Answers
Answer:
The correct option is;
The variable x has a coefficient
Step-by-step explanation:
The given vertex form of a quadratic function and the quadratic function can be written as follows;
Vertex form of a quadratic function, f(x) = (3·x + 1/3)² + 8/9
The quadratic function, f(x) = 9·x² + 2·x + 1
The vertex form of a quadratic function f(x) = a·x² + b·x + c is f(x) = a·(x - h)² + k
Where;
h = -b/(2·a) = -2/(2×9) = -1/9
k = f(h) = f(-1/9) = 9 × (-1/9)² + 2 × (-1/9) + 1 = 8/9
Which gives the vertex form a s f(x) = 9·(x - (-1/9))² + 8/9
f(x) = 9·(x + 1/9)² + 8/9
Therefore, f(x) = (3·x + 1/3)² + 8/9 is not the vertex form of f(x) = 9·x² + 2·x + 1 because the variable x has a coefficient.
Related Questions
You have —1 ounce of whole wheat grains. How many more ounces do you need to 8
make the recipe?
Answers
idek
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The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14
Answers
Answer:
r = 5 cm
Step-by-step explanation:
A = πr²
78.53 = (3.14)r²
divide by 3.14
25 = r²
r = ±5
r = 5
I need help on this problem. (-5)^5/(-5)^-6
Answers
Answer: (-5)¹¹ of (-5)^11
Step-by-step explanation:
Since the base of the two exponents are teh same at -5, we can subtract the exponents.
5-(-6)=11
Now, we know that the new exponent will be 11, with the base staying the same.
PLZ HELP ME 100 POINT AND BRAINEST Solve the Quadratic Equation X^2 = -8x -7
A. 7, -1
B. -1, -7
C. 8, 1
D. 7,1
E. -8, -1
Answers
Answer:
B
Introduction:Given equation: [tex]x^2 = -8x -7[/tex]
To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.
[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]
[tex]\implies 0= -8x -7 - x^2[/tex]
To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.
[tex]\implies 0= -1(8x + 7 + x^2)[/tex]
[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]
Finally, factor the expression on the right hand side.
Factoring a quadratic equation can be done in 2 ways.
1) Splitting methodIn this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.
The product of the suitable terms must be equal to the product of the first and last terms of the expression. The sum of the suitable terms must be equal the middle term.Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.
However, this method follows a condition. If the middle term cannot be split into two suitable terms, then the second method should be followed to determine a solution. 2) The Quadratic FormulaIn this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).
[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.
-----------------------------------------------------------------------------------------------------
Solving for x using the splitting methodWe can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.
[tex]\implies 0= x^2 + 8x+ 7[/tex]
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
Now, factor the first two terms and the last two terms separately.
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]
We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.
[tex]\implies 0= (x + 7)(x + 1)[/tex]
Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.
[tex]\implies x + 7 = 0; x + 1 = 0[/tex]
[tex]\implies x = -7; x = -1[/tex]
Solving for x using the Quadratic formulaNow, let us try to solve using the Quadratic formula.
[tex]0= x^2 + 8x+ 7[/tex]
Tip: Standard form: 0 = ax² + bx + c
Comparing both equations will allow us to determine the a, b, c variables.
⇒ a = 1; b = 8; c = 7
Now, let us plug these values into the quadratic formula and simplify.
[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]
Therefore, in both methods, the answer is -1, -7 (B).
Learn more about quadratic formula: brainly.com/question/22364785
Learn more about splitting method: brainly.com/question/13874704
please help me on this
Answers
Answer:
Step-by-step explanation:
coordinate of O(2,1),Y(3,-2),T(-3,-3)
let the reflected points are O',Y',T'
distance of O from y=2 is 1 unit.
∴ ordinate of O' =1+2(1)=3
or O' is (2,3)
distance of Y from y=2 is2+2=4
ordinate of Y'=-2+2(4)=6
so coordinate of Y' is (3,6)
distance of T from y=2 is (2+3)=5
so ordinate of T' =-3+2(5)=7
coordinate of T' is(-3,7)
How many times does 27 go into 1714???
Answers
Answer:
27/3 = 9
Step-by-step explanation:
"How many times does 3 go into 27?" is the same as asking "How much is 27 divided by 3?" Thus, the answer can be calculated as follows:
27/3 = 9"How many times does 3 go into 27?" is also the same as asking "What (x) do you multiply by 3 to get 27?" We solve the problem with an easy algebra equation:
3(x) = 27
x = 9
Tip: When you get a question like "How many times does 3 go into 27?", just think of it as how many times you can fit 3 into 27.
The answer on this page is rounded to the nearest decimal if necessary.
solve the equation -3+(1) −3+(1)
Answers
Answer:
-4
Step-by-step explanation:
you can just plug this into a calculator.
OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4
Answer:
-4
Step-by-step explanation:
-3 + (+1)= -2
2(-3 + (+1)) = -4
7. Bryce is making a model building.
He raises the walls of the building
by 2 centimeters five times. By how
many centimeters does Bryce raise
the walls all together?
(A) 2 cm
© 10 cm
(B) 5 cm
D20 cm
Answers
After raising the walls of the building of height 2cm 5 times the height of the wall will be 10cms.
What is multiplication ?Multiplication is a short hand of addition like if we have to add 2 by100 times it is same as multiplying 2 with 100 which is 200.
According to the given question Bryce is making a model building.
Said that he raises the walls of the building by 2 centimeters five times.
So, Either we can sum 2 centimeters 5 times which is (2 + 2 + 2 + 2 + 2) which is
= 10cms.
Or we can multiply the height of the building which is 2 cm by the no. of times he raised it which is 5.
∴(2×5) = 10cms.
learn more about these type of problems here :
https://brainly.com/question/16756360
#SPJ2
Riley is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 6 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Answers
Answer:
After 6 minutes, the oven temperature will be: [tex]125^o[/tex]
Step-by-step explanation:
If the increase in temperature is [tex]10^o[/tex] per minute, then in 6 minutes, the increase in temperature would be [tex]6\,*\,10^o=60^o[/tex], therefore, since the initial temperature of the oven was [tex]65^o[/tex], its temperature after 6 minutes would be:
[tex]65^o+60^o=125^o[/tex]
what is the difference between -8 to the power of 2 and (-8) to the power of 2?
Answers
Answer:
0
because -8 powered 2 and -8 powered 2 is same. 64-64=0
Step-by-step explanation:
What equation represents a population of 300 animals at the crease and an annual rate of 23%
Answers
Answer:
300 + 69xStep-by-step explanation:
Given initial population of animals = 300 animals
If the population increases by 23% annualy, yearly increment will be expressed as:
Yearly increment = 23% of 300
Yearly increment = 0.23*300
Yearly increment for = 69
Let the total number of years of be x
Increment after x years = 69x
Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years
= 300 + 69x
Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x
A rectangle is 10 inches smaller than it is wide. The perimeter of the rectangle is 80 inches. Find the length and the width of the rectangle.
Answers
Answer:
l = 15 and w = 25
Step-by-step explanation:
[tex]l - w = - 10[/tex]
[tex]l + w = 40[/tex]
Adding both equations
[tex]2l = 30[/tex]
[tex]l = 15[/tex]
subtracting both equation
[tex]2w = 50[/tex]
[tex]w = 25[/tex]
Hope it helps..........
BRAINLIEST PLEASE
Answer:
Length=30 Width=10
Step-by-step explanation:
ifran manages a coffee shop.
The rest of the question is in the screen shot
Answers
Answer:
230 capsules.
Step-by-step explanation:
The following data were obtained from the question:
Taste >>>>>>>>>>> Frequency
Volluto >>>>>>>>>> 12
Livanto >>>>>>>>>> 7
Ristretto >>>>>>>>> 23
Cosi >>>>>>>>>>>> 3
Other >>>>>>>>>>> 5
Next, we shall determine the total frequency.
This is illustrated below:
Total frequency = 12 + 7 + 23 + 3 + 5
Total frequency = 50
Finally, we shall determine the number of Ristretto in 500 capsules.
This can be obtained as follow:
Number of Ristretto = Frequency of Ristretto /total frequency x total capsule
Frequency of Ristretto = 23
Total frequency = 50
Total capsule = 500
Number of Ristretto = 23/50 x 500
Number of Ristretto = 23 x 10
Number of Ristretto = 230.
Therefore, the number of Ristretto in the 500 capsules is 230.
Figure A is a scale image of Figure B.
27
Figure A
Figure B
45
35
What is the value of x?
Answers
Greetings from Brasil...
According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....
So
BIG/small = BIG/small
or
small/BIG = small/BIG
27/X = 45/35
OR
35/45 = X/27
27/X = 45/35
45X = 27·35
45X = 945
X = 945/45
X = 21The interquartile range is determined by the formula _____________. A. Third quartile – First quartile B. Maximum – minimum C. Third quartile + first quartile D. First quartile – third quartile
Answers
Answer:
A. Third quartile – First quartile
Step-by-step explanation:
The interquartile range is found by taking the third quartile minus the first quartile. It is also found by taking the right side of the box in a box and whisker plot and subtracting the left side of the box in a box and whisker plot
A contractor purchases 7 dozen pairs of padded work gloves for $102.48. She incorrectly calculates the unit price as $14.64 per pair for the expense report. What is the correct unit price? What is the error?
Answers
Answer:
The correct unit price can be calculated by dividing the total price paid by 84 that was the number of pairs of padded work gloves that were bought:
$102.48/84=$1.22
The correct unit price is $1.22.
-The error is that the person calculated the unit price by dividing the total price paid by 7 but the statement indicates that the contractor purchased 7 dozen pairs, which means: 7*12= 84. According to this, the contractor purchased 84 pairs of padded work gloves.
given the relation y=x+2, if the input is 3, what is the output
Answers
Answer:
The output is 5
Step-by-step explanation:
y=x+2,
Let x =3
y = 3+2
y = 5
The output is 5
Answer:
5
Step-by-step explanation:
We are given the relation:
y=x+2
The input is also called "x", and the output is also known as "y". We want to find the output, or y, when x is equal to 3.
Therefore, we must substitute 3 in for x and solve.
y= x+2 at x=3
y=3+2
Add 3 and 2.
y=5
If the relation is y=x+2 and the input is 3, then the output is 5.
A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3.00 + 0.50 m = 9.50, where m represents the number of miles traveled.
Answers
Answer:
Value of miles traveled (m) = 13 mile
Step-by-step explanation:
Given:
Equation
3.00 + 0.50 m = 9.50
Find:
Value of miles traveled (m)
Computation:
3.00 + 0.50 m = 9.50
0.50 m = 9.50 - 3.00
0.50 m = 6.50
m = 6.50 / 0.50
m = 13
Value of miles traveled (m) = 13 mile
Answer:
The question is not complete, below is the complete question:
A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3.00 + 0.50 m = 9.50, where m represents the number of miles traveled.
Which statement shows the meaning of the driver's equation? Check all that apply.
a.) Three dollars added to $0.50 is the same as $9.50.
b.) Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.
c.) Three dollars more than the quotient of $0.50 and the number of miles is nine dollars and fifty cents.
d.) The product of the number of miles and the sum of $3 and $0.50 is equal to $9.50.
e.) The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
Answers
The correct answers are:
b
e.) The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
Step-by-step explanation:
The formula written by the driver is: 3.00 + 0.50 m = 9.50
where m = number of miles travelled
This means that when the product of 0.50 and the number of miles travelled 'm' is added to $3, the result is 9.50
And this is the same explanation as the following options:
a.) Three dollars($3) plus $0.50 times the number of miles is equal to nine dollars and fifty cents($9.50).
e.) e.) The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents;
note that 50 cents is the same as $0.50
Simplify by combining like terms: -4\left(2x-y\right)+y+5\left(x+y\right)−4(2−)++5(+) − 4 ( 2 x − y ) + y + 5 ( x + y ) ; use NO spaces when typing in your answers.
Answers
Answer:
-3x+10y
Step-by-step explanation:
Given the expression [tex]-4\left(2x-y\right)+y+5\left(x+y\right)[/tex], we are to simplify by combining the like terms. On simplification we have;
[tex]= -4\left(2x-y\right)+y+5\left(x+y\right)[/tex]
Open the parenthesis:
[tex]= -4(2x)-4(-y)+y+5(x)+5(y)\\\\= -8x+4y+y+5x+5y[/tex]
Collect the like terms:
[tex]= -8x+5x+4y+y+5y[/tex]
Sum up the resulting expression
[tex]= -8x+5x+4y+y+5y\\= -3x+10y[/tex]
Hence the required expression on simplification is -3x+10y
Pls help answer ASAP I will give Brainlyist
Answers
Answer:
Letter B because it is less than. < is less than
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
c < 27.50
The sign < means less than.
Plug the numbers in and you've got:
The cost is less than $27.50
Good luck mate :)
PLeasE HELP, I DONT UNDERSTAND THIS.......Bob has $112 more than Martha. If they have $500 in total, how much does each person have?
Answers
Answer:
He has $138
Step-by-step explanation:
you would divide 500/2 and then subtract one side by 112 to get the answer.
step by step explanation pls?
Answers
Answer:
x = 34
Step-by-step explanation:
x/3 - 7/3 = 9
Combine like terms
(x-7)/3 = 9
Multiply each side by 3
(x-7)/3 * 3 = 9*3
x-7 = 27
Add 7 to each side
x-7+7 = 27+7
x = 34
please help right now
Answers
Answer:
4sqrt(2) + 1
Step-by-step explanation:
Well you know that cos 0 is 1
this means that a+b = 9
cos 60 is 1/2
this means 1/2 a + b = 5
a = 8
b = 1
now plug in for x = 45
cos 45 = sqrt(2)/2
(x^3-2x^2+3x-4)(x-1)-(2x-3)(x^2-x+1)
Answers
Answer:
x^4−5x^3+10x^2−12x+7
Step-by-step explanation:
Distribute:
=(x^3)(x)+(x^3)(−1)+(−2x^2)(x)+(−2x^2)(−1)+(3x)(x)+(3x)(−1)+(−4)(x)+(−4)(−1)+−2x^3+5x^2+−5x+3
=x^4+−x^3+−2x^3+2x^2+3x^2+−3x+−4x+4+−2x^3+5x^2+−5x+3
Combine Like Terms:
=x^4+−x^3+−2x^3+2x^2+3x^2+−3x+−4x+4+−2x^3+5x^2+−5x+3
=(x^4)+(−x^3+−2x^3+−2x^3)+(2x^2+3x^2+5x^2)+(−3x+−4x+−5x)+(4+3)
=x^4+−5x^3+10x^2+−12x+7
what is the slope of the line shown below? (1,-4) (2,2)
Answers
Your question has been heard loud and clear.
Slope formula when two points are given= y2-y1/x2-x1
Here y2= 2
X2=2
Y1= -4
X1= -1
= 2-(-4)/2-(-1)= 2
Slope of line= 2
Thank you.
Answer:
[tex]\huge \boxed{\mathrm{B. \ 2}}[/tex]
Step-by-step explanation:
The line crosses two points.
The two points are (-1, -4) and (2, 2).
The slope of a line can be found through two points.
[tex]\displaystyle \sf slope = \frac{rise}{run}[/tex]
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2=2 \\ y_1 = -4 \\ x_2=2 \\ x_1=-1[/tex]
Plug in the values and evaluate.
[tex]\displaystyle m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]\displaystyle m=\frac{2+4}{2+1}[/tex]
[tex]\displaystyle m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
The slope of the line is 2.
A dealer sold a painting for $800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.
Answers
She paid $640 for the painting
Step-by-step explanation:
her selling price SP = 800
CP+25%of CP = 800
1.25CP=800
CP=640
Answer:
$640
Step-by-step explanation:
paint sold for $800
profit 25%
the price she paid for the painting = $800 / 1.25 = $640
Which equation is equivalent to 7w – 1 = –15?
A: 1 - 7w = -15
B: 7w = -15 + 1
C: 7w = –15 – 1
D: 7w = 15 - 1
Answers
Answer:
i believe the answer is A
Step-by-step explanation:
Show that the statement is true. If DF has endpoints D(-1,8) and E(3,-2), then the midpoint M of DE lies
I
in Quadrant I.
The midpoint M is
and the y-coordinate is (select)
). M lies in (select)
since the x-coordinate is (select) v
Answers
please help me with my homework
Graph the function and its parent function. Then describe the
transformation.
g(x) = 1/3x^2
Answers
Answer: find the answer in the explanation
Step-by-step explanation:
Given the function and its parent function, to describe the
transformation of g(x) = 1/3x^2
First sketch the graph of the parent function which is g(x) = x^2
For every value of x, g(x) will take the value it would have had at kx, that is, the graph of g(x) = x^2 is stretched by a factor of 1/3 in the x - direction.
Find the attached files for the graph and solution
Find the standard form of the quadratic equation: f(x)=(2x-1)(x+4)
Answers
Answer:
[tex] f(x) = 2x ^{2} + 7x - 4[/tex]
Step-by-step explanation:
[tex] \because \: f(x) = (2x - 1)(x + 4) \\ \therefore \:f(x) = 2x(x + 4) - 1(x + 4) \\ \therefore \:f(x) = 2x ^{2} + 8x - x - 4 \\ \therefore \:f(x) = 2x ^{2} + 7x - 4 \\ [/tex]