Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing the basic shape of the garden. That is, the family wants to ensure that the length of the garden remains twice the width (see figure).
1. Write an equation for the area of the new garden.
2. Write an equation that calculates how much more area the new garden will have as compared to the current garden. Simplify the equation into a quadratic equation in standard form.
3. Using the equation from Exercise 2, determine what effect increasing the width of the garden by two feet will have on the length of the garden and the total area of the garden.
4. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be 160 square feet larger than its original area.
5. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be four times its original area.
Answers
Answer:
See below
Step-by-step explanation:
Sides of the garden
16 feet and 8 feetNew dimensions of the garden
16 + 2x and 8 + x1. The area of the new garden
(16 + 2x)(8 + x) = 2x^2 + 32x + 1282. The difference in area
2x^2 + 32x + 128 - 16*8 = 2x^2 + 32x3. x= 2 effect on the area
2*2^2 + 32*2 = 8 + 64 =72 ft²4. Area difference = 160
2x^2 + 32x = 160x^2 + 16x - 80 = 0Solving we get positive root of 4 ft5. Area difference = 4 times
2x^2 + 32x = 128*32x^2 + 32x - 384 = 0x^2 + 16x - 192= 0Solving we get positive root of 8 ftRelated Questions
an 8 inch candle burns 1/4 inch every hour. a 12 inch large candle burns 1/2 inch every hour. after how many hours will the two candles be the same height?
Answers
Answer:
69
\
Step-by-step explanation:
According to the system of equations above, what is
the value of x ?
Need someone to explain how to do it
Answers
Answer:
7
Step-by-step explanation:
try substituting
crossmultyply
x=-9-y
substituting
-9-y=-25+9
y=16
substituting
pick one of the equations
x+y=-9
x-16=-9
x=-9+16
x=7
Noah receives a $5 discount each month on his cell phone bill because he signed up for a auto pay from his bank account. Over the last 8 months ,Noah has paid a total of $280 for his cell phone bill. What would Noah be charged for his cell phone bill each month if he stopped using auto-pay?
Answers
You could do this two ways:
Divide 280 by the 8 months to get the original charge per month including the discount, which would be $35 per month. He would've been charged an additional $5 for every month, so add 5 to the 35 to get $40 per month.
He would've been charged an additional $5 for every month, so multiply 5 by 8 to get 40, then add that to 280 to get 320. That's how much he would've paid without the discount over 8 months. Divide that by the 8 months, and you get $40 per month.
Answer:
Step-by-step explanation:
280÷8=35+5=$40
For what values of [tex]x[/tex] is the product [tex](x+5)(x-1)[/tex] positive? Explain.
Answers
Answer:
[tex]x<-5\text{ or } x>1[/tex]
Step-by-step explanation:
We have:
[tex](x+5)(x-1)[/tex]
And we want to find the value of x such that the expression is positive. So, we can write this as the following inequality:
[tex](x+5)(x-1)>0[/tex]
Solve for the inequality. First, we can solve for the zeros like a normal quadratic. So, pretend the inequality is with an equal sign:
[tex](x+5)(x-1)=0[/tex]
Zero Product Property:
[tex]x+5=0\text{ or } x-1=0[/tex]
On the left, subtract 5.
On the right, add 1.
So, our zeros are:
[tex]x=-5, 1[/tex]
Since our inequality is a greater than, our answer is an "or" inequality with our answer being all the values to the left of our lesser zero and all the values to the right of our greater zero.
So, our solution is:
[tex]x<-5\text{ or } x>1[/tex]
And we're done!
Answer:
The regions where (x+5) (x-1) >0 is x< -5 or x>1
Step-by-step explanation:
(x+5) (x-1) >0
First find the zeros
(x+5) =0 x-1 =0
x= -5 x=1
We then have to check the regions
x< -5 -5 <x<1 x>1
First x< -5
(x+5) (x-1)
X+5 will be negative ( x-1) will be negative
(-) * (-) = + so the values will be positive
Then -5 <x<1
X+5 will be positive ( x-1) will be negative
( +) * (-) will be negative
First x>1
(x+5) (x-1)
X+5 will be positive ( x-1) will be positive
(+) * (+) = + so the values will be positive
The regions where (x+5) (x-1) >0 is x< -5 or x>1
Help meeeeee. Thank you
Answers
9 is not a prime number
in the expression of (x + 1)^n, the coefficient of the x^3 term is two times the coefficient of the x^2 term. Find the value of n.
Answers
According to Khayyam-Pascal triangle ,
the value of n is 8.
[tex] look \: \\ \\ {(x + 1)}^{8} = {x}^{8} + 8 {x}^{7} + 28 {x}^{6} + 56 {x}^{5} + 70 {x}^{4} + 56 {x}^{3} + 28 {x}^{2} + 8x + 1 \\ \frac{56}{28} = 2 [/tex]
Recall the binomial theorem:
[tex](a+b)^n=\displaystyle\sum_{k=0}^n\binom nk a^k b^{n-k}[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient. So
[tex](x+1)^n=\displaystyle\sum_{k=0}^n\binom nk x^k[/tex]
The x² term occurs for k = 2, which has coefficient
[tex]\dbinom n2=\dfrac{n!}{2!(n-2)!}=\dfrac{n(n-1)}2[/tex]
The x³ occurs for k = 3, with coefficient
[tex]\dbinom n3=\dfrac{n!}{3!(n-3)!}=\dfrac{n(n-1)(n-2)}6[/tex]
The latter coefficient is twice the other one, so that
[tex]\dfrac{n(n-1)(n-2)}6=2\cdot\dfrac{n(n-1)}2[/tex]
Solve for n :
[tex]\dfrac{n(n-1)(n-2)}6=n(n-1)[/tex]
[tex]n(n-1)(n-2)=6n(n-1)[/tex]
[tex]n-2=6[/tex]
[tex]\boxed{n=8}[/tex]
Solve the inequality.
8(x − 4) > −8
Answers
Answer:
x>3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > 3
Interval Notation:
( 3 , ∞ )
Solve: -(6x+ 8) = 4(17 - x) *
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = − 38
Step-by-step explanation:
Answer:
−38
Step 1: Simplify both sides of the equation.
−(6x+8)=4(17−x)
−6x+−8=(4)(17)+(4)(−x)(Distribute)
−6x+−8=68+−4x
−6x−8=−4x+68
Step 2: Add 4x to both sides.
−6x−8+4x=−4x+68+4x
−2x−8=68
Step 3: Add 8 to both sides.
−2x−8+8=68+8
−2x=76
Step 4: Divide both sides by -2.
−2x−2=76−2
x=−38
Can someone please help me with my homework???
Answers
Answer:
Step-by-step explanation:
Yes I would be glad to help you
PLEASE HELP ME ASAP I DONT WANT TO FLUNK MATH
Find the slope given these points:
(-8,4) & (-5,1)
A. -1
B. 1
C. 3/13
D. 5/13
Answers
Answer:
A:-1
Step-by-step explanation:
Duke is a part-time student at Horizon Community College. He currently has 22 credits, and he plans to take 6 credits per semester until he is finished.
Duke's friend Kila is also a student at the college. She has 4 credits and plans to take 12 credits per semester. After how many semesters will Duke and
Kila have the same number of credits?
Answers
Answer:
3
Step-by-step explanation:
22=6c=4+12c
-6c -6c
22=4+6c
-4 -4
18=6c
/6 /6
3=c
I need sum help please and thanks :)
Answers
Answer:
6/16n is your answer I think
HELP PLEASEEEE!!!!! [Easy]
Answers
Answer: 120
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Carlo’s Bakery is having a special where he packages 6 muffins together for a low price and he packages 20 cookies together for a low price. His baker realized they sold the same amount of muffins and cookies yesterday due to this great sale. What is the minimum amount of muffins that were sole yesterday? Is this a GCF or LCM problem?
Answers
Answer:
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
Step-by-step explanation:
6 muffins together
20 cookies together
To sell the same amount of muffins and cookies,
Find the lowest common multiple of 6 muffins and 20 cookies
6 muffins = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78
20 cookies = 40, 60, 80
The lowest common multiple of 6 muffins and 20 cookies is 60
Therefore,
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
The clocks shows when Tisa’s movie started and ended. How long did the last movie last? Plz hurry I need to finish
Answers
Answer:
it last 2 hours and 30 min
Step-by-step explanation:
find the value of a
Answers
Answer:
45
Step-by-step explanation:
81° + a° + 2a° = 180°
81° + 3a = 180°
3a = 180 - 81
3a = 99°
a = 99 ÷ 3
a = 33°
Therefore , a = 33° .
Which expression is equivalent to
Answers
Answer:
a
Step-by-step explanation:
What is the value of
-8(17-12)
—————
-2(8-(-2) )
• -4
• -2
• 2
• 4
Answers
Answer:
2
Step-by-step explanation:
-8(17-12)
------------
-2(8-(-2)
= -8(5)
--------
-2(10)
= -40
----------
-20
Ans 2What is the product of the expression (-2.2)(1.5)(-4.2)
Answers
Answer:
13.86
Step-by-step explanation:
(-2.2)(1.5)(-4.2) =
Use a calculator. Start with -2.2 * 1.5.
= (-3.3)(-4.2)
= 13.86
Answer:13.86
Step-by-step explanation:
((−2.2)(1.5))(−4.2)
=(−3.3)(−4.2)
=13.86
F(x)=-4x+3 vertical translation of 5 units down
Answers
Answer:
Gigi Jojo Jojo hip-hop Dutch him
so do Cob zoom from chick dunno drink gum
Step-by-step explanation:
hjjjhb. bjkn
jkk.
hj. hm.
gin
ghb.
8vb.
ucnluh itg.hboy
-6a - 4(a - 3) = -6a + 15
Answers
Step-by-step explanation:
-6a - 4(a - 3) = -6a + 15
=> -6a - 4a + 12 + 6a - 15 = 0
=> -4a - 3 = 0
=> -4a = 3
=> a = -3/4
For part of a science experiment, Andre adds 0.25 milliliters of dye to 12.3 milliliters of water. How many milliliters does the mixture contain?
Answers
Answer:
12.55 milliliters
Step-by-step explanation:
0.25+12.3=12.55
Good luck!
The mixture contains 12.55 milliliters.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that For part of a science experiment, Andre adds 0.25 milliliters of dye to 12.3 milliliters of water.
we need to find the amount of milliliters does the mixture contain.
Add twelve point three plus zero point two five.
12.3+0.25
12.30
+ 0.25
_______
12.55
Hence, the mixture contains 12.55 milliliters.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ3
Answer plzzzzzzzzzzzzzzz
Answers
Answer:
1 63636363 /1000000000
Step-by-step explanation:
Since it is 1. ..., it would be a mixed number with the 1 out front. There are 9 numbers after the decimal, making the denominator one billion, and then take the actual numbers (63) and make them the numerator.
Solve and show how you did 5 (x-1) + 3 = 13
Answers
5x - 5 + 3 = 13
5x -2 = 13
5x = 15
x = 15/5
x = 3
Answer:
x=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5(x−1)+3=13
(5)(x)+(5)(−1)+3=13(Distribute)
5x+−5+3=13
(5x)+(−5+3)=13(Combine Like Terms)
5x+−2=13
5x−2=13
Step 2: Add 2 to both sides.
5x−2+2=13+2
5x=15
Step 3: Divide both sides by 5.
5x
5
=
15
5
x=3
Answer:
x=3
if 3(x+1)=7 find the value of 3x
Answers
Answer:
3x=4
Step-by-step explanation:
3x+3=7
3x=4
A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be ... at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak. 2.
Answers
Answer:
concrete jungles where dreams are made of
Step-by-step explanation:
Answer:
There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.
Step-by-step explanation:
Sample response :)
If two angles have the same measure, then they are right angles true or false
Answers
Answer:
False
Step-by-step explanation:
Answer: true
Step-by-step explanation:
State of the two triangles are congruent. if they are, state how you know.
Answers
Answer:
Both Triangle are congruent because they have equal sides (the same amount of ticks on each side) The triangles are congruent.
Step-by-step explanation:
I'm really lost?? help please
Answers
M=−8j−9k+9 solve for k?
Answers
Answer:
k= -8/9j+ -1/9m+ 1
Step-by-step explanation:
Let's solve for k.
m=−8j−9k+9
Step 1: Flip the equation.
−8j−9k+9=m
Step 2: Add 8j to both sides.
−8j−9k+9+8j=m+8j
−9k+9=8j+m
Step 3: Add -9 to both sides.
−9k+9+−9=8j+m+−9
−9k=8j+m−9
Step 4: Divide both sides by -9.
-9k/-9= 8j+m-9/-9