Micaela is 2 years older than Sam. In 4 years, the sum of their ages will be 40. How old is Micaela now?

Describe and fix any errors in the solution.
Let m = Micaela’s age and s = Sam’s age.
m = s + 2 (s + 4) + (s + 2 + 4) = 40
s = 15

Answer:

The diameter of the largest pen you could build is [tex]\frac{100}{\pi }[/tex] or [tex]31.8309[/tex] ft

Step-by-step explanation:

As the equation for the circumference of a circle is

[tex]C=d\pi[/tex]

We can plug in the known value for C, which is 100 and solve for d

[tex]100=d\pi[/tex]

[tex]d=\frac{100}{\pi }[/tex]

ANSWER

The diameter of the largest pen you can build is 31.8 feet to the nearest tenth.

EXPLANATION

You have 100 feet of fencing to build a circular sheet pen.

The largest diameter you can get is when you use all the 100 feet of fencing to build the sheet pen.

The circumference of the circular sheet pen must then be 100 feet.

Then using the formula for circumference, we have:

C=πd

100=πd

[tex]d = \frac{100}{\pi} [/tex]

d=31.83 ft.

The equation of the line that passes through (5,-2) and (-3,4) is y = (-3/4)x + 7/4.

To find the equation of the line that passes through (5,-2) and (-3,4), we can use the formula for the equation of a straight line, which is y = mx + b.

Answer:

x = π/2 or

x = π/2 + 2πn (for any value of n)

Step-by-step explanation:

We need to find the numerical value of the trigonometric function sinx+1/sinx=1+cscx

Subtract 1+cscx on both sides

sinx + 1/sinx -(1+csc x) = 1+cscx - (1+cscx)

sinx + 1/sinx -1 -csc x = 0

Taking LCM i.e, sinx and solving

(sinx)(sinx) + 1 - sinx -cscx(sinx) / sinx = 0

Multiplying sinx on both sides

sin^2 x + 1 -sinx - cscx(sinx) =0

as we know, cscx = 1/ sinx

sin^2 x + 1 -sinx - (1/sinx)(sinx) = 0

Solving,

sin^2 x + 1 -sinx - 1 = 0

sin^2 x - sin x =0

Let u = sinx

Putting it in above equation

u^2 - u =0

Solving the equation:

u= 1 , u= 0

Putting back the value of u

sin(x) = 1 and sin(x) = 0

x = sin ⁻¹ (1) and x = sin ⁻¹ (1) =0

x = 90° or π/2 and x = 0 (undefined for the question)

So, x = π/2 or

x = π/2 + 2πn (for any value of n)

Answer: 0, 4, -9

Set the equation equal to zero.

x(x - 4)(x + 9) = 0

Solve for x by setting each factor equal to zero.

The factors in the equation are x, (x - 4), and (x + 9).

        x = 4

        x = -9

The zeros of the function are 0, 4, and -9.

You can find length by knowing the formula for perimeter: 2l+2w= p; where l= length, w= width, and p= perimeter. Substitute the things you know and solve.

In this case, the length would be 11 feet.

Answer:

120

Step-by-step explanation:

x/6=20

×=20×6

=120

Answer:

[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]

Step-by-step explanation:

Blue:

The inequality for the blue line is

[tex]y\geq 3x-2[/tex]

Yellow

The inequality for the yellow line is

[tex]y\leq \frac{1}{2} x+3[/tex]

This means that the correct answer is the third option,

[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]

The graph shows the solution for the inequalities y ≥ 3x - 2 and y ≤ x + 3.

The inequalities can be found by substituting the coordinates of a point within the shaded area in both inequalities and seeing if they are satisfied.

The options are given.

Let us take the options one by one:

Now, substitute (0,0) in the inequalities:

0 ≥  2 and 0 ≤  3

This is not true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ - 3

This is not true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ 3

This is true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ - 3

This is not true.

Therefore, we have found that the inequalities are y ≥ 3x - 2 and y ≤ x + 3. The correct answer is option C.

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Answer:

all real numbers greater than or equal to 3

Step-by-step explanation:

There's some ambiguity in your "3/x+2-sqrt x-3."  I will assume that you meant:

   3

---------- - sqrt(x - 3).       Using parentheses often changes everything.

 x + 2  

Here we see that x cannot = -2, because x + 2 would be zero then.  And x must be greater than or equal to 3, so that the input to the sqrt function will be 0 or greater.  The domain for f(x) is all real numbers greater than or equal to 3.  The prohibition against x = -2 has no bearing on the overall domain of this function.

Answer:

The domain for f(x) is all real numbers GREATER than or equal to 3

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

since that arc is 120 you subtract that form 360 and voila!

Answer:

Maximum value of the function is 4.

Step-by-step explanation:

Given function of simple harmonic motion is [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].

Now we need to find about what is the maximum value of [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].

We know that value of sine function varies from -1 to 1.

that means for any value of t, maximum value of sine function is 1.

[tex]\sin\left(\frac{\pi}{8}t\right) \leq 1[/tex]

[tex]4 \sin\left(\frac{\pi}{8}t\right) \leq 4[/tex]

[tex]d \leq 4[/tex]

Hence maximum value of the function is 4.

Answer:

There is not enough information

Step-by-step explanation:

If you wanted to find all the factors, here’s a list.

1,2,4,8,16

Answer:

Step-by-step explanation:

Let's say R is roses, L is lilies, and O is orchids.

R = 2L

O = R + 5

R + L + O = 45

Let's substitute the second equation into the third:

R + L + (R + 5) = 45

2R + L = 40

Now substitute the first equation:

2(2L) + L = 40

4L + L = 40

5L = 40

L = 8

Therefore:

R = 2L = 16

O = R + 5 = 21

There are 16 roses, 8 lilies, and 21 orchids.

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.

__

Comment on the answer choice:

The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.

The domain of the original function with the positive slope is restricted to x > 4, and the range of f(x) is y ≥ 6. Therefore, the domain of the inverse function is x ≥ 6.

The function given is f(x) = |x – 4| + 6. When restricting the domain to the portion of the graph with a positive slope, the function increases. In the absolute value function, the slope changes at the vertex, which here is when x = 4. For x > 4, the slope is +1 because the graph of the function is increasing. So, considering the domain x > 4 makes the graph of the function only represent the portion with a positive slope.

The range of the original function with the restricted domain is f(x) ≥ 6, because the lowest value of |x – 4| is 0 when x ≥ 4, which results in f(x) = 0 + 6 = 6 when x = 4. Consequently, the corresponding range of the inverse function must be the domain of the original function, and thus, the domain of the inverse function must be x ≥ 6.

Answer:

A  = $2200(7.612) = $16,747.28

Step-by-step explanation:

You don't say whether this is simple interest or compound interest.  I will assume you meant compound interest, for which the appropriate formula is

A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years.  Then:

A = $2200(1 + 0.0725)^29, or

A = $2200(1.0725)^29, or

A  = $2200(7.612) = $16,747.28

The amount in the account after 29 years will be approximately $8484.64.

To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:

A = 2200(1 + 0.0725/1)^(1*29)

A = 2200(1.0725)^29

A ≈ $8484.64

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Answer and Explanation :

Given : The data represents the number of traffic tickets written by two police officers in one day over the course of a week.

Officer 1: 21, 11, 14, 16, 10, 18, 5

Officer 2: 16, 19, 20, 17, 6, 13, 23          

To find : (a) Draw a box and whiskers plot for each officer

(b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?        

Solution :

a) We plot the box plot with the help of graphing calculator of both data.

Refer the attached figure below.

Figure 1 shows the data 1 with Median 14.

Figure 2 shows the data 2 with Median 17.

b) On comparing the median of both Officer's are different first officer has 14 median and second officer has 17 median.

Answer:

Opt B. y=5-3x

Step-by-step explanation:

We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.

To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:

Subtraction of -5 in both sides of equality sign.

-y=3x-5

Lets multiply by -1 the equation from above:

y= 5-3x.

From the above we can find the slope, is the coefficient of x. in this case -3

And the y-intercept point is 5.

Answer:

Around 79.17 weeks

Step-by-step explanation:

Answer:

if you want to know how many weeks are in one year and 27 weeks, i can help out

Step-by-step explanation: 1 year has 365 days in it and one week has 7 days in it. Divide 365 by 7.

365/7= about 52 weeks.

52+27=79 weeks.

The exact amount of weeks is 79.177457

hope this helped!!

Answer:

The formula for the area of a polygon is 1/2*a*p.

a = apothem, which is a line segment that is the shortest distance from the center to a side.

p = perimeter

Hope this helps. :)

Answer:

Step-by-step explanation:

There's no one formula for finding the area of any polygon.

There are specialized formulas for finding the area of a square, of a triangle, of a trapezoid, etc.  Beyond these, you have to invent approaches, such as breaking up an octagon into 8 triangles, finding the area of 1 such triangle, and then multiplying that area by 8.

Answer:

The principal of the loan is $350000

$26844 is not half 54886 so the statement is not true

Step-by-step explanation:

* Lets use the given rule to solve the question

- The total loan amount to be paid = p (1 + r)^t , where

# t is time in years,

# r is interest rate as a decimal

# p is the principal of the loan

- To find t divide the number of months by 12

∵ t = 30/12 = 2.5 years

∵ r = 6/100 = 0.06 ⇒ the interest rate in decimal

∵ The total loan amount to be paid = $404,886

∴ 404,886 = p (1 + 0.06)^2.5

∴ 404,886 = p (1.06)^2.5 ⇒ divide both sides by (1.06)^2.5

∴ p = 404,886 ÷ [(1.06)^2.5] ≅ $350,000

* The principal of the loan is $350,000

- To check the statement of the manager lets find the difference

  between the total loan amount and the principal

∵ The principal of the loan is $350,000

∵ the total loan amount to be paid is $404,886

∴ The difference = 404,886 - 350,000 = $54886

- Lets find the total loan amount to be paid when the interest rate

 was cut in half

∵ The total loan amount to be paid = p (1 + r)^t

∵ t = 30/12 = 2.5 years

∵ The half of 6% is 3%

∴ r = 3/100 = 0.03 ⇒ the interest rate in decimal

∵ p = $350,000

∴ The total loan amount to be paid = 350,000 (1 + 0.03)^2.5

∴ The total loan amount to be paid = 350,000 (1.03)^2.5

∴ The total loan amount to be paid = $376,844

- Lets find the difference between the total amount to be paid and

 the principal

∴ The difference = 376,844  - 350,000 = $26844

∵ $26844 is not half 54886

* The statement is not true

Answer:

Subtract the flat fee from the total amount, then divide that amount by the cost per mile.

