The length of the rectangle is 12 meters and its width is 4 meters.
A rectangle is a four sided figure, whose opposite sides are equal and the angle formed by any two adjacent sides is 90 degrees.
Here, we are given that the perimeter of the rectangle is 32 meters.
Let the length of the rectangle be L and breadth or width be B
We known that perimeter of a rectangle = 2(L + B)
Now, it is given that the length is 4 m more than two times the width
⇒ L = 4 + 2B
Thus, the area of the perimeter will be-
Perimeter = 2(4 + 2B + B)
⇒ 32 = 2(4 + 2B + B)
32/2 = 4 + 2B + B
16 = 4 + 3B
16 - 4 = 3B
12 = 3B
or 3B = 12
B = 12/3
B = 4
Thus, the width of the rectangle is 4 meters.
Therefore, L = 4 + 2(4)
L = 4 + 8
L = 12
Thus, the length of the rectangle is 12 meters.
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this week Jada bought a 3 1/2 pound of cat food. her cat eats 5/8 of a pound each day. show your work and remember to include units. check your work with multiplication
Answer:
5 days.
Step-by-step explanation:
The food will last her 5 days.
[tex]3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1-\frac{5}{8}[/tex][tex]=\frac{3}{8}[/tex]
If an individual makes $4,000 in salary per month and has a side job making $20 per hour for 10 hours a week for 4 weeks in a
month, and they receive $1,000 per month in rent from a roommate, what is their gross income?
O $4,000
O $4,800
O $5,800
O Cannot be determined, because taxes and deductions are not provided
The gross income will be $5,800.
It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.
We have to calculate the gross income.
What do you mean by gross income ?
Gross income refers to the total income of a person or business from all resources.
As per the question ;
Per month salary = $4000
Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.
i.e.,
= 20 × 10 × 4
= $800 for 4 week
and
the rent they receive = $1000
So ;
The gross income will be ;
= 4000 + 800 + 1000
= $5,800
Thus , the gross income will be $5,800.
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A number, x, rounded to 1 decimal place is 12.3
Write down the error interval for x.
The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place
In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.
From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :
=> x ≥ 12.25 and x < 12.35
So, the x lies between 12.25 and 12.35 which defines the error of interval for x.
Hence, the error of interval for x will be [12.25, 12.35)
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for each table, find the constant of proportionality. use decimal notation if neccescry
Step-by-step explanation:
the constant k of proportionality is defined by
y = kx
or in our case
b = ka
so, let's see
14 = k×2
k = 14/2 = 7
this also works for the other data pairs :
7×5 = 35
7×9 = 63
7 × 1/3 = 7/3
perfect.
so, the constant of proportionality is 7.
The diameter, D, of a sphere is 9.4 m. Calculate the sphere's volume, V.
Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
V = m^3
Answer: v=M^3
Step-by-step explanation:
What are the solutions to the inequality (x-3)(x+5) ≤0?
O {x| 3≤x≤5}
O {xl-5≤x≤-3}
O x1-5≤x≤ 3}
O {xl-3≤x≤5}
Answer: -5<=x≤3 ==> 3rd option
Step-by-step explanation:
(x-3)(x+5)≤0
x-3>=0 and x+5≤0
x>=3 and x≤-5 ==> Not possible since a number subtracted by 3 can't be greater than the same number added by 5.
x-3≤0 and x+5>=0
x≤3 and x>=-5 ==> -5<=x≤3 ==> 3rd option
The solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is (x-3)(x+5) ≤0
To solve this inequality, we first find the critical points by setting the expression inside the inequality to zero:
(x-3)(x+5) = 0
This gives us two critical points: x=3 and x=-5.
We want to find where the expression is less than or equal to zero, so we include the endpoints of the intervals where the expression is zero or negative.
Hence, the solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.
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A surveyor is estimating the distance across a river. The actual distance is 279.8 m. The surveyor's estimate is 300 m.
Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.
Absolute Error = ___ m
Percent Error = ___%
Answer:
Absolute error = 20.2m
% error = 6.73%
Step-by-step explanation:
Absolute error = 300-279.8= 20.2m
% error = 20.2 ÷ 300 = 6.73%
I need help on question 82 a,b,c,d,e
Answer:642
Step-by-step explanation:
Look at the book and solve it
At what coordinate would you place point e so that is partitions df in a ratio of 5:3
PLEASE HELP I DONT UNDERSTAND
According to the image, the figure moved four times to return to its initial position.
What is the initial position of the figure?The starting position of the figure is in the lower left corner of the frame.
How does it move from position 1 to position 2?The movement made by the figure from position 1 to position 2 is that it moves from the lower left corner to the lower right corner.
How do you move from position 2 to position 3?The movement made by the figure from position 2 to position 3 is that it moves from the lower right corner to the upper right corner. Additionally, the figure rotates to the left 180°.
How does it move from position 3 to position 4?The movement that the figure performs from position 3 to position 4 is that it moves from the upper right corner to the upper left corner.
How does it move from position 4 to position 5?The movement made by the figure from position 4 to position 5 is that it moves from the upper left corner to the lower left corner. Additionally, the figure is rotated 180° to the left again.
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pedro wants to make 3 1/2 batches of granola bars. His dad tells him that he needs 5 1/4 cup of oatmeal. How much oatmeal does pedro need for a single batch
Pedro requires [tex]1\frac{1}{2}[/tex] cups oatmeal for a single batch of granola bars as calculated by division of fractions.
A fraction is a piece of a whole or, to put it more broadly, any number of equal portions.
The Latin word fractus, which means "broken," is where the word fraction originates.A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of components of a particular size as it is represented in common English. There is a non-zero denominator and a common, or simple fraction below (or after) that line.Compound fractions, mixed numeral fractions, and difficult fractions are examples of uncommon fractions that use numerators and denominators.Total batches required [tex]= 3 \frac{1}{2} = \frac{7}{2} = \frac{14}{4}[/tex] cups
Total oatmeal required [tex]= 5 \frac{1}{4} =\frac{21}{4}[/tex] cups
Therefore now to calculate the amount of oatmeal needed for single
batch we divide the fraction [tex]\frac{21}{4}[/tex] by [tex]\frac{14}{4}[/tex] cups
1 batch requires = [tex]=\frac{21}{4}\div\frac{14}{4}=\frac{3}{2} = 1\frac{1}{2}[/tex] cups.
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Which expression is equivalent to (a2/3 1/31/22
OA 7/665/6
OB. 44/32/3
Oca1/261/2
C.
OD. a4/361/6
OE.al/361/6
Answer:
E. a^(1/3)b^(1/6)
Step-by-step explanation:
You want an expression equivalent to (a^(2/3)b^(1/3))^(1/2).
Rules of exponentsThe applicable rules of exponents are ...
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
ApplicationThe given expression simplifies to ...
[tex](a^{2/3}b^{1/3})^{1/2}=a^{(2/3)(1/2)}b^{(1/3)(1/2)}=\boxed{a^{1/3}b^{1/6}}[/tex]
A baby American bison weighs 20kg. A baby blue whale weighs 100 times as great as a baby American bison. how much does a baby blue whale weigh
a baby blue whale weigh= 2000 kg
Simple equation :
A linear equation that involves only one variable is known as a simple equation or a linear equation in one variable. For example, \(3x + 2 = 23,x = 7,2x + 6 = 3x – 4,\)etc., are simple equations.Let us assume a situation, in which you go to the market to buy mangoes in a supermarket. Your mother gave you Rs.100 and said that you can keep Rs.40 for buying chocolates and for the remaining amount, you need to buy mangoes. When you went to the market, you found out that the price of one kg of mangoes was Rs.12. So, the final question is how many mangoes you should buy, so that everyone is satisfied. Recall the concept of simple equations from previous classes and proceed. Let us assume that you have to purchase kg of mangoes, so the total amount of money that you will be spent on buying mangoes will be Rs.12x. Now, you have Rs.40 for yourself, so you have an equation:
12 x + 40 = 100
12x = 100 – 40
12x = 60
x = 60/12 = 5, This is the same equation as above. Now when you will solve this, you will get to know the value of 5kg of mangoes. It means that you can buy 5 kg mangoes and spend Rs.40 on buying chocolates
weigh: to measure how heavy something is, especially by using a machine (scales)
given :
A baby American bison weighs=20kg
The solution according to Question =
Let the weight of baby blue whale = b
the baby blue whale weighs =100(a baby American bison)
b=100(20)
b=2000 weigh
a baby blue whale weigh= 2000 kg
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If 3 times a number is decreased by 2 the principal square root of this difference is 4 less than the number. Find the number(s).
The numbers are -3 and 6
How to determine the numberFrom the information given, let the number be x;
the expression is given as;
(√3x + 2) = x - 4
To determine the number, find the square of both sides, we have;
(√3x + 2) ^2 = (x - 4)^2
Find the square of both sides
3x + 2 = ( x - 4)(x + 4); difference of two squares
expand the bracket
3x + 2 = x^2 + 4x - 4x - 16
collect like terms
x^2 - 3x - 16 - 2
x^2 - 3x - 18
x^2 - 6x + 3x - 18
Factorize the expression
x( x - 6) + 3( x - 6)
(x + 3) or (x - 6)
x = -3 or x = 6
Thus, the numbers are -3 and 6
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PLEASE HELP ASAP 100POINTS AND BRAINLIEST
Identify two segments that are marked congruent to each other on the diagram
below. (Diagram is not to scale.)
R
is congruent to
Answer:
I believe R is congruent to U
Step-by-step explanation:
I don't exactly remember much about these types of problems but I hope it helps! =D
Answer:
∠VS is congruent to ∠UR
Step-by-step explanation:
congruent means same size or shape and the markings are the little lines
the little curves over the angles are congruent as well
Points A and B are plotted on a number line at -4 and 3. respectively. Find the coordinate of the point that represents the weighted averag
of A and B if point A has a weight of 2 and point B has a weight of 5.
The coordinate of the pointed that represented the weighted average of A and B is: 1
What is the explanation for the above?Note that X = [x1w1 + x2w2 +.......xnwn]/w1+w2 +....wn
Where x is the numbers and w is the weight.
Given,
A = - 4 : Weight = 2
B= 3 : Weight = 5
Hence, average is given as;
([-4 x 2] + [3 x 5])/2+5
= (-8 + 15)/7
= 7/7
= 1
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Find a + b, 9a + 3b, |a|, and |a − b|. a = 9i − 4j + 3k, b = 6i − 9k
1) a + b = ?
→ (9i − 4j + 3k) + (6i − 9k)
→ 15i - 4j - 6k
2) 9a + 3b = ?
→ 9(9i − 4j + 3k) + 3(6i − 9k)
→ (81i - 36j + 27k) + (18i - 27k)
→ 99i - 36j
3) |a| = ?
→ |9i − 4j + 3k|
→ 9i + 4j + 3k
4) |a − b| = ?
→ |(9i − 4j + 3k) - (6i − 9k)|
→ |3i - 4j + 12k|
→ 3i + 4j + 12k
Answer:
[tex]a+b=15i-4j-6k[/tex]
[tex]9a+3b=99i-36j[/tex]
[tex]|a| = 9i+4j+3k[/tex]
[tex]|a-b| = 3i+4j+12k[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]
[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]
[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]
[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]
[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]
A car company uses the table below to show customers the approximate amount of gas used when a car has been driven a certain number of miles.
Gas Use
Miles driven
Gallons of gasoline used
120
6
300
15
360
18
480
?
If the car always uses the same amount of gasoline each mile, how many gallons of gasoline would be needed to travel 480 miles?
A.20
B.24
C.33
D.39
Use the formula S=n(n+1)/2 to find the sum of 1+2+3+...+600
1+2+3+...600=
Answer:
eueueue
Step-by-step explanation:
Manu makes some money on the side by producing and selling customized drink glasses for family reunions. To make the glasses, it costs him a flat fee of $10 per order, plus $8 per glass. He sells the glasses for $13 per glass. How big must the order be in order to earn a profit of $100? Let x = the number of glasses and y = profit from selling x glasses. Set up the equation for this situation and solve it. You must show all calculation in order to earn any credit.
To earn $100 profit Manu should get the order of 22 glasses.
Given that, the cost price of a drinking glass=$8 and the selling price = $13.
What is profit?When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. The basic formula used for calculating the profit is Profit = Selling Price - Cost Price.
Let x = the number of glasses and y = profit from selling x glasses.
Now, y=(13-8)x-10
Assumed that the order is x glasses to earn a profit of $100.
(13-8)x-10=100
⇒5x-10=100
⇒5x=110
⇒x=22
Therefore, to earn $100 profit Manu should get the order of 22 glasses.
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11. STEM Connection The world's biggest submarine
can sail at a speed of about 25.5 miles per hour on
the surface. How can you describe the relationship
between 5 and 0.5?
5 is at the one-place value, and 0.5 is at the tenth-place value. 5 is ten times the value of 0.5.
What is described as the once and tenth place?There are one or more digit numbers in a number. 43 has the digits 4 and 3. The value of a numeral is determined by its position in the number.The number one in the number twelve is located in the tens place. The 2 in 12 is now in the one position. 95 has a 9 with in tens position and a 5 with in ones position.The number 0 is significant. The zero in twenty indicates there are no ones. That tells us that the 2 in 20 are in the tens. 20 is made up of two tens and zero ones.For the given question;
The speed of the world's biggest submarine is 25.5 miles per hour on the surface.
Thus, in the value of 25.5, the digit 5 lies on the once place.
The value 0.5 lies on the tenth place.
Now, it is clear that the 5 is the 10 times the value of 0.5, which is the required relation.
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A square that is 7 yd on a side is placed inside a rectangle that has a width of 9 yd and a length of 14 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 77 yd^2
Step-by-step explanation:
S=Area of Square. s=side length of square. w=width of rectangle
l=length of rectangle. R=Area of Rectangle
S=s^2
S=7^2
S=49 yd^2
R=l*w
R=9*14
R=126 yd^2
R-S=
126-49=77 yd^2
WILL GIVE BRAINLIEST!!!
I have 200 hours to make as much Lemonade as possible, and I can make 1 pitcher every 10 minutes.
Write an inequality to represent my time constraint.
Answer:
33.33
Step-by-step explanation:
Well, we already know the amount of time it takes to make the lemonade, and we know the rate as well.
We need to find out how many pitchers you can make in an hour. If you can make one pitcher in 10 minutes, then you can make 6 pitchers in 60 minutes, AKA an hour.
So we make 6 pitchers per hour.
If we make 6 an hour, then we multiply 6 by 200 to get the number of pitchers we can make in 200 hours.
We can make 33.33 pitchers in 200 hours
Let U= {x | x is a whole number and 0 ≤ x ≤ 19) and C= {15, 16, 17, 18, 19). Write U U C using the listing method.
UUC=
set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.
Let C=15, 16, 17, 18, and 19) and U=x | x is a full number and 0 x 19). Use the listing technique to write U U C.
UUC=
D U E = { 16, 18, 19, 20, 21 }
U stands for the union of sets.
We combine all of the components from the two groups.
16, 19, 21, and 16, 18, 19, 20 are the elements in sets D and E, respectively.
Therefore, we combine all of their components. The shared components of both sets are written just once.
As a result, there are 16, 18, 19, 20, and 21 elements in the set D U E.
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Tim always eats strawberries in multiples of three. Todd eats them in multiples of four and Rick in multiples of six. Gavin is not fussy
about it but likes cream to go with them. Uncle Sam wants each of the four kids to eat the same number of strawberries. What is the
minimum number of strawberries that he has to give to each kid?
Answer:
12
Step-by-step explanation:
3*4 = 12
12/6 = whole number
6/4 is not a whole number
12 is the lowest it could be.
Also those kids have issues.
i need help with this assignment can anyone help
Answer: 18.25
Step-by-step explanation:
5.5*4=22
401.5/22=18.25
Answer:
$18.25
Step-by-step explanation:
Since area is given as A=LW, and we are given the values of the dimensions of the floor, we get:
5.5×4=22
So, the area is 22 yards, and it costs $401.5 to carpet it. Now, We simply need to divide the cost by the area to get the "cost per-square yard" as needed in the question. We get:
401÷22=18.25
So, the cost of the carpet per square yard is $18.25
If z/4+3=-2 what is the value of z/4+7?
Put your answer in the form of [x]
Answer: x=2
Step-by-step explanation:
x=z/4+7
x=z/4+3+4
x=(z/4+3)+4
x=-2+4
x=2
Write the linear function y that has the given function values.
f(−6) = −7, f(1) = 2
The equation of this linear equation is f(x) = 9/7(x - 1) + 2
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The given parameters are
f(−6) = −7, f(1) = 2
Start by calculating the slope (m) using
m = [f(-6) -f(1)]/[-6 - 1]
This gives
m = [-7 - 2]/[-6 - 1]
Evaluate
m = 9/7
The linear equation is then calculated as
f(x) = m(x - x1) + f(1)
So, we have
f(x) = 9/7(x - 1) + 2
Hence, the equation of this linear equation is f(x) = 9/7(x - 1) + 2
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What numbers are a distance of 34 unit from 18 on a number line?
Select the locations on the number line to plot the points.
Answer:
[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]
Step-by-step explanation:
To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]
One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away
Compute [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4} :[/tex]Please refer to the picture, thank you!!!
An equation that relates T to N can be written as T = 750 + 630N.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).
How to write an equation relating T to N.Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:
T = A + B
Substituting the given parameters into the formula, we have;
T = (750 + 135N) + 495N
T = 750 + 135N + 495N
T = 750 + 630N.
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Complete Question:
Raina and her husband are each starting a saving plan. Deshaun will initially set aside $750 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+135N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=495N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.
Simplify your answer as much as possible.
