The completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.
What is polynomial?Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).
The polynomial equation given in the problem is,
[tex]p^4 - 16[/tex]
Let the factor form of the polynomial is f(p). Thus,
[tex]f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2[/tex]
Using the formula of difference of squares, we get,
[tex]f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)[/tex]
Thus, the completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.
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Answer:
D Edge 2022
Step-by-step explanation:
(Need Help ASAP (Willing to give 10 points for 1 question)
Answer:
a) -2 and 4
b) function 2
Step-by-step explanation:
a)
rate of change is rise over run: change in y / change in x.
function 1:
- i will use first 2 pairs of data
- change in y: 5 - 3 = 2
- change in x: -2 - (-1) = -1
-rate of change = 2/-1 = -2
function 2:
- same idea, but find two points on the graph!
- (0,4) and (-1,0) for example! pick easy points
- change in y is 4. chabge in x is 1
- rate of change is 4
b)
function b has greatest rate of change. 4 > -2
Calculate the mean of the electric bills for Family A. Round your answer to the nearest cent.
Month | Family A | Family C
January | $88.82 | $134.51
February | $84.80 | $118.06
March | $62.35 | $109.28
April | $65.17 | $90.15
May | $60.20 | $91.20
June | $74.86 | $96.36
July | $92.15 | $130.71
August | $99.89 | $129.16
September | $96.45 | $107.77
October | $81.63 | $100.95
November | $64.12 | $107.64
December | $72.58 | $123.82
Answer:
The mean for Family A=78.585 , ≈78.59
Step-by-step explanation:
I solved this with a TI-84 CE calculator. To do this you press stat-edit-put in the numbers-2nd+mode-stat-right arrow key-calc-1_Var_Stats-Calculate. Then X with the _ over it would be your mean.
Kaya's family spends \$ 105$105 to rent a boat for 77 days. The total cost, cc, of the boat rental is proportional to the number of days, dd, the family rents the boat.
A. How much does it cost, in dollars, to rent the boat for one day?
B. Create an equation using c and d to represent the proportional relationship.
A. \$$
B.
[tex]c = 15d[/tex]
Step-by-step explanation:
find the value of the constant of proportionality k
[tex]k = \frac{v}{d} [/tex]
c =total cost
d =days
brainlist for correct answer =]
Answer:
4
Step-by-step explanation:
The mode is the number that appears the most!!!!
Now lets solve :)
2, 2, 3, 3, 4, 4, 4, 4,
There are 2 2s.
There are 2 3s.
There are 4 4s.
The mode is 4!!! :)
Have an amazing day!!
Plese rate and mark brainliest!!
The mode of the data set is 4
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.
Mode in math can be defined as the number which appears the most often in a given data set.Therefore, the mode of the data set is 4
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KEYWORDS:value datathe most ofSolve x² + 11x +18=0 by factoring.
A
x = 3 or x=6
B
x=-6 or x = -3
C
x = 2 or x = 9
D
x = -9 or x = -2
Read the following description of a relationship:
The sea turtle at a zoo is 2 years older than the stingray.
Let s represent the stingray's age and t represent the turtle's age.
Complete the equation that represents the relationship between s and t.
t =
Answer:
t=2s
Step-by-step explanation:
This is saying that the turtles age is two times the stingrays age because no matter how old the stingray is, the turtle is 2 times older.
Answer: t=s+2
Step-by-step explanation:
The sea turtle is 2 years older than the stingray.
Sea turtle's age = 2 years + stingray's age.
t = s+2
plug in 3 for the equation y=-x^2+12x-20
Step-by-step explanation:
y=(-x^2)+12x-20
=(-(3)^2)+12(3)-20
=(-9)+36-20
=16-9=7
y=7
I hope it helped you
Plot the data points into the calculator. Resize the window to fit the data and use the power regression function.
What is the power regression equation for these data points? Round to the nearest hundredth.
A )y = 71. 59x0. 49
B) y = 72. 49x0. 50
C) y = 73. 48x0. 51
D) y = 72. 34x0. 50
Answer:
y = 72.49x0.50
Step-by-step explanation:
A grandfather is six times as old as his grandson. If the grandfather was 45 when his grandson was born, how old is the grandson?
Calvin works two different jobs. He worked a total of 40 hours last week. Of the time he worked, 16 hours were spent at the
job where he makes $18 per hour. The rest of the time was spent at the job where he makes $20 per hour.
How much money did Calvin make from both jobs last week?
