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3 years ago

Write a linear function f with the values f(0) = 6 and f(4) = -6.

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

3 0

Answer:

f(x) = -3x + 6

Step-by-step explanation:

The general linear function is;

y = mx + b

it can also be written as (x , f(x))

f(x) = mx + b

where m is the slope and b is the y-intercept

so we have the points ;

(0,6) and (4,-6)

So we have;

for f(0) to be 6, it means that the y-intercept b is 6

This is because the value of x at the y-intercept is 0

So we have this as;

f(x) = mx + 6

Now, let’s substitute the other point so as to get m

For the other point;

x = 4 and f(x) = -6

that means;

-6 = 4m + 6

4m = -6-6

4m = -12

m = -12/4

m = -3

So we have the equation as;

f(x) = -3x + 6

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3 years ago

Answer my questions plz help

coldgirl [10]

9514 1404 393

Answer:

a = -2/3, b = 8, c = -24
y-intercept: (0, -24)
x = -b/(2a) = -8/(2(-2/3)) = 8(4/3)
x = 6
DOWN
Max: (6, 0)
Vertex: (6, 0)
Domain: {x | x ∈ ℝ}
Range: {x | x ≤ 0}

Step-by-step explanation:

To find a, b, c, compare the given function to ...

f(x) = ax² +bx +c

You will see that ...

a = -2/3
b = 8
c = -24

The y-intercept is the function value for x=0. It is the constant term:

y-intercept = f(0) = -24

Use the above values of a, b to find the line of symmetry.

$x = \dfrac{-b}{2a}=\dfrac{-8}{2\cdot\dfrac{-2}{3}}=8\cdot\dfrac{3}{4}=6$

Per the calculation, the line of symmetry is ...

x = 6

The negative leading coefficient tells you the parabola opens DOWN.

Because it opens down, the vertex at (6, 0) is a Maximum.

As with any polynomial, the domain is "all real numbers", hence any x that is an element of Reals.

The range is all values below the vertex (including the vertex), so is ...

x ≤ 0

3 0

2 years ago

Evaluate the function for x = m/4

attashe74 [19]

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8 0

3 years ago

Jason earns $35.50 on Monday, spends $24.00 on Tuesday, and earns $12.50 on Wednesday. Which equation shows how the Associative

madam [21]

The answer is 24. 35.50-24.00 is 11.50 and you add that with the 12.50 that he earned on Wednesday and you get 24 as the answer

5 0

3 years ago

7. for normal situations, the minimum speed limit throughout the u.s. interstate highway system is 72 km/hr which is 45 miles pe

gladu [14]

Answer:

Question 7: Distance = 237.6 km

Question 8: Distance = 399.3 km

Step-by-step explanation:

Question 7:

Given:

Minimum speed (s) = 72 km/hr

Time taken (t) = 3.3 hours.

We know that, distance traveled is equal to the product of speed and time.

Therefore using distance formula, we get:

Distance = Minimum speed × Time

Distance = $s\times t$

Distance = $72\times 3.3 = 237.6\ km$

Therefore, distance traveled at this speed is 237.6 km.

Question 8:

Maximum speed (S) = 121 km/hr

Time taken (T) = 3.3 hours.

We know that, distance traveled is equal to the product of speed and time.

Therefore using distance formula, we get:

Distance = Maximum speed × Time

Distance = $S\times T$

Distance = $121\times 3.3 = 399.3\ km$

Therefore, distance traveled at this speed is 399.3 km.

3 0

3 years ago