Given:
A graph of a polynomial passes through the point (-1, 60) and has three x-intercepts: (-4,0), (1, 0), and (3, 0).
To find:
The equation of the polynomial.
Solution:
A polynomial is defined as:
[tex]P(x)=a(x-c_1)(x-c_2)...(x-c_n)[/tex]
Where, a is a constant and [tex]c_1,c_2,...,c_n[/tex] are the zeros of the polynomial.
The given polynomial has three x-intercepts (-4,0), (1, 0), and (3, 0). It means [tex]-4,1,3[/tex] are the zeroes of the given polynomial and [tex](x+4),(x-1),(x-3)[/tex] are the factors of the given polynomial.
So, the equation of the polynomial is:
[tex]P(x)=a(x+4)(x-1)(x-3)[/tex] ...(i)
It passes through the point [tex](-1,60)[/tex].
[tex]60=a(-1+4)(-1-1)(-1-3)[/tex]
[tex]60=a(3)(-2)(-4)[/tex]
[tex]60=24a[/tex]
Divide both sides by 24.
[tex]\dfrac{60}{24}=a[/tex]
[tex]2.5=a[/tex]
Putting [tex]a=2.5[/tex] in (i), we get
[tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex]
Therefore, the equation of the given polynomial is [tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex].
Which scenario would most likely show a negative association between the variables? A. the height of a tree and the amount of time it takes to climb to the top of the tree
B. the number of people in the mall and the number of cars in the parking lot
C. miles traveled in a car and the amount of gasoline used
D. time spent reading a book and the number of pages left to read
Answer: i would say B because it makes the most sence
Step-by-step explanation:
Slove the system of linear equations by graphing y=-x+7 y=x-1
Answer: Point Form: ( 4 , 3 ) Equation Form: x = 4 , y = 3
Step-by-step explanation: Solve for the first variable in one of the equations, then substitute the result into the other equation.
Brainliest or a thank you please? :))
I am the number that is 40 less than the largest number u can make using five of the digits what number am I
Only can use 1 8 3 4 9 6 2 7 I think
Answer:
9 876 391
Step-by-step explanation:
arrange the numbers in ascending order
9 876 391
subtract 40 from the number
9876431 - 40
9 876 391
Help me pls I give points
Answer:
c=14.87
Step-by-step explanation:
use pythagorean theroem
10^2 + 11^2 =c^2
solve
100+121=c^2
c^2=221
c=14.87(rounded to nearest hundredths )
A bag contains 7 red, 3 yellow, and 4 blue marbles. What is the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first?
Answer:
2/13
Step-by-step explanation:
P(Red,Blue) = 4/14 × 7/13
simplified it becomes 2/13
Find the axis of symmetry and the vertex of the graph (Desmos)
Answer:
The axis of symmetry is x=3, the vertex of the graph is (3,-2)
Step-by-step explanation:
[tex]f(x)=(x^{2} -6x+9)-9+7[/tex]
[tex]=(x-3)^{2} -2[/tex]
pls answer this i have no clue
Answer:
90 degrees
Step-by-step explanation:
The three angles of a triangle always add up to 180 degrees, so knowing this, all three of the measures given should add up to 180.
First, you need to solve for x:
S(x+10) + R(2x+60) + T(50+x) = 180
Add up all of the like terms:
10 + 60 + 50 = 120
x + 2x + x = 4x
So now you are left with 4x + 120 = 180
And solve for x:
4x/4 + 120/4 = 180/4
x + 30 = 45
x + 30-30 = 45-30
x = 15
Now that we have the value of x, plug it into the measure given for angle R:
(2x+60)
= (2(15)+60)
= (30 + 60)
= 90
So the measure of angle R is 90 degrees.
I hope this helped! :)
HELPPP (will mark brainliest)
Vera wants to prove that any rectangle is also a parallelogram.
B
A
D
Select the appropriate rephrased statement for Vera's proof.