89 - 44 = 45

45 / 0.24 = 187.5 miles total.

To change the graph of f(x) = [tex]x^2[/tex] into g(x) = 4[tex]x^2[/tex] + 24x + 30, the transformations include a vertical stretch by a factor of 4 and a shift to the left by 3 units and up by 6 units. Completing the square helps identify these shifts.

To transform the graph of f(x) = [tex]x^2[/tex] into the graph of g(x) = 4[tex]x^2[/tex] + 24x + 30, we can analyze the changes applied. First, the coefficient of x2 in g(x) is 4, which means the original parabola is vertically stretched by a factor of 4. Second, the term 24x indicates a horizontal transformation, specifically a shift, which is revealed when we complete the square.

To complete the square for the quadratic part of g(x), we rewrite the equation as 4([tex]x^2[/tex] + 6x) + 30 and add and subtract the square of half the coefficient of x inside the parentheses, giving us 4((x + 3)2 - 9) + 30. This simplifies to 4(x + 3)2 + 6, indicating that the graph of f(x) was also shifted to the left by 3 units and up by 6 units.

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the equation that can be used to find width is B

Answer:

It's a

Step-by-step explanation:

I did it

Answer:

±i√55

Step-by-step explanation:

Answer:

8cm

Step-by-step explanation:

Since the area of a square is Side X Side (s x s) it is also s². The s² is also equivalent = 64cm². To find the length of a side you do the √64cm² and you get 8cm for a side. Great Job!

Answer:

x = - [tex]\frac{1}{4}[/tex], x = 2

Step-by-step explanation:

Given

8x² - 14x - 4 = 0 ( divide through by 2 to simplify )

4x² - 7x - 2 = 0

To factorise the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 2 = - 8 and sum = - 7

The factors are - 8 and + 1

Use these factors to split the x- term

4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )

4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(4x + 1) = 0

Equate each factor to zero and solve for x

4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = - [tex]\frac{1}{4}[/tex]

x - 2 = 0 ⇒ x = 2

21.6 x 5.9 x 0.5 = 63.72

The area of the triangle is 63.72 ft²

Answer:

63.72 ft^2

Step-by-step explanation:

The base and the height of the triangle are given:  21.6 ft and 5.9 ft.

Apply the area-of-a-triangle formula:

A = (1/2)(base)(height)

Here, the area is

A = (1/2)(21.6 ft)(5.9 ft) = 63.72 ft^2

Answer:

Step-by-step explanation:

Convert the fractions to the decimals (you can use the calculator):

2/3 = 2 : 3 = 0.6666...

3/5 = 3 : 5 = 0/6

We have

0.65

0.666...

0.6

0.5

The order from least to greatest:

0.5

0.6

0.65

0.666..

[tex]\begin{array}{c|c|c|c|c}0&.&5\\0&.&6\\0&.&6&5\\0&.&6&6&6...\end{array}[/tex]

Hello There!

To find the mean we have to add up all the numbers and divide by how many numbers there are.

6+15+16+20+13+5+10+16

Now, I will add 2 numbers at a time to make it easier for myself.

21+36+18+26

Once I add up these numbers, I will get a sum of 101

Finally, I divide 101 by 8 and get a quotient of 12.625

6 + 15 + 16 + 20 + 13 + 5 + 10 + 16 = 101/8 = 12.6

mean: 12.6

Answer:

x < 6

Step-by-step explanation:

Let's isolate x first.  Add 3 to both sides, obtaining (1/3)x < 2.  Now multiply both sides by 3 to eliminate the fraction:  x < 6

Let's do the same thing to evaluate g(-5):

-5Answer:

Step-by-step explanation:

Never heard of "synthetic substitution."  I think you meant "synthetic division," which is a great method of evaluating polynomials for given input values.

g(x) = x^5 – 8x^3 – 2x + 7 is missing two terms.

With all terms showing, it would read:

g(x) = x^5 – 0x^4 + 8x^3 – 0x^2 - 2x + 7.  The coefficients are {1, 0, 8, 0, -2, 7}.

Let's evaluate g(3).  Use 3 as divisor in synth. div.:

3   )  1   0   8   0   -2   7

            3   9  51  153 453

    ------------------------------

       1    3   17  51  151  460      Since the remainder is 460, the value of g(3) is also 460.

-5  )   1    9    8    0    -2       7

              -5  -20  60 -300 1510

    ----------------------------------

       1      4    -12   60 -302   1517

The remainder is 1517, and so g(-5) = 1517.

Answer:

28, -2,108

Step-by-step explanation: