Given:
P(x) is a 2nd degree polynomial.
[tex]P(1)=0,\ P(2)=3,\ P(-3)=0[/tex]
To find:
The polynomial P(x).
Solution:
If P(x) is a polynomial and P(c)=0, then c is a zero of the polynomial and (x-c) is a factor of polynomial P(x).
We have, [tex]P(1)=0,\ P(-3)=0[/tex]. It means 1 and -3 are two zeros of the polynomial P(x) and (x-1) and (x+3) are two factors of the polynomial P(x).
So, the required polynomial is defined as:
[tex]P(x)=a(x-1)(x+3)[/tex] ...(i)
Where, a is a constant.
We have, [tex]P(2)=3[/tex]. So, substituting [tex]x=2,\ P(x)=3[/tex] in (i), we get
[tex]3=a(2-1)(2+3)[/tex]
[tex]3=a(1)(5)[/tex]
[tex]3=5a[/tex]
[tex]\dfrac{3}{5}=a[/tex]
Putting [tex]a=\dfrac{3}{5}[/tex] in (i), we get
[tex]P(x)=\dfrac{3}{5}(x-1)(x+3)[/tex]
Therefore, the required polynomial is [tex]P(x)=\dfrac{3}{5}(x-1)(x+3)[/tex].
3. When pasta is cooked, it doubles in weight. When Ms. Morrison finished cooking
pasta for her family, the cooked pasta weighed 550 gram. How much did it
weigh before she cooked it?
Answer:
275
Step-by-step explanation:
550 divided by 2 is 275.
2+2=?
i dont remember this, its too complex for me someone help asap
ahem ahem
2+2=69
it's 4 thanks for the points
The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is What is the value
of b?
-18
-9
9
18
Answer:
B.) -9
Step-by-step explanation:
The value of b if 3/2 is the axis of symmetry for the graph of the function f(x)=3x2+bx+4 is -9
How to calculate the axis of symmetry of a function?The standard equation of a function in vertex form is given as:
f(x) = (a + x)^2 + h
Given the function f(x)=3x^2+bx+4 with an axis of symmetry of 3/2, the vertex is expressed as:
3/2= -b/2a
-b/2(3)=3/2
-b/6=3/2
Cross multiply
-2b = 18
-b=9
Hence the value of b if 3/2 is the axis of symmetry for the graph of the function f(x)=3x2+bx+4 is -9
Learn more on axis of symmetry here: https://brainly.com/question/21191648
The ages of eight different students in a college math class were used to make the box plot shown above. Which of the following numbers below is the median of the ages?
A. 21.5
B. 20.5
C. 22.5
D. 24.5
DUS is a 30°-60°-90° triangle with short leg SU. If SU = x, determine the
length of the long leg and the length of the hypotenuse.
Answer:
SD = 2x
UD = x[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The hypotenuse of a 30-60-90 triangle is 2 times the length of the shorter leg.
SU is the shorter leg = x
So, SD = 2x
The longer leg of a 30-60-90 triangle is [tex]\sqrt{3}[/tex] times the shorter leg.
So, UD = x[tex]\sqrt{3}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
In a 30-60-90 triangle the sides are in the ratio 1:√3:2 so if the shortest side SU = x then the long leg = √3x and the hypotenuse = 2x.
An example for my question before
Answer:
angle c is 82 degree because 82 degree and angle c are corresponding angles.
Step-by-step explanation:
note :corredponding angles are always equal.
the sum of co interior angle id 180 degree.alternate angle are equalthe sum of co exterior angle is 180 degreethe sum of alternate exterior angle is 180 degree28.
If 30% of a number is 15, what is the number?
No links!!
I will report if say something wrong.
Will give brainlest
Answer:
50
Step-by-step explanation:
30% * n = 15
Change to decimal form
.30 *n = 15
Divide each side by .30
.30n/.30 = 15/.30
n =50
The number is 50
Enter an estimate. Round each mixed number to the nearest whole in your estimate
Answer:
1. 4-2=2
2.2 10/21
Step-by-step explanation:
PLEASE HELP!!!
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget. Assume there are four weeks in a month.
If you think the data is inconclusive, explain why.
Answer:
Yes, they should increase the budget, because both 8 (Manuel) and 9 (Gretchen) are at least 8. 8 times per month is equivalent to 2 times per week.
Step-by-step explanation:
Answer from Plato
Hence, the answer is Plato.
What is the measurement?
Measurement is the process of finding a number that shows the amount of something. Time the ongoing sequence of events is time. We can measure time in seconds, minutes, hours, days, weeks, months, and years.
Here given that,
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget.
As per this we get that,
Yes, they can increase the budget, because both Manuel has [tex]8[/tex] and Gretchen [tex]9[/tex] are at least [tex]8[/tex] and [tex]8[/tex] times per month is equivalent to the two times per week.
Hence, the answer is Plato.
To know more about the measurement
https://brainly.com/question/18076822
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PLS HELPP GUYS !!!! in a hurry !!!!!!!
Answer:
A because it uses all of domains
Step-by-step explanation:
find the length of CD.
BRAIN TO CORRECT ANSWER!!
A clothing store conducts a survey to determine customer satisfaction.
Which of these methods will produce the most representative sample of the population of store customers?
A. Survey all customers as they arrive at the store on a Monday.
B. Survey all customers who purchase shoes
C. Survey every 10th customer to enter the store.
D. Survey all customers who leave the store without making a purchase
Answer:
C
Step-by-step explanation:
This method is the best because it will survey the customers under one condition : every 10. If the store gets a lot of customers, then this should be easier to do. The rest are mostly dependent on what they do and that influences the survey. However, C makes it so that every 10 people are surveyed.
Answer:
A isnt the correct answer. B doesnt seem reasonable because its one specific item. D means they arent exactly a customer since they didnt buy anything therefore the answer would be C
C is your answer.
not sure about it tho but its what i would put
There are 19 birds in a pond, all of which are ducks or geese. If the number of ducks in the pond is 1 more than twice the number of geese in the pond, how many geese are in the pond?
A. 6
B. 9
C. 10
D. 13
d I think d
Step-by-step explanation:
yayasjsjamaaak
What is the quotient of 6.58* 10^6 and 4.7×10^3
expressed in scientific notation?
Answer:
1.4 · 10³
Step-by-step explanation:
6.58 · [tex]10^{6}[/tex] ÷ 4.7 · 10³
6.58 ÷ 4.7 = 1.4
[tex]10^{6}[/tex] - 10³ = 10³
1.4 · 10³
Answer:
3.0926 x 10^10
Step-by-step explanation:
A TV is priced at $475.25. There is a 7% sales tax rate. What is the sales tax for the TV in dollars and cents?
Answer:
$33.27
Step-by-step explanation:
I 1) James ran 1.8 miles, Kyle ran 1 miles, and Frank ran 1.85 miles. Put the boys in order from the
shortest distance run to the longest distance run.
2
6
5
1 2) Write an algebraic expression for the phrase "19 less than x squared."
4
3
2
-2
3) When Michael woke up in the morning, the temperature was - 3. F. Later that day
the temperature was 10' F, so Michael said that the temperature had gone up
7 degrees. Is he correct? Explain why or why not.
--3
Answer:
lkjhgvcghjklm, bvhgyiuoklmnbgjhjk;.m, nb
Step-by-step explanation:
If you were to use the “Completing the Square” method to solve the equation below for k, what number would you add to both sides of the equation? k 2- 8k = -4
A) 16
B) –16
C) 24
D) –24
Answer:
The number you would add to both sides of the equation to use the "Completing the Square" method would be 16.
Step-by-step explanation:
To find the number to add to both sides of an equation to complete the square, divide the first-degree term's coefficient by 2 and square your remainder. In this case, the coefficient of the first-degree term is -8. After dividing by 2 and squaring it, you'll get 16, so that is the number you must add to both sides of the equation in order to complete the square.
Answer:
give him brainliest
Step-by-step explanation:
lol
A bag contains 9 marbles: 3 are green, 4 are red, and 2 are blue. Teresa chooses a marble at random, and without putting it
back, chooses another one at random. What is the probability that the first marble is blue and the second is green? Write
your answer as a fraction in simplest form.
Answer:
Probability[First marble blue, second is green without replacement] = 1/12
Step-by-step explanation:
Given:
Number of green marble = 3
Number of red marble = 4
Number of blue marble = 2
Total marble = 9 marble
Find:
Probability[First marble blue, second is green without replacement]
Computation:
Probability of an event = Number of favorable outcome / Number of total outcome
Probability[First marble blue] = 2 / 9
Probability[second is green] = 3 / [9-1]
Probability[second is green] = 3 / 8
Probability[First marble blue, second is green without replacement] = Probability[First marble blue] x Probability[second is green]
Probability[First marble blue, second is green without replacement] = [2/9][3/8]
Probability[First marble blue, second is green without replacement] = 6 / 72
Probability[First marble blue, second is green without replacement] = 1/12
There is a photo. No explanation needed just answer thank you
Complete the missing parts of the table for the following function. y=7x
Answers: 49, 1, 49
Those values go in the blanks from left to right
=====================================================
Explanation:
The rule we use is x^(-k) = 1/(x^k)
That means if we're evaluating something like 7^(-1), then it's the same as 1/(7^1) = 1/7 which explains how x = -1 leads to y = 1/7.
Similarly, 7^(-2) = 1/(7^2) = 1/49 is the y value when x = -2. So you'll type 49 into the first box to fill in that missing denominator.
Raising any nonzero value to the zeroth power leads to 1. That rule is x^0 = 1 where x can be anything you want but it can't be zero. Therefore 7^0 = 1 goes in the second box.
Lastly, 7^2 = 7*7 = 49 will go in the third box.
The equation y = (-16t – 2)(t-1) represents the height in feet of a beach ball thrown by a child as a function of time, `t`, in seconds.
from What height is the beach ball thrown? explain or show your reasoning
2 ft
Step-by-step explanation:
The height from which the beach ball was thrown happens when t = 0. So setting t = 0 to get y, we get
y = [-16(0) - 2](0 - 1)
= (-2)(-1)
= 2 ft
Therefore, the ball was thrown from a height of 2 ft.
X + 2x - 7/4=1 - x/2 -x ayudaaaaa
Answer:
|x| - |-x| = 0
Step-by-step explanation:
Answer:
no se
Step-by-step explanation:
no se
………………………………………………….
Answer:
Tan(Ф) = [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Tan(Ф) = [tex]\frac{opposite}{adjacent}[/tex]
Tan(Ф) = [tex]\frac{12}{5}[/tex]
Hope this helps!
PLZ HELP ME GUYS
Jsjsjsjshs
The speed of light is about 1.1 x 10^12 meters per hour. What is the number in meters per minute?
Answer:
Mansah obtained 150 mark out of 240 mark in an English test .what was her percentage score
Alan and Margot each drive from City A to City B, a distance of 147 miles. They take the same route and drive at constant speeds. Alan begins driving at 1:40 p.m. and arrives at City B at 4:15 p.m. Margot’s trip from City A to City B can be described with the equation y = 64x, where y is the distance traveled in miles and x is the time in minutes spent traveling. Who gets from City A to City B faster?
Answer:
Margot gets from A to B faster
Step-by-step explanation:
Alan takes 2 hr and 35 min = 2. 58... hr
Margot takes 147/64 hr = 2.296.. hr
Guys I need help on all three please
Answer:
graph 1 proportional
graph 2&3 is non proportional
i think
A mountain has a 21-degree slope. The mountain reaches an altitude of 468 feet. If you hike to the top of the mountain, starting at sea level, how far will you hike?
Answer:
1306 feet
Step-by-step explanation:
sin∅ = opp/hyp
sin21 = 468/hyp
hyp = 468/sin21
hyp = 1305.920355304657206
Rounded
1306 feet
The measure of an angle is 2.8.what is the measure of its complementary angle
Answer:
87.2º
Step-by-step explanation:
Complimentary angles total 90º
c + 2.8 = 90
c = 90 - 2.8
c = 87.2º
Answer:
87.2°Step-by-step explanation:
When angles are complementary, it means that they both add up to 90°.
In this case, one of the angles measures 2.8°.
So, to find the other one, we subtract 2.8 from 90.
90 - 2.8 = 87.2
The measure of the complementary angle is 87.2°
I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!
Maya invests $3,500 into an ETF which earns 7% per year. In
30 years, how much will Maya's investment be worth if
interest is compounded semiannually (twice a year)? Round to
the nearest dollar.