Answer:
Find a polynomial function whose graph passes through (6,13), (9,-11), (0,5)
1 Answers
Assuming a quadratic, we have that
y = ax^2 + bx + c
Since (0,5) is on the graph, c =5
And we have the remaining system
a(9)^2 + b(9) + 5 = -11
a(6)^2 + b(6) + 5 = 13 simplify
81a + 9b = -16 multiply through by 6 ⇒ 486a + 54b = - 96 (1)
36a + 6b = 8 multiply through by -9 ⇒ -324a -54b = -72 (2)
Add (1) and (2)
162a = -168
a = -28/27
To find b we have
36 (-28/27) + 6b = 8
-112/3 + 6b = 8
⇒ b = 68/9
The function is
y = - (28/27)x^2 + (68/9)x + 5
Answer:
See below
Step-by-step explanation:
Let the function be quadratic as the given points are not collinear, not a linear function
Standard form of quadratic equation:
y = ax^2 + bx + cSubstituting the coordinates, we get:
13 = a(6)^2 + b(6) + c-10 = a(10)^2 + b(10) + c5 = a(0)^2 + b(0) + cFrom equation 3 we get c = 5, considering this in the other equations and simplifying:
13 = 36a + 6b + 5 ⇒ 36a + 6b = 8 ⇒ 18a + 3b = 4-10 = 100a + 10b + 5 ⇒ 100a + 10b = -15 ⇒ 20a + 2b = -3Subtract 3 times the second equation from 2 times the first:
2(18a) + 2(3b) - 3(20a) - 3(2b) = 4(2) - 3(-3)36a - 60a = 8 + 9-24a = 17a = - 17/24Finding the value of b:
18(-17/24) + 3b = 43b = 4 + 51/4b = 67/12The quadratic function is:
y = -17/24x^2 + 67/12x + 5So the graph of any polynomial function:
y = -17/24x^2 + 67/12x + 5 + g(x)(x-6)(x-10)(x-0)will pass through the given 3 points
If f(x) = 8x2 + 4x - 12. Find f(2)
f(2)=
Answer:
f(2) = 28
Step-by-step explanation:
[tex] \rm f(x) = 8 {x}^{2} + 4x - 12 [/tex]
[tex] \rm Evaluate \: 8 x^2 + 4 x - 12 \: where \: x = 2: \\ \\ \rm \implies f(2) = 8 \times {2}^{2} + 4 \times 2 - 12 \\ \\ \rm \implies f(2) = 8 \times 4 + 8 - 12 \\ \\ \rm \implies f(2) = 32 - 4 \\ \\ \rm \implies f(2) = 28[/tex]
The area model below shows a way to solve 7,776 ÷ 24 using place value. The 3 partial quotients missing from the model represent hundreds, tens, and ones
To find the quotient, the 3 partial quotients are added together. What is the quotient?
Answer: The answer is 324 all you have to do is just divide 7,776 by 24 then Breaking it into expanded form.
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
the eighth root of two to the fifth power
the fifth root of two to the eighth power
the square root of two to the five eighths power
the fourth root of two to the sixth power
Answer:
Eight root of to the fifth power.
Step-by-step explanation:
2^7/8 / 2^1/4
= 2^(7/8 - 1/4)
= 2^5/8
= eight root of to the fifth power.
Answer:
the eighth root of 2 to the fifth power .
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
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Select three ratios that are equivalent to 5:2. Choose 3 answers:
А 2 : 5
B 10:4
C 20 : 50
D 35 : 14
E 55 : 22
Answer:
B, E, D
Step-by-step explanation:
You just look for the ones that have the same factors as 5:2
Answer:
A
C
D
Step-by-step explanation:
if I'm not wrong, I'm sure is that
What is the slope of this line?
5
1/5
-1/5
-5
Answer:
1/5
Step-by-step explanation:
You do rise over run so your rise is 1 and your run is 5 so the answer is 1/5.
And it is positive because it is pointed to the right side.
Hope this helps
Find the 10th term in a sequence whose general term is an = n2 – 8. Question 7 options: A) 92 B) 108 C) 12 D) 113
Answer:
92
Step-by-step explanation:
The 10th term in a sequence whose general term is [tex]a_n = n^2 - 8[/tex] will be 92. so option A is correct.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
We need to find the 10th term in a sequence whose general term is
[tex]a_n = n^2 - 8[/tex].
So, the 10th term is (10)²- 8
= 100 - 8
= 92
Therefore, the 10th term in a sequence whose general term is
[tex]a_n = n^2 - 8[/tex] will be 92. so option A is correct.
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Carl can type 180 words in 2 minutes. How many words can Carl type in 1 minute
Answer:
90 words per minute
Step-by-step explanation:
180/2=90
Answer:
1 minutes = 90 wordsStep-by-step explanation:
180 words = 2 minutes
x = 1 minutes
1 minutes = 180/2
1 minutes = 90 words
What is the sum of 1/8 and (-3/16)
Answer:
D, or [tex]\frac{-1}{16}[/tex]
Step-by-step explanation:
To add (or subtract) fractions, you need to have a common denominator.
You might notice that the 16 on the bottom is a multiple of 8.
8*2 as a matter of fact
If we multiply [tex]\frac{1}{8\\}[/tex] by 1, it doesn't do anything, it stays as 1/8
1 is the same thing as [tex]\frac{1}{1}[/tex] and is also the same as [tex]\frac{2}{2}[/tex]
If we multiply [tex]\frac{1}{8}[/tex] by [tex]\frac{2}{2}[/tex], we get a bigger fraction, which is [tex]\frac{2}{16}[/tex]
So, our problem can be re-written as [tex]\frac{2}{16}+(-\frac{3}{16} )[/tex]
To add (or subtract) fractions with common denominators, you keep the common denominator and add (or subtract) the numerator.
[tex]\frac{2}{16}+(-\frac{3}{16})=\frac{2-3}{16}=\frac{-1}{16}[/tex]
The last step is to see if our answer can be reduced.
A fraction can't be reduced if there is a prime number in either the numerator or the denominator.
There is a -1 in the numerator, which is prime, and therefore, the fraction can't be reduced.
I’ll give Brainly! Match each problem with the answer!
Jason had $284.31 on his student lunch account at the
beginning of the school year. During the year, he mowed
lawns for extra money to add to his lunch account. He
mowed 13 lawns and earned $30 for each lawn. By the
end of the school year, he had spent $782.75 on his
lunches. What was the balance in Jason’s account at the
end of the school year?
Answer:
674.31-782.75 = -108.44Step-by-step explanation:
30x13=390.00390.00+184.31=674.31674.31-782.75=-180.44what is the value of y when x = 43
A. 87
B. 85
C. 49
D. 45
Answer:
A x
=
3
,
−
1x
=
3
,
−
1
Step-by-step explanation:
x
=
3
,
−
1
Plot the points (-3, -4) (−3, −4) and (6, -4) (6, −4) on the coordinate plane below. What is the distance between these two points?
Answer:
Where is the coordinate plane? Anyways: (9, -4)
Which expression is equivalent to −6(23−12)?
A
3(−2−1)
B
(4−3)
C
2(−3+1)
D
(−4+3)
Answer:
C
Step-by-step explanation:
Transform the equation if necessary, and then solve it to find the value of that makes the equation true.
−4 − 2(8 + 1) = −(−2 −10)
x = ?
If there is no solution, type n as your answer.
Answer:
False
Step-by-step explanation:
HELP IMMA FAIL THIS TEST! HELLLPP ASAP! Pls! DUE IN 10 MINUTES!! 10. Write an equation that represents the relationship between the x-values & the y-values.
0|3
2|7
4|11
6|15
Step-by-step explanation:
y = mx + c
m = y2 - y1 / x2 - x1
m = 7-3 / 2-0
m = 4/2 = 2
using the first x and y values in the equations if a line
3 = 2(0) + c
c = 3
so substitute the values into the eqn
y = 2x + 3
Please please please help quickly!
Um th eanswer is 56-64-34-3402-30 = 19038
Enter an equivalent expression for 2x + 3 + 5x + 6 in simplest form.
Sasha purchased paint that will cover 400 square feet per gallon. Sasha needs to paint a 4704-square-foot surface with 2 coats of paint.
How many gallons of paint will she need for this project?
A.11
B.12
C.23
D.24
Answer:
D. 24
Explanation:
First you would need to find how many you need for one coat.
400 times 12 = 4,800
(That will give you a little extra paint)
Then just double 12 to get two coats and you would get D.
Have a nice day!
Hope this helped.
Pls help me, im not understand this
Answer:
Step-by-step explanation:
Mr Thompson wants to cut a 5-ft rope into a 1/4-ft sections how many 1/4 sections will he have
Answer:
20 pieces of rope
Step-by-step explanation:
Mr. Thompson has a 5-ft rope. If he cuts the rope into 1/4-ft pieces, that means for every foot, there are 4 pieces of rope. There are 5-ft of rope, so we multiply 5 and 4 to get the number of pieces of rope.
5 x 4 = 20 pieces of rope.
I hope that this helps! :)
1/x+x/2=11/6 transformable to quadratic equations
Note: Consider we need to find the solution of given equation.
Given:
The equation is
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
To find:
The solution of the equation.
Solution:
We have,
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]
By cross multiplication, we get
[tex]6(2+x^2)=11(2x)[/tex]
[tex]12+6x^2=22x[/tex]
[tex]6x^2-22x+12=0[/tex]
[tex]2(3x^2-11x+6)=0[/tex]
Divide both sides by 2.
[tex]3x^2-11x+6=0[/tex]
Splitting the middle term, we get
[tex]3x^2-9x-2x+6=0[/tex]
[tex]3x(x-3)-2(x-3)=0[/tex]
[tex](x-3)(3x-2)=0[/tex]
Using zero product property, we get
[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]
[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]
Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].
Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).
Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
We are given the algebraic equation: 1/x+x/2=11/6
Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.
LCD(x,2,6) = 6x
Multiply all through the fractions by 6x
(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)
6 + 3x² = 11x
Rewriting the equation:
3x² - 11x + 6 = 0
Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
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62 is divisible by which of the following numbers? (1 point)
O 1, 3, 31, 62
O1, 2, 3131
O 1, 4, 16, 62
O1, 2, 31, 62
Answer:
1, 2, 31, 62
Step-by-step explanation:
Help I Dont Understand?
which of the following would you expect to have the highest interest? a 5-year CD a 10-year CD and online savings account or savings account at a Traditional Bank
Answer:10-year CD
Step-by-step explanation:
No
hectare is equal to 2.471 acres. A land developer buys a hectare of land to build homes. Each home will be built on 0.25 acres of land. How many homes can the land developer build on the hectare of space?
Answer:
2.221
Step-by-step explanation:
Multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. To check if your answer is reasonable, estimate the quotient by rounding the divisor and dividend to the nearest whole numbers.
ANSWER:
try 2.721....................
what is the y intercept of y= -1/2x +3
Hurryplz!
Answer:
Y-intercept is 3
Step-by-step explanation:
Remember y=mx+b
b is the y-intercept
mx is the slope
A store owner uses pieces of tape to paint a window advertisement. The letters are slanted at an 80 degree angle. What is the measure of angle 1?
Answer:
∠1 is 180° − 80° = 100°.
Step-by-step explanation:
Using the corresponding angles, the 80° angle is congruent to the angle that is supplementary to ∠1, as shown. The measure of ∠1 is 180° − 80° = 100°.
The measure of ∠b comes to be 100°.
As we know,
In window advertisement,
∠b and 80° are supplementary angles to each other.
What are the supplementary angles?When the sum of Two angles is 180°, each angle is said to be the supplement of the other angle.
As ∠b +80° =180°
∠b = 180°-80°
∠b = 100°.
Therefore, The measure of ∠b comes to be 100°.
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Please give me the correct answer.
Answer:
[tex] -m + 6 = 3m + 14 [/tex]
Step-by-step explanation:
Given:
[tex] -(m - 6) = 3m + 14 [/tex]
Required:
Multiply (m - 6) by -1.
Solution:
To multiply (m - 6) by -1, we would be applying the distributive property. This means that we would multiply each term in the parentheses by -1.
Thus:
[tex] -1(m) -1(-6) = 3m + 14 [/tex]
The result would be:
[tex] -m + 6 = 3m + 14 [/tex] (negative times negative = positive)
help on picture 15 points
Answer:
2/3
Step-by-step explanation: