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
Zagia is taking a bicycling trip across the United States. Her destination is 3, 150
miles away. If Zagia travels 90 miles per day, how far does she have left to travel
after 20 days of bicycling?
The distance left after 20 days is
miles.
Answers
Answer: The distance left after 20 days is 1350 miles
Step-by-step explanation:
To calculate the distance, we use the formula:
[tex]s=\frac{d}{t}[/tex]
where,
s = speed of the bicycle = 90 miles/day
t = time taken = 20 days
d = distance travelled = ? miles
Putting values in above equation, we get:
[tex]d=(90miles/day\times 20days)=1800 miles[/tex]
Total distance to the destination = 3150 miles
Distance travalled in 20 days = 1800 miles
Distance left after 20 days = [3150 - 1800] = 1350 miles
Hence, the distance left after 20 days is 1350 miles
Jimmy wants to draw a 50° angle. Fill in the missing step to make sure his drawing is completed in the correct order:
Step 1: He draws a ray.
Step 2: He lines up his protractor with the baseline on the ray and the origin of the protractor on the vertex.
Step 3: ________
Step 4: He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
Step 5: He draws arrows on both ends to make them rays.
Anwsers:
1. He lines up his ruler with the ray and the zero on the ruler.
2. He finds 50° on the protractor and draws a mark on the paper.
3. He lines up his protractor with a straight line and draws a mark on the paper.
4. He draws parallel lines.
Answers
Answer:
2. He finds 50° on the protractor and draws a mark on the paper.
Step-by-step explanation:
Construction is a topic that requires a step wise procedure during the process. In the given question, since Jimmy wish to draw an angle of 50°, he should locate the angle on his protractor and draw a mark on the paper. This is with respect to the previous steps observed.
The essence of the protractor is for Jimmy to accurately measure the angle. Thus he has to determine the angle by the use of a protractor before the construction can be complete.
Therefore the required procedure in step 3 is he finds 50° on the protractor and draws a mark on the paper.
Answer He finds 50° on the protractor and draws a mark on the paper.
You invest $24,000 at a simple interest rate of 12% for 9 years, and your
investment grows by $25,920. What is the principal?
Answers
Answer:
The principal is $2400
Step-by-step explanation:
Given
[tex]P = \$24000[/tex]
[tex]t = 9[/tex]
[tex]r =12\%[/tex]
[tex]I = \$25920[/tex]
Required
The principal amount
The principal amount is the amount invested.
From the question, we understand that $24000 was invested.
Hence, the principal is $24000
Find value of x of angles
Answers
Answer:
32
Step-by-step explanation:
52=x+20
52-20=x+20-20
32=x
In a class of 40 students, 2
5
of the total number of students like to study English and 3
5
of the
total students like to study Mathematics.
a) How many students like to study English?
b)How many students like to study Mathematics?
Answers
I’m pretty sure this is right.
give 10 rational numbers between 2/3 and 4/5
Answers
Step-by-step explanation:
2/3=0.66666666666
4/5=0.80000000000
10 rational numbers between them
0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79
Answer:
67/100, 68/100, 69/100, 70/100, 71/100 72/100, 73/100, 74/100, 75/100, 76/100.
HELP ME PLSSS!
The graph below have a same shape what is the equation of the red graph?
A) g(x)=(3-x)2
B) g(x)=3-x2
C) g(x)=2-x2
D) g(x)=(2-x)2
Answers
============================================================
Explanation:
The y intercept of the blue curve f(x) is (0,5)
The y intercept of the red curve g(x) is (0,2)
We see that the y intercept has been shifted down 3 units when going from f(x) to g(x). Overall, the entire f(x) curve has been shifted down 3 units to get the g(x) curve.
Based on that, we would say
g(x) = f(x) - 3
g(x) = (5-x^2) - 3
g(x) = -x^2 + (5 - 3)
g(x) = -x^2 + 2
g(x) = 2 - x^2 ..... answer is choice C
Answer:
2-x^2
Step-by-step explanation:
Avery's piggy bank has 300 nickels
Answers
Answer:
Step-by-step explanation:
?
In the following function defined by an equation in the form y = a x squared + b x + c, identify the values of a, b, and c. y = negative x squared + 5 x a. a = 0, b = 5, c = 0 b. a = negative 1, b = 5, c = 0 c. a = 1, b = 5, c = 0 d. a = 5, b = negative 1, c = 0
Answers
Answer:
b. a = negative 1, b = 5, c = 0
Step-by-step explanation:
y = negative x squared + 5 x
y = -x² + 5x
a = -1
b = 5
c = 0
Find the value of this expression if x = -2.
x^2 – 8/x + 6
Answers
Answer:
-1
Step-by-step explanation:
x^2 – 8
-----------
x + 6
Let x = -2
(-2)^2 – 8
-----------
-2 + 6
Exponents first
4 – 8
-----------
-2 + 6
Then complete the numerator and denominator
-4
-----
4
Then divide
-1
Answer:
-1
Step-by-step explanation:
((-2)^2 - 8)/ -2+6
=>(4-8)/4
=>-4/4
=>-1
How many inches are in 1.8 yards?
Answers
Answer:
64.8 inches is the correct answer.
Step-by-step explanation:
64.8in
what is the equation of a circle with a center (-7, -3) and radius 2?
i’ll mark you brainliest!!
Answers
Answer:
2nd
Step-by-step explanation:
bvfhmvdv funny Kahn just list Kay have also off weit
für mich
du ich
You deposit $3000 in a bank account that pays 4% annual interest. Find the balance after 7 years if the interest is compounded quarterly.
Answers
Answer:
$3840.
Step-by-step explanation:
First, write down the formula: I= PRT (Interest= Principle, rate, time). Then you multiply all of the numbers (3000x0.04x7). You get 840, but then you need to add it to the $3000 which already exist, therefor you get your answer of $3840.
What is the answer for this one
Answers
Answer: 2617 centimeters cubed
Step-by-step explanation:
The formula for finding volume of a cylinder is [tex]V=\pi r^2h[/tex]
The radius is half of the diamerter which will be 7 for this figure.
The height is marked 17
[tex]\pi 7^2(17)\\\pi (49)(17)\\833\pi \\[/tex]
833π is about 2616.95
Rounded to the nearest whole number it is 2617
(3^3 × 3^2 ÷ 3^6)^-4
Answers
[tex]{\huge{\boxed{\boxed{\red{\bm{\mathsf{Answer}}}}}}}[/tex]
[tex]{\huge{\frac{3^3×3^2}{3^6}^-4}}[/tex]
[tex]{\huge{\frac{3^5}{3^6}^-4}}[/tex]
[tex]{\huge{\frac{1}{3}^-4}}[/tex]
[tex]{\huge{=81}}[/tex]
[tex]{\large{\bm{\mathsf{Be\:Brainly}}}}[/tex]
Answer:
81
Step-by-step explanation:
(3^3 × 3^2 ÷ 3^6)^-4
(27 * 9/ 729)^-4
(243/729)^-4
(1/3)^-4
81
An expression is shown below.
3m + 9
Which expression is equivalent to the given expression?
A 12m
B 3(m + 3)
C 27m
D 3(m + 9)
Answers
Answer:
B 3(m + 3)
Step-by-step explanation:
A 12m no constant
B 3(m + 3) Distribute 3m +9 yes
C 27m no constant
D 3(m + 9) Distribute 3m +27 wrong constant
Which expression is not equivalent to 8 + (n – 4)?
12+n
n+4
(8 + n) – 4
(8 – 4) +n
Answers
Answer: n+4
Step-by-step explanation:
Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?
x less-than negative 5
x greater-than negative 5
x greater-than negative 1
x less-than negative 1
Answers
Answer:
B
Step-by-step explanation:
Let the number = x
2/5 (x - 1)
<
3/5 (x + 1)
2/5 (x - 1 ) < 3/5(x+ 1) Multiply both sides by 5
2(x - 1) < 3 ( x + 1) Remove the brackets.
2x - 2 < 3x + 3 Add 2 to both sides
2x < 3x + 5 Subtract 3x from both sides
2x - 3x < 5
- x < 5 Here's the tricky part . Divide by - 1
x > -5 Notice what happened. The < become > That happens because you have divided (or multiplied) by a negative number.
The original question 2/5 (x - 1 ) < 3/5(x+ 1) was graphed. The red part is every value that satisfies the inequality. You should be using a y and x together to find a more suitable answer using this program. But if you just look along the x axis, you will see that the < has been turned around.
B The second one from the top.
Create a number line to illustrate the following operations and find the solution.
Answers
Answer:
416
Step-by-step explanation:
26 times 16 is 416
What is the length of leg s of the triangle below?
459
872
90+
45
A. 8
B. v
C. 8-12
D. 4.2
E. 1
F. 2
Answers
Answer:
option A
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 = opposite / hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] = s/[tex]8\sqrt{2}[/tex]
[tex]\frac{1}{\sqrt{2} } *8\sqrt{2}[/tex] = s
root 2 and root 2 gets cancel
8 = s
if 4lm+3=18 then m =
Answers
Answer:
4(m+3)=18
m+3=18/4=9/2
m=9/2-3
m=9-6/3
m=3/3=1
so,
m=1
Step-by-step explanation:
Find the area of the parallelogram in the figure below. Round your final answer to the nearest tenth.
