The length of a rectangle is 3 meters longer than its width. If
the area of the rectangle is 40 square meters, what are the
dimensions?
Answer:
Length=8 Width=5
Step-by-step explanation:
Set this up as a system of equations with l standing for length and w standing for width.
w+3=l
l×w=40
Substitute rhe first equation into the 2nd one.
w(w+3)=40 --------> w^2+3w=40
Move all the terms to the left side
w^2+3w-40=0
Factor
(w+8) (w-5)
Set both factors equal to 0.
w+8=0 -----> w=-8
w-5=0 ------> w=5
Since distance cannot be negative we can eliminate -8. So w=5
Plug it back into any one of the equations and solve for l.
5+3=l -----> 8=l
So the answer is the length is 8 and the width is 5.
The dimensions of the rectangle are:
Length = 8 meters.
width = 5meters.
We are given that the length of a rectangle is 3 meters longer than its width and the area of a rectangle is 40 square meters.
We need to find the length and width of the rectangle.
What is a rectangle?A rectangle is a closed 2-dimensional shape that has two dimensions, the length, and the width. Length is the longer side and width is the shorter side of the rectangle.
The area of a rectangle is given by :
A = Length x Width.
Let the area, length, and width of the rectangle be A, L, and W.
The length of a rectangle is 3 meters longer than its width.
We can write it as,
L = 3 + W
The area of a rectangle is 40 square meters.
We can write it as,
A = 40 square meters
We can write it as,
L x W = 40
Substituting L = 3 + W.
(3 + W) W = 40
[tex]3W + W^2 = 40\\W^2 + 3W = 40 \\W^2 + 3W - 40 = 0[/tex]
This is a quadratic equation and we will apply middle-term factorization.
[tex]W^2 + 3W - 40=0\\W^2 + (8-5)W - 40=0\\W^2 + 8W - 5W - 40=0\\W(W + 8) - 5 ( W + 8)=0\\(W+8)(W - 5)=0\\W+8 = 0~~and~~W-5=0\\W = -8~~and~~W=5[/tex]
The distance can not be negative so W = -8 is eliminated.
We have, W = 5
Substituting W = 5 in L = 3 + W.
We get,
L = 3 + 5 = 8
L = 8.
The dimensions of the given rectangle are:
Length = L = 8 meters.
Width = W = 5 meters.
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what is the square root of 674 in simplest radical form
Answer: Here we answer "What is the square root of 674 (√674) in simplest radical form?"
The square root of 674 in its simplest form means to get the number 674 inside the radical √ as low as possible.
The square root of 674 is already in the simplest radical form. Therefore, the answer is:
√674
hope this helps.. Stay safe and have a great day/night!!! :D
The square root of 674 is expressed as √674 in the radical form.
What is square root?A square root of a number is a value that, when multiplied by itself, gives the number.
Given that, what is the square root of 674 in the simplest radical form,
The square root of 674 is expressed as √674 in the radical form,
The square root of 674 rounded up to 7 decimal places is 25.9615100. It is the positive solution of the equation x² = 674.
Hence, the square root of 674 is expressed as √674 in the radical form.
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I NEED HELP ASAP DUE IN 3 MINUTES WHOEVER ANSWERS IT RIGHT GETS BRIANIST
Answer:
It is D.
Step-by-step explanation:
What’s the answer plzzz hurry
Answer:
dude i can't even see that sorry
Step-by-step explanation:
I like your cut G
Hi please help :D it says 'toO sHorT' so just ignore this next part jhdvwbfyugbwcqiugbn
472 students are going on a field trip. 120 students will be returning home and the rest will be spending the night in cabins. If 8 people can sleep in one cabin, how many cabins need to be rented for the students?
470 kids went on the trip, and 120 students returned home, the total of kids staying is 350.
One cabin= 8 students
The equation i came up with is 350/8 = 43.75
They need 44 cabins to fit all the kids
write 3.9 x 10 exponent -4 in standard form
Answer:
0.00039
Step-by-step explanation:
jerry started doing sit ups everyday. the first day he did 19 sit-ups. everyday after he did 4 more sit-ups than he had than the previous day. Today jerry did 81 sit-ups. write an equation that could be solved to find the number of days jerry has been doing sit-ups, not counting the first day. let n represent number of days.
