Answer:
It would be the sum of x and 4
Step-by-step explanation:
Amy wants to fence off a rectangular area that is 24 feet squared in size for a vegetable garden.
She is considering three garden lengths of 6 ft, 8 ft, and 12 ft. She wants to determine which garden would require the least amount of fencing.
Determine the dimensions of the garden that would require the least amount of fencing.
Length
12, 8, or 6ft
Width:
3, 4, or 2ft
Answer:
Let y = length of side parallel to the side with no fence
x = length of each of the other two sides
Then, y+2x = 64. So, y = 64-2x
Area = A = xy = x(64-2x)
The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).
By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.
So, the area is maximized when x = 16 ft
y = 64 - 2x = 32 ft
Maximum area = xy = (16)(32) = 512 ft2
To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.
9/4x -1/2y = -3
Find x and y intercepts
Answer:
x-int: (-12/9, 0)
y-int: (0, 6)
Step-by-step explanation:
x-int ==> on x-axis when y=0
y-int ==> on y-axis when x=0
9/4x -1/2y = -3
x-int: 9/4x -1/2(0) = -3
9/4x = -3
9x/4 = -3
9x*4/4=-3*4
9x=-12
x=-12/9 ==> x-int: (-12/9, 0)
y-int: 9/4(0) -1/2y = -3
-1/2y = -3
1/2y=3
y/2=3
y=6 ==> y-int: (0, 6)
Determine whether the given conclusion is based on inductive or deductive reasoning.
If Beth turns in her report early, she receives extra credit. Beth turned in her report early. She concludes that she will receive extra credit.
The given conclusion is deductive reasoning.
What are Inductive reasoning and Deductive Reasoning?Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.
Given the statements; If Beth turns in her report early, she receives extra credit.
Beth turned in her report early.
She concludes that she will receive extra credit.
From the sentences, the first sentence is a general statement, the second statement is a specific statement. And, the third statement is a conclusion statement.
Therefore, the given conclusion is deductive reasoning.
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Distance between the points
(a cos (0 + 25+), a sin (
3
2π
3
and
(acos (0+), asin (0+5)) is
3
3
1) 2a
2) 3a
3) a/2
4) a
Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.
Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].
Putting values in above formula:
AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]
AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]
AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]
AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]
AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]
AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]
AB= [tex]a\sqrt{2-1} =a[/tex]
Hence, the distance between the two given points is [tex]a[/tex].
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Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=3, b=-7
Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=3, b=-7
How to write the equation in slope-intercept form?
Given:
m=3(slope)
b=-7(y -intercept)
The slope-intercept form is given by,
y=mx+b
y=3x-7
Thus, y=3x-7 is the slope-intercept form.
How to rewrite the equation in standard form?
Standard form is given by,
Ax+By=C
Since, slope-intercept form is y=3x-7
⇒3x-y=7
Thus,3x-y = 7 is the standard form.
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5/25, 25%, and 0.3 ordered least to greatest
Answer:5/25,25, 0.3
Step-by-step explanation:
Answer:
5/25 , 25% , 0.3
Step-by-step explanation:
first let's change everything into decimals
0.3 is already a decimal
25% can be changed into 0.25
5/25 can be changed into a percentage first like 25%
so:
[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex] (you multiply both sides by 4 because you need to have the denominator as a 100 and 25 x 4 = 100)
[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{100}[/tex]
this means that the percentage is 20% now lets change that into a decimal like we did with 25% earlier:
20% = 0.20
we can then order everything from least to greatest:
0.20 , 0.25 , 0.3
or
5/25 , 25% , 0.3
y varies directly with x .
If y=25 when x=15 , find y when x=6 .
The required value of y is 10.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx, —-- 1
Now, find k for given x = 15 and y = 25, we need to put these values in equation 1, i.e.
25 = k(15)
k = 25 / 15
k = 5 / 3
Further calculate y for given x = 6 and constant of proportion = 5/3 i.e.
y = (6)(5 / 3)
y = 10
Hence, the required value of y is 10.
