Answer:
The dimensions of the wall are 100 ft x 100 ft
Step-by-step explanation:
we know that
The perimeter of a rectangular wall is
[tex]P=2(x+y)[/tex]
where
x is the length
y is the width
we have
[tex]P=400\ ft[/tex]
so
[tex]400=2(x+y)[/tex]
simplify
[tex]200=x+y[/tex]
[tex]y=200-x[/tex] ----> equation A
The area of a rectangular wall is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-x)\\A=-x^2+200x[/tex]
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
Convert the quadratic equation in vertex form
[tex]A=-x^2+200x[/tex]
Factor -1
[tex]A=-(x^2-200x)[/tex]
Complete the square
[tex]A=-(x^2-200x+100^2)+100^2[/tex]
[tex]A=-(x^2-200x+10,000)+10,000[/tex]
Rewrite as perfect squares
[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form
The vertex is the point (100,10,000)
The x-coordinate of the vertex represent the length of the wall for a maximum area
so
[tex]x=100\ ft[/tex]
Find the value of y
equation A
[tex]y=200-(100)=100\ ft[/tex]
therefore
The dimensions of the wall are 100 ft x 100 ft
To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.
Explanation:To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,
which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.
Given the following absolute value function sketch the graph of the function and find the domain and range.
ƒ(x) = |x + 3| - 1
explain in words not with a graph plsss
Step-by-step explanation:
The given absolute value expression is
[tex]f(x) = |x + 3| - 1[/tex]
This absolute value function is of the form
[tex]f(x) = |x + h| + k[/tex]
where (h,k)=(-3,-1) is the vertex.
This function opens upwards, hence the the minimum point is (-3,-1)
The domain is the values of x for which the function is defined.
The domain is all real numbers.
The range is the values of y for which x is defined.
The is y≥-1 because the minimum value is -1.
The graph is shown in attachment.
How much is 1+1x3x6+2x20-100/3x20
Answer:
-41/60
Step-by-step explanation:
Type the whole thing into a calculator.
Answer:
The answer is -41/60
Step-by-step explanation:
can someone explain how to simplify a (b+c) ?
Answer:
ab + ac
Step-by-step explanation:
a (b+c)
a is multiplying everything in the bracket
axb + axc
ab + ac
Answer:
ab + ac
Step-by-step explanation:
a (b + c) *multiply
a x b + a x c
ab + ac
I hiking trail is 20 km long. Park organizers want to build five rest ops for hikers with one on each end of the trail in the other three spaced evenly between. How much distance will separate successive rest stops
Answer:
5km
Step-by-step explanation:
There are 5 rest ops where 2 of them are at 2 ends and the other 3 are spaced evenly between. This would create 4 equal separated spaces. If the total distance is 20km, then the length for each space would be 20 / 4 = 5 km
Which expression is equivalent to (x - 2)(x + 4) ?
(x + 1)2 – 9
(x - 1)² – 9
(x + 1)² – 7
(x - 1)² – 7
Answer:
Step-by-step explanation:
hello :
(x + 1)2 – 9 is equivalent to (x - 2)(x + 4)
because (x + 1)2 – 9 =(x + 1)2 – 3²
= (x+1-3)(x+1+3) =(x-2)(x+4)
Answer:
(x + 1)² - 9
Step-by-step explanation:
Expand each of the factors using FOIL
(x - 2)(x + 4)
= x² + 4x - 2x - 8 ← collect like terms
= x² + 2x - 8
Now consider the expansions of
(x + 1)² - 9
= x² + 2x + 1 - 9
= x² + 2x - 8 ← equivalent to (x - 2)(x + 4)
--------------------------------------------------------------
(x - 1)² - 9
= x² - 2x + 1 - 9
= x² - 2x - 8 ← not equivalent to (x - 2)(x + 4)
-----------------------------------------------------------------
(x + 1)² - 7
= x² + 2x + 1 - 7
= x² + 2x - 6 ← not equivalent to (x - 2)(x + 4)
--------------------------------------------------------------------
(x - 1)² - 7
= x² - 2x + 1 - 7
= x² - 2x - 6 ← not equivalent to (x - 2)(x + 4)
Explain the error in the work shown. Find the
correct answer.
1/64 = 16^2a 4^-3=(2^4)^2a 4^-3=2^8a -3=8a
-3/8 = a
Answer:
[tex]a = - \frac{3}{4}[/tex]
Step-by-step explanation:
The correct solution of the given equation is as follows :
We have,
[tex]\frac{1}{64} = 16^{2a}[/tex]
⇒ [tex]4^{- 3} = (2^{4} )^{2a}[/tex]
⇒ [tex]2^{(2 \times (-3))} = 2^{8a}[/tex]
⇒ [tex]2^{- 6} = 2^{8a}[/tex]
Comparing the power of equal base, we get
- 6 = 8a
⇒ [tex]a = - \frac{6}{8}[/tex]
⇒ [tex]a = - \frac{3}{4}[/tex]
Therefore, before equating the powers of two terms the base of the terms should be equal and here this is the error. (Answer)
Answer:
The bases were not the same when the exponents were set equal to each other.
16 should have been written as 4 squared.
The exponent on the right should be 4a instead of 8a.
The correct solution is a = -3/4
Step-by-step explanation:
correct on edge
I need to know the values of X and Y
Answer:
x=25, y=113
Step-by-step explanation:
5x=3x+50 (alternate angles)
5x-3x=50
2x=50
Dividing both sides by 2
x=25
Now
5x=y+12 (vertical angles)
5(25)=y+12
125=y+12
y=125-12
y=113
Marcus and Phillip are in the Robotics Club. They are both saving money to buy materials to build a new robot. They plan to save the same amount of money.
Marcus decides to open a new bank account. He deposits $25 that he won in a robotics competition. He also plans on depositing $15 each week that he earns from
tutoring. Phillip also opens an account. He deposits $40 he has saved from mowing lawns over the summer. He plans to save $10 a week from his allowance. After
how many weeks will they have the same amount of money saved?
3 weeks
4 weeks
5 weeks
6 weeks
Answer:
Step-by-step explanation:
marcus : deposits 25 + 15 each week(w)
25 + 15w
Philip : deposits 40 + 10 each week(w)
40 + 10w
when will they be equal.....set them equal and solve for w, the number of weeks
25 + 15w = 40 + 10w
15w - 10w = 40 - 25
5w = 15
w = 15/5
w = 3 <==== they will be equal at 3 weeks
The number of weeks for both Marcus and Phillip to have the same amount of money saved is 3 weeks
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of weeks be = A
The amount Marcus deposits in the bank account = $25
The amount Marcus deposits each week = $15
So ,
After A weeks , Marcus will deposit = $ 15A
And , Total deposit in the bank for Marcus =
Amount Marcus deposits in the bank account + Amount Marcus deposits for A weeks
Total deposit in the bank for Marcus = 25 + 15A
And ,
The amount Phillip deposits in the bank account = $40
The amount Phillip deposits each week = $10
So ,
After A weeks , Phillip will deposit = $ 10A
And , Total deposit in the bank for Phillip =
Amount Phillip deposits in the bank account + Amount Phillip deposits for A weeks
Total deposit in the bank for Phillip = 40 + 10A
Now , for both Marcus and Phillip to have the same amount after A weeks ,
Total deposit in the bank for Marcus = Total deposit in the bank for Phillip
Substituting the values , we get
25 + 15A = 40 + 10A
Subtracting 10A on both sides , we get
5A + 25 = 40
Subtracting 25 on both sides , we get
5A = 15
Divide by 5 on both sides , we get
A = 3 weeks
Hence , The number of weeks for both Marcus and Phillip to have the same amount of money saved is 3 weeks
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[30points] What is the formula used to make an equation when we know the zeroes (alpha+beta) and (alpha x beta) ?
Answer:
If it is a quadratic equation then it's zeroes are alpha and beta. Sum of zeroes is -b/a. So alpha plus beta is -b divided by a.
Step-by-step explanation:
The formula used for making an equation when you know the zeroes is;
k(x² - (sum of zeroes)x + (product of zeroes)k(x² - (α+β)x + (αβ))k here,is a constant; for better clarification follow this example;
Say
(α+β) = 1(αβ) = 2According to the formula the equation must be;
k(x² - (α+β)x + (αβ))k(x² - (1)x + (2))k(x² - 1x + 2)Now, the k can be replaced with any variable, i.e, 3,4,5/6,7 etc anything. Hope it was clear.
How do you Solve 9k+m=6p for k
Answer:
k=[tex]\frac{2p-m}{3}[/tex]
Step-by-step explanation:
9k+m=6p
9k=6p-m
k= [tex]\frac{6p-m}{9}[/tex]
k= [tex]\frac{2p-m}{3}[/tex]
The product of a number m and 6 is no less than 30.
Answer:
x= anything less than 5
Step-by-step explanation:
We know that 5*6 is 30, so x would have to be anything less than five.
Answer:m+6<30
Step-by-step explanation:
Write 2 numbers that cannot be divided evenly by 8 or 9. Write 1 number that can be divided evenly by both 8 and 9.
Answer:
17 and 26 (cannot be divided evenly by 8 and 9)
72 (LCM for 8 and 9)
Step-by-step explanation:
The value of 2 numbers that cannot be divided evenly by 8 or 9 are 17 and 19.
And, The value of 1 number that can be divided evenly by both 8 and 9 is 72.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The value of 2 numbers that cannot be divided evenly by 8 or 9 are,
⇒ 17 and 19
Cleary. Both number cannot divide by 8 or 9.
And, The value of 1 number that can be divided evenly by both 8 and 9 is,
⇒ LCM of {8, 9}
⇒ 72
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Conditional Probability
Yo sup??
P(A|B)=P(A∩B)/P(B)
P(A∩B)=probability of finding a girl and is sophomore
P(B)=probability of finding a sophomore
P(A|B)=9/10
Hope this helps.
Answer:
Step-by-step explanation:
Total number of persons = 37
Number of girl and sophomore= 9
Prob(girl/sophomore) = 9/37
Please this is very urgent!!!!!
39 degrees
51 degrees
129 degrees
180 degrees
Please help!!!
Savannah says that 1 kilogram is equivalent to 1000000 milligrams is savannah correct? Explain
Answer:
Savannah is correct
Step-by-step explanation:
helpppppppppppppp plsss :)
Answer:
i think the answer is a
Step-by-step explanation:
Answer: The answer is C
Step-by-step explanation:
You have to remember to convert the fractions into equal denominators in order to solve it. In this case, it is 12.
A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period?
The rate of change in profit for this time period is $1$$ per month.
Rate of change of profit for this period is $2750 per month
Solution:
Given that,
Profit of $6500 in January and $17,500 in May
To find: Rate of change
Since,
January is the first month of the year (1) while May is the fifth month (5)
Therefore, we get two points
(1, 6500) and (5, 17500)
Using these points we can find the rate of change in profit for this time period
The rate of change using the following formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here from the points,
[tex](x_1, y_1) = (1, 6500)\\\\(x_2, y_2) = (5, 17500)[/tex]
Therefore, rate of change is given as:
[tex]m = \frac{17500-6500}{5-1}\\\\m = \frac{11000}{4}\\\\m = 2750[/tex]
Thus rate of change of profit for this period = $2750 per month
PLS HELP....I WILL MARK YOU BRAINLIEST What is the value of 8(3 + X) when X = 7?
Answer:
80
Step-by-step explanation:
8(3+7)
8*3=24
8*7=56
24+56=80
Answer: 80
Step-by-step explanation: To solve this problem, we first substitute 7 in for x inside the parentheses and we have 8 (3 + 7).
Following your order of operations, you should simplify what's inside the parentheses first. So 3 + 7 simplifies to 10.
Bring down your 8 and you have 8 (10) which equals 80.
What number is 25% more than 84
Answer:
105
Step-by-step explanation:
The number that is 25% more than 84 is 105.
To find 25% more than a given number, one can calculate 25% of that number and then add it to the original number. Here's the step-by-step calculation:
1. First, calculate 25% of 84:
[tex]\[ 25\% \text{ of } 84 = \frac{25}{100} \times 84 = \frac{1}{4} \times 84 = 21 \][/tex]
2. Then, add this value to the original number to find the increased amount:
[tex]\[ 84 + 21 = 105 \][/tex]
Therefore, 25% more than 84 is 105.
Together, two people earn $28,000. One earns$2,000 more than the other. How muchistheSmaller income?
Step-by-step explanation:
Let one person earns $ x
Therefore other earns = $(x + 2000)
According to the given condition:
[tex]x + (x + 2000) = 28000 \\ \\ \therefore \: x + x + 2000 = 28000 \\ \\ \therefore \: 2 x = 28000 - 2000\\ \\ \therefore \: 2 x = 26000\\\therefore \: x = \frac{26000}{2} \\ \\ \therefore \: x = 13000 \\ \implies \: x + 2000 \\ \: \: \: \: \: \: \: \: \: \: = 13000 + 2000 \\ \therefore \: x + 2000= 15000 \\ [/tex]
Hence, smaller income is $13000.
On a scale drawing, a park is 4.5 inches long. The scale is 0.5inch=10 feet. What is the actual length of the park ?
Answer:
90 feet
Step-by-step explanation:
4.5in/0.5in=9
9 times 10 is 90 feet
Answer:
90 feet
Step-by-step explanation:
chevy have some yarn that he wants to use to make hats and scarves. each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. chevy wants to make a total of 15 items. let h be the number of hats chevy makes and s be number of scarves he makes.
Chevy has some yarn that he wants to use to make hats and scarves. Each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. Chevy wants to use 2 kilograms of yarn to make a total of 15 items.
Let h be the number of hats Chevy makes and s be the number of scarves he makes.
Which system of equations represents this situation?
Answer:The system of equations represents this situation are:
h + s = 15
0.2h + 0.1s = 2
5 hats and 10 scarves are made
Solution:From given,
Let "h" be the number of hats Chevy made
Let "s" be the number of scarves made
They made a total of 15 items
Therefore, we get,
h + s = 15 --------- eqn 1
Also given that,
Each hat uses 0.2 kilograms of yarn
Each scarf uses 0.1 kilograms of yarn
Chevy wants to use 2 kilograms of yarn
Therefore, we frame a equation as:
[tex]0.2 \times h + 0.1 \times s = 2[/tex]
0.2h + 0.1s = 2 --------- eqn 2
Thus eqn 1 and eqn 2 represents the system of equations
Let us solve eqn 1 and eqn 2
From eqn 1,
h = 15 - s ------ eqn 3
Substitute eqn 3 in eqn 2
0.2(15 - s) + 0.1s = 2
3 - 0.2s + 0.1s = 2
0.1s = 1
s = 10
Substitute s = 10 in eqn 3
h = 15 - 10
h = 5
Thus 5 hats and 10 scarves are made
19125 people, exactly 75%, what is the total population of the town
Answer:
25500 people
Step-by-step explanation:
We are given;
Number of people is 19125
The percentage representing the number is 75%
We need to determine the total population;
The total population will be 100%
Therefore;
If 75% = 19125 people
Then, 100% will represent;
= (19125 ÷ 75) × 100
= 255 × 100
= 25500 people
Therefore, the total population of the town is 25500 people
Final answer:
To find the total population of the town, divide 19,125 (75% of the population) by 0.75, resulting in a total population of 25,500.
Explanation:
To find the total population of the town when given that 19,125 people represent 75%, we need to use the concept of percentages. The number 19,125 is 75% of the total population, so if we let total population equal 'x', we can set up the equation 0.75x = 19,125. To solve for 'x', we divide both sides of the equation by 0.75.
Therefore, the equation to find the total population is:
x = 19,125 / 0.75
Calculating this gives us:
x = 25,500
So, the total population of the town is 25,500.
Square root of 5 •-4 Square root of 20x
Answer:
[tex] - 40 \sqrt{x} [/tex]
Step-by-step explanation:
We want to simplify:
[tex] \sqrt{5} \times - 4 \sqrt{20x} [/tex]
We rewrite the radicand using prime factorization:
[tex] \sqrt{5} \times - 4 \sqrt{4 \times 5x} [/tex]
This gives us
[tex]\sqrt{5} \times - 4 \sqrt{4} \times \sqrt{5} \times \sqrt{x} [/tex]
Create perfect squares and simplify:
[tex](\sqrt{5} )^{2} \times - 4 \sqrt{4} \times \sqrt{x} [/tex]
[tex]5 \times - 4(2) \sqrt{x} [/tex]
[tex]5 \times - 8 \sqrt{x} = - 40 \sqrt{x} [/tex]
Distance to the earth's center kilometer
Answer:
its 6,371 in kilometers
Solve 6 - x - x = 18
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{Solve: 6 -x- x=18}[/tex]
[tex]\mathsf{Combine\ your\ like\ terms}\\\mathsf{6 -\bf{x - x}\mathsf{= 18}}\\\mathsf{-x-x=-2x}\\\mathsf{Your\ new\ equation: -2x+6=18}\\\\\mathsf{Do\ the\ OPPOSITE\ symbol\ on\ both\ sides\ of\ the\ equation}\\\mathsf{Addition\ opposite\ symbol\ is\ subtraction}\\\mathsf{Subtract\ by\ 6\ on\ your\ sides}\\\mathsf{-2x+6-6=18-6}\\\mathsf{Cancel\ out{6-6\ because\ it\ gives\ us\ 0}}\\\mathsf{Keep:18-6\ because\ it\ helps\ us\solve\ for\ the\ answer}\\\\\mathsf{Next,\ divide\ both\ sides\ by\ -2}[/tex]
[tex]\mathsf{\dfrac{-2x}{-2}=\dfrac{12}{-2}}\\\\\mathsf{Cancel\ out: \dfrac{-2x}{-2}\ because\ it\ gives\ you\ the\ result\ of 1}\\\\\mathsf{Keep:\dfrac{12}{-2}\ because\ it\ gives\ the\ answer\ of\ x}\\\\\\\boxed{\bf{Answer:\mathsf{x=-6}}}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst:)}[/tex]
Which of the following Expressions is not equivalent to -8? a. 2×(-4) b. 4×(-2) c. -4×2 d. -4×(-2)
D
Negative times negative is positive
Solve for v: -4(v - 2) + 3 > -3(v + 9)
Answer:
-4v + 8 > -3v - 9
-v + 8 > -9
-v > -17
v < 17
Answer:
vhgxyghfjugcfydcf
Step-by-step explanation:
what is the mean,mode,median,and range of 5,5,5,6,6,6,7,7,7,7,7
Answer:
median=6, range=2 mean=61 mode=7
the median is the middle which is 6
The range is the lowest-biggest number which would be 2
mean=average
mode is the one that appears most
Answer:
68 / 11 = mean
7 = mode
6 = median
2 = range
Step-by-step explanation:
Mean means the average
Mode means the most common
Median means the middle
Step 1: Find the mean by adding all the values then dividing by the amount of values
5 + 5 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 7 = 68
68 / 11 = mean
Step 2: Find the mode which is the most common
5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7
5 is repeated 3 times, 6 is repeated 3 times, 7 is repeated 5 times
7 = mode
Step 3: Find the median which is the middle
5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7
6 = median because it is in the middle
Step 4: Find the range which is the difference the highest and lowest number
7 - 5 = 2
2 = Range
Which of the following expressions represent the distance between -4 and 1
Answer: i dont see expressions but it would be 5
Step-by-step explanation:
Answer:
|-4-1|
Step-by-step explanation:
i got it right