The combined area of a square and a rectangle is 225 square yards. the length of the rectangle is 8 times the width of the rectangle and the length of a side of the square is the same as the width of the rectangle. find the dimensions of the square and the rectangle.
Answers
Answer:
The rectangle: L = 40 yards. W = 5 yards
The square: The length and width are both 5 yards.
Step-by-step explanation:
Let L and W be the length and width of the rectangle.
Let l and w be the length and width of the square.
Area for each is:
Rectangle: L*W
Square: l*w
We are told that L*W + l*w = 225 yards^2
We are also told that
L = 8W
and that
l = W
Since the sides of a square are all equal, w is also W: w=W
Summarizing and substituting:
L*W + l*w = 225 yards^2
(8W)*W + W*W = 225 yards^2
8W^2 + W^2 = 225 yards^2
9W^2 = 225 yards^2
W^2 = 25
W = 5 feet
---------------------
Therefore, since L = 8W , L = 40 yards. W = 5 yards for the rectangle.
The square: l=W, so l = 5 yards, and thus w=5 yards
--------------------------
Check:
Do a rectangle of 40' x 5' plus a square of 5' x 5' have a total combined area of 225 yards^2?
40yd x 5yd + 5yd x 5yd = 225 yards^2?
200 yd^2 + 25 yd^2 = 225 yards^2?
YES
Related Questions
Dale wants to order business cards for his new job.
• Company A charges a flat fee of $0.15 per card.
• Company B charges $0.10 per card plus an additional $10.00 for delivery
Write an inequality for the amount of business cards, c, that Dale would need to buy for Company to be cheaper
Answers
Dale would need to buy more than 200 cards for Company B to be cheaper.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Company A charges a flat fee of $0.15 per card.
Company B charges $0.10 per card plus an additional $10.00 for delivery
Let x = number of cards
Company A charges = $0.15x
Company B charges = $10.00 + $0.10x
For company B to be the cheaper option ( B < A )
$10.00 + $0.10x < $0.15x
$10.00 < $0.05x
subtracting positive from both sides to retains the sense of the inequality and x is positive
200 < x
x > 200
So, Dale would need to buy more than 200 cards for Company B to be cheaper.
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Tran has a credit card with a spending limit of $2000 and an apr (annual percentage rate) of 12%. during the first month, tran charged $450 and paid $150 of that in his billing cycle. which expression will find the amount of interest tran will be charged after the first month? (0.01) (300 dollars) (0.01) (450 dollars) (0.12) (300 dollars) (0.12) (450 dollars)
Answers
The expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
ExpressionFirst step
Monthly interest rate = (Annual percentage rate ÷ Number of months in a year)
Monthly interest rate= 0.12 ÷ 12
Monthly interest rate= 0.01
Second step
Amount left = Amount charged - Amount paid
Amount left = $450 - $150
Amount left = $300
Third step
Amount of interest=Monthly rate ×Amount left
Amount of interest=(0.01) (300 dollars)
Amount of interest=$3
Therefore the expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
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Bob sells part of a 50-acre rectangular plot of land he owns so that he can still own a smaller rectangular plot within the original. After he makes the sale, Bob's remaining plot of land is half as long and half as wide as his original plot. What is the area of Bob's remaining plot of land?
Answers
Considering the area of a rectangle, it is found that the area of Bob's remaining plot of land is of 12.5 acres.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, that is:
A = lw.
In this problem, both the length and the width are divided in half, hence the proportion remaining is given by:
A = 0.5l x 0.5w = 0.25lw = 25% of the initial area.
Hence:
0.25 x 50 = 12.5.
The area of Bob's remaining plot of land is of 12.5 acres.
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what is the solution for the equation -15=5(3y-10)-5y
Answers
Answer:
[tex]\Large\boxed{\sf{y=\dfrac{7}{2} }}[/tex]Step-by-step explanation:
Isolate the variable of y from one side of the equation.
-14=5(3y-10)-5y
First, switch sides.
[tex]\sf{5\left(3y-10\right)-5y=-15}[/tex]
Use the distributive property.
DISTRIBUTIVE PROPERTY:
A(B-C)=AB-AC
5(3y-10)
Multiply by expand.
5*3y=15y
5*10=50
15y-50-5y
15y-5=10y
= 10y-50
10y-50=-15
Add by 50 from both sides.
10y-50+50=-15+50
Solve.
10y=35
Then, you divide by 10 from both sides.
10y/10=35/10
Solve.
Divide the numbers from left to right.
35/10=7/2
y=7/2
Divide is another option.
7/2=3.5
[tex]\Longrightarrow: \boxed{\sf{y=\dfrac{7}{2}}}[/tex]
Therefore, the correct answer is y=7/2.I hope this helps. Let me know if you have any questions.
