Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answers
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
Related Questions
For d the question is asking after four months, the heat is turned off. The excess amount, electricity from the solar panels begins to build back up according to the function. E(d)=38d+500. How do you interpret the 38 in the 500 and this model, we’re doing our presents the number of days since the heat was turned off. How would I solve this?
Answers
From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The standard equation of a straight line is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let E represent the electricity from the solar panels after d days.
Since:
E(d) = 38d + 500
The y intercept is 500 and the slope is 38
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Find the difference between -14w - 3 and 5w.
A -9 w - 3
B -19 w + 3
C -19 w - 3
D -22 w
Quick pls
Answers
Answer:
c
Step-by-step explanation:
cause -14w-3-(5w)
-14w-5w-3
-19w-3
(HELP ASAP) ABC Is Isosceles m
Answers
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
Pls help me, giving brainliest 50 POINTS!
Pls show your work and not only your answers pls
Answers
9) LCM = 36; GCF = 3
10) LCM = 108; GCF = 6
11) LCM = 48; GCF = 4
Explanation:
9)
36 = 2 x 2 x 3 x 3 = 2² x 3²
3 = 3
12 = 2 x 2 x 3 = 2² x 3
LCM = 2 x 2 x 3 x 3 = 36
GCF = 3
10)
6 = 2 x 3
54 = 2 x 3 x 3 x 3 = 2 x 3³
12 = 2 x 2 x 3 = 2² x 3
LCM = 2 x 2 x 3 x 3 x 3 = 108
GCF = 2 x 3 = 6
11)
16 = 2 x 2 x 2 x 2 = 2⁴
8 = 2 x 2 x 2 = 2³
12 = 2 x 2 x 3 = 2² x 3
LCM = 2 x 2 x 2 x 2 x 3 = 48
GCF = 2 x 2 = 4
I would appreciate it if you mark my answer as brainliest.
Please help I'm currently very desperate.
Answers
A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.
What is the explanation of the above transformation?Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.
Hence the first sequence of reflection was such that:
∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.
Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.
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If the sales tax rate is 5% in Texas, then how much sales tax would you pay in Houston for a $52 bag of dog food?
Please answer quickly!
Thank you ^^
Answers
The cost of the sales tax in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60
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 ,
The sales tax percentage in Texas = 5 %
= 5 / 100
= 0.05
The cost of 1 bag of dog food in Houston = $ 52
Now ,
The sales tax cost is calculated by the equation ,
The sales tax cost =
Sales tax percentage in Texas x cost of 1 bag of dog food in Houston
The sales tax cost = $ 52 x 0.05
= $ 2.60
And , the total cost of 1 bag of dog food = cost of 1 bag of dog food in Houston + sales tax cost
Total cost of 1 bag of dog food = $ 52 + $ 2.60
= $ 54.60
Therefore , the sales tax cost is $ 2.60
Hence , the sales tax cost to pay in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60
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A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-5, 3). What is the vertex of the function defined as g(x) = f(x) + 2?
Answer:
Submit Answer
Answers
Vertex of g(x) is: (-2, -4)
What is vertex?An element of a line is a line segment. A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle. Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question:
Vertex form of a quadratic function:
f(x) = (x - h)² + k
We have (h, k) = (3, -4)
The function f(x) is:
f(x) = (x - 3)² - 4
The function g(x) is: g(x) = f(x + 5) =
(x + 5 - 3)² - 4 = (x + 2)² - 4Vertex of g(x) is:(-2, -4)
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litterly help asap
The retail price of a golf club is $342. If the golf store has marked up the price by $42, what is the markup rate?
Answers
A golf club costs $342 at retail. The markup rate is 71.4% if the golf store has increased the price by $42.
What is meant by markup rate?The markup percentage is the difference between what an item costs the seller and what the customer pays. The greater the markup, expressed as a percentage of the cost, the greater the profit. While there is no "ideal" markup percentage, most businesses set it at 50%. A 50 percent markup, also known as a "keystone," means you are charging a price that is 50% higher than the cost of the good or service. Both terms are used to help determine profitability, but they are not the same! The markup is the percentage difference between a product's selling price and its cost.Given,
The difference in prices is $342 - $42 = $300
So, we need to find what percentage of 42 is 300
We do this by dividing: 300/42 = 7.14
which is 71.4 %.
So, the markup is 71.4 %.
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Write the slope-intercept form for the equation of a line with slope m = -9 and y-intercept (0, 5).
