Answer:
a = 2
b = - 6
c = 0
Step-by-step explanation:
Since, -3,0 and 2 are the zeroes of the polynomial
[tex] Plug \:x = 0\: in \:p(X) \\
\implies p(0)= 0\\
\therefore 0= 0^3 +(a-1)(0)^2 +b(0)+c\\
\therefore 0= 0 +(a-1)\times 0 +b(0)+c\\
\therefore 0= 0 +0+0+c\\
\red{\bold{\therefore 0=c}}.....(1)\\\\
p(X)=x³+(a-1)x²+bx+c. \\
Plug \:x = -3\: in \:p(X) \\
[tex] \implies p(-3)= 0\\
\therefore 0= (-3)^3 +(a-1)(-3)^2 +b(-3)+c\\
\therefore 0= -27 +(a-1)\times 9 +b(-3)+c\\
\therefore 0= - 27 +9a-9 - 3b+c\\
\therefore 0= - 36+9a-3b+c\\
\therefore 36 =9a-3b+c... (2)\\
Plug \:c= 0\: in \:equation \: (2)\\
36= 9a - 3b + 0\\
36= 9a - 3b\\
36= 3(3a - b) \\
\purple {\bold{12 = 3a - b}} .... (3)\\\\
Plug \:x = 2\: in \:p(X) \\
\implies p(2)= 0\\
\therefore 0= 2^3 +(a-1)(2)^2 +b(2)+c\\
\therefore 0= 8 +(a-1)\times 4 +b(2)+c\\
\therefore 0= 8 +4a-4+2b+c\\
\therefore 0= 4 +4a+2b+c\\
\therefore - 4=4a+2b+c.....(4)\\
Plug \:c= 0\: in \:equation \: (4)\\
- 4 = 4a +2b+0\\
-4= 2(2a+b)\\
\orange{\bold{-2=2a + b}} .......(5)\\\\[/tex]
Adding equation (3) and (5), we find:
12 = 3a - b
-2 = 2a + b
_________
10 = 5a
10/5 = a
a = 2
Plug a = 2 in equation (5)
-2= 2(2) + b
-2 = 4 + b
-2 - 4 = b
-6 = b
b = - 6
Which of the following describes a rate?
1. A volleyball team won 8 out of 12 games.
2. Anisa gets paid $12 per hour
3. Bradley's class has 8 boys and 14 girls.
4. A restaurant has 5 waiters for every 10 tables.
Answer:
2. Anisa gets paid $12 per hour describes a rate.
Step-by-step explanation:
A rate is something that says (something) per (something.) For example, the cheetah ran 240 miles per minute is considered a rate.
Rates usually end with one, since they say that (something) every 1 (minute, hour, etc.) whether it's a place or thing.
Hope this helps! :)
The 6% state income tax on a $40,000 salary
Answer:
2400
Step-by-step explanation:
because 6 percent of 40000 is 2400 please mark brianliest
Hi does anyone know the answer to these two math questions? ( order of operations )
Answer: here's the answers to the problems
6) 17
8) 2.5
Answer:
6. 17
8. 2.5
Step-by-step Explanation:
4 x 3 + 6+9/3 12/3 + 2+7/5-3 - 6
12 + 15/3 4 + 9/2 - 6
12 + 5 4 + 4.5 - 6
= 17 8.5 - 6
= 2.5
What is the slope of the line graphed on the coordinate plane?
Answer:
3/4 slope
Step-by-step explanation:
Mark me brainleist please ;c
don’t make me cry ;c
Step-by-step explanation:
When the line moves up 3 blocks, it also moves across 4 blocks.
Therefore the slope of the line is 3/4.
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dysodjd kfudoandudslfhsotn
Please answer quickly, thanks. :)
Answer:
11 cars/day
Step-by-step explanation:
What we know:
After two days, Car-Mart has 43 cars left. After 3 days, it is 32. After five, 10 cars.
Saying that, subtract 32 from 43 to get your rate of 11 cars sold a day.
I can further deduce they started with 76 cars. On day 1 they had 65 cars. On day 4 they had 21 cars. They will have sold all of their cars after day 6.
Sam calls a friend to get help with his math homework. Which instructions would best help Sam solve the inequality shown below? 15 3/4 < -2 + x
F. Add 15 3/4 to both sides of the inequality.
G. Subtract 2 from both sides of the inequality.
H. Add 2 to both sides of the inequality.
J. Subtract 15 3/4 from both sides of the inequality.
Am not sure what this answer is
Answer:
100 pieces
Step-by-step explanation:
11/220 = 5/x
1100=11x
x=100
BRAINLIEST! Write an equation that is true when x is equal to -5, 4, or 0 and for no other values of x , and where one side of the equation is a 4th degree polynomial. (Look at graph for more info)
Answer:
y = x^3 + x^2 − 20x
Step-by-step explanation:
Find the factors from the roots, then multiply the factors together.
f(x) = x³ + x² − 20x that is equation when x is equal to -5, 4, or 0 and for no other values of x.
