You have d dollars to buy fence to enclose a rectangular plot of land. the fence for the top and bottom costs $a per foot and for the sides it costs $b per foot.
To find the dimensions of the plot with the largest area.
Total Money = D dollars
Total cost for top and bottom fence = $4(2x)
Total cost for sides fence = $8(2y)
Hence total cost of fencing = 4(2x)+8(2y) = 8x+16y
C = 8x+16y
Given cost (c) = D dollars
D = 8x+16y
Now Area of the plot A = xy
A = xy is optimizing function and D = 8x+16y
= [tex](\frac{D-16y}{8})=x[/tex]
A = [tex]\frac{D-16y}{8}y[/tex]
For A to be maximum [tex]\frac{dA}{dy}=0[/tex]
A = [tex]\frac{D}{8}y-\frac{16}{8}y^{2}[/tex]
[tex]\frac{dA}{dy} = \frac{D}{8}-\frac{16}{8}(2y)[/tex]
[tex]\frac{dA}{dy} = \frac{D}{8}-4y[/tex]
[tex]\frac{dA}{dy} = 0 = \frac{D}{8}-4y=0[/tex]
[tex]\frac{D}{8} = 4y = y = \frac{D}{32}[/tex]
Now [tex]\frac{d^{2}A }{dy^{2}} = -4 = -ve number[/tex]
for y = [tex]\frac{D}{32}[/tex] area is maximum
[tex]x = \frac{D-16y}{8} = \frac{D-16 (\frac{D}{32} )}{8} = \frac{D}{16}[/tex]
Say the top and bottom dimensions are = [tex]\frac{D}{16}[/tex]
Sides dimensions are = [tex]\frac{D}{32}[/tex]
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Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x 4 - 81) (x - 3).
The final polynomial equation after synthetic division is [tex]x^5-3x^4-81x+243[/tex]
We need to solve;
Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.
The polynomial equation given is;
[tex]\left(x^4-81\right)\left(x-3\right)[/tex]
By using synthetic division;
⇒ [tex]x^4x+x^4\left(-3\right)-81x-81\left(-3\right)[/tex]
[tex]x^5-3x^4-81x+243[/tex]
→ The required final equation in descending powers of x is [tex]x^5-3x^4-81x+243[/tex] .
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Help rqqqqqqqqqqqqqqqqqqqqqqqqqq thanks
Planet B has the larger mass. The mass of planet B is 50 times as large as the mass of planet A.
Mass of planet A = A = 8 * [tex]10^{23}[/tex]
Mass of planet B = B = 4 * [tex]10^{25}[/tex]
[tex]\frac{A}{B}=\frac{8 * 10^{23} }{4*10^{25} }[/tex]
= [tex]\frac{2}{100}[/tex]
= [tex]\frac{1}{50}[/tex]
50A = B
Hence, mass of Planet B is 50 times mass of planet B.
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Solve for x: 138 = 6 + 3(6x + 2)
Answer:
x=7
Step-by-step explanation:
Use the Distributive Property to simplify the equation.
Multiply 5c(9 − 4c).
Answer:
45c−20c2
Step-by-step explanation:
have great day
In triangle WXY , angle X cong angle W.; WX = 10 and YW = 8 Find XY .
the average gas mileage of a certain model car is 30.0 miles per gallon. if the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon.
By using normal distribution, it is obtained that the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is
[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]
where, z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
For x = 29.8, z = [tex]\frac{29.8-30}{0.75}[/tex] = -0.27
For x = 30.2, z = [tex]\frac{30.2-30}{0.75}[/tex] = 0.27
so, P(29.8 < x < 30.2) = P(-0.27 < z < 0.27)
= 2 [tex]\times[/tex] P(z < 0.27)
= 2 [tex]\times[/tex] 0.1064
= 0.2128
Probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128
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Select the correct answer. A line passes through point C and is parallel to AB ⟷ . What equation represents this line?
The line parallel to line AB will have the same slope with different
y-intercepts.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines parallel to each other have the same slope with a different y-intercept.
Suppose the line AB has an equation y = mx + b.
∴ The line parallel to line AB will have an equation y = mx + c.
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Answer:
y=1/2x-3
Step-by-step explanation: if you are using edmentum this is correct.
please help what is the solution
Answer:
1 < x ≤ 6 is the solution
Step-by-step explanation:
Given
6 < x + 5 ≤ 11
Solution
Subtract 5 from the 3 terms. You do this so you can isolate x
6 - 5 < x + 5 - 5 ≤ 11 - 5
1 < x≤ 6
x lies between 1 and 6.
ܘܐ
a. x =
b. x =
54%
54°, y = 54°
27°, y = 108°
c. x = 27°, y = 54°
d. x = 54°, y = 108°
Answer:
d
Step-by-step explanation:
angles on the circle subtended by the same arc are congruent
54° and x° are subtended by the same arc y , then
x = 54°
the measure of an inscribed angle is half the measure of its intercepted arc.
x and 54 are inscribed angles intercepted by arc y , then
y = 2 × 54° = 108°
Factor completely.
x² − 8x+16
(-4)²
(z+4)²
2(z + 2)?
2(x - 2)²
Answer:
(x-4)^2 [I assume the (z+4)² option was mistyped. Who wants zzzzzzzzz?]
Step-by-step explanation:
x² − 8x+16
Lok for a pattern that would allow us to fill in the missing numbers in
(x+a)*(x+b)
We know that a and b must equal +16 when multiplied together. We also know their sum must be -8.
a*b = 16
a+b = -8
Is there anything that ties these numbers together? The number 4 comes to mind: 8 and 16 are known to be friendly to 4. We need the sum to be -8, so lets make the 4 negative and put it into both expressions.
(-4)+(-4) = -8 YES
(-4)*(-4) = 16 YES
Assinging -4 to both a and b produces the factored expression:
(x-4)*(x-4) = x² − 8x+16 YES
4. Find the positive square root, then the negative square root of each of the following numbers:
16
0.36
25
0.64
1.21
0.25
1.44
2 500.
The positive square root, then the negative square root of each of the following numbers are:
4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.
Given,
In the question:
Find the positive square root, then the negative square root of each of the following numbers:
The numbers are given as:
16, 0.36, 25, 0.64, 1.21, 0.25, 1.44, 2500
Now, According to the question;
Square Root:
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } square root of, end square root . Finding the square root of a number is the opposite of squaring a number.
We have to find the Arithmetic Square Root Method
and, Add a minus sign to the Arithmetic root.
a) [tex]\sqrt{16}[/tex] = 4
[tex]-\sqrt{16}[/tex] = -4
b) [tex]\sqrt{0.36}[/tex] = 0.6
[tex]-\sqrt{0.36}[/tex] = -0.6
c) [tex]\sqrt{25}[/tex] = 5
[tex]- \sqrt{25}[/tex] = -5
d) [tex]\sqrt{0.64}[/tex] = 0.8
[tex]-\sqrt{0.64}[/tex] = -0.8
e) [tex]\sqrt{1.21}[/tex] = 1.1
[tex]-\sqrt{1.21}[/tex] = -1.1
f) [tex]\sqrt{0.25}[/tex] = 0.5
[tex]-\sqrt{0.25}[/tex] = -0.5
g) [tex]\sqrt{1.44}[/tex] = 1.2
[tex]-\sqrt{1.44}[/tex] = -1.2
h) [tex]\sqrt{2500}[/tex] = 50
[tex]-\sqrt{2500}[/tex] = -50
Hence, The positive square root, then the negative square root of each of the following numbers are:
4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.
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Find the value of x.
Answer:
x = 6Step-by-step explanation:
According to triangle proportionality theorem we have equal ratios:
(6x - 1 - 14)/14 = (15 - 6)/6(6x - 15)/14 = 9/6(6x - 15)/14 = 3/22(6x - 15) = 3*1412x - 30 = 4212x = 72x = 6The value of x will be 6 units.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown is figure.
Now,
By the definition of triangle proportionality theorem, we get;
⇒(6x - 1 - 14)/14 = (15 - 6)/6
Solve for x as;
⇒ (6x - 15)/14 = 9/6
⇒ 6x - 15 = 9×14/6
⇒6x - 15 = 21
⇒ 6x = 21 + 15
⇒ 6x = 36
⇒ x = 6 units
Thus, The value of x will be 6 units.
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Which expression has a value of -18?
Answer:
C. 34 - 16 = 18
ALSO
D. -4 - (-22)
-4 + 22 = 18
Step-by-step explanation:
This is the REAL Question!
Which expressions have a value of 18?
Choose all answers that are correct.
A. –3 – 21 B. 7 – (–25) C. 34 – 16 D. –4 – (–22)
) dave will swim one day, run one day, and bike another day in a week. he does at most one activity on any particular day. how many ways are there for him to select his workout schedule (i.e. which activities he does which days)?
