Once put into the quadratic formula the numbers in the square root of they are negative no solutions if it is 0 then 1 solution if more then more than one solution
Answer:
Step-by-step explanation:
what is 3/9 of 612??
Answer:
204
Step-by-step explanation:
First you divide 612 by 9 (612÷9) which gives 68.
Then multiply 68 by 3 (68×3) giving the answer 204.
Answer:
3/9 of 612 = 204
Step-by-step explanation:
Step 1: convert 3/9 into a decimal so that its easier to work with, that will be 0.3333333333
Step 2: since we know that "of" means "X" in math, we times it by 612 to get the answer of 204
Dose anyone know number 7.
Answer: B
Step-by-step explanation: The Answer is B. 30 Sides.
The number of sides of the regular polygon each interior angle measuring 168° is 30. Thus, the correct option is B.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The measure of interior angles of a regular polygon is given by the formula,
[tex]\text{Measure of an interior angle} = \dfrac{(n-2) \times 180^o}{n}[/tex]
where n is the number of sides in the polygon.
Since it is given that measure of an interior angle of the polygon is 168°. Therefore, the number of sides will be,
[tex]168 = \dfrac{(n-2) \times 180^o}{n}[/tex]
168n = 180n - 360
180n - 168n = 360
12n = 360
n = 30
Hence, The number of sides of the regular polygon each interior angle measuring 168° is 30.
Learn more about Polygon:
https://brainly.com/question/10441863
#SPJ2
How do u solve this?
Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}f(1)=5\\f(n)=f(n-1)\cdot(-2)\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=5\cdot(-2)^{n-1}\\\\f(1)\to\text{put n = 1 to the equation of}\ f(n):\\\\f(1)=5\cdcot(-2)^{1-1}=5\cdot(-2)^0=5\cdot1=5\\\\\text{calculate the common ratio:}\ \dfrac{f(n+1)}{f(n)}\\\\f(n+1)=5\cdot(-2)^{(n+1)-1}=5\cdot(-2)^{n+1-1}=5\cdot(-2)^n\\\\r=\dfrac{f(n+1)}{f(n)}=\dfrac{5\!\!\!\!\diagup^1\cdot(-2)^n}{5\!\!\!\!\diagup_1\cdot(-2)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=(-2)^{n-(n-1)}=(-2)^{n-n+1}=(-2)^1=-2\\\\\text{Therefore}\\\\f(n)=f(n-1)\cdiot(-2)[/tex]
John has a ribbon that was 1 1/2 meters long. He used 2 pieces that were each 1/3 of that length. How much ribbon did John use?
Answer:
1 meter.
Step-by-step explanation:
1 1/2 * 1/3
= 3/2 * 1/3
= 3/6
= 1/2.
So John used 2*1/2 = 1 meter of the ribbon.
Bob and Dave go to PizzaScoff. Starting with 35 pizzas, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. How many are left?
Answer:
19.87 Pizzas are left
Step-by-step explanation:
To solve, just take 35 the number of starting pizzas and then subtract the number pizzas both of them consumed. So, 35 - 6.8 given 4/5 converts to 0.8 this leaves use with Bob's pizza consumption only at 28.2 pizza's left. Next, we are going to take 28.2 - 8.33 given 1/3 is .3333 repeating this then gives us the answer with having 19.87 pizzas left - although if it asks how many whole pizzas you would say 28 given you can't have .87 of a pizza.
A fraction is a way to describe a part of a whole. The amount of pizza left is 19 13/15.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given the total number of pizzas is 35. Also given, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. Therefore, the amount of pizza both together eat are,
Amount of pizza Bob and Dave eat = 6 4/5 + 8 1/3
= 34/5 + 25/3
= 102/15 + 125/15
= (102+125)/15
= 227/15
Amount of pizza left = 35 - 227/15
= (525 - 227)/15
= 298/15
= 19 13/15
Hence, the amount of pizza left is 19 13/15.
Learn more about Fraction:
https://brainly.com/question/1301963
#SPJ2
If f(x) =x^2-2x and g(x) =6 x+4 for which value of x does (f+g) (x)=0
-4
-2
2
4
Answer:
-2Step-by-step explanation:
[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=x^2-2x\\\\g(x)=6x+4\\\\\text{Substitute:}\\\\(f+g)(x)=(x^2-2x)+(6x+4)=x^2-2x+6x+4\\\\\text{combine like terms}\\\\(f+g)(x)=x^2+(-2x+6x)+4=x^2+4x+4\\\\(f+g)(x)=0\Rightarrow x^2+4x+4=0\\\\x^2+2x+2x+4=0\\\\x(x+2)+2(x+2)=0\\\\(x+2)(x+2)+0\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\\\x=-2[/tex]
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The line plot shows the weights of pumpkins available at a farm stand. The pumpkins cost $0.30 per pound. A baker purchases all of the pumpkins to make pies. If she uses a $100 bill to pay for the pumpkins, how much change will she receive?
If she uses a $100 bill to pay for the pumpkins, then the amount of change that she receives will be $ 32.5.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The line plot shows the weights of pumpkins available at a farm stand. The pumpkins cost $0.30 per pound. A baker purchases all of the pumpkins to make pies.
Then the weight of all the pumpkins will be
→ 6 x 3 + 8 x 5 + 9 + 10 x 7 + 12 x 4 + 13 x 2 + 14
→ 225 pounds
Then the amount of money of 225 pounds will be
→ 225 x 0.3
→ $ 67.5
If she uses a $100 bill to pay for the pumpkins, then the amount of change that she receives will be
→ $ 100 - $67.5
→ $ 32.5
More about the subtraction link is given below.
https://brainly.com/question/4319655
#SPJ2
im confused on this one
Answer:
The first choice is correct;
(-∞,∞)
Step-by-step explanation:
We have been given the following functions;
[tex]f(x)=x^{2}-1\\\\g(x)=2x-3[/tex]
We are to determine the domain of (fog)(x).
The composite function, (fog)(x) is obtained by substituting g(x) in place of x in the function f(x);
(fog)(x) = f[g(x)] = [tex](2x-3)^{2}-1[/tex]
Clearly the function will be defined everywhere on the number line since it has no undefined points or domain constraints. The domain is thus;
(-∞,∞)
For this case we have the following functions:
[tex]f (x) = x ^ 2-1\\g (x) = 2x-3[/tex]
We must find [tex](f_ {0} g) (x):[/tex]
By definition of composite functions we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {0} g) (x) = (2x-3) ^ 2-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 9-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 8[/tex]
The domain of the function is given by all the values for which the function is defined.
The function is defined for all real numbers.
Answer:
Domain: (-∞,∞)
If p is a zero of 2x^2 - 5x + 3 then find the value of p.
The answer is zero 2x -3=0 x-1=0
A radio transmission tower is 190 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 31 with the ground? Give your answer to the nearest tenth of a foot.
Answer:
343.7 ft
Step-by-step explanation:
The wire is anchored 190 -13 = 177 ft from the ground. That distance is opposite the given angle (31°). The measure you want is the hypotenuse of the triangle with that side and angle measures.
The mnemonic SOH CAH TOA reminds you that the relation between the opposite side, hypotenuse, and angle is ...
Sin(angle) = Opposite/Hypotenuse
Filling in the given information, you have ...
sin(31°) = (177 ft)/hypotenuse
Solving for hypotenuse gives
hypotenuse = (177 ft)/sin(31°) ≈ 343.7 ft
The length of the guy wire should be 343.7 ft.
To find the length of the guy wire attached 13 feet from the top of a 190-foot tall tower at an angle of 31° with the ground, we can use the sine function and trigonometry. The length of the guy wire is approximately 380.8 feet.
Explanation:To find the length of the guy wire, we can use trigonometry. The guy wire, the height of the tower, and the distance from the top of the tower to the attachment point form a right triangle. We can use the sine function to find the length of the guy wire: sin(31) = height of the tower / length of the guy wire. Rearranging the equation gives us length of the guy wire = height of the tower / sin(31). Plugging in the values, we get length of the guy wire ≈ 190 / sin(31) ≈ 380.8 feet. Therefore, the guy wire should be approximately 380.8 feet long.
Learn more about trigonometry here:
https://brainly.com/question/31896723
#SPJ3
Abe Cassidy wants to deposit the following into his savings account: 32 one-dollar bills, 4 five-dollar bills, 32 quarters, 25 dimes, 82 pennies, a check for $43.56, and a check for $122.90. He wants to receive a $50.00 bill in cash. How much will he deposit?
136.22
10.44
$229.78
$179.78
Answer:
179.78
Step-by-step explanation:
Let's count how much Abe has exactly:
32 one-dollar bills: $32
4 five-dollar bills: $20
32 quarters: $8
25 dimes : $2.50
82 pennies : $0.82
First check: $43.56
Second check: $122.90
Total = $229.78
And he wants a $50 bill... so he'll deposit $179.78 ($229.78 - $50).
Final answer:
Abe Cassidy will deposit $179.78 into his savings account.
Explanation:
Let's calculate how much Abe Cassidy will deposit into his savings account, considering he wants to receive a $50.00 bill in cash. To do this, we need to add up all the various types of money he has and then subtract the $50 he wishes to keep in cash.
32 one-dollar bills = $324 five-dollar bills = $2032 quarters = $8 (since 4 quarters = $1)25 dimes = $2.50 (since 10 dimes = $1)82 pennies = $0.82 (since 100 pennies = $1)1 check for $43.561 check for $122.90Adding all these amounts gives us a total of $229.78 before removing the $50 he wants in cash.
To find the amount he will deposit, we subtract the $50 from the total amount:
$229.78 - $50 = $179.78
Hence, Abe Cassidy will deposit $179.78 into his savings account.
6(2x + 3) − 4(5x + 2)
Answer:
-8x+10
Step-by-step explanation:
=(6)(2x)+(6)(3)+(−4)(5x)+(−4)(2)
=12x+18+−20x+−8
Combine Like Terms:
=12x+18+−20x+−8
=(12x+−20x)+(18+−8)
=−8x+10
Answer:
-8x+ + 10
Step-by-step explanation:
Stop deleting my answer scooby Doo, i really need points now
Joe wants to paint the outside of a wooden box. He needs to find the surface area of the box
in order to buy paint. A net of the box is shown. What is the surface area of the box?
4*2=8
4*1.5=6
2*1.5=3
8*2=16
2*6=12
2*3=6
16+12+6=34 ft
Total surface area is sum of area of all parts of surface. The surface area of the box is 34 squared feet.
How to find the area of surface of a figure if its split in parts?The area of surface of a figure is sum of area of all sub-parts of it. It is because we want to get the total area of its surface.
For the given case, the box given has:
Area of top = Area of bottomArea of back = Area of frontArea of left side = Area of right side.(its all because of assuming box is cuboid or say rectangular prism)
Thus,
Surface area of box = twice of (area of top + area + left side + area of back)
Calculating these sub areas:
Area of top:Area of top = [tex]2 \times 4 = 8 \: \rm ft^2[/tex]
Area of back:Area of back = [tex]1\dfrac{1}{2} \times 4 = \dfrac{2+1}{2} \times 4 = 6 \: \rm ft^2[/tex]
Area of left:Area of left side: [tex]1\dfrac{1}{2} \times 2 = \dfrac{2+1}{2} \times 2 = 3 \: \rm ft^2[/tex]
Thus,
Surface area of box = [tex]2(8 + 6 + 3) = 2 \times 17 = 34 \: \rm ft^2[/tex]
Thus,
The surface area of the box is 34 squared feet.
Learn more about total surface area here:
https://brainly.com/question/15096475
round 9,631.4725 to the nearest thousandth
The answer would be 9,631.473. Since there is a 5 after the two, you round up one value. Hope this helps!
Answer:
9,631.473
Step-by-step explanation:
The five would make 2 into a 3.
If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in simple complete sentences
Answer:
[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]
[tex]tan(x) =\±\sqrt{2}[/tex]
Step-by-step explanation:
By definition we know that:
[tex]sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = \frac{sin(x)}{cos (x)}[/tex]
in this case we know that
[tex]cos(x) =\frac{1}{2}[/tex]
So how:
[tex]sin ^ 2(x) = 1-cos ^ 2(x)[/tex]
Substitute the values of cosine in the function
[tex]sin ^ 2 (x) = 1-\frac{1}{2}[/tex]
[tex]sin ^ 2 (x) = \frac{1}{2}[/tex]
[tex]sin(x) =\±\sqrt{\frac{1}{2}}[/tex]
[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]
Then how:
[tex]tan(x) = \frac{sin(x)}{cos (x)}[/tex]
Substitute the values of sine and cosine in the function
[tex]tan(x) = \±\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}=\sqrt{2}[/tex]
Your parents ask you to choose between two offers for an allowance. The first offer is to receive one penny on the first day, 2 penny’s on the second day, 4 pennies on the third day, 8 pennies on the fourth day and so on. (365 days). Second offer is to receive 10 the first week, 20 the second week, 30 the third week, and so on, for the entire year (52 weeks). Which offer should you choose to make more money?
Answer:
pennies/first offer
Step-by-step explanation:
you would be rich
1x2=2 2^364= a lot of pennies
the pennies gives u the most money
Help please I need help
Answer:
x = 4Step-by-step explanation:
Look at the picture.
ΔABC and ΔACD are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]
We have:
[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]
Substitute:
[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=4[/tex]
i am a number. i am half of the square root of 100. i am __________
Answer:
i believe it is five
Step-by-step explanation:
Answer:
The answer is 5
Step-by-step explanation:
the square root of 100=10 10/2=5
Can I get brainliest
Martin orders a pasta dish that is priced at $11.99. He also orders a drink. The total cost for the pasta and drink is $14.48. Which of the following equations can be used to find the cost of the drink?
14.48 + d = 11.99
11.99 + d = 14.48
11.99 + 14.48 = d
11.99 - d = 14.48
Nora has a coupon for $3 off of a calzone. She orders a beef and olive calzone, and her bill, with the discounted price, is $9.49. Which of the following equations can be used to find the regular price of the calzone?
c - 3 = 9.49
9.49 - c = 3
c + 3 = 9.49
c + 9.49 = 3
Martin's drink equation = option b, 11.99 + d = 14.48
Nora's calzone equation = option a, c - 3 = 9.49
Hope this helps
On average, a herd of elephants travels 10 miles in 12 hours.
You can use that information to answer different questions.
Type each expression to show which question it answers.
Expressions:
10÷12
10×112
110×12
12÷10
How many miles does the herd travel in 1 hour?
How many hours does it take the herd to go 1 mile?
10/12 for 1. 12/10 for 2
Answer:
Look at explanation
Step-by-step explanation:
1. How many miles does the herd travel in an hour? : 10 divided by 12 and 10 divided by 1/12
2. How many hours does it take the herd to go 1 mile? : 12 divided by 10 and
1/10 x 12
This answer works on Imagine Math
Which line segment is a diameter of circle L?
1. HL
2. GJ
3. GK
4. IL
the diameter is 2. GJ as it goes across the whole circle
Answer:
GJ
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
Diameter = Any straight line segment that passes through the centre of the circle.
Place is highest to lowest 3/4 84% 1/3 0.82
ANSWER
84%,0.82,¾,⅓
EXPLANATION
Convert everything to decimals.
[tex] \frac{3}{4} = 0.75[/tex]
[tex] 84\% = 0.84[/tex]
[tex] \frac{1}{3} = 0.333....[/tex]
The last one is already in decimals.
[tex]0.82[/tex]
We can now see clearly, that
[tex]0.84 \: > \: 0.82 \: > \: 0.75 \: > \: 0.3333...[/tex]
This implies that,
[tex]84\% \: > \: 0.82 \: > \: \frac{3}{4} \: > \: \frac{1}{3} [/tex]
Hence from highest to least, we have
84%,0.82,¾,⅓
Which is a solution to (x - 3)(x + 9) = -27?
х=-9 x = -3
х = 0
х = 6
Answer:
x=0
Step-by-step explanation:
x^2+6x-27=-27
x^2+6x=0
x(x+6)
x=0, x=-6
The solution to (x - 3)(x + 9) = -27 is x=6, the correct option is D.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that;
(x - 3)(x + 9) = -27
Now,
If we plug in x = 6 into the equation,
we get: (6 - 3)(6 + 9) = -27.
Simplifying, we get: (3)(15) = -27.
Multiplying, we get: 45 = -27. This is true, so x = 6 is a solution.
The other values of x do not satisfy the equation.
For example, if we plug in x = -9, we get: (-9 - 3)(-9 + 9) = -27. Simplifying, we get: (-12)(0) = -27.
Multiplying, we get: 0 = -27. This is false, so x = -9 is not a solution
Therefore, by quadratic equations the answer will be x = 6.
Learn more about quadratic equations;
https://brainly.com/question/17177510
#SPJ7
The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?
Answer:
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]
Step-by-step explanation:
From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.
[tex]V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r[/tex]
Therefore:
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]
Answer:
The formula for radius of sphere is r = ∛(3V/4π)
or
r = (3V/4π)¹/³
Step-by-step explanation:
It is given formula for volume of sphere.
Volume of sphere = 4/3 πr³
Where r is the radius of sphere
To find the radius r of sphere
Volume V = 4/3 πr³
r³ = 3V/4π
r = ∛(3V/4π)
Therefore formula for radius of sphere is r = ∛(3V/4π)
or
r = (3V/4π)¹/³
Johnny and his family arrived in Williamsburg Virginia at 1:15 p.m. they drove for 45 minutes after they stopped for lunch their lunch break was 20 minutes they drove for 2 hours and 10 minutes before stopping for lunch what time did they leave home?
Answer:
1:15 P.M. - (:45 + :20 + 2:10) =
1:15 P.M. - 2:75 = 13:15 - 3:15 =
10:00 A.M.
Johnny and his family left home at 10:00 A.M.
simplify (-6^1/3)^(-2)=
For this case we must simplify the following expression:
([tex](-6 ^ {\frac {1} {3}}) ^ {- 2}[/tex]
So, by definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex]\frac {1} {(- 6 ^ {\frac {1} {3}}) ^ 2} =\\\frac {1} {(- 6 ^ {\frac {1} {3}}) * (- 6 ^ {\frac {1} {3}})} =\\\frac {1} {(6 ^ {\frac {1} {3}}) * (6 ^ {\frac {1} {3}})} =\\\frac {1} {6 ^ {\frac {2} {3}}}[/tex]
ANswer:
[tex]\frac {1} {6 ^ {\frac {2} {3}}}[/tex]
The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 514inches apart on the map. The scale on the map is 12 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
Answer:
Step-by-step explanation:
1/2 over 4 = 15/4 over x
4/1=/15/4= 60/4*2/1=120/4=30
repeat the step but instead of 15/4 to 21/4
anyways it's 72
Final answer:
The actual distance the Patel family will travel from Smithville to Clarksville is approximately 282.66 miles.
Explanation:
The scale on the map is 12 inches equals 4 miles. To find the actual distance the Patel family will travel from Smithville to Jonesville, we can set up a proportion:
12 inches / 4 miles = 334 inches / x miles
Cross multiplying, we get:
12x = 1336
Dividing both sides by 12, we find that x = 111.33 miles. So, the Patel family will travel approximately 111.33 miles from Smithville to Jonesville.
Similarly, to find the actual distance they will travel from Jonesville to Clarksville, we can set up another proportion:
12 inches / 4 miles = 514 inches / y miles
Cross multiplying, we get:
12y = 2056
Dividing both sides by 12, we find that y = 171.33 miles. So, the Patel family will travel approximately 171.33 miles from Jonesville to Clarksville.
Therefore, the total actual distance the Patel family will travel by the time they reach Clarksville is approximately 111.33 miles + 171.33 miles = 282.66 miles.
https://lh5.googleusercontent.com/nNcMGuld4KbRoBooDf5Liva-NAJyj-IEknnSniAdiBKPNhKWtKqEw2SwN2uQUidgVX1Vh4rDHA=w739
Answer:
The answer is F: 108
Step-by-step explanation:
144 - 108 = 36
108 ÷ 3 = 36
Answer:
giytg8h0ygrubigrfbk
Step-by-step explanation:
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A pizza shop has 27 adult customers every hour. It has 12 younger customers every hour. It is open from 12 p.m. to 10 p.m. each day.
Write an expression for the total number of customers it would have in 3 days.
A. 27×10×3+12×10
B. (27+12)×10×3
C. (27+10)×12×3
D. 27+10×12×3
How many customers would it have in 3 days?
A. 387 customers
B. 930 customers
C. 1,170 customers
D.1,332 customers
387 customers or 930 customers
(27+12)x10x3 and 1,170
given [tex]f(x)= 4x^2 + 6x and g(x) = 2x^2 +13x+15 \\[/tex], find (f/x) (x)
Answer: [tex](f/g)(x)=\frac{2x}{x+5}[/tex]
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=4x^2+6x[/tex]
And the function g(x):
[tex]g(x)=2x^2+13x+15[/tex]
To find [tex](f/g)(x)[/tex] you need to divide the function f(x) by the function g(x).
Therefore, knowing this, you get:
[tex](f/g)(x)=\frac{4x^2+6x}{2x^2+13x+15}[/tex]
You can simplify the numerator by factoring out 2x:
[tex](f/g)(x)=\frac{2x(2x+3)}{2x^2+13x+15}[/tex]
You have to simplify the denominator:
Rewrite the term 13x as a sum of two terms whose product be 30:
[tex](f/g)(x)=\frac{2x(2x+3)}{2x^2+(10+ 3)x+15}[/tex]
Apply Distributive property:
[tex](f/g)(x)=\frac{2x(2x+3)}{2x^2+10x+ 3x+15}[/tex]
Make two groups of two terms:
[tex](f/g)(x)=\frac{2x(2x+3)}{(2x^2+10x)+ (3x+15)}[/tex]
Factor out 2x from the first group and 3 from the second group:
[tex](f/g)(x)=\frac{2x(2x+3)}{(2x(x+5))+ 3(x+5)}[/tex]
Factor out (x+5):
[tex](f/g)(x)=\frac{2x(2x+3)}{(2x+3)(x+5)}[/tex]
Simplifying, you get:
[tex](f/g)(x)=\frac{2x}{x+5}[/tex]
ANSWER
[tex]( \frac{f}{g} )(x) = \frac{2x }{x + 5}[/tex]
where
[tex]x \ne - \frac{3}{2} \: or \: x = - 5[/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 4 {x}^{2} + 6x[/tex]
and
[tex]g(x) =2 {x}^{2} + 13x + 15[/tex]
We want to find ,
[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{4 {x}^{2} + 6x }{2 {x}^{2} + 13x + 15} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{2x(2x + 3) }{2{x}^{2} + 10x +3x + 15} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{2x(2x + 3) }{2{x}(x + 5) +3(x + 5)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{2x(2x + 3) }{(2x + 3)(x + 5)} [/tex]
We cancel out the common factors to get:
[tex]( \frac{f}{g} )(x) = \frac{2x }{x + 5} [/tex]
where
[tex]x \ne - \frac{3}{2} \: or \: x = - 5[/tex]