Given a rectangle with the following dimensions: Area = 100 units squared Length = x + 10 units Width = x units Find the value of x by completing the square method
Answers
Answer:
The value of x is: \(5 (\sqrt5-1)\ units\)
Step-by-step explanation:
Given that:
Area of rectangle = 100 sq units
Length = (x+10) units
Width = x units
We know that area of a rectangle is given by the formula:
\(A = l \times w\)
Where l is length of rectangle and
w is the width of rectangle
Putting the values in formula:
\(x(x+10) = 100\\\Rightarrow x^2+10x=100\\\text{Trying to make square on both sides by Adding 25 on both sides}:\\\Rightarrow x^2+10x+25=100+25\\\Rightarrow x^2+2 \times 5 \times x+5^2=125\\\text{Formula: } a^{2} +2 \times a \times b+ b^{2} = (a+b)^2\\\Rightarrow (x+5)^2 = 25 \times 5\\\text{Taking square root on both sides:}\\\Rightarrow (x+5) = 5\sqrt5\\\Rightarrow x = 5\sqrt5-5\\\Rightarrow x = 5 (\sqrt5-1)\)
So, The value of x is: \(5 (\sqrt5-1)\ units\)
Related Questions
Pls, help me with this question!!!
Answers
Answer: the answer is 6
Step-by-step explanation:
— mEmberS of a book club have 12 bOoks to chOosE frOm this mOnth whAt arE 2 diffErent tOoLs the cLub mEmberS cOuld US3 to simmuLate rΔndOmly choOsing a boOk??
Answers
Answer:A spinner wheel or a 12 sided die
Step-by-step explanation: It’ll be randomized so hopefully no one gets angry.
Alexis ordered an ice cream cake from Molly Moo Creamery. The box that it was packed in was a rectangular prism. The dimensions of the box are shown in the diagram.
What is the total surface area of the box of in square inches?
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Please help quick(10 points &brainleist)
Evaluate.
(1/5)^−1 ⋅ 40
0
1
5
20
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200
the minus 1 is separated with 1 and 5 and it is reciprocal due to the power of minus 1 and 5 comes up and multiplies with 5
I only need help with the one that are highlighted, thanks. ( if you dont know the answer,
please don't bother.)
Answers
What is the slope of the line that contains the points negative 2, negative seven halves and (4, −4)?
Answers
Answer:
-1/12
Step-by-step explanation:
Formula to find the slope: Y2-Y1 / X2 - X1
Plug in:
(-4 + 7/2) / (4 + 2)
(-8/2 + 7/2) / (4 + 2)
( - 1/2) / (6)
= -1/12
Answer:
-1/12 negative one over 12
please help :( I cant figure it out
Answers
Answer:
Step-by-step explanation:
0.628
HEEELLLPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[Image: A coordinate plane ranging from 5 to –5 counting by 1s.]
Vertex C and vertex D are plotted on the graph. Plot vertexes A and B to form a rectangle with an area of 36 square units. Plot vertex E at (2, 4).
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Answer:
I'm not sure I can make a rectangle in a coordinate that ranges from +5 to -5 and get the area of the rectangle to be 36 squared units.
I am very sorry.
Step-by-step explanation:
(Urgent!) Please answer these quick, show how you did each as well.
Answers
Answer:
1) A = π(14 cm)² = 196π cm²
= about 616 cm²
2) A = π(7.5 ft)² = (15/2)²π ft² = 225π/4 ft²
= about 177 ft²
Answer:
circle: 616 cm²target: 1.77 ft²tortilla: 113.10 in²Step-by-step explanation:
You want the areas of the circle figures:
circle, radius 14 cmtarget, diameter 1.5 fttortilla, diameter 12 inAreaThe area of a circle is given by the formulas ...
A = πr² = (π/4)d² . . . . . where r is the radius, d is the diameter = 2r
CircleThe area of the circle of radius 14 cm is ...
A = π(14 cm)² ≈ 616 cm²
TargetThe area of the target with diameter 1.5 ft is ...
A = (π/4)(1.5 ft)² ≈ 1.77 ft²
TortillaThe area of a 12-inch tortilla is ...
A = (π/4)(12 in)² ≈ 113.10 in²
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Use a number line to order the numbers from least to greatest.
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Assign the numbers to the number line in the following order:
2.15=2.15
220%=2.2
9/4=2.25
*2.15* is easy enough to place as it is already in decimal form. However, the other 2 options need to be converted to decimals in order to be placed. We have the fraction 9/4 and percentage 220%. 9/4 can either be simply divided on a calculator or turned into the mixed fraction 2 and 1/4, which is *2.25*. Finally, we know that converting a decimal to a percentage we multiply the decimal by 100. Therefore, to convert a percentage to a decimal we divide 100 or move the decimal to the left 2 places. With this conversion rule, 220% transforms to *2.2* and we have the third and final number for our number line. Arranging these three numbers from least to greatest:
2.15, 2.2, 2.25
if 4/4 is 1 then 9/4 is 2 whole with 1/4 left
220%=2.2 and 2.15 is still 2.15
Please help ASAP! -screenshot-
Brainlist 2 correct answers!
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Answer:
P(not blue) = 1 - P(blue) = 1 - 10/50 = 40/50
= 4/5
P(2) = 5/20 = 1/4 = 25%
What is the measure of angle 1? (Picture attached) HELPP
A. 112°
B. 45°
C. 102°
D. 68°
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Answer: A. 112
Step-by-step explanation:
becuase 1, 2, 6 , 7 multiplied and added up negative 4 and 3 equal 109 and if you add 3 from the top you get 112
100 POINTS MATHAMATICS PLEASE ANSWER ASAP
look in image and answer ALL 4 PROBLEMS
Answers
2. Pencils measuring less than 5 inches: 3 + 2 + 3 = 8 inches in total.
3. False. To determine if more than half of the pencils are 6 inches or shorter, we need to find the total number of pencils and calculate how many of them are 6 inches or shorter.
Total number of pencils = 4 + 3 + 2 + 3 + 7 + 8 = 27
Number of pencils that are 6 inches or shorter = 4 + 3 + 2 + 3 = 12
To find out if more than half of the pencils are 6 inches or shorter, we need to divide the number of pencils that are 6 inches or shorter by the total number of pencils and multiply by 100%:
12/27 x 100% = 44.44%
Since 44.44% is less than 50%, the statement is false.
4. There are three pencils that measure more than 5.5 inches but less than 7.5 inches: 6, 6, and 7. Therefore, the answer is 3 pencils.
(Make sure you look over this and if you have any questions about this comment before you submit make sure this seems right to you and if you understand this or not)
2. Would be the number 8
3. Would be false
4. Would be the number 3
The inequality 7h+45≥143 represents the minimum number of hours, h, it will take a chef to make at least 143 croissants. The table shows the steps the chef takes to solve the inequality.
Answers
Answer:
d
Step-by-step explanation:
The first step should have been 7h>98
PLEASE HELP if you can
they might be mixed up but portland, missippi, then questions
(file below)
Answers
Answer:c
Step-by-step explanation:
Tim incorrectly rewrote the expression 1/2p - (1/4p + 4) as 1/2p + 1/2p - 4. Rewrite the expression without parentheses. What was Tim's error?
Answers
Answer:
1/2p - 1/4p - 4.
Step-by-step explanation:
1/2p - (1/4p + 4)
= 12p - 1/4p - 4
≠ 1/2p + 1/2p - 4
Instead of writing -1/4p, Tim wrote 1/2p
Which associations best describe the scatter plot?
Select each correct answer.
Nonlinear association
Positive association
Linear association
Negative association
Answers
Answer:
positive association
Step-by-step explanation:
Scatter Plot: Strong Linear (positive correlation) Relationship
Explanation: The line is not necessarily straight so it’s not linear, it’s nonlinear. as the time increases the distance decreases therefor it is negative.
X Y
-7 0
0 1
What is the slope of the linear function represented in
the table?
*-7
07/1
01/1
07
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the formula for slope is rise over run, or y1-y2 divided by x1-x2. we can choose either number as y1 or y2 but it needs to stay consistent with x
so let’s plug in from your table.
0-1 divided by -7 -0
(you could also do 1-0 divided by 0-(-7))
-1/-7 which equals 1/7
so, your slope is 1/7
I hope this helps! :)
PLS HELP, WILL REWARD BRAINLIEST !!
Answers
Answer:
A) the median of brand a is higher than brand b
Step-by-step explanation:
Typically means usaully and that means the weights that the bars usaully are so if you compare the meadian weights that the two brands typically are, brand A would usually be heaver.
I'm bad at explaining things but I hope this helps.
1. A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect to prefer comic books?
A. 10
B. 20
C. 70
D. 80
E. 100
2. About how many students do not prefer non-fiction?
A. 60
B. 75
C. 100
D. 150
E. 180
3. Overall, about how many students prefer literature (poems, plays, or novels)?
A. 45
B. 90
C. 100
D. 130
E. 180
Answers
Answer:
1) a. 80
2) d. 150
3) e. 90
2. d
3. e hope this helps!
Write a word problem where the solution will be |20| = 20.
6th grade
Answers
Factor the expression completely.
6x+7x
Answers
Answer:
Step-by-step explanation:
6x+7x= ?
- factor x
x(6+7)
x(13)
= 13x
therefore, 13x is your answer.
Mr. Toro saved up $440 from his salary to go on vacation. He wants to spend 20% of his savings on a ticket to Disneyland. How much did the ticket to Disneyland cost?
Answers
Answer:
440 X 1/5=88 answer:88
Step-by-step explanation:
Answer:
The answer is 88
Step-by-step explanation:
It is because 440 of 20% is 80
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
Answers
The amount of money raised and the number of students who attended the dance will be directly proportional to each other, meaning both are positively dependent on each other. This type of a relationship is called a linear relationship, which can be represented by a type of graphical method called the "linear graph".
To accurately represent the data, on the x axis you need to plot the the number of students attending the dance; and on the y axis you need to plot the amount raised and you'll obtain a positive slope of 10.
The starting point of the graph would have the coordinates (0,100) or x = 0 and y = 100, because even if there are no students attending the event, the decoration cost of 100 dollars would still have to be paid.
The equation for the same should be written as: Amount of money raised = 10 x no. of students + 100
Here's a link to similar graph based questions for practice
https://brainly.com/question/25671164?referrer=searchResults
Please help! I need it asap.
Answers
Answer:
What?
Step-by-step explanation:
Determine which graph shows y as a function of x.
i will mark brainliest if correct
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Answer:
I think it is b
help me this one plssssssssssss
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Answer:
The integer that describes the translation from B to B' is (-2,1)
giving brainlyest need anser Bud and his friends stopped at a local fast food restaurant after the football game Friday night. Bud ate a one-fourth pound cheeseburger and a large order of fries. The cheeseburger contained 30 grams of total fat. If the recommended daily allowance of total fat for a 2,000 calorie diet is 64 grams, what percent of the daily allowance did Bud have when he ate the cheeseburger? Show your work.
Answers
To find out what percentage of the daily allowance of total fat Bud had when he ate the cheeseburger, we first need to calculate how many grams of total fat he consumed, and then divide that by the recommended daily allowance, and finally multiply by 100 to get the percentage.
Bud ate a cheeseburger containing 30 grams of total fat. The recommended daily allowance of total fat for a 2,000 calorie diet is 64 grams. Therefore, we can calculate the percentage of the daily allowance that Bud had by dividing the amount of fat he consumed by the recommended daily allowance and then multiplying by 100:
Percentage of daily allowance = (30 / 64) x 100 = 46.875%
So, Bud had 46.875% of the recommended daily allowance of total fat when he ate the cheeseburger.
Answer:
46.875 %
Step-by-step explanation:
30 grams of fat out of 64 grams
30/64 =.46875
Change to percent form
46.875 %
The grocery store is having a sale that offers 45% off the original price. What fraction is taking off the prices? (simplify your fraction)
Answers
9/20
Step by Step:
you divide 45 by 5(GCF) which equals to 9 then divide 100 by 5 which is 20
Answer:9/20
50 POINTS PLS HELP AND BRAINLIEST
