Answers
Answer:
[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Step-by-step explanation:
The division between functions is defined as:
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]
So:
[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]
Since [tex]g(x) \neq0[/tex] , let's find its roots:
[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]
For (2)
[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]
Therefore the roots are:
[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]
Finally the complete answer is:
[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Related Questions
please help ASAP
the vertices of pqr are p(-3, 8), q(-6, -4), and r(1, 1). if you reflect pqr across the x-axis, what will be the coordinates of the vertices of the image p'q'r'?
Answers
A zoo has 15 emperor penguins. The emperor penguins make up 30% of all the penguins at the zoo. How many penguins live at the zoo?
Answers
1% = 15/30
= 1/2
100% = 100 x 1/2
= 50
there are 50 penguins in the zoo.
Answer:
30% = 15
1% = 15/30
= 1/2
100% = 100 x 1/2
= 50
there are 50 penguins in the zoo.
Find the perimeter and the area of the polygon with the given vertices. J (1,2), K (7,2), L (7,8), M (1,8)
Answers
recall, the perimeter is all sides summed up, and the area is just length * width.
Answer : The perimeter and the area of the polygon with the given vertices is, 24 unit and 36 unit² respectively.
Step-by-step explanation :
First we have to calculate the distance of JK, KL, LM and MJ.
Using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance between the two coordinates
x and y are the coordinates.
To calculate the distance of JK:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(7-1)^2+(2-2)^2}[/tex]
[tex]d=\sqrt{(6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of KL:
[tex]d=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]
[tex]d=\sqrt{(7-7)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of LM:
[tex]d=\sqrt{(x_4-x_3)^2+(y_4-y_3)^2}[/tex]
[tex]d=\sqrt{(1-7)^2+(8-8)^2}[/tex]
[tex]d=\sqrt{(-6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of MJ:
[tex]d=\sqrt{(x_4-x_1)^2+(y_4-y_1)^2}[/tex]
[tex]d=\sqrt{(1-1)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
The distance of JK, KL, LM and MJ is, 6, 6, 6 and 6.
Now we have to calculate the perimeter of the polygon.
Perimeter of polygon = JK + KL + LM + MJ
Perimeter of polygon = 6 + 6 + 6 + 6
Perimeter of polygon = 24 unit.
Now we have to calculate the area of polygon.
As the distance between the coordinates are equal that means the geometry will be square because in square the all four sides are equal.
Now we have to calculate the area of polygon by using area of square formula.
Area of polygon = Area of square = (side)²
Given: Side = 6
Area of polygon = Area of square = (6)²
Area of polygon = Area of square = 36 unit²
Thus, the area of polygon is, 36 unit²
A grocery bag can withstand 300 n of force before it rips apart. how many kilograms of apples can it safely hold?
Answers
The grocery bag can handle roughly 30.6 kg of apples safely. This conclusion is drawn based on the concept of forces, weight, and the Physics formula for calculating weight.
Explanation:The subject field for this question is Physics and it relates to the High School level. This question is about the concept in physics known as force, in particular, the force related to weight and how it pertains to carrying capacity.
In physics, force is typically given in units of Newton's (N), named after Sir Isaac Newton. The force exerted by a mass due to gravity is its weight. Specifically, weight is calculated through the formula F = m * g, where F is the force (weight), m is the mass in kilograms, and g is the acceleration due to gravity in m/s² (approximately 9.8 m/s² on Earth).
To find out how many kilograms of apples a bag can hold before it rips, we can use this formula and solve for m (mass). Given that the force the bag can withstand before ripping is 300 N, we have 300 N = m * 9.8 m/s². Isolating m gives us m = 300 N / 9.8 m/s² which is approximately 30.6 kg. Therefore, the bag can safely hold around 30.6 kg of apples.
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There are twenty-three red marbles and two blue marbles in a box. a marble is randomly chosen from the box, its color noted, then put back in the box. this process is repeated. what is the probability that (a) the first marble is blue? (b) the first four marbles are red? (c) the first four marbles are red and the fifth is blue?
Answers
B. 4/25
C. 6/25
I'm sure about the first one, not so much about the last 2 though...
(60 POINTS)
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2) degrees. The measure of D, the angle of depression from point B to point A is (x + 14) degrees. Find the measure of each angle.
Answers
[tex]\sf 5(x-2)=(x+14)[/tex]
Distribute 5 into the parenthesis:
[tex]\sf 5x-10=x+14[/tex]
Add 10 to both sides:
[tex]\sf 5x=x+24[/tex]
Subtract 'x' to both sides:
[tex]\sf 4x=24[/tex]
Divide 4 to both sides:
[tex]\sf x=6[/tex]
So this is our value of 'x', we can plug it into any of the two equations to find the measurement for both angles:
[tex]\sf x+14[/tex]
[tex]\sf 6+14[/tex]
[tex]\boxed{\sf 20\textdegree}[/tex]
So the length of both angle E and angle D is 20 degrees.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees
Hey, I have some questions on some math problems for Algebra 2. Think you can help? Here's the first one :)
Some investments in the stock market have gained 10% annually. the total value of the investment, A, and this rate can be found using A= P(1.10)^n where P is the initial value of this investment, and N is the number of years the money is invested. if $1,000 is invested in the stock market at this annual rate of return, what is the expected total value after 18 years?
1. $4,054.47
2. $5,559.92
3. $18,700.00
4. $19,800.00
I originally thought it was $18,700.00 but I don't know
Answers
A=P(1.10)^N
P=$1000
N=18
A=1000 (1.10)^18
A = 1000 * 5.55991731349
A=5559.91731349
Rounding off to the nearest hundredths, we get
A = $5559.92
The expected total value after 18 years is $5,559.92
Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.
Answers
Answer: D.The domain and range of the function are the same.
Step-by-step explanation: Given function f(x)=-√-x.
The given function is a square root function and we have minus sign in front of x inside square root.
A square root always defined for positive values or 0.
In order to get a positive number or 0 inside square root, let us solve the inequality:
[tex]-x\geq 0[/tex]
On dividing both sides by -1, the inequality sign would get flip and we get
Domain: [tex]x \leq 0.[/tex]We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.
Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.Answer:
hi thereee, the answer to this question is
d. the domain and range of the function are the same
hope this helps :)
have a good day!
Step-by-step explanation:
i just took the test
MEDAL PLEASE HELP
A compact disc is designed to last an average of 4 years with a standard deviation of 0.9 years. What is the probability that a CD will last less than 3 years?
1.11%
13.35%
86.65%
100%
Answers
As a part of their weather unit, Anoki’s science class took a hot air balloon ride. As they passed over a fenced field, the angle of depression of the closer side of the fence was 32°, and the angle of depression of the farther side of the fence was 27°. If the height of the balloon was 800 feet, estimate the width of the field. Round your answer to the nearest foot. 2016_01_25_17_23_501.png The width of the field is about feet
Answers
Steps needed to find the width of the field (CD):
First, we should note that angle d would be equal to 27 degrees because there are two parallel lines that are cut by a transversal. Furthermore, angle a would be equal to 5 degrees since we just need to subtract 27 from 32.
We then subtract 27 and 5 from 180 to get angle c. [tex]180-27-5=148[/tex]. Angle c is therefore 148 degrees.
Next, we need to find angle e which is just the supplementary of angle c. Angle e therefore measures [tex]180-148=32[/tex] degrees.
For the next step we use sine law to find the length of segment AC:
[tex] \frac{sin(32)}{800} = \frac{sin(90)}{AC} [/tex]
[tex]AC=1509.66[/tex]
Lastly, we need to utilize the sine law again to find the length of segment CD or the width of the field:
[tex] \frac{sin(27)}{1509.66} = \frac{sin(5)}{CD} [/tex]
[tex]CD=290[/tex]
ANSWER: The width of the field is 290 ft.
Choose the correct simplification of (7x3y3)2.
14x6y6
49x5y5
49x6y6
14x5y5
Answers
The correct simplification of (7x3y3)2 = 49x6y6
What is simplification?Simplification is defined as the removal of parentheses in an algebraic expressions in such a way that it would be understood.
From the expression given,
(7x3y3)2 = 2 × 7x × 3y × 3
= 49x6y6
Therefore, the correct simplification of (7x3y3)2 = 49x6y6
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Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Answers
Why must bowhunters use broadhead points when hunting big game?
Answers
There are states that require a certain measurement of the broadhead point arrows. Theses arrows must be solidly built and must always be razor sharp to ensure quick penetration to the animals thick skin and layers of tissues.
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
We have,
Bowhunters use broadhead points when hunting big game for several reasons:
- Greater Cutting Surface
Broadhead points have a larger cutting surface area compared to target or field points.
This increased surface area allows for more effective cutting and penetration, which is essential when hunting big game animals that have tough hides, muscles, and bones.
- Penetration and Lethality:
Big game animals often require deep penetration to reach vital organs for an ethical and humane kill.
Broadheads are designed to maximize penetration by creating large wound channels and causing significant tissue damage.
This helps ensure quick and effective kills, minimizing suffering for the animal.
- Blood Trails
- Terminal Performance
- Ethical Considerations
Thus,
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
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find the roots of the polynomial equation x^3-x^2+x+39=0
Answers
x^2-4x+4=-9,
(x-2)^2=-9
x-2=+-3i,
x=2+3i or 2-3i.
The roots are -3, 2+3i, 2-3i.
Round the answer to the nearest cent.
A 30% discount on $47.50 is $
Answers
Answer:
14. 25
Step-by-step explanation:
Find the side of a square whose diagonal is of the given measure. Given = 12 square root 2ft.
Answers
diagonal^2 / 2 = side^2
144 * 2 / 2 = side^2
144 = side^2
side = 12
I need help please Brainliest
Answers
2. A
3. A
4. D
Hope i helped plz tell me how i did thanks
Find the distance between the two points. Round to the nearest tenth if necessary. (10, –4), (5, 8)
169
7
13
16
Answers
If you ask this question may be you do not know the formula of the distance between two points or you do not know how to use it, so I am going to explain you both.
1) Formula of the distance betweer two points:
Say the point A has coordinates (x1, y1) and the point B has coordinates (x2, y2), the distance, d, between the points A and B is given by the formula:
[tex]d^2= (x_1-x_2)^2+(y_1+y_2)^2} = d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
2) So, to apply that formula you need the coordinates of the two points.
In this case the coordinates of the point (10,-4) are: x = 10, y = -4
The coordinates of the point (5,8) are: x = 5, y = 8.
3) This is the application:
[tex]d= \sqrt{(10-5)^2+(-4-8)^2}= \sqrt{(5)^2+(-12)^2}= \sqrt{25+144} d= \sqrt{169}=13 [/tex]
So, the answer is 13.
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment
Answers
Answer:
Using a compass.Step-by-step explanation:
Using a compass ensures that the new segment has the same length as the original one. Taking a pivot point and then drawing a arc, this distance is the copy.
Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?
Answers
(35 points) Fred played golf and for the past 5 times had a score of 72, 79, 73, 81, and 70. What was his average score? A. 75 B. 77 C. 85 D. 375
Answers
A. 75
The average score of Fred is 75.
What is the average value?The common cost of a characteristic over language is described to be crucial of the feature divided by way of the period of the interval.
calculation:-
a score of 72, 79, 73, 81, and 70.
nu,ber of times = 5
total score = 72+79+ 73+ 81+ 70.
= 375
average score = 375/5
= 75
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The quotient property of radicals requires the indices of the radicals to be the same. Does this mean that it is not possible to write es002-1.jpg as a single radical? Explain.
Answers
The radicands are powers of the same base, so they can be written using rational exponents.
Simplify the quotient of the exponential expressions by getting a common denominator and subtracting exponents.
The simplified expression is the 4th root of y
The expression can be written as a single radical by covertong the expression to a rational format such that both the denominator and numerator have the same base as y¼
Numerator = The 4th root of y³ = y¾Denominator = squareroot of y = y½Using indices :
Division sign signifies the powers should be subtracted[tex] \frac{y¾}{y½} = y^{¾ - ½} = y¼[/tex]
Therefore, the expression can be written as a single radical thus y¼
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Find the length of both arc AB and arc APB, where
Answers
The measure of arc AB is twice that of angle APB, so is
2*108° = 216°.
The measure of arc APB is the difference between that and 360°, so is
360° -216° = 144°.
as you can see, the angle at P is the inscribed angle, and the intercepted arc is AB, thus 2P = arcAB.
and since a circle has a total of 360°, the other arc is just 360 - arcAB.
True or false ? A car taking a turn at a constant speed is accelerating.
Answers
Combine like terms to simlify the expression: 2/5k—3/5+1/10k
Answers
(5/10)k - 3/5
(1/2)k - 3/5 is the answer to the question
THen
4/10K - 3/5 + 1/10k = 5/10k - 3/5
Simplify 5/10k
1/2k - 3/5 is your answer
Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?
Answers
4 * 12 = 48
70-48 = 22
so the remaining 4 sides need to = 22 cm
22 / 4 = 5.5
each remaining side = 5.5 cm
Answer:
It would be 5.5 cm
Step-by-step explanation:
In which way do REITs resemble mutual friends
Answers
___________________________________________________________
REITs resemble mutual funds in that they both allow investors to pool their money to invest in a diversified portfolio. REITs consist of a variety of real estate properties, while mutual funds consist of stocks or bonds. Both provide individuals with an opportunity to invest in a professionally managed portfolio.
Explanation:REITs (Real Estate Investment Trusts) resemble mutual funds in that they both allow investors to pool their money together to invest in a diversified portfolio. Just as mutual funds consist of a variety of stocks or bonds from different companies, REITs consist of a variety of real estate properties such as office buildings, apartments, and shopping centers. Investors buy shares of a REIT and receive a return based on the performance of the real estate portfolio as a whole. Both REITs and mutual funds provide individuals with an opportunity to invest in a professionally managed portfolio without having to directly invest in individual stocks or properties.
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Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
Answers
Let xx be the width of the river. It is given that, when they have met the first time, boat11 has travelled 14001400 m and boat22, (1400−x)(1400−x) metres.
When they meet for the second time, boat11 has travelled 600+(x−1400)=(x−800)600+(x−1400)=(x−800) m, and boat22, 1400+(x−600)=(x+800)1400+(x−600)=(x+800) m.
Note that, the relationship of the distances each traveled, is the same to both meetings. Thus,
14001400−x=x−800x+80014001400−x=x−800x+800⇒x=?⇒x=?Hope you can take it from here.a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x)=-16x62-4x+382 How long after the rock is thrown does it hit the ground
Answers
We have then:
f (x) = - 16x ^ 2-4x + 382
The moment the rock hits the ground we have f (x) = 0
0 = -16x ^ 2-4x + 382
We solve the polynomial looking for its roots which are:
x1 = -5.012803699004288
x2 = 4.762803699004288
We ignore the negative root. The solution is:
x = 4.76
Answer:
it hits the ground 4.76 s after is thrown
It takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
Explanation:To find the time when the rock hits the ground, we need to find the value of x when the distance between the rock and the ground is 0. In the given equation, f(x) = -16x^2 - 4x + 382, where f(x) represents the distance between the rock and the ground. We can set this equation equal to 0 and solve for x:
-16x^2 - 4x + 382 = 0
This is a quadratic equation. We can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from the equation, we get:
x = (-(-4) ± sqrt((-4)^2 - 4(-16)(382))) / (2(-16))
This simplifies to:
x = (4 ± sqrt(16 + 24512)) / (-32)
x = (4 ± sqrt(24528)) / (-32)
x ≈ (-4 ± 156.49) / (-32)
Since we're dealing with time, the negative value doesn't make sense in this context. So, we take the positive root:
x ≈ (4 + 156.49) / (-32)
x ≈ 160.49 / (-32)
x ≈ -5.0
Therefore, it takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
Solve for all values of r 3r/r-5 - 2/r+3=r/r+3
Answers
(3r)(r+3)=(r-5)(r+2)
3r^2 +9r= r^2-3r-10
2r^2+12r+10=0
2(r^2+6r+5)=0
2(r+5)(r+1)=0
r=-1 or r=-5