HELP please this is due soon
Answers
Answer:
Step-by-step explanation:
Side Opposite to ∠x is called YZ
The side Opposite to ∠y is called XZ (that's the hypotenuse of the triangle)
Side Opposite to ∠Z is XY
Answer:
Side apposite to angle X is YZ
Side apposite to angle Y is XZ
Side apposite to angle Z is XY
Hope this helps you
have a great day
Multiplying by 1.19 is the same as increasing by
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1.19 - 19%
PLEASE HELP
i have no clue what im doing wrong but i cannot find the answer
Answers
hello what is 5x6 and what is 24 divide by 50
Answers
Answer:
5×6=30
24÷50=0.49....following long division method
A composite figure is formed by combining a square and a triangle. Its total area is 49.5 ft. The area of the
triangle is 33.5 ft. What is the length of each side of the square? Complete the explanation.
The area of the square is
it?, so each side of the square is
ft.
Answers
Answer:
The length of each side of square is 5ft.
Step-by-step explanation:
A composite figure is formed by combining a square and a triangle. Its total area is 32.5ft squared.
The area of the triangle is 7.5ft squared.Area of combined figure - area of triangle = area of square.
32.5 ft squared - 7.5 ft squared = 25 ft squared.
So, area of square = 25 ft squared.
Now, by putting the formula for getting the length of each side:
Let the side = a.
Area of square = 25 ft squared
Area of square = a²
Using square root both sides we get:
So, the side = 5 ft.
Therefore, the length of each side of square is 5ft.
find the measure of the missing angle?
Answers
56+72+x =180 ( therefore sum of angle in a triangle)
128+x=180
x=180-128
x=52
Answer:
THE MISSING ANGLE = 52°
Step-by-step explanation:
Sum of all angles = 18°0
Let the missing angle be x°
56° + 72° + x° = 180°
x° = 180° - 72° - 56°
x° = 52°
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
The sum of a number x and 2,496 is 17,344. What is the value of x?
Answers
x = 17,344 - 2,496
x = 14,848
what are the mean,median,mode, and range of the data set given the altitude of lakes in feet:-11,-28,-17,-25,-28,-39,-6,and -46? i dont know the answer
Answers
Answer:
Read explanation.
Step-by-step explanation:
The average is -22.2 (mean)
-46,-39,-28,-28,-25,-17,-11.-6 You cross out the lowest and highest until you reach the middle, which is -26.5(median)
The mode is -28 as it is the most repeated number
The range is 40 as when you subtract a negative it turns into the absolute value.
Kate packs snow into 5 identical jars. each jar represents a different depth of snow. kate then lets the snow in each jar completely melt. the table shows the height of the liquid in each jar as it relates to the original depth of snow in the jar. a 2-column table with 5 rows. the first column is labeled snow depth (inches), x with entries 2, 4, 6, 8, 10. the second column is labeled water depth (inches), f(x) with entries 0.4, 0.8, 1.2, 1.6, 2.0. which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? select two options. the points on a graph representing the relationship lie on a line. there is 0.4 inch of water to every 1 inch of snow. a line through the points will pass through (0, 0). the function relating snow depth to water depth is quadratic. the data can be represented by f(x) = 0.2x.
Answers
The true statements include the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
How to illustrate the table?From the table, the water depth changes for about (0.8 - 0.4) = 0.4 inches. Here, the function is a linear model.
In this case, the the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
Learn more about graphs on:
https://brainly.com/question/19040584
Answer:
A & C
Step-by-step explanation:
hope this helps
Find the least common denominator of 11/10 and 1/15
Answers
Answer: The least common denominator is 30.
Step-by-step explanation: Look at the image I have uploaded.
Good luck!
Martina's inground swimming pool is finally finished, and all that's left to do is fill it with water. Martina's family decides to fill their pool using their garden hose to save money, even though they know it will take a really long time. The swimming pool is 10 meters long and 5 meters wide, and Martina's family wants the water to be 2 meters deep. Water from the garden hose flows at a rate of 2,500 liters, or 2.5 cubic meters, per hour.
How long will it take to fill the pool?
Write your answer as a whole number or decimal. Do not round.
hours
Answers
Answer:
40 hoursStep-by-step explanation:
Find the required water volume using the volume of prism formula
V = lwhV = 10*5*2 = 100 m³Find the time required
100/2.5 = 40 hoursAnswer:
40 hours
Step-by-step explanation:
The swimming pool can be modeled as a rectangular prism.
Volume of a rectangular prism
[tex]V = lwh[/tex]
where:
l = lengthw = widthh = heightFirst, calculate the volume of water needed:
Given:
l = 10 mw = 5 mh = 2 mSubstitute the given values into the formula and solve for V:
[tex]\implies V=10 \cdot 5 \cdot 2=100\:\: \sf m^3[/tex]
If the water flows as a rate of 2.5 m³/h, divide the volume by the rate to calculate how long it will take to fill the pool:
[tex]\implies \sf Time=\dfrac{Volume}{rate}[/tex]
[tex]\implies \sf Time=\dfrac{100}{2.5}[/tex]
[tex]\implies \sf Time=40\:\:hours[/tex]
What is the area for 12ft and 8.5 for a parallelogram
Answers
Answer:
102 ft^2
Step-by-step explanation:
Im pretty sure area for a parallelogram is the same as a rectangle, so A = bh which would be 12 x 8.5
Solve the system of equations using elimination: 8x - 8y = 0 and
-5x - 7y= -12.
Answers
Answer:
My answers were (1,1) for both lmk if it works ;)
Step-by-step explanation:
PLS HELPP WHAT IS THE ANSWER???
Answers
Answer:
-220
Step-by-step explanation:
Answer:
Let us start by plugging in x=2 into all variables x and y=1 into all y's
so: The result is -220
Which absolute value inequality is modeled by this graph?
A. y ≥ |x − 3|
B. y ≥ |x| − 3
C. y > |x + 3|
D. y > |x| + 3
Answers
Answer:
c
Step-by-step explanation:
sorry if it is wrong
Just plug in 0 and you have to get -3 because there is a point (0,-3)
A: you get |0-3| = |-3| = 3. Not A.
B: you get |0| -3 = -3. Correct
C: you get |0+3| =|3|=3. Not C
D: you get |0| +3 =3 Not D
What is the volume of the prism if its 2 centimeters long tall 12 centimeters wide and 25 centimeters long
Answers
Answer:
600 cm
Step-by-step explanation:
L*W*H SO IT WILL BE 2*12*25
Which side is opposite angle C?
None
BC
AB
AC
Answers
Answer:
AB
Step-by-step explanation:
opposite is AB
How do you solve this? In volume...
Answers
Twenty-one less than a number is seven. What is the number? 3 14 28 147
Answers
Answer:
Option C, 28
Step-by-step explanation:
Step 1: Make an expression
Twenty-one less than a number is 7
[tex]x - 21 = 7[/tex]
Step 2: Solve the equation for x
[tex]x - 21 = 7[/tex]
[tex]x - 21 + 21 = 7 + 21[/tex]
[tex]x = 28[/tex]
Answer: Option C, 28
Answer:
28
Step-by-step explanation:
because twenty eight subtracted by twenty one equals seven
Please help, thank you!
Answers
Answer:
Vertical Asympote, but I might be wrong, haven't done this math in years
A bag contains 3red, 4white, 5green balls. Three balls are selected without replacement. Find the probability that the three balls chosen are:
A) all red
B) all green
C)one of each color
Answers
Answer:
A. 1/220 B. 1/22 C. 3/11
Step-by-step explanation:
This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).
Notations for combinations:
The number of ways to select r things from a set of n things is
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex] where the exclamation points mean factorial.
[tex]n!=1\cdot2\cdot3\ldots\cdot n[/tex] and 0! is defined to be 1.
There are two other commonly used symbols for this:
[tex]_nC_r[/tex] and [tex]n \choose x[/tex].
In all three parts, the number of ways to choose 3 balls from a set of 12 is
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}[/tex]
Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220[/tex]
A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.
B) The number of ways to choose 3 green balls from the set of 5 green balls is [tex]C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10[/tex] out of 220, so the probability is 10/220 = 1/22.
C) The number of ways to choose 1 red is C(3, 1) = 3. Choose 1 green in C(5, 1) = 5 ways. Choose 1 white in C(4, 1) = 4 ways.
The probability is [tex]\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}[/tex]
Answer:
a) 1/220
b) 1/22
c) 3/11
Step-by-step explanation:
Check the attachment.
What is the value of the remainder?
Answers
[tex] \underline{ \boxed{ \sf{✰\: Option\:D. \:81✓ }}}[/tex]
Refer to the attachment for solution ☘️
Hope it helps
A train travels from Washington D.C. to New York (225 miles). The train departs at 4:55 PM and arrives in New York at 7:55 PM. What is the average speed of the train?
Answers
7:55 pm - 4:55 pm = 3 hours
225 miles / 3 hours = 75 miles per hour
Average speed = 75 miles per hour
what is area of the polygon
Answers
hii ,
area of polygon : 18
1 A triangle ABC ,AB = 7.8 cm,AC= 7 cm an
Isosceles Triangle
Scalene triangle
Equilateral triangle
Right angled Triangle
Answers
Answer:scalene
Step-by-step explanation:none of the sides are equal length
y = 6x - 3 non linear or linear
Answers
Answer:
Linear
Step-by-step explanation:
The equation is in the form y = mix + b, which means it is linear.