6. Here are some lengths, widths, and areas of a garden whose perimeter is
40 feet. (Lesson 6-1)
. Complete the table with the missing
measurements.
b. What lengths and widths do you think will produce
the largest possible area? Explain how you know.
Length
4
8
10
12
14
16
Width
(ft)
16
12
Area
(sq ft)
64
96
64
If the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 [tex]feet^{2}[/tex], if the length of garden is 12 and the area of the garden is 96 [tex]feet^{2}[/tex],then the width be 8 feet, if the length of garden is 16 feet and the area is 64 [tex]feet^{2}[/tex], then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.
Given a table of various combinations of length and breadth of garden.
We are required to fill the blanks and find the length and widths which produce largest area.
Length Width Area
4 16 64
8 12 96
10
12 8 96
14
16 4 64
The bold values were the blanks. The blanks which is not filled cannot be filled because we need atleast two values whether they will be length and breadth , breadth and area or length and area. The largest area is 96 [tex]feet^{2}[/tex]. The length and breadth are 8 feet and 12 feet. They can be interchanged because we have two such combinations.
Hence if the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 [tex]feet^{2}[/tex], if the length of garden is 12 and the area of the garden is 96 [tex]feet^{2}[/tex],then the width be 8 feet, if the length of garden is 16 feet and the area is 64 [tex]feet^{2}[/tex], then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.
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Question is incomplete. It should include the attached picture.
GUYS PLEASE HELPPPP (and dont take the points pls)
Answer:
12.9
Step-by-step explanation:
Let's understand this,
Angle of elevation is 30° and the is standing perpendicularly, we have to find the distance from the branch to the mouse.
According to question,
cosine or cos thita = Base/Hypotenuse
Cos 30° = 15/H
0.86 = 15/H
H = 0.86 × 15
H = 12.9 (Round off 13)
Hope it helps!
Factor the expression.
25a + 15 =
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Which statement is true about the graph of a quadratic function on the left?
A.the axis of symmetry is x=-3
B.the range is y > 0
C.the y-intercept is at 2
D.the vertex (-1,-3)
The true statement for the given graph is the vertex is (-1, -3).
What is a parabola?A parabola is a curve where any point is at an equal distance from: a fixed point called the focus, and the fixed straight line called the directrix.
Given is a graph of a parabola, we need to determine the correct statements for the graph,
The graph is having the axis of symmetry at x = -1, so the first option is wrong.
The range y is y < 0, so the second option is also wrong,
There is no y-intercept.
Lastly, the vertex is at (-1, -3) therefore this option is correct.
Hence, the true statement for the given graph is the vertex is (-1, -3).
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A 16 oz bottle of a new soda costs $3.59. What is the unit rate, rounded to the nearest tenth of a cent?
The unit rate is __ cents per oz.
The unit rate is 22.5 cents per oz .
The unit rate of any quantity is calculated by dividing (total cost) with (total units purchased).
For Example : If 12 bananas cost $120 then 1 banana will cost 120/12=$10.
In the given question
16oz bottle costs $3.59.
As we have to find the unit rate in cents per oz , we first convert $3.59 to cents.
We know that
$1=100cents
$3.59=100*3.59
=359cents
So the price of 16 oz bottle = 359 cents
Unit rate = (total price ) / (units purchased)
Substituting the total price as 359 cents and units purchased as 16oz.
Unit rate = 359/16
=22.4375
≅22.5
Therefore , the unit rate is 22.5 cents per oz.
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triangle LMN is reflected about line y=3
where is point M on the transformed triangle?
A.(3,6)
B.(9,6)
C.(-3,-6)
D.(-3,0)
please answer it I need it for a test pls help
Answer:
the correct answer is: c (-3,-6)
Max has $17 in a fund he is creating to save for a bike. He adds $6 per week of his babysitting
earnings to the fund. If his weekly fund balance is represented by an arithmetic sequence, find
the 27th term.
The 27th term is $173.
In an arithmetic progression the difference between the two consecutive terms is same.
Here it is given that the first term of the AP which is represented by a is $17.
And Max adds $6 after every week in his fund so the common difference d is $6.
We know the general expression to find the nth term of an AP is
= a+(n-1)d
Here we have to find the 27th term. so the value of n will be 27.
Now the 27th term of the AP = 17+(27-1)6
= 17+156
= $ 173
The balance in the fund after 27th week will be $173.
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Suppose you borrow $680 for a term of three years at simple interest and 3.94% APR. Determine the total (principal plus interest) you must pay back on the loan.
The total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.
We are given that:
Principal amount = P = $ 680
Time period = t = 3 years
Simple interest rate = r = 3.94 %
We know that, the formula for simple interest is given by:
SI = P × r × t
SI = 680 × 3.94 % × 3
SI = 80.376
Amount will become:
Amount = $ 680 + $ 80.376
Amount = $ 760.376
Therefore, we get that, the total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.
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1. You borrow P200,000 and promise to pay back P212,000 at the end of 1year. Compute the interest rate.
2. JPIA invested P10 million to buy a tract of land and plant some young pine trees. The trees can be harvested in 5 years at which time JPIA plans to sell the forest at an expected price of P15 million. What is JPIA’s expected rate of return?
3. While I was a student at USC, I borrowed P200,000 in student loans at an annual interest rate of 5%. If I repay P50,000 per year, then how long will it take me to repay the loan?
4. A mortgage company offers to lend you $85,000; the loan calls for the payments of $8,273.59 at the end of each year for 30 years. What interest rate is the mortgage company charging you?
Round off your answer up to four decimal places.
The interest on the P200,000 is borrowed is 6.0000% rounded to 4 decimal places.
What is the future value of amount borrowed now?
The future value of borrowed is the initial loan plus the interest over the 1 year period that would be repaid to the lender when the matures in 1 year
FV=PV*(1+r)^N
FV=loan repayment=212,000
PV=initial loan=200,000
r=rate of interest=unknown
N=duration of loan=1
212000=200,000*(1+r)^1
212000=200,000*(1+r)
212000/200,000=1+r
1.06=1+r
r=1.06-1
r=6.0000%
15=10*(1+r)^5
15/10=(1+r)^5
1.5=(1+r)^5
1.5=(1.5)^1
(1.5)^1=(1+r)^5
divide indexes on both sides by 5
(1.5)^(1/5)=1+r
r=(1.5)^(1/5)-1
r=8.4472%
Using a financial calculator, we can determine the number of years it takes to repay the loan
I/Y=annual interest rate=5(without the % sign)
PMT=50000(annual payment)
PV=loan amount=-200000
FV=future value which is not applicable in this instance
CPT(press compute)
N= 4.5735 years
N=number of years of repayment=30
PMT=8273.59(annual payment)
PV=loan amount=-85000
FV=future value which is not applicable in this instance
CPT(press compute)
I/Y=9.0000%
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what values of a,b,c make this equation true? (2x-5)(x+2)+(ax^2+bx+c)=6x^2-4x-7
Answer:
A - a = 4, b = -3, c = 3
Step-by-step explanation:
When you substitute in a, b, and c you get
(2x - 5) (x + 2) + (4x^2 + -3x + 3)
collect like terms
(2x)(x) + (2x)(2) + (−5)(x) + (−5)(2) + 4x^2 + −3x + 3
combine like terms
2x^2 + 4x + −5x + −10 + 4x^2 + −3x + 3
(2x^2 + 4x^2) + (4x + −5x + −3x) + (−10 + 3)
6x^2 + −4x + −7
6x^2 + −4x −7
PLEASE HELP (will give brainiest) (please dont steal it would mean Alot)
Answer:
87, if it were 45 degrees, it would be 90, closest to 90 is 87
Answer:
87 feet
Step-by-step explanation:
We have an angle that's 44 degrees and we know that Susan is 90 feet from the base of the tree. We need to know the height of the tree, which is the value opposite from the angle we know.
