Answer:
C) The y-intercept will always be the vertex.
Step-by-step explanation:
We have the quadratic function in the form:
[tex]f(x)=ax^2+bx+c[/tex]
And we want to determine the true statement when b = 0.
Let's go through each of the choices and examine its validity.
Choice A)
Recall that according to the quadratic formula, the roots of a function is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
If b = 0, then we acquire:
[tex]\displaystyle x=\frac{-(0)\pm\sqrt{(0)^2-4ac}}{2a}=\pm\frac{\sqrt{-4ac}}{2a}[/tex]
As we can see, as long as the inside of the square root is positive, the graph will have x-intercepts. So, b equalling zero does not guarantee that the graph does not have any x-intercepts.
A is false.
Choice B)
A quadratic has a minimum if it curves upwards and a maximum if it curves downwards.
This is decided by the leading coefficient a. b does not affect whether a quadratic curves downwards or upwards.
B is false.
Choice C)
The vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
If b = 0, then the x-coordinate of the vertex is given by:
[tex]\displaystyle x=-\frac{(0)}{2a}=0[/tex]
Then the y-coordinate will be:
[tex]f(0)=a(0)^2+b(0)+c=c[/tex]
So, the vertex is (0, c).
This is also the y-intercept as, by definition, the y-intercept is the value when x = 0.
So, Choice C is the correct choice.
Choice D)
The axis of symmetry is the x-coordinate of the vertex. As we saw earlier, the x-coordinate of the vertex will always be:
[tex]\displaystyle x=-\frac{(0)}{2(a)}=0[/tex]
Zero is neither positive nor negative. Thus, D is false.
Answer:
The y-intercept will always be the vertex.
Step-by-step explanation:
its c
answer both correctly for brainliest
2. B 60 meters
3. C. 10yd
Refer to the attachment for complete calculation
Let g(x) = 4x - 20 and h(x) = -1/2x + k. For what value of k is the zero of h(x) equivalent to the zero of g(x)
Answer:
Step-by-step explanation:
The zero of a function is also known as the x-intercept of a function. The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:
4x - 20 = 0 and -1/2x + k = 0 and then solve each for x:
4x = 20 so
x = 5 and
-1/2x = -k and
1/2x = k so
x = 2k. Now we set the 2 x expressions equal to each other and solve for k:
5 = 2k so
k = 5/2
The value of the K in the given equation is 5/2.
The zero of a function is also known as the x-intercept of a function.
The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:
4x - 20 = 0 and
-1/2x + k = 0 and then solve each for x:
What is the substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
4x = 20 so
x = 5 and
-1/2x = -k and
1/2x = k so
x = 2k. Now we set the 2 x expressions equal to each other and solve for k
5 = 2k so
k = 5/2
Therefore the value of the K in the given equation is 5/2.
To learn more about the expression visit:
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HELP ASAP IM BEING TIMEDD
Answer:
53/100
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
8 / 15 = 0.533
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 533
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule I applies, so 8/15 (or 0.533) rounded to the nearest hundredth in decimal format is:
0.53
Next, we will make 8/15 rounded to the nearest hundredth in fraction format. Since you can divide our decimal format answer above by 1 and keep the same value, you can make it like this:
0.53 = 0.53/1
Then, we multiply the numerator and denominator by 100 to get rid of the decimal point:
(0.53 x 100) / (1 x 100) = 53/100
That's it. 8/15 rounded to the nearest hundredth is displayed below (simplified if necessary):
53/100
Answer:
53.33% is the correct answer
7
45°
X
Find the value of x . Write your answer in simplest form.
Answer:
7√2
Step-by-step explanation:
From the diagram given;
Hypotenuse = x
Opposite = 7
Angle = 45 degrees
According to SOH CAH TOA identity
Sin theta = opposite/hypotenuse
Sin 45 = 7/x
x = 7/sin45
x = 7/1/√2
x = 7 * √2/1
x = 7√2
Hence the value of x is 7√2
A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 2475 ft2.
Answer:
[tex]l =45[/tex] --- length
[tex]w = 55[/tex] --- width
Step-by-step explanation:
Given
[tex]P = 200[/tex] --- perimeter
[tex]A = 2475[/tex] --- area
Required
The dimension of the farm
Let
[tex]l \to length; w \to width[/tex]
So:
[tex]p = 2(l+w)[/tex] --- perimeter
[tex]2(l+w)=200[/tex]
Divide by 2
[tex]l+w=100[/tex]
Make l the subject
[tex]l = 100 - w[/tex]
Also:
[tex]A= l*w[/tex] --- area
[tex]l * w = 2475[/tex]
Substitute: [tex]l = 100 - w[/tex]
[tex](100 - w) * w = 2475[/tex]
Open bracket
[tex]100w - w^2 = 2475[/tex]
Rewrite as:
[tex]w^2 - 100w +2475 = 0[/tex]
[tex]w^2 - 45w - 55w +2475 = 0[/tex]
Factorize
[tex]w(w - 45) - 55(w -45) = 0[/tex]
Factor out w - 45
[tex](w - 55)(w -45) = 0[/tex]
Take any one of the expression and solve for w
[tex]w -55 = 0[/tex]
[tex]w = 55[/tex]
Recall that: [tex]l = 100 - w[/tex]
[tex]l =100 - 55[/tex]
[tex]l =45[/tex]
if you spin the spinner twice what is the probability of spinning orange then brown
Answer:
Is there any image for the question ???
