Answer:
3x³ + 3x² - 30x - 48
Step-by-step explanation:
3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3
= (3x + 6)(x² - x - 8)
each term in the second factor is multiplied by each term in the first factor
= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis
= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms
= 3x³ + 3x² - 30x - 48
See photo for problem, please help
Considering the given functions in the graph, we have that:
(f + g)(3) = 4.(f - g)(1) = -2.How to find (f + g)(3) looking at the graph?We look at the graph, and find f(3) and g(3), then add them. Hence:
g(3) = 4.f(3) = 0.Then the addition is:
(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.
As for (f - g)(1):Same logic, at the graph we have that:
f(1) = -1.g(1) = 1.Hence:
(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.
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The radius of circle A is 4.4 units.Which element of circle A has a measure of 27.65 units
Answer:
The circumference
Step-by-step explanation:
[tex]circumference \: = 2\pi \times radius \\ c = 2\pi(4.4) \\ c = 8.8\pi = 27.65[/tex]
Which equation represents exponential decay? * a y=3^x-4 b y=2(4)^x c y=1/2(3)^x d: y=6(1/3)^x
The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]
Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].
Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].
Decay means when x value increases ,the y value decreases.
We haveto put 3 values for x in the equations to check.
1)y=[tex]3^{x} -4[/tex]
put x=0,y=-3
put x=1, y=-1
put x=2, y=5
No,itdoes not represents exponential decay.
2) y=2[tex]4^{x}[/tex]
put x=0,y=2
put x=1, y=8
put x=2, y=32
No,it does not represents exponential decay.
3) y=[tex]3^{x}/2[/tex]
put x=0,y=0.5
put x=1, y=1.5
put x=2, y=4.5
No,it does not represents exponential decay.
4)y=6[tex](1/3)^{x}[/tex]
put x=0,y=6
put x=1, y=2
put x=2, y=0.67
Yes ,it represents exponential decay.
Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].
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Factor the greatest common factor: −6m2 18m − 36. −6(m2 − 3m 6) −1(6m2 − 18m 36) −6m(m2 − 3m 6) −6(m2 3m − 6)
Answer:
Step-by-step explanation:
−6m2 18m − 36
= -6(m2 - 3m + 6)
can someone please help me
Answer:
[tex]\frac{13\pi }{9}[/tex] radians
Step-by-step explanation:
to convert degrees to radians
degrees × [tex]\frac{\pi }{180}[/tex]
= 260 × [tex]\frac{\pi }{180}[/tex]
= 26 × [tex]\frac{\pi }{18}[/tex]
= 13 × [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{13\pi }{9}[/tex]
How to determine instantaneous rate of change with pi
The instantaneous rate of change of the function is 5/π
How to determine the instantaneous rate of change?The function is given as
[tex]f(x) =\cos(x - \pi) + 4[/tex]
Where
[tex]x = \pi[/tex]
Calculate f(π) as follows
[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]
This gives
[tex]f(\pi) =\cos(0) + 4[/tex]
Evaluate the expression
[tex]f(\pi) =5[/tex]
The instantaneous rate of change is then calculated as;
[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]
This gives
[tex]f'(x) = \frac{5}{\pi}[/tex]
Hence, the instantaneous rate of change of the function is 5/π
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solve this pls>>>>>>>there’s a pic
Answer:
x = 5, 1
Step-by-step explanation:
To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.
How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
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Given the following results from a spinner game after spinning 20 times.
What is the experimental probability of landing on red?
The experimental probability of landing on red is 7/20 or 0.35 or 35%
How to determine the experimental probability of landing on red?The complete question is added as an attachment
From the question, we have the following outcomes:
Red = 7
Green = 5
Blue = 5
Yellow = 3
The total number of spins is
Total = Red + Green + Blue + Yellow
This gives
Total = 7 + 5 + 5 + 3
Evaluate the sum
Total = 20
The experimental probability of landing on red is the calculated as:
P(Red) = Red/Total
Substitute the known values in the above equation
P(Red) = 7/20
Evaluate
P(Red) = 0.35
Express as percentage
P(Red) = 35%
Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%
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problem plot two points that are 8 88 units from point b bstart color #11accd, b, end color #11accd and also share the same x xx-coordinate as point b bstart color #11accd, b, end color #11accd.
The two points are B'=(-6,-8).
What is the plot?A plot is a graphical technique for depicting data collection, typically in the form of a graph that depicts the relationship between two or more variables. The storyline can be created either by hand or by computer. Previously, mechanical or electrical plotters were used.To plot the points:
Plot a new point that is 8 units down and also has the same x coordinate.
Given - Point B = ( -6, 0 )
Represent the new point with B':
In Point B = ( -6, 0 )
[tex]x=-6,y=0[/tex]
This means that B' has an x coordinate of -6.
Next, is to determine the y coordinate:
If a point (x,y) is translated b units down, the new point is (x, y, -b)
In this case:
The y coordinate of B is 0 and b = 8.
So, the new y coordinate is 0 - 8 = -8
So, we have B'=(-6,-8).
Therefore, the two points are B'=(-6,-8).
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One number is 4 more than another and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following is the value of the smaller number?
The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding
Calculate the value of the numbers:Given that one number is 4 more than another,
⇒x = y + 4 (equation (1))
Their sum is 60,
⇒x + y = 60
y + 4 + y = 60 (From (1))
2y + 4 = 60
2y = 56 ⇒ y = 28
x = y + 4 = 28 + 4 = 32
Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.
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Identify each expression that represents the slope of a tangent to the curve y = 1/x+1 at any point (x,y)
The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
How to find an expression for the slope at any point of a function
The slope at any point of the function can be found by definition of derivative following algebraic handling:
[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]
[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]
[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]
Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
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In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?
Check the picture below.
The requried measure of the angle m∠C in the given circle is 15°.
In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.
Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82
Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.
∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°
Thus, the requried measure of the angle m∠C in the given circle is 15°.
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there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,
The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents lolas purchase
The graph that represents Lola's Purchase is as shown in the attached file.
How to interpret Inequality Graph?Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
Representing expense in the equation form gives us;
Expense on pencils + expense on erasers < 3
Thus;
0.25X + 0.50Y < 3
Dividing through by 0.25, we have;
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)
The correct graph is attached below.
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Total area=
Help me please, thankss
The Area of given figure is 341.6 square.
According to the statement
we have to find the total area of given figure.
Here a= 10 and h= 11
So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))
where the a represent the base of given solid or sides of the equilateral triangle
And h represent the slant height of the solid.
So, Substitute the values in above formula then
A = 10(10 + √((10)^2 + 4(11)^2))
A = 10(10 + √((100 + 4(121))
A = 10(10 + √(100 + 484)
A = 10(10 + √(584)
A = 10(10 + 24.16)
A = 10(34.16)
A= 341.6
So, The Area of given figure is 341.6 square.
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Which of the following parabolas has its vertex the furthest away from the x-axis
Oy
x² - 1
y = 3x² + 4
Oy
=
Y =
1/2x²
Oy = x² - 10
Question 12 (1 point)
Answer:
y=x^2-10
Step-by-step explanation:
The triangle below is being reduced by a scale factor of two-thirds. What is the base of the new drawing? 15 m
Answer:
10
Step-by-step explanation:
A scale factor of 2/3 means multiplying all side lengths by 2/3
15*2/3=10
PR=
Help me please thanks so much
Formula: U*V=R*T
3*1=4*x
3=4x
x=3/4
Hope it helps!
Answer:
[tex]\sf PR =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Intersecting chords theorem:It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.
TP * PR = UP * PV
4 * PR = 3 * 1
[tex]\sf PR = \dfrac{3}{4}[/tex]
What equation shows that 9 is a factor of 72?
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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help pls im so confused
10(1^2*2^-2)
Answer:
2.5(or 5/2 or 2 1/2)
Step-by-step explanation:
Remember PEMDAS
10 * (1^2 * 2^-2)
10 * (1 * 0.25)
10 * 0.25 =
2.5
The circumference of a circular field is 222.94 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
35.5
Step-by-step explanation:
→ Write down the formula
2 × π × r = 222.94
→ Simplify
6.28 × r = 222.94
→ Divide both sides by 6.28
r = 35.5
Answer:
35.5 = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r where r is the radius
222.94 = 2 * 3.14 * r
222.94 = 6.28 r
Divide each side by 6.28
222.94/6.28 = r
35.5 = r
A machine manufactuers 300 nails a day. how many did it produce in the month of april 2007
The machine produces 3000 nails in the month of April 2007.
Production of Nails in the Month of April
According to the given information,
Number of nails manufactured per day by the machine, x = 300
And, we know that April is the fourth month of a year which has total 30 days.
Hence, number of days the machine is manufacturing nails in the month of April, y = 30
So, the number of nails that will be produced by the machine in the month of April is given by,
N = Number of nails produced per day × Number of days in April
N = xy
N = 300 × 30
N = 9000
Therefore, the machine produces 9000 nails in the April month of year 2007.
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If she was vaping every 15 minutes, assuming she was awake from 7 am- 11 pm (16 hours) how many times in a day would she vape?
Answer:
64 times
Step-by-step explanation:
16 hours to minutes: 16*60 = 960 minutes
vaping every 15 minutes: 960/15 = 64
Hi! It’d be really helpful if someone could explain he two questions below, thanks!
I need help with cancelling units please
Answer:
D
Step-by-step explanation:
You are looking for what you would need to cancel the yards in 800 yards.
800 yards (1 mile/ 1760 yards). You have yards in the numerator of your original measurement. You will cross cancel out the yard on the the top and the yards on the bottom.
100 POINTS OKK!!!!
1. If y varies directly as x and y=5, when x=3, find the equation that relates x and y.
2. If v varies directly as w and v=21, when w=8. find the equation that relates v and w.
3. If p varies inversely with q and p=5 when q=6, find the equation that relates p and q.
4. If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.
5. The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1.5-foot-long board, how many pounds of pressure would he need to use to break a 6-foot-long board?
Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;
y = [tex]\frac{5}{3}[/tex] xv = [tex]\frac{21}{8}[/tex]wp = [tex]\frac{30}{q}[/tex]y = [tex]\frac{33}{x}[/tex]F = 5 poundsVariation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.
The required answers to the given questions are:
1. y [tex]\alpha[/tex] x
⇒ y = kx
where k is the constant of proportionality.
Given that, y = 5 and x =3, then;
5 = 3x
x = [tex]\frac{5}{3}[/tex]
Thus,
y = [tex]\frac{5}{3}[/tex] x
2. v [tex]\alpha[/tex] w
v = kw
Given: v = 21, w = 8
Then,
21 = 8k
k = [tex]\frac{21}{8}[/tex]
Thus,
v = [tex]\frac{21}{8}[/tex]w
3. q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]
y = [tex]\frac{k}{q}[/tex]
Given: q = 5, q = 6
Then,
5 = [tex]\frac{k}{6}[/tex]
k = 5 x 6
k = 30
Thus,
p = [tex]\frac{30}{q}[/tex]
4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]
y = [tex]\frac{k}{x}[/tex]
Given: y = 11, x = 3
Then,
11 = [tex]\frac{k}{3}[/tex]
k = 11 x 3
k = 33
Thus,
y = [tex]\frac{33}{x}[/tex]
5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]
F = [tex]\frac{k}{l}[/tex]
Given; F = 20 pounds, l = 1.5 ft
20 = [tex]\frac{k}{1.5}[/tex]
k = 20 x 1.5
k = 30
F = [tex]\frac{30}{l}[/tex]
When l = 6 ft, then;
F = [tex]\frac{30}{6}[/tex]
F = 5 pounds
The amount of force required is 5 pounds.
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y≤1/2x-3
y + 2x > 6
I need help solving this problem shjsdjjsjdndjskdjdkkdndnsjsjmsmskdndnd
Answer:
6-2x < y < ½x-3Step-by-step explanation:
The first part tells us that y is, or is anywhere below ½x-3
The second part tells us that above 6-2x
Since we don't know what x is, we cannot actually find y.
The best answer to this question is:
6-2x < y < ½x-3
Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.
Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.
The vectors are linearly independent if and only if?
The vectors are linearly independent if and only if k ≠ -11
How to solve the vectorIn mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.
Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.
In this question,
We have 2v - 3w
We have to multiply 2 by the values of v and multiply 3 with the values of w
this would produce
[2,6,8]-[6,6,12]
subtract w from v
= [-4, 0, -4]
We u as -1, 0 and 10+k
It is not possible to -1 = 10 + k
-11 = k
Hence we have to conclude that they are linearly independent if and only if k ≠ -11
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GCSE MATHS PLEASE HELP
Answer:
A) y = 16/(x^2), B) 4/5
Step-by-step explanation:
For A, we can plug in some of the table values to check it. I will try 2 and 3
2. 4 = 16 / (2^2)
16/4 = 4
3. 16/9 = 16 / (3^2)
16/9 = 16/9
B) We can just input y into the formula 25 = 16 / (x^2)
This leaves us with +-4/5
Answer:
see explanation
Step-by-step explanation:
(a)
given y varies inversely as x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k substitute any ordered pair from the table into the equation
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , then
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is x = [tex]\frac{4}{5}[/tex]