The answer is 12 points
I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12
Multiplying monomials and binomials
Answer:
[tex]28w^2-476w[/tex]
Step-by-step explanation:
The general rule we are going to use to multiply this out is the distributive property. Which is:
a(b+c) = ab + ac
Note: x * x = x^2
Now multiplying, we get:
[tex]28w(w-17)\\=28w*w-28w*17\\=28w^2-476w[/tex]
This is the multiplied out form, answer.
Find the area of the equilateral triangle whose sides are 4 yd.
Answer:
The first one. 4 times square root of 3.
Step-by-step explanation:
The side of the equilateral triangle that represents the height of the triangle will have a length of because it will be opposite the 60o angle. To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.
Answer:
Remember:
Triangle area= [tex]\frac{b*h}{2}[/tex]
h of equilateral triangle = [tex]\frac{\sqrt{3}}{2}*a[/tex]
Step-by-step explanation:
b=4yd
a=4yd
h = [tex]\frac{\sqrt{3}}{2}*a[/tex]
h = [tex]\frac{\sqrt{3}}{2}*4yd[/tex]
4/2=2
h= [tex]2\sqrt{3} yd[/tex]
area= [tex]\frac{b*h}{2}[/tex]
area= [tex]\frac{4 yd*2\sqrt{3} yd}{2}[/tex]
2/2=1
Finally
area= [tex]4\sqrt{3} yd^2[/tex]
what is -3x^2-4x-4=0
Answer:
no real solutionStep-by-step explanation:
[tex]-3x^2-4x-4=0\qquad\text{change the signs}\\\\3x^2+4x+4=0\\\\\text{use the quadratic formula:}\\\\\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then an equation has no solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then an equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac>0,\ \text{then an equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have}\ a=3,\ b=4,\ c=4.\\\\\text{Substitute:}\\\\b^2-4ac=4^2-4(3)(4)=16-48=-32<0\\\\\bold{no\ real\ solution}[/tex]
An abundant number is a positive integer N such that the sum of the factors of N (not including N) is greater than N. What is the smallest abundant number?
What does the line y = 2x + 5 look like?
Answer:
A line with slope 2 and y-intercept 5.
Step-by-step explanation:
y=mx+b is the slope-intercept form of a line with slope,m, and y-intercept ,b.
y=2x+5 is in this exact form.
This means y=2x+5 is a line with slope 2 and y-intercept 5.
You can graph this by first plotting the y-intercept (0,5).
You can then use the slope to find another point. Keep in my the slope=rise/run so you might want to write it as a fraction.
The slope=2/1, this means you will rise 2 units and go right 1 unit.
So if you start at (0,5) then you can find another point by going to (0+1,5+2)=(1,7).
So if you graph (0,5) and (1,7) and then connect them with a straight-edge you have graphed y=2x+5.
If x= 6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the
equation?
Answer:
discriminant is zero (0)
Step-by-step explanation:
Actually, you have a double root here: {6, 6}: "two real, equal roots." That tells us immediately that the value of the discriminant was zero (0).
Answer:
The discriminant of the equation is zero.
Step-by-step explanation:
The given graph is a quadratic equation. If x = 6 is the only x-intercept of the graph, then the roots must be equal.
The quadratic equation will have two solutions. Here the two solutions are equal x = 6.
If the roots are equal, then the discriminant is zero.
The factors of the quadratic equation (x - 6) (x - 6)
= [tex]x^2 - 6x - 6x + 36[/tex]
= [tex]x^2 -12x + 36[/tex]
Discriminant = [tex]b^2 - 4ac[/tex]
Here a = 1, b = -12 and c = 36
Discriminant = [tex](-12)^{2} - 4.1.36[/tex]
= 144 - 144
= 0
Therefore, the answer is "The discriminant of the equation is zero."
What are the zeros of the function below? Check all that apply.
F(x) =x(x-2)/(x+3)(x-5)
Answer:
x = 0 and x = 2Step-by-step explanation:
[tex]\text{The domain:}\\\\(x+3)(x-5)\neq0\iff x+3\neq0\ \wedge\ x-5\neq0\\\\x\neq-3\ \wedge\ x\neq5\\\\========================\\\\f(x)=\dfrac{x(x-2)}{(x+3)(x-5)}\\\\\text{The zeros are for}\ f(x)=0\\\\\dfrac{x(x-2)}{(x+3)(x-5)}=0\iff x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\x=0\in D\ \vee\ x=2\in D[/tex]
The vertex of this parabola is at (2,-4). When the y value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} h=2\\ k=-4 \end{cases}\implies y=a(x-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y = -3\\ x = -3 \end{cases}\implies -3=a(-3-2)^2-4\implies 1=a(-5)^2 \\\\\\ 1=25a\implies \boxed{\cfrac{1}{25}=a}[/tex]
Answer:
it is not 5
so there are only three options left
Quadrilateral ABCD is reflected across the x-axis and then reflect across the y-axis to form quadrilateral A′B′C′D′. If the coordinates of vertex A are (-7, 3), what are the coordinates of vertex A′?
A.
(7, 3)
B.
(-7, -3)
C.
(7, -3)
D.
(-7, 3)
E.
(3, 7)
Answer:
B(-7,-3)
Step-by-step explanation:
When you reflect across the x axis, your y coordinate is multiplied by -1.
(-7,-1(3))
(-7,-3)
The only answer choice that is the same as my result is B.(-7,-3).
identify the domain and range of each situation using words and inequalities.
Victoria recently switched to a new electric
company. If she uses between 0 and 400
kilowatt-hours (kWh) of electricity per month,
the cost is a set price of $30. If she uses 400
kWh or more per month, the price is $0.097
per kWh.
Answer:
When x=0 to 400, y=30. This makes ths domain for this inequality 0 to 400 and the range is just 30. When x>400, y=.097x. This makes the domain from 400 to infinity and the range .097(401) to infinity.
Step-by-step explanation:
The price is set between 0 and 400 kWh at $30 dollars flat. The price, however, for any usage of electric greater than 400 kWh is $.097 for every kWh used, making it multiply by the kWh.
The domain (electricity usage) is 0 to infinity kilowatt-hours (0 ≤ kWh < ∞), and the range (cost) has two parts: a fixed cost of $30 (for 0-399 kWh) and a variable cost that starts at $38.80 and can increase infinitely ($30 < Cost < ∞) for usage of 400 kWh or more.
Explanation:To identify the domain and range of the cost of electricity based on Victoria's usage, let's consider two situations described:
When Victoria uses between 0 and 400 kilowatt-hours (kWh) of electricity per month, the cost is a flat rate.When Victoria uses 400 kWh or more per month, the cost is based on the amount she uses at a rate of $0.097 per kWh.Domain (Electricity Usage in kWh): This refers to the amount of electricity used. Victoria's electricity usage is between 0 kWh and any upper limit (which isn't specified but is typically determined by practical or contractual limits). So, we can express the domain in inequalities as 0 ≤ kWh < ∞ (where ∞ represents infinity).
Range (Cost in $): For the first situation, since the cost is set no matter the usage between 0 and 400 kWh, the range is a single value of $30. In the second situation, the cost starts at $0.097 per kWh for 400 kWh, which is $38.80, and increases as more electricity is used. Thus, the range for the second part is $30 < Cost < ∞.
The domain is specified in kilowatt-hours and is not capped, indicating it's a continuous set of values over a range from 0 to infinity. The range for the cost has two distinct parts: a fixed cost for usage under 400 kWh, and a variable cost that starts at a minimum value and increases potentially without bound for usage above 400 kWh.
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Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.
Answer:
The standard form of the equation is 49t² - 75t + 3 = 0
The solution of the equations are 1.49 and 0.041
Step-by-step explanation:
* Lets explain how to solve the problem
- The standard form of the quadratic equation is ax² + bx + c = 0,
where a , b , c are constant and a can not be 0
∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1
- Lets make the left hand side equal to 0
∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides
∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10
∴ 49t² - 75t + 3 = 0
* The standard form of the equation is 49t² - 75t + 3 = 0
∵ ax² + bx + c = 0
∴ a = 49 , b = -75 , c = 3
- Lets use the formula [tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] to solve
the equation
∴ [tex]x=\frac{-(-75)+\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=1.49[/tex]
∴ [tex]x=\frac{-(-75)-\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=0.041[/tex]
* The solution of the equations are 1.49 and 0.041
A pastry chef wants to bake and sells fries. Before they start production, they need to make sure they can make a profit with the materials and labor force they have. Their accountant has given them a cost equation of y=0.65x+1410 and a revenue equation of y=0.8x. How many pies will they need to sell in order to reach the break order point?
Answer:
They need to sell 9400 pies to reach the break-order point
Step-by-step explanation:
* Lets explain the break-order point
- The break-order point is the point at which total cost and total
revenue are equal
∴ The total cost = The total revenue
* Lets solve the problem
∵ The equation of the total cost is y = 0.65x + 1410
∵ The revenue equation is y = 0.8x
- To find the break-order point equate the two equations
∴ 0.65x + 1410 = 0.8x
- Subtract 0.65x from both sides
∴ 1410 = 0.8x - 0.65x
∴ 0.15x = 1410
- Divide both sides by 0.15
∴ x = 1410/0.15 = 9400
∵ x is the number of pies
* They need to sell 9400 pies to reach the break-order point
Plz convert 5/10 into a simplified fraction and a decimal.
Step-by-step explanation:
[tex]\dfrac{5}{10}=\dfrac{5:5}{10:5}=\dfrac{1}{2}\\\\\dfrac{5}{10}=0.5[/tex]
Tyreese is using algebra tiles to solve the equation below.
2x + 5 = -x + (1)
answers
A. remove one x-tile from both sides. B. remove two x-tiles from the left side. C. add one positive x-tile to both sides. D. add two positive x-tiles to both sides.
for this case we have the following equation:
[tex]2x + 5 = -x + 1[/tex]
To resolve:
We add x to both sides of the equation:
[tex]2x + x + 5 = -x + 1 + x[/tex]
[tex]3x + 5 = 1[/tex]
We subtract 5 on both sides of the equation:
[tex]3x + 5-5 = 1-5\\3x = -4[/tex]
We divide between 3 on both sides of the equation:
[tex]x = - \frac {4} {3}[/tex]
Answer:
We add x to both sides of the equation
Answer:
The correct option is C) add one positive x-tile to both sides.
Step-by-step explanation:
Consider the provided equation.
2x + 5 = -x + 1
Now to solve the above equation first isolate the variables.
To isolate the variables add x to the both the side of the equation.
2x + 5 + x = -x + 1 + x
Now add the like terms.
3x + 5 = 1
Here we add the x tiles to the both the side of the equation.
Now consider the options.
The correct option is C) add one positive x-tile to both sides.
if A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5, then P(A and B)=
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.
Explanation:If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.
Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa. Therefore, the probability of both A and B occurring together is zero.
what is the intercept for the graph of this line? 5x -3y =11
Step-by-step explanation:
[tex]5x-3y=11\\\\x-intercept\ is\ for\ y=0\\\\5x-3(0)=11\\5x-0=11\\5x=11\qquad\text{divide both sides by 5}\\x=\dfrac{11}{5}\\\\y-intercept\ is\ for\ x=0\\\\5(0)-3y=11\\0-3y=11\\-3y=11\qquad\text{divide both sides by (-3)}\\y=-\dfrac{11}{3}[/tex]
Find the LCD for the following fractions: , 25x3 60x3 25x5 60x5
Answer:
We need to find the lowest common divisor which is the smallest possible number that is dividable by ALL numbers.
We have the following numbers:
[tex]\frac{25}{3}[/tex]
[tex]\frac{60}{3}[/tex]
[tex]\frac{25}{5}[/tex]
[tex]\frac{60}{5}[/tex]
For the denominators (3, 3, 5, 5) the least common multiple (LCM) is 15.
LCM(3, 3, 5, 5) . Therefore, the least common denominator (LCD) is 15.
Rewriting the original inputs as equivalent fractions with the LCD:
125/15, 300/15, 75/15, 180/15
Solve for x in the equation x2 - 4x - 9 = 29.
Answer:
[tex] x = 2 + \sqrt{42} [/tex] or [tex] x = 2 - \sqrt{42} [/tex]
Step-by-step explanation:
[tex] x^2 - 4x - 9 = 29 [/tex]
Subtract 29 from both sides.
