The diagram gives information about two paintings, P and Q.
Each painting is in the shape of a rectangle.
Painting P has an area 1400 cm more than the area of painting Q.
Work out the area of painting P.
Answers
Answer: 2600 cm^2
Step-by-step explanation:
FORMULA
Painting P area = Painting Q area + 1400
so...
40(3x-10) = 30(x+15) + 1400
EXPAND EXPAND
120x - 400 = 30x + 450 + 1400
SIMPLIFY
120x-400 = 30x + 1850
+400 +400
120x = 30x + 2250
- 30x - 30x
90x = 2250
DIVIDE BY 90 DIVIDE BY 90
x = 25
SO... Now we have to find the AREA of PAINTING P
LENGTH: (3x - 10)= 3(25) - 10 = 65cm
HEIGHT: 40cm
AREA OF PAINTING P = 65cm X 40cm = 2600cm^2
By solving a system of equations, we will see that the area of painting P is 2,600 cm^2
How to get the area of painting P?Remember that the area of a rectangle of length L and width W is:
A = L*W
Then the area of painting P is:
A = 40cm*(3x - 10)cm
The area of paint Q is:
A' = (30 cm)*(x + 15)cm
And que know that:
A = A' + 1400cm^2
Then we havea system of equations:
A = A' + 1400cm^2
A = 40cm*(3x - 10)cm
A' = (30 cm)*(x + 15)cm
First, we can replace the third equation into the first one to get:
A = (30 cm)*(x + 15)cm + 1400cm^2
And that must be equal to:
A = 40cm*(3x - 10)cm
So now we can solve:
40cm*(3x - 10)cm = (30 cm)*(x + 15)cm + 1400cm^2
for x.
It gives:
120cm*x - 400cm^2 = 30cm*x + 1850 cm^2
120cm*x - 30cm*x = 1850cm^2 + 400cm2
x = (2250cm^2)/(90cm) = 25cm
Now that we know x, we can get the area of painting P.
A = 40cm*(3*25cm - 10cm) = 2,600cm^2
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
Related Questions
What is the surface area and volume of this triangular prism?
Answers
joe has a bicycle with a front wheel that is 2 feet in diameter. how far does joe travel if his wheel turns exactly 100 complete revolutions in one directions?
314 feet
628 feet
1256 feet
6280 feet
Answers
Given:
The diameter of the wheel is 2 feet.
Number of revolution = 100
To find:
The total distance covered by the bicycle.
Solution:
The circumference of a circle is:
[tex]C=2\pi r[/tex]
Where, r is the radius of the circle.
The diameter of the wheel is 2 feet. So, the radius of the circle is 1 feet.
Putting [tex]\pi =3.14, r=1[/tex] in the above formula, we get
[tex]C=2(3.14)(1)[/tex]
[tex]C=6.28[/tex]
It means the distance covered by the wheel in one revolution is 6.28 feet.
Number of revolution is 100. So, the total distance covered by the wheel in 100 revolution is:
[tex]6.28\times 100=628[/tex]
The total distance covered by the bicycle in 100 revolution is 628 feet.
Therefore, the correct option is B.
hi! can someone help!? asap!!
Answers
solve the system of equations y=8x+5 y=6x+25
Answers
Answer:
(10,85)
Step-by-step explanation:
x=10
y=85
Pply the converse of the pythagorean theorem to determine if it's a right triangle. Is the triangle a right triangle? No, 92+402=412. No, 9 squared + 40 squared not-equals 41 squared Yes, 92+402=412. Yes, 9 squared + 40 squared not-equals 41 squared
Answers
Answer:
Yes, 9^2+40^2=41^2
Step-by-step explanation:
From the Pythagoras’ theorem, the square of the hypotenuse of a right triangle equals the sum of the squares of the two other sides
From what we have , the side lengths are 9, 40 and 41
As we can see, 41 is the longest side length and that makes it the hypotenuse
The square of the two other sides is 40^2 + 9^2 = 1,681
Also, 41^2 = 1,681
As we can see, the sum of the squares equal the square of the hypotenuse
Since this follows the theorem, we can conclude that the triangle is a right triangle
Answer:
C, Yes, 92+402=412.
Step-by-step explanation:
How much more is 9,00,000 than 4,50,000
Answers
Answer: 4,50,000 or 63
Step-by-step explanation: I add
Answer and Step-by-step explanation:
450,000 is half of 900,000, so that means 900,000 is 450,000 more than 450,000.
#teamtrees #PAW (Plant And Water)
no scam link or report
Answers
Answer:
For the first part, it would be: 15/4 - 9/4 = 6/4
The second part would be 1 1/2
Step-by-step explanation:
You would do 3*4 + 3 to get 15/4, you would do 2*4 + 1 to get 9/4, then you would subtract 9 from 15 to get 6. 6/4 is 1 1/2
The question is in photo
Answers
Answer:
option D
Step-by-step explanation:
The volume of the garage is 64 times the volume of the model
What is the media for my test pls help me and I’m new to this app
Answers
Answer:
17
Step-by-step explanation:
Answer: the answer is 17
Step-by-step explanation:
Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
If the distance and time is known how would you use the distance formula to determine the rate that a car travels
Answers
Answer:
Distance traveled / time taken
Step-by-step explanation:
Given :
The distance traveled by a car and the time taken to cover the distance
Take :
Distance = d
Time taken to cover distance = t
The rate the car travels is related by the equation :
Speed or rate = Distance traveled / time taken
which number is irrational?
A) square root 12
B) square root 36
C) square foot 64
D) square root 144
Answers
the square root of 12 is about 3.4641, irrational numbers most often have decimal points
Write the slope-intercept form of the equation of each line.
3x − 2y = −16 2) 13x − 11y = −12
Answers
Answer:
1. y= 3/2x + 8
2. y= 13/11x+12/11
Step-by-step explanation:
Answer:
y = 3/2x + 8 , y = 13/11x + 12/11
Step-by-step explanation:
While Dorothy had her garage sale, she kept track of how many toms sold within different price ranges. Look at the table and then give the relative frequency for the interval of 511 to $15. The relatie
frequency for $11 to 515
Frequency
Relative
Frequency
Interval
Sl to S5
S6 to S10
Sil to S15
S16 to $20
S21 to $25
S26 to 530
S31 to $35
8
6
4
2
4
6
2
Answers
Answer:
Interval $11 - $15 = 0.2
Step-by-step explanation:
Sum of frequency, Σf = (8+6+4+2+4+6+2) = 32
Relative frequency = f / Σf
Interval :
1 - 5 = 8 / 20 = 0.4
6 - 10 = 6 / 20 = 0.3
11 - 15 = 4 / 20 = 0.2
16 - 20 = 2 / 20 = 0.1
21 - 25 = 4 / 20 = 0.2
26 - 30 = 6 / 20 = 0.3
31 - 35 = 2 / 20 = 0.1
Please help. Give all 3 expressions.
Answers
Answer:
(15/100*percentage fee* x O*Original price* + C*car price*)
1 expression: (15/100 x O) + C
2 expression: (15/100 + C) x (O + C)
3 expression: C + (O x 15/100)
The distance around the inner circle of a
rubber tyre is 220 cm.
a. Find the inner radius.
b If the thickness of the tyre is 14cm, find
the distance around the outside of the
Areas of rectangles
Answers
Answer:
inner circle is 44ft and outer circle is 3ft
Find the missing length of the right triangle.
Answers
Answer:
20
Step-by-step explanation:
the pythagorean theory a^2 + b^2 = c^2
16^2 + 12^2 =
144 + 256 = 400
sqr root of 400 is 20
:)
Find the number such that five times this number is seven less than 82
Answers
Answer:
15
Step-by-step explanation:
5n = 82 - 7
82 - 7 = 75
75/5 = 15
n = 15
PLEASE HELP FOR FINALS!!!!!!
Let sd be the speed (in meters per second) of an object after t seconds of motion.
Explain the meaning of each statement.
3. s (0) = 9
b. s(9) =k
c. s(10) > (20)
Answers
Answer:
If I say to you that we are travelling along at a "constant" speed of 25 m/s... a. ... So every seem 28 mis covend. b. What does the "m/s" after the number 25 mean? ... The object's motion will change - au acceleration will occur. 9. A car is moving ... c. What do you think a graph of velocity versus time would look like? Sketch it.
Step-by-step explanation:
PLEASE HELP...
Find the area of the composite shape. Show your work for BRAINLIST and if it’s correct
Answers
10.38
i multiplied each number and the answers that i got i added them to get the area
whats the slope of the line
Answers
Explanation: to find the slope an easy way find two points on the line. You’ll go up one over one on this graph!
Have a Bomb day!
B.
1. Name the triangles that are congruent.
2. What postulate support your answer?
3. Name all other angles and segments that are congruent.
4. What can you say about UN in relation to <JUG and JG
Answers
Answer:
1. ΔUJN ≅ ΔUGN by SAS rule of congruency
2. Side Angle Side Rule of congruency
3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU
4. UN bisects angle ∠JUG and UN bisects segment JG
Step-by-step explanation:
The given figure consists of three triangles
1. ΔUJN, 2. ΔUGN, and 3. ΔUJG
Whereby segment UN is perpendicular to segment JG, we have;
ΔUJN and ΔUGN are right triangles
∴ ∠UNJ = ∠UNG = 90° by definition of segment UN being perpendicular to segment JG
NU ≅ NU by reflexive property
Whereby UN bisects ∠JUG and segment JG, we have;
JN = GN by definition of a bisected segment
Therefore, we have;
1. ΔUJN ≅ ΔUGN by SAS rule of congruency
2. Side Angle Side Rule of congruency
3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU
4. UN bisects angle ∠JUG and UN bisects segment JG
How many centimeters are equal to 5 inches?
Answers
A rectangle measures 15 2 inches by 4 3 inches. What is its area?
Answers
Answer:
65.36
Step-by-step explanation:
15.2 x 4.3 = 65.36
ASAP
-WILL MARK BRIANiST
Answers
A garden hose is 15 yards long. What is the length of the hose in inches?
Answers
I need to type more so here is more
Answer:
540 inches
Step-by-step explanation:
each yard is 3 feet in 1 foot is 12 inches 12 times 3 is 36 so 15 times 36 gives you 540 inches
brainliest plz
find the loss if cp= Rs550 sp= Rs494
Answers
Answer:
loss =Rs 56
Step-by-step explanation:
loss =cp-sp
550-49456stay safe healthy and happy.Explain how to determine the x- and y- intercepts of a line from a given equation in y = mx + b form.
Answers
Answer:
Step-by-step explanation:
x-intercept: Set y = 0 and solve for x:
0 = mx + b, or mx = -b, or x = -b/m. x-intercept is then (-b/m, 0)
y-intercept: Set x = 0 and solve for y: y = m(0) + b, or y = b. y-intercept is then
(0, b).
what is the mean absolute deviation of the following set 3 1 5 5 2 3 2 3 4 2
Answers
Answer:
30-3=27
Step-by-step explanation:
Finding the deviation of this is pretty simple
1) Find the mean
By finding the mean, you add the numbers together, and divide the sum by the number of numbers, in this case there are 10 numbers, so divide by 10
2) Subtract the data value, basically adding all of the numbers up, and subtracting it by 3, the mean.
the number sets:
3,1,5,5,2,3,2,3,4,2
mean=
30/10
by finding this, i added the numbers and divided it by the amount of numbers.
This would equal to 3.
Now, all you have to do is subtract 3 from the data value
The data value is 30, subtracted by 3 would be 27
Sorry if I am wrong, I am just 4th grade :(
I am sure I am right, but in case it IS wrong, use the formula in the explanation :)
I might've gotten it wrong because the numbers were unclear, but I think it is correct:)
Answer: 1
Step-by-step explanation:
3+1+5+5+2+3+2+3+4+2= 30
30/10 =3
3 - 3 =0
3 - 1 = 2
3 - 5 =2
3 - 5 =2
3 - 2 = 1
3 - 3 =0
3 - 2 = 1
3 - 3 = 0
3 - 4 = 1
3 - 2 = 1
0+2+2+2+1+0+1+0+1+1
10/10 is 1
Mark makes $60 for every six hour shift he works. How much will he make if he works an eight hour shift
Answers
Answer:
Mark will make $80 if he works an eight-hour shift.
Step-by-step explanation:
For every six hour shift he works, Mark makes $60
This implies that for every hour, he makes $10 ($60/6)
Therefore, for working an eight-hour shift, Mark will make $80 ($10 * 8) or ($60/6 * 8).
We can conclude that Mark's employer pays him $10 per hour.
This hourly rate can be used to work out how much Mark will earn if he works for a month or a year, as the case may be.
Find h.
10 in.
h = [?] in.
5.
4 in.
PLEASE ILL DO ANYTHING
Answers
10 * 2 - 2 * 2= height*2
100- 4 = height *2
96= height *2
Under-root 96 = height
Answer:[tex]h=\sqrt{96}in.[/tex]
Step-by-step explanation:
.