16.8
D
23.2
23.2
12.4
B
Answers
Expand & simplify ( 3 x − 2 ) ( 3 x - 2 ) + ( x + 6 ) ( x − 8 )
Answers
Answer:
x=2,92 or x=_1.51
Step-by-step explanation:
factories out all the brackets first
(3x_3)(3x_2)+(x+6)(x_8)
9x^2_6x_6x+4+x^2_8x+6x_48
add and sutract only like terms
10x^2_14x_44
solve the equation using the quadratic fomula
x =2.91 and x= _1.51
24.
What is the value of x to the nearest tenth?
A. 4.8
B. 9.2
C. 7.2
D. 12.0
Answers
I'm not sure it its prob D
There are 12 people in an office with 3 different phone lines. If all the lines begin to ring at once, how many groups of 3 people can answer these lines
Answers
Answer: the required answer is 1320
Step-by-step explanation:
Total people = 12
Different phone lines = 3
We will choose the person to answer the first phone in 12 ways.
Then choose the second person in 11 ways. (11 people left)
Then choose the third person in 10 ways. ( 10 people left)
The number of groups of 3 people can answer these lines[tex]12 \times11\times10=1320[/tex]
Hence, the required answer is 1320
i need to figure this out, but im d*mb.
If i can get 1000 of something for 15$, then how much can i get of it for 10$? need help asap
Answers
Answer:
666Step-by-step explanation:
1000 off ⇒ $151 off ⇒ $15/1000 = $0.015Let the required number is x, then we have:
x off ⇒ $10x * 0.015 = 10x = 10/0.015x = 666 (rounded down to whole number)Answer:
We get 666 of something in $ 10.
Step-by-step explanation:
Given that :-
We get 1000 of something for $ 15
Find that :-
How much we can get it in $ 10
Let as assume that : -
Let required number be x.Solution :-
$ 15 = $ 10
1000 = x
Using cross multiplication method
15 × x = 10 × 100 0
multiply ,
15 x = 10000
Divide each side by 15.
15 x / 15 = 10000 / 15
x = 666
express 0.484848..... in p/q form
Answers
It's in p/q form where p = 16 and q = 33.
=======================================================
Work Shown:
x = 0.484848.....
100x = 48.4848.....
I multiplied both sides by 100 to move the decimal over 2 spots. Both decimal values for x and 100x have an infinite string of "48"s repeated after the decimal point. When we subtract, those infinite strings will cancel out
100x - x = 99x
48.4848..... - 0.484848..... = 48
So after subtracting straight down, we have the new equation 99x = 48 which solves to x = 48/99
Divide both parts by the GCF 3 to fully reduce
48/3 = 16
99/3 = 33
Therefore, x = 48/99 = 16/33 = 0.484848...
I recommend using a calculator to confirm that 16/33 = 0.484848...
Side note: your calculator may round the last digit, but this is of course rounding error
Which of the following represents the factorization of the trinomial below?
X2 - 2x - 48
ANSWER
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x + 6)(x - 8)}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 2x - 48[/tex]
[tex] = {x}^{2} - 8x + 6x - 48[/tex]
Taking [tex]x[/tex] as common from first two terms and 6 from last two terms, we have
[tex] =x \: ( \: x - 8 \: ) + 6 \: ( \: x - 8 \: )[/tex]
Taking the factor [tex](x-8)[/tex] as common,
[tex] = (x + 6)(x - 8)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
(X+6)(x-8)
Step-by-step explanation:
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford? Round your answer to the nearest dollar.
S
b) How much total money will you pay the loan company? Round your answer to the
nearest dollar.
C) How much of that money is interest? Round your answer to the nearest dollar.
S
Question Help: D Postito forum
Submit Question
Answers
9514 1404 393
Answer:
loan: $157,823repaid: $378,000interest: $220,177Step-by-step explanation:
For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...
A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495
Then the amount repaid after 360 payments is ...
360A = 2.39508898 . . . times the principal amount
__
a) For a monthly payment of $1050, the principal can be ...
$1050/0.00665302495 ≈ $157,823
__
b) The amount repaid to the loan company is ...
$157,823×2.39508898 ≈ $378,000
__
c) The amount that is interest is ...
$378,000 -157,823 = $220,177
Find the measure of angle X. The horizontal lines are parallel. HINT: The sum
of all interior angles in a triangle is 180 degrees.
Answers
===========================================================
Explanation:
The angle adjacent and supplementary to the 107 degree angle is 73 degrees because 107+73 = 180.
Or you could say 180 - 107 = 73.
The base angles of the upper isosceles triangle are 73 degrees each, which means the third remaining angle (let's call it y for now) is
73+73+y = 180
146+y = 180
y = 180-146
y = 34
Refer to the diagram below. Notice how the 34 degree angle shows up twice because we have vertical angles. Consequently, the base angles of the bottom isosceles triangle are y = 34 degrees each
We can now solve for x
y+y+x = 180
34+34+x = 180
68+x = 180
x = 180-68
x = 112, so the answer is choice D