Hey all! Pls help
They are easy questions, pls show the working
Answer:
7. x = 6
8. x = 15/4
9. x = -7
Answer:
Hello there user, looks like your looking for help!
The correct answers should be:
7. x = 6
8. x = 3 3/4
9. x = -7
Step-by-step explanation:
3/2 = x/4
6/4 = x/4
x = 6
x/3 = 1 1/4
4x/12 = 15/12
x = 15/4
x = 3 3/4
(x + 1)/3 = (x-1)/4
(4x + 4)/12 = (3x-3)/12
x/12 = -7/12
x = -7
[tex]9.3x = 9 {^2} [/tex]
Answer:
If you are asking for what x is equal too, then x = 8.70968...
Hope that this helps!
Use the function below to find f(-2).
F(x)= 3^x
A. 1/6
B. -9
C. -6
D. 1/9
Answer:
D. 1/9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationExponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
f(x) = 3ˣ
f(-2) is x = -2 for function f(x)
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-2) = 3⁻²Exponents: f(-2) = 1/9Kind of confused on this question, please help
Answer:
4th option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{5}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{3}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{5} }[/tex] = - [tex]\frac{5}{3}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - [tex]\frac{5}{3}[/tex] and (a, b ) = (- 2, 5 ) , then
y - 5 = - [tex]\frac{5}{3}[/tex] (x - (- 2) ) , that is
y - 5 = - [tex]\frac{5}{3}[/tex] (x + 2)
median 10 24 9 18 15 28 12 27 25 29 10 26
Answer:
The median is 21
Step-by-step explanation:
Since you have 12 numbers in order, that's an even number, once you put them in numerical order and start crossing them off on both sides, you'll have 18 and 24 left, add them together and divide them by 2 and you'll have your median 21.
HELP QUICK
(question in picture)
Answer:
Step-by-step explanation:
There’s a total of 10+16+20+18 = 64 candies.
There’s 10 red candies.
10 / 64 = 0.15625
Rounded: 0.2
can anyone help meh with this i wasn't paying attention in class when my teacher was explaining how to do this :,)
Answer:
W=42°
X=29°
Step-by-step explanation:
180-138=42
90-42-19=29
What is the amplitude of this function f (x)?
f(x) = 3 cos (2x) + 5
Enter your answer in the box.
The amplitude of this function is 3.
Sketch the graph of y = 2 x squared + 7 x using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (0, 0) and (-3.5, 0) d. (-1.5, 0) and (-0.5, 0) Please select the best answer from the choices provided A B C D
Answer:
y= 2x²+7x
B is the answer
how to we work out (x-3)(x-9) in product of 2 binomials
Answer:
2−12+27
Step-by-step explanation:
(−3)(−9)
x(x-9) -3(x-9)
x2 (square lol) - 9x -3 (x-9)
x2-9x-3x+27
x2-12x+27
solution:
2−12+27 answer.
Answer:
Step-by-step explanation:
(x-3)(x-9)
x(x-9)-3(x-9)
x^2-9x-3x+27(add like terms)
x^2-12x+27
Doug can download new songs for $1.19 each Write an equation to show how many songs he can download fir $12.00
Answer:
10.
Step-by-step explanation:
[tex]1.19X10=11.90.[/tex]
You will get 10 songs and have 10 cents left.
what is the slope of the line i will make you brainlest!
Answer:
1x
Step-by-step explanation:
the slope goes up one a positive slope of 1
please answer these I need to pass
Somebody please help meee!!!!
Answer:
[tex]area = 4\pi {r}^{2} \\ = 4 \times 3.14 \times {7.5}^{2} \\ = 706.86 \: {cm}^{2} [/tex]
A plane leave an airport and flies due north. (more in photo)
Answer:
104 miles (nearest whole number)
Step-by-step explanation:
Applying Pythagorean theorem which is: c² = a² + b². Where,
c = distance between the two planes = ?
a = distance of the first plane from the airport = 80 - 1 = 79 miles
b = distance of the second plane from the airport = 68 - 1 = 67 miles
c² = 79² + 67²
c² = 10,730
c = √10,730
c = 103.585713
c = 104 miles (nearest whole number)
Jane bought 6 banana at $250 per dozen. she sells four and a half dozen at $35 each and the others were sold at %20 each determine if she made a profit or loss state her profit or loss as a percentage. show working
Answer:
34.4% profit
Step-by-step explanation:
C.P. = 1500
S.P. = 2016
Profit% = 34.4%
What is the area of a circle with a radius of 8 feet?
