The length of the rectangular pool is 50 meters
How to determine the value
The formula for perimeter of a rectangle is expressed as;
Perimeter = 2 ( l + w)
Where:
l is the lengthw is the widthFrom the information given, we have;
Perimeter = 160 meters
Length = 20 + w
Substitute into the formula
160 = 2( 20 + w+ w)
expand the bracket
160 = 2(20 + 2w )
160 = 40 + 4w
collect like terms
160 - 40 = 4w
4w = 120
w = 120/ 4
w = 30 meters
But length = 20 + w = 20 + 30 = 50 meters
Thus, the length of the rectangular pool is 50 meters
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Which system of equations is represented by the matrix below?
[4 0 5
2 -117
47576777...................
ashley drove 605 miles in 11 hours at the same rate how long would it take her to drive 495 miles
Answer:
9 hours
Step-by-step explanation:
605 miles/11 hours = 55miles/hour
495 miles (time) = 495 / 55 =9
So, 9 hours
i need all 3 im confused on them
Answer:
1. 5/12 in exact form and 0.416 in decimal form
2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.
On each "6" there's a - on top!
what is 2169 rounded to the nearest hundred
Answer: 2169 rounded to the nearest hundred is 2200
Step-by-step explanation: Since 6 in the tenth place is greater than 5 the number in the hundred place which is 1 goes up to 2. That is how you get 2200
-5; -1/2; -0.05; -45% least to greatest
Answer:
-5, 1/2, -0.45, -0.05 would be the solution
WITHOUT GRAPHING identify the coordinates of A(-3, 7), B(4, 9), and C(0, -2) after the following transformations. 1. Translation 2 units up and 7 units right.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Dilation is a transformation that affects the size of a figure.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
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Find the midpoint of the segment with the following endpoints (4,6) (1,3)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]
what is the slope of the line that passes through the points (6, -5) and (6, -4)?
Answer (y2 -y1) / (x2 - x1)
hope this helps
Answer:
(y2 -y1) / (x2 - x1)
Step-by-step explanation:
Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.
Find the inverse of each function. Is the inverse a function?
f(x)=2x² /5 +1
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
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Question Completion:How many T-shirts were purchased by the Team?
Someone answer this plsss
The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
From the question, we are to determine the equation of the line that is perpendicular to the given equation.
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
That is,
If m₁ is the slope of one of the lines
and m₂ is the slope of the other line
Then,
m₁ = -1/m₂
First, we will determine the slope of the given line
The equation of the given line is
y = 3x - 9
Compare the equation to the general form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
By comparison,
m = 3
∴ The slope of the given line is 3
Thus,
The slope of the line that is perpendicular to this line is -1/3
Now,
To determine the equation this line,
We have that the line passes through the point (3, 1)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
m = -1/3
x₁ = 3
y₁ = 1
Putting the parameters into the equation,
y - 1 = -1/3(x - 3)
Expressing the equation in standard form
3(y -1) = -1(x - 3)
3y - 3 = -x + 3
3y + x = 3 + 3
x + 3y = 6
Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
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Enterprise will allow you to rent a car for $10 per day plus a $20 fee. Hertz will allow you to rent a car for $40 a
day. After how many days, x, will Enterprise cost more than Hertz?
Yes..............................
The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $ 1200 . The party must have 13 adult chaperones.
b. The class wants to promote the event by giving away 30 spots to students in a drawing. How does the model change? Now how many paying students must attend so the cost for each is no more than $ 7.50 ?
The function model will be -
Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.
How many pupils must enroll in order for the price per pupil to not exceed $7.50?1200/N ≤ 7.50
1200 / 7.50 ≤ N
N ≥ 1200/7.5
N ≥ 160
To keep the price per kid to no more than $7.50, there must be more than 160 participants.
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Kim has a part-time job assembling bicycles for a local store. each day, she earns $20 plus $15 for each bike assembled. kim's boss daily goal is to assemble no more than 6 bicycles a day. if x represents the number of bikes assembled, the total amount she earns can be represented by . what is the range for the function for this situation?
The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.
The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).
The total amount she earns can be represented by
y = 15x + 20
where y is her daily earnings and x is the number of bikes she assembles
If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).
domain : {x| 0 ≤ x ≤ 6}
where x is a whole number
Substituting the minimum and maximum value of x in the function.
y = 15(0) + 20 when x = 0
y = 20
y = 15(6) + 20 when x = 6
y = 110
range : $20 ≤ y ≤ $110
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Simplify. (3⁻²) (3⁵) .
A school dedicated 50% of the courtyard area for students to start a garden. The students want to know how much of the 632 yard the will be able to use?
The students will have 316 yards of the courtyard
The number of yards left for the students can be calculated as follows;
A school dedicated 50% of the courtyard area for students to start a garden
= 50/100
= 0.5
The number of yards is 632, the number of yards left for the students can be calculated as follows
= 0.5 × 632
= 316
Hence 316 yards are left for the students
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At the local movie theatre, there are 115 boys, 92 girls, and 28 adults.
a. Write the ratio of the number of boys to the number of girls.
115:92
b. Write the same ratio using another form (: vs. to ).
115 to 92
c. Write the ratio of the number of boys to the number of adults.
115:28
d. Write the same ratio using another form.
115 to 28
A. The ratio of the number of boys to the number of girls is; 115:92
B. The same ratio using another form is; 115 to 92
C. The ratio of the number of boys to the number of adults is; 115:28
D. The same ratio using another form is; 115 to 28
What is the Ratio?We are told that there are 115 boys, 92 girls, and 28 adults. Thus;
Number of boys = 115
Number of girls = 92
Number of Adults = 28
Now, we want to find some ratios and they are;
A) The ratio of boys to the number of girls = 115 : 92
B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;
115 to 92
C) The ratio of the number of boys to the number of adults is;
115:28
D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28
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For the function f(x)=∛2x , find f⁻¹(x) . Then determine the value of x when f(x)=16 .
The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex] when f(x) = 16 is [tex]x=2^\frac{11}{3}[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the functionWe have given a function [tex]f(x)=x\sqrt[3]{2}[/tex]. ....(1)
Let y = f(x)
[tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]y=\frac{x}{\sqrt[3]{2} }[/tex]
[tex]f^{-1}(x)=y[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]
It is given that f(x) = 16 on comparing it with equation (1) , we get
[tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]
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which option/graph
PLEASE PLEASE HELP
Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(g⁰g)(1)
Value for (g⁰g)(1) = 17
What is the domain of the function (g⁰g)(1)?Now, (g⁰g)(x) = g[g(x)]
let g(x) = 3x + 2
(g⁰g)(x) = g(3x + 2)
(g⁰g)(1) = g(5)
(g⁰g)(1) = 3(5) + 2
(g⁰g)(1) = 17
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About how much farther did she bike on Wednesday than Thursday?
the answer is 71 miles far
The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
According to the given question:
Each block of horizontal is 1/8 hr = 7.5 min
Each block of vertical is 10 km/hr
Time Velocity (km/hr)
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
The acceleration in first 15 minutes = (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
The distance between the two cities =
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of train during the journey = 125/2 = 62.5 km/hr
Therefore,
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
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A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
The side length of the square in centimeters is 13 centimeters
What are areas?The area of a shape is the amount of space on the shape
How to determine the side length?The equation of the area of the square is given as
p² = 169
The area of a square is the product of its length
This means that we simply take the square root of both sides of the equation to determine the side length
Next, we take the square root of both sides of the equation
So, we have
√p² = √169
Evaluate the square roots
So, we have
p = 13
Hence, the side length of the square in centimeters is 13 centimeters
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PLSSSPLSS PLS HELP ME WILL GET BRIANLIEST
Which angles are vertical to each other?
A survey finds that 110 people ate breakfast and 30 people skipped breakfast. Of those who ate
breakfast, 10 people felt tired. Of those who skipped breakfast, 10 people felt tired. Make a
two-way table that shows the conditional relative frequencies based on the breakfast totals.
Here is the two-way table :
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
What is the two way table?A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns. A conditional relative frequency is the ratio of the frequency of a class to the total frequency.
People who ate breakfast and did not feel tired = 110 - 10 = 100
People who did not breakfast and did not feel tired = 30 - 10 = 20
Felt tired Did not feel tired Total
Ate breakfast 10 100 110
Did not eat breakfast 10 20 30
Total 20 130 140
Felt tired Did not feel tired Total
Ate breakfast 10 / 140 100 / 140 110 / 140
Did not eat breakfast 10 / 140 20 / 140 30 / 140
Total 20 / 140 130 / 140 140 / 140
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
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Quotients Great and Small
Diving fractions
Thanks so much please show work!
1. 5/6 ÷ 5/8 or. 5/6 x 8/5=
2. 5/9 ÷ 1/2 or. 5/9 x 2/1 =
3. 9/10 ÷ 3/5 or. 9/10 x 5/3=
Step-by-step explanation:
GOOD RIGHT?
x/a=y/b solve for x please help my homework is due today
h3lp
Which graph is the graph of the function [tex]g(x)=\frac{x^{2}-x }{x^{2} -1}[/tex]
see screenshot for answer choices
Answer:
A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.
Step-by-step explanation:
What would happen to a monthly payment if the interest rate increased?
OA. The payment would go up.
B. The payment would go down.
OC. The payment would remain the same.
OD. None of the above