Question 23) Triangle PQR Triangle XYZ
PQ = 3a + 4 and XY = 5a - 12. Find a and PQ.
Answers
the way I solved the problem is attached. hope this helped.
The value of 'a' will be 8.
And, The value of side PQ will be 28 units.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle PQR ≅ Triangle XYZ
Now,
Since, Triangle PQR ≅ Triangle XYZ
So, we get;
Measure of PQ = Measure of XY
Substitute the given values of sides, we get;
Measure of PQ = Measure of XY
⇒ 3a + 4 = 5a - 12
Solve for a as;
⇒ 3a + 4 = 5a - 12
⇒ 3a - 5a = - 12 - 4
⇒ - 2a = - 16
⇒ 2a = 16
⇒ a = 8
Hence, Measure of PQ = 3a + 4
= 3 × 8 + 4
= 24 + 4
= 28
Thus, The value of 'a' will be 8.
And, The value of side PQ will be 28 units.
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Related Questions
Justin and Tyson are beginning an exercise program to train for football season and want to build muscle. Justin weighs 150 pounds and hopes to gain 2 pound per week. Tyson weighs 160 pounds and hopes to gain 1 pound per week. After how many weeks will they weigh the same amount?
Answers
Answer:
At 15 weeks they will both weigh 180
Step-by-step explanation:
150 + 2w = 195 - w
2w + w = 195 - 150
3w = 45
w = 45/3
w = 15 <=== they will weigh the same at 15 weeks
150 + 2(15) = 150 + 30 = 180...and they will both weigh 180 lbs
I hope this helps you :)
An investment company pays 7% compounded semiannually. You want to have $24000 in the future. How much should you deposit now to have that amount 5 years from now?
Answers
Answer: You should deposit about $17014 or little more
Step-by-step explanation:
use the compound interest formula.
A= p( 1 + r/n)^nt
Where A is the amount you will save over some years .
p is the principal or start up amount mostly known as the initial fee.
r is the interest rate represent by a decimal so 7% will be 0.07.
n is the number of times the interest is being applied annually. Semiannually means twice. So n will be 2.
T is the time the money will elapsed. So in 5 years the money will elapse. Now input the values into the formula and solve for p the principal.
24,000 = p( 1 + 0.07/2)^2*5
24,000= p( 1 + 0.035)^10
24000 = p( 1.035)^10
24000 = p( 1.41059876062) Divide both sides by 1.41059876062
p = 17104
Which means you should deposit about $17014 or little more
Sarah sold 12 boxes of girl scouts cookies. If Sarah sold three times as many boxes as Amiyah, how many boxes did Amiyah sell?
Answers
Answer:4
Step-by-step explanation:
you would set this up as 3x = 12.
to solve, just divide the 12 by 3, leaving you with X = 4.
what is this answer and please show me how you got it so I can know how you got it.y= 3 [tex]\sqrt{x + 4} -6[/tex] please hurry also :0 giving 35 points to those who answer first
Answers
To find -intercept/zero, substitute y=0
Divide both sides of the equation by 3
The only way a root could be 0 is when the radicand equals 0
Calculate the difference
And you should get x=2
How do I do solving systems by substitution please help
The problem I'm on is x-y=-5 with x+y=1
Please show steps I need an answer before my report card comes in tomorrow
Answers
Answer:
I believe the answer is x=-2, and y=3.
Step-by-step explanation:
Given: x-y=-5
Fill in: -2-3=-5
Calculate: -5=5
-------------------------------
Given: x+y=1
Fill in: -2+3=1
Calculate: 1=1
Answer:
x = -2.
y = 3.
Step-by-step explanation:
x-y=-5
x+y=1
From the first equation
x = y - 5
Substitute this in the second equation:
y - 5 + y = 1
2y = 1 + 5 = 6
y = 3.
Substitute this into the second equation:
x + 3 = 1
x = -2.
Which of the following is supporting evidence of the given statement?
When dividing two numbers, the quotient is always less than the dividend.
A. −3÷(−14)=12
B. 14÷(−3)=−112
C. 3÷14=12
D. −14÷3=−112
Answers
Answer:
B
Step-by-step explanation:
killa queen disan no bakuda bites za dusto
what is 987 rounded to the nearest tenth? plzzzzz help
Answers
Answer:
990 that's the answer .
Answer:
990
Step-by-step explanation:
can someone help solve this math problem with steps and detail pls :) I really confused
Answers
Division first:
-2/5 / 8/15
When dividing two fractions flip
The second one over and multiply:
-2/5 x 15/8 = (-2x15)/(5x8) = -30/40 = -3/4
Now you have:
2-3/4-3/4
2-3/4 = 1 1/4
1 1/4 - 3/4 = 1/2
The answer is 1/2
What is the missing statement and the missing reason in step 5? A 2-column table with 7 rows. Column 1 is labeled statements with the entries measure of angle A D E = 60 degrees and measure of angle C D F = (3 x + 15) degrees, angle A D E and angle C D F are vertical angles, angle A D E is-congruent-to angle C D F, measure of angle A D E = measure of angle C D F, question mark, 45 = 3 x, and, 15 = x. Column 2 is labeled reasons with the entries given, definition of vertical angles, vertical angles congruent, definition of congruency, question mark, subtractive property, division property. Statement: 60 = 3x + 15; Reason: substitution Statement: x = 15; Reason: subtraction property of equality Statement: 60 = 3x + 15; Reason: transitive property Statement: x = 15; Reason: subtraction and division properties of equality
Answers
Answer:
Statement: 60 = 3x + 15; Reason: substitution
(aka A)
Step-by-step explanation:
The missing statement and the missing reason in step 5 is;
Statement: 60 = 3x + 15; Reason: substitution
Here,
We have to find the missing statement and missing reason.
What is Substitution method?
Substitution method is algebraic method to solve the linear equations .
Now,
Column 1 and column 2 are labeled here as;
Angle A D E = 60 degrees ( entries given)
Angle C D F = (3 x + 15) degrees
Angle A D E and Angle C D F are vertical angles. (definition of vertical angles)
Angle A D E is-congruent-to Angle C D F. ( definition of congruency)
Measure of angle A D E = Measure of angle C D F.
⇒ 60 = 3x + 15 ( substitution )
⇒ 45 = 3 x ( subtractive property )
⇒ 15 = x ( division property )
Hence, The missing statement and the missing reason in step 5 is;
Statement: 60 = 3x + 15; Reason: substitution
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Wats the equation??
9/4 = Division 4
Answers
Juan purchased 16 lemons and used 5 on the first day of making lemonade. On the second day, he purchased 12 lemons and used 11. Juan wrote this expression to find how many lemons he should have left.
(16 – 5) + (12 – 11)
Answers
So:
11+1=12
Answer:
Juan purchased 16 lemons and used 5 on the first day of making lemonade. On the second day, he purchased 12 lemons and used 11. Juan wrote this expression to find how many lemons he should have left.
Step-by-step explanation:
11+1=12
f(x) = 2x – 5
g(x) = 4x – 1
Find f (g(x)).
help please !!
Answers
Answer:
Hey there!
g(x) is 4x-1
f(g(x) is f(4x-1)
f(4x-1)=2(4x-1)-5
f(4x-1)=8x-2-5
f(4x-1)=8x-7
The answer is 8x-7
Let me know if this helps :)
the cost split among 4 people
Answers
Answer:1 dollar each
Step-by-step explanation:
The midpoint of segment AB is (1,4). The coordinates of point A are (-2, -3). Find the coordinates of point B.
A)
(3,7)
B)
(4, 11)
(4, -10)
D)
(-5, -10)
Answers
Answer:
B) (4,11)
Step-by-step explanation:
Plot the points and count how far point A is to the midpoint.The rise is 7 and run is 3 so count 3 right and 7 up from point AB to get B.
The formula c =5p +235 relates c, the total cost in dollars of hosting a birthday party at a skating dnk to p, the number of people attending. If Allie's parents are willing to spend $340 for a party, how many people can attend? The number of people that can attend the party is
Answers
-235 -235
105=5p
— —
5 5
Answer is 21
Anna has amask collection of 60 masks. She keeps 45% of the masks on her wall. How many masks does she keep on her wall?
Answers
Answer:27
Step-by-step explanation:
60x.45=27
absolute value of 100
Answers
Answer:
100
Step-by-step explanation:
Think of the absolute of a number as the distance from that number to zero on the number line. The distance from 100 to 0 on the number line is 100, so absolute value of 100 is 100. Notice that -100 is also at a distance of 100 from zero, so |-100| = 100.
|100| = 100
can someone help me i will mark
Answers
Answer:
8+3/4w
Step-by-step explanation:
+) Six times the sum of a number and -1 is the same as 2 more than 8 times the number. Find the number.
Answers
Answer:
-4
Step-by-step explanation:
6(a+(-1)) = 8a + 2
then:
6(a-1) = 8a + 2
6*a + 6*-1 = 8a + 2
6a - 6 = 8a + 2
6a - 8a = 2 + 6
-2a = 8
a = 8/-2
a = -4
Check:
6(-4-1) = 8*-4 + 2
6*-5 = -32 + 2 = -30
Find the endpoint of Segment AB, if A(2,5) and the midpoint is (0, 2).
Find the other end point!
Answers
Answer:
Step-by-step explanation:
(x + 2)/2 = 0
x + 2 = 0
x = -2
(y + 5)/2= 2
y + 5 = 4
y = -1
(-2, -1) the other endpoint
the correct simplified form of 2y5+4y5−3y3−5y3
Answers
Hey there! I'm happy to help!
Numbers with the same variable and exponent are like terms and can be simplified.
[tex]2y^5+4y^5=6y^5[/tex] (variable is y, exponent is 5)
[tex]-3y^3-5y^3=-8y^3[/tex] (variable is y, exponent is 3)
So, our final simplified form is [tex]6y^5-8y^3[/tex].
Have a wonderful day! :D
answerers about Caca Andika from Indonesia
What is the product of 5/8 x 3/4 ?
Answers
Answer:
15/32 or 0.46875
Step-by-step explanation:
Answer:
Step-by-step explanation:
B
Why is thinking about the problem before you work important?
Answers
Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D
(7x7x7x7x7x7x7)-3x-3x-3
Answers
Answer:
823516
Step-by-step explanation:
hope this helps
Answer:
7^7 times -3^3, or -22235661
Step-by-step explanation:
Someone help ! It’s talking about Integers !!
Answers
Step-by-step explanation:
The numbers to the right of 0 are positive. The numbers to the left of 0 are negative. 0 is neither positive nor negative.Answer:
1) Numbers which are to the left of 0 are negative numbers.
2) Numbers which are to the right of 0 are positive numbers.
3) 0 is neither positive nor negative
When it comes for plotting the numbers on the number line , just point out the numbers in accordance to their sign. In the given number line ( in the attachment ) , only mark those numbers which are being asked to plot in the number line .
Step-by-step explanation:
NEED HELP ASAP!!! Which of the following correctly uses absolute value to show the distance between −70 and 15? Question 6 options: 1) |−70 − 15| = |−85| = −85 units 2) |−70 + 15| = |−55| = 55 units 3) |−70 − 15| = |−85| = 85 units 4) |−70 + 15| = |−55| = −55 units
Answers
Answer:
3) |−70 − 15| = |−85| = 85 units
Step-by-step explanation:
Absolute value ignores negative values so the equation when finding the distance between −70 and 15 is 70 + 15 which equals 85.
A small toy car costs $3 a large toy car costs 5 times as much as the small one Aaron want to buy 1 of each which equation can be used to find the cost a of the 2 cars
Answers
Answer:
$18
Step-by-step explanation:
small -$3
large - $15
3+15=18
Answer: The equation is $3 + ($3 x 5)
Step-by-step explanation:
You add $3 to 3 multiplied by 5 to get the cost of the second car which will then give you the cost of both cars. Then you simplify and get $3 + $15 which gives us the answer $18. So the cost of both the cars is $18.
Can 65^ ,45^ and 80^ represent the measure of three angles of a triangle explain why or why not?
Answers
Answer:
No, because 65+45+80=190 and a triangle can only be 180
Step-by-step explanation:
What is the value of m in the equation below?
2 m - 3 = - m + 6
Answers
Answer: m=3
2m-3= -m+6
3m=9
m =3
Hope this helps!
The perimeter of a rectangle is 50 inches.if the width of the rectangle is 5 inches smaller then twice the length,find the AREA of the rectangle in square inches