Answers:
(a) 9 cm
(b) 2 cm
======================================
Work shown for part (a)
A = s^2
s = sqrt(A)
s = sqrt(81)
s = 9
-----------------
Work shown for part (b)
P = 4s
s = P/4
s = 8/4
s = 2
The side length of the square with area of 81 cm² is :
↬ 9 cmThe side of the square with the perimeter of 8 m is :
↬ 2 mSolution:
We're given the area of a square : 81 cm².
To find one of its sides, we need to take the square root of that.
So we have:
[tex]\sf{Side\:length{\square}=\sqrt{81}} \\ \\ \sf{Side\:length\square=9}[/tex]
We know that if we take the square root of 81, we will get two solutions: 9 and -9; however we cannot use -9, because having a negative side length is impossible.
So the side length is 9 cm.__________________________
To find the side length when given the perimeter, we divide it by 4, because the formula for a square's perimeter is P = 4a.
So if we rearrange that for a, we will get : a = P/4.
where a = side length
Solving,
a = 8/2a = 4Hence, the length of each side is 4 m.HELP PLEASE!!!!!! Find the speed of an athlete who makes 4and3/4 laps in 3mins45 seconds on a 400m field in m/s
Given:
An athlete who makes [tex]4\dfrac{3}{4}[/tex] laps in 3 mins 45 seconds on a 400m field.
To find:
The speed of the athlete in m/s.
Solution:
We know that,
Distance covered in 1 lap = 400 m
Distance covered in [tex]4\dfrac{3}{4}[/tex] laps = [tex]4\dfrac{3}{4}\times 400[/tex] m
= [tex]\dfrac{19}{4}\times 400[/tex] m
= [tex]1900[/tex] m
We know that,
1 minute = 60 seconds
3 minutes = 180 seconds
3 minutes 45 second = 180 + 45 seconds
= 225 second
The speed of the athlete is:
[tex]Speed=\dfrac{Distance}{Time}[/tex]
[tex]Speed=\dfrac{1900}{225}[/tex]
[tex]Speed\approx 8.44[/tex]
Therefore, the speed of the athlete is about 8.44 m/s.
complete the square to rewrite the following equation in standard form
By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided below, we have the following equation of a circle:
x² - 4x + y² + 8y = -4
x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²
x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16
(x - 2)² + (y + 4)² = 16
(x - 2)² + (y + 4)² = 4²
Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.
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Complete Question:
Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.
please help quickly!
Answer:
answer I have no clue sorry dude
A time series graph is useful for which of the following purposes?
Representing relative frequencies of categories in a specific year
Representing the cumulative frequencies of the data in a specific year
Representing the frequencies of the data, sorted from largest to smallest
Representing the frequencies of a data category over a period of several years
Answer: A time series graph is useful for representing the frequencies of a data category over a period of several years.
Explanation: Time series graphs are usually employed when it is critical to examine data values and trends over time. A time series graph displays changes in data over time. It is usually used to depict economic, social, or physical characteristics that are measurable over time. A time series is a collection of observations or data taken at regular intervals over time and used to track and analyze changes in data over time.
Time series graphs display data over time on a graph with time on the x-axis and a measured value, such as temperature or height, on the y-axis. The graph can display change trends over time as well as seasonal or other patterns, in addition to providing insight into how data values are changing over time.
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An isosceles triangle has a base of 20cm and legs measuring 36cm. How long are the legs of a similar triangle with a base measuring 50cm?
Answer:
90 cm
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, then
50 ÷ 20 = 2.5
The legs of the similar triangle are 2.5 times the original legs, that is
legs of similar triangle = 2.5 × 36 cm = 90 cm
(x2-1)dy/dx+2y=(x+1)4 (integrating factor)
The integrating factor for the given differential equation is |x^2 - 1|.
To find the integrating factor for the given differential equation, we start by rearranging the equation in the form:
dy/dx + (2y)/(x^2 - 1) = (4(x + 1))/(x^2 - 1)
The integrating factor (IF) is given by the exponential of the integral of the coefficient of y, which in this case is (2/(x^2 - 1)). Therefore, the integrating factor IF is:
IF = exp ∫ (2/(x^2 - 1)) dx
To evaluate this integral, we can use a substitution. Let u = x^2 - 1, then du = 2x dx. Substituting this back into the integral, we get:
IF = exp ∫ (1/u) du = exp(ln|u|) = |u|
Since u = x^2 - 1, we have:
IF = |x^2 - 1|
Therefore, the integrating factor for the given differential equation is |x^2 - 1|.
