Answers
Answer:
Dimensions: 125 m x 250 m
Area: 31,250 m²
Step-by-step explanation:
Given information:
Total amount of fencing = 500mOnly 3 sides of the land need to be fencedFirst, let us assume that the land is rectangular in shape.
Let [tex]y[/tex] = length of the side opposite the river
Let [tex]x[/tex] = length of the other 2 sides of the land
Therefore, we can create two equations from the given information:
Area of land: [tex]A= xy[/tex]
Perimeter of fence: [tex]2x + y = 500[/tex]
Rearrange the equation for the perimeter of the fence to make y the subject:
[tex]\begin{aligned} \implies 2x + y & = 500\\ y & = 500-2x \end{aligned}[/tex]
Substitute this into the equation for Area:
[tex]\begin{aligned}\implies A & = xy\\& = x(500-2x)\\& = 500x-2x^2 \end{aligned}[/tex]
To find the value of x that will make the area a maximum, differentiate A with respect to x:
[tex]\begin{aligned}A & =500x-2x^2\\\implies \dfrac{dA}{dx}& =500-4x\end{aligned}[/tex]
Set it to zero and solve for x:
[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 500-4x & =0 \\ x & = 125 \end{aligned}[/tex]
Substitute the found value of x into the original equation for the perimeter and solve for y:
[tex]\begin{aligned}2x + y & = 500\\\implies 2(125)+y & = 500\\250+y & = 500\\y & = 250\end{aligned}[/tex]
Therefore, the dimensions that will give Christine the maximum area are:
125 m x 250 m (where 250 m is the side opposite the river)
The maximum area is:
[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 125 \cdot 250\\& = 31250\: \sf m^2 \end{aligned}[/tex]
Related Questions
Find the equation that is parallel to 2x-y=7
Answers
Answer:
Below
Step-by-step explanation:
Lines that are parallel have the same slope, so all lines parallel to the one given have the same slope as it does. That slope value is most easily seen by transforming the given equation to slope-intercept form
(y = mx + b).
This line would be y = 2x -7, so the slope of any line parallel to it must have a slope value of 2.
Hi there.
[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]
First of all, we can't find the equation of the line that is parallel to the line we are provided with in this problem, which is [tex]\bf{2x-y=7}[/tex], until we convert this equation into another form.
.
.
This form has a name, and it's called "[tex]\bf{Slope-Intercept\:Form}[/tex].
.
.
So first, what we need to do is subtract 2x from both sides:
.
[tex]\bf{-y=7-2x}[/tex]
.
It's not mandatory, but we can re-arrange the terms "7" and "-2x":
.
[tex]\bf{-y=-2x+7}[/tex]
.
Last step: Divide both sides of the equation by -1:
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[tex]\bf{y=2x-7}[/tex]
.
"-2x" turned into "2x" because a negative number multiplied or divided by a negative number equals a positive number.
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"7" turned into "-7" because a positive number multiplied or divided by a negative number equals a negative number.
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Now, our equation is in "Slope-Intercept Form".
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Remember that "Slope-Intercept Form" looks like this:
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[tex]\bf{y=mx+b}[/tex].
.
Now what we need to find is the equation of the line.
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Let's skim through the provided information to see whether or not there's some information that can help us find the equation.
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We're also provided with the fact that these lines, or equations, are parallel.
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What that means is if two lines are parallel, their slopes are the same.
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The slope of the line whose equation we just found is -2 (it's the number next to "x").
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I hope that this helped clear your doubts; if any are left, please ask.
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I wish you a nice rest of your day.
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[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\sf{n}\bf{g}\:\sf{A}\:\bf{L}\sf{e}\bf{t}\sf{t}\bf{e}\sf{r}.[/tex]
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the table shows the cost of the daycare for Lucy's dog this week her dog went 3 full days of day care and 2 half days of day care write an expression for the total cost of this week day care then evaluate the expression
Answers
An expression for the total cost of the daycare for Lucy's dog this week is T = 3F + 2H and the total cost is equal to $114.
How to write an expression for the total cost?In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:
Let the cost for full-day be F.Let the cost for half-day be H.Let total cost be T.Thus, the total cost of the daycare is given by:
T = 3F + 2H
Evaluating the expression, we have:
T = 3(28) + 2(15)
T = 84 + 30
T = $114.
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The sum of four consecutive integers is -6. What are the four integers?
Answers
Answer:
-3 ,-2 ,-1, 0
Step-by-step explanation:
x is the smallest integer then, x+x+1+x+2+x+2=-6
4x+6= -6 4x=-12 x= -3 so the integers are..
Find the volume (m^3) of the rectangular prism. 5 m 10 m 4 m
Answers
Answer:
200m^3.
Step-by-step explanation:
Volume of a rectangular prism = lenght x width x height.
(5m)(10m)(4m) = 200m^3.
400 people were asked if they liked their school lunch.10% said yes. 32 of those that said yes were boys.152 of those that were surveyed were girls. Complete the table to display this data. How many boys said no to liking their school lunch?
Answers
Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.
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Find the height in feet of the missile after 5 seconds in the air
Answers
The height in feet of the missile after 5 seconds in the air is; 875 ft
How to find the height of a Projectile?
We are given the quadratic function of the height in terms of time, x, in seconds as; h(x) = - 17x² + 260x
where;
h(x) is height after x seconds
x seconds is time of missile in air when thrown.
Thus, after five seconds, we have;
h(5) = - 17(5)² + 260(5)
h(5) = -425 + 1300
h(5) = 875 feet
Complete question is;
A missile is launched from the ground. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.
After 1 second, the missile is 243 feet in the air; after 2 seconds, it is 452 feet in the air.
The height of the can be represented by this function:
h(x) = - 17x² + 260x
Find the height, in feet, of the missile after 5 seconds in the air.
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14.Evaluate the expression 4x2+3y for x = 5 and y =6.
answer?
Answers
Step-by-step explanation:
Given: x=5 and y=6
=>4x2+3y
=> 8+3(6)
=> 8+18
=> 26
Hope it helps
The value of this expression is 58
Algebraic expression is a mathematical sentence that involves all mathematical operations.
In an algebra - a real number is always accompanied by some letter, which can represent a variable or unknown.
— To solve this expression, just: change the letters for the numbers and multiply/add.
⚘ Resolution
[tex]\large \sf 4x2+3y[/tex]
[tex]\large \sf 4 \cdot 5 \cdot 2 +3 \cdot 6[/tex]
[tex]\large \sf 40 +18[/tex]
[tex]\red{\boxed{\boxed{\green{\large \sf \ 58 \ }}}}\\[/tex]
Therefore, the value of this expression will be 58
Solve for x. 2^x-1 = 31, give your rounded answer to four decimal places.
Answers
The value of x for the given equation is 5.
What is Equation?An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.
Here, as per the given Equation
[tex]2^x-1 = 31[/tex]
[tex]2^x = 31 + 1[/tex]
[tex]2^x = 32[/tex]
[tex]2^x = 2^5[/tex]
On comparing both sides, we get
x = 5
Thus, the value of x for the given equation is 5.
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Which expression is equivalent to
(5x³)(4x) ³2
Answers
Answer:
640[tex]x^{6}[/tex]
Step-by-step explanation:
(5x³)(4x) ³2
(4x) ³ is the same as
4³ * x³ = 64x³
--
(5x³)(64x³)2
5*64*2 = 640
x³ * x³ = [tex]x^{6}[/tex]
640[tex]x^{6}[/tex]
A cylindrical tank has diameter 3.2 m and length
12.7 m.
What is the surface area of the tank, to 1 decimal
place?
Answers
Answer:
143.8m^2
Step-by-step explanation:
surface area of a cylinder has the formular
2πr(r+h)
from the question,
radius= diameter/2 = 3.2/2 = 1.6m
height (h) = 12.7m
Area= 2× 3.142×1.6(1.6+12.7)
Area= 10.0544(14.3)
Area= 143.77
Area= 143.8m^2 to 1 decimal places
Answer: 174.3
Step-by-step explanation: diameter of cylindrical tank = 3.2m
so radius is half of 3.2m
length= 12.7m
T.S.A of tank = 2pie r ( r+h)
2 x 3.14 x 3.2/2 ( 3.2/2 + 12.7 )
= 174.29
rounding it off to one decimal the answer would be 174.3
A quadratic function has zeros at 1 and -8. Which of the following could be the function?
Answers
Answer:(x-1)(x+8)
Step-by-step explanation: You need to set it up as (x+y)(x+z) format. To get that you need to flip the zeroes making them the opposite. So the answer in this case would be (x-1)(x+8).
Fill in the missing number in this sequence:
400, 200, { } , 50, 25
Answers
Answer:
100
Step-by-step explanation:
In this sequence, we can observe that the consistent change between each number in the series is divided by half.
From 400, we divide by 2 to get 200.
400 / 2 = 200
From 50, we divide by 2 to get 25.
50 / 2 = 25
So, to fill in the number after 200, we should logically divide by 2:
200 / 2 = 100
100 also fits into the following numbers, because 100 / 2 is 5.
Answer:
The missing number would be 100
Step-by-step explanation:
You're essentially cutting the numbers in half. For example:
half of 400 would be 200
half of 200 is 100
half of 100 is 50
half of 50 is 25
What is the probability of rolling two dice, and having a total of 8 dots showing? Express your answer as a percent
rounded to the nearest hundredth.
11.11%
15%
16.67%
13.89%
Answers
The value of the first die can be any number except for 1 because even if the second die rolls a 6, the total will only be 7. This means that there is a 5/6 chance of rolling an appropriate number with the first die. The second die has a 1/6 chance of rolling any given number. Any given number can be added to only one of the five numbers from the previous die to equal an 8. As a result, both numbers must be multiplied.
5/6 x 1/6 = 5/36 or 13.89%
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
YX ≅ Y'X'
XZ = 2X'Z'
mAngleYXZ = 2mAngleY'X'Z'
Answers
The options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'How to illustrate the triangle?It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.
This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.
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Answer:
∆XYZ ~∆X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
XZ = 2X'Z'
Step-by-step explanation:
took test
What is the inverse of function f? A) B) C) D)
Plato
Answers
Answer:
(7x-3)/-1
Step-by-step explanation:
swap the x and y and then move the y by itself
x=(3-y)/7
7x=3-y
7x-3=-y
(7x-3)/-1=y
can someone please help me with this
Answers
Answer:
[tex]d = \sqrt{109}[/tex]
Step-by-step explanation:
Use the distance formula.
[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Your points are (-4, 11) and (6, 8).
[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]
Is this an example of inductive reasoning, deductive reasoning, or neither?
At the grocery store Mia saw a sign indicating that 3 grapefruit cost $2.50, so Mia bought 3 grapefruit.
A. Inductive
B. Deductive
C. Neither
Answers
Since the specific conclusion is based on a general premise, this is a case of deductive reasoning.
What is deductive reasoning?The term deductive reasoning has to do with the process of arriving at a specific conclusion based on a more general premise.
In this case, the conclusion arrived at was based on the fact that Mia saw a general sign that read that 3 grapefruit cost $2.50. Hence, this is a case of deductive reasoning.
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440 meters is 14
of the way around the race track. How far is it around the whole race track?
Answers
Answer:
440x4=2200
Step-by-step explanation:
I'm guessing you meant 1/4, which is also known as 0.25, and if you know that 440 meters is equal to 1/4th of the whole race track you just have to multiply 440 by 4.
For item numbers 7-11, tell what relationship exists between the measures of each pair of angles.
Answers
Answer:
7-B (congruent)
8-D (supplement)
9-B (congruent)
10-B (congruent)
11-D (supplement)
Step-by-step explanation:
7- 1 and 3 are congruent using the corresponding angles theorem
8- they are supplements using the same side interior angle theorem
9- they are congruent using alternate interior angle theorem
10- they are congruent using the alternate exterior angle theorem
11- they are supplements using the same side exterior angle theorem
ur wlcm :)
brainliest?
Consider 8x-4 = 8^10
Answers
You have one cubic mile of water. you release it at 1000 gallons per
minute. how long will it take to empty??
Answers
It will take 764664.6875 days to empty the water
How to determine the time to empty?The given parameters are:
Volume = 1 cubic mileRate = 1000 gallons per minutesThe time is calculated as:
Time = Volume/Rate
So, we have:
Time = 1 cubic mile ÷ 1000 gallons per minute
Convert gallons to cubic mile
Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute
Divide
Time = 1.10111715 × 10^9 minute
Convert to days
Time = 764664.6875 days
Hence, it will take 764664.6875 days to empty the water
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Sofia invested $360 in an account in the year 2005, and the value has been growing
exponentially at a constant rate. the value of the account reached $420 in the year
2009. determine the value of the account, to the nearest dollar, in the year 2015.
Answers
well, from 2005 to 2009 is 4 years, so, in 4 years that account went from 360 to 420 at a rate "r", let's find that rate.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$420\\ P=\textit{initial amount}\dotfill &360\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4\\ \end{cases} \\\\\\ 420=360(1 + \frac{r}{100})^{4} \implies \cfrac{420}{360}=(1 + \frac{r}{100})^{4}\implies \cfrac{7}{6}=\left( \cfrac{100+r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{7}{6}}=\cfrac{100+r}{100}\implies 100\sqrt[4]{\cfrac{7}{6}}=100+r[/tex]
[tex]100\sqrt[4]{\cfrac{7}{6}}-100=r\implies 3.92899\approx r \\\\[-0.35em] ~\dotfill\\\\ \underset{2015~~ - ~~2005}{\stackrel{\textit{in the year 2015}}{t=10}}\hspace{5em}A=360\left(1 + \frac{3.92899}{100} \right)^{10}\implies A\approx 529.26[/tex]
Find the difference or type
"impossible"
Answers
Subtract each term in the right matrix from the corresponding term in the left matrix. For this question it’s (-7) - 7 = -14, which is the value in the bottom matrix. Here’s my work:
find the volume of the pyramid. round to the nearest hundredth
Answers
Answer:
A. 17.35 mm³
Step-by-step explanation:
Volume of a Pyramid
[tex]V = \frac{1}{3}Bh[/tex]
V ... volume
B ... area of base
h ... height
The base of this pyramid is a square. Area of a square is side times side.
[tex]B = 3.5 \times 3.5[/tex]
Let's substitute in the formula.
[tex]V = \frac{1}{3}Bh\\\\V = \frac{1}{3}(3.5\times 3.5)(4.25)\\\\V = \frac{1}{3}(12.25)(4.25)\\\\V \approx 17.35417 \text{ mm}^3[/tex]
Now let's round to the nearest hundredth.
V = 17.35 mm³
Show problem set up for full credit.
Answers
Answer:
If the arcs are the same
4x+25=5x
x=25
So, QPR is 4(25)+25
QPR is 125
Work out the value of 2⁰
Answers
Answer:
1
Key:
[tex]a^0=1,\:\quad \:a\ne \:0[/tex]Step-by-step explanation:
[tex]2^0=1[/tex]
Please just help me with my last 3 question 8 and 9 area and perimeter
Answers
9.perimeter : 8.2+4.2+9.17
Area:(8.2*4.1)/2
This is a dot plot of the number of text messages sent in a day by a sample of students at a local high school. The sample consisted of 30 students and was selected as representative of the population.
a. What do the six values of 0 on the dot plot represent?
b. Since the sample is representative of the population, describe what you think the dot plot of the entire population will look like.
Answers
The six values of 0 shown on the dot plot represent that 6 students out of the 30 sampled did not send any text messages daily.
With the sample being representative of the population, a dot plot for the entire population would have the same proportions as the sample but with a larger number of students.
What does the dot plot show?The number of dots above a number indicates the number of students who send that number of text messages daily.
As there are 6 dots over 0, it means that 6 students do not send any text messages daily.
Seeing as the sample is representative of the entire population, a dot plot for the whole school would have a larger number of dots over each number but the proportions would be the same as the sample.
For instance, the proportion of total students who don't send any messages per day is:
= 6 / 30
= 20%
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How many sides do 2 nonagons and 3 decagons have in all?
Answers
Answer:
48 sides
Step-by-step explanation:
A nonagon has 9 sides
A decagon has 10 sides
10 + 10 + 10 = 30
9+9 = 18
30 + 18 = 48
48 sides in total
Give brainliest please!
Hope this helps :)
Guys, can you please correct my answer for Question #45 of The Quadratic Relations for me, please?
Answers
Answer:
[tex]y=3(x-7)^2[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
Parent function
[tex]y=x^2[/tex]
Translated 7 units to the right
Subtract 7 from the x-value:
[tex]f(x-7) \implies y=(x-7)^2[/tex]
Vertically stretched by a factor of 3
Multiply the whole function by 3:
[tex]3f(x) \implies y=3(x-7)^2[/tex]
Streched 7 units right means change in x
So new equation
y=(x-7)²Vertically streched by 3
y=3(x-7)²