Answer:
Length = 90 feet
Width = 70 feet
Step-by-step explanation:
The area of a rectangle is found by finding the product of the length. Therefore, the following formula equation can be made:
[tex]A=lw[/tex]
The problem tells us that the area of the garden is 6,300 square feet and that the length is 20 feet longer than the width. Therefore, our equation can be rewritten as such:
[tex]6300=(w+20)(w)~or~6300=w(w+20)[/tex]
Now that there are no longer two different variables, we can solve for w.
[tex]6300=w(w+20)\\\\6300=w^2+20w\\\\0=w^2+20w-6300[/tex]
We are left with a trinomial so we'll use the quadratic formula to further solve for w.
[tex]w=\frac{-20\pm\sqrt{20^2-4(1)(-6300)} }{2(1)}\\\\w=\frac{-20\pm\sqrt{400+25200} }{2}\\\\w=\frac{-20\pm\sqrt{25600} }{2}\\\\w=\frac{-20\pm160}{2}\\\\\\w=70\\or\\w=-90[/tex]
Since distance cannot be negative, w = -90 cannot be a solution for this problem. Therefore, the width of the rectangular garden is 70 feet.
Now that the width has been found, we know the length is 20 feet longer than it. Therefore, the length is 90 feet.
2^x+2=4081
Solve the following exponential equation
Which of the following is a solution to the given equation?
y=-3x - 7
A)
(-2,-1)
B)
(-1,-10)
C
(4,-5)
D
(3,-2)
Answer: A
Step-by-step explanation:
By replacing in the given equation:
y=-3x-7
y=-3(-2)-7
y=6-7
y=-1
But for choices B, C and D the given x values don't fit with the images.
3. the smallest number by which 168 must be multipled to get the perfect square number. ICA) 3 1(B)2 (c) 4 (o)5
Answer:
42
Step-by-step explanation:
168 factors into
2•2•2•3•7
two of the 2's make a perfect square
(2•2)•2•3•7
2²•2•3•7
as none of the product of the remaining factors makes a perfect square
2•3 = 6, 2•7 = 14, 3•7 = 21
we need to multiply the remaining factors together to find another perfect square
2²•(2•3•7)²
2•3•7 = 42
42(168) = 7056 = 84²
2 short questions 20 POINTS
Step-by-step explanation:
13.
oh, come on !
you never had and solved the situation "one piece costs that much, how much will be 2 or 5 or 10 of them ?"
it is a simple multiplication.
and hence the answer B.
the first hint is already in the table with 1 pizza costing $5.25.
2 pizzas are then 2×$5.25, 3 pizzas 3×$5.25, ...
so, the cost c = number of pizzas × $5.25
or short
c = p×5.25 or 5.25p
14.
the domain is the interval or set of valid values for the input variable (x) of a function/relation.
and the range is the interval or set of valid values for the result variable (y) of a function/relation.
so, the domain is the set {-3, -1, 0, 1, 3}.
and the range is the set {-4, 0, 2, 4}.
In mathematics, a function is a binary relation between two intervals or sets that associates each element of the first interval/set (domain) to exactly one element of the second interval/set (range).
and that's what is done here.
it is a function.
each value of x is associated exactly with 1 result value of y.
a y value can be associated with more than one x value - no problem.
but no x value can have more than one associated y value - otherwise that would break the principle of a function.
Find the equation of the line shown below
Y=mx+c
Answer:
y = -1/4x + 2
Step-by-step explanation:
1. First you find m. Because the line is slanting downwards, you know it is negative. Then you can find the number by looking at the rise over run (rise/run). We can go up 1 (rise) and then to the side 4 (run). We go to the right side 4 because that is where the line intersects with up 1. So because the rise goes over the run, the number would be 1/4. But remember that it is negative so m = -1/4
2. Now we have to find c. For this you just have to go up or down the y-axis until you find the point where it intersects with the line. On this graph it intersects on positive 2. So c = + 2
Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on he first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
n x¯¯¯ s x¯¯¯ s x¯¯¯ s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
Construct, using the conservative estimate for degrees of freedom, a 98% confidence interval for the difference, μc−μu between the mean gain of all students who are coached and the mean gain of all students who are uncoached.
PLSSSS GUYS NOW FAST, This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Adrian pays his niece $30 to babysit for 5 hours.
Which expression models the change in the amount of Adrian's cash each hour that his niece babysits?
Multiple choice question.
A)
30−5
B)
–30·5
C)
−30÷5
D)
–5÷30
Part B
What was the change in Adrian's cash each hour?
Multiple choice question.
A)
–$150
B)
–$6
C)
–$3
D)
$25
Answer:
Part A would be C because divided 30 by 5 to get the unit rate.
Part B would be B
Answer:
C). −30÷5
B). –$6
Step-by-step explanation:
(-5)⁶ ÷ (-5)⁸
Solution
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Upload the entire proof below.
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m
STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m∠1 + m∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m∠1 + m∠2 = m∠1 + m∠3 5.
6. 6.
7. l || m 7.
Line m and line l are parallel as m∠2 = m∠3
Equation
An equation is an expression that shows the relationship between two or more variables and numbers.
Two angles are said to be supplementary if they add up to 180 degrees.
m∠1 + m∠2 = 180° (Given)
m∠1 + m∠3 = 180° (sum of angles on a straight line)
Hence:
m∠1 + m∠2 = m∠1 + m∠3
m∠2 = m∠3
Line m and line l are parallel as m∠2 = m∠3
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50 points! Help (Vectors)
[tex]2v - 3u\\\\=2<3,7> - 3<-5,4>\\\\=<6,14>-<-15,12>\\\\=<6+15, 14-12>\\\\=<21,2>[/tex]
Answer:
Step-by-step explanation:
what is the solution of the equation ? 3=2w
Answer:
w = 1.5Step-by-step explanation:
Question:To find the solution that is 'w'Equation:3 = 2wSolution:3 = 2w
=> 2w = 3
[tex] = > w = \frac{3}{2} [/tex]
=> w = 1.5 (Ans)
Which set of ordered pairs lies along the same vertical line?
Answer:
All ordered pairs with the same x value
Step-by-step explanation:
A vertical line can be represented by the equation x=k for some value k. So any pair with x value equal to k satisfies the equation and is thus in the set
Jiro uses fabric to make costumes for a show choir
Answer:
Print it
Step-by-step explanation:
Write an equation of the line that is parallel to the y-axis and passes through the point (−3,1). Then determine whether the slope of the line is positive, negative, zero, or undefined.
An equation is
.
Question 2
The slope is positive.
The slope is positive.
The slope is negative.
The slope is negative.
The slope is zero.
The slope is zero.
The slope is undefined.
Answer:
The slope is undefined
Step-by-step explanation:
A vertical line has points that have the same x-coordinate.
The equation is x = -3
The slope of a vertical line is undefined.
Answer:
The slope is undefined
Help help help help help help help help help
Answer:
(-1,1)
Step-by-step explanation:
Im pretty sure the answer to A'' would be the inverse of A, as the triangle was mirrored on the opposite quadrant of the graph. (The inverse or opposite of (1,-1) would be (-1,1) ).
Hope this helped!
Find the slope given these points:
(4,-4) & (2,0)
Answer:
The slope is -2
Step-by-step explanation:
[tex]m = \frac{0 - ( - 4)}{2 - 4 } \\ m = \frac{4}{ - 2 } \\ m = - 2[/tex]
Answer:
this is correct
Explanationsigns
1 quadrant = (+,+)
2 quadrant = (-,+)
3 quadrant = (-,-)
4 quadrant = (+,-)
From 8:00 am to 8:20 am, Lisa picked 1/4 of a pound of strawberries. If she continues picking strawberries at this rate, how many pounds of strawberries will she pick in 4 hours?
Answer:
3 lbs
Step-by-step explanation:
20 mins is 1/4 lb (4oz)
1 hr is 3/4 lb (12 oz)
4 hrs= 3/4 lb or 12 oz × 4
4 hrs= 3 lbs or 48 oz
How do you do -9-(-2)-(-6)-4?
The circle below represents one whole . …. What percent is represented by the shaded area ?
Answer:
50%
Step-by-step explanation:
shaded area = 2/4
shaded area as a percentage ;
2 / 4 x 100
= 1 / 2 x 100
= 1 / 1 x 50
= 50%
A square piece of paper has a perimeter of 36 cm. What is the area of a square piece of paper with twice that perimeter? *
323 sq.cm
324 sq.cm
81 sq.cm
---------------------
( perimeter = l+ b )
(area = l × w )
(l= length)
(b= breadth )
(w= width)
Answer:
Area= 18 x 18=324 sq.cm
Step-by-step explanation:
p=36 x2=72 (as it is twice that of the original paper)
since it is a square, length of 1 side = 72/4= 18
so, the area = l x l= 18 x 18= 324 sq.cm
Answer:
Area= 18 x 18=324 sq.cm
Step-by-step explanation:
p=36 x2=72 (as it is twice that of the original paper)
Since it is a square, length of 1 side = 72/4= 18
Therefore, the area = l x l= 18 x 18= 324 sq.cm
Hope this helps :)
need help with my math please <3
Answer:
wth that's hard I can't answer that
A warehouse placed 10 equal weight bones on a scale. Total they weighed 6 pounds. Each
box weighed
of a pound
A car rental agency charges $150 per week plus $0.20 per mile to rent a car. How many miles can
you
travel in one week for $290?
A) 208
B) 1450 miles
C) 700 miles
D) 675 miles
What is the median of these figure skating ratings? 5.0 6.0 7.0 7.5 8.0 9.0 10.0
Select the correct answer from each drop-down menu.
A machine cuts a strip of carpet into two pleces. The length of the smaller plece is 5 meters greater than 4 the length of the larger piece. If
the length of the smaller piece is 12 meters, the length of the bigger plece is meters and the total length of the carpet is
meters.
Length of larger piece be x
Smaller piece=4x+5x=12m
[tex]\\ \sf\longmapsto 4x+5=4(12)+5=60+5=65m[/tex]
Total length=65+12=77m
The length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.
Given that length of the smaller piece is 12 meters.
The length of the smaller piece is 5 meters greater than 4 times the length of the larger piece.
Let's represent the length of the larger piece as "x."
Length of the smaller piece = 4 times the length of the larger piece + 5
12 = 4x + 5
Subtracting 5 from both sides:
12 - 5 = 4x
7 = 4x
Dividing both sides by 4:
7/4 = x
1.75 = x
So, the length of the bigger piece is 1.75 meters.
To calculate the total length of the carpet, we add the length of the smaller piece and the length of the bigger piece:
Total length of the carpet = Length of the smaller piece + Length of the bigger piece
Total length of the carpet = 12 + 1.75
Total length of the carpet is approximately 13.75 meters.
Therefore, the length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.
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9) You want to buy a backpack which costs $34.82. Now it is on sale of 30% off. What is the
discount amount? What is the final cost with the discount?
Answer:
10.446
Step-by-step explanation:
Use the function g(x)=11 to find the following values
g(-3)
Answer: https://www.bing.com/search?q=https%3A%2F%2Fwww.chegg.com%2Fhomework-help%2Fquestions-and...%0A&form=IPRV10
Step-by-step explanation: There you will find your answer
The value of g(-3) comes to be 11 because g(x) is a constant function.
Given function is:
g(x) =11
Function g(x) is a constant function because g(x) is independent of x.
How graph of a constant function look like?The graph of a constant function is parallel to the y-axis and gives the same output for any input given to the function.
So, The value of g(-3) will be the same as the value of g(x) i.e. 11
So, value of g(-3) = 11
Therefore, The value of g(-3) comes to be 11 because g(x) is a constant function.
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2. Michael Evans works a basic week of 40 hours. During a certain week he works 52 hours. If his weekly wage is $100.80 and overtime is paid at time and a half, what is his gross wage for the week? 3. In an engineering factory, employees work 38 hour basic Week. Any overtime worked from Monday to Friday is paid at time and half whilst overtime worked on Saturday and Sunday is paid at double time. If the basie wage is $2.48 per hour, find the gross ways for a man who works 12 hour overtime from Nlonday to Friday, 4 hours on Saturday and . 4 hours on Sunday
Answer: 3 :3 :3
$8.88
Step-by-step explanation:
Select two answers from below. x=_ and then which theorem justifies your answer.
(2x + 2)
(3x -63)
m
a
x=63
x=64
Ob
c
roob.
X=65
X=66
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Same Side Interior Angles
f
Answer:
c. x=65
f. Alternate Exterior Angles
Step-by-step explanation:
2x+2=3x-63
2x=3x-65
-x=-65
x=65
They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles
Dеtеrmіnе tһе rаnցе օf tһе fսnсtіօn f(х) = 2х + 1 ԝһеn tһе ԁօmаіn іѕ {-3, 9, 15}.
Answer:
Range: {-5, 19, 31}
Step-by-step explanation:
Given the linear function, f(x) = 2x + 1, and the domain, {-3, 9, 15}.
In order to determine the range of the given linear function, simply substitute each domain value as inputs into the function.
x = -3f(x) = 2x + 1
f(-3) = 2(-3) + 1
f(-3) = -6 + 1
f(-3) = -5
x = 9f(9) = 2x + 1
f(9) = 2(9) + 1
f(9) = 18 + 1
f(9) = 19
x = 15f(15) = 2x + 1
f(15) = 2(15) + 1
f(15) = 30 + 1
f(15) = 31
Therfore, the range of the function is: {-5, 19, 31}.