P and L : 12 and 20 cm
Perimeter : 64 cm
Diagonal = 4√34
Further explanationThe playground is a rectangular shape. There are several properties possessed by rectangular shapes, namely:
• 1. each angle is equal and is a right angle
• 2. the diagonals intersect and divide each other equally
• 3. sides facing the same length
There are two rectangular shapes namely square and rectangle
Square if all sides are the same length
The formula used in rectangular is:
• 1.Area
Rectangle
[tex]\large{\boxed{\bold{Area=w\:\times\:l}}}[/tex]
w = width
l = length
Square
[tex]\large{\boxed{\bold{area=a^2}}}[/tex]
a = length of side
• 2. perimeter
Rectangle
[tex]\large{\boxed{\bold{perimeter=2\times(w+l)}}}[/tex]
w = width
l = length
Square
[tex]\large{\boxed{\bold{perimeter=4\times\:a}}}[/tex]
a = length of side
P+L = 32 cm
Area = 240 cm²
Then
P = 32-L
Area = (32-L) x L
Area =32L-L²
240 = 32L-L²
-L²+32L-240=0
L²-32L+240 = 0
(L-12)(L-20)=0
L = 12 or L = 20
Then =P= 20 or 12
B)Perimeter= 2 x (P +L) = 2 x (12+20) = 64 cm
C) Diagonal
Phytagoras :
[tex]\rm diagonal=\sqrt{20^2+12^2}\\\\diagonal=\sqrt{400+144}\\\\diagonal=\sqrt{544}=4\sqrt{34}[/tex]
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Solve the equation for w
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The system of equations is graphed on the coordinate plane.
y=−x−2
y=3x+2
Enter the coordinates of the solution to the system of equations in the boxes.
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Jorge bought 16 apples for $8.00. Let x represent the number of apples purchased, and let y represent the total cost. Graph the line that represents the proportional relationship.
(it doesn't have a graph because i need to graph it)
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
Jorge bought [tex]16[/tex] apples for [tex]\$8.00[/tex]
This is a direct variation problem
Let
x-----> the number of apples purchased
y-----> the total cost
[tex]y/x=k[/tex]
The value of k is equal to the value of the slope m
Substitute
[tex]8/16=k[/tex]
[tex]k=0.5\frac{\$}{apple} [/tex]
The linear equation is
[tex]y=0.50x[/tex]
using a graphing tool
see the attached figure
The answer in the attached figure
A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent
to which set of numbers does -5.2 belong? F. rational g. integer or H. irrational
your answer is rational because it has a decimal value
An investment is currently worth 1.2×107 dollars . Twenty years ago, the investment was worth 9.6×105 dollars. How many times greater is the value of the investment today than the value of the investment twenty years ago? a. 0.125
b. 12.5
c. 125
d. 12,500
Current worth of the investment = [tex]1.2(10^{7} )[/tex]
Worth of the investment 20 years before = [tex]9.6(10^{5} )[/tex]
To find the number of times greater, we have to divide.
Number of times greater = [tex]\frac{current worth}{worth 20 years before}[/tex]
[tex]=\frac{1.2(10^{7} )}{9.6(10^{5} )}[/tex]
[tex]=\frac{1.2(10^{2} )}{9.6}[/tex]
[tex]=\frac{120}{9.6}[/tex]
= 12.5
Hence, the correct option is (b).
Please help!!! What is 10-2(3-2x=0)
All of the following represent the same expression except _____. -8ab -8(a)(b) 8 - ab -8 · a · b
Simplify. 46√+26√−6√
6√6
5√18
5√6
6√18
Answer:
46√+26√−6√ It Is 5√-6
Answer:
The answer is: [tex]5\sqrt{6}[/tex]
good luck!
Two consecutive whole numbers that 106 square root lies between
The square root of 106 is between 10 and 11. So, the two consecutive whole numbers are 10 and 11.
