Answer:
The area of the patio is 1,116 ft^2
Step-by-step explanation:
Here in this question, we are interested in calculating the area of the patio.
Mathematically, area of patio is;
length * width
Unfortunately we do not have these values. Thus we need to get this from the value of the perimeter of the fencing and the relationship between the width and the length.
Mathematically, the total length of the fencing is the perimeter of the fencing.
Now, we are also told that the patio is 5 feet less wide than it is long.
So if the length is x ft, the width is (x-5) ft
Mathematically;
the perimeter of a rectangle is;
2(l + b)
Writing this in the x terms and equating to the perimeter, we have;
2( x + x -5) = 134
divide through by 2
2x -5 = 67
2x = 67 + 5
2x = 72
x = 72/2
x = 36 ft
Thus since the length is 36 ft, the width would be x -5 = 36 -5 = 31 ft
Done? No!
The question asks to calculate the area. Let’s move these values to the initial equation of the area in the start of the question.
Thus, we have 31 * 36 = 1,116 ft^2
Write the Pythagorean triplet whose one of the numbers is 4. Explain your method.
Answer:
3,4,5 is the Pythagorean triplet
Step-by-step explanation:
A pythagorean triplet is when you have 3 consecutive numbers (for example 1,2,3 or 9,10,11). So since they've already given one of the numbers you can try doing trial and error to find out(use different combinations like 3,4,5 or 4,5,6) and see whether the Pythagoras theorem applies to it.
Find the volume of the rectangular prism below.
2 1/2yd
5 3/4yd
8 yd
I hope this helps you
Find the coordinates of the midpoint of a segment with the given
endpoints. S (10, 9), P (8,2) *

Answer:
(9,5.5)
Step-by-step explanation:
what is the ratio of boys and girls in a classroom of 18 girls and 27 boys
Answer:
2:3Step-by-step explanation:
[tex]18\: girls \\ 27 \:boys\\\\Girls\:: Boys\\18 \: \:\:\:\:\:\:: 27\\\\Use\:3\:to\:divide\:through\\6:9 = 2:3\\[/tex]
please help asap!! Thank youu
Answer: Option 2. x≥-78
Step-by-step explanation:
(x/-6)+2≤15
x/-6≤13
x≥-78 ⇔ REMEMBER you need to change the direction of the sign
when you multiply/divide a negative number
Option 2. x≥-78
Hope this helps!! :)
Please let me know if you have any question
Mark is paddling his kayak across a lake at a constant velocity of 64 meters
per minute to the east. He has 15 minutes to finish his trip before it gets
dark. How long will it take Mark to move 480 meters?
Answer:
7.5r minutes
Step-by-step explanation:
480 divided by 64 = 7.5
the remainder when the polynomial f(x) =2x^3 + px^2 + qx 18 is divided by (x-1) is 10. When it is divided by x+1 the remainder is 12. Find the values of the consonants p and q
Answer:
p = 29 and q = -3
Step-by-step explanation:
Using long division, the remainder when we divide by x − 1 is p+q−16. The remainder when we divide by x + 1 is p−q−20.
Therefore:
p + q − 16 = 10
p − q − 20 = 12
Add the equations together:
2p − 36 = 22
2p = 58
p = 29
Plug into either equation to find q:
q = -3
-5 1/4 + -3 how do you solve this problem
Answer:
8 1/4(Decimal:-8:25)
Step-by-step explanation:
simplify:
-51/4 - 3
=8 1/4 (decimal:-8.25)
Answer:
The answer would be 8 1/4
Step-by-step explanation:
-5 1/4 + (-3)
let's start with the whole numbers:
-5 + (-3) = -8 because it's just like adding positives but add a negative sign
so then we just add the -1/4 and you get -8 1/4
*you have to put the second number in parentheses because its how you properly write the equation Ex: -2+8+(-3)+(-1 5/6)=...
* also note that when you add two negatives it becomes a positive!!!
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter, when did the tree die?
Answer:
t =2654.01465 year
Step-by-step explanation:
Given that the half-life of carbon-14 is 5600 years and if a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter.
we know
[tex]y=a(b)^{t/h}[/tex]
where y= final amount
a= initial amount
b= growth/decay
t= time elapsed
h= half time
plugging the values we get
[tex]0.72 =(\frac{1}{2})^{t/5600}\\[/tex]
taking log on both side
log 0.72 = t/5600 log(1/2)
solving we get t =2654.01465 year
Evaluate the square root of 121.
Answer:
It's 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
divide 121 by 11 then boom, there u go
a student has 5 blouses 4 skirts and 4 sweaters in how many ways can she select an outfit comprising 3 items.
Answer:
80
Step-by-step explanation:
This is a combination question that contains multiple clothing items and to solve such question we multiply the given numbers :
5 × 4 × 4 = 80
Please help me with this probability Questions Pls Explain Thanks
Answer:
I think it's 1/2
Step-by-step explanation:
32+25 is 60 and the total number of students are 50, meaning 10 offer both, and your question says chemistry only so I guess you'll have to subtract the 10 from the 35.
therefore, 25/50= 1/2.
find the sum: 9²+ 10²+11²+.........20².
Answer:
2666Step-by-step explanation:
9² + 10² + 11² + ......... 20² =
= 9² + 10² + 11² + 12² + 13² + 14² + 15² + 16² + 17² + 18² + 19² + 20² =
= 81 +100 +121 +144 +169 +196 +225 +256 +289 +324 +361 +400 =
= 2666
What is the approximate value of 8√?
Answer:
B, between 2.8 and 2.9
Step-by-step explanation:
it is exactly 2.828427125
Which line is perpendicular to y =
[tex] \frac{x}{2} [/tex]
+1
If [tex]y=\frac{x}{2}+1[/tex] then [tex]y_{\perp}=-2x+1[/tex].
The slope in first line is [tex]1/2=0.5[/tex], therefore the slope of perpendicular line must be [tex]-1/0.5=-2[/tex].
Hope this helps.
72p-25p compine like terms
Answer:
47p
Step-by-step explanation:
Since both have coefficients times the same variable we can combine like terms
72p-25p
(72-25)p
47p
10 points
Mr. Right spent $64.75 for five light fixtures and $12.50 for four light
switches. Each light fixture cost the same amount. How much did each
light fixture cost? *
Answer:
$12.95
Step-by-step explanation:
Let L represent the cost of a light fixture. The amount Mr. Right paid is ...
5L = $64.75
L = $64.75/5 = $12.95
Each light fixture cost $12.95.
_____
You may notice that the light switches and their cost are irrelevant to the question.
Solve & Justify: 7(x + 3) + 9 = 5(x - 2) - 3x
Answer:
x = -8
Step-by-step explanation:
[tex]7(x + 3) + 9 = 5(x - 2) - 3x\\\\\mathrm{Expand\:}7\left(x+3\right)+9:\quad 7x+30\\\\\mathrm{Expand\:}5\left(x-2\right)-3x:\quad 2x-10\\7x+30=2x-10\\\\\mathrm{Subtract\:}30\mathrm{\:from\:both\:sides}\\7x+30-30=2x-10-30\\\\Simplify\\7x=2x-40\\\\\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}\\7x-2x=2x-40-2x\\\\Simplify\\5x =-40\\\\Divide both sides by 5\\\frac{5x}{5}=\frac{-40}{5}\\\\Simplify\\x = -8[/tex]
Justification [tex]7(x + 3) + 9 = 5(x - 2) - 3x\\x=-8\\\\7(-8+3)+9=5(-8-2)-3(-8)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(-8+3\right)\::\quad -5\\=7\left(-5\right)+9\\\\=-35+9\\\\=-26\\\\5\left(-8-2\right)-3\left(-8\right)\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(-8-2\right)\::\quad -10\\=5\left(-10\right)-3\left(-8\right)\\\\=-50-3\left(-8\right)\\\\=-50-\left(-24\right)\\\\=-26\\[/tex][tex]-26 =-26[/tex]3k - 2c + 8
use k = 7 and c = 4
Answer:
21
Step-by-step explanation:
3 (7) - 2(4) + 8
21 - 8 + 8
13 + 8
21
Answer:
21
Step-by-step explanation:
3k - 2c + 8
k = 7 and c = 4
Substitute the values of k and c in the algebraic expression
3(7) - 2(4) + 8 = 21 - 8 + 8 = 21
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Answer:
It would be B. Fuction 1 has the larger maximum at (4,1)
Step-by-step explanation:
because the maximum point for Fuction 1 is at (4,1) becuase that the highest point/vertex it goes.
You can use a graph to identify the vertex or you can find the minimum or maximum value algebraically by using the formula x = -b / 2a. This formula will give you the x-coordinate of the vertex. Simply replace the x in your original equation with the value of the x-coordinate and then solve for y.
Answer:
It would be B. Fuction 1 has the larger maximum at (4,1) because the maximum point for Fuction 1 is at (4,1) becuase that the highest point/vertex it goes.
Step-by-step explanation:
Help anyone this is hard
Answer: Juanita
Step-by-step explanation: The question is referring to ratios of the lemon flavor. Juanita's lemonade is 4:2 and Lydia's is 5:3. 4:2 is a larger ratio than 5:3, so that means that Juanita's recipe has a higher concentration of lemon flavor.
evaluate the expression
-53
Step-by-step explanation:
[tex] \frac{( { - 8)}^{2} }{5 - 9} - ( - 1)^2 + 4( - 9) \\ = \frac{64}{ - 4} - 1 - 36 \\ = - 16 - 1 - 36 \\ = - 52 - 1 \\ = - 53[/tex]
Choose all the fractions that are equivalent to 1/8 HELP ME A.2/14 B .4/28 C.5/35 D.2/8 E.7/49 F.7/40
Answer:
None of the options seem to be equivalent to 1/8 but A, B, and C all are equivalent.
Step-by-step explanation:
Let's simplify each fraction as much as possible.
A:
2/14 = 1/7
B:
4/28 = 1/7
C:
5/35 = 1/7
D:
2/8 = 1/4
E:
7/49 = 1/7
F:
7/40 (cannot be further simplified)
I think you may have a typo in your question as there are no answers. However if the question is asking for 1/7, the answers are A, B, C, E.
A drink is made from 1.5 litres of orange juice and 7.5 litres of lemonade. What fraction of the drink is orange juice? (simplest form)
==================================================
Explanation:
1.5 liters of orange juice
7.5 liters of lemonade
1.5+7.5 = 9 liters total
1.5/9 = 15/90 is the fractional amount of orange juice. Note how I multiplied top and bottom of the first fraction by 10 to get 15/90. This is the same as moving the decimal point 1 spot to the right for each value.
----------
From here you divide both parts by the GCF 15 to reduce
15/15 = 1
90/15 = 6
Meaning 15/90 = 1/6
So 1/6 of the drink is orange juice.
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She works on Saturday and Sunday. Assuming she sells the same amount on both days, how much will her sales have to be each day in order to earn at least $500 over the two days?
A. $1,572
B. $350
C. $648
D. $786
Answer:
A. $1572
Step-by-step explanation:
Saturday and Sunday Base Salary: 140+140 = 280
Subtract Base Salary: 500-280 = 220
Find Percent: (220/14)* x 100 = 1571.43
Round up: 1572
Answer:
A. $1,572
Step-by-step explanation:
She earns $140 per day as her base salary.
And she earns 14% of her daily sales for both days.
So 280 + 1, 292 = 1,572!
Hope dis helps! :P
- Anna
A factory produces 30,360 bolts in 12 hours. If the same number of bolts are produced each hour, how many bolts does the factory produce in 4 hours? The factory produces blank bolts in 4 hours.
Answer:
10,120
Step-by-step explanation:
plz help me im so stuck
Bernard's bird feeder holds 4 1/2 cups of birdseed. Bernard is filling the bird feeder with a scoop that holds 9/10 of a cup. How many scoops of birdseed will Bernard put into the feeder? Write your answer as a fraction or as a whole or mixed number.
Answer:
5 scoops
Step-by-step explanation:
Given
[tex]Feeder = 4\frac{1}{2}[/tex]
[tex]Scoop = \frac{9}{10}[/tex]
Required
Determine the number of scoop in a feeder
To do this, we simply divide the size of the feeder by the size of the scoop as follows;
[tex]Number = \frac{Feeder}{Scoop}[/tex]
[tex]Number = 4\frac{1}{2}/\frac{9}{10}[/tex]
Convert Fractions to improper
[tex]Number = \frac{9}{2}/\frac{9}{10}[/tex]
[tex]Number = \frac{9}{2}*\frac{10}{9}[/tex]
[tex]Number = \frac{9 * 10}{2 * 9}[/tex]
[tex]Number = \frac{90}{18}[/tex]
[tex]Number = 5[/tex]
Hence, there are 5 scoops in a feeder
there are 12 students in the gym class if 4 students can sit on 1 bench how many benches are needed for all the students
A. 12+4= 16
B. 12×4= 48
C. 12÷4= 3
E. 12-4= 8
Answer:
C. 12÷4= 3 is correct
as in the question 4 students can sit on one bench than 4×3=12 which is equal to the total number of students in class.
Step-by-step explanation:
hope it will help ^_^
3 bench are needed for all students
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value
We have
Students in the gym = 12
how many students can sit in 1 bench = 4
Based on the given conditions formulate:
12 ÷ 4 = 3
Hence , 3 bench are needed for all students and option C is correct.
learn more about unitary problem from here
https://brainly.com/question/21626677
#SPJ2
Write a real world problem involving multiplication by a decimal factor then solve the problem
Answer:
See Explanation
Step-by-step explanation:
We start by writing a real world problem
The cost of a pack of candle and a dozen of eggs is $12.5 and $11.3 respectively. If Ridwan intends to buy 2 dozen eggs and half pack of a candle, what should be Ridwan's budget.
Next; is to solve the above problem
We continue by listing out the given parameters
A pack of candle = $12.5
A dozen of egg = $11.3
Required
What is the cost of 2 dozen egg and half pack of candle?
We start by calculating the cost of 2 dozen egg
[tex]Cost = 2 * 1\ dozen\ egg[/tex]
[tex]Cost = 2 * \$11.3[/tex]
[tex]Cost = \$22.6[/tex]
Then, we calculate the cost of half pack of Candle
[tex]Cost = \frac{1}{2} * 1\ pack\ of\ candle[/tex]
[tex]Cost = \frac{1}{2} * \$12.5[/tex]
[tex]Cost = \$6.25[/tex]
Lastly, we add up the two costs;
[tex]Total = \$22.6 + \$6.25[/tex]
[tex]Total = \$28.85[/tex]