Find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5). check that your answers make sense.

The fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is \(a_{n} = a_{n -1} 5\).

According to the given question.

We have a formula for finding the general term of a sequence is

\(a_{n} = a_{n -1} 5\)

Also,

The first term of the sequence, \(a_{1} = 2\)

Therefore,

The fifth term of the sequence is given by

\(a_{5} = a_{5-1} 5\)

⇒ \(a_{5} = a_{4} 5\)

⇒ \(a_{5} = (a_{4-1}5) 5\)

⇒ \(a_{5} = a_{3}25\)

⇒ \(a_{5} = (a_{3-1}5) 25\)

⇒ \(a_{5} = a_{2} 125\)

⇒ \(a_{5} = a_{2 -1} (5)125\)

⇒ \(a_{5} = a_{1} 625\)

⇒ \(a_{5} = 2(625)\)

⇒ \(a_{5} = 1250\)

Hence, the fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is \(a_{n} = a_{n -1} 5\).

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Okay, here we have this:

We will take as the first term the upper squares and as the second term the lower ones, and we obtain that:

Here we obtain that the correct answer is the option D.

Answer:

x = 108

Step-by-step explanation:

(x - 5) and 103 are Alternate exterior angles and are congruent, then

x - 5 = 103 ( add 5 to both sides )

x = 108

Answer:

If each square (from the squared paper) has side length 1, then that hexagon has four sides of length √12+42=√17 and two sides of length √32+32=√18.Step-by-step explanation:

Answer:

i couldnt fined a good number line charrt for am example but it ruffle right here  in the pic

Step-by-step explanation:

I'm going to assume they are the same angle.

Steps to solve:

(8x - 8) = (7x + 8)

~Add 8 to both sides

8x = 7x + 16

~Subtract 7x to both sides

x = 16

Best of Luck!

Answer:

Step-by-step explanation:

Volume of the cylinder is = π x r x r x h = π x 2 x 2 x 9 = 113.097

The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).

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Answer:

Numerical.

Step-by-step explanation:

A number sentence is a statement of equality between two numerical expressions!

Hope this helps!

Andre's account after t years is \(V_h=538.45(1.025)^t\) since is option C.

The Amount accumulated at the end of a interest year is the sum of the principla amount and the interest gained on the principal amount.

As Andres start the savings account after 3 years so, the equation representing the value of Andre's account after t years is-\(v_h=500(1.025)^{t-3}\).

Also, the amount accumulated in the mean 3 years will be-

\(A=500(1.025)^3\)

=$538.45

Hence, another way of writing the equation representing the value of Andre's account after t years is-\(V_h=538.45(1.025)^t\)

As a result, option C is the correct answer.

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).

As given in the question,

Population mean of the random variable 'μ' = 141

Standard deviation 'σ' = 8.85

Sample size 'N' = 43 observations

Standard error of the sample mean

= σ / √N

= 8.85 / √43

= 8.85 / 6.56

= 1.349

= 1.35 (round to 2 decimal places )

Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.

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Answer:

515

Step-by-step explanation:

- For x less than 0, f(x) is -5.
- For x between 0 and 3, f(x) is 2x - 5.
- For x greater than or equal to 3, f(x) is x - 6.
- Evaluating f(3) results in -3.

The given function is a piecewise function, which means that its definition varies depending on the value of x. In this case, the function f(x) is defined as follows:

- For x less than 0, f(x) is equal to -5.
- For x between 0 (inclusive) and 3 (exclusive), f(x) is equal to 2x - 5.
- For x greater than or equal to 3, f(x) is equal to x - 6.

To evaluate f(3), we need to find the value of f(x) when x is equal to 3.

Since 3 is greater than or equal to 3, the third part of the piecewise function applies. Therefore, we substitute x = 3 into the expression x - 6.

f(3) = 3 - 6
    = -3

Therefore, f(3) is equal to -3.

In summary:
- For x less than 0, f(x) is -5.
- For x between 0 and 3, f(x) is 2x - 5.
- For x greater than or equal to 3, f(x) is x - 6.
- Evaluating f(3) results in -3.

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Answer:

29 when rounded up 27 when rounded down and 28.56 in genral

Step-by-step explanation:

Answer:

28 or 30

Step-by-step explanation:

42 to 40 and 68 to 70 then

hope this helps :b

Step-by-step explanation:

the slope (m) of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, going from (-8, 19) to (4, -2)

x changes by +12 (from -8 to 4).

y changes by -21 (from 19 to -2).

the slope (m) is therefore

-21/+12 = -7/4

and by using (4, -2) as the point, we get

-2 = -7/4 × 4 + b = -7 + b

5 = b

and the full equation is

y = (-7/4)x + 5

You can only add or subtract radicals together if they are like radicals.

√28

Factor 4 out of 28.

√4(7)

Rewrite 4 as 22.

2 2.7

Pull terms out from under the radical.

217

The result can be shown in multiple forms.

