Answer:
18 minutes
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the time,
and T is the half life.
A = 140 when t = 10. Solve for the half life:
140 = 700 (½)^(10 / T)
0.2 = ½^(10 / T)
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31
When A = 40, t is:
40 = 700 (½)^(t / 4.31)
0.057 = ½^(t / 4.31)
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8
Rounded to the nearest whole number, it takes 18 minutes.
The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
The half-life decay formula is given as,
N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]
Where T is half-life while t is the time taken.
N₀ is the initial amount,
As per the given,
N(t) = 140 when t = 10.
140 = 700 [tex](1/2)^{(t / T)}[/tex]
Take log both sides,
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31 minutes
Put N(t) = 40
40 = 700[tex](1/2)^{(t / 4.31)}[/tex]
Take log both sides,
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8 ≈ 18 minutes
Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".
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look at the image below
Answer:
37.3m**3
Step-by-step explanation:
1/3*7*4*4 = 37.3m**3
Answer:
Pyramid Volume = (area of base * height) / 3
Pyramid Volume = (4 * 4 * 7) / 3
Pyramid Volume = 112 / 3
Pyramid Volume = 37.33333 cubic meters
http://www.1728.org/volpyrmd.htm
Step-by-step explanation:
Equation for parabola that has points (-4,2) (0,2) (-2,3)
Step-by-step explanation:
What is the equation of the parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
?
To solve this you need to use the vertex form of the equation of a parabola which is
y
=
a
(
x
−
h
)
2
+
k
, where
(
h
,
k
)
are the coordinates of the vertex.
Explanation:
The first step is to define your variables
h
=
−
4
k
=
2
And we know one set of points on the graph, so
x
=
−
7
y
=
−
34
Next solve the formula for
a
y
=
a
(
x
−
h
)
2
+
k
−
34
=
a
(
−
7
+
4
)
2
+
2
−
34
=
a
(
−
3
)
2
+
2
−
34
=
9
a
+
2
−
36
=
9
a
−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k
y
=
−
4
(
x
+
4
)
2
+
2
y
=
−
4
(
x
2
+
8
x
+
16
)
+
2
y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62
Find the sum of 1 + 3/2 + 9/4 + …, if it exists.
Answer:
Option (4)
Step-by-step explanation:
Given sequence is,
[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]
We can rewrite this sequence as,
[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]
There is a common ratio between the successive term and the previous term,
r = [tex]\frac{\frac{3}{2}}{1}[/tex]
r = [tex]\frac{3}{2}[/tex]
Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.
Since sum of infinite geometric sequence is represented by the formula,
[tex]S_{n}=\frac{a}{1-r}[/tex] , when r < 1
where 'a' = first term of the sequence
r = common ratio
Since common ratio of the given infinite series is greater than 1 which makes the series divergent.
Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.
Option (4) will be the answer.
In 2014, the population of Ohio was 11.59 million people. One-hundred years earlier the population was 5.109 million people. Using scientific notation, how much did the population grow over the hundred-year span?
The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million
Also given that One-hundred years earlier of the year 1914, the population = [tex]5.109[/tex] million people
One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years
One-hundred years earlier in the year 2014 = Year 1914
The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]
The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]
How much did the population grow over the hundred-year span?
Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]
Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]
Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
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jeff buys 44 watermelons, he gets into a car accident and loses 31, how many does jeff have left
Answer:
Jeff has 3 watermelons left
Step-by-step explanation:
44-31=13 watermelons
Answer:
13
Step-by-step explanation:
44
-31
13
The length of a rectangle is five times its width.
2
If the area of the rectangle is 180 in find its perimeter.
Answer:
72
Step-by-step explanation:
l = 5w
A = l*w
180 = 5w *w
180 = 5w^2
Divide each side by 5
180/5 = 5w^2 /5
36 = w^2
Taking the square root of each side
sqrt(36) = sqrt(w)^2
6 =w
l = 5w = 5*6 = 30
The perimeter is
P = 2(l+w)
P = 2(6+30) = 2(36) = 72
Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.
Answer:
3 miles
Step-by-step explanation:
5 + m=8
Subtract 5 from each side
5-5 + m=8-5
m = 3
She needs to swim 3 more miles
Answer:
Yelena needs to swim 3 more miles
Step-by-step explanation:
You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:
[tex]5+m=8[/tex]
To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:
[tex]5-5+m=8-5[/tex]
Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:
[tex]m=3[/tex]
The total miles left that Yelena needs to swim is 3 miles.
:Done
If the legs of an isosceles right triangle have a length of 15 StartRoot 2 EndRoot ft, what is the length of the hypotenuse?
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
(A LOT OF POINTS) Given the linear equation 2x + y = 6, perform the necessary operations to put the equation into the proper general form. Explain in complete sentences how you knew that the equation was in the proper general form. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the entire process for establishing the general form of the equation and the general form.
Answer:
[tex]\huge\boxed{2x + y - 6 = 0}[/tex]
Step-by-step explanation:
2x + y = 6
Subtracting both sides by 6
2x + y - 6 = 0
Comparing it with the general form of equation [tex]\sf Ax+By +C = 0[/tex] , we get:
A = 2, B = 1 and C = -6.
So, the equation is in proper general form.
Answer:
[tex]\boxed{2x+y-6=0}[/tex]
Step-by-step explanation:
[tex]\sf The \ general \ form \ for \ the \ equation \ of \ a \ line \ is \ given \ as \ Ax+By+C=0.[/tex]
[tex]2x+y=6[/tex]
[tex]\sf Subtract \ 6 \ from \ both \ sides.[/tex]
[tex]2x+y-6=6-6[/tex]
[tex]2x+y-6=0[/tex]
[tex]\sf A=2 \ \ \ B = 1 \ \ \ C=-6[/tex]
[tex]\sf The \ equation \ is \ in \ general \ form.[/tex]
[tex]\sf Graph \ equation:[/tex]
8. (01.02)
Given that f(x) = x2 + 2x + 3 and g(x)
X+4.
3
solve for f(g(x)) when x = 2.
2
5
11
33
Answer:
51.
Step-by-step explanation:
f(x) = x^2 + 2x + 3 and g(x) = x + 4.
f(g(x)) = (x + 4)^2 + 2(x + 4) + 3
= x^2 + 4x + 4x + 16 + 2x + 8 + 3
= x^2 + 8x + 16 + 2x + 11
= x^2 + 10x + 27.
x = 2.
f(g(2)) = 2^2 + 10 * 2 + 27
= 4 + 20 + 27
= 31 + 20
= 51.
Hope this helps!
Help with this please
[tex](f+g)(x)=\sqrt{4x+6}+\sqrt{4x-6}[/tex]
Answer:
[tex]\huge\boxed{Option \ 4: (f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{4x+6}\\ g(x) = \sqrt{4x-6}[/tex]
Adding both
[tex](f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}[/tex]
(-72)(-15)= explain
prove that sin30/cos30+sin60/cos60=sin90
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
you just have to expand the trig. functions into their corresponding values and then finish them off.
f(x )=x square +6x + 5 what is the x intercept to graph f(x)
Answer:
(-5, 0)
(-1, 0)
Step-by-step explanation:
x-intercepts are points where the graph intersects the x-axis (or when y = 0)
Step 1: Write out function
f(x) = x² + 6x + 5
Step 2: Factor
f(x) = (x + 5)(x + 1)
Step 3: Find binomial roots
x + 5 = 0
x = -5
x + 1 = 0
x = -1
Alternatively, you can graph the function and analyze the graph for x-intercepts:
Please help. I’ll mark you as brainliest if correct.
Answer:
Infinite number of solutions.
Step-by-step explanation:
There are an infinite number of solutions. If you graph both lines, you find they are the same line. If you multiply the send equation by -4, you’ll end up with the first equation. I’m not sure what your teacher means by specifying their form.
15 POINTS AND BRAINLIEST JUST HELP ME PLZZZZZ 4x^2 + 28x + 49 = 0 Rewrite equation (x + __ )^2 = __
Answer:
[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]
Step-by-step explanation:
[tex]4x^2 + 28x + 49 = 0[/tex]
[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]
[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]
[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]
[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]
[tex](x+7)^2 =-3x^2-14x[/tex]
Answer:
(x+7)² = -3x² -14x
Step-by-step explanation:
4x^2 + 28x + 49 = 0
Subtract 3x² and 14x from each sides.
x^2 + 14x + 49 = -3x² -14x
Next step will be factoring.
(x+7)² = -3x² -14x
the ration of men to women in a certain factory is 3 to 4. there are 204 men. how many workers are there?
Answer:
476 workers
Step-by-step explanation:
Men: women : total
3 4 3+4 = 7
We want 204 men
204/3 =68
Multiply each by 68
Men: women : total
3*68 4*68 7*68
204 272 476
Answer:
There are 476 workers
Step-by-step explanation:
9 hundred thousands = how many
ten thousands
Answer:
90 is the answer:)
Step-by-step explanation:
I hope it helps you. Have a marvellous day!
Answer:
90 is the answer
Step-by-step explanation:
a) Show that the equation 2 x + 3 cos x + e^x = 0 has a root on the
interval (-1,0)
b) Use the Bisection method to find the solution of 2 x + 3 cos x +
e^x = 0. accurate with in 10-3. On (-1,0). (Use four digits-Rounding)
a) The equation has a root in the interval (-1,0)
b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]
a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.
A formal definition of this theorem is written like this:"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"
So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]
Let's now test for x=0
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(0)+3cos(0)+e^{0}=4[/tex]
So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.
b) The zero is located at x=-0.9977
The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:
x=-1 and x=0
so we find the value in the middle by using the following formula:
[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]
so we get:
[tex]mid-value=\frac{-1+0}{2}[/tex]
mid-value=-0.5
Next, we evaluate the given function for that value:
[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]
Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:
[tex]mid-value=\frac{-1-0.5}{2}[/tex]
mid-value=-0.75
Next, we evaluate the given function for that value:
[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]
and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.
Learn more about the intermediate zero theorem here:
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Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.
0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8
Answer:
Thus percentile lies between 53.3% and 55.6 %
Step-by-step explanation:
First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N
where n is the ordinal rank of the given value
N is the number of values in ascending order.
The data in ascending order is
0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3
1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5
Number of observation = 45
4.9 lies between 3.3 and 5.5
x*n = 24 observation x*n = 25 observation
x*45= 24 x*45= 25
x= 0.533 x= 0.556
Thus percentile lies between 53.3% and 55.6 %
Help! Marking as brainlyest
What is the effect on the graph of the function () = 1/ when () is replaced with 1/2() + 7? A) compressed vertically and shifted 7 units up B) stretched vertically and shifted 7 units down C) compressed vertically and shifted 7 units left D) stretched vertically and shifted 7 units right
Answer:
Step-by-step explanation:
I used x instead of ()
The initial function is:
● x = 1
The function after the changes is
● (1/2)x + 7
The function was shifted 15 unit to the left
What is the equation of this graph
Answer:
y-1=x^2
Step-by-step explanation:
That is the equation of a parabola with vertex at (0,1). The equation is y-1=x^2.
Help Please. Whoever answers it right with an explanation will get brainliest
Answer:
The answer is
ab( 11 + 9b)( a - 3b)Step-by-step explanation:
11a³b - 24a²b² - 27ab³
To factor the expression
First factor ab out
That's
ab ( 11a² - 24ab - 27b²)
Factor the terms in the bracket
Write - 24ab as a difference
That's
ab ( 11a² + 9ab - 33ab - 27b²)
Factor out a from the expression
ab [ a( 11a + 9b) - 33ab - 27b²) ]
Factor -3b from the expression
That's
ab [ a( 11a + 9b) - 3b( 11a + 9b) ]
Factor out 11a + 9b from the expression
We have the final answer as
ab( 11 + 9b)( a - 3b)Hope this helps you
Suppose that two.integers from the set of 8 integrs {1,2,3....8} are chosen at random. Find the probability that i. both numbers match. ii. Sun of the two numbers picked is less than 4?
Answer: a) 0.003
b) 0.125
c) 0.047
Step-by-step explanation:
We have a set of 8 numbers {1,2,...,8}
Let's analyze each case:
a) 5 and 8 are picked. The probability here is:
In the first selection, we have two possible picks (we can pick 5 or 8), so we have two possible outcomes out of 8 total outcomes, the probability for the first selection is:
P = 2/8 = 1/4.
Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8, or if in the first selection we picked an 8, here we only can pick a 5.)
the probability is:
P = 1/8
The joint probability is equal to the product of the individual probabilities, so here we have:
P = (1/4)*(1/8) = 1/32 = 0.003
b) The numbers match (we draw two sixes, for example) :
In the first selection, we can have any outcome (the only requirement is that in the second selection we pick the same outcome), so the probability is:
P = 8/8 = 1
in the second selection, we can have only one outcome, so here the probability is:
P = 1/8
The joint probability is p = 1/8 = 0.125
c) The sum is smaller than 4:
The combinations are:
1 - 1 , 1 - 2 and 2 - 1
We have 3 combinations, and the total number of possible combinations is:
8 options for the first number and 8 options for the second selection:
8*8 = 64
The probability is equal to the number of outcomes that satisfy the sentence (3) divided by the total number of outcomes (64):
P = 3/64 = 0.047
Repeated-measures and matched-subjects experiments Aa Aa Repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. Which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? Check all that apply.
A. The researcher computes difference scores to compute a t statistic
B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times
A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?
A. 20
B. 10
C. 18
D. 9
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?
A. 12
B. 22
C. 24
D. 11
Answer:
1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.
2. B. 10
3. A. 12
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.
How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.
Answer:
(MOE) the Margin of Error will decrease by the square root of 2
Step-by-step explanation:
The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400, the Margin of Error will decrease by the square root of 2
8 less than one-fourteenth of some number, w
Answer:
The answer is 1/14w-8
mr. jones has a patio in the sahpe of a trapezoid. a round fountain having a circumference of 14 pi linear feet is placed in the corner as showin in the accompanying diagram. to the nearest square foot, how much of the patio s area ins not taken up by the fountanin? reall tha the circumferencie of a circle is calculated using c = 2
The area of the patio not taken up by the fountain is 241ft²
Please find attached an image of the patio
Area of the patio not taken up by the fountain = area of patio - area of fountain
The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices It has 4 edges If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogramArea of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.
Pythagoras theorem can be used to determine the the height of the trapezoid
The Pythagoras theorem : a² + b² = c²
where a = height
b = base = 20 ft - 12 ft = 8ft
8ft / 2 = 4
c = hypotenuse
a² + 4² = 25²
a² = 625 - 16
a² = 609
√609 = 24.68 ft
Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²
The fountain is in the shape of a circle.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
The radius would have to determined from the circumference
circumference of a circle = 2πr
14π = 2πr
r = 14π / 2π
r = 7
Area of the circle = [tex]\frac{22}{7}[/tex] × 7²
[tex]\frac{22}{7}[/tex] × 49 = 154 ft²
Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²
To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²
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the age of furaha is 1/2 of the age of her aunt if the sum of their ages is 54 years. find the age of her aunt
Answer:
I think it is twenty seven
Consider the polynomial 2x5 + 4x3 - 3x8
Part A The polynomial in standard form is:
Part B: The degree of the polynomial is:
Part C: The number of terms in the polynomial is:
Part D: The leading term of the polynomials:
Part E: The leading coefficient of the polynomial is:
Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3