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12. Let f(x)= -8x+5. Find f(1/2)
13. Let g(x) = -x^2+5x+2. Find and simplify g(-3)
14. Let f(x) = -5x+6. Find and simplify f(x+3)
f(x+3) =
What is the sum of each finite series?
b. Σ ⁴ n=1 n³
The sum of the given finite series is 100
The summation notation tells us how to sum each term in a series.
Example:
[tex]\sum\limits^5_{n=1} {3n+1}[/tex]
means we need to evaluate the sum of (3n+1) as n moves from 1 to 5. Here 1 is the lower limit, while 5 is the upper limit.
The given series is:
[tex]\sum\limits^4_{n=1} {n^{3}}[/tex]
Expand this series:
[tex]\sum\limits^4_{n=1} {n^{3}}=1^{3}+2^{3}+3^{3}+4^{3}[/tex]
1³ = 1
2³ = 8
3³ = 27
4³ = 64
Hence,
1³ + 2³ + 3³ + 4³ = 1 + 8 + 27 + 64 = 100
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does someone mind helping me with this question? Thank you!
Answer:
84 Meters^3
Step-by-step explanation:
Since this is a three dimensional object, you need to have an exponent of 3
Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.
a. Find the probability that 0scar sits between Morgan and Phil.
If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.
Probabilitya. 0scar sits between Morgan and Phil
First step is to calculate the total distance
Total distance=2 feet+4 feet+3 feet
Total distance=9 feet
Since Morgan is 2 feet from Phil.
Hence,
P(Oscar sits between Morgan and Phil)=2/9
b. Oscar sits between Phil and Tyreese.
First step is to calculate the distance between Phil and Tyreese
Distance= 4 feet + 3 feet
Distance =7 feet
Hence,
P(Oscar sits between Phil and Tyreese)=7/9
Therefore If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.
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The complete question is:
Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.
a. Find the probability that 0scar sits between Morgan and Phil.
b. Find the probability that Oscar sits between Phil and Tyreese.
Find the value of x .
24=2 x √2
Answer:5
Step-by-step explanation:
B
Find AB in AABC.
Round to the nearest tenth.
65°
81°
C
A
10
Answer:
(10 *sin(81))/sin(34)=17.66>>>17.7
Determine whether each number is a solution of the inequality below.
Please help determine whether A, B and C (at the top) is a solution.
Answer: yes it is a solution
g(x) =
2x²-8
x²-x+6
IN
2
Answer:
Use the formula L(x)=f(a)+f'(a)(x−a) to find the linearization.
L(x)=2
Step-by-step explanation:
Solve each equation or inequality.
2-3 x<11
After solving the equation, x < -3 is the value of inequality 2-3 x<11
⇒ 2-3x < 11
⇒ -3x < 11 - 2
⇒ -3x < 9
⇒ x < -9/3
⇒ x < -3
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Given f(x)= 3 x 2 + 2, find the value of f(−2)
Answer:
f(- 2) = 14
Step-by-step explanation:
substitute x = - 2 into f(x)
f(- 2) = 3(- 2)² + 2 = 3(4) + 2 = 12 + 2 = 14
A large cheese pizza costs $11.45. A premium
topping on the large pizza costs $2.75, while a
standard topping on the large pizza costs
$1.75. Beverly orders a large cheese pizza
with 3 premium toppings and 4 standard
toppings. How much will the pizza cost?
Simplify.
√6 / √3 . √8 / √3
The simplified value of the given expression is √6√8 / 3.
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(√6 / √3) (√8 / √3) we have a common denominator.
√6 √8/(√3)²
√6√8 / 3 is the result.
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x+1/7y=4 y=3x-2 how do you find x and y
The values for the variables 'x' and 'y' are (3,7).
According to the question, to calculate the value of 'x' and 'y' then equate both the equations.
The given expressions are:
Equation (1): x + (1/7)y = 4 ⇒ 7x + y = 28
Equation (2): y = 3x - 2
Solving equation (1) and equation (2) by substituting the value of the 'y':
Therefore, 7x + 3x - 2 = 28 ⇒ 10x = 30 ⇒ x = 3
Now: y = 3(3) - 2 = 7
Hence, the values are: x = 3 and y = 7.
What is simplification?
Simplification of an expression can be defined as by making the complicated expression as less complicated. And through this method, it become easy to solve it and find the correct answer.
