Akiko wants to fence in her [tex]12[/tex] ft by [tex]10[/tex] ft vegetable garden. There will be a path [tex]x[/tex] ft wide between the garden and the fence. The area to be enclosed by the fence will be [tex]360[/tex] sq ft. Write a quadratic function that can be used to determine the value of [tex]x[/tex].
Answers
Answer:
see below
Step-by-step explanation:
The length is 12 + 2x and the width is 10 + 2x
A = l*w
360 = ( 12+2x) ( 10+2x)
FOIL
360 = 120 + 24x+20x + 4x^2
Combine like terms
360 = 4x^2 +44x+120
Subtract 360 from each side
0 = 4x^2 +44x +120-360
0 = 4x^2+ 44x -240
For fun, lets solve
0 = 4( x^2 + 11x - 60)
0 = 4( x+15) ( x-4)
Using the zero product property
x= -15 x=4
Since we cannot have negative length
x=4 ft
![Akiko Wants To Fence In Her [tex]12[/tex] Ft By [tex]10[/tex] Ft Vegetable Garden. There Will Be A Path](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/9ntEMD0zRzGuETRmr6uLhDjSCEtcJM4C.png)
Answer:
[tex]x^2+11x-60=0[/tex]
Step-by-step explanation:
Refer to the drawing.
We know that the area enclosed by the fence is 360 square feet. Remember that the area for a rectangle is given by the following formula:
[tex]A=bh[/tex]
So, let's substitute 360 for A, (12+2x) for b, and (10+2x) for h. This yields:
[tex]360=(12+2x)(10+2x)[/tex]
We can simplify this. On the right, factor out a 2 from the first term and a 2 from the second. This yields:
[tex]360=2(6+x)\cdot2(5+x)[/tex]
Multiply:
[tex]360=4(x+6)(x+5)[/tex]
Divide both sides by 4:
[tex]90=(x+6)(x+5)[/tex]
Multiply on the right:
[tex]90=x^2+6x+5x+30[/tex]
Add on the right:
[tex]90=x^2+11x+30[/tex]
Subtract 90 from both sides. So, our equation is:
[tex]x^2+11x-60=0[/tex]
And we're done!
![Akiko Wants To Fence In Her [tex]12[/tex] Ft By [tex]10[/tex] Ft Vegetable Garden. There Will Be A Path](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/Wn7qCxgojr2qPWDT9M56EMCAeJbkSiZk.png)
Related Questions
For f(x) = 2x + 1 and g(x) = x^2 - 7, find (f * g)(2)
Answers
Answer: x= -5
Step-by-step explanation: Plug 2 into g(x). Plug that answer into f(x).
Which table represents a linear function?
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(1,-3)
(2,-5)
(3,-7)
(4,-9)
9e^2x - 30e^x + 25 = 0
Please I need a step by step solution urgently
Answers
Answer:
Here you go
Step-by-step explanation:
The first term is, 9e2 its coefficient is 9 .
The middle term is, +30e its coefficient is 30 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 9 • 25 = 225
Step-2 : Find two factors of 225 whose sum equals the coefficient of the middle term, which is 30 .
15 + 15 = 30 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 15 and 15
9e2 + 15e + 15e + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
3e • (3e+5)
Add up the last 2 terms, pulling out common factors :
5 • (3e+5)
Step-5 : Add up the four terms of step 4 :
(3e+5) • (3e+5)
Which is the desired factorization
PLEASE HELPP!!!!!!!!
Answers
Answer:
2800, 320
350, 40
2800+320+350+40=3510
Step-by-step explanation:
(40*70)+(40*8)+(5*70)+(5*8)
In a world problem, the rate of change is
A. the y-intercept
B. the initial value
C. the slope of linear equation
D. the y-value
Answers
Answer:
the y intercept is the right answer
Which explains how to find the question of the division below
-3 1/3 divided by 4/9
Answers
Answer:
B /second bubble -3 1/3 is 10/3 and 4/9 is a reciprocal 9/4
Katy's 4 dogs eat a total of 16 dog biscuits every day. How many biscuits will they eat in 45 days?
Answers
Answer:
720
Step-by-step explanation:
16*45=720
Answer:
720
Step-by-step explanation:
If in 1 day they eat 16 biscuits, then in 45 days they eat 45 * 16 biscuits.
45 * 16 = 720
Answer: 720
((-2,3) and (4,7)
what is the distance of this
Answers
Answer:
Step-by-step explanation:
(-2, 3 ) ; (4 , 7)
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]=\sqrt{(4-[-2])^{2}+(7-3)^{2}}\\\\=\sqrt{(4+2)^{2}+(7-3)^{2}}\\\\=\sqrt{6^{2}+4^{2}}\\\\=\sqrt{36+16}\\\\=\sqrt{52}\\\\=\sqrt{2*2*13}\\\\=2\sqrt{13}[/tex]
PLEASE HELP. EASY POINTS.
Answers
Answer:
2x^2+11x+12
Step-by-step explanation:
solve using FOIL
x + 4
_________ ________
2x | 2x² | 8x |
__________________
3 | 3x | 12 |
-----------------------------------
(x + 4) (2x + 3) = 2x² + 11x + 12
Someone please helppp.
Answers
Answer:
11 times
Step-by-step explanation:
For every muffin, she uses 1/3 cup of sugar. 3 2/3 = 11/3
11/3 divided by 1/3 is 11.
One side of a hexagon is 9 units. What is the perimeter of the hexagon?
Answers
Answer:
10
Step-by-step explanation:
Answer:
9 times 6
Step-by-step explanation:
One side of the hexagon is 9 units. Because a hexagon has 6 sides, and you are trying to find the perimeter, you would multiply 9 times 6 to get the answer.
the amount of money rachel earns varies directly with the number of hours she works. if sue earns $600 when she works 40 hours , how much will she earn for working 85 hours ?
Answers
Answer: She will earn $1275
Step-by-step explanation:
it says sue earns 600 for working 40 hours so divide 600 by 40 to find out how much earns per hour which is $15 (600/40=15) then you take 15 time 85 to find out how much she earns (15x85=1275).
i need help with this q9
Answers
Answer:
no
Step-by-step explanation:
A proportional relationship must go through the point ( 0,0). This does not go through the origin so this is not proportional
The relationship is linear but non proportional. The graph is a line but it does not go through the origin.
Identify the reference angle Ф for each given angle, Ф.
When ∅=300°, Ф=
Answers
=====================================================
Explanation:
The given angle is ∅ = 300. This x value is between 270 and 360, so we're in quadrant IV (the southeast quadrant)
The rule to get the reference angle y for this quadrant is
Ф = 360-∅
This tells us the angle made with the positive x axis
Ф = 360-∅
Ф = 360-300
Ф = 60
A 60 degree angle forms with the positive x axis as shown in the diagram below.
Which equation is equivalent to the given equation? x2 - 6x = 8
Answers
Answer:
See photo below
Answer:
(x-3)^2=17
Step-by-step explanation:
just took the test
When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3?
A• 1:8
B• 8:1
C• 1:9
D• 9:1
(Worth 30+ Points)
Answers
Answer:
c
Step-by-step explanation:
If two number cubes are rolled, the odds in favor of getting two numbers less than 3 is 1 : 9.
What is the probability?Probability determines the odd that an event would happen. The odd the event occurs is 1 and the odd that the event does not occur is 0.
Odds in favor of getting two numbers less than 3 = (numbers less than 3 / total numbers) x (numbers less than 3 / total numbers)
2/6 x 2/6 = 1/9
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ2
Un padre está usando una manguera de jardín para llenar una pequeña piscina inflable para su hijo pequeño. La piscina tiene una capacidad de 90 galones. Apaga el agua después de 5 minutos, pero deja la manguera en la piscina durante otros 3 minutos antes de guardarla. En esta situación, la relación entre los galones de agua en la piscina y los 8 minutos desde que el padre comenzó a llenar la piscina puede verse como una función. 1. En esa función, ¿qué variable es independiente? ¿Cuál es dependiente?
Answers
Answer:
Water is being collected at the rate of 11.25 gallon per minute.
Step-by-step explanation:
In this function the filling of water in the pool is dependent on the number of minutes. The more time the tap is opened the greater amount of water can be accumulated in the pool .
So time is independent and water is the dependent variable.
The function can be represented by
f(x)= xt where t is the time in minutes
90 gallons= x * 8 minutes
or x= 90/8 = 11.25 gallon per minute.
So water is being collected at the rate of 11.25 gallon per minute.
Spanish
En esta función, el llenado de agua de la piscina depende de la cantidad de minutos. Cuanto más tiempo se abre el grifo, mayor cantidad de agua se puede acumular en la piscina.
Entonces el tiempo es independiente y el agua es la variable dependiente.
La función se puede representar por
F (x) = xt donde t es el tiempo en minutos
90 galones = x * 8 minutos
o x = 90/8 = 11,25 galones por minuto.
Entonces, el agua se recolecta a una velocidad de 11.25 galones por minuto.
Which one is the vertical axis?
Answers
Answer:
Step-by-step explanation:
Vertical by definition means up and down. The y-axis fits this description. Look at a picture of a Cartesian coordinate system
Answer:
the y-axis
Step-by-step explanation:
vertical is up and down
horizontal is side to side or left and right
y is up and down
An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge. 16 ounces = 1 pound. 2,000 pounds = 1 ton. If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton? 8,000 ounces on the model is equal to ounces on the actual bridge. Convert ounces to pounds. The actual bridge can hold pounds. Therefore, the bridge hold 1 ton.
Answers
Answer:
The bridge can hold 1 ton
Step-by-step explanation:
Given that :
Model of bridge built is exactly 4 times smaller than actual bridge
Model bridge : actual bridge
1 : 4
From test,
Model bridge can hold 8000 ounces
Since actual bridge is 4 times the model bridge,;
Then, actual bridge should hold (8000 * 4) ounces = 32000 ounces
16 ounces = 1 pound
2000 pound = 1 ton
Hence,
32,000 ounces = (32000 / 16) pounds = 2000 pounds
Hence,
2000 pounds = 1 ton
Answer: 1 ton
Step-by-step explanation:
Ashley Sigler gave 2/5 of her bonus check of $255 to a missionary family. How much
money did she give to the family?
Answers
Answer:
102
Step-by-step explanation:
i think it is right
What is b squared + 12 if b = 102?
I give brainliest if you right
Answers
Answer:
10416
Step-by-step explanation:
102 squared is 10404. 10404 + 12 = 10416
Need some help please...
Answers
Answer:
C: Starting at 1103 you gain 91 feet each additional hour of climing.
Step-by-step explanation:
3.4z + 6.3 = -1.7z + 41.7
What’s z?
Answers
Answer:
z= 118/17 or 6.94
Step-by-step explanation:
i hope this is the right answer but try using Symbolab its what I use all the time
PART A:
A car traveled 180 miles at a constant rate.
complete the table to show the rate at which the car was traveling if it was completed the same distance in each number of hours
travel time | rate of travel
5
4.5
3
2.25
PART B:
In the scenario in part a write an equation that would make it easy to find the rate at which the car was traveling in miles per hour r, if it traveled t hours
Answers
Answer:
Part B: r = 180/t
Step-by-step explanation:
1.3 as a fraction answer please quick
Answers
Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of 0.001). Of those who have the disease, 95% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the test: a) Calculate P(positive test) b) Calculate P(has disease | positive test)
Answers
We're given
P(has disease) = 0.001
P(positive test | has disease) = 0.95
P(negative test | does not have disease) = 0.90
(a) By the law of total probability,
P(positive test) = P(positive test AND has disease) + P(positive test AND does not have disease)
Recall that the probability of an event A conditioned on another event B is
P(A | B) = P(A AND B) / P(B)
so that
P(positive test) = P(positive test | has disease) * P(has disease) + P(positive test | does not have disease) * P(does not have disease)
P(positive test) = 0.95 * 0.001 + (1 - 0.90) * (1 - 0.001)
P(positive test) ≈ 0.10
(b) From the definition of conditional probability, we hvae
P(A | B) = P(A AND B) / P(B) = P(B | A) P(A) / P(B)
so that
P(has disease | positive test) = P(positive test | has disease) * P(has disease) / P(positive test)
P(has disease | positive test) = 0.95 * 0.001 / 0.10
P(has disease | positive test) ≈ 0.0094
The probability will be "0.017699".
Given:
Incident rate,
0.1% or 0.001[tex]P(D) = 0.001[/tex][tex]P(D')= 1-0.001[/tex][tex]= 0.999[/tex]
[tex]P(\frac{P}{D} ) = 0.95[/tex][tex]P(\frac{N}{D} ) = 0.9[/tex]Now,
→ [tex]P(\frac{N}{D'} ) = 1-P(\frac{N'}{D'} )[/tex]
[tex]= 1-0.95[/tex]
[tex]= 0.05[/tex]
then,
→ [tex]P(\frac{D}{N} ) = \frac{Pr(D)\times P(\frac{N}{D} )}{P(N)}[/tex]
or,
[tex]= \frac{Pr(D)\times P(\frac{N}{D} )}{P(D) \ P(\frac{N}{D} )+P(D') \ P(\frac{N}{D'} )}[/tex]
By substituting the above values, we get
[tex]= \frac{0.001\times 0.9}{0.001\times 0.9+0.999\times 0.05}[/tex]
[tex]= \frac{0.0009}{0.0009+0.04995}[/tex]
[tex]= \frac{0.0009}{0.05085}[/tex]
[tex]= 0.017699[/tex]
Learn more:
https://brainly.com/question/16972053
In a school of 450 students, 48% are
girls. How many are girls?
Answers
Answer:
216
Step-by-step explanation:
.48 * 450 = 216
Answer:
There are 216 girls in that school.
Step-by-step explanation:
hope this helps! have a great day.
The length of a rectangle is 6 feet and the width is 3 feet. Find the perimeter
of the rectangle.
Answers
Answer:
18
Step-by-step explanation:
6+6+3+3
6+6+6
18
Eduardo has to make a 10 minute video of his test corrections for his Algebra 2 teacher in order to be eligible to retest. His teacher said he must stay within three minutes of the 10 minute requirement. Write an absolute value inequality that represents video lengths that meet the requirement. No spaces. On your keyboard,
Answers
Answer:
7 ≤ v ≤ 13
Step-by-step explanation:
Length of video required must be within 10 minutes
Submitted length of video must be with 3 minutes of the 10 minutes video
To create an absolute value inequality :
Let v = the range of value for which the required video will be :
|v - 10| = ±3
Lower boundary :
|v - 10| = - 3
v = - 3 + 10
v = 7
Upper boundary :
|v - 10| = 3
v = 3 + 10
v = 13
Hence,
7 ≤ v ≤ 13
Triangle MNO is rotated 180degree using the origin as the center of rotation.
On a coordinate plane, triangle M N O has points (negative 3, 2), (negative 3, 3), (negative 5, 2). Triangle M prime N prime O prime has points (3, negative 2), (3, negative 3), (5, negative 2).
Which sequences of transformations will produce the same results? Check all that apply.
a reflection over the x-axis and then a reflection over the y-axis
a reflection over the y-axis and then a reflection over the x-axis
a 90degree clockwise rotation about the origin and then a 90degree counterclockwise rotation about the origin
a translation 6 units right and then a reflection over the x-axis
a translation 4 units down and then a reflection over the y-axis
Answers
Answer:
The answer is (a) and (b).
Step-by-step explanation:
Just took the unit test on edge and got it right.
Answer:
A n B
Step-by-step explanation:
Trust
