Given:
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ=3a+4[/tex]
[tex]XY=5a-12[/tex]
To find:
The value of a and PQ.
Solution:
We have,
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ\cong XY[/tex] (CPCTC)
So,
[tex]PQ=XY[/tex]
[tex]3a+4=5a-12[/tex]
Isolating variable terms, we get
[tex]3a-5a=-4-12[/tex]
[tex]-2a=-16[/tex]
Divide both sides by -2.
[tex]a=\dfrac{-16}{-2}[/tex]
[tex]a=8[/tex]
Now,
[tex]PQ=3a+4[/tex]
[tex]PQ=3(8)+4[/tex]
[tex]PQ=24+4[/tex]
[tex]PQ=28[/tex]
Therefore, the value of a is 8 and the value of PQ is 28.
Find three consecutive natural numbers such that the sum of the first and the second is 15 more than the third
Answer: 16, 17 and 18
Step-by-step explanation:
Let the consecutive natural numbers be x, x+1, and x+2. We are informed that the sum of the first and the second is 15 more than the third. This will be:
[x + x + 1] = [x + 2] + 15
2x + 1 = x + 2 + 15
2x + 1 = x + 17
2x - x = 17 - 1
x = 16
The numbers are 16, 17 and 18.
I NEED HELP WITH ALL 4 I WILL GIVE BRAINLIEST
Answer 1 8.40 precent 2 23.4% 3 16% 4 f 10%
Step-by-step explanation:
PLS HELP ME NWWWWWWWWWWWWW
Answer:
total score was 2
Step-by-step explanation:
have a good day ;*
Answer:
2
Step-by-step explanation:
2 + -6 + 7 + -1= 2
( I actually need to add something to make this comment long enough)
I need help please and thank you
please help I need you
Answer:
The answer is B.
Step-by-step explanation:
Diameter x Pi = Circumference
8 x 3.14 = 25.12
Answer:
B
Step-by-step explanation:
?? anyone know thank you
Answer:
19/20 is the correct answer
Answer:
19/20 quart
Step-by-step explanation:
the denominator should be the same so find some thing that is common to 4 and 5 so 20 and find what 4 in to 20 go 5 times so multiply 5×3=15 and 4×1=4 so add them together 15+4 = 19 so put 19 and 20 together equal 19/20
There are 5 boys and 10 girls in the glee club. Which ratio represents the number of boys in the club to the total number of students in the club? One-third One-half Two-thirds StartFraction 3 Over 1 EndFraction
Answer:
1:3
Step-by-step explanation:
Given that,
Total no. of boys = 5
Total no. of girls = 10
We need to find the ratio of the number of boys in the club to the total number of students in the club.
Total no. of students = no. of girls + no. of boys
= 5 +10
= 15
Ratio,
[tex]R=\dfrac{5}{15}\\\\=\dfrac{1}{3}[/tex]
Hence, the required ratio is 1/3 or one third.
Answer:
1/3
Step-by-step explanation:
Justin set his watch 19 seconds behind, and it falls behind another 1 second every day. How
many days has it been since Justin last set his watch if the watch is 50 seconds behind?
Answer:
31 days
Step-by-step explanation:
Hope this helps!
Brainiest?
Answer:
31 days
Step-by-step explanation:
you have a set number already 19 if every day the watch goes back 1 day 31+19=50
52,428 divided by 34
Answer:
1542
Step-by-step explanation:
Sonya had 20 dollars to spend on 3 gifts. She spent 8 1 4 dollars on gift A and 4 4 5 dollars on gift B. How much money did she have left for gift C?
Answer:
6 19/20 dollars
Step-by-step explanation:
Sonya had 20 dollars to spend on 3 gifts.
She spent 8 1 4 dollars on gift A and 4 4 5 dollars on gift B.
Gift A + Gift B + Gift C = $20
Gift C = $20 - (Gift A + Gift B)
Gift A = $8 1/4
Gift B = $4 4/5
Hence:
The amount she had left for gift C is :
Gift C = $20 - ($8 1/4 + $ 4 4/5)
Gift C = $20 - $13 1/20
Gift C = $ 6 19/20
3. Select all answers that would create a dilation.
O (x,y) -----> (2x,4y)
O (x,y) -----> (-2x,-2y)
O (x,y) -----> (92x,2y)
O (x,y) -----> (3x,3y)
O (x,y) -----> (1.2x,1.2y)
Answer:
Option B,D and E will create dilation.
Step-by-step explanation:
Dilation is the enlarging or shrinking of an element using a common scale factor.
If the same factor is multiplied by the elements, the dilation is created.
Looking at the options:
Option A
O (x,y) -----> (2x,4y)
if we take 2 as common we get 2 (x,2y) not the original coordinates (x,y). So, no dilation.
Option B
O (x,y) -----> (-2x,-2y)
if we take -2 as common we get -2(x,y) which is same as original coordinates. It would create dilation.
Option C
O (x,y) -----> (92x,2y)
if we take 2 as common we get (46x,y) not the original coordinates (x,y). So, no dilation.
Option D
O (x,y) -----> (3x,3y)
if we take 3 as common we get 3(x,y) which is same as original coordinates. It would create dilation.
Option E
O (x,y) -----> (1.2x,1.2y)
if we take 1.2 as common we get 1.2(x,y) which is same as original coordinates. It would create dilation.
So, Option B,D and E will create dilation.
Solve 24 ≤ -6t
The solution is ___
Graph the solution.
