Answer: P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
Step-by-step explanation:
The factored form of a polynomial is:
P(x) = A*(x - r₁)*(x - r₂)*(x - r₃)....
Where:
A is a real number.
r₁, r₂,.... etc
are the roots.
In this case, we know that the roots are:
-4, -4, and 6.
Then the polynomial will be:
p(x) = A*(x + 4)*(x + 4)*(x - 6)
Now we also know that this polynomial passes through the point (2, 36)
This means that:
P(2) = 36 = A*(2 + 4)*(2 + 4)*(2 - 6) = A*6*6*(-4) = A*(-144)
36 = A*(-144)
-36/144 = A
-0.25 = -1/4 = A
Then the polynomial is:
P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
A student is learning about positive and negative numbers with manipulatives. Each black cube represents + 1 , and each white cube represents − 1 . If there are currently 15 black cubes on the student's desk, how many white cubes must the student add to the desk for the combined value of the cubes to represent 0 ?
Answer:
15 white cubes
Step-by-step explanation:
Given
[tex]White\ Cubes = -1[/tex]
[tex]Black\ Cubes = +1[/tex]
[tex]Number\ of\ Black\ Cubes = 15[/tex]
Required
Determine the number of white cubes needed to represent 0
To solve this question, we make use of the following equation.
[tex]Black\ Cubes +White\ Cubes = 0[/tex]
If there are 15 black cubes, the the 15 black cubes is worth: +1 * 15
Substitute +1 * 15 for the Black Cubes
[tex]+1 * 15 +White\ Cubes =0[/tex]
[tex]+15 +White\ Cubes =0[/tex]
Collect Like Terms
[tex]White\ Cubes = 0 - 15[/tex]
[tex]White\ Cubes = - 15[/tex]
Recall that 1 white cube is worth -1
So, the number of white cubes is:
[tex]Number = \frac{-15}{-1}[/tex]
[tex]Number = 15[/tex]
Hence, the student needs 15 white cubes
Synthetic Division
(6n^3 - 57n^2 + 69n - 14) ÷ (n - 1/2)
Answer:
[tex]Lets\ consider\ the\ divisor\ (n-\frac{1}{2})\ as\ g(x) \\In\ order\ to\ perform\ synthetic\ division\ we\ need\ to\ find\ the\ zero\ of\ the\ divisor\ . \\Hence,\\g(x)=0\\n-\frac{1}{2}=0\\n= \frac{1}{2}\\[/tex]
[tex]Now\ we\ must\ write\ the\ dividend\ in\ its\ standard\ form\ and\ seperate\ out\ its\ coeffeicient.[/tex][tex]So,\\\\The\ Coefficients\ will\ be\ in\ this\ order\ : 6,-57,+19,-14[/tex]
[tex]\frac{1}{2}[/tex] | 6 -57 19 -14
+ | 3 -27 -4
Q = [6 -54 -8] |-18 =R
[tex]Hence,\\The\ acquired\ quotient\ is\ 6n^2-54n-8[/tex]
Hence,
As the divisor is rational,
The quotient would be multiplied by the zero(1/2).
[tex]Hence,\\the\ final\ quotient\ = 3n^2-27n-4[/tex]
[tex]Remainder =-9[/tex]
Jon owns a hamburger stand. He creates a function for the number of dollars in his register (d) in relation to the number of hamburgers (h) he sells. d=3h+8 How much does he charge for a hamburger? 1 dollar 1 dollar 2 dollars 2 dollars 3 dollars 3 dollars 8 dollars
Answer:
The amount charged for a hamburger is $11
Step-by-step explanation:
The function relating the amount d charged with the number of hamburgers is;
d = 3h + 8
The amount charged for a hamburger can be calculated by substituting the value 1 for h
Thus, we have;
d = 3(1) + 8 = $11
Fill in the blank: A student earned a grade of 80% on a math test that had 20 problems. The student answered ______ questions correctly on the math test. (Write the number only.) *
hahahahahahahahahahahahahahah
The number is 16
PS: had to type more than 20 words
Answer:
16
Step-by-step explanation:
80 X 20 = 16 questions answered correctly.
please help me out....
Answer:
It is the first one, so
7u + 5v
Answer:
7u+5v (A)
Step-by-step explanation:
3u+4u=7u
7v-2v=5v
7u+5v
PLS GIVE BRAINLIEST
Please solve for y P=2x+2y+4
Answer:
Step-by-step explanation:
P=2x+2y+4
y=p/2-x-2
The equation can represent as y = P/2 - x - 2 after solving for y if the equation is P = 2x + 2y + 4.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Solve for y P=2x+2y+4
From the data given in the question:
The linear equation is:
P=2x+2y+4
To solve for make the subject as y:
2y = P - 2x - 4
y = (1/2)[P - 2x - 4]
Or
y = P/2 - x - 2
Thus, the equation can represent as y = P/2 - x - 2 after solving for y if the equation is P = 2x + 2y + 4.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
The radius of Earth is 6,371.0 kilometers and the radius of Earth's Moon is 1,737.5 kilometers. What is the approximate difference in the circumferences, in kilometers, of Earth and Earth's Moon? Round your answer to the nearest tenth of a kilometer.
Answer:
Step-by-step explanation:
Circumference of a circle is expressed as;
C = 2πr
r is the radius
Given
radius of Earth r1 = 6,371.0 kilometers
the radius of Earth's Moon r2 = 1,737.5 kilometers
The difference in their circumference will be expressed as;
C = 2π(r1-r2)
C = 2π(6371.0-1737.5)
C = 2π(4633.5)
C = 2(3.14(4633.5))
C = 29,098.38km
C = 29,098.4
Hence the difference in their circumference to the nearest km is 29,098.4km
Answer:
We calculate for the circumferences of Earth and moon by using the equation,
C = 2πr
For Earth,
C = 2π(6371 km) = 40030.2 km
For Moon,
C = 2π(1737.5 km) = 10917.0 km
The difference between the two circumferences is 29113.2 km approximately.
Which statement is true about the lengths of the sides?
Each side has a different length,
Two sides have the same length, which is less than
the length of the third side.
The three sides have the same length.
The sum of the lengths of two sides is equal to the
length of the third side.
Answer:
The three sides have the same length.
Step-by-step explanation:
Answer:
B. Two sides have the same length, which is less than the length of the third side.
Step-by-step explanation:
I think, :-P
5 AB is the diameter of a circle whose center is the point (4,-3). If the coordinates of A are (-1,5), Find AB>
Given:
AB is the diameter of a circle whose center is the point (4,-3).
Coordinates of A are (-1,5).
To find:
The measure of AB.
Solution:
Let point O(4,-3) be the center of the circle.
Then, OA is the radius of the circle.
We know that, diameter of a circle is twice of its radius.
So, [tex]AB=2(OA)[/tex] ...(i)
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between O and A is
[tex]OA=\sqrt{(-1-4)^2+(5-(-3))^2}[/tex]
[tex]OA=\sqrt{(-5)^2+(5+3)^2}[/tex]
[tex]OA=\sqrt{25+(8)^2}[/tex]
[tex]OA=\sqrt{25+64}[/tex]
[tex]OA=\sqrt{89}[/tex]
Now, using (i), we get
[tex]AB=2(OA)[/tex]
[tex]AB=2(\sqrt{89})[/tex]
[tex]AB=2\sqrt{89}[/tex]
Therefore, the measure of AB is [tex]2\sqrt{89}[/tex] units.
DO NOT GIVE ME THE ANSWER! Please just tell me how I can find the answer!
Answer:
9x$1.92
Step-by-step explanation:
Reflections of the coordinate plane homework 3
Answer:
can we have more info please?
Step-by-step explanation:
Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represent the amount of money in Alaina’s account?
–73
–27
–23
–17
Answer:-17
Step-by-step explanation:
45-28=17
can you help pls jhgyihjopk[[knbh
Answer:
The lower right table
Step-by-step explanation:
The table of that's the right answer consists of f(x) and x points that when plugged into the equation make the equation equal.
Let's go through each of the tables to check.
Upper Left Table:
(Remember that f(x) and y are interchangeable)
- Let's plug in the first paired set (0,6) into the equation
[tex]y = -2x + 6 \\6 = -2(0) + 6\\6 = 6[/tex]
So, this one seems right so far. It also let's us eliminate some answers!
The upper right and lower left tables can't be right because in order for the equation to be equal, f(x) has to be 6 when x equals 0
Let's plug more paired sets into the equation from the upper left table
[tex]y = -2x + 6\\10 = -2(2) + 6 \\10 = -4 + 6 \\10 = 2[/tex]
This doesn't work so let's check to see if the lower right table is correct!
[tex]y = -2x + 6 \\2 = -2(2) + 6\\2 = -4 + 6\\2 = 2[/tex]
Since the equation is equal, this has to be the right answer!
Hope this helps!!
- Kay
i need help plzzzzzz
thanks
Answer:
Step-by-step explanation:
5/6b+5-2/3b-2
1/6B+ 3
Vocabulary Explain why each relationship is not linear PLEASE HELP ASAP
Answer:
11) This table is not linear because linear tables and graphs have a constant rate of change, so in the table, we can see that the x-value goes up by 1 every time but the y-value is not constant. It goes up by 2 from 4.5, 6.5, 8.5, but then at 8.5 to 11.5, it went up by 3 which means that it's not a constant rate of change and is not linear.
12) This table is not linear because linear tables and graphs have a constant rate of change, so in the table, we can see that the x-value goes up by 2 every time but the y-value is not constant. It went down by 14 then 16 and 18. All these numbers and different which means that the table does not have a constant rate of change and is not linear.
Step-by-step explanation:
Always remember that linear tables, graphs, etc have a constant rate of change.
Hope this helps you
3y + 2 = -6x
in slope-intercept form : y=mx+b
oh and please show work! Thank youuu
Answer:
y= -2x- [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
3y+2=-6x
3y=-6x-2
y= [tex]\frac{-6}{3}[/tex]x - [tex]\frac{2}{3}[/tex]
y= -2x - [tex]\frac{2}{3}[/tex]
You isolate for y in this example by moving the 2 to the other side and then dividing the -6x and -2 by 3 to get the y by itself.
. One of the roots of the equation x2−bx+c=0 is equal to 5. Find c in terms of b.
Answer:
c=5b-25
Step-by-step explanation:
The ratio of the perimeter of two similar polygons is 5:7. The area of the smaller polygon is 30 sq. cm. Find the area of the larger polygon.
Answer:
42sq
Step-by-step explanation:
5:7
30 sq: x sq
30/5=6 sq for 1 of the ratio
6*7=42 sq for 7 of the ratio
Help ASAP if you want brainliest
Answer:
A. 1. mph
C. 3. hpm
Step-by-step explanation:
What is the value of x in the equation 2.5(5x-5)=10+4(1.5+0.5x)
Answer:
x= 19/7
Step-by-step explanation:
Simplify 3 x + 6 x 2 - 5 x - x 2 .
A 5 x 2 - 2 x
B 6 x 2 + 2 x
C 5 x 2 + 2 x
D 6 x 2 - 2 x
The equation y = 1.2x represents the rate, in beats per second, that Lee's heart beats. The graph represents the rate that Nancy's hear beats. Determine whose heart is beating at a faster rate.
does anybody even understand algebra?
Answer:
I do not understand thank you for asking
Step-by-step explanation:
thank you
Answer:
B (2,22)
Step-by-step explanation:
y + 2x = −1
3y − x = 4
Answer:
Step-by-step explanation:
Let's solve for x.
y+2x=−1
Step 1: Add -y to both sides.
2x+y+−y=−1+−y
2x=−y−1
Step 2: Divide both sides by 2.
2x
2
=
−y−1
2
x=
−1
2
y+
−1
2
Answer:
x=
−1
2
y+
−1
2
Answer:
Answers below
Step-by-step explanation:
Q1. 2x=−1−y
=
2
−1−y
Q2. −x=4−3y
x=−4+3y
x=3y−4
help first to answer gets brainlyset On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the field trip. How many students are there?
Answer: There are 80 students.
Step-by-step explanation: 20x4=80
3x4=12
12+80=92
$12.50 for 5 ounces Write a unit rate for the situation.
Answer:
$2.50 per ounce
Step-by-step explanation:
12.50÷5= 2.50
Answer:
$2.50c
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
7x+3 = 8x +1
x=2
the answer is 2
Given the expressions: 5x+2(x-4) and 7x-8 first prove that they are both equivalent and explain why your method proves this.
1. What is the value of x in this equation? 5x – 2(2x - 1) = 6 *
A.3
B.4
C.7
D.8
Answer:
Answer B. 4
Step-by-step explanation:
Equations
Solve the equation:
5x - 2( 2x - 1 ) = 6
Operate the parentheses:
5x - 4x + 2 = 6
Collect like terms:
x + 2 = 6
Subtract 2:
x = 6 - 2
x = 4
The value of x is 4
Answer B. 4
Find the slope!! Pls help
Answer:
1/3
Step-by-step explanation:
The slope goes up one over three. if u need a whole equation then it would be y=1/3x
if you need a slope intercept equation then it would be y=1/3x-4.
Answer: -5,3
Step-by-step explanation: the bottom boxes on the left are negative so i counted until the dot was and thats how i got my negative five. For the three I did the same thing just the right side inst negative so that is how i got 3.