The equation of this line is
Answers
The equation of the line is ,y= -9x+5.
What is an equation?A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.Acc to our question-,
We should use the slope-intercept formula to solve this problem.
The point-slope formula states:= [ y = mx + c]
Where m is the slope and c is the y-intercept for the point (0,y1)
Substituting the information provided we get the equation: y= -9x+5.
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Apples cost 1.85 per kilogram
Work out the cost of 1.6 kilogram of apples
for 20 points
Answers
Answer:
1.6 kg = $2.96
Step-by-step explanation:
The given statement is,
→ 1 kg of apple = $1.85
→ a = 1.85
Now the cost of 1.6 kg of apple is,
→ 1.6 × a
→ 1.6 × 1.85
→ $2.96
Hence, 1.6 kg of apple is $2.96.
Find the volume of the rectangular prism.
8 m
8 m
8 m
Answers
Answer:
Step-by-step explanation:
I believe that the volume of the rectangular prism is 512.
Explanation: V = whl = 8 · 8 · 8 = 512
V=Volume
W= Width
H= Height
L= Length
Complete the following ratios: Current assets = $13,000 Inventory = $4,400 Current liabilities = $10,000 Net income = $7,700 Net sales = $24,400 A. Profit margin on net sales (round to nearest tenth percent) B. Acid test (round to nearest tenth percent.)
Answers
The completion of the following accounting ratios is as follows:
A. Profit margin on net sales is 31.6%.
B. Acid test is 86.0%.
What are accounting ratios?Accounting ratios enable financial analysts to understand the relative magnitude of one financial statement account to another.
By their nature, accounting ratios compare or represent an entity's financial performance or position in relative terms.
Current assets = $13,000
Inventory = $4,400
Current liabilities = $10,000
Net income = $7,700 Net sales = $24,400
The profit margin on net sales = Net Income ÷ Net Sales x 100
= $7,700 ÷ $24,400
= 31.6%
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($13,000 - $4,400) ÷ $10,000
= 0.86
= 86%
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Which expression is equivalent to
-2 + 4/5h -1
Answers
Answer:
1/2=0.5
Step-by-step explanation:
-2+4/5°-1=1/2
The price of a technology stock was $9.69 yesterday. Today, the price fell to $9.56. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answers
Answer:
1.3% decrease
Step-by-step explanation:
% change = (9.69 - 9.56) / 9.69) x 100 = 1.3% decrease
9.69-9.56 = 0.13
0.13/0.69= 0.0134158972
Multiply by 100 and you get 1.34158927
Round to nearest tenth and you get = 1.3%
Therefore, the percentage decrease is 1.3
The temperature dropped 2 f every hour for 6 hours.what total number of degrees the temperature changed in the 6 hours?
Answers
The total number of degrees the temperature changed in the 6 hours is 12°F
Here,
The temperature dropped 2°F every hour for 6 hours.
We have to find,
The total number of degrees the temperature changed in the 6 hours.
Fahrenheit is a scale for measuring temperature, in which water freezes at 32 degrees and boils at 212 degrees. It is represented by the symbol ° F.
Now,
The temperature dropped 2°F every hour for 6 hours.
1 hour = 2°F
6 hour = 6 x 2 = 12°F
Hence, The total number of degrees the temperature changed in the 6 hours is 12°F.
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(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Answers
Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].
Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]
Perimeter = a + b + c
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
s = [tex]\frac{a+b+c}{2}[/tex]
Given, B(3,2), C(1,-2), F(-3,5).
BC = a = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]
= [tex]\sqrt{2^{2} +4^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= [tex]\sqrt{20}[/tex]
= 4.47 units
CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]
= [tex]\sqrt{4^{2} +7^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= [tex]\sqrt{65}[/tex]
= 8.06 units
BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]
= [tex]\sqrt{6^{2} +3^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
= 6.71 units
Perimeter = a + b + c
= 4.47 + 8.06 + 6.71
= 19.24 units
s = [tex]\frac{a+b+c}{2}[/tex]
= [tex]\frac{19.24}{2}[/tex]
= 9.62
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]
= [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]
= [tex]\sqrt{224.91}[/tex]
= 14.99
≈ 15 [tex]units^{2}[/tex]
Hence, perimeter is 19.24 units and area is 15 [tex]units^{2}[/tex].
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Andrew solved the following inequality, and his work is shown below:
−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≤ 9
What mistake did Andrew make in solving the inequality?
Answers
Answer:
Andrew failed to change the direction of the inequality
Step-by-step explanation:
You want to know the mistake in Anderw's work solving the inequality ...
−4(x + 8) + 25 ≤ −2 + 1(x − 50)
Solution−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≥ 9
Andrew's mistake was failing to reverse the inequality symbol when dividing by a negative number (-5) at the last step.
__
Additional comment
The last steps of the solution could be written ...
-5x ≤ -45
45 ≤ 5x . . . . . . . add 5x+45 to both sides
9 ≤ x . . . . . . . . . divide by 5 (no reversal of ≤ is needed)
Find the Surface Area for the following:
(Use 3.14 for . Do not round and do not type your units.)
Surface Area = ______ in²
Answers
The shape has a surface area of: Surface Area = 282.6 in²
How to determine the surface area?The given parameter is represented on the figure
In this case, the figure is a cone with the following parameters
Radius, r = 5 inches
Height, h = 12 inches
The surface area of the cone is then calculated as
A = πr * (r + √(h² + r²))
Substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 5 * (5 + √(12² + 5²))
Evaluate the expression
A = 282.6
Hence, the surface area is 282.6 square inches
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17).
A chef has 31 litres of cooking oil. He uses 7, of it during an evenings cooking.
How much does he
a).
use,
b).
have left over ?
Answers
Answer:
a) He obviously used 7 liters of cooking oil.
b) He has 24 liters of cooking oil left.
X+6=3x we just learned how to do this math today I need help
Answers
Answer:
x=3
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!
-----------------------
So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!
A relation is shown: {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)} Which set of information is true about the relation shown?
Answers
The set of information that is true about the relation is:
Domain: {3, 4, 5, 6}
Range: {-8, -1, 2, 7}
The relation is not a function.
How to Determine a Relation that is a Function?A relation that represents a function will have each of its domain elements related to exactly one range element.
All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,
Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.
Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:
The domain of the relation is: {3, 4, 5, 6}
The range of the relation is: {-8, -1, 2, 7}
The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.
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The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given
by the function D(h) = 111.7√/h. Find the height that would allow a person to see 40 kilometers.
h=km
(Round to two decimal places as needed.)
...
Answers
Answer:
0.13 km
Step-by-step explanation:
Rearrange the formula to solve for [tex]h[/tex]:
[tex]D(h)=111.7\sqrt{h}[/tex]
[tex]\frac{D(h)}{111.7}=\sqrt{h}[/tex]
[tex](\frac{D(h)}{111.7})^2=(\sqrt{h})^2[/tex]
[tex](\frac{D(h)}{111.7})^2=h[/tex]
Then, substitute the distance of 40 km:
[tex](\frac{40}{111.7})^2=h[/tex]
[tex]0.13\approx{h}[/tex]
Which shows all the critical points for the inequality 2x+5/x-2 => x-1/x-2
x = 1, and x = 2 x = –6 and x = 2 x = –4 and x = 2 x = 2
Answers
The critical points of the given inequality are; x=-6 and x=2
What are the critical points of the Inequality?1) When the denominator is equal to zero, at that point, we will have a critical point.
We are given the inequality;
(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)
Thus, x - 2 = 0
x = 2.
Thus, x = 2 is a critical point
2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.
Thus, at p(x) = zero, we have other critical point(s)
Multiply both sides by (x - 2) to get;
2x + 5 = x - 1
2x - x = - 1 - 5
x = - 6
Then, the two critical points are x = 2 and x = - 6.
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If angle 1 is 7 degrees in the parallelogram pictured above, what is angle 2
Answers
Answer:
m∠2 = 173°Step-by-step explanation:
1 and 2 are supplementary angles and hence sum to 180°.
m∠1 + m∠2 = 180°7° + m∠2 = 180° m∠2 = 180° - 7° m∠2 = 173°Find the sum: (2x² + x + 3) + (3x² + 2x + 1)
A. 3x² + 5x+4
B. 5x²+3x+4
OC. 6x + 2x + 3
OD. 5x²+2x+4
Answers
Answer:
B
Step-by-step explanation:
Combine 2x^2 and 3x^2 to get 5x^2.
5x²+x+3+2x+1Combine x and 2x to get 3x.
5x²+3x+3+1Add 3 and 1 to get 4.
5x²+3x+4The correct option is B.A road has a speed limit sign at the beginning that is noticed by 84 % of people. 95 % of people who didn't notice the sign speed on the road. Of those who notice the sign, 75 % follow the speed limit.
How many percent of people speeding on this road noticed the sign? In other words, how many people on this road speed on purpose. Give your answer in percentage.
Answers
The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
Percentage of people who notice the speed limit = 84%
The percentage of people who notice the sign and follow the speed limit is 75%.
Therefore, 84% - 75% = 9% are the percentage speeding and noticed.
Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".
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3. A company’s penetration rate is the percent of the market that uses its product. A market research firm is testing the
penetration rate for ACME widgets. In a random sample of 425 widget consumers, 185 purchased the ACME brand.
(a) Do these data provide good evidence that ACME’s penetration rate for widgets is greater than 40%? Test at the
2.5% level of significance.
(b) Explain the meaning of the P-value in the context of the data.
Answers
No, the data provided does not give good evidence that ACME’s penetration rate for widgets is greater than 40%, Test at the
2.5% level of significance
P-value in the data is 40% and this refers to the probability that the assumed penetration rate is greater tan 40 %
How to get the p value penetration rateThe central limit theorem is frequently employed in situations when it is necessary to identify the features of the population but it is challenging to analyze the entire population.
The central limit theorem gives the formula
Z = (X - μ) / σ
Definition of variables
sample mean, X = 185
population mean, μ = ?
standard deviation, σ = ?
sample size, n = 185
significance level = 2.5% = 0.025
confidence level = 1 - significance level = 1 - 0.025 = 0.975 = 97.5%
z score, z
Z score for 97.5% confidence level = 1.96
substituting into the formula
Z = (X - μ) / σ
The given variables are not enough for the calculation
population mean, μ = ?
standard deviation, σ = ?
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Determine a so that A(t)=A0at describes the amount of nitrogen-16 left after t seconds, where A0 is the amount at time t=0. Round to six decimal places.
Answers
using the power rule of logarithm, the value of a is 1.1021.
In the given question we have to determine a so that [tex]A(t)=A_{0}a^t[/tex] describes the amount of nitrogen-16 left after t seconds, where [tex]A_{0}[/tex] is the amount at time t=0.
The given exponential function is [tex]A(t)=A_{0}a^t[/tex].
The amount of nitrogen-16 is approximately 7.13 seconds.
According to the question, [tex]A(t)=A_{0}/2[/tex] and t = 7.13 seconds.
Putting the value in the given function;
[tex]A_{0}/2=A_{0}a^{7.13}[/tex]
Divide by [tex]A_{0}[/tex] on both side, we get
[tex]1/2=a^{7.13}[/tex]
Taking In on both side
[tex]\text{In}(1/2)=\text{In}(a^{7.13})[/tex]
Using the power rule of logarithm
In(1/2)=7.13In(a)
Divide by 7.13 on both side
In(a)= -0.693/7.13
In(a)= -0.0972
Taking exponential on both side
[tex]e^{\text{In}(a)}= e^{-0.0972}[/tex]
a = 1.1021
Hence, the value of a is 1.1021.
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One number exceeds another by 7. The sum of the numbers is 27. What are the numbers?
The numbers are
(Use a comma to separate answers.)
K
Answers
Answer:
10, 17
Step-by-step explanation:
let the number be n then the other number is n + 7 and
n + n + 7 = 27
2n + 7 = 27 ( subtract 7 from both sides )
2n = 20 ( divide both sides by 2 )
n = 10
n + 7 = 10 + 7 = 17
the numbers are 10, 17
The Americans with Disabilities Act (ADA) gives businesses and cities requirements, rules, for making sure that people in wheelchairs and scooters can use slopes. The ADA requires a 1:12 slope for wheelchairs and scooters. (This means that for every one unit of vertical distance, the ramp must have 12 units of horizontal distance.) Mrs. Giles has a small business. She wants to make sure she builds the entrance to her building correctly. The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store. According to the ADA rules, how long (horizontal distance) does the ramp need to be, in feet?
Answers
The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.
What is ratio?Comparing one quantity to another is what it is. For instance, the weight ratio is 1:3 if you weigh 30 kg and your father weighs 90 kg.
Given:
The ratio of vertical and horizontal distance = 1:12,
The vertical distance of Mrs. Giles's business = 28 inches,
If for every one unit of vertical distance, the ramp must have 12 units of horizontal distance, so or 28 inches vertical distance the horizontal distance would be = 28 × 12 = 336 inches,
([tex]1 feet = 12inches[/tex])
= 336 / 12 = 28 feet
Therefore, The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.
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