MATHEMATICS HIGH SCHOOL

Which of the following is the graph of f(x) = x2 − 5x + 4?

Answers

Answer 1

Answer:

Answer:

refer attachment for the graph.

Step-by-step explanation:

Given: The equation $f(x)=x^2-5x+4$

We have to draw the the graph for the given equation.

Consider the given equation $f(x)=x^2-5x+4$

The vertex of the parabola of the form $f(x)=ax^2+bx+c$ is given by $x=-(b)/(2a)$

Here, a = 1 , b = -5 and c = 4

Thus, vertex is

$x_v=-(\left(-5\right))/(2\cdot \:1)=(5)/(2)$

Also, the y coordinate at $x=(5)/(2)$ is

$y_v=\left((5)/(2)\right)^2-5\cdot (5)/(2)+4$

Simplify, we get,

$y_v=-(9)/(4)$

Thus, The vertex of parabola is $\left((5)/(2),\:-(9)/(4)\right)$

y - intercept is the point where x = 0

Plug x = 0 in given equation $f(x)=x^2-5x+4$

$f(0)=0^2-5(0)+4=4$

Thus, y - intercept is (0,4)

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

$x^2-5x+4=0$

Solving the given quadratic equation using quadratic formula ,we have

$x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)$

we have a = 1 , b = -5 and c = 4

$x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:1\cdot \:4))/(2\cdot \:1)$

Simplify, we have,

$x_(1,2)=(5\pm√(9))/(2)$

Thus, $x_1=4, x_2=1$

Thus, The x - intercept are (4,0) and (0,1)

Plot the graph and we obtain as shown below.

Answer 2

Answer: I made a graph of the equation hope this helps.

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A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x + 6y = 7.50 10x + 5y = 8.75

Answers

Given:
let x = apples
let y = oranges

Equation 1: 6x + 6y = 7.50
Equation 2: 10x + 5y = 8.75

Equation 1 - Equation 2
6x + 6y = 7.50
- (10x + 5y = 8.75)
-4x+ y = -1.25
y = -1.25 + 4x

6x + 6y = 7.50
6x + 6(-1.25 + 4x) = 7.50
6x - 7.50 + 24x = 7.50
30x = 7.50 + 7.50
30x = 15
x = 15/30
x = 1/2 or 0.50 cost of one apple

y = -1.25 + 4x
y = -1.25 + 4(0.50)
y = -1.25 + 2
y = 0.75 cost of one orange

6x + 6y = 7.50
6(0.50) + 6(0.75) = 7.50
3 + 4.5 = 7.50
7.50 = 7.50

10x + 5y = 8.75
10(0.5) + 5(0.75) = 8.75
5 + 3.75 = 8.75
8.75 = 8.75

Answer:

The cost of one apple would be 0.5 :)

Step-by-step explanation:

Just took the test, hope this helps :)

1. How many centimeters are there in meter? a. 1
b. 10 c. 100
d. 1000 e. 10000

Answers

There are 100 centimeters in one meter, the correct option is (C) 100

A meter is a unit of length in the International System of Units (SI) that is used to measure distance or length. One meter is defined as the distance traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.

A centimeter, on the other hand, is a smaller unit of length in the SI system.

1 centimeter = 1 / 100 meter

One centimeter is equal to one-hundredth of a meter,

Therefore, the conversion factor = 100

Which means that there are 100 centimeters in one meter.

Therefore, the correct option is (C) 100

Learn more about conversion factor here

brainly.com/question/23718955

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Do you guys know the domain and range to this?