Choose 1 answer:
Answer:
B
Step-by-step explanation:
I did it on khan academy
An electrician bent a section of copper wire into a partial circle as shown. The dimensions are
given in feet (ft).
2.5 f
880
2.5
ft
What is the length of the section of wire to the nearest hundredth of a foot?
Answer:
3.84 feets
Step-by-step explanation:
Given that:
θ = 88°
Radius, r = 2.5
The length of section of the wire, L ; Length of an arc
L = θ / 360° * 2πr
L = 88/360 * 2*π*2.5
L = (88/360) * 15.707963
L = 3.8397
Length of section of wire = 3.84 feets
What is the best definition for “sample” as used in statistics?
the entire population of the group
a part of the population that represents the entire population
the difference between the maximum and minimum values observed
a measure of how much the values within a population vary
Answer:
a part of the population that represents the entire population
Step-by-step explanation:
Answer:
I think it is the second option
I hope it helps you
A diver begins rising toward the surface from 180 feet below sea level. A few
minutes later, the diver is 40 feet below sea level. How many feet did the diver rise in
those few minutes?
Answer:
140
Explanation: cause -180 + 40 = -140 (but absolute value is 140)
m - 12 = 11
A. -23
B. -1
C. 1
D. 23
Answer:
D. 23
Step-by-step explanation:
m-12-(11)=0
m-23 = 0
m = 23
plsssssssssssssssssssssssssssssss help!!
Answer:
Look for 75% of 1 1/2, I got 1.125 or 1 1/8
Step-by-step explanation:
A soccer field is 100 meters long. What could be its length in yards? A. 33.3 B. 91 C. 100 D. 109
Answer:
D. 109
Step-by-step explanation:
100 meters into yards is 109.361
the ratio is 1.094 so 109
how many 5-digit passwords can I make out of the English alphabet. lowercase only
Answer:
7,893,600 different combinations
Step-by-step explanation:
Answer:
We have a total.of 26 alphabets in the english language and numbers 0 to 9 will be 10.
Since there are no other limitations, we have to arrange 8 places with the 36 options we have.
It will simply be 36c8.
The answer will be 3,02,60,340.
Please help me solve this.
Answer: 59
Step-by-step explanation:
Given
2b³+5 and b=3 ⇒ 2b³+5=2(3)³+5
Simplify exponents
2(3)³+5
=2(3×3×3)+5
=2×27+5
Multiplication
=54+5
Addition
=59
Hope this helps!! :)
Please let me know if you have any questions
Find the equation of the exponential function represented by the table below:
Answer:
[tex]y=0.01(4)^x[/tex]
Step-by-step explanation:
please help me out here I really appreciate any answers
Answer:
ok
Step-by-step explanation:
convert 53 m = cm
help pls
Darius finds a leaf that is 6 cm long. Which measurement is equivalent to 6 cm?
OA. 0.6 mm
OB. 60 mm
OC. 0.06 mm
OD. 600 mm
Answer:
B: 60mm
Step-by-step explanation:
Answer:
B. 60 mm
Step-by-step explanation:
1 cm = 10 mm
6 cm = 6 * 1 cm = 6 * 10 mm = 60 mm
Answer: B. 60 mm
Use complete sentences to describe the domain of the consine function.
Answer:
The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.
The cosine function takes x values from all real numbers.
Therefore, the domain of the cosine function is a real numbers.
Step-by-step explanation:
How many toys would Louis build in 10 hours if she built 3 toys every 20 minutes?
Answer:
90 toys
Step-by-step explanation:
We should use the same unit for time. Rewrite 20 minutes as 1/3 hour.
The unit rate is then:
3 toys 9 toys
----------------- = -----------
1/3 hour hour
Multiply this unit rate by 10 hours, obtaining 90 toys
Question 4 of 15
When asked to find the sum of two mixed numbers with different
denominators, you should before you add.
A. round each fraction
B. find the difference
C. find a common denominator
When asked to find the sum of two mixed numbers with different denominators, you should find a (C) common denominator before you add.
To add fractions with different denominators, it is necessary to find a common denominator for both fractions. Once the fractions have the same denominator, you can add or subtract the numerators while keeping the denominator unchanged. This allows for a meaningful addition of the fractions.
To find a common denominator, you need to determine the least common multiple (LCM) of the denominators. The LCM is the smallest multiple that both denominators can divide evenly into. Once you have the common denominator, you can convert each fraction to an equivalent fraction with that denominator and then perform the addition.
After finding the common denominator, you add the numerators of the fractions and keep the common denominator. This will give you the sum of the two mixed numbers with different denominators. The correct answer is C. find a common denominator.
To know more about mixed numbers click here:
https://brainly.com/question/28994473
#SPJ2
simplify log(16x²) ± 2㏒(1÷×)
Answer: just simplify condense it then your answer will be log(16)
Please help me find the value of x for this trig question
Answer:
11.330
Step-by-step explanation:
Answer:
x=11.3
Step-by-step explanation:
Hello There!
We can use trigonometry to solve for x
Remember these are the trigonometric ratios
SOHCAHTOA
Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
We can use the angle that has a measure of 31 degrees
We are given the hypotenuse and we need to find its opposite side
hypotenuse and opposite corresponds with sine so we will use sine to create an equation
(remember sin = opposite over hypotenuse)
[tex]sin(31)=\frac{x}{22}[/tex]
now that we have created an equation we solve for x
step 1 multiply each side by 22
[tex]sin(31)*22=22sin(31)\\\frac{x}{22} *22=x\\x=22sin(31)\\sin(31)=0.5150380749\\0.5150380749*22=11.33083765\\x =11.33083765[/tex]
finally we round to the nearest tenth and get that x = 11.3
HELP
I WILL GIVE YOU BRAINLIEST
Give the solution to this quadratic.
y = 3(x-1)^2
Answer:
y=3x^2-6x+3
Step-by-step explanation:
What percentage of videos on the streaming site are between 264 and 489 seconds? 0.15% 49.85% 95% 99.7%
Answer:
49.85%
Step-by-step explanation:
Streaming is defined as sending and receiving an video or an audio content in continuous flow over any network. It allows one to begin the playback and while it sends the rest of the data.
In the context, the percentage of the videos on a streaming site that is between 264 and 489 seconds is 49.85% which is found by a graph where the distribution of the lengths of the videos in seconds on a popular video streaming sites.
4 Luke's math scores for this grading period are listed below. 84, 86, 83, 78, 92, 87, 92, 90, 88, 86 What is the mean of the data set graphed on the dot plot? (10 Points) X X Х ХХ ХХХ xx 日中 85 90 95 70 75 80 F H
Answer:
86.6
Step-by-step explanation:
Add them all up and divide by how many scores
a square has f the diagonals of a square bisects its angles?
Answer:
ok so i can have i insteaof f too
Step-by-step explanation:
Which function would be produced by a horizontal stretch of the graph of y = sqrt(x) followed by a reflection in the x - axis ?
Answer:
the answer is the first one
Step-by-step explanation:
Explanation: be im smart
Function transformation involves changing the form of a function
A function that could represent the transformed function is function (c) [tex]f(x) = -\sqrt{\frac 12 x}[/tex]
The equation of the function is given as:
[tex]f(x) = \sqrt x[/tex]
The rule of horizontal stretch is:
[tex](x,y) \to (ax,y)[/tex]
Where:
[tex]0 < a < 1[/tex]
Take for instance:
[tex]a = \frac 12[/tex]
So, we have:
[tex]f(x) = \sqrt{\frac 12 x}[/tex]
Next, the function is reflected in across the x-axis.
The rule of this transformation is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]f(x) = -\sqrt{\frac 12 x}[/tex]
Hence, a function that could represent the transformed function is function (c)
Read more about function transformation at:
https://brainly.com/question/1548871