First Dave picks his swimming day, then his running day, and then his biking day. Since each activity is different, the order in which he selects the days matters. Therefore the number of selections is P(7, 3).
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 1/2.
Here,
He does 3 activities in 7 days,
P(7,3) is the ways to select the schedule.
Dave chooses his swimming, running, and biking days in that order. The sequence in which he chooses the days is important because each activity is distinct. Consequently, P is the number of choices (7, 3).
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During one day in a hardware tore, 37 people came in and made a purchae, and 13 people looked around but didn’t purchae anything
The required ratios: a. Purchasers to non purchasers is 37:13 b. Non Purchasers to purchasers is 13:37 c. Purchasers to total customers is 37:50 d. Non Purchasers to total customers is 13:50
So, based on the information-
Non purchasers = 13
Purchasers = 37
Total customers = 50
Finding ratio by keeping the values as per the requirement -
a. Purchasers to non purchasers = 37:13
b. Non Purchasers to purchasers = 13:37
c. Purchasers to total customers = 37:50
d. Non Purchasers to total customers = 13:50
Hence, the ratios are a. 37:13, b. 13:37, c. 37:50 and d. 13:50.
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Determine the length of the line egment hown. Line egment from negative 5 comma 5 to 3 comma negative 1
6 unit
8 unit
10 unit
36 unit
The length of line segment is 10 units.
Writing the start and end points of line segment in (x, y) axis. First point = (-5, 5) and second point = (3, -1).
To calculate the line segment the formula to be used is -
d = ✓([tex] x_{2}[/tex] - [tex] x_{1}[/tex] )² + ([tex] y_{2}[/tex] - [tex] y_{1}[/tex] )²
Keep the values in formula
d = ✓(3 - (-5))² + (-1 - 5)²
d = ✓(3 + 5)² + (-6)²
Performing subtraction and addition based on sign
d = ✓8² + 36
Taking square on Right Hand Side of the equation
d = ✓64 + 36
Performing addition on Right Hand Side of the equation
d = ✓100
Taking square root on Right Hand Side of the equation
d = 10 units
Hence, the distance is 10 units.
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5/6 divited by -3 1/3
Answer:
0.00896057348
Step-by-step explanation:
maybe I think I read it right but don't count on me
Answer: 1/4
Step-by-step explanation: If you divide them both you get 0.25 and that's just 1/4. Hope it helps.
The price of a technology stock was $9.45 yesterday. Today, the price rose to $9.61 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase in the price of a technology stock is 1.69%.
According to the question,
We have the following information:
The price of a technology stock was $9.45 yesterday. Today, the price rose to $9.61.
We know that following formula is used to find the percentage increase:
Percentage increase = 100*(final price- initial price)/initial price
Percentage increase for the technology stock = 100*(9.61-9.45)/9.45
Percentage increase for the technology stock = 100*0.16/9.45
Percentage increase for the technology stock = 16/9.45
Percentage increase for the technology stock = 1.69%
Hence, the percentage increase in the price of a technology stock is 1.69%.
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If 21 less than 11 times a number results in 7 times a number decreased by 29, what is the number?.
The number is -2. By using the concept of Linear Equation we get the number -2 as Answer of this question.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
Let the number be ‘x’
So According to the Question,
The number that is 11 times less than 21 which results in seven times of the number decreases by 29 can be written in the numerical form as
11x – 21 = 7x- 29
11x – 7x = -29+21
4x = -8
x = -8/4
x = -2
So that’s how we got the value of the x = -2
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What is the periodic interest rate for an account that is billed monthly with an APR of 32.99%? Round your answer to the nearest hundredth.
2.75%
3.29%
0.28%
2.74%
The periodic interest rate for an account that is billed monthly with an APR of 32.99% will be 2.74%
Periodic interest rate is rate of interest over a short period of time. It is found by dividing APR ( annual percentage rate ) by the period of time given to us.
In this question it is given to us that the account is billed monthly so
periodic interest rate = 32.99 / 12
= 2.74%
Therefore periodic interest rate will be 2.74 for this account.
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a food marketing institute found that 32% of households spend more than $125 a week on groceries. assume the population proportion is 0.32 and a simple random sample of 145 households is selected from the population. what is the probability that the sample proportion of households spending more than $125 a week is less than 0.3?
Using the normal distribution, the probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.
Normal distribution refers to a continuous probability distribution wherein values lie in a symmetrical fashion mostly centered around the mean. In a normal distribution, the probability is calculated using the z-score of a measure X. A Z-score refers to a numerical measurement that defines a value's relationship to the mean (of a group of values).
In order to determine the probability of the sample proportion, the z-score of a measure X is determined.
z-score = (X - µ)/σ where µ is the mean and σ is the standard deviation.
The standard deviation σ = √(p(1-p)/n
From the given data:
n = no of random sample = 145
p = probability of success (household spending more than $125) = 0.32
Hence,
σ = √((0.32(1-0.32)/145) = 0.0387
Calculating the z-score when X = 0.3
z-score = (0.3 – 0.32)/0.0387 = -0.516
From the table, the probability of z = -0.516
P(X<z) = 0.30293 or 30.29%
The probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.
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Whats the answer to 5/8-2/8?
Answer:
0.375
Step-by-step explanation:
Carlos graphed the system of equations that can be used to solve x cubed minus 2 x squared + 5 x minus 6 = negative 4 x squared + 14 x + 12.
The graph of the given equations is (see in attachments). The roots are (-3,-2,3)
From the question, we have
x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
The roots are (-3,-2,3)
Graph:
A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.
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Answer:
A on edge
Step-by-step explanation:
because i said so
What is the sum of (x - 8x² - 15) and (2 + 12x - 3x²)?
A -5x² - 11x - 17
B -112² + 13x - 13
C 11r2 + 11x - 17
D 2x² + 4x - 18
Answer:
-11[tex]x^{2}[/tex] + 13x- 13
Step-by-step explanation:
(x - 8x² - 15) + (2 + 12x - 3x²)
(x + 12x) + (- 8x² - 3x²) + (- 15 + 2) [Combine like terms]
-11[tex]x^{2}[/tex] + 13x- 13
Identify the congruent triangles by a triangle congruent statement.
Answer:
If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.
Luigi uses 39 mozzarella pearls (small cheese balls) for every 6 pizzas they make.
Complete the table using equivalent ratios.
Pearls
39
13
Pizzas
6
4
The equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.
What is the ratio?
A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)
Luigi uses 39 mozzarella pearls for every 6 pizzas they make.
So the equivalent ratio would be 39/6
= 13:2
And similarly, Luigi uses 13 mozzarella pearls for every 4 pizzas they make.
So the equivalent ratio would be 13/4
= 13:4
Hence, the equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.
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A tudent olve the following equation and determine that the olution i −2. I the tudent correct? Explain. 3
a 2
−
6a
a2 − 4
=
1
a − 2
a = -2 is the value of linear equation .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Step 1 - Write the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 2 - rewrite the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 3 - Take the LCM.
3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4
Step 4 - Further simplify the above expression
3a - 6 - a - 2/a² - 4 = 6a/a² - 4
Step 5 - Cancel out the denominator of both sides and then further simplify.
2a - 8 = 6a
a = -2
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The complete question is -
A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.
3/a + 2 − 6a/a2 − 4 = 1/a − 2
If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The largest Volume of the box possible is 4000 cm³ .
In the question ,
it is given that
the box has a square base ,
let the length and width of the box = "x" , because it is a square
let the height of the box [tex]=[/tex] h
the total surface area of the box = 1200
also the total surface area with open top is = x² + 4xh
So , x² + 4xh = 1200
h = (1200 - x²)/4x
According to the question ,
the volume of the box = x²h
Substituting the value of h = (1200 - x²)/4x ,
we get ,
Volume = x² × (1200 - x²)/4x
V = (1/4)(1200x - x³)
to Maximize the volume dV/dx = 0
(1/4)(1200 - 3x²) = 0
1200 - 3x² = 0
3x² = 1200
x² = 400
x = -20 , +20
length cannot be in negative , hence x = 20 ,
So , Volume = (1/4)[1200(20) - 20³]
= 4000 cm³
Therefore , The largest Volume of the box possible is 4000 cm³ .
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how do you write an=an-1+6;a1=9 in explicit formula
an=an-1+6, written in explicit formula when a = 9 is aₙ = 9n+5
How to write an arithmetic sequence explicit formula?
An explicit formula is given as aₙ= a + (n - 1) d
where,
aₙ = nth term of the arithmetic sequence
a = the first term of the arithmetic sequence
d = the common difference
Given: aₙ = an-1+6 ;a1= 9
Substitute a = 9 into the equation:
aₙ = 9n-1+6
aₙ = 9n+5
Therefore, an=an-1+6, when a = 9 written in explicit formula, is aₙ = 9n+5
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In the diagram below, FG = 10.9, FH = 6.5, and GD = 9.1. Find the length Round your answer to the nearest tenth if necessary.
