Umm... plz help! Before 8 plz

The other roots of the given polynomial equation are 2 and -2.

Given polynomial equation is:

\(x^{6} -16x^{2} =4x^{4} -64\).....(1)

A polynomial is the sum of monomials of the form axⁿ where n is a whole number.

Rewriting the (1) as:

\(x^{6} -4x^{4} -16x^{2} +64=0\)

\(x^{4} (x^{2} -4)-16(x^{2} -4)=0\)

\((x^{2} -4)(x^{4} -16)=0\)

\(x^{2} -4=0\)

\(x^{2} =4\)

\(x=2\)

\(x=-2\)

So, the other roots are 2 and -2.

Hence, the other roots of the given polynomial equation are 2 and -2.

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Answer:

its b

Step-by-step explanation:

took it

Answer:

Diego's mistake is that he multiplied the exponents, instead of adding. The answer should be \(2^{3+2} = 2^{5}\)

Step-by-step explanation:

Suppose we have a base a, and two exponents, b and c, we have that:

\(a^{b} \times a^{c} = a^{b+c}\)

In this problem:

\(a = 2, b = 3, c = 2\)

Diego's mistake is that he multiplied the exponents, instead of adding. The answer should be \(2^{3+2} = 2^{5}\)

The condition that ensures a solution for the mentioned equation is :

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0.

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.

According to the Question:

Given that:

x₁+ 2x₂= b₁       ------------------------- (1)

2x₁ + 4x₂ = b₂  ------------------------- (2)

3x₁ + 7x₂ = b₃   ------------------------ (3)

3x₁ + 9x₂ = b₄   ------------------------ (4)

From equation (1) and (2), we get:

b₂ = 2b₁

After analysis equation (1), we have:

  6b₁-3b₃ +b₄ = 0

Using equation (1), (3) and (4), we get:

3(x₁+2x₂) -6(3x₁+7x₂) + 3x₁ + 9x₂ ≠ 0

Putting the value from equation (1),(3) and (4), we get:

6(x₁+2x₂) -3(3x₁+7x₂) + 3x₁ + 9x₂ = 0

Hence option (1) is correct.

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Complete Question:

Consider the following system of linear equations:

x₁+ 2x₂= b₁

2x₁ + 4x₂ = b₂

3x₁ + 7x₂ = b₃

3x₁ + 9x₂ = b₄

which one of the following conditions ensures that a solution exists for the above system.

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0

2. b₃ = 2b₁ and 6b₁-3b₃ +b₄ = 0

3. b₂ = 2b₁ and 3b₁-6b₃ +b₄ = 0

4. b₃ = 2b₁ and 3b₁-6b₃ +b₄ = 0

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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Answer:

?????

Step-by-step explanation:

a. The population of interest is University of California Berkeley undergraduates, and the sample consists of 129 undergraduates from that population. b. The results of the study cannot be generalized to the population, and the findings do not establish a causal relationship between social class identification and candy taking behavior.

a. The population of interest in this study is University of California Berkeley undergraduates. The sample in this study consists of 129 University of California Berkeley undergraduates who were selected to participate in the study.

b. The results of the study cannot be generalized to the entire population. The findings are limited to the specific sample of 129 University of California Berkeley undergraduates who participated in the study. Generalizing the results to a broader population would require a larger and more diverse sample that represents a wider range of demographics.

As for establishing causal relationships, the study can provide evidence for a correlation between social class identification and candy taking behavior. However, it cannot establish a definitive causal relationship. Other factors or variables that were not measured or controlled for could potentially influence the observed relationship. To establish a causal relationship, further research using experimental designs and rigorous controls would be necessary.

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The two choices that reflect one for the center and one for the spread are:

A. Better measure of spread: the interquartile range (IQR)

B. Better measure of center: the median

For the first data set, the values appear to be unordered, so it would be difficult to determine the mean. The median is a more appropriate measure of center for this data set, as it would provide a value that separates the data into two halves.

The interquartile range (IQR) is a better measure of spread for this data set, as it provides a robust measure of spread that is less sensitive to outliers. The IQR is the difference between the 75th percentile and the 25th percentile of the data, and it provides a measure of the spread of the middle 50% of the data.

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Answer:

DFG= 52

JKL=38

Step-by-step explanation:

complementary angle means that the sum of the two angles are equal to 90° so

(x+5)+(x-9)=90

= x+5+x-9=90

= 2x-4=90

= 2x=94

= x= 94÷2=47

DFG= x+5= 47+5=52

JKL= x-9= 47-9=38

hope it helps

Answer:

you can make it a decimal.

Step-by-step explanation:

3/4= 0.75

Answer:

To convert any fraction to decimal form, we just need to divide the numerator by the denominator. Here the fraction is 3/4 which means we need to divide: 3 ÷ 4. Therefore, 3/4 = 0.75.

Answer:

where are the answers???

Step-by-step explanation:

Answer: x = 0

Step-by-step explanation:

Cross multiply 4 to (x+1)

4x + 4 = 3x + 4

Move all terms of X to one side of the equations, and non variable integers to the other side

4x (-3x) = 4 (-4)

x = 0

The answer is:

Work/explanation:

To solve this, I will distribute 4 on the left side:

\(\sf{4(x+1)=3x+4}\)

\(\sf{4x+4=3x+4}\)

Next, I subtract 3x from each side:

\(\sf{x+4=4}\)

Then, I subtract 4 from each side:

\(\sf{x=0}\)

Hence, in answering the stated question, we may say that We can travel slope intercept down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

The intersection point in mathematics is the point on the y-axis where the slope of the line intersects. a point on a line or curve where the y-axis intersects. The equation for the straight line is Y = mx+c, where m represents the slope and c represents the y-intercept. The intercept form of the equation emphasises the line's slope (m) and y-intercept (b). The slope of an equation with the intercept form (y=mx+b) is m, and the y-intercept is b. Several equations can be reformulated to seem to be slope intercepts. When y=x is represented as y=1x+0, the slope and y-intercept are both set to 1.

We must solve for y in order to find the slope-intercept form of the equation:

6x + 2y = 4

2y = -6x + 4

y = -3x + 2

As a result, the slope is -3 and the y-intercept is 2.

To graph the line, first plot the y-intercept at the point (0, 2). The slope can then be used to find another point on the line. We can travel down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

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Answer:

5(9y + 4).

Step-by-step explanation:

GCF of 45y and 20 is 5

Answer is 5(9y + 4).

Answer:

9a^3b^3.

Step-by-step explanation:

The GCF of 9 and 27 is 9.

For a^4 and a^3 it is a^3.

For b^4 and b^3 it is b^3.

Answer is therefore:

9a^3b^3.

Answer:

9a^3 b^3

Step-by-step explanation:

hope this helps you have a nice day :)

i use to use this but its whatever works for you the second picture for prime factors

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer:

84 cm^2

Step-by-step explanation:

Area of triangle + area of rectangle

Area of triangle = 1/2*l*b

= 1/2*8*3= 12 cm^2

Area of rectangle = l*b

= 12*6 = 72 cm^2

Total area= 72+12

= 84 cm^2

Answer:

slope = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (1, - 2)

m = \(\frac{-2-2}{1-(-1)}\) = \(\frac{-4}{1+1}\) = \(\frac{-4}{2}\) = - 2

Answer:

AB = 4.5

Brainliest, please!

Step-by-step explanation:

A (-1, 2) B (1, -2)

y = +4

x = +2

a^2 + b^2 = c^2

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

c = 4.5 (rounded)

The sample proportion is 0.68 and the 95% confidence interval for the population proportion is between 0.631 and 0.729.

To calculate a confidence interval for the percentage of people who have a yearly physical exam, we first need to calculate the sample proportion:

p' = 238/350 = 0.68

Next, we need to find the appropriate z-score for a 95% confidence level. From the table of common z-scores, we can see that the z-score for a 95% confidence level is 1.96.

Now we can use the formula for the confidence interval:

\(p' \pm z * \sqrt{((p' * (1 - p')) / n) }\)

where p' is the sample proportion, z is the z-score for the desired confidence level, sqrt is the square root, and n is the sample size.

Plugging in the values, we get:

0.68 ± 1.96 * sqrt((0.68 * (1 - 0.68)) / 350)

Simplifying this expression, we get:

0.68 ± 0.049

Therefore, the 95% confidence interval for the percentage of people who have a yearly physical exam is:

0.631 ≤ p ≤ 0.729

Rounding to three decimal places, we get:

0.631 ≤ p ≤ 0.729.

