Let the base of the rectangle be of length 2x, so its vertices on the parabola are (−x, 49 − x²) and (x, 49 − x²).
The area A of the rectangle is given by A = 2x(49 − x²), which simplifies to A = 98x − 2x³.
What is Rectangle?A rectangle is a four-sided polygon with opposite sides being congruent and parallel to each other, and all interior angles measuring 90 degrees.
To find the maximum possible area, we need to find the value of x that maximizes A. To do this, we take the derivative of A with respect to x and set it equal to zero:
dA/dx = 98 - 6x² = 0
Solving for x, we get x = ±√(98/6) ≈ ±4.1
Since the rectangle is symmetric about the y-axis, we only need to consider positive values of x. Therefore, the length of the base of the rectangle is 2x ≈ 8.2.
The height of the rectangle is 49 − x² ≈ 47.9.
The maximum area of the rectangle is then A ≈ 392.18 square units.
Learn more about area of rectangle at:
https://brainly.com/question/20693059
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G.1.- Una Recta contiene los puntos (-3,7)
y (9,-5) Calcule la ecuación de la recta en la
FORma y=mxtb. Explicar los pasos
Given:
A line passes through the points (-3,7) and (9,-5).
To find:
The equation of the line in the form of [tex]y=mx+b[/tex].
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-3,7) and (9,-5). So, the equation of the given line is:
[tex]y-7=\dfrac{-5-7}{9-(-3)}(x-(-3))[/tex]
[tex]y-7=\dfrac{-5-7}{9+3}(x+3)[/tex]
[tex]y-7=\dfrac{-12}{12}(x+3)[/tex]
[tex]y-7=-1(x+3)[/tex]
On further simplification, we get
[tex]y-7=-x-3[/tex]
[tex]y-7+7=-x-3+7[/tex]
[tex]y=-x+4[/tex]
Therefore, the equation of the required line is [tex]y=-x+4[/tex].
Show number that 0.245 is Rational number
Answer:
A rational number is one that may be represented in the manner p/q.
245/1000 = 0.245
Step-by-step explanation:
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)
x −36 −26 −15 −4
P(X = x) 0.32 0.36 0.21 0.11
Mean
Variance
Standard deviation
Mean = 24.47
Variance = 108.31
Standard deviation = 10.41
Step-by-step explanation:The probability distribution table has been attached to this response.
(1) To calculate the mean (m)
(a) First multiply each of the values of x by their corresponding probability values.
This is shown in the third column of the table.
(b) The sum of the results in the third column gives the mean of the distribution. i.e
m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44
m = 24.47
(2) To calculate the variance (σ²).
(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e
(x - m)²
The result is shown in the fourth column of the table.
(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e
(x - m)²(P(X = x))
The result is shown in the fifth column of the table.
(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e
σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923
σ² = 108.3091
σ² = 108.31 [to 2 decimal places]
(3) To calculate the standard deviation (σ)
The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.
σ = √σ²
σ = [tex]\sqrt{108.31}[/tex]
σ = 10.4072
σ = 10.41 [to 2 decimal places]
Find the value of x?
Answer:
X=2.
Step-by-step explanation:
3 times 2 is equal to 6, and 4 times 2 is equal to 8, 6+8=14.
Find the common ratio of the geometric sequence − 1 , − 9 , − 81 ,
Step-by-step explanation:
everything can be found in the picture
When solving inequality
If in the numerator i had a imaginary number when factoring what should i do???
Answer:
we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.
you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number
for instance,
we've given a complex number as follows
[tex] \frac{x}{3x + 4i} [/tex]
factorising
[tex] \frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i} [/tex]
as 3x -4i is the conjugate of 3x + 4i
and 4i is the imaginary number
[tex] \frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }[/tex]
and since i² = -1
[tex]\frac{ x(3x - 4i)}{9x {}^{2} + 4}[/tex]
hence factorised
A) work out the value of g.
Give your answer in standard form correct to three significant figures.
B) work out the new value of g. Give your answer in standard form correct to 3 significant figures. (M is increased by 8% and T is increased by 5%).
Answer:
4547.14
Step-by-step explanation:
m increased by %8 so it'll be
[tex]6.588 \times {10}^{ - 5} [/tex]
and t will be
[tex]1.785 \times {10}^{ - 6} [/tex]
so G =
[tex] \sqrt{ \frac{(6.588 \times {10}^{ - 5}) }{ {(1.785 \times {10}^{ - 6}) }^{2} } } [/tex]
G= 4547
Help me please with this math problem
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
[tex](5x-14)+(8x+12)=180[/tex]
These two angles on the line is 180°
Solve the equation:
[tex]5x-14+8x+12=180[/tex]
[tex]5x+-14+8x+12=180[/tex]
[tex](5x+8x)+(-14+12)=180[/tex] {combine the like terms}
[tex]13x-2=180[/tex]
[tex]13x=180+2[/tex]
[tex]13x=182[/tex]
[tex]x=182/13[/tex]
[tex]x=14[/tex]
PROOF:
{substitute 14 in the place of x}
[tex](5(14)-14)+(8(14)+12)=180[/tex]
[tex]56+124=180[/tex]
[tex]180=180[/tex]
hope this helps....