Answer:
157
Step-by-step explanation:
Answer:
can you explain what two number you added to get that number "157"
Step-by-step explanation:
given vectors u=(-2,3) and v=(-6,9) what is the measure of the angle between u and v?
a. 0
b. 86
c. 91
d. 180
Answer: 91
Step-by-step explanation:
Angle between the two vectors u and v is option (a) 0 degree
What is Vector?Vector, in mathematics, a quantity that has both magnitude and direction
Given,
u=(-2,3)
v=(-6,9)
Angle between the two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]
[tex]u.v=(-2)(-6)+(3)(9)\\u.v=12+27\\u.v=39[/tex]
[tex]|u|=\sqrt{-2^{2}+3^{2} } \\|u|=\sqrt{13}[/tex]
[tex]|v|=\sqrt{-6^{2}+9^{2} } \\|v|=\sqrt{117}[/tex]
Angle between two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]
θ=[tex]cos^{-1} \frac{39}{\sqrt{13}.\sqrt{117} } \\cos^{-1}\frac{39}{39}\\ cos^{-1}1=0[/tex]
Hence, the angle between the vectors u and v is 0 degree
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Order each set of integers froin least to greatest.
9. -7,-9, -19,-8
10. 1, -5, 6, 8, -2
11. 5,-31, -4, -10
12. -2, -22, 10, -7
Which expression can be simplified to find the slope of the trend line in the scatter plot?
D is 8-2
78-87
(B) [tex]\frac{78-87}{8-2}[/tex]
The slope of the trend line:A linear relationship is depicted by a trend line. [tex]Y=mx+b[/tex], where [tex]x[/tex] is the independent variable, [tex]y[/tex] is the dependent variable, m is the slope of the line and [tex]b[/tex] is the y-intercept, is the equation for a linear relationship.Scatter plot -Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with [tex]x-y[/tex] coordinates that correspond to those values.Therefore, (B) [tex]\frac{78-87}{8-2}[/tex] can be simplified to find the slope of the trend line in the scatter plot.
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Which Equation represents a Non-Proportional relationship between X and Y?
A. y=x
B. y=7x
C. y= 2/3x -1
D. y=3x + 0
Answer: C
Step-by-step explanation:
proportional relationship will have an equation that goes through the origin (0,0)
The equation for C will not go through the origin because it has a y-intercept of -1 and the line will be going through (0,-1) instead of (0,0).
All the other equations will be going through the origin because they have no y intercepts.
In the city of Carmen, there is a drawbridge that is opened twice per hour over the summer. The graph below shows the number of feet that the top of the bridge was above the water versus the amount of minutes that the
drawbridge was open
Answer:
1) Between 0 and 1 minute the rate of change is 25 ft./min
2) Between 1 and 2 minute the rate of change is 0 ft./min
3) Between 2 and 4 minute the rate of change is -12.5 ft./min
Step-by-step explanation:
1) Between 0, and 1 feet, we have;
The rate of change = (Final height - Initial height)/(Final time - Initial time)
The rate of change = (40 - 15)/(1 - 0) = 25 ft/min
Between 0 and 1 minute the rate of change = 25 ft./min
2) Between 1, and 2 feet, we have;
The rate of change = (40 - 40)/(2 - 1) = 0 ft/min
Between 1 and 2 minute the rate of change = 0 ft./min
3) Between 2, and 4 feet, we have;
The rate of change = (15 - 40)/(4 - 2) = -12.5 ft/min
Between 2 and 4 minute the rate of change = -12.5 ft./min
Evaluate 5x - 8.35y when x=12 and y=4
Answer:
26.6
Step-by-step explanation:
(12*5)-(8.35*4)
60-33.4
26.6
plz, answer the question in the photo.
Answer:
H
Step-by-step explanation:
Step 1 of 2: Subtract, sub-step b: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
2 and 1 over 32
1
3
= ( 2 × 3 ) over 3
2 × 3
3
+ 1 over 3
1
3
= ( 6 + 1 ) over 3
6 + 1
3
= 7 over 3
7
3
Step 1 of 2: Subtract, sub-step c: Find common denominator.
Find common denominator
32 over 9
32
9
− 7 over 3
7
3
= ( 32 × 1 ) over ( 9 × 1 )
32 × 1
9 × 1
− ( 7 × 3 ) over ( 3 × 3 )
7 × 3
3 × 3
= 32 over 9
32
9
− 21 over 9
21
9
9 is the least common multiple of denominators 9 and 3. Use it to convert to equivalent fractions with this common denominator.
Step 1 of 2: Subtract, sub-step d: Subtract.
Subtract
32 over 9
32
9
− 21 over 9
21
9
= ( 32 − 21 ) over 9
32 − 21
9
= 11 over 9
11
9
Step 1 of 2: Subtract.
Step 2 of 2: Simplify.
Simplify
11 over 9
11
9
= 1 and 2 over 91
2
9
Order these lengths in order from least to greatest.
0.65 m
0.6 m
0.52 m
0.55 m
0.545 m
Answer:0.52, 0.545, 0.55, 0.6, 0.65
Source:trust me bro
Answer:
O.52 m, 0.545 m, 0.55 m, 0.6 m, 0.65m. :)
Step-by-step explanation:
A clothing bought a shirt from a manufacturer for $85 and marked up the price by 10% . A month later the store reduced the shirts price by 10% . What was the shirts price after that reduction
Answer: The shirt's price after reduction = $ 84.15
Step-by-step explanation:
Given: Price of shirt= $ 85
Marked up percent = 10%
Reduced percent = 10%
Price after mark up = (Price of shirt) + 10% of (Price of shirt)
= $ (85+10% x 85)
= $ (85+(0.1) x (85))
= $ (85+8.5)
= $ 93.5
Price after 10% reduction = (Price after mark up)- 10% of (Price after mark up)
= $ (93.5-0.1 x 93.5)
= $ (93.5-9.35)
= $ 84.15
Hence, the shirt's price after reduction = $ 84.15
plz help me answer step by step 2+7/x=-12
Answer:
x = -1/2
Step-by-step explanation:
First, subtract 2 from both sides to get 7/x alone. Then muliply both sides by x to get rid of 7/x's denominator. Divide both sides by -14 to get rid of x's coefficient and to get x alone. You will then get -1/2 as your answer.
2 + 7/x = -12
-2 -2
7/x = -14
*x *x
7 = -14x
÷-14 ÷-14
- 1/2 =x
x = -1/2
When y varies directly with x,
slope = _______ = _______ = ________ = ________ = ________
Answer:
As you can see, these are all set up in slope intercept form (with a y-intercept of 0). These equations are called "direct variation" because y varies directly with x. If x increases, then y increases as well. If x decreases, then y decreases.
Step-by-step explanation:
As you can see, these are all set up in slope intercept form (with a y-intercept of 0). These equations are called "direct variation" because y varies directly with x. If x increases, then y increases as well. If x decreases, then y decreases.
ASAP pls help me with this
Answer:
x = 20
Step-by-step explanation:
If A || B, then ∠2 should equal to ∠3 (Alternate angles).
3x - 10 = x + 30
Isolate like terms.
3x - x = 30 + 10
Evaluate like terms.
2x = 40
Find x.
x = 40 ÷ 2
x = 20
Answer:
x = 20.
Angles 2 and 3 are measured as 50 degrees.
Step-by-step explanation:
Angles 2 and 3 are congruent, meaning that they are equal.
Set the two equations equal to each other and solve for x.
3x-10=x+30 (subtract x from the left side and add 10 to the right. This gets the x's and the plain numbers on the same side of the equation)
2x=40 (Divide by 2)
x = 20
Check your work by plugging in 20 for x in each expression. If the two expressions are equal when you do so, then you know you've worked out the problem correctly.
Angle 2:
3(20)-10
60 - 10 = 50
Angle 3:
20 + 30 = 50
Both expressions equal 50 when plugging in 20 for x, so this is the correct answer.
What's the difference between weather vanes and anemometers?
Answer:
The second one
Step-by-step explanation:
some one help first answer gets brainliest
Answer:
Y=3 is a horizontal line. So, a line perpendicular to y=3 must be vertical. The only vertical line among the choices is x=-3, so C must be the answer.
Step-by-step explanation:
Which set of integers is listed from least to greatest.
