If f(x) = 3x + 2, what is f(5)?

Answers

Answer 1
If X is 5
Then f(5) = 3(5) + 2
= 17
Answer 2

Answer:

If a numbed substitutes x in f (x), you must substitute that number in the function for x.

Step-by-step explanation:

f(5) = 3(5) + 2

f(5 )= 17


Related Questions

A. 2
C
C. 3
5
4
3
-3-2 A-10
-1
2
-2
-3
B
1
N
D
3 4
5
E
6
F
In the similarity
transformation of AACB
to AEFD, AACB was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B. 1/2
D. 1/3

Answers

Answer: x-axis

Step-by-step explanation:

If you visualize the line of reflection, it must be vertical. Option A is the only option that has a vertical line.

graph the solution set of this inequality 3x-2y <_ 12

Answers

The graph of the solution set for the inequality can be seen below.

How to graph the solution set?

Here we have the inequality:

3x - 2y < -12

If we isolate y, we get:

3x + 12 < 2y

(3x + 12)/2 < y

(3/2)x + 6 < y

Now, we just need to graph the line y = (3/2)x + 6 with a dashed line (because the points on the line are not solutions).

And then we need to shade the region above the line.

The graph of the solution set can be seen below.

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What is the percentage of salt in the solution made of 9 on of water and 3 lb of salt

Answers

The percentage composition of salt in the solution is; 84.2%.

What is the percentage composition of salt?

Since, it follows that there are 16 ounces in 1 pound. Then the 3 lb of salt is equivalent to; 3×16 = 48ounces.

Consequently, the percentage of salt in the solution as described is;

{48/57} × 100%

Percentage composition of salt is therefore;

= 84.2%.

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The term can also be written as:

Answers

The correct expansion is the one in option b:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

How to rewrite the term?

Here we must use the logarithmic property:

[tex]Log(a) -Log(b) = Log(\frac{a}{b})[/tex]

Our expression in this case is:

[tex]Log_9(\frac{6}{11})[/tex]

Using the above property, we can rewrite the expression as:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

From this, we conclude that the correct option is B.

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write the zeros of this function: f(x) = 25 - 75x - 100x^2

Answers

The answer would be x=2

How many surgeon are either office-based or ophthalmologist.?

Answers

Answer:

Is there a graph related to this question?

suppose that there are two types of tickets to show; advance and same -day. Advance tickets cost $35 and same-day tickets cost $30. For one performance, there were 50 tickets sold in all, and the total amount paid for them was $1650. How many tickets of each type were sold?

Answers

Answer:

#of advanced tickets (x) = 30

#of same-day tickets (y) = 20

Step-by-step explanation:

x-#of advanced tickets

y-#of same-day tickets

[tex]x+y=50,\\35x+30y=1650[/tex]

5x+30(x+y)=1650

5x+30(50)=1650

5x=150

x=30

y=20

Find the volume of a cone with a diameter of 12 m and a height of 7m.

A. 84 m^3
B. 84π m^3
C. 336 π m^3
D. 252 π m^3

Answer Fast!
I am giving 100 points and brainliest!

Answers

Answer:

84π m^3

Step-by-step explanation:

1. The formula of a cone is: (1/3) · π · r^2 · h

2. The radius is 6m. (Diameter / 2)

3. (1/3) * π * (6^2) * 7

4. Multiply all numbers besides pi to get the answer in terms of pi

5. (36 / 3 ) = 12 * 7 = 84

6. 84π

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]

Diameter = 12 Radius = 12/2 = 6mHeight = 7m

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]

Volume of cone

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]

[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]

Where,

r is radiush is height

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]

Substituting the given values in formula.

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]

[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]

Hence , option b is the correct answer

i need to get this done, please help

Answers

The expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

What is a sum of cubes?

An expression that is a sum of cubes is given as follows:

a³ + b³.

For the sum, all numeric factors have to be powers of 3, while all exponents have to be multiples of 3. Hence the expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

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Jenny is preparing a roast chicken dinner in honour of her daughter coming back for the holidays after studying abroad. Her daughter will be on Flight BM1264. Jenny will arrive at the airport ten minutes before the flight arrives and will leave with her daughter fifteen minutes after it lands. Her journey to the airport takes 25 minutes. Jenny wants to do all the preparation for the meal before leaving for the airport. It takes 30 minutes to prepare. She will leave for the airport straight after finishing the preparation. Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Jenny will start cooking five minutes after getting back from the airport. QUESTION IS: HOW LATE CAN THEY EAT DINNER, ALSO PLANE ARRIVES AT 4PM

Answers

The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.

What is Addition?

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

The time can be calculated as,

Time taken for preparation = 30 minTime is taken to travel to airport = 25 minsShe will wait for 10 mins before the flight arrive = 10 min

Flight lands at 4 pm

She will leave 15 mins after the flight lands = 15 minsIt takes 25 mins to travel back home ⇒ 15 + 25 minsShe will start cooking after 5 mins ⇒ 15+25+5 min

Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min

⇒ 15+25+5+142.5 min

Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins

Since the flight lands at 4 pm

⇒ 4 pm + 3 hours 7.5 mins

⇒ 7 pm and 7.5 mins

Hence, Jenny can have dinner at 7 pm and 7.5 mins.

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Please help I am behind on this questions!!

Answers

Answer:

  $83,802

Step-by-step explanation:

The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.

Formula

The future value of an annuity due is given by the formula ...

  FV = P(1 +r)((1 +r)^t -1)/r

where P is the annual payment, r is the annual interest rate, and t is the number of years.

This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).

Application

For P=$1000, r = 0.06, and t = 30, the future value is ...

  FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68

To the nearest dollar, the account value will be $83,802.

__

Additional comment

Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.

20. Find the solution to the system of linear equations below:
x - 3y = -5
2x + 5y = 12
O (-5, 12)
O (3,2)
O (-2,7)
O (1,2)

Answers

Answer:

The last option

Step-by-step explanation:

When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!

First accurate answer gets brainliest

Answers

Answer: [tex]20x^2 + 47x+24[/tex]

Step-by-step explanation:

We just multiply the values on the edges like we are finding the area of a square, L * L = area.

4x * 5x = 20x^2

4x * 8 = 32x

3 * 8 = 24

3 * 5x = 15x

Next add the answers together

20x^2 + 47x + 24

Answer:

option 3

Step-by-step explanation:

you need to times (4x+3) by (5x+8)

so you basically need to expand the brackets and collect like terms


Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.

Answers

The triangle is Obtuse and scalene , Option C is the correct answer.

What is a Triangle ?

A triangle is a polygon with three sides , three angles and three vertices.

A triangle can be classified as Acute , Right or Obtuse on the basis of the angle in a Triangle .

and it is classified as scalene , equilateral and isosceles on the basis of the length of the sides of a triangle.

The triangle given in the question has all the sides different , so it is a scalene triangle.

One of the angle is obtuse angle and so it can be classified as a Obtuse Angle Triangle.

Therefore , Option C is the correct answer.

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Answer:

right angle

Step-by-step explanation:

Can someone help me fully simplify this step by step pleaseeeee

Answers

[tex]2x - 7x + 2 + 1 - 2[/tex]

[tex]2x - 7x + 3 - 2[/tex]

[tex] - 5x + 1[/tex]

factorize it
evaluate it
factorise it
evaluate
factorize



Answers

Answer:

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Step-by-step explanation:

Rewrite the middle term.

[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]

Rerrange terms.

[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]

Factor first three terms by perfect square rule.

[tex](x^2+y^2)^2-x^2y^2[/tex]

Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].

[tex](x^2+y^2)^2-(xy)^2[/tex]

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].

[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]

Remove parentheses.

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Select the correct answer from each drop-down menu. Which system of equations is represented by this graph? Graph shows system of equations plotted on a coordinate plane. A line goes through (minus 6, 0) and (0, minus 3). Another line goes through (0, 3) and (minus 4, minus 5). y = x + 3 y = x − 3 Reset

Answers

The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation of the line going through (-6, 0) and (0, -3) is:

y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))

y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is:

y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)

y = 2x + 3

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Answer:

2

-1/2

Step-by-step explanation:

add 37 +31 by counting in tens​

Answers

Answer:

(30+30) +(7+1) = 68

Step-by-step explanation:

hope this helps you (ʘᴗʘ✿)

Add 37 + 31 by counting in tens equals 68

(06.02 LC)
Line AB contains points A (-2, 3) and B (4, 5). Line AB has a slope that is

Answers

Rise 5-3=2
Run 4-(-2)= 6
Slope =2/6

Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight

Answers

The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

What is a System of Equations?

A system of equations is a set of equations that have a common solution.

The first system of equations is

y+12 = x² +x

x+y = 3

To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.

The solution is (-5,8) (3,0)

The second system of equation is

y-15 = -x² +4x

x+y = 1

The solution to the system is (7,-6) (-2,3)

The third system of equation is

y+5 = x²-3x

2x+y = 1

The solution to the system is (3,-5) (-2,5)

The fourth system of equation is

y-17 = x²-9x

-x+y =1

The solution to the system is (2,3) , (8,9)

Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

The graphs are attached with the answer.

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Change 192 feet to inches

Answers

Answer:

2304 inches

Step-by-step explanation:

please mark brainiest

Answer:

2304

Step-by-step explanation:

If you would like a step-by-step explanation, please just let me know. I sincerely hope this helps.

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At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answers

The distance between the ships is 26.65.

How to illustrate the distance?

Based on the information given, after 3 hours, the distance of ship B will be:

= 20 + (17 × 3)

= 71.

A = 21 × 3 = 63

Well calculate the square root which will be:

A² + B² = 71² + 63²

= 5041 + 3969

= 9010

Therefore, ✓9010 = 94.92

Finally, the distance will be:

= (63 × 21) + (71 × 17) / 94.92

= (1323 + 1207)/94.92

= 26.65

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Write an equation that represents the transformations formed by the following items: (a) horizontally shifting the graph of f(x) = square root over x, 9 units to the right and then vertically shrinking the graph by a factor of 2/3.
(b) vertically stretching the graph of f(x) = square root over x by a factor of 8 and then vertically shifting the graph 4 units down.
(c) horizontally stretching the graph of f(x) = square root over x, by a factor of 7 and then vertically shifting the graph 5 units up
(d) reflection of the graph of f(x) square root over x, across the y-axis and then vertically shifting the graph 10 units down. Answer:​

Answers

The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]

How to transform the functions?

The function #1

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is shifted right by 3 units.

So, we have:

[tex]f(x) = \sqrt{x - 3}[/tex]

It is shrunk vertically by a factor of 2/3

[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

The function #2

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched vertically by a factor of 8

[tex]f(x) = 8\sqrt{x }[/tex]

It is shifted down by 3 units.

So, we have:

[tex]f(x) = 8\sqrt{x }-3[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]

The function #3

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched horizontally by a factor of 7

[tex]f(x) = \sqrt{\frac x7}[/tex]

It is shifted up by 5 units.

So, we have:

[tex]f(x) = \sqrt{\frac x7} + 5[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]

The function #4

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is reflected across the y-axis

[tex]f(x) = \sqrt{-x}[/tex]

It is shifted down by 10 units.

So, we have:

[tex]f(x) = \sqrt{-x} - 10[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]

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An automobile travels 140 miles in 4 hours. Find the average rate of speed

Answers

Answer:

35mph

Step-by-step explanation:

divide 140/4=35

Find the locus of a point P which moves so that the sum of squares of squares of its distance A(3,0)and B(-3,0) is 4 times the distance between A and B​

Answers

Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.

How to find the locus of a point?

First of all, we would determine the distance between points A and B as follows:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-3 - 3)² + (0 - 0)²]

Distance = √[-9² + 0]

Distance = √81

Distance = 9.

Four (4) times the distance between points A and B​ is given by:

Distance = 9 × 4

Distance = 36.

Translating the word problem into a mathematical expression, we have:

a² + b² = 36

Also, from the distance formula we have:

a = √[(h + 3)² + (k - 0)²]

a² = h² + 6h + 9 + k²    

Similarly, b² is given by:

b = √[(h - 3)² + (k - 0)²]

b² = h² - 6h + 9 + k²

Equating the equations, we have:

a² + b² = 36

h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36

2h² + 2k² = 36 - 18

2h² + 2k² = 18

Dividing both sides by 2, we have:

h² + k² = 9   ⇒ x² + y² = 9.

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Which expression is equivalent to

Answers

The expression that is equivalent to the given expression is 16⁴

Evaluating an Expression

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex](\frac{1}{16} )^{-4}[/tex]

Evaluating

[tex](\frac{1}{16} )^{-4}[/tex]

[tex]= (16^{-1} )^{-4}[/tex]

[tex]= 16^{-1 \times -4}[/tex]

[tex]= 16^{4}[/tex]

Hence, the expression that is equivalent to the given expression is 16⁴

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Find three consecutive odd integers whose sum is 489

Answers

Answer:

162, 163, and 164.

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 489

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 489

3X + 3 = 489

3X + 3 - 3 = 489 - 3

3X = 486

3X/3 = 486/3

X = 162

Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.

162 + 163 + 164 = 489

We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.

Answer:

161, 163, 165

Step-by-step explanation:

x + x+2 + x +4 =489.

This is how we calculate three consecutive odd integers!

Combine like terms:

3x+6=489

3x=483

x=161

Three numbers are:

161, 161+2, 161+4.

161, 163, 165

What is the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6)?

Answers

Step-by-step explanation:

general form of a parabola :

y = ax² + bx + c

we have 3 points of the parabola to calculate the 3 variables :

the 2 intercepts are actually

(-2, 0)

(6, 0)

and then

(8, 6)

so, we get the 3 equations

0 = a(-2)² + b×-2 + c = 4a - 2b + c

0 = a×6² + b×6 + c = 36a + 6b + c

6 = a×8² + b×8 + c = 64a + 8b + c

from the 1st equation we get

c = -4a + 2b

using that in the 2nd equation we get

0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b

b = -4a

therefore,

c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a

using all that in the 3rd equation we get

6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a

a = 6/20 = 3/10 = 0.3

b = -4a = -4×3/10 = -12/10 = -1.2

c = -12a = -12×3/10 = -36/10 = -3.6

so, we have

y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)

Area of Rectangle: A = length*width
One side of a rectangle is twelve kilometers longer than three times another side of the rectangle. Find the
sides if we also know that the area of the rectangle is 135 km².
shorter side:
longer side:

Answers

Answer:

shorter side: 5 km

longer side: 27 km

Step-by-step explanation:

So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135

"Known" Values: one side=x, other side=3x+12, area=135 km^2

[tex]135=x(3x+12)[/tex]

Distribute the x

[tex]135=3x^2+12x[/tex]

Subtract 135 from both sides

[tex]0=3x^2+12x-135[/tex]

Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135

[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]

Simplify denominator and multiply inside of the radical

[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]

If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical

[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]

Simplify the radical

[tex]x=\frac{-12\pm 42}{6}[/tex]

Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution

[tex]x=\frac{-12+42}{6}[/tex]

Add values

[tex]x=\frac{30}{6}[/tex]

Divide

[tex]x=5[/tex]

Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27

Short side: 5 kmLong side: 27 km

Step-by-step explanation:

let x = length of shorter side

[tex](3x + 12)(x)= 135[/tex]    This is the equation

[tex]3x^2+12x=135[/tex]        use distributive property to multiply out

[tex]3x^2+12x-135=0[/tex]   subtract 135 from both sides to get in position to factor

[tex]3(x^2+4x-45)[/tex]           factor out a 3

[tex]3(x-5)(x-9)[/tex]           factor the resulting expression

[tex]x=5,9[/tex]                       two answers (we want one so see which one works)

Check both values of x

[tex]5*3+12=27[/tex]

[tex]27*5=135[/tex]

Therefore, we know the shorter side is 5 km and the longer side is 27 km.

At this point, we do not even need to check x=9

If you stand 100 feet away from a flagpole, and the angle of elevation to the top of the pole is 31°, what is the height of the flagpole?

Answers

The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.

Let h represent the height of the flagpole, hence:

tan(31) = h/100

h = 60.086 feet

The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

Find out more on equation at: https://brainly.com/question/2972832

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