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Function: g(x) = 2x² - 8
For x ≥ 0, the inverse function is f(x)=
For x ≤ 0, the inverse function is d(x)= -√√x +4
X
-8
0
10
f(x)
0
r
S
d(x)
q
-2
t
q=
= ין
=√√₂x + 4
S=
t =
1
870
Answer:
(5,15)
Step-by-step explanation:
we know that c=12 is 5 so your answer is 5,15
Question
Evaluate the expression when a=4, b=−5, and c=−8.
a+b=
???
Answer:
a+b= (-1)
Step-by-step explanation:
4+(-5)=
4-5= (-1)
Answer:
-1
Step-by-step explanation:
a = 4
b = -5
4 + -5 = -1 ( +- turns to -)
Jackson eats 1/4 part of a banana in 1/2 minute. How much time will he need to eat a full banana?
a. Write an equation of the line through (-2,6) with slope 2
Answer:
Step-by-step explanation:
Point slope form:
y - y1 = m(x-x1)
y - 6 = 2(x + 2)
y - 6 = 2x + 4
y = 2x +10
A scientist collected a 1 liter sample of sea water and then examined it to see how many viruses, bacteria, phytoplankton, and protozoa it contained, The scientist found that there were 5x10^5 protozoa and 3x10^9 viruses in the sample. How many times greater was the number of viruses than the number of protozoa that were found in the sea water sample? Estimate by rounding to the nearest whole number
In the sample that is used number of viruses were 6000 times greater than the number of protozoa.
Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population.
It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.In situations where it is impractical to assess the complete population, sampling offers insights and is more affordable and quicker than doing so.Given the number of protozoa in the sample as 5 × 10⁵ and the number of viruses in the sample as 3x10⁹.
This is represented in the scientific notation.
To calculate the number of times the viruses in the sample is more than the protozoa in the sample we divide the amount of virus by the amount of protozoa.
∴ (3x10⁹) ÷ (5 × 10⁵)
= 6000
Therefore in the sample that is used number of viruses were 6000 times greater than the number of protozoa.
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PLEASE HELP
ALSO DO THE CHECK UR BOX WORK AND SHOW ME
The coordinates of the vertices of a triangle are (2, 3), (5, 1), and (6, 4). After one reflection, the coordinates of the vertices of the triangle's image are (2, -3), (5, -1), and (6,-4). Over what line has the triangle been reflected? Select the answer from the drop-down list to correctly complete the sentence. is it x-axis or y-axis
Answer: x-axis
Explanation:
The point (2,3) moves to (2, -3)
The x coordinate stays the same, but the y coordinate flipped from positive to negative. Therefore, the rule used is [tex](\text{x},\text{y}) \to (\text{x}, -\text{y})[/tex] which is a reflection over the horizontal x axis.
Find the reciprocal of 3/5
How do I solve this equation 10=-9-x
Answer:
Step-by-step explanation: 10=-9-x > add 9 to 10 > 19=-x> divide 19 by -x> x=-19
Alexa has 38 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 140 square meters. List each set of possible dimensions (length and width) of the field.
The possible dimensions ( width and length) plot of land are 9.5 m and 19 m.
What is defined as the rectangle?A rectangle is a confined two-dimensional structure with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel.
Area of a rectangle
area of rectangle = l×w
where, l = length and w = width.
Thus, the perimeter for 2 side of width and 1 side of length is;
perimeter = 2w+ l
Perimeter of river = 38 m.
38 = 2w + l
l = 38 - 2w
Hence, Put the value of l in the area.
area = w(38 - 2w)
The area of the land is 140 sq.m.
140 = 38w - 2w²
-2w² + 38w - 140 = 0
-w² + 19w - 70 = 0
The equation is in the form of quadratic. Thus use the relation of coefficients and the roots to evaluate the width.
w = - b / a
Comparing the coefficients;
where,
a = -1
b = 19
w = - 19 / 2( -1)
w = 9.5 meters
Then,
l = 38 - 2w
l = 38 - 2(9.5)
l = 19 meters
Therefore, the dimensions of the plot of land are 9.5 meters and 19 meters.
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