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Answer: b. 1923

Step-by-step explanation:

If y is normally distributed with parameters μ and σ and you observe y and then build a rectangle with length |y | and width 3|y |, then e(a) = 3(σ\(^2\) + μ\(^2\))

To find E(A), the expected value of the area A of the rectangle, we need to consider the distribution of Y and the dimensions of the rectangle.
Given that Y is normally distributed with parameters μ (mean) and σ (standard deviation), we know that the length of the rectangle is |Y| and the width is 3|Y|. Therefore, the area A of the rectangle can be expressed as:
A = |Y| * 3|Y|
Now, let's find the expected value of A, E(A):
E(A) = E(|Y| * 3|Y|)
Since 3 is a constant, we can take it out of the expectation:
E(A) = 3 * \(E(|Y|^2)\)
We need to find the expected value of \(|Y|^2\). Notice that \(|Y|^2\) = \(Y^2\), as squaring a number removes its sign. So, we need to find \(E(Y^2)\).
For a normal distribution with parameters μ and σ, we know that:
\(E(Y^2)\) = Var(Y) + \((E(Y))^2\)
Here, Var(Y) represents the variance of Y, which is σ\(^2\), and E(Y) represents the expected value of Y, which is μ. Therefore:
\(E(Y^2)\) = σ\(^2\)+ μ\(^2\)
Now, we can substitute this value back into our expression for E(A):
E(A) = 3 * \(E(Y^2)\) = 3 * (σ\(^2\) + μ\(^2\))
So, the expected value of the area A of the resulting rectangle is:
E(A) = 3(σ\(^2\) + μ\(^2\))

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\(g(x) = (24 - x)2 + 7\\= 48 - 2x + 7\\g(6) = 48 - 2 \cdot 6 + 7\\= 48 - 12 + 7\\= 43\)

Answer:

66?lol

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

hope this helped i had this same question and i answered it

Based on the given chart, Dwayne has constructed a probability model for the number of occupants of a randomly-selected car on his street. The chart shows the probabilities of different numbers of occupants in a car. These probabilities add up to 1, as the number of occupants in a car can only be one of the given possibilities.

The chart shows that the most likely number of occupants in a car is 1, with a probability of 0.5. This means that half of the cars on the street have only one person in them. The second most likely possibility is 2 occupants in a car, with a probability of 0.25. This means that one-quarter of the cars have two people in them. The probabilities for 3, 4, and 5 occupants are progressively lower, with probabilities of 0.15, 0.06, and 0.04, respectively.

Therefore, Dwayne's model is a discrete probability distribution, where the possible outcomes are the number of occupants in a car, and the probabilities of each outcome are given by the chart. This model is based on the data that Dwayne collected on the number of occupants of cars travelling on the road past his house for the past week. The model can be used to predict the likelihood of different numbers of occupants in a car on Dwayne's street.

Dwayne's probability model for the number of occupants in a randomly-selected car on his street can be represented by the given chart. The chart shows the probabilities for different numbers of occupants:

1. Probability of 1 occupant: 0.5 (50%)
2. Probability of 2 occupants: 0.25 (25%)
3. Probability of 3 occupants: 0.15 (15%)
4. Probability of 4 occupants: 0.06 (6%)
5. Probability of 5 occupants: 0.04 (4%)

To confirm that this is a valid probability model, we need to ensure that the sum of all probabilities is equal to 1:

0.5 + 0.25 + 0.15 + 0.06 + 0.04 = 1

Since the sum is 1, the chart represents a valid probability model for the number of occupants in a car on Dwayne's street. This model can be used to make predictions about the number of occupants in future cars passing by Dwayne's house, based on the data he collected during the past week.

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The simplified expression with positive exponents for the given expression is 16r^11.

To simplify and express the answer using positive exponents, we can use the product rule of exponents which states that when multiplying two terms with the same base, we add their exponents.

Using this rule, we can simplify 4r^7 as:

4r^7 = 4 * r * r^6

Similarly, we can simplify (4r)(r^3) as:

(4r)(r^3) = 4 * r * r^3

Now we can multiply these two simplified terms:

4r^7 * (4r)(r^3) = (4 * r * r^6) * (4 * r * r^3)

= 16 * r^(6+1) * r^(1+3)

= 16 * r^7 * r^4

= 16r^(7+4)

= 16r^11

Therefore, the simplified expression with positive exponents for the given expression is 16r^11.

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Step-by-step explanation:

Radius of the circle=8

We know that

\(\boxed{\sf Area=\pi r^2}\)

\( \sf \rightharpoondown \: area = \frac{22}{7} \times {8}^{2} \\ \sf \rightharpoondown \: \frac{22}{7} \times 64 \\ \sf \rightharpoondown \: \frac{22 \times 64}{7} \\ \sf \rightharpoondown \: \frac{1408}{7} \\ \sf \rightharpoondown \: 201.1units {}^{2} \)

\(\sf More\:to\:know\begin {cases}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {cases}\)

Answer:

Step-by-step explanation:

If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/