What is polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Given that
f(x) = (x + 5)(x - 4)(x)
Multiply the factors together.
f(x) = (x + 5)(x² - 4x)
we have to open the brackets above
f(x) = x³ - 4x² + 5x² - 20x
Rearrange the likewise terms and apply the arithmetic operations,
f(x) = x³ + x² − 20x
This equation is true when x is equal to -5, 4, or 0 and for no other values of x.
Learn more about the polynomial here:
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A line passes through point A (14,21). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value
that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
?:(
Answer:
The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].
Step-by-step explanation:
According to the statement, let [tex]A(x,y) = (14,21)[/tex] and [tex]B(x,y) = (1.25\cdot x_{A},0.75\cdot y_{A})[/tex]. The equation of the line in point-slope form is defined by the following formula:
[tex]y-y_{A} = m\cdot (x-x_{A})[/tex] (1)
Where:
[tex]x_{A}[/tex], [tex]y_{A}[/tex] - Coordinates of the point A, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
In addition, the slope of the line is defined by:
[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (2)
If we know that [tex]x_{A} = 14[/tex] and [tex]y_{A} = 21[/tex], then the equation of the line in point-slope form is:
[tex]x_{B} = 1.25\cdot (14)[/tex]
[tex]x_{B} = 17.5[/tex]
[tex]y_{B} = 0.75\cdot (21)[/tex]
[tex]y_{B} = 15.75[/tex]
From (2):
[tex]m = \frac{15.75-21}{17.5-14}[/tex]
[tex]m = -\frac{3}{2}[/tex]
By (1):
[tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex]
The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].
An invested sum of $600000 to generate simple interest $3.9000 at 3 (whole number) 1/4% per annum if you don't know please don't answer
Answer:
20 years
Step-by-step explanation:
We can find the time it took to invest
Using the formula for calculating simple interest as shown
SI = PRT/100
Given
Principal P = $600,000
SI = $39,000
Rate R = 3 1/4%
Required
Time
Substitute
39,000 = 600,000*13/400 * T
39,000 * 400 = 600,000*13 * T
15,600,000 = 7,800,000T
T = 15,600,000/7,800,000
T = 20
Hence it took 20years for the sum invested to generate the interest
The between two points can be found by drawing a triangle. The length of this is the of the right triangle, the other two sides are and Example One: Determine the distance between the two points: (-2, -3) and (3, 4) (1) the points and the segment. a right triangle, and the units for the legs. (3) the right triangle, with and (4) Set up an equation. → Simplify and solve a² + b² = c²
Answer:
Don't let anyone bring you down you matter you rock!
Step-by-step explanation:
graph y=3/4x-4 pls helppppppp.......,,,,,,,,,,.,,,,,
Step-by-step explanation:
Plug in y=3/4x-4 into desmos :)
Write the equation of the table shown below.
Х
0
2
5
9
12
у
4
6
9
13
16
Answer:
sorry... but the image is all black
I cant see anything
in each one section there are 27 student and there are 17 section how many students are in total
Answer:
459 students.
Explanation:
Since you are given the number of how many students are in each section, simply multiply to find the total answer.
27 x 17 = 459
There are 459 students.
Answer:
459 students
Step-by-step explanation:
Since there are 27 students, and 17 sections, multiply the two numbers:
27 × 17 = 459
HELP PLEASE
find the area of the polygon with the given vertices P(1,1), Q(-2,1), R(-1,-4)
Answer:
Area = 7.5
Step-by-step explanation:
The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
Given the triangle with vertices P(1,1), Q(-2,1), R(-1,-4)
Length between two coordinates (x₁,y₁) and (x₂,y₂) is given by
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
By using this formula
PQ = 3 , QR = 5.099 and PR = 5.385
Now,
The area of a triangle with all three sides is given by
A = [tex]\sqrt{S(S - A)(S - B)(S - C)}[/tex] where A,B and c are sides and s = (A + B + C)/2
So,
S = (3 + 5.099 + 5.385)/2 = 6.742
Now,
A = [tex]\sqrt{6.742(6.742- 3)(6.742 - 5.099)(6.742 - 5.385)}[/tex]
A = 7.499 ≈ 7.5
Hence "The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square".
For more about triangles,
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1620, 540, 180, 60, 20,...
Find common ratio.
Answer:
multiplying by 3
Step-by-step explanation:
20x3=60 60x3=80. and the rest is the same.
PLEASE I WILL GIVE BRAINLIEST
Write the SLOPE INTERCEPT form of a line that passes through point A at (4,-3) and point B at (2,1)
Answer:
y = -2x + 5
Step-by-step explanation:
A(4, -3) ; B(2, 1)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-[-3]}{2-4}\\\\= \frac{1+3}{2-4}\\\\= \frac{4}{-2}\\\\= -2[/tex]
m = -2 ; A(4,-3)
[tex]y - y_{1}=m(x-x_{1})\\\\y -[-3] = (-2)(x - 4)\\\\y + 3 = -2*x -4 *(-2)\\\\y + 3 = -2x + 8\\\\ y = -2x + 8 - 3 \\\\ y = -2x + 5[/tex]
27) What is the formula of area of a circle?
Answer:
πr^2
Step-by-step explanation:
My 11th grade teacher taught me this song to remember the formula for area and circumference of a circle (to the tune of "Twinkle Twinkle Little Star"):
"Twinkle twinkle little star circumference equals 2πr. Area if you ever cared always equals πr^2."
Answer:
A=πr2
Step-by-step explanation:
i believe this is the formula
4x + 9 = 2x + 15 .. I need help
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
4x + 9 = 2x + 15
Step 2: Solve for x
Subtract 2x on both sides: 2x + 9 = 15Subtract 9 on both sides: 2x = 6Divide 2 on both sides: x = 3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 4(3) + 9 = 2(3) + 15Multiply: 12 + 9 = 6 + 15Add: 21 = 21Here we see that 21 does indeed equal 21.
∴ x = 3 is the solution to the equation.
I need to know where to place the dot
Answer:
in your but
Step-by-step explanation:
nah jk its 3,-3
What is the m=
And what is the equation
Please help me asap its almost due
Answer:
m = 1[tex]\frac{1}{7}[/tex], y = 1[tex]\frac{1}{7}[/tex]x + 10
Step-by-step explanation:
The equation of a line is y = mx + c where m is the slope and c is the y-intercept. I will be calculating the slope using the points (7, 2) and (0, 10)
m = [tex]\frac{rise}{run}[/tex]
= [tex]\frac{2-10}{7-0}[/tex]
= [tex]\frac{8}{7}[/tex]
= 1[tex]\frac{1}{7}[/tex]
Based on the graph, the y-intercept is 10. Thus, the equation of the line is 1[tex]\frac{1}{7}[/tex]x + 10.
please help me, this isn't a test or quiz I just need some help.
the right is answer is B) alternate exterior
Please help I’ll give you brainliest UwU
A. 8 regular light Bulbs
B. 19 regular light bulbs
C. 84. Regular light bulbs
D. 96. Regular light bulbs
Answer:
84 regular light bulbs
Step-by-step explanation:
When there are 7 regular light bulbs to every 1 energy saving one, there will be 7 more added for every 1 energy saving light bulb that there is. So if there is 12 energy saving light bulbs, just multiply 7 by 12 and you will get your answer.
simplify the expression -3/8(-4y+z)
Answer:
3/2y-3/8z
Step-by-step explanation:
-3/8(-4y)-3/8z
Garret paid 20$ for five movie tickets find the cost per ticket
Megan paid 22$ for 7 books determine the cost per book
Answer:
Step-by-step explanation:
Cost of a ticket = Total cost ÷ number of tickets
= 20 ÷ 5
= $ 4
2) Cost of 7 books = $ 22
Cost of a book = 22 ÷ 7
= $ 3.11
Answer:
4 dollars each for 1st question and 3.1 dollars for second question
Please answer 1 - 3! thank you!
Answer:
The first one is
5x * 10
(x is the variable) TIMES 10
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIEST I JUST NEED THE ANSWER
Answer:
WHATT IS THIS MATH IT LOOKS SO HARD:0
PLS HELP ILL MARK AS BRAINLESS
Answer: Area is 2250 and the peremiter is 210
Step-by-step explanation:
Answer:
Area :2250
Perimeter: 210
Step-by-step explanation:
For area just multiply the two side lengths and for perimeter just add them all together-75,75,30,30.
please help me!!! i will gladly give brainliest :)
Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?
A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.
B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.
C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.
D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN.
Given:
ΔONP and ΔMNL.
To find:
The method and additional information that will prove ΔONP and ΔMNL similar by the AA similarity postulate?
Solution:
According to AA similarity postulate, two triangles are similar if their two corresponding angles are congruent.
In ΔONP and ΔMNL,
[tex]\angle ONP\cong \angle MNL[/tex] (Vertically opposite angles)
To prove ΔONP and ΔMNL similar by the AA similarity postulate, we need one more pair of corresponding congruent angles.
Using a rigid transformation, we can prove
[tex]\angle NOP\cong \angle NML[/tex]
Since two corresponding angles are congruent in ΔONP and ΔMNL, therefore,
[tex]\Delta ONP\sim \Delta MNL[/tex] (AA postulate)
Therefore, the correct option is A.
Similar triangles may or may not be congruent.
The additional information to prove ΔONP and ΔMNL are similar by AA similarity postulate is (a) Use a rigid transformation to prove ∠NOP ≅ ∠NML.
From the question, we have:
[tex]\mathbf{\triangle ONP \sim \triangle MNL}[/tex] --- ONP and MNL are similar triangles
Because the similarities of the triangles are to be proved by AA postulate, the following angles must be corresponding and congruent
[tex]\mathbf{\angle ONP \cong \angle MNL}[/tex]
[tex]\mathbf{\angle NOP \cong \angle NML}[/tex]
[tex]\mathbf{\angle PON \cong \angle LMN}[/tex]
Option (b) is incorrect because angles NOP and ONP are not corresponding angles
Options (c) and (d) are incorrect, because they prove the similarities by lines segments.
Hence, the correct option is (a).
This is so because, it proves the similarities of both triangles by using corresponding angles.
Read more about similar triangles at:
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