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HELPL ME QUICK I STUCK
Answer:
red = 28 apples
green = 13 apples
equations:
r + g = 41
r = g + 15
Step-by-step explanation:
r = number of red
g = number of green
r = g + 15 (the number of red apples is 15 more than the number of green apples)
r + g = 41
Substitute the first equation into the second and solve for a numerical value of g
(g + 15) + g = 41
2g + 15 = 41
2g = 26
g = 13
Now solve for a numerical value of r
r = g + 15
r = 13 + 15
r = 28
checking the math:
r + g = 41
28 + 13 = 41
Please lmk if you have any questions.
A right cylinder has a radius of 5 and a height of 9. What is its surface area? A. 457 units2 B. 1407 units2 C. 907 units? D. 700 units2
Answer: B
The surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Step-by-step explanation:
We have formula to find the surface area of a right cylinder.
Surface area = 2πr(h + r)
Given: r = 5 and h = 9,
Now plug in the value of r and h in the above formula, we get
Surface area = 2π.5 (9 + 5)
= 10π(14)
Surface area = 140π
The value of π = 3.14, when we plug in the value of π, we get
The surface area = 140 × 3.14
= 439.60 cubic units.
Therefore, the surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Hope this helped!!!
Use the following information for the next two questions: • A portfolio consists of 16 independent risks. • For each risk, losses follow a Gamma distribution, with parameters 0 = 250 and a = 1. The Central Limit Theorem: Suppose that X is a random variable with mean u and standard deviation and suppose that X, X2...., Xy are independent random variables with the same distribution as X (i.e. Independent and Identically Distributed or IID assumption). Let Y = X2, X2..... X... Then E[Y] = nu and Var(Y) = ng2. As n increases, the distribution of Y approaches a normal distribution Nínu, no4). This is also known as normal approximation. (a) Without using the Central Limit Theorem, determine the probability that the aggregate losses for the entire portfolio will exceed 6,000. (b) Using the Central Limit Theorem, determine the approximate probability that the aggregate losses for the entire portfolio will exceed 6,000.
The probability that the aggregate losses for the entire portfolio will exceed 6,000 can be determined by calculating the cumulative distribution function (CDF) of the Gamma distribution without using the Central Limit Theorem. Alternatively, using the Central Limit Theorem, the approximate probability can be estimated by treating the sum of 16 independent risks as a normal distribution with a mean of 4000 and a standard deviation of 4.
(a) Without using the Central Limit Theorem, the probability that the aggregate losses for the entire portfolio will exceed 6,000 can be determined by calculating the cumulative distribution function (CDF) of the Gamma distribution for the sum of 16 independent risks. Since each risk follows a Gamma distribution with parameters θ = 250 and α = 1, the sum of 16 risks will follow a Gamma distribution with parameters θ' = 16 * 250 = 4000 and α' = 16 * 1 = 16. By evaluating the CDF at the value of 6,000, we can find the probability that the aggregate losses exceed 6,000.
(b) Using the Central Limit Theorem, we can approximate the distribution of the sum of 16 independent risks as a normal distribution. According to the theorem, as the number of independent and identically distributed (IID) risks increases, the distribution of their sum approaches a normal distribution with mean μ' = n * μ and standard deviation σ' = √(n * σ^2), where n is the number of risks, μ is the mean of each risk, and σ is the standard deviation of each risk.
In this case, with 16 independent risks, the approximate distribution of the aggregate losses will be a normal distribution with mean μ' = 16 * 250 = 4000 and standard deviation σ' = [tex]\sqrt{ (16 * 1^2)}[/tex] = 4. By calculating the probability that the normal distribution exceeds 6,000, we can estimate the approximate probability of the aggregate losses exceeding 6,000.
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what is the 43th term of 11,16,21
for points sorry Answer:
Step-by-step explanation:
Which expression is evaluated first in the following statement?
if (a > b && c == d || a == 10 && b > a * b)?
a. a * b
b. b && c
c. d || a
d. a > b
e. none of the above
The expression "a > b" is evaluated before the other expressions.
How to evaluate an expression?
Follow the order of operations (PEMDAS/BODMAS). Evaluate the expression following the order of operations or the rules of precedence.
Let's break down the given statement and determine the order of evaluation for each expression:
if (a > b && c == d || a == 10 && b > a * b)
The statement consists of two logical expressions connected by the "&&" and "||" operators. To determine the order of evaluation, we need to consider operator precedence and associativity.
1. Parentheses: As there are no parentheses in the statement, we move on to the next step.
2. "&&" Operator: The "&&" operator has higher precedence than the "||" operator, so expressions connected by "&&" are evaluated before those connected by "||".