Answer:
T < - 4
Step-by-step explanation:
Answer:
t<-4
Step-by-step explanation:
A rectangular book measures 8 X 10. What is the length of its
diagonal?
Answer:
Length of the diagonals is[tex] \sqrt{ {8}^{2} +{10}^{2} } = \sqrt{64 + 100} = \sqrt{164} =2\sqrt{41}\\ =\boxed{12.8\: units} [/tex]
12.8 units is the right answer.The diagonal length of the rectangular book is 12.8 units.
What is rectangular?A rectangle is "four sided polygon, having all the internal angles is equal to 90 degree. The two sides of each corner is right angles".
According to the question,
The length of rectangle is 8 units and the breadth of rectangle is 10 cm.
To find diagonal of the rectangle: Using Pythagoras theorem a² + b² = c².
c = [tex]\sqrt{a^2 + b^2}[/tex]
= [tex]\sqrt{8^2 + 10^2}[/tex]
= [tex]\sqrt{64 + 100}[/tex]
= [tex]\sqrt{164}[/tex]
= 2[tex]\sqrt{41}[/tex]
= 12.8 units
Hence, the diagonal length of the rectangular book is 12.8 units.
Learn more about rectangle here
https://brainly.com/question/17043608
#SPJ2
The number of miles, x, that a cross country athlete can run is represented by the inequality
x+3<15
What conclusion can be made about the number of miles?
Answer:
That the number of miles is going to be less than 15
Step-by-step explanation:
If you wanted to solve the inequality then the answer would be x<12
Can you please give me brainliest
y = (x – 4)² - 4
Standard form
Answer:
y=x to the second power -8x+12
Step-by-step explanation:
Answer:
x²-4²-4
the ans
Step-by-step explanation:
this is ans
x2=120
solve for the exact variable answer
Answer:
60 ?
Step-by-step explanation:
60×2 = 120. .
when you have a x right behind a number that means multiply
12 m
15 m
8 m
5 m
5 m
45 because 12+15+8+5+5=45
What is the equation of the line in slope-intercept form
Answer:
y = -3/5x - 2
6. A bicycle store costs $2200 per month to operate. The store pays an average of $60
per bike. The average selling price of each bicycle is $80. How many bicycles must the
store sell each month to break even?
The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 10 percent as much of its carbon-14 as compared to a living sample. How old is the fossil?
Answer:
19050 or some other number very close like 19039
Step-by-step explanation:
I took test and got this one right.
Answer:
the guys above :)
Step-by-step explanation:
give him brainliest if you have not :)
Find the sum of the squares of 3, 2, 1, and -1
Answer:
15
Step-by-step explanation:
3 x 3=9
2 x 2=4
1x1=1
-1x-1=1
9+4+1+1=15
Answer:
15
Step-by-step explanation:
The square of 3 is 3 times 3, so 9.
2 times 2 is 4.
1 times 1 is 1.
-1 times -1 is 1, because the negative cancels out.
So, it's 9 plus 4 plus 1 plus 1, so the answer is 15.
Liam wants to buy a Nintendo Switch. The Switch costs $350 plus tax. He has $380. If tax is 9%, will he have enough to buy the Switch?
Step-by-step explanation:
I'm not a 100 % sure but 350.00 x 0.06 =21 so 350 +21 = 371.00
Answer:
No
Step-by-step explanation:
Switch=$350 + tax = ???
Liam's Money= $380
350*9/100=tax
tax=$31.50
350+31.50=$381.50
that's how much he would need to pay: 381.50
so:
no he won't have enough money. he's 1.50 short
Please help me
I need this ASAP
PLEASE HELP ME
Answer:
180 X 365 = 65700 litres
65700/1000 = 65.7 cubic metres
65.7 X 91.22 = 5993.154
5993.154 / 100 = 59.93154
59.93 + 28.20 = 88.13
yes Henry should have a water meter
The crowd at a concert estimated to be 3,500 people. The exact attendance is 3,486 people. What is the percent error?
Answer:
0.4016%
Step-by-step explanation:
Estimated Value = 3,500 people , Exact attendance = 3486 people
We can see that there is a Percentage decrease . So we will apply the formula.
%Decrease = Old Value - New Value /Old Value × 100%
%decrease = 14/3486 %
%Decrease = 0.4016% (Answer)
There’s a drawing and I don’t know how to explain it on it
the value of the 7 in 0.076 is 1/10 the value of the 7 in 2.79
Answer:
true
Step-by-step explanation:
the second 7 is in the tenth place and the first 7 is in the hundredth place, which is 1/10 the tenth place
I agree...................
Which of these factions are greater than 11/20
34.23 times one year is ....
Answer:
410.76
Step-by-step explanation:
34.23 * 12= 410.76
1 year = 12 months
Multiply to convert pounds to ounces. Write your answer as a fraction.
Answer:
There is nothing to multiply.
Include the problem please
Pleas help me with this F(x)=3x-x Find F(10)
Answer:
f(10) = 20
Step-by-step explanation:
Since the x is defined, you can plug it in, x=10.
Substitute the x with 10, f(10) = 3(10)-10.
Then, simply the equation, f(10) = 20.
WILL GIVE BRAINLIEST PLEASE HELP
Answer:
Yes they are similar using the SSS postulate
Step-by-step explanation:
All sides are in the same ratio!
Another tip is that one triangle is a dilated shape of the other