What are the coordinates of the vertex of the parabola described by the
equation below?
y= 2x+52-3
O A (-5.3)
0
B. (-3.-5)
C. (3.5)
O D. (5-3)
ANSWER ASAP!
Step-by-step explanation:
please type the question properly
please help me please help me please help me please help me please help me please help me please
Answer:
1. -4
2(12,35,37). hope helpful answerAnswer:
Question 1 = 256
Question 2 = ( 7, 8, 12)
For the diagram below, which of the following represents the length of line MN to the nearest tenth?
help me find answer i need answer please hlep
Answer:
7
Step-by-step explanation:
This is correct answer bro...
Answer:
7
Step-by-step explanation:
So first off, two numbers that are to the same root can be combined.
In this case we can combine these two values, since they are to the 5th root and are both 7:
[tex]\sqrt[5]{7*7^4}[/tex]
=
[tex]\sqrt[5]{49^4}[/tex]
This can be broken down into 7^2
This gets us [tex]\sqrt[5]{7^5}[/tex]
Remember that we add exponents, together, so in this case it adds up to 5.
You might be wondering...well if its 7^2 and 7^4, wouldnt it be 7^6?
Well, remember this. One of the 7s in 7^2 is from the 7^4, so tecnically it is 7^3 + 7^2, which is 7^5
Anyway, now we have:
[tex]\sqrt[5]{7^5}[/tex]
When you root a exponent, it works like subtraction.
In this case we have a exponent of 5, and a root of 5.
This is 5-5 = 0
So it will just be 7. Because the square and root cancel each other out, leaving us with 7.
Hope this helps!
Also, I just watched you waste someone elses answer so you could ask your own question. Instead of wasting other peopes answers, message me on one of my questions or answers, I will help you for free. :D
Trigonometry help please? I need the three answers
Answer:
Both triangles are triangle rectangles, but the triangles are not similar.
Step-by-step explanation:
By the Pythagorean's theorem, we know that for a triangle rectangle the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Where the cathetus are always the two sides of smaller length.
We also know that two figures are similar if all the correspondent sides are proportional to each other, this means that the figures have the same shape but different size.
First, for triangle A the measures of the sides are:
48, 55, 73
Here the two catheti are 48 and 55, and the hypotenuse is 73.
Then to answer the first question we need to try to apply the Pythagorean's theorem, we should have:
48^2 + 55^2 = 73^2
solving that we get:
5,329 = 5,329
This is true, thus triangle A is a triangle rectangle.
Now for triangle B the measures are: 36, 77 and 85.
So the catheti are 36 and 77, and the hypotenuse is 85
So to check if triangle B is a triangle rectangle the equation:
36^2 + 77^2 = 85^2
must be true, solving both sides we get:
7,225 = 7,225
This is true, so triangle B is a triangle rectangle.
Finally, to check if the figures are similar we need to compare the correspondent sides of both triangles, such that the quotient of correspondent sides must be always the same.
For the hypotenuses, if we compute:
(hypotenuse B)/(Hypotenuse A) we get:
85/73 = 1.16
Now if we do the same for the two smaller catheti we get:
36/48 = 0.75
The quotients are different, thus the triangles are not similar.
I need help with the problem
Answer:
Non-linear
Step-by-step explanation:
While the difference in x terms remains constant at 1
The difference between y terms varies.
Answer:
Non-linear.
Step-by-step explanation:
solve the paper with the correct answer
Answer:
I did question no 2 , 4 , 5 , 6
from question attempt any two questions i did 4 and 5.
Step-by-step explanation:
Hope this helps u !!
How much is 12,856 ounces in pounds ?
Anyone knows what the answer for this is I am really confused on it
The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
Find the z score for each state.
Answer:
The z-score for a home priced at $200,000 in Florida is of -2.5.
The z-score for a home priced at $200,000 in Ohio is of 2.5.
The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. Home of $200,000.
This means that [tex]\mu = 240, \sigma = 16, X = 200[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 240}{16}[/tex]
[tex]Z = -2.5[/tex]
The z-score for a home priced at $200,000 in Florida is of -2.5.
The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Home of $200,000.
This means that [tex]\mu = 170, \sigma = 12, X = 200[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 170}{12}[/tex]
[tex]Z = 2.5[/tex]
The z-score for a home priced at $200,000 in Ohio is of 2.5.
Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.
What is the value of x in the equation 1/5x-2/3y = 30, when y = 15
Answer:
x=200
Step-by-step explanation:
(1/5)x-(2/3)y=30, y=15
(1/5)x-(2/3)*15=30
(1/5)x=40
x=200
Which of the following is the graph of f(x)=║x║translated 2 units right, 2 units up, and dilated by a factor of 1/3?
Answer:
c on edge2021
Step-by-step explanation:
Inscribe a circle in a unit square and to r= 1000 random.
a. Suppose that 760 of those darts land in the circle.
b. What would our estimate be if we let n â oo and we applied the same ratio strategy?
Step-by-step explanation:
area of square = 1
area of a circle in square = [tex]\pi r^2 = \pi *(1/2)^2 = \frac{\pi }{4}[/tex]
bu estimate [tex]p^ = X/n = 760/1000 = 0.76
Therefore,
[tex]\frac{\pi }{4} \approx 0.76[/tex]
[tex]\pi \approx 0.76*4 =3.04[/tex]
b) if n tend to infinity
[tex]\pi will approach 3.14[/tex]
Answer:
uvfhmfa
Step-by-step explanation:
A system of equations is shown below:
y = 3x − 7
y = 2x + 1
What is the solution to the system of equations?
(8, 17)
(−8, 17)
(−8, −17)
(8, −17)
Answer:
(8, 17)
Step-by-step explanation:
y= 3x -7 -----(1)
y= 2x +1 -----(2)
Substitute (1) into (2):
3x -7= 2x +1
Being x terms to one side, constant to the other:
3x -2x= 7 +1
x= 8
Substitute x= 8 into (2):
y= 2(8) +1
y= 16 +1
y= 17
∴ The solution is (8, 17).
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth.
a. $0.13 / Ib.
b. $4.00 / Ib
c. $6.25 / Ib.
d. $7.75 / Ib.
Answer:
a. $0.13 / Ib.
Step-by-step explanation:
Slope of a line:
Suppose we have two data-points in a line. The slope is given by the change in the output divided by the change in the output.
In this question:
Input: weight(in pounds)
Output: Weekly cost to feed.
A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.
Inputs: 0.5, 62.5
Outputs: 2, 10
Change in the outputs: 10 - 2 = 8
Change in the inputs: 62.5 - 0.5 = 62
Slope: [tex]m = \frac{8}{62} = 0.13[/tex]
So the correct answer is given by option A.
Answer:
0.13
Step-by-step explanation:
Which table represents a linear function?
Answer:
First table from left.
Step-by-step explanation:
Equal step of a half.
1,7
2,9
3,13
4,21
Step-by-step explanation:This is the linear function graph i plotted the points
What is the generalization of a point which is
reflected over the x axis?
Answer:
If a point is reflected over the x-axis, the x- coordinate of the image remains the same as the pre-image and the y- coordinate is the opposite of the pre-image. ... If a point is reflected over both axes, both coordinates of the image are opposite of the pre-image.
Hall and Mindy are playing a guessing game. Hall tells Mindy: ""The difference between 17 and the square root of my mystery number is 5"". What are two possible numbers that Hall could be thinking of?
Answer:
The possible number that Hall could be thinking of is 144.
Step-by-step explanation:
Difference between 17 and the square root of my mystery number
This is represented by:
[tex]17 - \sqrt{x}[/tex]
is 5
Then:
[tex]17 - \sqrt{x} = 5[/tex]
What are two possible numbers that Hall could be thinking of?
We have to solve the equation, for x. So
[tex]17 - \sqrt{x} = 5[/tex]
[tex]\sqrt{x} = 12[/tex]
[tex](\sqrt{x})^2 = (12)^2[/tex]
[tex]x = 144[/tex]
The possible number that Hall could be thinking of is 144.
Solve for T: 10t-4x=3S Explanation plz
Please answer part A and B.
Answer:
Percent who walk 45%
Percent in car 22.5%
Step-by-step explanation:
The total number of students is
36+26+18 = 80
Percent who walk is 36/80 = .45 =45%
Percent in car is 18/80 =.225= 22.5%
25^2 6^3 find prime factorization
Answer:
With Exponents: 32 × 7 × 401
Without Exponents: 3 × 3 × 7 × 401
Step-by-step explanation:
Hello,
[tex]25^2*6^3\\\\=(5^2)^2*(2*3)^3\\\\=\boxed{2^3*3^3*5^4}\\[/tex]
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 30 months at 8% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
$
Answer:
13.33
Step-by-step explanation:
Because it's only payment one we can easily figure out the interest portion
we first need the effective rate
.08/12= .006666667
We the just mulitply this by loan amount
2000*.006666667= 13.33
Step-by-step explanation:
its your answer
I hope it's help you