The first expression connected by "&&" is "a > b". Let's call this Expression 1.
The second expression connected by "&&" is "c == d". Let's call this Expression 2.
3. "||" Operator: The "||" operator has lower precedence than the "&&" operator.
The first expression connected by "||" is Expression 1 (a > b) && (c == d).
The second expression connected by "||" is "a == 10" && "b > a * b". Let's call this Expression 3.
Now, let's evaluate each expression in the given order:
Expression 1: a > b
Expression 2: c == d
Expression 3: a == 10 && b > a * b
Therefore, the expression evaluated first in the given statement is Expression 1: a > b.
To summarize, in the statement "if (a > b && c == d || a == 10 && b > a * b)", the expression "a > b" is evaluated first.
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A recent study focused on the method of payment used by college students for their cell phone bills. Of the 1,220 students surveyed, 600 stated that their parents pay their cell phone bills. Use a 0.01 significance level to test the claim that the majority of college students' cell phone bills are paid by their parents.
Identify the null and alternative hypotheses for this scenario.
Test the claim that the majority of college students' cell phone bills are paid by their parents.
The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
The null and alternative hypotheses for testing the claim that the majority of college students' cell phone bills are paid by their parents can be stated as follows:
Null hypothesis (H0): The majority of college students' cell phone bills are not paid by their parents.
Alternative hypothesis (Ha): The majority of college students' cell phone bills are paid by their parents.
In this scenario, the null hypothesis assumes that the proportion of college students whose parents pay their cell phone bills is less than 50% (not a majority), while the alternative hypothesis suggests that the proportion is greater than or equal to 50% (a majority). The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
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PROVING THEOREMS OF SQUAD can someone help me pleasee ASAP
Answer:
40 units
Step-by-step explanation:
For a square, all the sides are equal and the interior angles are equal and all equal to 90. Hence;
m<BOJ = 90 degrees
m<BOJ = 4x - 6
Equating both to get x;
4x - 6 = 90
4x = 90+6
4x = 96
x = 96/4
x = 24
Since all the sides are equal, hence BO = JO = 2x-8
JO = 2x - 8
Substitute x = 24 into JO
JO = 2(24) - 8
JO = 48 - 8
JO = 40
Hence the measure of JO is 40 units
The following data set shows the bank account balance for a random sample of 17 IRSC students. 343 45 340 SN 105 343 29 340 101 343 alelse 1 340 343 101 312 142 340 36 Round solutions to two decimal places, if necessary. What is the mean of this data set? mean What is the median of this data set? median What is the mode of this data set? If no mode exists type DNE. If multiple modes existenter the values in a comma-separated list. Round solutions to two decimal places, if necessary. What is the mean of this data set? mean What is the median of this data set? median- What is the mode of this data set? If no mode exists, type DNE. If multiple modes exist, enter the values in a comma-separated list. mode =
The mean of the data set is approximately 210.94. The median of the data set is 101. The mode of the data set is 343.
To determine the mean, median, and mode of the data set:
Data set: 343, 45, 340, SN, 105, 343, 29, 340, 101, 343, alelse, 1, 340, 343, 101, 312, 142, 340, 36
To calculate the mean, we need to find the average of all the values in the data set. However, it seems that there are some non-numeric entries like "SN" and "alelse." We need to remove these non-numeric entries before calculating the mean.
After removing the non-numeric entries, the data set becomes: 343, 45, 340, 105, 343, 29, 340, 101, 343, 1, 340, 343, 101, 312, 142, 340, 36.
Mean: Sum all the values and divide by the number of values.
Mean = (343 + 45 + 340 + 105 + 343 + 29 + 340 + 101 + 343 + 1 + 340 + 343 + 101 + 312 + 142 + 340 + 36) / 17
Mean ≈ 210.94 (rounded to two decimal places)
To calculate the median, we need to find the middle value of the data set when it is arranged in ascending order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
Arranging the data set in ascending order: 1, 29, 36, 45, 101, 101, 105, 142, 312, 340, 340, 340, 343, 343, 343, 343, 340.
Median: Since the number of values is odd (17), the median is the middle value.
Median = 101
To calculate the mode, we need to find the value(s) that appear(s) most frequently in the data set.
Mode: In this data set, the value 343 appears most frequently, so the mode is 343.
In summary:
Mean ≈ 210.94
Median = 101
Mode = 343
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what is the value of A and B (5x + b)(5x - b) = ax^2 - 49
Answer:
a=25
b=7
Step-by-step explanation:
the scatterplot shows the number of hours that 12 people spent learning to type on a keyboard and each persons average typing speed. Based on the scatterplot, what is the best prediction of a persons average typing speed in words per min. if the person has spent 70 hours learning to type?
Answer:
85 wpm
Step-by-step explanation:
From the scatter plot, we can see the following;
At 20 hours, average typing speed = 34 wpm
At 30 hours, the average typing speed = 40 wpm
At 40 hours, the average typing speed = 51 wpm
At 50 hours, the average typing speed = 65 wpm
Average differences = ((40 - 34) + (51 - 40) + (65 - 51))/3 = 10.3
Approximating to a whole number = 10
Now, we can approximate that at 60 hours, average typing speed = 65 + 10 = 75 wpm
At 70 hours, the average typing speed = 75 + 10 = 85 wpm
Answer:
85 wpm
Step-by-step explanation:
I took this test!
Can someone help me solve these equations?
1. 2y^2+5Y+2 |
2. 5x^2-18x+9 |
3. 16b^2+60b-100 | 4.-6a^2-25a-25 |
5. 49x^2-14x+1 |
6. 81x^2-49
Ok So could you please tell me where I went wrong?
Answer:
lateral surface area =perimeter of base×height=
={4+7+7+11)×6=174 km²
Step-by-step explanation:
Mrs. DeRossett's sister goes to the bank to get a loan to purchase a new home. The bank advises that she make sure her mortgage payment does not exceed 30% of her monthly take home pay. If Mrs. DeRossett's sister makes roughly $5,000 per month, then what would be her recommended maximum monthly mortgage?
Answer:
1,500
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
2/11
Step-by-step explanation:
Let's say x = 0.18181818..
Then, 100x = 18.1818181....
so, if you put x in the repeating decimal in 18.1818,
you get the equation,
100x = 18+x
so, 99x = 18
x = 18/99 = 2/11
Answer:
18/100 = 9/50
Answer is 9/50
Do you really think you’re going to give me brainliest lol
a simple random sample of 800 elements generates a sample proportion p= 0.77 ( round awsners to 4 decimal places)
a) provide a 90% confidence interval for the population proportion
b) provide a 95% confidence interval for the population proportion
The 95% confidence interval for the population proportion is approximately (0.7465, 0.7935).
(a) To calculate a 90% confidence interval for the population proportion, we can use the formula:
Confidence Interval = sample proportion ± z * sqrt((sample proportion * (1 - sample proportion)) / sample size)
Given that the sample proportion is p = 0.77 and the sample size is n = 800, we need to find the critical value, z, corresponding to a 90% confidence level.
Using a standard normal distribution table or a statistical software, the critical value for a 90% confidence level is approximately 1.645.
Substituting these values into the formula, we have:
Confidence Interval = 0.77 ± 1.645 * sqrt((0.77 * (1 - 0.77)) / 800)
Calculating the confidence interval, we get:
Confidence Interval = 0.77 ± 0.0191
Therefore, the 90% confidence interval for the population proportion is approximately (0.7509, 0.7891).
(b) Similarly, to calculate a 95% confidence interval, we need to find the critical value corresponding to a 95% confidence level. The critical value is approximately 1.96 for a 95% confidence level.
Using the same formula and substituting the values, we have:
Confidence Interval = 0.77 ± 1.96 * sqrt((0.77 * (1 - 0.77)) / 800)
Calculating the confidence interval, we get:
Confidence Interval = 0.77 ± 0.0235
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Find the factor form for each problem. (Show work)
1. 12x²+8x
2. 2x²-16x
Step-by-step explanation:
12x^2 + 8x
4x ( 3x + 2)
2x^2 - 16x
2x ( x - 8)
Which of the following is false? (No (i) |ez| = |e³|, Vz #0
The false statement among the following statements is: |ez| = |e³|. Here, e is the Euler number, and z is a complex number. Therefore, the correct answer is option (i) |ez| = |e³|.
We know that e^(ix) = cos(x) + i sin(x)
It is also known as Euler's formula, where e is the Euler number, i is the imaginary unit, x is the angle in radians. This formula connects the trigonometric functions with the exponential function. In this question, e is the Euler number, and z is a complex number. So, ez = |ez| × e^(iθ), where θ is the angle of the complex number z from the positive real axis. In the same way, e³ = |e³| × e^(i3θ)Here, the modulus of ez is |ez|, and the modulus of e³ is |e³|. It is not necessary that both will be equal because the value of θ may differ. Hence, the false statement is |ez| = |e³|.
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This tutorial will show you how to do an independent samples t test in SPSS and how to
interpret the result.
Steps
1. Independent-Samples T Test Compare Means 1. Click on Analyze
2. Drag and drop the dependent variable into the Test Variable(s) box, and the grouping
variable into the Grouping Variable box
3. Click on Define Groups, and input the values that define each of the groups that make
up the grouping variable (i.e., the coded value for Group 1 and the coded value for
Group 2)
4. Click Continue, and then click on OK to run the test
5. The result will appear in the SPSS data viewer
This tutorial provides step-by-step instructions on how to perform an independent samples t-test in SPSS and interpret the results.
The tutorial outlines the following steps to conduct an independent samples t-test in SPSS:
Access the Analyze menu.
Select "Compare Means" and then "Independent-Samples T Test."
Drag and drop the dependent variable into the "Test Variable(s)" box and the grouping variable into the "Grouping Variable" box.
Define the groups by clicking on "Define Groups" and inputting the coded values that represent each group.
Click "Continue" and then "OK" to run the test.
The results will be displayed in the SPSS data viewer.
By following these steps, users can conduct an independent samples t-test to compare means between two groups and assess whether there is a statistically significant difference. The result provides information such as the t-value, degrees of freedom, and p-value, which is used to interpret the significance of the difference between the means of the two groups. Researchers can then make conclusions based on the statistical findings from the independent samples t-test.
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Computer world has all computer has all computers on sale for 20% off. If the regular price of a laptop is $750, what is the sale price?
Answer:
Selling price of the laptop is $600.
Step-by-step explanation:
Let the sale price of the laptop = $x
Regular price of the laptop = $750
Discount on each computer = 20%
Selling price of the laptop 'x' = 750 - (20% of 750)
= 750 - [tex](\frac{20}{100}\times 750)[/tex]
= 750 - 150
= $600
Therefore, selling price of the laptop is $600.
A rectangle has a width of 3 cam and a length of 9cm. the rectangle is to be enlarged by a scale factor of 8 what is the length of the enlargement. (include units)
Answer:
72 cm
Step-by-step explanation:
It would be multiplied by 8 so the length would become 72 cm
Define a relation Ron R by for a,beR (a,b) e Rif and only if a-bez Which of the following properties does have? Reflexive Symmetric Antisymmetric Transitive
In summary:
The relation R is reflexive. The relation R is not symmetric. The relation R is antisymmetric. The relation R is transitive.
Let's analyze the properties of the relation R:
Reflexive:
A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if (a, a) belongs to R for every a in the set.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - a = 0, (a, a) satisfies the condition and is in R for every a in the set. Therefore, the relation R is reflexive.
Symmetric:
A relation R is symmetric if for every (a, b) belongs to R, (b, a) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
However, if a - b = 0, it does not imply that b - a = 0. Therefore, the relation R is not symmetric.
Antisymmetric:
A relation R is antisymmetric if for every distinct (a, b) belongs to R, (b, a) cannot be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - b = 0 implies b - a = 0, it means that if (a, b) and (b, a) are in R, then a must be equal to b. Thus, for distinct elements a and b, it is not possible for both (a, b) and (b, a) to be in R. Therefore, the relation R is antisymmetric.
Transitive:
A relation R is transitive if for every (a, b) and (b, c) belongs to R, (a, c) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
If a - b = 0 and b - c = 0, it implies that a - c = 0. Therefore, if (a, b) and (b, c) are in R, then (a, c) is also in R. Thus, the relation R is transitive.
In summary:
The relation R is reflexive.
The relation R is not symmetric.
The relation R is antisymmetric.
The relation R is transitive.
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What substitution should be used to rewrite 16(x^3 +1)^2 – 22(x^3+1) – 3 = 0 as a quadratic equation? a. u = (x3) b. u = (x3+1) c. u = (x3+1)2 d. u = (x3+1)3
The correct substitution to rewrite the equation 16(x^3 + 1)^2 - 22(x^3 + 1) - 3 = 0 as a quadratic equation is:
c. u = (x^3 + 1)^2
By substituting u = (x^3 + 1)^2, the equation can be rewritten as 16u - 22u - 3 = 0, which is a quadratic equation in terms of u.
To solve the quadratic equation for u, you can use factoring, completing the square, or the quadratic formula. Once you find the solutions for u, you can substitute back (x^3 + 1)^2 for u to obtain the solutions for the original equation.
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A reporter surveyed 300 randomly selected people of all ages about their opinion of a new song. The results are shown in the table. Which of the following is a valid conclusion about data? select all that apply.
Answer:
the answers is A and E <3
Step-by-step explanation:
i took this test
Please help me I will give u points whenever u wanna only Percy answers pleaseee ❤️
And don’t forget about explain
Answer:
this point is 72 digri ok