Explanation:The student is asking about the whole numbers that the square root of 106 lies between. To determine this, we calculate the square roots of numbers near 106. The square root of 100 is 10 and the square root of 121 is 11. Therefore, the square root of 106 lies between 10 and 11. So, the two consecutive whole numbers that the square root of 106 lies between are 10 and 11.
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Look at the picture. Kylie has 832 songs on her portable media player. Lance has 3 times as many songs. how fewer songs can lance add to his player than Kylie can add to hers
A portable media can hold up to 9,000 songs. Therefore:
Kylie can add = 9000 – 832 = 8168
Lance can add = 9000 – 3 * 832 = 6504
So the difference is:
8168 – 6504 = 1664
Therefore lance can add 1664 fewer songs than kylie
What is 0.94 divide by 5?'
what is equal groups division with an unknown multiplier mean?
Equal groups division with an unknown multiplier in mathematics refers to a division problem where you know the total and the number of groups, but not the number of items in each group. You solve it by dividing the total by the number of groups. This concept assists in understanding division and acts as a stepping stone to algebra.
Explanation:In Mathematics, the term 'equal groups division with an unknown multiplier' refers to a division problem where you are given the total and the number of groups, but not the number of items in each group. This is a concept typically introduced in middle school Math.
For example, if you have 24 apples and want to divide them up into 4 equal groups, but you don't know how many apples will be in each group, that's division with an unknown multiplier. The solution would be to divide 24 (the total) by 4 (the number of groups), which gives you 6. So each group has 6 apples.
This concept helps students to better understand division and is often a precursor to learning about algebra, where the unknown multiplier is replaced with a variable.
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Will the standard form of 8.5 × 10–3 be more or less than 1? Explain what effect the negative exponent has.
What is the equation of the graph? y=−43x+3 y=3x+43 y=−3x−43 y=43x+3
The equation of the given graph will be y=-3/2x+3 so none of the options will be correct.
How to plot a graph?
A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
After that, we need to substitute the values of x's and y's into the coordinate geometry.
The point of intersection of the line and x-axis = (2,0)
The point of intersection of the line and y-axis = (0,3)
The slope of the graph or line
Slope = differcne in ys coordinate/difference in xs coordinate
Slope(m) = (3-0)/(0-2) = -3/2
Now equation of a line is given by
y = mx + c
Now keep point (2,0) and slope-3/2
0 = (-3/2)2 + c
c = 3
So, the equation would be
y = (-3/2)x + 3
Hence, The equation of the given graph will be y=-3/2x+3
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The equation of the graph is - y = [tex]\frac{-3}{2} x + 3[/tex]
We have a graph of a equation of a straight line.
We have to find the equation of the straight line.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question -
The slope of line = [tex]\frac{3-0}{0-2}[/tex] = [tex]\frac{-3}{2}[/tex]
c = 3
Substituting the values in the general equation of line, we get -
y = [tex]\frac{-3}{2} x + 3[/tex]
Hence, the equation of the graph is - y = [tex]\frac{-3}{2} x + 3[/tex]
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Solve for x- 3x+ 7=22
a thermometer measures temperature to the nearest 0.5 degrees celsius which measurement shows an appropriate level of precision for the thermometer
The temperature which has best degree of precision would actually be the temperature reading which has similar decimal place with the error. So the best answer would have 1 decimal and from the choices given above, this would be:
16.0°C
Answer:
16.0c
Step-by-step explanation:
A P E X Verified
the sum of two numbers 18 and their difference is 4. what are the two numbers?
The values of a and b in the expression given are 11 and 7 respectively
Let the numbers be : a and b
The sum of the numbers equals 18 :
a + b = 18 - - - (1)The difference of the numbers equal 4 :
a - b = 4 - - - (2)From (1):
a = 18 - b - - - (3)Substitute the value of a in (3) into (2)
18 - b - b = 4
Collect like terms
18 - 2b = 4
-2b = 4 - 18
-2b = - 14
b = 14 / 2
b = 7
From (3)
a = 18 - 7 = 11Therefore, the values of a and b are 11 and 7 respectively
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how do i graph –73x+2
What are the variables in this expression? f+2g+h/4-7.1 f and g only
2 g and h only
3 f, g, and mc014-2.jpg only
4 f, g, and h only
Answer:
4. [tex]f,g\text{ and }h[/tex] only.
Step-by-step explanation:
We have been given an expression [tex]f+2g+\frac{h}{4}-7[/tex]. We are asked to find the variables in the given expression.
We know that variable is a symbol or letter that represents an unknown value in a mathematical expression.
We can see that in our given expression [tex]f,g\text{ and }h[/tex] are unknown, therefore, these are variables for our given expression.
What is the slope of the line on the graph?
Right now Seth's age is 4/5 the age of his brother Eric. Twenty-one years ago, Eric was twice as old as Seth. What are their ages now?
Final answer:
To find Seth and Eric's current ages, we can set up two equations using the given information and solve them simultaneously.
Explanation:
To solve this problem, let's start by assigning variables to the ages of Seth and Eric. Let Seth's age be represented by 'S' and Eric's age be represented by 'E'. We are given that currently Seth's age is 4/5 the age of Eric:
S = (4/5)E
We are also given that twenty-one years ago Eric was twice as old as Seth:
E - 21 = 2(S - 21)
Now we can solve these equations simultaneously to find their current ages. Let's substitute the value of S from the first equation into the second equation:
E - 21 = 2((4/5)E - 21)
Simplifying the equation, we get:
E - 21 = (8/5)E - 42
Moving all the terms with 'E' to one side, we get:
(8/5)E - E = 42 - 21
Simplifying further, we get:
(3/5)E = 21
To solve for E, we can multiply both sides of the equation by 5/3:
E = (5/3) * 21 = 35
Now that we know Eric's age, we can substitute this value back into the first equation to find Seth's age:
S = (4/5) * 35 = 28
Therefore, Eric is currently 35 years old and Seth is currently 28 years old.
Name two integers that have a product between -10 and -15
Which comparison symbol makes each inequality statement true?
Enter <, > , or = to make each statement true.
Enter your answers in the boxes.
−6.809 −6.812
|−6.809| |−6.812|
Answer:
-6.809 > -6.812 and [tex]|-6.809 | < |-6.812 |[/tex]
Step-by-step explanation:
It is clear that 6.809 < 6.812. Hence, -6.812 < -6.809, since the minus sing reverses the order. On the other hand,
[tex]|-6.809 |= 6.809 < 6.812=|-6.812 |[/tex]
Eder needs 6 cookies and 2 brownies for every 4 plates he makes for a bake sale.
How many cookies and brownies would Eder need for 10 plates?
The sales tax rate in jans town is 7.5%. If she Buys 3 lamps for 23.59 each and a sofa for 769.99 how much sales tax does she owe
Can someone plz help.
Use the modle to find 2x137
There are 6 gallons of distilled water in the science supplies. If 10 students each use an equal amount of distilled water and there is 1 gal left in the supplies, how much will each student get?
By decreasing each dimension by 2 units, the area of the rectangle decreased from 24 square feet to 6 square feet. Find the percent increase
The percent increase after decreasing the dimensions of a rectangle is 66.67%
The question asks for the percent increase in area when the dimensions of a rectangle are decreased, which necessitates understanding of area calculations and percentages. Initially, the rectangle had an area of 24 square feet, which reduced to 6 square feet upon decreasing each dimension by 2 units.
To find the percent increase, one should first understand that a decrease in area actually implies a percent decrease, rather than an increase.
Find the area of the original rectangle: 4 units x 6 units = 24 square feet
Find the area of the new rectangle: (4 - 2) units x (6 - 2) units = 8 square feet
Calculate the percent increase: ((24 - 8) / 24) x 100% = 66.67%