among all rectangles that have a perimeter of 48 Then the dimensions of the one whose area is largest is 12 by 12
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 48
2L + 2W = 48
L + W = 24
W = 24 - L
The area of the rectangle is expressed as:
A = LW
A = L(24-L)
A = 24L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 24 - 2L
0 = 24 - 2L
2L = 24
L = 24/2
L = 12
Recall that 2(L+W) = 48
2(12 + W) = 48
12 + W = 24
W = 24 - 12
W = 12
Hence the dimensions of the one whose area is largest is 12 by 12
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The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
The length of the rectangle is 10, the width is 2.5 and the perimeter is 25
Let the width of the rectangle be x
The length of rectangle = 2x + 5
The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.
Perimeter = 10 times of width
= 10*x
= 10x
The formula for the perimeter of a rectangle is given:
Perimeter = 2(Length+Breadth)
10x = 2(x + 2x+5)
10x = 2(3x+5)
10x = 6x + 10
4x = 10
x=2.5
Length = 10
Width = 2.5
Perimeter = 25
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3 x blank x blank x blank = 36
Answer:
3x2x2x3
Step-by-step explanation:
3x2x2x3= 36
I hope that was helpful!
My pleasure to help!!
What is 39,400,000 in scientific notation?
Answer:
3.94*10^7
Step-by-step explanation:
Answer:
3.94 * 10^7
Step-by-step explanation:
:]
Which of the following is a balanced equation?
KCIO(3)-->KCI + O(2)
KCIO(3)-->3 KCI + O(2)
2KCIO(3)-->KCI + 3 O(2)
2KCIO(3)-->2 KCI + 3 O(2)
Select one:
a. A
b. B
c. C
d. D
Based on the chemical equations given, the balanced equation would be d. D.
How to find a balanced equation?In Chemistry, a balanced equation is one that has the same number of atoms on the left side of the equation, as on the right side of the equation.
The balanced equation is therefore:
2KCIO₃ -->2 KCI + 3 O₂
This is because there are 2 KCI atoms and 6 Oxygen atoms on the left side, and there are also 2 KCI atoms and 6 Oxygen atoms on the right side.
In conclusion, option D is correct.
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arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. to be happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden be?
The dimension of the flower garden, which located in the middle of the backyard surrounded by a strip of grass, is 26 m length and 16 m width.
The situation can be depicted on the attached picture.
We need to translate the word problem into algebraic expressions.
Let x be the width of the grass strip.
Let A be the area of the grass strip.
Then,
A = 2 . 22x + 2 . (32 - 2x)x
288 = 2 . 22x + 2 . (32 - 2x)x (divide by 2)
144 = 22x + x(32 - 2x) (divide by 2)
72 = 11x + x(16 - x)
72 = 27x - x²
x² - 27x + 72 = 0
This is a quadratic equation. One of the methods to solve a quadratic equation is by factorization.
Factorize the left side:
(x - 3) (x - 24) = 0
x = 3 or x = 24
The length of the flower garden = 32 - 2x
The width of the flower garden = 22 - 2x
Substitute x = 3:
The length of the flower garden = 32 - 2 . 3 = 32 - 6 = 26 m
The width of the flower garden = 22 - 2 . 3 = 16 m
Note that if we substitute x = 24, it will results in negative values while the dimension is always positive.
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5(1-1)+10=
5(2-1)+10=
5 (3-1) +10=
5(4-1)+10=
Step-by-step explanation:
First is
5(1-1)+10= 5×0+10= 0+10 = 10
2nd is
5(2-1)+10=5× 1+10= 5+10=15
3rd= 5(3-1)+10= 5×2+10=10+10=20
4th=5(4-1)+10=5×3+10=15+10=25
I hope it will be helpful for you.
Nitin and Sharat were going to Delhi by different trains.
Their trains were scheduled to reach at 10:30 am and 11:15am respectively.
Nitin’s train reached late but Sharat’s train reached on time.
Nitin’s train reached 10 minutes AFTER Sharat’s train.
By how many minutes was Nitin’s train late?
Answer:
55 minutes
Step-by-step explanation:
sharat's train arrived on time (11.15) but Nitin's was after and 10 mins later it'd be 11.25
a certain bacteria doubles every 2 seconds. Starting from a single bacterium, how many bacteria will be there after 20 seconds?
The answer will de 10 bacterias
Answer: 1024
Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.
Find the area of the figure below, formed from a triangle and a parallelogram. A figure is formed from a triangle and a parallelogram. The base of the triangle is 8 millimeters and the height is 2 millimeters. The bottom and top of the parallelogram are 6 millimeters and the height is 4 millimeters.
The total area of the figure is; 32 millimeters sq.
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
We have been given that a parallelogram has a base is 6 millimeters and a height is 4 millimeters
The area of a parallelogram = Base x Height
= 6 x 4
Area = 24 millimeters sq.
Similarly, The area of the triangle = 1/2 x b x h
= 1/2 x 8 x 2
= 8 millimeters sq.
The total area of the figure is;
Total = area of the triangle + area of a parallelogram
Total = 24 + 8 = 32
Hence, the total area of the figure is; 32 millimeters sq.
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What is y=1x+0 in standard form?
Answer:
0
Step-by-step explanation:
Where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 Therefore, the standard form for y = 0 is: 0x + 1y = 0
what is x=.30(729). explain
Answer:
x = 218.7
Step-by-step explanation:
To solve for x, we multiply .30 by 729. Once multiplied, we get the answer 218.7. Therefore, x = .30(729) is the same as x = 218.7.
The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election. What percentage of the members voted?
The percentage of members that voted is 70%.
How to find the percentage of members that voted?The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.
Therefore, the percentage of the members that voted can be calculated as follows;
percentage that voted = number of people that voted / total number members × 100
Therefore,
number of people that voted = 42
total number members = 60
Hence,
percentage that voted = 42 / 60 ×100
percentage that voted = 4200 / 60
Therefore,
percentage that voted = 70%
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What is the
Domain??
Someone pls help me outtt
Answer:
:]
Step-by-step explanation:
[tex]-2\leq x\leq 2[/tex]
Answer:
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the function
13 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answer:
1/9
Step-by-step explanation:
There is 1/3 gallon of water in a 3 gallon container. The fraction of the container that is filled is 1/9
(1/3 of a gallon divided by 3 gallons equals 1/9)
Brown bears attempt to catch salmon. during the day, 20% of the attempts are successful. during the night, 36% of attempts are successful. a bear tries to catch 40 fish during the day and makes 50 attempts at night. use probability to estimate the number of fish the bear caught.
The probability for the number of fish the bear caught is 0.289
Given,
Number of fish the bear tries to catch during day = 40
Number of attempts made by the bear at night = 50
Percentage of successful attempts during day = 20%
Percentage of successful attempts at night = 36%
Number of fish the bear caught during day = 40 × (20/100) = 4 × 2 = 8 fish
Number of fish the bear caught at night = 50 × (36/100) = 36/2 = 18 fish
Total number of fish the bear caught = 8 + 18 = 26 fish
Now,
Probability for the number of fish the bear caught:
Probability = Number of fish caught / Total attempts
Probability = 26 / (40 + 50)
Probability = 26 / 90
Probability = 0.289
Therefore,
The probability for the number of fish the bear caught is 0.289
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What are the coordinates of the point on the directed line segment from (3,−3) to (7,5) that partitions the segment into a ratio of 5 to 3
The coordinates along the directed line segment is (37/7, 11/7)
How to find the coordinates of the point?The points are given as:
A = (3, -3)
B = (7, 5)
The ratio on the segment can be represented as;
m : n = 4 : 3
So, we have the coordinates of the point that lies along the directed line segment to be
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have:
Point = 1/(4 + 3) * (4 * 7 + 3 * 3, 4 * 5 + 3 * -3)
Evaluate
Point = 1/7 * (37, 11)
Evaluate the products
Point = (37/7, 11/7)
Hence, the coordinates of the point is (37/7, 11/7)
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how long would it take to drive 1km at a speed of 1.71km/h (with working)
It would take 35 minutes to drive 1 km at a speed of 1.71 km/h.
How do distance and speed compare?Speed is the ratio of distance traveled in a given time. Speed is given by distance/time.
The time can be computed by dividing distance by speed.
This implies that time is the quotient of distance and speed.
The total distance drove = 1 km
The driving speed = 1.71 km/h
Time = Distance/Speed
= 1/1.71
= 0.58 hours
= 0.58 x 60 seconds
= 35 minutes 5 seconds
Thus, to travel 1 kilometer at the speed of 1/71 kilometers per hour would take 35 minutes.
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13 What value of x makes the equation modeled below true? PHONE 1 1 1 A x = 1 B x = -1 C x = 7 D x = -5 I
SOLUTION
Step 1 : We need to recognize the value of x in 5 places means 5 x
and the value of 1 in 6 times means 6,
so we have that: 5 x + 6 = 1 .
Step 2 : We need the linear equation: 5 x + 6 = 1
collecting like terms, we have that:
5 x = 1 - 6
5 x = - 5
Divide both sides by 5 , we have that:
x = - 1
CONCLUSION : The value of x = -1 ( OPTION B )
The finish line is 253 m away. You begin to run from rest. You must reach a velocity of 53.2 m/s or you will explode. What must your acceleration be?
The acceleration require for the body to not explode will be 0.2941[tex] m/s^2 [/tex]
The finish line as given is 253m away so that distance to be covered will be 253m.
Also we had started to run from rest so that initial velocity will be 0m/s.
We should take care that we could not explode and this is possible only if we reach to the velocity of 53.2m/s. So our final velocity will be 53.2m/s.
Now average velocity will be the sum of initial velocity and final velocity divided by 2.
∴ Average velocity = (initial velocity + final velocity) / 2.
∴ Average velocity = (0 + 53.2) / 2 = 53.2 / 2 = 26.6m/s
As we know that average velocity will give us an average time of the run by formula average speed = distance / average time.
∴ Average time = distance / average speed
∴ Average time = 253 / 26.6 = 9.51s.
Now as we know by the formula to calculate acceleration we need the average velocity, average time and we have both of them.
∴ Acceleration = [tex] \frac{average\ velocity}{(average\ time)^2}[/tex]
∴ Acceleration = [tex] \frac{26.6}{(9.51)^2}[/tex]
∴ Acceleration = [tex] \frac{26.6}{90.44}[/tex]
∴ Acceleration = 0.2941[tex] m/s^2 [/tex]
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32 is 80% of what number?
Answer:
40
Step-by-step explanation:
Given :
32=0.8x
( x is unknown number )
x=32/.8
x=40
Your test in math class has problems worth 2 points and problems worth 4 points. Altogether the test has 100 points. Write an equation that represents the total points on the test formed by the number of 2-point problems and the number of 4-point problems. Let x represent the number of 2-point problems. Let y represent the number of 4-point problems. Total amount of points = point worth  x + point worth  \
The equation that represents the total points on the test formed by the number of 2-point problems and the number of 4-point problems will be 2x + 4y = 100.
What is an equation?An equation is used to show the relationship between the variables that are given.
In this case, the test in math class has problems worth 2 points and problems worth 4 points and altogether the test has 100 points.
Let x represent the number of 2-point problems. Let y represent the number of 4-point problems.
The appropriate equation will be:
2x + 4y = 100
This illustrates the equation
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Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible.
(2,-6); y = 2/3x-4
Answer:
Step-by-step explanation:
2
Combine multiplied terms into a single fraction
3
Find common denominator
4
Combine fractions with common denominator
5
Multiply the numbers
the larger number is 18 more than twice the smaller. If the sum of the two numbers is 93, find
oth numbers.
Answer:
The larger number is 68 and the small number is 25
Step-by-step explanation:
Large number y
small number is x
y=2x+18
x+y=93
22. A student recorded her scores on weekly math quizzes that were marked out of a
possible 10 points. Her scores were as follows:
8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7
What is the mode of her scores on the weekly math quizzes?
Answer:
6 since it occurs the most times
Larry plants to invest 275,000 for 30 years at an anticipated rate of 6% per annum compounded yearly what is the approximate difference in his ending balance of the actual rate is 5% instead of six
Answer:
$390,000
Explanation
To do this, we will use the compound interest formula;
A = P(1+r)^t
P = 275000
rate r = 6%
Time t = 30years
Substitute
A = 275000(1+0.06)^30
A = 275000(1.06)^30
A = 275000(5.7435)
A = 1,579,460.07
For the rate of 5%
A = 275000(1+0.05)^30
A = 275000(1.05)^30
A = 275000(4.3219)
A = 1,188,534.15
Takeing their difference;
Difference = 1,579,460.07-1,188,534.15
Difference =390,925.92
Hence the approximate difference in his ending balance of the actual rate is 5% instead of six is about $390,000
-53 = 8y + 4y - 17 solve for y and simplify as much as possible
Answer:
y = -3
Step-by-step explanation:
-53 = 8y + 4y - 17
combine y terms on right side:
-53 = 12y - 17
add 17 to both sides:
-53 + 17 = 12y - 17 + 17
-36 = 12y
divide both sides by 12:
-36/12 = 12y/12
y = -3
What is the slope of this image?? I NEED HELP
Answer:
Positive, so the answer would be y=4/2 or 2. y=2x-4
Step-by-step explanation:
Slope formula y=mx+b
The mx is the rise/ over run
The b is the y-intercept
You can check in the end by checking so to see if the rise over the run is correct
Also, you can check the b by looking at the y-intercept, which is -4
Hope this helps!
plsssss helpp me out asap
Answer: [tex]m = 7.3\pi[/tex]
I multiplied both sides by pi to isolate m.
Eden is creating a presentation about bee hummingbirds in PowerPoint Online, She would like to add an image to her side about how they collect nectar. What is the most relevant image she should add to her slide?
From following steps, she can add relevant pictures to her slide.
What is PowerPoint?It is a presentation-based program that employs graphics, movies, etc. to enhance the interactivity and appeal of a presentation. A saved PowerPoint presentation has the ".ppt" file extension. PPT is another name for a PowerPoint presentation that includes slides and other elements. Create presentations from scratch or using a template with PowerPoint on your PC, Mac, or mobile device. Include text, pictures, artwork, and videos. Using PowerPoint Designer, pick a polished layout. Cinematic motion, transitions, and animation should be added.
Given Data
Eden is creating a presentation about bee hummingbirds in PowerPoint Online, She would like to add an image to her side about how they collect nectar.
From following steps, she can add relevant pictures to her slide.
Open the slide to which you wish to add a photograph.
Point to Picture in the Insert menu, and then click Photo Browser.
Navigate to the image you want to insert in the dialogue box that appears, click it to pick it.
Then drag it to the slide.
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Vinny is serving punch to guests at a party. He has $\frac{3}{4}$ of a gallon of punch, and he pours $\frac{5}{64}$ of a gallon into each guest's cup, filling each to the top. At the most, how many guests' cups can he fill to the top?
In serving punch to guests at the party, Vinny can fill 9 guests' cups to the top based on this unit rate.
What is a unit rate?The unit rate is the ratio of a variable to another.
The whole number here is the total gallons of punch available to serve the guests.
The unit rate is the volume that each guest's cup can hold or contain.
This implies that the ratio is 5/64: 3/4
The total number of gallons of punch = 3/4 or 0.75 gallons.
The volume or capacity of each guest's cup = 5/64 gallons or 0.078125.
The number of guests' cups to fill to the brim = 9.6 cups (0.75/0.078125)
= 9 guests' cups.
Thus, Vinny can fill 9 guests' cups to the brim, using the given ratio or unit rate.
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