Answer:
201.06
Step-by-step explanation:
93% sure lol
PLEASE HELP MEEEEEEEEEEEEE
Jeb and Lori went to a florist to buy flowers. Jeb bought 6 roses and 3 carnations for $20.25. Lori bought 8 roses and 3 carnations for $25.75. Find the price of one rose and the price of one carnation.
Answer:
first create an equation for Jeb flower then for Lori
then solve them by simultaneous linear equations
Answer:
One rose = $2.75
One carnations = $1.25
Step-by-step explanation:
Lets make the rose = x
and carnations = y
Jeb >> 6x + 3y = 20.25
Lori >> 8x + 3y = 25.75
Solve simultaneously using elimination method.
8x + 3y = 25.75
- 6x + 3y = 20.25
_______________
2x =5.5
2x/2 = 5.5/2
x = 2.75
plug 2.75(x) into any of the two equations to find y.
6(2.75) + 3y = 20.25
16.5 + 3y = 20.25
3y = 20.25 - 16.5
3y = 3.75
3y/3 = 3.75/3
y = 1.25
Sharma draws a floor plan of the local supermarket on a coordinate plane.
Part A Which is the location of the dairy?
A : 0, 1)
B : (1, 0)
C : (1, 1)
D : (1, 2)
Part B : What are the coordinators of the bakery in the boxes .
Part C : Bakery , Frozen foods , Dairy , produce ?
Answer:
The answer woupd be B, 1, 0
The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0) thus option (B) will be correct.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
As per the given floor plan,
Th coordinate of dairy is the horizontal and vertical distinctions from the reference axes(0,0).
Since it is 1 unit apart in the x and 0 apart in the y direction.
Thus (1,0) is the right coordinate.
Hence "The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0)".
For more about coordinates,
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I need help with this question
Answer:
the number that goes there is 7
Step-by-step explanation:
Leon graphed y = 10 -0.05x to represent the number of gallons of gas left in
his car after driving x miles.
gallons
10
miles
200
What is a reasonable range for this situation?
O A. All real numbers
B. y20
O c. Osys 200
O D.Osys 10
Answer:
0≤y10
Step-by-step explanation:
Given the expresssion;
y = 10 - 0.05x
To get the range, we will first substitute for the value of y by substituting the value x =0
y = 10 - 0.05(0)
y = 10
Hence the required range of values falls between 0 and 10;
0≤y10
Brian sent 9 more messages than salma and Chang sent 2 times more than Brian and they have 55 messages total how many messages do they have each
Answer:
Number of messages Salma sent = 7
Number of messages Brian sent = 16
Number of messages Chang sent = 32
Step-by-step explanation:
Let
Number of messages Salma sent = n
Number of messages Brian sent = n + 9
Number of messages Chang sent = 2(n + 9)
Total messages sent = 55
n + (n + 9) + 2(n + 9) = 55
n + n + 9 + 2n + 18 = 55
4n + 27 = 55
4n = 55 - 27
4n = 28
n = 28/4
n = 7
Number of messages Salma sent = n = 7 messages
Number of messages Brian sent = n + 9 = n + 9 = 16 messages
Number of messages Chang sent = 2(n + 9)
= 2(7 + 9)
= 2(16)
= 32 messages
Graph the line with the equation y= -1/3x - 2
Answer:
I hoped this helped!
Step-by-step explanation:
Answer:
See attached image.
Step-by-step explanation:
You can either use a graphing calculator or make a table to find values for yourself.
X | 0 | 3
Y | -2 | -3
and so forth.
Samples of viewers were taken from two different movies to compare the ages of those
watching the movie. Fifty participants were asked their ages as they exited each movie. The
results are shown on the double box plot below. Which statistical measure was equal for the
two samples?
Movie
Answer:
The median are equal
Step-by-step explanation:
Given
I will answer this question with the attached plot (see attachment 2)
Required
The equal statistical measures
See attachment 1 on how to read a box plot
Using attachment 1 as a guide, we have the following observation
Movie 2 Movie 1
[tex]Minimum=7.5[/tex] [tex]Minimum=10[/tex]
[tex]Q_1 = 22.5[/tex] [tex]Q_1 = 15[/tex]
[tex]Median = 30[/tex]
[tex]Q_3 = 35[/tex] [tex]Q_3 = 40[/tex]
[tex]Maximum = 47.5[/tex] [tex]Maximum = 52.5[/tex]
By comparison, they have equal median (30)