Answer:
[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -8x^3 - 16x^2 - 4x\\f(x) = \frac{3}{4}x^2 + 2x - 5\\f(x) = \frac{4}{x^2} - \frac{2}{x} + 1\\f(x) = 0x^2 - 9x + 7[/tex]
Required
Which of the above is a quadratic function
A quadratic function has the following form;
[tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
So, to get a quadratic function from the list of given options, we simply perform a comparative test of each function with the form of a quadratic function
[tex]1.\ f(x) = -8x^3 - 16x^2 - 4x[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = ax^3 + bx^2 + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]
This function has an exact match with [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
By comparison; [tex]a = \frac{3}{4}\ b = 2\ and\ c = -5[/tex]
[tex]3.\ f(x) = \frac{4}{x^2} - \frac{2}{x} + 1[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = \frac{a}{x^2} + \frac{b}{x} + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
[tex]4.\ f(x) = 0x^2 - 9x + 7[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = ax^2 +bx + c = 0\ but\ a = 0[/tex]
Unlike the quadratic function where [tex]a\neq 0[/tex]
So, from the list of given options, only [tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex] satisfies the given condition
A falling object travels a distance given by the formula d= 3t + 3t ^2, where d is measured in feet and t is measured in seconds. How many seconds will it take for the object to travel 50 feet?
Answer:
3.61 sec
Step-by-step explanation:
Set the given d= 3t + 3t ^2 equal to 50 and solve for t:
3t^2 + 3t - 50 = 0
This is a quadratic equation with coefficients 3, 3 and -50. The discriminant is b^2 - 4ac, or 3^2 - 4(3)(-50), or 9 + 600 = 609
The roots of this quadratic are therefore:
-(3) ± √609 -3 ± 24.68 21.68
t = -------------------- = ------------------- = ----------- = 3.61 sec
2(3) 6 6
Select solutions that satisfy the inequality (picture)
Hey so I'm doing slope-intercept and I understand it and have been moving on, but I'm confused at this: "2 = -4 + b 6=b" How did the -4+b turn into 6=b?
Answer:
By adding 4 to both sides.
2= -4 +b
2= b -4
2+4= b-4 +4
6= b
Another way to look at it is to move all the constants to one side. Here we have the constant 2 on the left hand side, and on the right we have the constant -4 and the variable b.
To isolate b, we move the constant -4 to the left hand side. Moving a number to the other side of the equal sign changes the sign of the number. So, -4 becomes a +4 on the left hand side.
2 +4= b
6= b
What is the product? (x^4)(3x^3-2)(4x^2)(4x^2+5x)
(A 12x^9+15x^8-8x^6-10x^5
(B 12x^24+15x^12-8x^8-10x^4 (C 12x^9-10x^5
(D 12x^24-10x^4
Answer:
Definitely A
Step-by-step explanation:
When multiplying you add exponents.
[tex]x^{4} (3x^{2} -2) = 3x^{7} -2x^{4} \\FOIL (3x^{7} -2x^{4})(4x^{2} +5x) = 12x^{9} +15x^{8} -8x^{6} -10x^{5}[/tex]
Answer:
A)
Step-by-step explanation:
1000% sure. Use foil method and add exponents together... Also on edge.
if f(x)=4^x-8 and g(x)=5x+6, find (f+g)(x)
Answer:
work is shown and pictured
The space shuttle is accelerated off its launch pad to a velocity of 525 m/s in 18.0 seconds.
What is its average acceleration?
Answer:
29.17m/s²Step-by-step explanation:
Acceleration is defined as the change in velocity of a body with respect to time.
Acceleration = velocity/time
Given velocity of the space shuttle = 525m/s and time = 18.0seconds
Its average acceleration = 525/18
Its average acceleration (in m/s²) = 29.17m/s²
Write the equation of the line passing through the points (10, 50) and (25, 20).
To write the equation, we need the slope and y-intercept.
Remember that slope is the same as rate of change
or the change in y over the change in x.
Start by setting up a table with x and y values
which I have provided below.
Filling out our table, our given points are (10, 50) and (25, 20).
In the y column, we can see that the value of y
goes from 50 to 20 so it decreases by -30.
This means that the change in y is -30.
In the x column, we can see that the value of x goes from 10 to 25
so it increases by 15 which means that the change in x is 15.
So the rate of change is -30/15 which simplifies to -2.
To find b, we can use any ordered pair
in our table as the values for x and y.
Let's use the first ordered pair.
So we have 50 = -2(10) + b.
Solving from here, we get 50 = -20 + b.
Now add 20 to both sides to get 70 = b.
So if our slope is -2 and our y-intercept is 70,
we can substitute these values into our formula.
This gives us y = -2x + 70.
In what ways are sine and cosine graph similar? Be sure to include a discussion of intercepts, maxima, minima, and period.
Answer:
The sine and cosine functions are similars in:
They are periodic functions with a period of 2π.
The domain of each function is (−∞,∞) and the range is [−1,1]. Both has maxima in 1 and a minimal in -1.
Find the infinite geometric sum of 4+2.4+1.44+...
Answer:
4+2.4=6.4+1.44=7.84
The infinite geometric sum of 4+2.4+1.44+... will be 10.
What is the common ratio?At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.
It is given that, the sequence is 4+2.4+1.44+...
The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is obtained that the common ratio is,
r=2.4/4
r=0.6
The Sum of an infinite geometric sequence is,
S = a / (1-r)
S=4 / (1-0.6)
S=10
Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.
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Marcus can carry a maximum of 25kg of gravel at one time
How many joumeys will he need to make to shift one and
half tonnes of gravel?
Answer: 60 journeys
Step-by-step explanation:
1 ton = 1000 kgs
1.5 tons = 1500 kgs
1500/25 = 60 journeys
Answer:
55 journeys.
Step-by-step explanation:
907185 gm = 1 ton
453592.5 gm = 1/2 ton
1360777.5 gm = 1 1/2 ton
Convert to kg (1000g= 1kg)
Then divide by 25kg
=1360.7775/25 = 54.4311
Round up decimal to 1
= 55 journeys
Find the volume round to the nearest tenth ( show work)
Answer:
2,144.7
4 x pi x (radius x radius x radius / 3)
4 x pi = 12.5663706
8 x 8 x 8 / 3 = 170.66
12.5663706 x 170.67 =2,144.66 rounded is 2,144.7
Hope this helps
Step-by-step explanation:
Determine the value of y in the figure, and identify whether the triangle is isosceles or equilateral. answers: y = 30°; equilateral y = 30°; isosceles y = 60°; equilateral y = 60°; isosceles
Answer: equilateral y=60
Step-by-step explanation:
The sum of all the angles in a triangle add up to 180 degrees. So, because you have the angle measurement of two sides, you can set up an equation to solve for the third side: 60+60+x=180 (do the math and you end up with y=60)
And because all three of the angle measures are equal, the triangle is defined as an equilateral triangle.
The value of y is 60° and the given triangle is Equilateral.
What are Triangles?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
We have a triangle where one of the angle is unknown.
Sum of the interior angles of a triangle is 180 degrees.
60° + 60° + y° = 180°
120° + y° = 180°
y° = 180° - 120°
y° = 60°
Equilateral triangles are those triangles whose all sides and all angles are equal.
Isosceles triangles are those whose 2 sides or 2 angles are equal.
Since all angles are equal to 60° here, this is an equilateral triangle.
Hence the given triangle is an equilateral triangle with the unknown angle equals 60°.
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Select two ordered pairs that satisfy the function y = –4x – 1.
Answer:
(-0.25,0) and (0,-1)
Step-by-step explanation:
I used a graphing calculator.
Put function the the calculator
then ind two points on the function and that is your answer
An isosceles triangle has legs whose lengths are 10 inches and a base whose length is 12 inches. Which of
the following is the area of the triangle in square inches?
(1) 34
(2) 48
(3) 60
(4) 84
Answer:
48
Step-by-step explanation:
We have to find the height of the triangle to find its area. The altitude to the base of an isosceles triangle is also the median, meaning the altitude forms a 6-8-10 right triangle, so the length of the height is 8, and therefore the area is 0.5 * 8 * 12 = 48.
HLP ! HLP ! HLP ! Last one
Jason wants to cut a rope that is 60 feet long into several equal pieces with nothing left over. How many pieces will he have if the length of each piece is the greatest integer possible?
Answer:
2 pieces, 30ft each
Step-by-step explanation:
rope : 60ft long
we are trying to figure out how many equal pieces we can cut the rope into with the length of each piece to be the greatest possible integer:
if jason wants the length of rope to be the longest than the answer is 2, if he divides the length of 60 by 2, each piece will be 30 feet long. If he divides the rope by any number larger, each piece will be shorter than 30 feet, and he wants the piece to be the largest possible length.
In the diagram below of circle o, chords AB and CD intersect at E.
If CE = 10, ED = 6, and AE = 4, what is the length of EB?
AWARDING MAX POINTS
Answer:
The length of EB is found 15
Step-by-step explanation:
As the diagram of the circle is not given in the question, I've found the diagram of the same question from internet and attached below. So that we can have a better understanding)
We can see in the diagram the chord AB and chord CD intersect each other at point E.
Each of the chord is divided into two segments.
According to the Intersecting Chords Theorem:
Products of the lengths of line segments on each chord are equal
Which means that
(AE)(EB) = (CE)(ED)
Substitute the given values;
(4)(EB) = (10)(6)
4(EB) = 60
EB = 15
Answer:
The length of EB is found 15
Step-by-step explanation:
As the diagram of the circle is not given in the question, I've found the diagram of the same question from internet and attached below. So that we can have a better understanding) We can see in the diagram the chord AB and chord CD intersect each other at point E. Each of the chord is divided into two segments. According to the Intersecting Chords Theorem: Products of the lengths of line segments on each chord are equal Which means that (AE)(EB) = (CE)(ED) Substitute the given values; (4)(EB) = (10)(6) 4(EB) = 60 EB = 15
(27)^-2/3 is equal to
Answer:
1/9
Step-by-step explanation:
(27)^-2/3=(3^3)^-2/3= 3^(-2/3*3)= 3^-2= 1/3^2= 1/9
Answer:
=1/9
Step-by-step explanation:
Apply exponent rule: a^-b=1/a^b
(27)^-2/3 = 1/(27)^2/3
Step-by-step method in attachment:
directions for constructing the centroid of a triangle?
Step-by-step explanation:
1.Draw a triangle
2. Measure one of the sides of the triangle
3. Place a point at the midpoint of one of the sides of the triangle.
4. Draw a line segment from the midpoint to the opposite vertex. The segment you just created is called a median.
5. Repeat steps 2-4 for the remaining two sides of the triangle.
plsssss help due todayy!!
[tex]answer \\ = 44 \ \frac{7}{8} \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Which graph represents the function f(x)=3x5^x
Answer:
top right corner
Step-by-step explanation:
A: y = 13 - 2x
B: y = 8 - x
At which point do these two lines intersect?
A. (1, 7)
B. (1.5, 3.0)
C, (1.6, 3.2)
D. (2, 9)
Answer:
Step-by-step explanation:
8 -x = 13 - 2x
x + 8 = 13
x = 5
y = 8 - 5
y = 3
(5, 3)
Evaluate 5 ÷ 4/6 Give your answer as a mixed number in its simplest form.
Answer:
15/2
Step-by-step explanation:
5*6/4=30/4=15/2
Answer: 7 1/2
Step-by-step explanation:
5 ÷ 4/6 = 7.5
7.5 as a mixed number is 7 1/2
7 1/2 simplified is 7 1/2
Ruth contributes 18% of the total cost of her individual health care. This is $67.50
deduction from each of her biweekly paychecks. What is the total value of her individual
coverage for the year?
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
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Answer:
Step-by-step explanation:
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
Kim’s family spends $62.50 on dinner. They leave an 18% tip. How much is their total bill after tip?
Answer:
51.25
Step-by-step explanation:
Multiply 62.5 by .18. You get 11.25. Subtract that from 62.5 and you get 51.25.
Answer:
Multiply the price with the tip rate
18% = 0.18
62.5 x 0.18 = 11.25
that is the tip. We add that on to find the total price
62.5 + 11.25 = 73.75
73.75 dollars is the answer. Hope this helps
Step-by-step explanation:
Can you help me out on this question?
Answer:
4. x= 18
Step-by-step explanation:
We solve the problem like this:
Since 3 is proportional to 6 and 9 is proportional to x, we set up a proportion.
3/9 = 6/x
We then use cross-multiplication to solve for x.
What is (-4,4) reflected on the x-axis
Answer:
(-4, -4)
Step-by-step explanation:
When reflecting coordinates onto x-axis, x sign doesn't change, y sign changes.
Answer:
(4,-4)
Step-by-step explanation:
That is the answer because it is like you are flipping the object so the opposite of -4 is 4 and the opposite of 4 is negative 4.
Consider the following simplified algebraic expression. 10 x squared y + 6 x squared minus 7 y squared minus 6 Which could be the original expression? 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared + 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x + 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 minus 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4
9514 1404 393
Answer:
(b) 8x^2y +7x^2 -5y^2 +3x -2 +2x^2y -x^2 -2y^2 -3x -4
Step-by-step explanation:
Detailed comparison of the answer choices seems to be required. The x^2y terms need to sum to 10x^2y, the 3x terms need to cancel, the constant terms need to sum to -6.
The appropriate choice on this list appears to be the second choice.
_____
Comment on the problem
In the form presented, it takes considerable time to sort the answer choices from one another and to determine what their differences are. It would be much more conducive to getting an answer if the problem were presented using the usual math symbols in a form that separates the question and the different answer possibilities.
Answer:
B
Step-by-step explanation:
i am smart
which of the following circles lie completely within the fourth quadrant? Check all that apply.
Answer:
B and D
Step-by-step explanation
Answer:
B and D
Step-by-step explanation:
Without graphing, determine whether the equation has a graph that is symmetric with
respect to the x-axis, the y-axis, the origin, or none of these.
y=x2 +8
Choose the correct answer below.
X-axis
y-axis
origin
none of these
Answer:
girl
Step-by-step explanation:
What in the world 3000%
