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
==========================================================
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.
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Which equation represents a line parallel to the line x-4y=-2
a: y=-4x - 2
b: y=-1/4 + 5
c: y= 1/4x - 3
d: y=4x - 8
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Answer:
c
Step-by-step explanation:
the slope of x-4y=-2 is 1/4
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Answer:
It would be D.
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A car rental agency charges $70 per day, which includes 100 miles. For each mile over 100 miles, there is an additional cost of $0.40 per
Write an equation relating m, the number of miles driven, if the total cost for a one-day rental was $212.
Answers
Answer:
212=70+(m X 0.40)
If $212 is the total cost for a one-day rental, the number of miles driven is 455 miles.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Cost of car rent per day for 100 miles = $70
Additional cost per mile = $0.40
Let m = number of miles driven
Total cost for one day rental = $212
The equation that represents the additional m = miles driven for a day that cost $212 is:
212 - 70 = 0.40m
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m = 142 / 0.40
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This means 355 additional miles were driven.
The number of miles driven for the day is:
= 100 + 355
= 455 miles
Thus if $212 is the total cost for a one-day rental, the number of miles driven is 455 miles.
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HOW to say 9,999,999,999 In word form how would you say it (SAY IT) if your 4th grades are smart and good for you but we are trying to find how to say 9,999,999,999 in word form (any grade can answer and lm fourteen)
Answers
Answer:
nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine
Answer:
nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine
Step-by-step explanation:
Hope it helped brainiest plz and thank you!!!!!!!!
45 is what percent of 60 as an equation
Answers
Answer:
75% of 60 = 45
Step-by-step explanation:
In order to find the answer to this question you need to divide the percentage of the number by one-hundred and then divide that number by the number the number you are trying to find the percentage of.
60/x=100/75
(60/x)*x=(100/75)*x
60=1.33333333333*x
(1.33333333333) to get x
60/1.33333333333=x
45=x
x=45
75% of 60 = 45
Hope this helps.
Explanation: 45 x 100 = 4,500
4,500 divided by 60 = 75
(secA - cosecA)^3+ 3secA.cosecA (secA - cosecA )
bru
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Answer: what?
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y=4x-36
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Answers
Answer: X = 9
Step-by-step explanation:
First insert the function into a graphing calculator.
We are trying to find the x intercepts, we substitute y=0.
With a graphing calculator look at where the line intercepts the x axis, (9,0) , and we find that x=9.
Solve for X
A) -6
C) 12
E) 9
B) 8
D) 3
Answers
Answer:
In my thinking the answer is 9.
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Answer:
Step-by-step explanation:
x-10=4
bring the 10 over and add it to the 4 and that equals 14 so
x=14 hope this helps have a great day
Marsha has $400 in a savings account. The interest rate is 5% per year and is not compounded. How much will she have in total in 1 year?
Answers
The total amount in the account after 1 year will be $420
Based on the information given, the following can be deduced:
Principal = $400
Interest rate = 5%
Time = 1 year
Therefore, the simple Interest will be:
= PRT/100
= ($400 × 5 × 1)/100
= $2000/100
= $20
Therefore, the amount will then be:
= Principal + Interest
= $400 + $20
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Therefore, the total amount is $420
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The length of a rectangle is 5 in longer than its width.
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Answers
Answer:
Length = 21
Width = 16
Step-by-step explanation:
We know that the formula for perimeter is:
P=2W+2L
And we also know that:
L=W+5
So then we put all that we know in the formula:
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Now we expand the brackets and do some algebra:
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16=W
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Answers
Answer:
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Step-by-step explanation:
Selena has been hired as a sales associate at Better Rooms furniture store. She has two salary options. She can choose to receive either a fixed salary of $850 per week or a salary of $400 per week plus a 6% commission of her weekly sales. Which solution set below represents the dollar amount of sales that she must generate each week in order for the option with commission to be the better choice? Let s represent the sales for the week
Answers
Answer:
Sales have to be more than $7,500.
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850 > 400 + 0.06s
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Answer:
A) Dilated 150% then reflected across the x-axis
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Answers
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(=)17 0x +170x+1530=2x²+18x
(=)-2 x² +322x+1530=0
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Δ=115924
[tex]\sqrt{}[/tex]Δ=340,476>0
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The table below shows Amelia's earnings on the job.
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4
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Answers
Answer:
15.25 hours
Step-by-step explanation:
her pay per hour is $27.2
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Step-by-step explanation:
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---- ----
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Answers
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so, here
y = 3×0 + 7 = 7
=>
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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the right answer is x = 9/2
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