Exact Form:

2√7

Decimal form:

5.29150262…

√63

Factor 9 out of 63.

/9 (7)

Rewrite 9 as 32.

Pull terms out from under the radical.

3√7

The result can be shown in multiple forms.

Exact form: 3√7

Decimal Form: 7.93725393...

Sqrt(24)

2√6

Pull terms out from under the radical.

√2^2.6

The result can be shown in multiple forms.

Exact Form:

2√6

Decimal Form:

4.89897948....

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The complete question is: Solve the following radicals:

a) 5 ± \(\sqrt{28}\)

b) 4 ± \(\sqrt{63}\)

c) 6 ± \(\sqrt{24}\)

Answer:

I think its 12

Step-by-step explanation:

because these half angels are equal to 30,90, and 60

if you are looking for AD then we have half of 10 which is 5

So then we had 5+13=18

If we add 18+12 it will equal to 30

and if we add them all up 13+10+12+13=48

and acute angle-an angle can equal to anything below 90

I think this is correct

It is calculated using the formula: z = (x - μ) / σ

The employee's z-score is approximately 1.2.

The z-score measures how many standard deviations an individual observation is from the mean of a normally distributed population. It is calculated using the formula:

z = (x - μ) / σ

where x is the individual observation, μ is the population mean, and σ is the population standard deviation.

In this case, the employee's score is 386, the population mean is 350, and the population standard deviation is 30. Let's calculate the z-score step by step.

Substituting the given values into the formula:

z = (386 - 350) / 30

Simplifying the expression:

z = 36 / 30

z = 1.2

Therefore, the employee's z-score is approximately 1.2. This indicates that the employee's score is 1.2 standard deviations above the mean of the population.


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Answer:

D

Step-by-step explanation:

The y-coordinate will be the average of 5 and -2 which is 3/2. This eliminates options A and B. C doesn't make sense because the x-coordinate (which is -7) of the midpoint can't be larger or smaller than the x-coordinates of the endpoints, so that means that the answer is D.

The correct option is B: V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the Volume of the solid generated when region R is revolved about the vertical line x = 1.

The volume of the solid generated when region R is revolved about the vertical line x = 1, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by revolving a region R about a vertical line is given by:

V = 2π ∫[a,b] x * f(x) dx

In this case, since we are revolving the region R about the vertical line x = 1, the limits of integration will be from y = 2 (where the horizontal line y = 2 intersects the graph y = 2x - 2) to y = 0 (where the graph y = 2x - 2 intersects the x-axis).

Let's analyze the options provided:

A. π ∫[1,2] ((y + 2)/2 - 1)^2 dy

B. π ∫[0,2] ((y + 2)/2 - 1)^2 dy

C. π ∫[1,2] (2 - (2x - 2))^2 dy

D. π ∫[0,2] ((y + 2)/2)^2 - 1^2 dy

Option A: The limits of integration are incorrect. We need to integrate with respect to y, not x.

Option B: This appears to be the correct integral setup, integrating with respect to y and using the correct limits of integration.

Option C: This option incorrectly uses the expression (2 - (2x - 2))^2, which doesn't match the function y = 2x - 2.

Option D: The limits of integration are incorrect. We need to integrate from y = 2 to y = 0.

Therefore, the correct option is B:

V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the volume of the solid generated when region R is revolved about the vertical line x = 1.

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Answer:

-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

g(x) tells us what the variable is and what variable should be replaced with a value.

g(1) tells us the value that will replace x.

Plug in 1 to the equation:

-5(1) + 1 = g(1)    (multiply)

-5 + 1 = g(1)       (combine like terms)

-4 = g(1)

Therefore, g(1) is equal to -4

Answer:

Option (3)

Step-by-step explanation:

By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.

From the figure attached,

Two tangents CD and DE are intersecting each other at point D outside the circle A.

Two intercepted arcs are minor arc CE and major arc CBE,

Measure of arc CE = 112°

Therefore, measure of major arc CBE = 360° - 112°

                                                               = 248°

m(∠CDE) = \(\frac{1}{2}(\text{arcCBE}-\text{arcCE})\)

                 = \(\frac{1}{2}(248-112)\)

                 = \(\frac{1}{2}\times 136\)

                 = 68°

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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Answer:

y=1/5x+7

Step-by-step explanation:

i hope this helps :)

Its components by their greatest common factor, which is 2:

To find a normal vector to the plane with the equation 8x - 14y - 6z = 0, we can simply read off the coefficients of x, y, and z and use them as the components of the normal vector. So, the normal vector is:

⟨8, -14, -6⟩

Note that this vector can be simplified by dividing all its components by their greatest common factor, which is 2:

⟨4, -7, -3⟩

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#a

Refer to attachment 1

#b

Refer to attachment 2

Answer:

m= 1/4

Step-by-step explanation:

6 - 5 = 1

6 - 2 = 4     1/4

Answer:

m=1/4

Step-by-step explanation: