-35x62+88-1x675
Answers
[tex]\longrightarrow{\blue{ -2753}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]2 + 2 - 35 \times 62 + 88 - 1 \times 675[/tex]
[tex] = 2 + 2 - 2170 + 88 - 675[/tex]
[tex] = 92 - 2170 - 675[/tex]
[tex] = 92 - 2845[/tex]
[tex] = - 2753[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Use the graph to estimate f(4)
Answers
Answer:
f(4) = 1
Step-by-step explanation:
Locate x = 4 on the x- axis, then go vertically up to meet the graph at (4, 1 ) , then
f(4) = 1
The value of the function f(4) is 1. The correct option is C.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The value of the function f(4) will be calculated as below:-
Locate x = 4 on the x- axis, then go vertically up to meet the graph at (4, 1 ) ,
f(4) = 1
Therefore, the value of the function f(4) is 1. The correct option is C.
To know more about functions follow
https://brainly.com/question/17365692
#SPJ5
Will mark BRAINLIEST!! This is pt.2
Answers
Answer:
See below.
Step-by-step explanation:
Problem 3.
1. <3, <4
Given
2. <1, <2
Given
3. KG
Congruence of segments is reflexive.
4. HKG, LKG
ASA
Problem 4.
1. MR, OR
Given
2. PR, NR
Given
3. <2
Vertical angles are congruent.
4. MPR, ONR
SAS