Use tangent to find height.
tan (44) = x / 90 then multiply both sides by 90
x = tan (44) * 90 evaluate tan(44) and substitute into the equation
x = 86.911
round to nearest whole foot: 87 feet
[(1.7×106)÷(2.63×105)]+7.33
Answer:
[(1.7×106)÷(2.63×105)]+7.33
=7.9825439073
I HOPE IT HELP YOU
The bakery sells each cake for $120. Last year, the bakery sold 98 cakes. How much money did the bakery earn selling cakes?
Answer:
The bakery earned $11760 by selling cakes
Step-by-step explanation:
Cost of 1 cake = $120
Bakery sold cakes = 98
We need to find how much money did the bakery earn selling cakes?
We are given cost of 1 cake, if we multiply cost of 1 cake by 98 we can get cost of 98 cakes. Solving:
Cost of 1 cake = 120
Cost of 98 cakes = 120 x 98
= 11760
So, The bakery earned $11760 by selling cakes
Help plz Translate this sentence into an equation.
The product of Jenny's savings and 2 is 36.
Use the variableſ to represent Jenny's savings.
Answer:
2j = 36
Step-by-step explanation:
First, look for keywords.
"Product" means you multiply, and when you multiply a number by a variable you set it up by putting them together as demonstrated. 36 is the product so it's your total.
Write the equation of the line in point-slope, slope-intercept, and standard form.
38. Line passing through points (-4, 2) and (0,3)
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, find
the probability that a blue marble will be drawn.
a.
b.
1
3
1
OC
OD
C. 1
7
Mark this and return
d.
Please select the best answer from the choices provided
3
14
NEED HELP ASAP
Answer:
3/14
Step-by-step explanation:
4 + 3 + 7 = 14
The blue marbles are 3,
So the probability will be total blue ÷ total marble
3 / 14 which is D
Determine the cubic function obtained from the parent function y=x^3 after each sequence of transformations.
a reflection across the x-axis; a translation 1 unit up; and a translation 2 units right
Answer:
-(y+3)=(x-2)^3
Step-by-step explanation:
Transformed function B is f' ( x ) = - ( x - 2 )³ + 1
The transformed function is given by y = - ( x - 2 )³ + 1
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be denoted as A
Now , the value of A is
y = x³
Let the transformed function be denoted as B
Now , the value of B is calculated by
Step 1 :
A reflection across the x-axis
So , the function changes to g ( x ) = -x³
Step 2 :
A translation 1 unit up
Up by d units: y = f(x) + d
So , the function changes to h ( x ) = -x³ + 1
Step 3 :
A translation of 2 units right
Right shift by c units: y=f(x-c)
So , the function changes to f' ( x ) = - ( x - 2 )³ + 1
Therefore , the value of B is f' ( x ) = - ( x - 2 )³ + 1
Hence , the transformed function B is f' ( x ) = - ( x - 2 )³ + 1
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Annisa wrote an expression that represents
“the product of 6.2 and the sum of 3c and 8.”
What are the factors of the expression?
Answer:
“the product of 6.2 and the sum of 3c and 8'' will be algebraically represented as:
⇒ (6.2) (3c + 8)
We know that the numbers that we multiply are the factors of the product.
Here, (6.2) and (3c+8) are the factors of the expression.
Step-by-step explanation:
Let us breakdown and translate the word expression into an algebraic expression.
The sum of 3c and 8 is algebraically represented as:
⇒ 3c + 8
Thus, “the product of 6.2 and the sum of 3c and 8'' will be algebraically represented as:
⇒ (6.2) (3c + 8)
We know that the numbers that we multiply are the factors of the product.
Here, (6.2) and (3c+8) are the factors of the expression.
What is the sum of three hundredths plus two?
Answer:
2.03
Step-by-step explanation:
To determine the number of trout in a lake, a conservationist catches 94 trout, tags them and throws them back into the lake. Later, 30 trout are caught; 10 of them are tagged. How many trout would the conservationist expect to be in the lake?
what’s the area
4x+2
6x
Solve the problem below
8 ÷ 2(2+2)=
Answer: 16
Step-by-step explanation:
do the parentheses first.
8 / 2 x 4
then calculate.
4 x 4 = 16
A
woman has
ten
skirts and
four
blouses. Assuming that they all match, how many different
skirt-and-
blouse combinations can
she wear?
Question content area bottom
Part 1
The
woman can wear
enter your response here
different
skirt-and-
blouse combinations.
An 80-foot diameter reservoir currently holds 825,000 gallons of water. What is the depth of water in this reservoir, measured in feet?
Answer:
Step-by-step explanation:
d=80 ft
r=80/2=40 ft
volume of cylinder=π r²h,where h is height or depth of cylinder.
π×40²×h=825,000
πh=825,000/40²=4125/8
h=4125/(8π)≈164.1285≈164.13 ft
The depth of water in the reservoir is approximately 21.92 feet.
To find the depth of water in the reservoir, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Where:
Volume is the total volume of water in the reservoir (in gallons),
π (pi) is a mathematical constant approximately equal to 3.14159,
r is the radius of the reservoir (half of the diameter), and
h is the depth of water in the reservoir (in feet).
Given:
Diameter = 80 feet
Volume = 825,000 gallons
We first need to calculate the radius (r) of the reservoir:
Radius (r) = Diameter / 2 = 80 feet / 2 = 40 feet
Now, we can convert the volume from gallons to cubic feet because we need the measurements to b²e in consistent units:
1 gallon ≈ 0.13368 cubic feet
Volume (in cubic feet) = 825,000 gallons * 0.13368 cubic feet/gallon ≈ 110,127 cubic feet
Now, we can find the depth (h) using the formula:
110,127 cubic feet = π * (40 feet)² * h
Solving for h:
h = 110,127 cubic feet / (π * 40 feet)² ≈ 110,127 cubic feet / 5026.5482 square feet ≈ 21.92 feet
Therefore, the depth of water in the reservoir is approximately 21.92 feet.
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(WILL MARK BRAINLIEST) answer the question in image below please follow the directions on the paper about answer as improper fraction in simplest form, Many thanks!
Answer:
43/24
Step-by-step explanation:
The solving steps are as follows:
rearrange the fractionsthen figure out the LCM of the denominator , that is 24 in this casedivide 24 by the the denominator of the first fraction and multiply the result with the numerator. Follow the same process as (3) for the latter fractionSubstract the result of (4) from (3) And we're done!![tex] - \dfrac{3}{8} + \dfrac{13}{6} \\ = \dfrac{13}{6} - \dfrac{3}{8} \\ = \dfrac{13 \times 4 - 3 \times 3}{24} \\ = \dfrac{52-9}{24} \\ = \boxed{\frac{43}{24} }[/tex]
Answer:
43/24
Step-by-step explanation:
Fraction addition: First find the LCM of the denominators 8 and 6.Using the LCM find equivalent fractions.Now, the denominators are same and so add the numerators.Simplify.LCM of 6 and 8 = 24
[tex]\sf \dfrac{-3}{8}=\dfrac{-3*3}{8*3}=\dfrac{-9}{24}\\\\\\\dfrac{13}{6}=\dfrac{13*4}{6*4}=\dfrac{52}{24}\\\\\\\dfrac{-3}{8}+\dfrac{13}{6}=\dfrac{-9}{24}+\dfrac{52}{24}[/tex]
[tex]\sf = \dfrac{-9+52}{24}\\\\= \dfrac{43}{24}\\\\[/tex]
please help i need the answer asap
Answer:
thanks for the free points! anways but i think it s c
Step-by-step explanation:
its c
Geno invested $2,000 into an account that earns 8.5% interest compounded annually. How
much interest will Geno earn after 3 years?
HELP
SOMEONE HELPPP I CANT DO IT
Answer:
???????
Step-by-step explanation:
Please I need help with this
Answer:
I believe it would be 8
Step-by-step explanation:
Step-by-step explanation:
it should be 8 but the calculation is not coming yet.....
For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day? –30 minutes –11 minutes 11 minutes 30 minutes
Answer:
it is on ed it is 30
Step-by-step explanation:
Answer:
30 minutes
Step-by-step explanation: