Answers
Answer:
The first option
Step-by-step explanation:
The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.
So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]
Related Questions
Two piecewise functions are shown below. What is the value of
6f (-2) + 3g (1)?
f(x) =
0-7
O-25
1/3
O 18
{
-3x
*+2'
if x < -2
³, if x ≥-2
(2|x-1| +3,
-5√x+3-1,
g(x) =
={
if x ≤ 1
if x > 2
Answers
Step-by-step explanation:
I am not sure what your problem here is.
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result.
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition.
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no.
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
(a) The average velocity of 25 taxies is 40 km/hr and the average velocity of 35 trucks is 30 km/hr. Find the combined average velocity of both types of vehicles. ( a ) The average velocity of 25 taxies is 40 km / hr and the average velocity of 35 trucks is 30 km / hr . Find the combined average velocity of both types of vehicles.
Answers
Answer:
10hr/m because the average velocity is divided by number
What is 21% of 456? Calculate the percentages. Make sure to show all your work!
Answers
Answer:
21% of 456 = 0.21 x 400 + 0.21 x 50 + 0.21 x 6 = 95.76
Step-by-step explanation:
Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The figures
and
have the same volume.
Answers
The figures Сone Z and Cylinder Y have the same volume.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.
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please help!!!
picture below
Answers
Answer:
4^3x=4^(4x+4)
Step-by-step explanation:
You can eliminate the first 2 options since those don’t make sense already, and the last option changed 64 to 2^6 which is correct, but when they changed the other side. They should have multiplied 8 to both x and 1 which would have made the whole term 2^(8x+8) and not 2^(8x+1). Left with the third option, 4 to the power of 3 is 64 so the left side makes sense, 4^3x=64^x, on the right side, 4^4 equals 256, so the whole exponent should multiply by 4 so from 256^(x+1) you get 4^4(x+1) giving 4^(4x+4) making the third choice the right answer.
Split 120 into the ratio
2:3
Answers
Answer:
48 : 72
Step-by-step explanation:
Use the Multiplication Law of Exponents to explain why 5^3*5^-3 = 1
(URGENT PLEASE)
Answers
The multiplication law states that
a^m×a^n=a^m+nSo
5³×5-³=15^(3-3)=15⁰=11=1Answer:
1 = 1
Step-by-step explanation:
5^3*5^-3 = 1We all know the law of exponents,the one we'll use to solve this is the multiplication law:
x^y * x^z = x^y+zIf the bases are equal or two numbers then the powers are equal too.Solved:
[tex]5^3 \: * \: 5^{-3} = 1[/tex][tex]5 {}^{3 + ( - 3)} = 1[/tex][tex]5 ^{0} = 1[/tex]x^0 = 1
[tex]1 = 1 \: ( \rm \: Proved)[/tex]Alternate method:
5^3*5^-3 = 15^3*1/5^3 = 15^3 and 5^3 cancels, which results to
1 = 1Find the surface area for the rectangular prism below.
Please answer with steps! :)
Answers
Expand and simplify x(x + 2)(x + 4)
Answers
Answer:
Step-by-step explanation:
Comment
Expand the second and 3rd factors first. Then worry about the x.
Solution
x(x + 2)(x + 4)
first: x * x = x^2
Outside: 4*x = 4x
Inside: 2*x = 2x
Last: 2*4 = 8
Combine
x^2 + 4x + 2x + 8
x^2 + 6x + 8
Now is the time to worry about the extra x
x(x^2 + 6x + 8)
remove the brackets.
x*x^2 + x*6x + 8*x
Combine
Answer: x^3 + 6x^2 + 8x
Question 17 of 25
You need to solve a system of equations. You decide to use the elimination
method. Which of these is not allowed?
3x-2y=7
3x+4y=17
Equation 1
Equation 2
OA. Subtract equation 2 from equation 1.
OB. Subtract the left side of equation 2 from the left side of equation
1.
OC. Multiply equation 1 by 2. Then add the new equation to equation 2.
Answers
Answer:
The only methods allowed are
- "Subtract equation 2 from equation 1," and "Multiply equation 1 by 2. Then add the new equation to equation 2"
-
Step-by-step explanation:
Subtract Eq 2 from Eq 1:
3x-2y=7
-3x-4y=-17
-6y = -10
y = (5/3)
Use y =(5/3) to solve for x in both equations.
x=(31/9)
Subtract the left side of equation 2 from the left side of equation No, this is not a legal operation.
Multiply equation 1 by 2. Then add the new equation to equation 2 Yes, this works. Instead of solving for y first, this method solves for x, which can then be used to find y:
2(3x-2y=7)
6x-4y=14
3x+4y=17
9x = 31 (y is eliminated)
x = (31/9)
Now use this to find y in either equation:
3x-2y=7
3x-2(31/9)=7
y = (5/3)
How to graph the linear inequality
Answers
Step-by-step explanation:
here I have done you can check it out
Solve for X
2x+ 17
3x-4
Answers
Answer:
x = 21
Step-by-step explanation:
3x - 4 = 2x + 17 because of alternate angles
3x - 2x = 17 + 4
x = 21
Please Help!10.<ADC and <FDA are a linear pair. What is the reason?
Answers
Answer:
Linear pair of angles are formed when two lines intersect each other at a single point. Therefore, <ADC and <FDA are a linear pair.
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
g(x) = x^2+4
Step-by-step explanation:
The graph of f(x) = x^2 is translated up 4 units to become g(x) = x^2+4
Is 40% of 90 closer to 10 or 30?
Answers
Answer:
Closer to 30.
Step-by-step explanation:
To answer this first find 40% of 90.
90*0.4=36
0.4 is the same as 40%
Hope this helps!
If not, I am sorry.
Toby has $31 to buy t-shirts for his bowling team. each t-shirt costs $5. how many t-shirts can he buy?
Answers
Answer:
6 because 30 divided by 5 is 6 so he would have 1$ change
Answer:
Toby can buy 6 T-shirts with 1 extra dollar leftover
Step-by-step explanation:
Hook me up with a 5 star and a thanks :)
Graph the system of inequalities presented here on your own paper; then use your graph to answer the following questions:
Y > -4x-1
y<3/2x-1
Part A:
Describe the graph of the system; including shading and the types of lines graphed Provide a description of the solution area: (6 points)
Part B: Is the point (-1,1) included in the solution area for the system? Justify your answer mathematically
Answers
It is to be noted that the Graph of the indicated inequalities is herewith attached.
What is the graph of the system?As indicated above, this is a graph of a system of inequalities, where:
Y > -4x-1 and
y <3/2x-1
Is the point (-1,1) included in the solution area for the system?No. the point (-1, 1) is not included in the solution area for the system.
How do we justify this mathematically?
Step 1 - Plug in (-1, 1) in to the first equation. where y = -1 and x = 1.
Hence,
-1 > -4(1) -1
4 +1 < -1
4 < 0 (This is False)
Step 2 - Plug in (-1, 1) in to the second equation. where y = -1 and x = 1.
-1 < (3/2)(1) - 1
-1 < 1/2 (This is true).
Thus (-1, 1) is only partially included in the solution area.)
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Dixie lives in a $67,000 wood house in the country whose contents are valued at $12,000. She wants to know her monthly property insurance premium. Use the table above to calculate her monthly property insurance premium.
Answers
Without the table indicating the stated premium rates and applicable discounts, the monthly property insurance cannot be computed. Hence, on the assumption that the rate is 2.5% and the discount applicable is 7.5% the premium per month will come to $152.24
What is Property Insurance?
The simple definition of Property Insurance is, it is an insurance policy that covers a policyholder for the structure of a building and its contents against stated or agreed perils.
What is the calculation for the above?Given (based on assumption) that the applicable annual rate is 2.5%
and that:
Value of Wooden House = $67,000Value of the contents of the House = $12,000Applicable discount = 7.5% of premium/annumHence annual premium will be:
= (67,000 + 12000) * (2.5/100) * 0.925
Annual Premium Payable = $1,826.89.............A
Recall that we are asked to derive the monthly Insurance premium.
This is thus given as: Answer in A/12
→ 1,826.89/12
= $152.24
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Two circles are concentric if they have the same center.
On a coordinate plane, a circle has center (4, 6) and has a radius of 2 units.
Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?
(x – 4)2 + (y – 6)2 = 4
(x – 4)2 + (y – 6)2 = 16
(x – 6)2 + (y – 4)2 = 16
(x – 6)2 + (y – 4)2 = 4
Answers
The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16
Equation of a circleFrom the question, we are to determine the equation of the circle
The equation of circle is given by
(x - h)² + (y - k)² = r²
Where (h, k) is the center
and r is the radius
From the given information,
The two circles are concentric
∴ (h , k) = (4, 6)
But the other circle has a radius that is twice as large
∴ r = 2 × 2
r = 4
Thus,
The equation of the circle becomes
(x - 4)² + (y - 6)² = 4²
(x - 4)² + (y - 6)² = 16
Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16
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william used 15 cm of tape to wrap 3 presents, Find the length of tape to wrap for 1 present?
Answers
What is the common difference of the following arithmetic sequence?
{15,11,7,3,...}
Answers
Answer:
Solution : AP = 19 , 15 , 11 , 7 , 3.....
Common difference ( d ) = 15 - 19 = -4.
Answer:
The common difference is -4.
Step-by-step explanation:
Subtract a term from the next term.
11 - 15 = -4
The common difference is -4.
Find the value of x in 3x + 4y = 12 and 9x - 4y = 24.
Answers
Answer:
x=3
Step-by-step explanation:
we first write both equations:
[tex]3x + 4y = 12 \\ 9x - 4y = 24[/tex]
then we add the Left hand sides from both, and compare to the Right hand sides from both:
[tex]3x + 4y + 9x - 4y = 12 + 24 \\ 3x + 9x = 36 \\ 12x = 36 \\ x = 3[/tex]
Which pair of functions are inverses of each other?
Answers
The pair of functions are inverse of each other is, [tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex].Option C is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
On checking the function one by one we get that option c satisfies the conditions;
[tex]\rm f(x)=5x-9[/tex]
Change the coefficient;
y=f(x) as x=f(y)
The function is written as;
y=5x-9
x=5y-9
Simply the function;
[tex]\rm y = \frac{x+9}{5} \\\\ y=g(x) \\\\\ g(x) = \frac{x+9}{5}[/tex]
The pair of functions are inverses of each other is,[tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex]
Hence option C is correct.
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Simplify x^5 •x^2 • x
Answers
Summer looked at the formula for the Pythagorean Theorem, a2 + b2 = c2, she said that it didn’t matter which sides of a right triangle were a, b, and c. Is she correct?
Answers
Answer:
Summer is incorrect
Step-by-step explanation:
It definitely matters which side is side "c". Side "c" must be the hypotenuse (the side across from the right angle).
The other two sides are the legs (sides touching the right angle), and either leg can be "a" or "b", but the hypotenuse must be "c".
Take the equation, a² + b² = c², and subtract c² from both sides:
[tex]a^{2} +b^{2} -c^{2} =0[/tex]
It won't matter which leg is "a" or "b", because of the commutative property of addition. Note that "a²" and "b²" are added together, and due to the commutative property of addition, we can add in either order and get the same result.
However, since the c² term is connected by subtraction, and subtraction doesn't have a commutative property, it can't be subtracted in any order. Meaning which side it is is important.
What is the range of the function?
-2
3
3
9
00
4
12
2
A. (3, 9, 12)
B. (-2, 2, 3, 4)
C. {3}
OD. (-2, 2, 3, 4, 9, 12)
Answers
Answer:
yeheheehejehejejejjejjejejejejje
Refer to the attached image
Answers
Answer: [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]
========================================================
Work Shown:
[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]
The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.
The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.
Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.
Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.
On a coordinate plane, 2 dashed lines are shown. The first straight line has a negative slope and goes through (0, 1) and (2, 0). Everything below and to the left of the line is shaded. The second straight line has a positive slope and goes through (negative 1, 0) and (0, 2). Everything above and to the left of the line is shaded. A point is shown at (negative 3, 1).
Which system of inequalities with a solution point is represented by the graph?
y > 2x – 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1)
y > 2x + 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)
Answers
Answer:
Using the concepts of coordinate system and equation of line, we find that y ≥ (1/3)x + 3 and 3x-y > 2 are represented by the graph.
Step-by-step explanation:
Equation of line passes through points (a, b) and (c, d) is given by:
y-b = [(d-b) / (c-a)] / (x-a)
Given that the first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).
y-3 = [(4-3) / (3-0)] / (x-0)
y-3 = x / 3
y - (1/3)x = 3
Also, everything above the line is shaded, i.e. the inequality represents the first graph: y ≥ (1/3)x + 3
The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).
y+2 = [(1+2) / (1-0)](x-0)
y+2 = 3x
3x-y = 2
Everything to the right of the line is shaded.
i.e. inequality represents the second graph: 3x-y > 2
Hence, the system of linear inequalities is represented by the graph :
y ≥ (1/3)x + 3
3x-y > 2
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Answer:
D
Step-by-step explanation:
Got it right on edge 2022
The following set of random numbers represents 20 simulations of three daily
flights from New York to Los Angeles, with 0, 1, 2, or 3 representing a late
departure and 4, 5, 6, 7, 8, or 9 representing an on-time departure. In how
many of the simulations was there an on-time departure for all three flights?
Answers
The number of simulations in which was there was an on-time departure for all three flights is; 6
How to carry out number simulations?
We are given;
Number of Simulations = 20
Numbers that represent late departure = 0, 1, 2 or 3
Numbers that represent On-time departure = 4, 5, 6, 7, 8 or 9.
Now, the 20 simulations as seen online are;
339 931 317 444 432 858 194 192 649 709
742 626 702 258 955 880 505 854 774 132
To know the number of simulations that were on-time departure, we need to find the ones that don't include 0, 1, 2 or 3.
Looking at the simulations, the ones that represent on-time departure are 444, 858, 649, 955, 854, 774.
Thus, there are 6 simulations in which was there an on-time departure for all three flights
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find the volume of the composite figure & round to the nearest tenth if needed!!
please answer correctly...
25 points!!
Answers
Answer:
(2*2*1.5*1/3)+(2*1.5*4)= 14
Step-by-step explanation:
To find the area of a pyramid, you use the equation of 1/3 *lwh. When we place the values in there, we get 2*2*1.5*1/3, which is equal to 2. Then we solve the bottom part. Since it is a rectangular prism, we use the equation of lwh. When we insert the values, we get 2*1.5*4, which is equal to 12. Now, we take these two values of 2 and 12 and we combine them, giving us our final answer of 14.