O 2,-1,-3
0 -3, 2,5
O 0,-1, 2
0 -3,-9,-12
Answer:
B
Step-by-step explanation:
One of my cats, Apollo, drives a cat car. He used 6/8 of a tank of gas to visit his friends for the weekend, and another 1 half of a tank to commute to work the next week. He then took another weekend trip and used a 1/4 tank of gas. How many tanks of gas did Apollo use altogether? Tanks of gas
Answer:
Total gas used = 3/2 of a tank of gas
Step-by-step explanation:
Visit to friend = 6/8 of a tank of gas
Commute to work = 1/2 of a tank of gas
Weekend trip = 1/4 of a tank of gas
Total gas used = Visit to friend + Commute to work + Weekend trip
= 6/8 + 1/2 + 1/4
= 6+4+2/8
= 12/8
= 3/2
Total gas used = 3/2 of a tank of gas
Please help! Me and my bestie are both stuck on this. . .
Use table to solve the inequality 2x<2
Answer:
x>1
Step-by-step explanation:
Answer:
-2, 0, 2, 4, 6 these are the answers for the boxes and they are in order. solution x<1
Step-by-step explanation:
if you look at the box you will see that it says x and 2x at the bottom. The x at the top is the same as the one at the bottom. So they want you to multiply the number in the row of x by the number below x I hope this helps
HELP PLEASE ITS MY LAST QUESTION!!
Jonathan and his band want to record and sell CDs. The recording studio charges an initial set-up fee of $250, and it charges $6.00 to burn each CD.
a) Define the variables:
Let n = _______
Let C = _______
Answer:
N=CD C=2-3 sentance
Step-by-step explanation:
Does the transformation represent a dilation? Why or
why not?
O no, because each vertex is not multiplied by the
same scale factor
O yes, because each vertex is multiplied by 4/3
O yes, because each vertex is multiplied by 2
Answer: A: no, because each vertex is not multiplied by the same scale factor.
Step-by-step explanation: got it right on Edge 2020!
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
O {-5 - 134,-5 + 34)
O {-5 -29, -5 + 29)
O {-12, 2)
O {-2, 12}
Plsss
The value of x from the quadratic equation is x = { 2 , -12 }
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 10x = 24 be equation (1)
Adding 5² on both sides of the equation , we get
x² + 10x + 25 = 24 + 25
( x + 5 )² = 49
Taking square roots on both sides , we get
x + 5 = ±7
Subtracting 5 on both sides , we get
x = 2
And , x = -12
Hence , the quadratic equation is solved and value of x is x = -12 or x = 2
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Ian's monthly allowance is $21. In January he starts saving for a birthday gift in June. Each month he saves of his allowance. The gift he wants to buy costs $110. Will Ian have enough money? Explain.
Answer:
Ian will have enough money to buy the giftStep-by-step explanation:
Step one:
given
monthly allowance= $21
from January to June= 6 months
total savings = 21*6= $126
cost of gift = $110
Step two:
Ian will have enough money to buy the gift
since he saved $126 which is greater than the cost of the gift of $110
he would have a balance of $16
Clue #1: The sum of the digits of a 3 digit number is 20. Clue #2: The tens digit is 2 less than the hundreds digit. Clue #3: The units digit is 12 less than the sum of the other two digits What is the 3 digit number, show or explain how you solved the problem. Help me! Please show work
Answer: The number is 974
Step-by-step explanation:
First, any 3 digit number can be written as:
N = a*100 + b*10 + c
Where a, b, and c are single-digit numbers.
a is the hundreds digit
b is the tens digit
c is the unit digit
We can write the clues as:
#1: a + b + c = 20
#2: b = a - 2
#3: c = a + b - 12
Then we have a system of equations:
a + b + c = 20
b = a - 2
c = a + b - 12
To solve this, we need to isolate one of the variables in one equation and then replace this in the other equations, we can see that b is already isolated in the second equation, then we can replace that in the first and third equations:
a + (a - 2) + c = 20
c = a + (a - 2) - 12
Now we can see that c is isolated in the second equation, then we can replace that in the first one to get:
a + (a - 2) + (a + (a - 2) - 12) = 20
Now we can solve this for a:
a + a - 2 + a + a -2 - 12 = 20
4*a - 16 = 20
4*a = 20 + 16
4*a = 36
a = 36/4 = 9
With this, we can find the values of b and c.
b = a - 2 = 9 - 2 = 7
c = a + b - 12 = 9 + 7 - 12 = 4
Then the 3-digit number is:
N = a*100 + b*10 + c = 9*100 + 7*10 + 4 = 974
N = 974