A man's age today is 2 years more than three time the age his son will be in 5 years from now. if a represent the age of the son write an expression to find the age of the man today

Answer: A

Step-by-step explanation:

Answer:

send the whole statement

Answer:

54.0054

Step-by-step explanation:

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Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

The answer will be 41/14

Step-by-step explanation:

2.928571429

Step-by-step explanation:

| - 5 | + | - 4 |

5 + 4

= 9

| - 6| - 4

6 - 4

2

I hope this answers your question.

Answer:

\(\frac{1}{16}\)

Step-by-step explanation:

Given;

\(\frac{1}{4}\div \:4\)

Solve;

\(\mathrm{Convert\:element\:to\:fraction}:\quad \:4=\frac{4}{1}\)

\(=\frac{1}{4}\div \frac{4}{1}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

\(\frac{1}{4}\times \frac{1}{4}\)

\(\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

\(=\frac{1\times \:1}{4\times \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:1\times \:1=1\)

\(=\frac{1}{4\times \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:4\times \:4=16\)

\(=\frac{1}{16}\)

Number line given below:

~Learn with Lenvy~

Answer:

Step-by-step explanation:

If f(x) is an even function, that means it has symmetry across the y-axis. In other words, if (a,b) is a point on the graph of f(x), then (-a,b) must also be on the graph.

We are given that f(2) = -5. Since 2 is a positive number, we know that (-2) is the corresponding negative value that also lies on the y-axis. Therefore, we can say that f(-2) = f(2) = -5.

So, the other point that must be on the graph of f(x) is (-2,-5).

Answer:

D.68 is greater than 112 because 68 is greater than the benchmark 12, and 112 is less than the benchmark 12.

Answer: 1/ 3 ^9

Step-by-step explanation:

Answer:

1/39

Step-by-step explanation:

3-9=1/39

The answer is 0ne over three exponent nine

Step-by-step explanation:

9 + 1/6 + 2 1/12

9 + 2.25

11.25

Answer:

1/3

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

i was just learning this stuff

The slope of the line = 3/4

"It is the ratio of change in the y values to the change in x values"

From given graph,

Consider AB,

assuming scale of 1 unit on each axis,

change in y = 3 and the change in x = 4

Therefore, the slope of the line  = 3/4

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Answer:

d = 2

Step-by-step explanation:

Using the formula

A=pq/2

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Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer: The value of \(g(a+2)=5a-8\).

Step-by-step explanation:

We are given that,

\(g(x)=5x-2\)                                            ...(i)

To find: \(g(a+2)\)

Substitute \(x=a+2\) in (i), we get

\(g(a+2)=5(a+2)-2\\\\g(a+2)=5a+10-2\\\\g(a+2)=5a+8\)

Therefore, the value of \(g(a+2)=5a-8\).

Answer:

\( \: \: \: \: \: \: \)

Miles is going to spend less than the hours that were spent last week since 2/3 is a fraction.

A fraction represents a part of a whole, and is therefore always less than the whole. For example, 2/3 represents two out of three equal parts of a whole.

The implication of this is that the time that Miles would have to spend on biking in the coming week would be wo out of three equal parts of a whole time that was spent in the last week and this would be less than the time spent last week.

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n = 1

i don't really know to to properly explain it

Answer:

n=1

Step-by-step explanation:

Answer:

-59

Step-by-step explanation:

x = -2

4(-2)³ - 6(-2)² + (-2) - 1

= -32 - 24 - 2 - 1

= - 59

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

\(We\ have \ A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3]\)

So ,we have to produced 25 matrix -

AA,AB,AC,AD,AE

BA,BB,BC,BD,BE

CA,CB,CC,CD,CE

DA,DB,DC,DD,DE

EA,EB,EC,ED,EE

To multiply two matrix column of first matrix equal to row of second matrix.

So we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

\(AA=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\AA=\left[\begin{array}{ccc}-2&-2&-2\\4&1&-2\\10&4&-2\end{array}\right] \\\\AD=\left[\begin{array}{ccc}0\\1\\6\end{array}\right] \\\\CC=\left[\begin{array}{ccc}2&2\\2&2\\\end{array}\right] \\\\EE=[9]\)

So we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

The complete question is :-

Let the matrices,

\(A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3]\)

Which of the 25-matrix products AA, AB, AC ......EE are defined? Compute those products that are defined.

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Answer:

$1.50

Step-by-step explanation:

If you do cost per quantity you would get $9 over 6 visits. Then you divide both sides by 6 because to get to one by 6 it's 6 so when you divide both sides by 6 you would get 1.5 over 1 and all you do is add a zero because you're dealing with money

Hope this helps :)

Answer: the y intercept is 330. the rate of change is -55. the domain is infinity since it is linear i'm pretty sure

Step-by-step explanation:

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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Answer:

$56,226

Step-by-step explanation:

x = investment

Earning interest of 3.57% is the equivalent of multiplying the initial balance (investment) by 1.0357;

Over 20 years, the new balance can be found by multiplying the initial balance by (1.0357)²⁰;

We can formulate an equation to solve to get the initial investment:

x(1.0357)²⁰ = 113400

(2.01687752)x = 113400

x = ¹¹³⁴⁰⁰/₍₂.₀₁₆...₎

x = 56225.5263 → 56226

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16