Answer:
77.3 to the nearest tenth.
Step-by-step explanation:
The total of the scores on the set of 27 tests
= 78*27 = 2106.
After 2 more had joined the total score is 2106 + 69 + 66
= 2241.
So the new mean score = 2241 / 29
= 77.3.
Answer:
77.3
Step-by-step explanation:
Recall that the arithmetic mean is found as follows:
sum of all data
a. m. = ---------------------------
number of data
sum
The mean score of 27 test results is thus 78 = --------
27
Note that we can find the sum of all 27 of the original scores by multiplying 78 by 27: 2106.
Now we include two more scores. Instead of the original sum, 2106, we have
2106 + 69 + 66
a. mean = ---------------------------
29
which comes out to 2241/29 = 77.3
flock of birds is flying south, toward the equator, at an hourly rate. A scientist created the function f(x)=−60x+1320 to represent how many miles away from the equator the birds are after a given number of hours.
Which of the answers are true of the scenario represented by this function?
There is more than one correct answer. Select all answers that apply.
The birds began 1320 miles from the equator.
It will take the birds 1320 hours to reach the equator.
The birds began 60 miles from the equator.
It takes the birds 60 hours to fly x miles.
The birds are flying toward the equator at a rate of 1320 mph.
The birds are flying toward the equator at a rate of 60 mph.
Answer: First and last option
The birds began 1320 miles from the equator.
The birds are flying toward the equator at a rate of 60 mph.
Step-by-step explanation:
Note that the function f(x) is a linear function.
[tex]f (x) = - 60x + 1320[/tex]
If x represents the number of hours and f(x) represents the distance from the equator, then x = 0 means that the first hour has not yet elapsed.
When x = 0 then:
[tex]f (0) = -60 * 0 +1320\\f (0) = 1320[/tex].
This means that the initial distance at which the birds of the equator are located is 1320 miles.
Then when x = 1 then:
[tex]f (x) = -60 * 1 + 1320\\f (x) = -60 +1320[/tex]
When x = 2 then:
[tex]f (x) = -60 * 2 + 1320\\f (x) = -120 +1320[/tex]
As x increases by one unit then the distance of the birds to the equator decreases by 60 miles. This means that birds travel at a speed of 60 miles per hour
Answer:
The birds began 1320 miles from the equator.
The birds are flying toward the equator at a rate of 60 mph.
Step-by-step explanation:
Which of these statements being true would show that x-10 is a factor of the polynomial p(x)
P(10)=0
p(0)=10
p(0)=-10
p(-10)=0
PLEASE HELP ASAP ALGEBRA 2
Answer:
P(10)=0
Step-by-step explanation:
As per factor theorem:
If x-10 is factor of polynomial p(x), then the remainder after division by x-10 should be zero. i.e. If we synthetic-divide a p(x) by x = 10 and get zero remainder as following
P(10)=0
it is reverse of remainder theorem!
DeMarco has the following coins in his
pocket: 5 nickels, 3 dimes, and 2 quarters.
What percent of one dollar does DeMarco
have in nickels?
Answer:
5=.25, 3=.30, 2=.50
Step-by-step explanation:
5×5=.25
Answer: 25%
Step-by-step explanation: A nickel is worth 5 cents. There are 5 nickels. Multiply 5 by 5. 5 x 5 = 25. You have 25 cents in nickels. There are 100 cents in a dollar, so divide 25 by 100. 25/100 = 0.25. To get the percent, multiply 0.25 by 100. 0.25 x 100 = 25%.
-f(3f-7)=0 solve equation
Answer:
F=0 or (7/3)
Step-by-step explanation:
When F is 0, the equation reads -0(3(0)-7)=0. The outside 0 will multiply by everything and make it equal 0. When F is 7/3, the inside of the parenthesis read 3(7/3)-7. This equals 7-7. It'll end up being (7/3)0, which equals 0.
If Kevin makes c toys in m minutes, how many toys can he make per hour?
Answer:
The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]
Step-by-step explanation:
we know that
Kevin makes c toys in m minutes
Remember that
1 hour=60 minutes
so
Using proportion find out how many toys can be make in 60 minutes (one hour)
Let
x -----> the number of toys that Kevin can make per hour
so
[tex]\frac{c}{m}=\frac{x}{60}\\ \\x=60\frac{c}{m}\ toys[/tex]
therefore
The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]
help me with the work
first off, let's check what's the slope of that line through those two points anyway
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{7-5}\implies \cfrac{2+2}{7-5}\implies \cfrac{4}{2}\implies 2[/tex]
now, let's take a peek of what is the slope of that equation then
[tex]\bf -5y+kx=6-4x\implies -5y=6-4x-kx\implies -5y=6-x(4+k) \\\\\\ -5y=-x(4+k)+6\implies -5y=-(4+k)x+6\implies y=\cfrac{-(4+k)x+6}{-5}[/tex]
[tex]\bf y=\cfrac{(4+k)x-6}{5}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{(4+k)}{5}} x-\cfrac{6}{5}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{since both slopes are the same then}}{\cfrac{4+k}{5}=2\implies 4+k=10}\implies \blacktriangleright k=6 \blacktriangleleft[/tex]
A bag contains 5 blue, 3 red, and 8 green marbles. You choose a marble, do not replace it, and then choose another one. What is the probability that both marbles are red?
Answer:
1/40
Step-by-step explanation:
A bag contains 5 blue, 3 red, and 8 green marbles
You have (5+3+8=16) marbles
P(red 1) = red/total = 3/16
You do not replace it
A bag contains 5 blue, 2 red, and 8 green marbles
You have (5+2+8=15) marbles
P(red 2nd) = red/total = 2/15
P(red 1, red 2) = P (red 1)* P (red 2) = 3/16 * 2/15
=1/40
a plain takes off at an angel of 20 degree. assuming a constant speed and trajectory, by the time it has travelled 25 kilo meter horizontally, how h8gh it will be fly
Answer:
9.10 km to the nearest hundredth.
Step-by-step explanation:
We have a triangle whose adjacent side is 25 km and angle 20 degrees.
If h is the height we have the equation:
tan 20 = h / 25
h = 25 tan 20
= 9.099 km.
Please help??
The equation of a standard pitcher’s mound in baseball is (x+5)^2+(y+7)^2=81. The diameter of the pitcher’s mound is____ units
The equation (x+5)^2 + (y+7)^2=81 is a variation of a circles standard formula (x - h)^2 + (y - k)^2 = r^2
To find the diameter you must first know the radius.
In this question the radius is 9.
9^2 = 81
The diameter is composed of the length of two radii, this means that the equation to find the diameter when the radius is known is (let diameter be D and radius be r): D = 2r
D = 9 * 2
D = 18
The diameter is 18 units
Hope this helped!
~Just a girl in love with Shawn Mendes
NEED HELP ASAP PLEASE
Answer:
AAS theorem
Step-by-step explanation:
Angle SUT = Angle TVS (given)
Angle SRY = Angle TRV (vertically opposite angles)
SU = TV (given)
So, Triangle SUR is congruent to triangle TVR by AAS theorem.
Please mark Brainliest if this helps!
Find the first six terms of the sequence. a1 = 4, an = an-1 + 8
[tex]\bf \begin{array}{llll} term&\stackrel{a_{n-1}+8}{value}\\ \cline{1-2} a_1&4\\ a_2&\stackrel{4+8}{12}\\ a_3&\stackrel{12+8}{20}\\ a_4&\stackrel{20+8}{28}\\ a_5&\stackrel{28+8}{36}\\ a_6&\stackrel{36+8}{44} \end{array}[/tex]
Answer:
The first 6 terms are 4,12,20,28,36,44
Step-by-step explanation:
So we have the recursive sequence
[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].
If you try to dissect what this really means, it becomes easy.
Pretend [tex]a_n[/tex] is a term in your sequence.
Then [tex]a_{n-1}[/tex] is the term right before or something like [tex]a_{n+1}[/tex] means the term right after.
So it is telling us to find a term all we have to is add eight to the previous term.
So the second term [tex]a_2[/tex] is 4+8=12.
The third term is [tex]a_3[/tex] is 12+8=20.
The fourth term is [tex]a_4[/tex] is 20+8=28.
The fifth term is [tex]a_5[/tex] is 28+8=36
The sixth term is [tex]a_6[/tex] is 36+8=44.
Now sometimes it isn't that easy to see the pattern from the recursive definition of a relation. Sometimes the easiest way is to just plug in. Let's do a couple of rounds of that just to see what it looks like.
[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].
[tex]a_2=a_1+8=4+8=12[/tex]
[tex]a_3=a_2+8=12+8=20[/tex]
[tex]a_4=a_3+8=20+8=28[/tex]
[tex]a_5=a_4+8=28+8=36[/tex]
[tex]a_6=a_5+8=36+8=44[/tex]
Find the domain of the graphed function.
-10
The domain is the X values.
There are two dots located at x = -4 and x = 9
The answer would be: D -4 < x < 9
The domain of the graphed function is - 4 ≤ x ≤ 9, that is option D. This can be obtained by finding all the x-values.
What is the domain of the graph?⇒Domain is all x-values of a function.
From the graph, we can say that the graph start from (-4,-4) to (8,9).
Thus x-values are from -4 to 9.
Since the endpoints are closed circles the points -4 and 9 are included.
∴The required domain is - 4 ≤ x ≤ 9
Hence the domain of the graphed function is - 4 ≤ x ≤ 9, that is option D.
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In graphing the equation y<2x -5, the line is dotted and shaded below the line drawn.
True
False
Answer:
True.
Step-by-step explanation:
This is 'less than' so the area below the line is shaded.
It is a dotted line because the solution does not contain points on the line as the inequality sign is < NOT ≤.
Answer:
First option: True.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Given this inequality:
[tex]y<2x -5[/tex]
We know that the line is:
[tex]y=2x -5[/tex]
Whose slope is 2 and the y-intercept is -5
The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.
Find the limit of the function by using direct substitution. (6 points) limit as x approaches zero of quantity x squared minus three.
Answer:
[tex]\lim_{x \to 0} x^2-3=-3[/tex]
Step-by-step explanation:
This limit can be written as follows
[tex]\lim_{x \to 0} x^2-3[/tex]
Direct substitution means that we substitute in the value for x to get our limit
[tex]\lim_{x \to 0} x^2-3\\\\0^2-3\\\\-3[/tex]
[tex]\displaystyle\\\lim_{x\to 0}(x^2-3)=0^2-3=-3[/tex]
GCF of 32ab cubed and 40a squared
Answer:
8a.
Step-by-step explanation:
32 = 2*2*2*2*2
40 = 2*2*2* 5
Thus the GCF of 32 and 40 is 2*2*2 = 8.
The GCF of a and ab = a.
For this case we must find the GCF of the following expressions:
[tex]32ab ^ 3\\40a ^ 2[/tex]
By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.
We look for the factors of 32 and 40:
32: 1,2,4,8,16
40: 1,2,4,5,8,10,20
Thus, the GCF is 8.
On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.
Finally, the GFC of the expressions is:
[tex]8a[/tex]
Answer:
[tex]8a[/tex]
Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh.
What is the volume of the pyramid after dilating by a scale factor of 1/4? Describe the effects.
A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.
B.) 64 m³. The volume of the new pyramid is the volume of the original pyramid times 1/16.
C.) 256 m³. The volume of the new pyramid is the volume of the original pyramid times 1/4.
D.) 1,024 m³. The volume of the new pyramid is equal to the volume of the original pyramid.
Answer:
Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.
Step-by-step explanation:
step 1
Find the volume of the original pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
we have
[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square
[tex]h=12\ m[/tex]
substitute
[tex]V=\frac{1}{3}(256)(12)[/tex]
[tex]V=1,024\ m^{3}[/tex]
step 2
Find the volume of the new pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z -------> the scale factor
x ------> the volume of the new pyramid
y -----> the volume of the original pyramid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{1}{4}[/tex]
[tex]y=1,024\ m^{3}[/tex]
substitute and solve for x
[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex]
[tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]
therefore
The volume of the new pyramid is the volume of the original pyramid times 1/64
Answer:
The answer is A
Step-by-step explanation:
5. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set, and P = {1, 3, 5, 7}. What is p'? (1
point)
{2, 4, 6, 8)
{1, 2, 3, 4, 5, 6, 7, 8
O {1, 3, 5, 7}
{1, 3, 5, 7, 8)
Answer:
p' = {2, 4, 6, 8}.
Step-by-step explanation:
The set p' has all the elements in the universal set U that are not in set p.
p' = {2, 4, 6, 8}.
Step-by-step answer:
U = universal set (all possible members)
P = given set
P' = complement of P, i.e. contains all members in U but NOT 1,3,5,7in P.
Thus, U=P or P'.
Here,
U={1,2,3,4,5,6,7,8}
P={1,3,5,7}
so P'={2,4,6,8}
Check: P or P' ={1,3,5,7} or {2,4,6,8} = {1,2,3,4,5,6,7,8} = U good !
Drag the correct steps into order to evaluate 27 – t • 3 for t = 6.
Answer:
Step-by-step explanation:
Step 1 : 27-t*3
Now put the value t=6
Step 2:
=27-6*3
According to the DMAS rule multiplication wll be solved first.
Step3:
=27-18
Step 4:
=9 ....
An equation was used to predict the number of possible enrollments in an afterschool program for the first 6 months of the year. The actual enrollments are also listed.
Actual enrollment 55 80 95 100 115 90
Predicted enrollment 75 80 85 90 95 100
The sum of the residuals is ______.
Answer:
70
Step-by-step explanation:
75-55=20
95-85=10
100-90=10
115-95=20
100-90=10
sum of the differences is 70
Answer:
A: 10
Step-by-step explanation:
Let's add the actual enrollments all together. 55 + 80 + 95 + 100 + 115 + 90 all added together is 535. The predicted enrollments, all added together, is: 75 + 80 + 85 +90 +95 + 100 = 525.
535 - 525 = 10 residuals.
The table below shows the cube roots of different numbers:
Number
(x) 8 27 64 125
Cube root
(y) 2 3 4 5
Part A: Does the table represent y as a function of x? Justify your answer. (5 points)
Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below:
f(x) = 10 + 20x
What is the value of f(100), and what does f(100) represent? (5 points)
part A)
[tex]\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}[/tex]
part B)
f(x) = 10 + 20x
so if you rent the bike for a few hours that is
1 hr.............................10 + 20(1)
2 hrs..........................10 + 20(2)
3 hrs..........................10 + 20(3)
so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.
f(100) = 10 + 20(100) => f(100) = 2010.
f(100), the cost of renting the bike for 100 hours.
Given the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, at what values of x do f(x) and g(x) intersect?
Answer:
The values of x are 0 and 4
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-2x-4[/tex] ------> equation A
[tex]g(x)=2x-4[/tex] ----> equation B
To find the values of x when f(x) and g(x) intersect
equate f(x) and g(x)
[tex]f(x)=g(x)[/tex]
[tex]x^{2}-2x-4=2x-4[/tex]
[tex]x^{2}-2x-4-2x+4=0[/tex]
[tex]x^{2}-4x=0[/tex]
Factor x
[tex]x(x-4)=0[/tex]
The solutions are
x=0 and x=4
Final answer:
The functions f(x) = x²- 2x - 4 and g(x) = 2x - 4 intersect at x = 0 and x = 4, found by setting the equations equal to each other and solving for x.
Explanation:
To find the intersection points of the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, we need to set the two functions equal to each other and solve for x.
Set f(x) equal to g(x): x ²- 2x - 4 = 2x - 4.
Move all terms to one side to set the equation to zero: x² - 4x = 0.
Factor the quadratic equation: x(x - 4) = 0.
Find the solutions for x by setting each factor equal to zero: x = 0 and x - 4 = 0, which gives us x = 0 and x = 4.
Therefore, the functions f(x) and g(x) intersect at the values x = 0 and x = 4.
all of the following expressions have the same value except... -4/5-1/5 -(4/5+1/5) -4/5+ -1/5 -4/5-(-1/5)
Answer:
-4/5-(-1/5)
Step-by-step explanation:
-4/5-1/5 is equivalent to -4/5+-1/5 which equals -1
-(4/5+1/5) when you add the expression in the parenthesis you get 1 and when you multiply that by -1 you get -1
-4/5+ -1/5 this is like the first choice so it equals -1
-4/5-(-1/5) this expression is the equivalent to -4/5+1/5 which gives you -3/5
The last option is -3/5 while the others are -1 which it the one with the different value
All of the expressions have the same value except -4/5 - (-1/5).
Explanation:In this case, all of the expressions have the same value except -4/5 - (-1/5).
To simplify each expression:
-4/5 - 1/5 can be simplified to -5/5 which is equal to -1.-(4/5 + 1/5) can be simplified to -5/5 which is also equal to -1.-4/5 + (-1/5) can be simplified to -5/5 which is still equal to -1.Finally, -4/5 - (-1/5) can be simplified to -4/5 + 1/5. Adding these fractions gives us -3/5.Therefore, the expression that has a different value is -4/5 - (-1/5).
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What is the range of this relation (2,-3),(-4,2),(6,2),(-5,-3),(-3,0)
Answer:
Range of this relation = -3, 2
Step-by-step explanation:
We are given the following relation and we are to find its range:
[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]
The set of all the possible dependent values a relation can produce from its values of domain are called its range. In simple words, it is the list of all possible inputs (without repeating any numbers).
Therefore, the range of this relation is: -3, 2
Answer: [tex]Range:[/tex]{[tex]-3,0,2[/tex]}
Step-by-step explanation:
The range of a relation is the set of y-coordinates of the ordered pairs (These are the second numbers of each ordered pair).
In this case you have the following relation:
[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]
Therefore, based on the explained bofore, you can conclude that the rsnge of the given relation is the following:
[tex]Range:[/tex]{[tex]-3,0,2[/tex]}
(Notice that you do not need to write the same number twice)
Rachel is making bouquets she has 72 carnations and 48 roses. Each bouquet has the same number of flowers, with no flowers left over. What is the greatest number of bouquets she can make?
There are 24 bouquets making by Rachel.
What is Factor?
A number which means to break it up into numbers that can be multiplied together to get the original number.
Now, To solve this problem,
Let us first lay out all the factors of each number.
72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
So, The greatest number of bouquets that can be made would be equal to the greatest common factor of the two numbers 72 and 48 will 24.
Hence, There are 2 bouquets making by Rachel.
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Rachel can make 24 bouquets with 72 carnations and 48 roses.
To determine the greatest number of bouquets Rachel can make with 72 carnations and 48 roses, we need to find the greatest common divisor (GCD) of 72 and 48. The GCD is the largest number that divides both 72 and 48 without leaving a remainder.
Here are the steps to find the GCD:
List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48Identify the common factors: 1, 2, 3, 4, 6, 8, 12, 24The greatest common factor is 24.Calculating cos-1 ( help is gladly appreciated :) )
Answer:
[tex]\frac{3\pi}{4}[/tex]
(Assuming you want your answer in radians)
If you want the answer in degrees just multiply your answer in radians by [tex]\frac{180^\circ}{\pi}[/tex] giving you:
[tex]\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}[/tex].
We can do this since [tex]\pi \text{ rad }=180^\circ[/tex] (half the circumference of the unit circle is equivalent to 180 degree rotation).
Step-by-step explanation:
[tex]\cos^{-1}(x)[/tex] is going to output an angle measurement in [tex][0,\pi][/tex].
So we are looking to solve the following equation in that interval:
[tex]\cos(x)=-\frac{\sqrt{2}}{2}[/tex].
This happens in the second quadrant on the given interval.
The solution to the equation is [tex]\frac{3\pi}{4}[/tex].
So we are saying that [tex]\cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2}[/tex] implies [tex]\cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4}[/tex] since [tex]\frac{3\pi}{4} \in [0,\pi][/tex].
Answer is [tex]\frac{3\pi}{4}[/tex].
Which phrase matches the algebraic expression below?
2(x − 7) + 10
Answer:
Two times the difference of a number x and 7 plus 10.
Step-by-step explanation:
We are to write a phrase which matches the following algebraic expression below:
[tex] 2 ( x − 7 ) + 1 0 [/tex]
We can see that there is a bracket with a coefficient outside it so we can express it as:
'Two times the difference of a number x and 7'.
While + 10 can be added to it to complete the phrase:
Two times the difference of a number x and 7 plus 10.
348,0 19.57 which digit is in the ten thousands place
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
See attached reference
Which statement best describes the polynomial -8x^4 ? first degree polynomial with two terms fourth degree polynomial with two terms fourth degree monomial second degree binomial
Answer:
fourth degree monomial
Step-by-step explanation:
-8x^4
There is one term so it is a monomial
The highest power is degree 4, so it would be a quartic
Consider the table of values for function f.
x: -1, 0, 1, 2, 3, 4, 5
f(x): 3.5, 4, 5, 7, 11, 19, 35
The function g is shown below:
g(x)=4x+5
In which of the following intervals is the average rate of change greater for f than for g?
A. [1,3]
B. [3,5]
C. [0,2]
D. [-1,0]
Answer:
B. [3,5]
Step-by-step explanation:
The rate of change of a function is the same as the slope between two given points from that same function,
Hence,
all we need to do is use the slope's equation, that is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
And eval it in every couple of ordered pairs given from the table we obtain the following>
x2 y2 x1 y1 m
0 4 -1 3,5 0,5
1 5 0 4 1
2 7 1 5 2
3 11 2 7 4
4 19 3 11 8
5 35 4 19 16
The rate of change from g(x) is 4 (its slope)
Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5
Use the grouping method to factor this polynomial completely.
4x3 + 8x2 + 3x+6
Answer:
(x + 2)(4x^2 + 3)
Step-by-step explanation:
The first two terms factor as follows: 4x^2(x + 2).
The last two factor as follows: 3(x + 2).
Thus, (x + 2) is a factor of 4x3 + 8x2 + 3x+6:
4x^2(x + 2) + 3(x + 2), or:
(x + 2)(4x^2 + 3).
Note that 4x^2 + 3 can be factored further, but doing so yields two complex roots.
Answer: (x + 2)(4x^2 + 3)
Step-by-step explanation:
4x3 + 8x2 + 3x+6 becomes 4x^2(x + 2) + 3(x + 2) and can also be written as (x + 2)(4x^2 + 3).
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Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!
- Cutiepatutie ☺❀❤