Which of the following are solutions to the equation below?
Check all that apply.
x² + 6x + 9 = 20
A. x= 2√5-3
B. x= √3+ 20
C. x= -2√5 +3
D. x = -√3+20
☐ Ex= 2√5 +3
OF x=-2√5-3

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

a. The restriction is that\(x+2 \neq 0\), which means that \(x \neq -2.\) So, the solution to this equation must satisfy this restriction.

b. The only solution that satisfies both the equation and the restriction is x=2.

The given rational equation is:

\(\frac{3}{x+2} + 4= \frac{19}{x+2}\)

a. To find the restrictions on the variable, we need to identify the values of the variable that make the denominator zero. In this case, the denominator is x+2. Therefore, the restriction is that\(x+2 \neq 0\), which means that \(x \neq -2.\) So, the solution to this equation must satisfy this restriction.

b. Now, let's solve the equation. To do this, we will first combine the fractions on the left-hand side:

\(\frac{3}{x+2} +4 = \frac{19}{x+2}\\ \\\\\frac{3+4(x+2)}{x+2} = \frac{19}{x+2}\\ \\\\\frac{4x+11}{x+2} = \frac{19}{x+2}\)

Now, we can cross-multiply to get rid of the denominators:

(4x+ 11) (x+ 2) = 19 (x+2)

Expanding both sides, we get:

\(4x^2+ 19x + 22= 19 x+38\)

Simplifying, we get:

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

Dividing both sides by 4, we get:

\(x^2 -4=0\)

Factoring, we get:

(x-2) (x+2)= 0

So, the solutions are x=2 and x=-2. However, we need to keep in mind the restriction we found earlier, which is that \(x \neq -2\). Therefore, the only solution that satisfies both the equation and the restriction is x=2.

Thus, the solution to the given rational equation is x=2.

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Answer:

x² + y² = 49

Since, the equation of a circle is,

\((x-h)^2 + (y-k)^2 = r^2\)

Where,

(h, k) is the center of the circle,

r = radius of the circle,

Here,

(h, k) = (0, 0) ⇒  ( origin ),

r = 7 units,

Hence, the equation of the circle is,

\((x-0)^2 + (y-0)^2 = 7^2\\\\x^2 + y^2 = 49\)

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Answer:

x=10

Step-by-step explanation:

The lines the angles are on are 180 degrees so

(11x+23) + (7x-23)= 180

Let's rearrange them first

11x+7x + 23-23=180

Combine the like terms

18x + 0=180

Remove the 0

18x=180

Then divide 18 on each side

x=10

Answer:

There are infinitely many solutions to the system of equations

Explanation:

Given the system of equations:

y = -2x + 4 .................................................(1)

2x + y = 4 ..................................................(2)

The graph for this system is shown below:

The line for equation (2) is directly on the line for equation (1)

This shows that the lines intersect at infinitely many points, so there a infinitely many solutions.

The new population mean is 13

The given parameters are:

n = 5 and mean = 12

The mean is calculated as:

Mean = Sum/Count

So, we have

12 = Sum/5

This gives

Sum = 60

When n = 6, and the additional score is 18, we have

Mean = (Initial sum + x)/6

This gives

Mean = (60 + 18)/6

Evaluate

Mean = 13

Hence, the new population mean is 13

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Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 30\ seconds\)

    The standard deviation is  \(\sigma = 3 \ seconds\)

     The sample size is  n  = 9

    The null hypothesis is \(H_o: \mu = 30\)

     The alternative hypothesis is  \(H_a : \mu \ne 30\)

    The level of significance is  \(\alpha = 0.01\)

    The sample mean is  \(\= x = 31.2\)

Generally the test statistics is mathematically represented as

      \(z = \frac{ \= x - \mu }{ \frac{\sigma}{\sqrt{n} } }\)

=>   \(z = \frac{ 31.2 - 30}{ \frac{3}{\sqrt{9} } }\)

=>   \(z = 1.2\)

From the z table  the area under the normal curve to the right corresponding to  1.2  is    

         \(P(Z > 1.2) = 0.11507\)

Generally the p-value is mathematically represented as

         \(p-value = 2 * P(Z > 1.2)\)

=>       \(p-value = 2 *0.11507\)

=>       \(p-value = 0.230\)

From the value obtained w can see that

         \(p-value > \alpha\) hence

The decision rule is  

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

The value of the summation notation \(\sum\limits^{12}_{i=1} {-25x_i}\) for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

From the question, we have the following parameters that can be used in our computation:

69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7

The summation notation is given as

\(\sum\limits^{12}_{i=1} {-25x_i}\)

The summation notation  \(\sum\limits^{12}_{i=1} {-25x_i}\) means we multiply each value by -25 and add the results

Using the above as a guide, we have the following:

Sum = -25 * (69 - 5 + 47 - 10 - 80 + 13 + 64 - 76 - 95 + 45 + 9 + 7)

Evaluate

Sum = 300

Hence, the value of the summation notation \(\sum\limits^{12}_{i=1} {-25x_i}\) for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

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The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer:

No, because the number in 2011 multiplied by three is less than the number in 2015.

Step-by-step explanation:

i dunno just makes sense

Answer:

I think that it did not because 555*3 is not 900 so it can't equal it.

Step-by-step explanation:

Answer:

\(\sqrt{325}\)

Step-by-step explanation:

This is because you use Pythagorean theorem. a^2 + b^2 = c^2.

The required co-terminate angles of 1817° between 0° to 360° is 343°.

Co-terminal Angles are points who share similar introductory side and terminal sides. Finding co-terminal points is just about as straightforward as adding or taking away 360° or 2π to each point, contingent upon whether the given point is in degrees or radians. There are a boundless number of co-terminal  Angles that can be found.

For calculating co-terminal of angle 1817°,

We will subtract given angle 1817° from 2160°(multiple of 360°)

Then,

2160° - 1817°

343°

Thus, the co-terminating angle of 1817° is 343°.

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Answer:

87.5%

Step-by-step explanation:

These wholes together include 7/8 parts that are shaded. This as a percentage is 87.5%.

Hope this helps you out!! Have a great day ^^

a) 50

b)12/6

.......................

Answer:

m<PTR = 140°

Step-by-step explanation:

First, find the value of x. To find the value of x, derive an equation which you'd use in solving for x.

m<PTQ = (x + 28)°

m<RTS = (2x + 16)°

m<PTQ = m<RTS (vertical opposite angles are congruent)

Therefore:

x + 28 = 2x + 16

Solve for x. Combine like terms

28 - 16 = 2x - x

12 = x

x = 12

Find m<PTQ

m<PTQ = (x + 28)

plug in the value of x

m<PTQ = 12 + 28 = 40°

m<PTR + m<PTQ = 180° (supplementary angles)

m<PTR + 40° = 180° (substitution)

m<PTR = 180 - 40 (subtracting 40 from each side)

m<PTR = 140°

To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer:hope i helped! sry for the wait .-.

Step-by-step explanation:

Answer:

The answer to your question is:  Area and Circumference Like all geometric shapes, circles take up space and a formula is required to calculate the area.

Step-by-step explanation:

I hope this helps and have a wonderful day!

The range of the function on the graph is y > -6

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -6 i.e. the point where it intersects with the y-axis

So, the range is y > -6

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The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

  \(\dfrac{y}{x}=\dfrac{1}{4}\)

Step-by-step explanation:

When the line goes through the origin (0, 0), we can say that y is proportional to x. Then the ratio of y (the vertical measure) to x (the horizontal measure) is the same as the ratio of "rise" (the vertical change) to "run" (the horizontal change).

  y/x = rise/run = 1/4

The equation of the line is ...

  y/x = 1/4

Answer:

Th answer is C

Step-by-step explanation:

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Answer:

x = 98

y = 126

Step-by-step explanation:

If you match triangle abc to triangle cde, you will match where x and y is.

168 ÷ 12 = 14

Now you multiply 14 by the other side lengths

9 • 14 = 126

7 • 14 = 98

It is similar to a dilation.

Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer:

6

Step-by-step explanation:

57 divided by 9.5 = 6

Answer:

ok so from looking at this if he earns 14 dollars he saves 5 so he saves

5/14 so lets just multiply this by the 56

56*5/14=20

so he saves 20

20

Hope This Helps!!!

Answer:

7 adults

Step-by-step explanation:

I'm assuming you need to know how many adults are needed for 56 children.

Use a ration to find your answer.

   1 adult           X adults

----------------  =  ---------------

 8 children      56 children

Cross multiply then solve for X.

8X = 56

X = 7