A large rectangle is made up of nine identical rectangles whose longer side equals 10. What is the area of the large rectangle?
Answers
• The middle row has 5 rectangles with all of their short sides equaling the top row, 20
• So 5x = 20 where x is the short side of the rectangle
• x = 4
• So each rectangle’s area = 4 x 10 = 40
• There are 9 rectangles
• So 9 x 40 = 360 = area of the large rectangle
• We can check our work
• Large rectangle side 1 = 10 + 10 = 20
• Large rectangle side 2 = 4 + 10 + 4 = 18
• 18 x 20 = 360
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Explanation:
Refer to the diagram below.
A small rectangle has its longer side equal to 10 and its shorter side is x, which is some real number on the interval 0 < x < 10.
Across the top, the two sides of length 10 add to 20. So the larger rectangle has a horizontal dimension of 20 units.
The vertical side of the larger rectangle is x+10+x = 2x+10 units
The area would be
area = length*width = 20(2x+10) = 40x+200
Each of the nine smaller rectangles has area of length*width = 10x. Since we have 9 identical copies, the smaller rectangle areas must add to 9*10x = 90x
---------------
Equate those two expressions and solve for x
90x = 40x+200
90x-40x = 200
50x = 200
x = 200/50
x = 4
So each smaller rectangle has area of 10*x = 10*4 = 40 square units. In total, the nine smaller rectangles combine to an area of 9*40 = 360 square units
Note how x = 4 leads 40x+200 to result in 360 as well.
Related Questions
The ratio of the number of men to the number of
women working at Forms, Inc. is 7:2. Altogether there
are 360 workers at the company. How many of the
workers are women?
Answers
Answer:
280 men; 80 women.
Step-by-step explanation:
this task can be solved used system of two equation (note, it is not the only and shortest way):
1) if number of men is 'm', women is 'w' and ratio is 7:2, then it is possible to write the first equation: m/w=7/2;
if together there are 360, then it is possible to write the second equation of the system: m+w=360.
2) after item 1 it is possible to make up and solve the system:
[tex]\left \{ {{m/w=7/2} \atop {m+w=360}} \right. \ => \ \left \{ {{7w=2m} \atop {m+w=360}} \right. \ => \ \left \{ {{m=280} \atop {w=80}} \right.[/tex]
In laissez-faire economics, what is the role of the government in the economy?
Answers
Answer:
In a laissez-faire economy, the only role of the government is to prevent any coercion against individuals.Step-by-step explanation:
HOPE IT HELPEvaluate (4/25) 1/2
A 4/5
B 4/25
C2/5
D2/25
Answers
D. 2/25
2/25
Step-by-step explanation:
[tex]\begin{aligned}\tt\left(\frac{4}{25}\right)\cdot\frac{1}{2}&=\tt\frac{4}{50}\to(\div~2)\\&=\tt\frac{2}{25}\end{aligned}[/tex]
The Mad Hatter is ordering cups from Teacups
Limited, for his tea party. The Tescups, Limited catalog
prices cups according to the number of cups ardered. For
orders of 20 or fewer cups, the price is $1.40 per cup plus
$12 shipping and handling on the order. For orders of
more than 20 cups, the price is $1.10 per cup plus $15
shipping and handling
a) Create a piece wise function to describe the
price of cups
b) How much will it cost the Mad Hatter if he orders
20 cups?
Answers
a) The piecewise function is:
[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
[tex]C(n) = 15 + 1.1n, n > 20[/tex]
b) Applying the piecewise function, it is found that it will cost $40.
A piecewise function is a function that has different definitions based on the input.
Item a:
20 or fewer cups, fixed cost of $12 for shipping plus $1.40 per cup. Thus, the first definition of the function for the cost of n cups is:[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
For more than 20 cups, price of $1.1 per cup plus a shipping and handling fee of $15. Then:[tex]C(n) = 15 + 1.1n, n > 20[/tex]
Then, the piece-wise function is:
[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
[tex]C(n) = 15 + 1.1n, n > 20[/tex]
Item b:
The cost of 20 cups is C(20).It is the first definition, which is valid for [tex]n \leq 20[/tex].Then:
[tex]C(20) = 12 + 1.4(20) = 12 + 28 = 40[/tex]
It will cost $40.
A similar problem is given at https://brainly.com/question/24815096
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Answers
Answer:
m = 1/4
Step-by-step explanation:
Remember to use y = mx + b
is 812 and 946 relativly prime?
Answers
No, they are not relatively prime.
PLEASE HELP ME!
Explain what the algebraic solution of a system of two linear equations is and what that means in terms of the graphs of the equations of the system. Use AT LEAST 2 complete sentence in
your explanation. (3 points)
Answers
San ine to you bhai account and I will
Perform the indicated operations. 8/12÷11/15 • -1/4
A.-5/22
B.5/22
C.-11/90
D.11/90
Others:______
Answers
Answer:
A.-5/22
Step-by-step explanation:
[tex]\frac{8}{12} /\frac{11}{55} *-1/4 = -5/22[/tex]
plug it into a calculator.
Please tall me if you have any other questions.
Have a nice day! :-)
In your own words, describe how you would use construction tools to construct a perpendicular to a line. Explain as if you were teaching a Geometry newbie. Use vocabulary in your explanation. Give an example of how you could then prove the line you created was perpendicular to the original line.
Answers
Ben has to unload a truck filled with 25 bags of grain for his horses. Each bag weighs 50.75 pounds. How many pounds does he have to lift? *
A) 12,687.50 pounds
B) 1, 268.75 pounds
C) 126.875 pounds
D) 1250 pounds
Answers
Answer:
50.75 x 25 = 1268.75 pounds
Answer:
B) 1,268.75 pounds
Step-by-step explanation:
Multiply the numbers: 50.75 * 25 = 1,268.75
Multiply. Enter the product in simplest form.
3/5 × 2/3
=
Answers
Answer:
0.4 or 4/10
Step-by-step explanation:
3. 2 5 4
-- x -- = -- = --
5 3 8 10
Two numbers multiply to be 20 and add to be 12. What are the numbers?
Answers
Answer:2 and 10
Step-by-step explanation:
What is Prefix? ︎︎ ︎︎ ︎︎ ︎︎
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Answer:
c
Step-by-step explanation:
Solve for x ... please help
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Answer:
[tex]7x + 49 \degree = 2x + 94\degree \\ 7x - 2x = 94\degree - 49 \degree \\ 5x = 45\degree \\ x = \frac{45}{5} \\ x = 9 \\ check \\ 7(9) + 49 = 112\degree \\ 2(9) + 94 = 112\degree[/tex]
the angle subtended by the minute hand in 25 minutes
Answers
Answer:
150
Step-by-step explanation:
60 minutes = 1 full rotation,
In 25 minutes, we have 25/60 rotation,
25/60 *360
150
Nicole can run 4
laps in 2/5 hour.
How long will it
Hake her to run 5
laps?
Answers
Answer:
15 minutos or
⁵/¹⁰ hour......
Step-by-step explanation:
ñññññññññlñ
Answer:
1/2 hour
2/5=4
x=5
Then cross-multiply
4x=2
x=1/2
In AIJK, k = 26 cm, ZI=135º and ZJ=11°. Find the length of i, to the nearest
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Answers
Answer:
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Step-by-step explanation:
I KNOW IT THAT ANSWER
You deposit $6500 in a savings account that has a rate of 9%. The interest is
compounded semiannually. How much money will you have after fifteen years?
Round to the nearest cent.
Answers
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Step-by-step explanation:
Choose the correct scientific notation. − 0.0003002
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Answer:
-4
3 × 10
Step-by-step explanation:
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Answer:
The 2nd answer is the correct
Step-by-step explanation:
Hope this helps:)
What is the slope of the function y = − 3/4 x + 5
Answers
-3/4 is the slope.
Good luck!
Answer:
M=3/4
Step-by-step explanation:
Use the figure to find the measures of the numbered angles.
Answers
Answer:
∠3 = 95°
∠4 = 85°
Step-by-step explanation:
Angle 3 and the angle that is already given are Corresponding angles meaning they will be equal.
Angle 3 and Angle 4 are Supplementary angles so their degrees add up to 180°.
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Help please help me please
Answers
Answer:
Step-by-step explanation:
Giải phương trình:
sin*2x+sinxx.cox=1/2
Answers
Answer:
x = 9.47 degrees ( in first quadrant.
Step-by-step explanation:
sin2x + sinx cos x = 1/2
Now sinx cos x = 1/2sin2x so:
3/2sin2x = 1/2
sin2x = 1/2 / 3/2
sin2x = 1/2 * 2/3 = 1/3
2x = arcsin 1/3 = 19.47 degrees
x = 9.74 degrees to nearest hundredth.
Simplify 11 square root 1215
Answers
Answer:
35
Step-by-step explanation:
Its 34.85685 but simplifies to 35.
Answer:
[tex]99\sqrt{15} \thickapprox \:383.42535[/tex]
Step-by-step explanation:
[tex]11\sqrt{1215}[/tex]
Factor [tex]1215[/tex] [tex]=9^{2} \times 15[/tex]. Rewrite the square root of the product [tex]\sqrt{9^{2} } \sqrt{15}[/tex], than take the square root of [tex]9^{2}[/tex].
[tex]11\times 9\sqrt{15}[/tex]
Multiply 11 and 9 which will give you 99.
[tex]99\sqrt{15}[/tex]
_________________________
Simplify using the distributive property:
5(n-3)=
Answers
Answer:
distributive property says x(a+b)
= xa+xb
so 5(n-3)
= 5n-15
Answer: 5n-15
Step-by-step explanation: 5(n-3). multiply n by 5 and -3 by 5 to get 5n-15
mulitiply: -23x(x+3)
Answers
Answer:
[tex] - 23x(x + 3) \\ { - 23x}^{2} - 69x \\ \\ \\ \\ \\ \\ hope \: it \: helps \\ stay \: safe \: healthy \: nd \:and \: happy[/tex]
Answer:
[tex]-23x^{2} -69x[/tex]
Step-by-step explanation:
Using the distributive property:
[tex]-23x(x+3)[/tex]
You will multiply both the x and the 3 inside the parantheses by the -23x outside.
[tex]-23x[/tex] · [tex]x = -23x^{2}[/tex]
Then:
[tex]-23x[/tex] · [tex]3 = -69x[/tex]
If you combine both you will recieve:
[tex]-23x^{2} -69x[/tex]
The question is in the picture
Answers
Therefore, we need to find the slope (“m”) of the line (change in y/change in x), which is rise/run. We also need to find the y-intercept (“b.”)
1.) (0, -3) (1, -1)
We took two points from the line to find the slope. We will use the 2 coordinate pairs to find the slope.
2.) m=(y2-y1)/(x2-x1)
This is the slope “m” formula.
3.) m=( -1+3)/(1-0)
Input the coordinate values into the formula. The +3 you see is due to -(-3)=+3.
4.) m=2/1
We simplified the above formula.
5.) m=2
By division.
We now have the slope or “m.” M=2. Therefore, the equation rises 2 units and runs 1 unit.
Now, finding the y-intercept:
The y-intercept or “b” is where the line intersects the y-axis. It is the starting point of a linear equation.
To find the y-intercept, we need to figure out what the output is when the input is 0. We can see on the table in the picture that with an input of 0, the output is -3.
Therefore, b=-3. This is because an input of 0 means that there is no movement on the x-axis, so we can determine where the where the linear intercepts the y-axis.
Therefore, the equation is y=2x-3, where m=2 and b=-3.
That’s the answer: y=2x-3
error error error error
Answers
Answer:
I really like helping people so can you take this app more seriously ..?
Step-by-step explanation: