Answer:
width of the sidewalk = 1 feet
Step-by-step explanation:
Area of the pool = length × width
Length = 10 feet
Width = 6 feet
Area of the pool = length × width
= 10 feet × 6 feet
= 60 feet²
Area of the pool = 60 feet²
Total area = Area of the pool + Area of sidewalk
96 feet² = 60 feet ² + Area of sidewalk
Area of sidewalk = 96 feet² - 60 feet ²
Area of sidewalk = 36 feet²
Length of pool + sidewalk = 10 + 2x
width of pool + sidewalk = 6 + 2x
( 10 + 2 x ) ( 6 + 2 x ) -60 = 36
60 + 20x + 12x + 4x² - 60 = 36
4x² + 32x - 36 = 0
4x² + 36x - 4x - 36 = 0
4x (x + 9) -4(x + 9) = 0
(4x - 4) (x + 9) = 0
4(x - 1) (x + 9) = 0
(x - 1) = 0 (x + 9) = 0
x = 1 or x = -9
The width of the side walk can't be a negative value
Therefore, width of the sidewalk = 1 feet
A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.
Given
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.
Let 'w' be the width of sidewalk
The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x
The length of the rectangular pool with side walk is 10+2x
The total area of the pool and side walk is length times width
Total area= [tex](6+2x)(10+2x)\\[/tex]
[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]
apply quadratic formula to solve for x
[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]
Width of the sidewalk cannot be negative
so the width of the sidewalk is 1 feet
Learn more : brainly.com/question/21860114
8. Identify the domain and range to the following relations and state whether or not the relations are functions. State why or why not the relation is a function.
Domain:
Range:
Is this a function? Yes or No? Explain your answer.
Answer:
this is not a function because y-values repeat
Step-by-step explanation:
PLEASE HELP!! ASAP!!
The two rectangles are scale drawings. What is the
measurement of x?
Answer:20
Step-by-step explanation:
7 divided by 28 is 4 so multiply 5x4
Answer: is 20
Step-by-step explanation:
The following numerically ordered sequence of numbers has a mean of 17 and a median of 18.
7, a, 12, 15, 17,5, 20, 22, 24, 25
Given this information, the values of a and b must be:
what are the values of a and b?
Please help me ;-;
What's the next term?
0, 1/3
3, 2
6, 12
9, ?
(Above is supposed to be a table btw)
Answer:
72
Step-by-step explanation:
Based on the table, the left and the right side have a pattern. When 3 is added to the left side, the right side is multiplied by 6. Since 12 multiplied by 6 is 72, the missing number is 72.
The length of a side of a regular hexagon is 6.8 cm, correct to one decimal place. Find the smallest possible perimeter of the length
Answer: 40.8cm
Step-by-step explanation:
A hexagon is a polygon that is made up of 6 sides. The perimeter of a regular hexagon is calculated by multiplying the side given by 6
Since the length of a side of a regular hexagon is 6.8 cm, the perimeter will be:
= 6 × 6.8
= 40.8cm
(-4x2 + 3x + 3) – (4x2 + 9)
Answer:
[tex]-8x^{2}+3x-6[/tex]
Step-by-step explanation:
The image below shows step-by-step on how to simplify the expression.
Hope this helps! :)
What is the measure of arc FLI?
Answer:
140
Step-by-step explanation:
By inscribed angles, arc FPI = 2<FLI = 2*110 = 220. Since the entire arc of a circle is 360, we know that arc FLI + arc FPI = 360. Solving, we get arc FLI = 360 - 220 = 140.
I hope this helps!
Susan got 72 marks in English out of 120 and 70 marks in
Hindi out of 150. The maximum marks in the mathematics
paper were 180. If she got 60% marks in all the three papers
how y marks did she get in mathematics?
Answer:
let the marks obtained in maths be x
total marks obtained by susan=142+x
then
A/Q
60%of 450 =(142+x)
270=142+x
x=270-142
x=128
hence marks obtained in maths=128
OR
Max marks 120+150+180=450
60% of 450 is 270
70 +72+x=270
x=270-142
x=128
A basketball costs $32.00. The sales tax rate is 7%. Find the amount of sales tax
The amount of the sales tax is $2.24.
Given that,
The cost of the basketball is $32.00And, the sales tax rate is 7%.Based on the above information, the amount of the sales tax rate is
[tex]= \$32 \times 7\%[/tex]
= $2.24
Here we simply multiply the cost with the sales tax rate.
Therefore we can conclude that the amount of the sales tax is $2.24.
Learn more: brainly.com/question/23461853
What is the question 15%of258
Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have the same amount of pasta and sauce and wants to use all of the items. Use the drop-down menus to complete the statements below about the number of bags Cesar can make.
Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have the same amount of pasta and sauce and wants to use all of the items. Use the drop-down menus to complete the statements below about the number of bags Cesar can make.
What is the greatest number of bags Cesar can make and Each bag would have _____ pasta and _____ jars of sauce
Answer:
The greatest number of bags Cesar can make is 16 bags.
Each bag would have 2 pasta and 3 of jars of sauce
Step-by-step explanation:
We solve the above question using Greatest Common Factor method
The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then the greatest common factor is 16.
Hence, the greatest number of bags Cesar can make is 16 bags.
For Pasta, We have 32 pasta
Each bag would have: 32/16
= 2 pasta
For Jars of sauce, we have 48 jars of sauce.= 48/16
= 3 jars of sauce
Simplify: 3a - 4 + 5a + 7 + 2(a + 1)
Answer:
10a + 5
Step-by-step explanation:
3a - 4 + 5a + 7 + 2(a + 1)
3a - 4 + 5a + 7 + 2a + 2
10a +5
Group the variables and non variables.
Determine the type of triangle that has angle measurements of 45°, 45°, 90°.
equilateral triangle
obtuse triangle
right triangle
acute triangle
Answer:
Right triangle
Step-by-step explanation:
90 degrees means that it's a right angle
Answer:
Acute triangle
Step-by-step explanation:
9.8(3x - 7.2) please help!!!
Answer:
29.4x-70.56
Step-by-step explanation:
Round 729 to the nearest 100
Answer:
700
Step-by-step explanation:
700
Write two numbers that multiple to the value on top & add the value on the bottom.
Answer:
23040
This is because math.
ABCD is a rectangle, where A (1, 2), B (6, 0), C (10,10) and D (x, y) is unknown. Find the coordinates of the fourth vertex Point D. Verify that ABCD is a rectangle providing evidence related to the sides and angles. 2. Find the perimeter and area
Answer:
So find the what?
Step-by-step explanation:
will someone tell me the equation for this word problem.
will give brainliest
Answer:
5c + 3d = 55
4c + 3d = 53
Step-by-step explanation:
lets pretend c= cost of chicken, d= cost of duck
5 chickens total cost would be 5c
3 ducks total cost would be 3d
in equation one added together would be 55 for total cost (given in word problem).
repeat for second equation.
please give thanks :)
Write the equation, in slope-intercept form, of the line that passes through (-2,0) and is parallel to the line represented by 5x-3y=-17 .
Answer:
[tex]y=\frac{5}{3}x+\frac{10}{3}[/tex]
Step-by-step explanation:
Firstly we rewrite the equation that is parallel to the line we need because parallel lines have the same slope by the rule
[tex]m_1=m_2[/tex]
so we rewrite the equation in slope-intercept form:
[tex]5x-3y=17\\-3y=-5x+17\\y=\frac{-5x+17}{-3}\\\\y=\frac{-5x}{-3}+\frac{17}{-3} \\\\y=\frac{5}{3}x-\frac{17}{3}[/tex]
and now we compare it with our slope-intercept form equation:
[tex]y=mx+b[/tex]
the coefficient of x which is m is the slope and since parallel lines have equal slopes the line that we need would also have the same slope which is 5/3.
now the next step is the line that we need passes through the point (-2,0) so it means that it should satisfy that specific point so we insert that point into our slope-intercept form and insert the slope which is 5/3 which is m.
