What is the first step in solving a quadratic equation of the form given below?
(ax + b)^2 = 0
A. Take the square root of both sides
B. Factor out a common factor
C. Divide both sides by c
D. Use the zero product rule

Answer:

N' (- 8, 2 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

N (8, 2 ) → N' (- 8, 2 )

Answer:

Step-by-step explanation:

All of these are done exactly the same way so I will work out one of them for you, and you can follow my example to get the answers to the rest of them. I will do #5. The formula for this is

7(7 + x) = 8(8 + 13) and then solve the equation to find x:

49 + 7x = 168 and

7x = 119 so

x = 17.

Follow that pattern for each of your problems and you should be fine.

The equation cannot be proven as it is not true. The statement is incorrect.

The statement provided is not true. Three times the square of any side of an equilateral triangle is not equal to four times the square of the altitude.

Let's consider an equilateral triangle with side length "s" and altitude "h". The area of an equilateral triangle can be calculated using the formula:

Area = (sqrt(3)/4) * s^2

The altitude divides the equilateral triangle into two congruent right-angled triangles. Using the Pythagorean theorem, we can find the relationship between the side length, altitude, and half the side length:

(h^2) + (s/2)^2 = s^2

Simplifying the equation:

h^2 + (s^2)/4 = s^2

h^2 = (3/4) * s^2

The equation shows that the square of the altitude is three-fourths the square of the side length, not four times. Therefore, the statement is incorrect, and we cannot prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

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Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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Answer:

3\15

Step-by-step explanation:

hope this helps

Answer:

\(\frac{2}{8}and\frac{5}{20}\)

Step-by-step explanation:

\(\frac{3}{15}=\frac{1}{5}\)

\(\frac{2}{8}=\frac{1}{4}\)

\(\frac{5}{20}=\frac{1}{4}\)

\(\frac{11}{40}=\frac{11}{40}\)

Answer:

34.69 years for the first part.

Step-by-step explanation:

I got it right

Answer:

StartFraction 1 Over 8 EndFraction

Step-by-step explanation:

Answer:

f(3) = 3

Step-by-step explanation:

f(1) = 1

f(2) = 2

f(n) = f(n − 2) + f(n − 1)

f(3) = f(3 - 2) + f(3 - 1)

     = f(1) + f(2) = 1 + 2 = 3

Special Note:  Have you heard of the Fibonacci sequence?  

The formula f(n) = f(n − 2) + f(n − 1) is used to find the terms of the of the  Fibonacci sequence

Part A: The measure of the two angles are 50° and 40° respectively.

Part B: The measure of the third angle is 90°

Part C: To construct a triangle when given the three angles, a compass, a ruler, and a protractor are required. The angles are constructed using the compass and the protractor, then, the sides of the triangle are joined together using a ruler.

Triangle construction is the process of drawing a triangle with particular dimensions while taking into account all of the relevant triangle attributes.

Triangles can be created with the aid of a protractor, a ruler, and a compass.

The construction of triangles can be carried out based on:

For the given triangles, the measurements of the two angles are 50° and 40° respectively from the protractor measurements

The measure of the third angle = 180° - (50° + 40°)

The measure of the third angle  = 90°

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This gives us the equation -2x + y = 0 and 4x - 3y = 0, which has the solution x = y/2. Therefore, the eigenvector for λ = 3 is v2 = [1; 2].

a) To find matrix A with eigenvalues 1 and 4 and corresponding eigenvectors v1 and v2 respectively, we can use the formula A = PDP^-1 where P is the matrix of eigenvectors and D is the diagonal matrix of eigenvalues.

We know that v1 and v2 are eigenvectors with eigenvalues 1 and 4 respectively, so we can set up the following equations:

Av1 = 1v1 and Av2 = 4v2

Multiplying both sides of each equation by P^-1, we get:

PDv1 = v1 and PDv2 = 4v2

Therefore, P = [v1 v2] and D = [1 0; 0 4], which gives us the matrix A = PDP^-1.

b) To find matrix B with eigenvalues 1 and 3, we can use the same formula A = PDP^-1. However, we don't know the eigenvectors yet. To find them, we can use the characteristic polynomial of B, which is (1-λ)(3-λ) = 0. This gives us eigenvalues λ = 1 and λ = 3.

To find the eigenvectors for λ = 1, we need to solve the equation (B-λI)v = 0, which gives us:

(B-1I)v = 0
[0 1; 1 2][x; y] = [0; 0]

This gives us the equation x + y = 0, so the eigenvector for λ = 1 is v1 = [1; -1].

To find the eigenvectors for λ = 3, we need to solve the equation (B-λI)v = 0, which gives us:

(B-3I)v = 0
[-2 1; 4 -3][x; y] = [0; 0]


Using these eigenvectors and the formula A = PDP^-1, we can find the matrix B = PDP^-1 where P = [v1 v2] and D = [1 0; 0 3].

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Answer:

A

Step-by-step explanation:

The correct for confidence interval is A. [25.8158, 28.1842].

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified level of assurance.

To find the 95% confidence interval for the population mean, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √(Sample Size))

Since the sample size is large (n = 36), we can use the z-score critical value for a 95% confidence level. The z-score for a 95% confidence level is approximately 1.96.

Plugging in the values:

Sample Mean = 27

Standard Deviation = 3.5

Sample Size = 36

Critical Value (z-score) = 1.96

Confidence Interval = 27 ± (1.96) × (3.5 / √36)

Calculating the confidence interval:

Confidence Interval = 27 ± (1.96) × (3.5 / 6)

Confidence Interval = 27 ± (1.96) × (0.5833)

Confidence Interval = 27 ± 1.1417

Confidence Interval = [25.8583, 28.1417]

Therefore, the correct answer is A. [25.8158, 28.1842].

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As a result, the answer to the provided coordinate plane problem is only choice C), which is the right answer.

The term "coordinate plane" refers to a two-dimensional region that consists of two number lines. It emerges when the X-axis & Y-axis intersect at a location known as the origin. Using the numbers on a coordinate grid, one can locate points.

Here,

Since, If there is a coordinate plane with both parallel lines, go with option A.

Therefore, there is no cure.

There are hence a finite number of solutions that could be found.

If two lines cross, there is only one potential result for Option B. Consequently, the quantity of potential solutions is.

According to Option C, there must be an endless number of solutions to the system because there are two coinciding lines that provide us an infinite number of junction sites.

The difference between Option D) and Option B) is noted.

Only choice C) is hence the proper one.

Therefore , the solution to the given problem of coordinate plane comes out to be Only choice C) is hence the correct one.

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Answer:

idk

Step-by-step explanation:

idk just responding

for points

Answer:

120 miles

Step-by-step explanation:

If 1 inch = 20 miles, you can multiply both sides by 6 to figure out how many miles 6 inches represent.

Answer:

x=33 and y= 75 is the answer.

Answer:

3

Step-by-step explanation:

8x2+4y÷z

when x=12,

y=34,

and z=2?

Answer:

1 - 22

2 -

\( - 4x {y}^{3} - 6 {x}^{4} {y}^{3} + 7 {y}^{4} - 8 {x}^{4} {y}^{4} \)

3- ( x = -4)

4 - Irrational numbers

\( \sqrt{53} \: \: \: \: \: \sqrt{19} \: \: \: \: \pi\)

integers

\(0 \: \: \: \: \: \frac{ - 12}{6} \)

rational

\( \frac{2}{3} \: \: \: \: \frac{6}{45} \)

natural numbers 8

Answer:

the answer is this hope it helps

Answer:

Dan and Anja are both correct.

Step-by-step explanation:

Base on the given;

Total: \(1 \frac{5}{8}\)

Dan:

1st Bottle: \(\frac{5}{8}\)

2nd Bottle: \(\frac{1}{8}\)

3rd Bottle: \(\frac{7}{8}\)

Anja:

1st Bottle: \(\frac{6}{8}\)

2nd Bottle: \(\frac{2}{8}\)

3rd Bottle: \(\frac{5}{8}\)

Since we know all the info now. Let's first add up all the bottles.

Dan:

\(\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=[?]\)    ⇒ Only add the numerator.

\(\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=\frac{13}{8}\) ⇒ Simplify

\(\frac{13}{8}=1\frac{5}{8}\)

Anja:

\(\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=[?]\)   ⇒ Only add the numerator.

\(\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=\frac{13}{8}\)⇒ Simplify

\(\frac{13}{8}=1\frac{5}{8}\)

Base on the given;

Total = \(1\frac{5}{8}\)

From what we solve:

Dan and Anja are both correct.

Since the drop-down menus wasn't given. I can not farther given more info. Please have a link to the image if help is needed.

RevyBreeze

Hence, the number of ways be assigned to runways without using the same runway is \(240\) ways.

What is the permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged.

Here given that,

Here are five airplanes ready to depart. runway \(A\) and runway \(D\) are available.

Number of ways to assign \(3\) planes to that runway is

\(^5C_3=^5C_2=10ways\)

Then for each group

Each group of three planes can be arranged in \(^3P_3=3!=6ways\)

Each group of three planes can be arranged in \(^2P_2=2!=2ways\)

So total number of arrangements are

\((2)(10)(6)(2)=240ways\)

Hence, the number of ways be assigned to runways without using the same runway is \(240\) ways.

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Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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Answer:

d.21

Step-by-step explanation:

840/40=21

Answer:

21 Weeks

Step-by-step explanation:

$840 ÷ 4 weeks = 21

You can also reverse work this by multiplying $40 by the other choices!

$40 x 40 = $1600

$40 x 35 = $1400

$40 x 32 = $1280

$40 x 21 = $840

As we can see, D is the only answer that makes sense, therefore 21 weeks is the answer.

≧◡≦

Mocha here! If this answer helped you, please consider giving it brainliest because I would appreciate it greatly. Have a wonderful day!

Answer:

0.6

Step-by-step explanation:

Answer:

[-5 3] [-5 6]

Step-by-step explanation:

Answer:

Your answer is on the pic...mate

Answer

$850.50

I think

Step-by-step explanation:

Answer:

874

Step-by-step explanation:

Couches: 2 × 677 = 1,354

Beds: 4 × 465 = 1,860

Lamps: 3 × 94 = 282

1,354 + 1,860 + 282 = 3496

Four equal payments: 3496 ÷ 4 = 874

Answer:

25+38= 63

Step-by-step explanation:

Used a calculator.

The correct decision is to accept the alternative hypothesis (Ha: M ≠ 5850) and conclude that the population mean is not equal to 5850 based on the given sample data.

To determine the correct decision for the hypothesis test, we need to compare the 95% confidence interval for the population mean with the null hypothesis value.

Null hypothesis (H0): M = 5850

Alternative hypothesis (Ha): M ≠ 5850

In this case, the null hypothesis assumes that the population mean (M) is equal to 5850, while the alternative hypothesis suggests that M is not equal to 5850.

The 95% confidence interval for the population mean is ($5938.42, $6546.32). If the null hypothesis value of 5850 falls within this confidence interval, we fail to reject the null hypothesis. If the null hypothesis value is outside the confidence interval, we reject the null hypothesis in favor of the alternative hypothesis.

Comparing the null hypothesis value with the confidence interval:

5850 < $5938.42 or 5850 > $6546.32

Since the null hypothesis value of 5850 falls outside the confidence interval, we reject the null hypothesis at the 5% level of significance. The correct decision is to accept the alternative hypothesis (Ha: M ≠ 5850) and conclude that the population mean is not equal to 5850 based on the given sample data.

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Answer:

the slope is 2 or 2 over 1

Step-by-step explanation:

the y intercept is 4

1.  the derivative of the function\(k(x) = x^2 + x - 1 / \sqrt{(x-1)}\)is:\(k'(x) = [(2x+1)\sqrt{(x-1)} - (x^2+x-1)] / [(x-1)\sqrt{(x-1)}\)

2. the derivative of the function\(m(x) = -5x\sqrt{ (x^2 - 9)^3}\) is: \(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2 / \sqrt{(x^2 - 9)}\)

To compute the derivative of the function we will use the quotient rule of differentiation.

First, let's simplify the expression under the square root sign:

√(x-1) = (x-1)^(1/2)

Now, we can rewrite the original function as:

\(k(x) = (x^2 + x - 1) / (x - 1)^{(1/2)\)

Using the quotient rule, we get:

\(k'(x) = [(2x+1)(x-1)^(1/2) - (x^2+x-1)(1/2)(x-1)^{(-1/2)}] / (x-1)\)

Simplifying this expression, we get:

\(k'(x) = [(2x+1)\sqrt{(x-1} ) - (x^2+x-1) / \sqrt{(x-1} )}] / (x-1)\)

\(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2 / \sqrt{(x^2 - 9)}\)

Therefore, the derivative of the function\(k(x) = x^2 + x - 1 / \sqrt{(x-1)}\)is:

\(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2 / \sqrt{(x^2 - 9)}\)

2.To compute the derivative of the function \(m(x) = -5x\sqrt{ (x^2 - 9)^3}\), we will use the chain rule of differentiation.

Let's first find the derivative of the expression inside the square root:

\(d/dx (x^2 - 9) = 2x\)

Using the chain rule, we get:

\(m'(x) = -5√(x^2 - 9)^3 + (-5x)(3(x^2 - 9)^2)(2x) / 2\sqrt{(x^2 - 9)}\)

Simplifying this expression, we get:

\(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2(x^2 - 9) / \sqrt{(x^2 - 9)^3}\)

\(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2(x^2 - 9) / \sqrt{(x^2 - 9)^3}\)

Therefore, the derivative of the function\(m(x) = -5x\sqrt{ (x^2 - 9)^3}\) is:

\(m'(x) = -5\sqrt{(x^2 - 9)^3} - 15x^2(x^2 - 9) / \sqrt{(x^2 - 9)^3}\)

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