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Explanation:
L = x = length of the rectangleW = 2x-9 = width of the rectangle, since its 9 less than twice the lengtharea of rectangle = L*W = 129
L*W = 129
x*(2x-9) = 129
2x^2-9x = 129
2x^2-9x-129 = 0
Apply the quadratic formula. We'll use a = 2, b = -9, c = -129.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-129)}}{2(2)}\\\\x = \frac{9\pm\sqrt{1113}}{4}\\\\x \approx \frac{9\pm33.36165464}{4}\\\\x \approx \frac{9+33.36165464}{4}\ \text{ or } \ x \approx \frac{9-33.36165464}{4}\\\\x \approx \frac{42.36165464}{4}\ \text{ or } \ x \approx \frac{-24.36165462}{4}\\\\x \approx 10.59041366\ \text{ or } \ x \approx -6.09041364\\\\[/tex]
We ignore the negative solution because a negative length makes no sense.
The length is approximately L = 10.5904 cm.
The width is 2L-9 = 2*10.5904-9 = 12.1808 cm approximately.
As a quick check,
L*W = 10.5904*12.1808 = 128.99954432
which isn't too far off from 129. We have rounding error which is why we don't perfectly land on the target area value. If you wanted to get closer to the value 129, then use more decimal digits in the approximations of L and W.
----------------------------
If you draw a diagonal in the rectangle, then you form two identical or congruent right triangles.
Focusing on one of those triangles, we have
a = 10.5904b = 12.1808c = unknown hypotenuse = diagonal lengthApply the pythagorean theorem
a^2+b^2 = c^2
c = sqrt( a^2 + b^2 )
c = sqrt( (10.5904)^2 + (12.1808)^2 )
c = 16.1408940520653
c = 16.14
The diagonal is roughly 16.14 cm long.
Solve the equation.
2
What is the first step to isolate the variable term on one side of the equation?
What is the second step to solve for x?
Please help and be fast
Answer:
Add 1/2x, Divide by 7/6
Step-by-step explanation:
Add 1/2x to both sides
Divide both sides by 7/6
What is the sale price with 15% off? Original price: $110 of bears head phones
Answer:
93.5
Step-by-step explanation:
use technology to find points and graph the line x - 3y = -6
What are the length and width of a rectangular traffic sign if the length exceeds the width by 4 inches and the perimeter is 152 inches?
Answer:
L = 40
w = 36
Step-by-step explanation:
P = 2*L + 2*w
L = w + 4
w = w
P = 152
P = 2*(w + 4) + 2*w Remove the brackets
P = 2w + 8 + 2w Combine and switch sides Use P = 152
4w + 8 = P
4w + 8 = 152 Subtract 8 from both sides.
4w = 152 - 8
4w = 144 Divide by 4
4w/w = 144/4
w = 36
L = w + 4
L = 36 + 4
L = 40
A store sells laptops for $720 each. This price is 20 percent more than what it cost the store to buy each of them. Before the next model's release, store employees can purchase any remaining laptops at 23% off the store's cost. How much would it cost an employee to purchase one of these laptops at the sale? PLS HELP
It would cost an employee $443.52 to purchase one of these laptops at the sale.
The selling price of the laptops is $720 each. The cost price is 20 percent more than the cost price.
Cost price = Selling price - 20% of cost price
Cost price = 720 - 20% * 720 = $576
At the release, the laptops are at 23% off the store's cost. Hence:
Price of laptop at release = 576 - 23% of 576
Price of laptop at release = $443.52
It would cost an employee $443.52 to purchase one of these laptops at the sale.
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An automobile manufacturer produces 79% of its cars at plant A. If 5% of the cars manufactured at plant A have defective emissions control devices, what is the probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device?
Answer:
79
over
2000 or 79/2000 or 3.95%
Step-by-step explanation:
The probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is 6.33%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, An automobile manufacturer produces 79% of its cars at plant A and 5% of the cars manufactured at plant A have defective emissions control devices.
∴ The probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is,
= (5/79)×100%.
= 6.33%.
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#SPJ2
6(31)+6(4)-6(15) mental math form
[tex]6(31)+6(4)-6(15)=6(31+4-15)=6(20)=120[/tex]
ok done. Thank to me :>
(5z+17.6)-(-3z+12.2)
A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax.
Bill was for $28.35. A 20% tip would come to $5.67. If we add this tip to the $28.35 bill, we get a total of $28.35 + $5.67 + 0.0625($28.35)
= $35.79 (total)
please give brainlist
Find the perimeter of the figure.
[tex]perimeter = 17 + 19 + 7 + 11 + 10 + 8 \\ [/tex]
[tex]perimeter = 72 \: \: cm[/tex]
help me please thanks
Answer:
9.25 would be the value of x
Explanation:
Perimeter = 2(l + w)
2(13.25 + 9.25)
= 45
You invested $5,000 in a 10 year CD at the age of 12. The account pays 2.5% interest compounded continuously. How much money will you have after 10 years? (Round to the nearest cent.)
Answer:
Do PRT: 5009.31
Step-by-step explanation:
Princable: 5000
Rate: 2.5
Time: 10
Answer:
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer:
y= -4/2x+ -4
Step-by-step explanation:
looked at the graph
Unit 4 Solving Quadratic equations {and complex number}
Question is in image
In the diagram below, ST is parallel to PR
Answer:
D.
Step-by-step explanation:
There is nothing in the figure to indicate the triangles are isosceles. This eliminates answer choices A, B, C.
Answer choice D is a required step in the proof, but only gets part of the way. The triangle similarity means ...
SQ/PQ = TQ/RQ
From here, you need to decompose each of the sides PQ and RQ into parts. Then you can get to the desired relationship.
(PQ -PS)/PQ = (RQ -RT)/RQ . . . segment sum theorem
1 - PS/PQ = 1 -RT/RQ . . . . . . . do the division
-PS/PQ = -RT/RQ . . . . . . . . subtract 1 (subtraction property of equality)
PS/PQ = RT/RQ . . . . . . . . multiply by -1 (multiplication property of equality)
Given the line segment AD. AD=24 BC=12,AB=CD Find AB ?
Answer:
I think its 6
Step-by-step explanation:
A market increased the price of cheese selling for $4.98 per pound by 3%. What is the new
price for two pounds of cheese?
QUICK
Answer:
$10.26
Step-by-step explanation:
$4.98x0.03= 0.1494,
4.98+0.1494= 5.13
2; 5.13+5.13= 10.26
Answer:
$10.26
Step-by-step explanation:
$4.98*103/100=x
x=5.1294
2 pounds=2x=$10.2588=$10.26
jamie uses 54 buttons to make shirts. jamie uses 6 buttons to make each shirt. how many shirts did she make?
Answer: 9 shirts I think
Step-by-step explanation: 54/6=9
Pre college need help with
Answer:
check online for more information
Jabari drives 20.4 miles in 17 minutes. He passes a sign which gives the speed limit as 55 mph. By how much, in mph, did Jabari's average speed exceed the speed limit?
Jabari's average speed exceed the speed limit by 17 miles per hour
Given:
Total distance = 20.4 miles
Time taken = 17 minutes
convert minutes to hour
60 minutes = 1 hour
17 minutes = 0.283333 hour
Average speed = Total distance ÷ Time taken
= 20.4 ÷ 0.283333
= 72.00008470598200
Approximately, 72 miles per hour
Speed limit = 55 miles per hour
Exceeded speed limit = 72 - 55
= 17 miles per hour
Therefore, Jabari's average speed exceed the speed limit by 17 miles per hour
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Six points are plotted on the number line.
Which points on the number line are opposites?
Answer: P and U
Step-by-step explanation:
need help with math probelem i will give you 5 stars and a good rating
Answer:
8 feet
Step-by-step explanation:
12 x 2 =24
40 - 24 = 16
16 /2 = 8
Hope it helps :)
–3 2/6 ÷ 1 1/2=
A. 9/20
B. -3 2/3
C. -2 2/9
D. -5
Answer:
its C
1.convert the mixed number to an improper fraction
([tex]\frac{-20}{6\\}[/tex] x [tex]\frac{2}{3}[/tex] )
2. reduce the numbers with the greatest common factor (2)
[tex]\frac{-20}{3}[/tex] x [tex]\frac{1}{3}[/tex]
3. then multiply and get
[tex]\frac{-20}{9}[/tex]
4. then reduce to get
-2[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
how do i solve for this?
math problem need help give 5 stars and good rating if do
Answer:
The answer is A, 20%.
Step-by-step explanation:
If you find 30 out of 150, it is 20%. A simple way to do it is add 30 up until you get 150. So in this case it is 5 times. Then you do 100% divided by 5 which is 20%. Hope this helps!
4) Change the recurring decimal 0.18 to a fraction. (2marks)
You must show all your working.
Answer:
18/100 or 9/50
Step-by-step explanation:
First, put 0.18 over 100 because there are 2 digits in the decimal, so you convert it to 18/100. Then, simplify it, and because the GCF is 2, divide the numerator and denominator. The final fraction ins 9/50.
Find the GCF and LCM for 16 and 24.
Greatest Common Factors (GCF) of 16 and 24 = 8
Least Common Multiple of 16 and 24 = 48
GCF means Greatest Common Factors
Factors of 16 = 1, 2, 8, 4, and 16
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Common Factors of 16 and 24 = 1, 2, 4, and 8
Greatest Common Factors (GCF) of 16 and 24 = 8
LCM means Least Common Multiples
Multiples of 16 = 16, 32,48, 54.....
Multiples of 24 = 24, 48, 72....
The Least Common Multiple of 16 and 24 = 48
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The scale of a map is known to be 1: 500 000. Find the actual distance (in km) between a mall and the bus interchange if the represented distance on the map is 3.2 cm.
Step-by-step explanation:
when the scale says 1:500000, then that means 1 unit in the map corresponds to 500000 units in reality.
and so, 3.2 cm on the map are
3.2 × 500000 cm in reality.
3.2 × 500000 = 1,600,000 cm = 16,000 m = 16 km
(01.04 MC)The elevation of city A is 80 feet below sea level; the elevation of city C is 16 feet below sea level. The elevation of city D is 1 over 2 of the elevation of city C. Part A: Write an expression to represent the elevation, in feet, of city D. (5 points) Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
A) The expression to represent the elevation in feet of city D is; ¹/₂ × (-16) ft
B) The solution to the expression of the elevation of City D is; -8 fr which is negative because it falls below sea level.
First of all, sea level is at 0 ft.
Thus;
If city A has an elevation of 80 ft below sea level, then;
Elevation of city A = -80 ft
The elevation of city C is 16 feet below sea level. Thus;
Elevation of city C = -16 ft
A) The elevation of city D is ¹/₂ of the elevation of city C. Thus;
Expression for Elevation of city D = ¹/₂ × (-16)
B) Solving the expression for elevation of city D gives;
Elevation of City D = -8 ft
The reason why the answer is negative is because any distance below sea level is considered to be negative and city C which is twice the elevation of city D is negative, and so city D must also have a negative elevation.
Read more about below sea level elevations at; https://brainly.com/question/14837848
Answer:
A) The expression to represent the elevation in feet of city D is; ¹/₂ × (-16) ftB) The solution to the expression of the elevation of City D is; -8 fr which is negative because it falls below sea level.First of all, sea level is at 0 ft.Thus;If city A has an elevation of 80 ft below sea level, then;Elevation of city A = -80 ftThe elevation of city C is 16 feet below sea level. Thus;Elevation of city C = -16 ftA) The elevation of city D is ¹/₂ of the elevation of city C. Thus;Expression for Elevation of city D = ¹/₂ × (-16)B) Solving the expression for elevation of city D gives;Elevation of City D = -8 ftThe reason why the answer is negative is because any distance below sea level is considered to be negative and city C which is twice the elevation of city D is negative, and so city D must also have a negative elevation.
Solveee
8 ( x - 1 ) + 17 ( x - 3 ) = 4 ( 4x - 9 ) + 4
118 - 65x - 123 = 5x + 35 - 20x
Answer:
1)[tex]x = 3[/tex]
2) [tex]x = - \frac{4}{5} [/tex]Step-by-step explanation:
To know the solution with Proof .Refer To the above attachments .Hope this helps you !!Answer:
Step-by-step explanation:
distribute the 8,17,and 4 throughout the parentheses to get
8x-8+17x-51=16x-36+4
combine like terms
25x-59=16x-32
subtract 16x from both sides and add 59 to both sides to get
9x=27
divide both by 9
x=3