[tex] x^2 - 4x - 9 - 29 = 29 - 29 [/tex]
[tex] x^2 - 4x - 38 = 0 [/tex]
There are no two integers whose sum is -4 and whose product is -38, so the trinomial is not factorable. We can use the quadratic formula.
a = 1; b = -4; c = -38
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-38)}}{2(1)} [/tex]
[tex] x = \dfrac{4 \pm \sqrt{16 + 152}}{2} [/tex]
[tex] x = \dfrac{4 \pm \sqrt{168}}{2} [/tex]
[tex] x = 2 \pm \dfrac{\sqrt{4 \times 42}}{2} [/tex]
[tex] x = 2 \pm \dfrac{2\sqrt{42}}{2} [/tex]
[tex] x = 2 \pm \sqrt{42} [/tex]
[tex] x = 2 + \sqrt{42} [/tex] or [tex] x = 2 - \sqrt{42} [/tex]
Factor completely.
5x^2 + 10x - 40
Answer:
5(x + 4)(x - 2)
Step-by-step explanation:
Start by factoring 5 out of all three terms. We then have
5(x^2 + 2x - 8), or
5(x^2 + 2x - 8), which is in proper quadratic form.
Note that (4)(-2) = 8 and that 4 - 2 = 2, which match the 3rd and 2nd coefficients of x^2 + 2x - 8.
Thus, in completely factored form, we have 5(x + 4)(x - 2)
Answer:
5 (x -2) (x +4)
Step-by-step explanation:
5x^2 + 10x - 40
Factor out a 5
5(x^2 +2x-8)
We can then factor inside the parentheses
What two numbers multiply to -8 and add to 2
-2*4 = -8
-2+4 = 8
5 (x -2) (x +4)
Identify the two rational numbers 2.7182818459, 2.777777, square root 3, -7/3
Answer:
2.777777 and -7/3
Step-by-step explanation:
2.7182818459 cannot be written in fraction form therefore it is irrational.
2.777777 is rational because it can be written as the fraction 25/9
The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.
-7/3 is rational because it is already in fraction form.
Answer:
2.777777 and -7/3
Step-by-step explanation:
If a number can be defined in the form of p/q where q≠0, then it is called rational number.
If a decimal number is repeating then it is a rational number because it can be written in the form of p/q.
For example: 1.222, 3/5, 2.5, -1/2, 4.0707007...
All real numbers which are not rational numbers are called irrational numbers.
For example: 0.2357835.., √2, π.
In the given numbers,
Rational numbers = 2.777777, -7/3
Irrational numbers = 2.7182818459 and √3
Therefore the two rational numbers are 2.777777 and -7/3.
Which triangle is a 300-60°-90° triangle?
10
5/3
15
5/3
Check the picture below.
Answer:
A)
Step-by-step explanation:
The 30-60-90° triangle has the side lengths of 1, √3, 2, so you should find the triangle that fits this measurement.
A) is your answer for:
Side with measurement 1 (30°): 5
5 is your measurement for the side measurement of 1. The next measurement (60°) must be x √3: 5 x √3 = 5√3 (Side on the bottom).
The last measurement (90°) 2 is twice the measurement of 1: 5 x 2 = 10 (Hypotenuse, side on top).
A) is your answer.
~
Please help!
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12?
20
90
150
180
Answer:
180
Step-by-step explanation:
According to the table, the relationship between the x and the y value is 20, (4*20 = 80) (5*20 = 100) etc.
The graph with the points has a relationship of 35 (2*35 = 70) (4*35 = 140) etc. Therefore, you can figure out what y-value 12 would have for the table and the graph by multiplying 12 by 20 or 35 respectively.
12*20 = 240
12*35 = 420
420-240 = 180
Answer:
180
Step-by-step explanation:
1. Find the number of real number solutions for the equation.
x2 - 18 = 0
A. cannot be determined
B 2
C 1
D O
Answer:
b. 2
Step-by-step explanation:
Simplify the expression.
-(10)^-2
1/10^2
-1/10^2
-1/-2^10
10^2
Answer:
the answer is 10^2
thanks. hope full it help you
Answer:
10^2
your welcome :>
Your beginning food inventory was 26,000. You have purchased an additional 24,000 and have accepted 12,000 in transfers from other locations. In total, you sold 39,000 worth of foodfor the same time period. Your ending inventory is 29,000. What is your gross profit margin percentage
?
Answer
130,000
Hope it helps!
The gross profit margin calculates as 15.38% for the given business scenario, calculated with the values provided in the sales, purchases, inventory, and transfers.
Explanation:The subject of this question is gross profit margin in a business, which can be calculated using certain financial figures and simple arithmetic. We start by determining the cost of goods sold (COGS), which includes the beginning inventory, any additional purchases, and transfers from other locations, subtracted by the ending inventory. Using your figures, we get the following calculation: $26,000 (beginning inventory) + $24,000 (purchases) + $12,000 (transfers) - $29,000 (ending inventory) = $33,000 (COGS).
Next, we subtract the cost of goods sold from the total sales to determine the gross profit: $39,000 (total sales) - $33,000 (COGS) = $6,000 (gross profit).
Finally, to find the gross profit margin percentage, we divide the gross profit by total sales, and then multiply by 100, which gives us: $6,000/$39,000 * 100 = 15.38%.So, your gross profit margin percentage is 15.38%.
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What is the length of BC in the right triangle 9 and 12 below
The length of BC in the right triangle with sides 9 and 12 is 15.
Explanation:In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the lengths of the other two sides are given as 9 and 12. Let's label the hypotenuse as BC. We can use the Pythagorean theorem to solve for BC:
a2 + b2 = c2
92 + 122 = c2
81 + 144 = c2
225 = c2
Taking the square root of both sides, we find that the length of BC is 15 units.
What will $110,000 grow to be in 9 years if it is invested today at 11%
Answer:
218,900
Step-by-step explanation:
110,000 x 11%= 12,100
12,100 x 9 = 108,900
110,000+108,900= 218,900
The future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years is approximately $278,984.57.
Explanation:The question is asking for the future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years. For such a calculation, we can use the formula for compound interest:
FV = PV * (1 + r)^n
Where,
FV is the future value of the investment PV is the present value or the initial amount invested which is $110,000 r is the annual interest rate which is 11% or 0.11 n is the number of periods the money is invested for which is 9 years
Plugging in the values, we get:
FV = $110,000 * (1 + 0.11)^9
After calculating the above expression, we find that the investment will grow to be approximately $278,984.57 after 9 years.
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simplify (square root 3)(5 square root 3)
[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{3} \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{\frac{1}{2}}\cdot 3^{\frac{1}{5}}\implies 3^{\frac{1}{2}+\frac{1}{5}}\implies 3^{\frac{5+2}{10}}\implies 3^{\frac{7}{10}}[/tex]
Solve to get brainliest ( Need 2 people ) TIME LIMIT 8:00 MINUTES
If 12% of the number is 24, what is the number?
Good luck!
Answer:
200
Step-by-step explanation:
12% is the same thing of .12
x = the number you are trying to find
.12(x) = 24 ----- This means that 12% of x is 24.
x = 24/.12
x = 200
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole
We want to know out of what number is 24 12% of. This means 24 is the part and the unknown (let's make this x) is the whole.
Here is your proportion:
[tex]\frac{24}{x} =\frac{12}{100}[/tex]
Now you must cross multiply
24*100 = 12*x
2400 = 12x
To isolate x divide 12 to both sides
2400/12 = 12x/12
200 = x
This means that 12% of 200 is 24
Hope this helped!
~Just a girl in love with Shawn Mendes
If f (x) = 3(x+5) + 4/x what is f(a+2)?
Answer:
f(a+2)= 3((a+2)+5) +4/(a+2)
Step-by-step explanation:
Since X was exchanged for a+2, you have to set a+2 as x in the problem.
Answer:
[tex]\large\boxed{f(a+2)=3(a+7)+\dfrac{4}{a+2}}[/tex]
Step-by-step explanation:
[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)-\text{put x = a + 2 to the equation of f(x):}\\\\f(a+2)=3\bigg((a+2)+5\bigg)+\dfrac{4}{a+2}=3(a+2+5)+\dfrac{4}{a+2}\\\\f(a+2)=3(a+7)+\dfrac{4}{a+2}[/tex]