$288
b$480
$752
$768
Answer: 768
Step-by-step explanation:
24 times 20 =480 dollars
16 x18=288
480+288= 768
so yea D IS THE ANSWER!!!
hope thats helps :)
A bag contains eight balls labeled 1 through 8. One ball will be randomly picked. What is the probability of picking an even number?
Write your answer as a fraction in simplest form?
Find the distance between the points (0, 0) and (4, 0).
02
04
O √8
Answer:
4 units
Step-by-step explanation:
(0, 0 ) and (4, 0 )
since the y- coordinates are equal then the distance between the points is the difference of the x- coordinates, that is
| 4 - 0 | = | 4 | = 4 or
| 0 - 4 | = | - 4 | = | 4 | = 4
⚠️‼️ HELP PLEASE GIVING POINTS
The area of the entire figure below is 1 square unit. How can we describe the area of the striped rectangle?
Answer:
0.267 square units (or 8/30 square units)
Step-by-step explanation:
width = 3 rectangles
length = 10 rectangles (left to right)
area = width * length = 30 rectangles
the striped rectangle is made up of 8 regular rectangles
thus, (area we want) / (total area) = 8/30 of the whole ≈ 0.267 of the whole
the whole is 1 square unit, so 0.267 of 1 square unit = 0.267 * 1 square unit = 0.267 square units
What is the y-coordinate of point D after a translation of (x, y) → (x + 6, y – 4)?
Translating the triangle DEF involves moving the triangle along the coordinate plane
The y-coordinate of point D after the translation (x, y) → (x + 6, y – 4) is 1
How to determine the y-coordinate of D'?From the figure the coordinate of D is:
D = (-2.5,5)
The rule of translation is given as:
(x, y) → (x + 6, y – 4)
So, we have:
(x, y) → (-2.5 + 6, 5 – 4)
Evaluate the sum and the difference
(x, y) → (3.5, 1)
Remove the x-coordinate
y → 1
Hence, the y-coordinate of point D after the translation is 1
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What is 20% of 350? Please explain
Answer:
70
Step-by-step explanation:
20% is the same thing as 1/5
350 times 1/5 is 70.
Answer:
70
Step-by-step explanation:
.2 * 350 = 70
A balloon rises to 100 feet in 4 minutes and 125 feet in 5 minutes. Write and solve an equation to find the distance the balloon rises in 8 minutes. Use d for distance and m for minutes. Write the equation and the answer separated by a semi-colon. Included the unit in your answer. For example, d = 5m; 35 feet
Answer:
A proportion is the name we give to a statement in which 2 ratios are equal. Proportions are built off of ratios. It is usually written in one of 2 ways
Step-by-step explanation:
Answer:
there are two different ways it can go up but it will be a ratio amount of air in the
Jimmy has a collection of baseball cards. He wants to make at most $50.00 by selling some of them for $3.00 per card. Which inequality best represents this goal?
\$3.00c\geq\$50.00
\$3.00c\leq\$50.00
\$3.00c=\$50.00
\$3.00c<\$50.00
\$3.00c>\$50.00
I don't know
Answer:
3c ≤ 50Step-by-step explanation:
Each card is sold by $3, the number of cards is c.
The total is 3c and it needs to be at most $50:
3c ≤ 50Is the correct inequality for this case
Let the no of cards be c
Rate per card=$3Now
The inequality is
3×c≤503c≤50Or
3.00c≤50.00A triangle has an angle that measures 70°. The other two angles are in a ratio of 2:9. What are the measures of those two angles?
5) A bowl has 20 marbles in it, 4 red, 5 blue, 8, green, and 3 yellow. What is the probability of picking yellow? a. 3/20 b. 4/20 c. 1/3 d. 5/8
Answer:
A. 3/20
Step-by-step explanation:
since there are 3 marbles, and 20 total marbles, you have a 3/20 chance of picking yellow
A circle has a diameter of 12 ft. What is the length of an arc intercepted by a 60° central angle?
Answer: It's 6.28319 feet
Step-by-step explanation:
Students in biology class are learning about the monarch butterfly’s life cycle. Each student is given a caterpillar. When a caterpillar turns into a chrysalis, it is placed in a glass enclosed with food and a heat lamp and examined.
A. Determine whether the situation describes a survey, an experiment or an observational study.
B. identify the sample, and suggest a population from which it was selected.
Answer: observational study
Step-by-step explanation:
i think its a observational study because they are learning about somthing and to learn about it you have to study and they are given a specemin to observe to that they can study it as it grows therfore why i think the answer is C. Observational study.
Ssolve 2 and 6, only if you know cuz I'm stuck on this
Answer:
2. Linear Pair Prostulate
6. Transitive Property
Step-by-step explanation:
REEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
im not writing all that lol
Step-by-step explanation:
So 1 would be 100%, 10/10 and 0 would be, 0/10 and 0% so for 50% for example would be 5/10, 0.5 and so on..
then just think of things that have a 100% chance and all the other percentages... example The sun rising tomorrow. and no chance 0% example the school flying away
The ratio of cups of orange juice concentrate to water in a punch recipe is 1 : 6. If Stefan used 18 cups of water, how many cups of orange juice concentrate did he use?
Answer:
Order your units;
Orange Juice 1 x____________ _______ = ________, solve for x; Water 6 181/6 = x/18
×18 ×18
18/6 = x
3 = x
He will be using 3 cups of orange juice.
PLEASEEEEEEEEEEEEEEEEEEEE HELP MEE YALL WITH ALL 4 QUESITONS
Answer:
Step-by-step explanation:
17. Domain is all real numbers because the equation has a y-value for all x-values as far as we can see with the information given.
18. Range is 3< y <8, because the equation only has values for x where y is between those numbers.
19. Range is 3> y >-∞ (negative infinity) because the parabola's vertex has a y-coordinate of 3 and the parabola goes on forever in the negative direction (as seen by the arrows).
20. Domain is -∞ < x < 4 because the parabola's vertex has an x-coordinate of 4 and goes on forever in the negative x direction.
Hope this helps! :)
A circle with two chords is shown below in the figure. Find the value of x.
X
8
x+12
12
X =
A circle with two chords is given with length X, 8, x-12, 12. Thus, The value of x is 24.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Using the theorem of intersecting chords
[tex]12x =8(x-12)\\\\12x = 8x - 96\\\\12x - 8x = 96\\\\4x = 96\\\\x = 24[/tex]
The value of x is 24.
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Find the equation of the perpendicular from the point P(-1,-2) on the line
3x + 4y - 12 = 0. also find the coordinates of the foot of the perpendicular.
Step-by-step explanation:-
The given line is 3x + 4y - 12 = 0
=> 4y = -3x + 12 ....(i)
=> y = -3x/4 + 3,
therefore, the slope of the line (i) = -3/4.
From P(-1,-2), draw PN perpendicular to the given line. (see attachment)
As we know,, m2 = -1/m1
So, the slope of the line PN = 4/3
the equation of the line through P(-1,-2) and having a slope 4/3 is :-
= > y - (-2) = 4/3 * (x - (-1))
= > 3y + 6 = 4x + 4
= > 4x - 3y - 2 = 0....(ii)
which is the required equation of the perpendicular from P to the given line. To find the coordinates of N (the foot of perpendicular), solve (i) and (ii) simultaneously. Multiplying (i) by 3 and
(ii) by 4, and on adding, we get
= > 25x - 44 = 0
= > x = 44/25
Multiplying (i) by 4 and (ii) by 3, and on subtracting, we get :-
= > 25y - 42 = 0
= > y = 42/25
Hence, the coordinates of the foot of the perpendicular are (44/25 , 42/25)
Hope it helps you!!(44/25 , 42/25)
these are the points
Find the arc length of the remaining portion if the bolded section was cut out of the circle. Round to the nearest tenth.
Answer:
69.6 ft
Step-by-step explanation:
The arc length can be found as a fraction of the circumference. That fraction is the ratio of the central angle measure to the measure for the whole circle.
__
Central angle of remaining arc:
360° -150° = 210°
Fraction of full circumference:
210°/360° = 7/12
The circumference of the circle is ...
C = 2πr = 2π(19 ft) = 38π ft.
Then the length of the remaining arc is ...
(7/12)(38π) ft ≈ 69.6 ft
help me! 50 points and brainlyist
A fireman needs to get water to a second-floor fire. His ladder is 33 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest tenth of a degree and show all your work.
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 55°. Will the ladder be safe the way it is positioned? Explain.
Answer: (a) 64°
(b) Yes, it is safe
Step-by-step explanation:
A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.
We solve the above question using the trigonometric function of Sine
sin θ = Opposite side/Hypotenuse sides
θ = Angle formed with the ground = ?
Opposite side = 27 ft
Hypotenuse side = 30 ft
Hence,
sin θ = 27 ft/30 ft
sin θ = 9/10 = 0.9
θ = arc sin (0.9)
θ = 64.158067237°
Approximately to the nearest whole number = 64°
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?
From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°
Hence:
64° < 70°
Therefore, the ladder will be safe the way it is positioned.