[tex]y=mx+b\\y=\frac{5}{3}x+b\\\\0=\frac{5}{3}(-2)+b\\\\0=\frac{-10}{3}+b\\\\b=\frac{10}{3}\\[/tex]
now we know that the y-intercept(b) of the line we need is 10/3 and slope(m) is 5/3 insert these values into our slope-intercept form:
[tex]y=mx+b\\y=\frac{5}{3}x+\frac{10}{3} \\[/tex]
so this is our given line.
Graph a line with a slope of 4 that contains the point (3,0)
Answer:
So the slope is rise over run. You need the y intercept and the slope to write an equation. To find the y intercept, use the formula : 0=4(slope)*3+b and you get 0=12+b then you subtract twelve from both sides, getting b=-12. Thats your y intercept. So your equation will be y=4x-12
The sum of two numbers is 20. Their difference is 4.
a. Write a system of equations that describe this situation
b. Solve by elimination to find the two numbers
Answer:
The two numbers are 12 and 8
Step-by-step explanation:
Well this is pretty simple
We can just list out everything that Adds up to 20
1+19
2+18
3+17
4+16
5+15
6+14
7+13
8+12
9+11
10+10
Now just subtract each one until you get the one that equals to 4
Which is 12 and 8 in this case
The graph shows the solution to which system of inequalities?
Answer:
is A B and D
Step-by-step explanation:
The logarithmic expression ln(√e/y^3) can be rewritten as
Answer:
[tex]\dfrac{1 - 6 \ln y}{2}[/tex]
Step-by-step explanation:
[tex] \ln \dfrac{\sqrt{e}}{y^3} = [/tex]
[tex] = \ln \dfrac{e^\frac{1}{2}}{y^3} [/tex]
[tex] = \ln e^\frac{1}{2} - \ln y^3 [/tex]
[tex]= \dfrac{1}{2} \ln e - 3 \ln y[/tex]
[tex]= \dfrac{1}{2} - 3 \ln y[/tex]
[tex]= \dfrac{1 - 6 \ln y}{2}[/tex]
The given logarithmic expression can be written as [tex]\frac{1-6ln\ y}{2}[/tex]
Given that,
The given logarithmic expression is [tex]ln \frac{\sqrt{e} }{y^3}[/tex].We need to rewrite the above logarithmic expression.Based on the above information, the calculation is as follows:
[tex]= ln \frac{\sqrt{e} }{y^3}\\\\= ln \frac{e^{1/2}}{y^3} \\\\= ln \e^{1/2} - lny3\\\\= \frac{1}{2}ln e - 3 ln y\\\\= \frac{1}{2} - 3 ln \ y \\\\= \frac{1- 6ln \y}{2}[/tex]
Therefore we can conclude that the given logarithmic expression can be written as [tex]\frac{1-6ln\ y}{2}[/tex]
Learn more: brainly.com/question/24169758
When is Cheryl's birthday?
Answer:
july 16
Step-by-step explanation:
PLEASE HELP HELP!!! PRECALC
Answer:
The base is 0.1
The base is less than 1 so the function is decreasing
The x intercept is (3,0)
Step-by-step explanation:
The base of a logarithm refers to the number that must be raised to the power of the number on the right hand side of the logarithmic equation in order to yield the number on the left hand side of the logarithmic equation. It is always written as a subscript below the log symbol. In this case, the base is 0.1.
When the base of a logarithm is less than 1, it means that the function is decreasing as is the case in this question.
Looking at the graph, the x axis is cut at the point (3,0). This is the x-intercept of the graph.
A little girl standing next to a telephone pole at 10 AM. The little girl is 4'6" tall and the telephone pole is 40 feet high. If the telephone pole cast 8 32 foot shadow, how long is a little girl shadow?
Answer:
The shadow of the pole is 1.2 feet long
Step-by-step explanation:
A little girl standing next to a telephone pole at 10 AM.
From the above question
Height of the girl = 4'6" tall = 4 feet and 6 inches tall
We convert to feet
= 12 inches = 1 foot
6 inches = x
Cross Multiply
12 × x = 6 × 1
x = 6/12 = 1/2 = 0.5 feet
Hence, the total height of the girl =
4 feet + 0.5 feet = 4.5 feet
The height of the telephone pole = 40 feet high.
The shadow of the telephone pole
= 8' 32 foot shadow
= 8 feet, 32 inches
We convert the inches to feet
12 inches = 1 foot
32 inches = x
Cross Multiply
12 × x = 32 × 1
x = 32/12 = 8/3 = 2.67 feet
Total length of the pole = 8 feet+ 2.67 feet = 10.67 feet
how long is a little girl shadow?
This is calculated using proportion
Shadow/Height
Shadow of the girl = x
Hence:
Shadow of the girl/Height of the girl = Shadow of the pole/Height of the pole
x/4.5 feet = 10.67 feet/40 feet
Cross Multiply
40 × x= 4.5 × 10.67
x = 4.5 × 10.67/40
x = 1.200375 feet
Approximately = 1.2 feet
Hence, the shadow of the pole is 1.2 feet long
Lucas took his bike to a local park to ride on some bike trail.Trail A is 6 3/4 miles long.Trail B is 8 1/2 miles long. How many miles long is Trail B then Trail A
Answer: Trial B is [tex]1\dfrac{3}{4}[/tex] miles longer then Trail A.
Step-by-step explanation:
Length of Trail A = [tex]6\dfrac34[/tex] miles
= [tex]\dfrac{24+3}{4}[/tex] miles = [tex]\dfrac{27}{4}[/tex] miles.
Length of Trail B = [tex]8\dfrac12[/tex] miles
= [tex]\dfrac{16+1}{2}[/tex] miles = [tex]\dfrac{17}{2}[/tex] miles.
Trial B is longer then Trail A by [tex]\dfrac{17}{2}-\dfrac{27}{4}[/tex] miles
[tex]=\dfrac{17\times2}{2\times2}-\dfrac{27}{4}[/tex] miles
[tex]=\dfrac{34}{4}-\dfrac{27}{4}[/tex] miles
[tex]=\dfrac{7}{4}[/tex] miles
[tex]=1\dfrac{3}{4}[/tex] miles
Hence, Trial B is [tex]1\dfrac{3}{4}[/tex] miles longer then Trail A.
Does this graph show a function? Explain how you know.
5
-5
5
-6
A. Yes; the graph passes the vertical line test.
B. No; there are y-values that have more than one x-value.
C. Yes, there are no y values that have more than one x-value.
D. No; the graph fails the vertical line test.
Answer:
D. No; the graph fails the vertical line test
The correct option is D. No, the graph fails the vertical line test.
What is vertical line test?The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function. It is done by visually examining the number of intersections of the curve with vertical lines.
In the given graph, the graph of a function intersects the y axis twice.
Any vertical line in the x y plane must intersect the graph of a function at most once.
Thus, the correct option is D.
Learn more about vertical line test.
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Can somebody plz help answer all the questions correctly thanks !
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDD
Answer:
what questions? I dont see any
Answer:
there are no questions here but i am willing to see if i can help you with what you need
Step-by-step explanation:
Your high school is having a competition where students have to guess how many candy canes are in a jar. The tens digit is 4 more than twice the ones digit. The sum of the digits is 4. How many candy canes are in the jar
Answer:
40
Step-by-step explanation:
let ones be x
tens is 4 + 2x
4 + 2x + x = 4
3x = 0
x = 0
tens is 4 + 2*0
tens = 4
40 candy canes