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4 years ago

Function f is represented by the equation shown.

Mathematics

1 answer:

aliya0001 [1]4 years ago

4 0

Answer:

$\boxed{\text{A. The y-intercept of function f is greater than the y-intercept of function g}}$

Step-by-step explanation:

A. y-Intercept of ƒ(x)

ƒ(x) = x² - 4x + 3

f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3

The y-intercept of ƒ(x) is (0, 3).

If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).

Statement A is TRUE.

B. y-Intercept of g(x)

Statement B is FALSE.

C. Minimum of ƒ(x)

ƒ(x) = x² - 4x + 3

a = 1; b = -4; c = 3

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

h = -b/2a = -(-4)/(2×1 = 2

k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1

The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).

Statement C is FALSE.

D. Minimum of g(x)

g(x) is a downward-opening parabola. It has no minimum.

Statement D is FALSE

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Evgen [1.6K]

Answer:

$\displaystyle 8$

Step-by-step explanation:

we would like to compute the following limit

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right)$

if we substitute 16 directly we'd end up

$\displaystyle = \frac{16 - 16}{ \sqrt{16} - 4}$

$\displaystyle = \frac{0}{ 0}$

which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right)$

simplify which yields:

$\displaystyle \lim_{x \to 16} \left( \frac{(x - 16)( \sqrt{x} + 4)}{ x - 16} \right)$

we can reduce fraction so that yields:

$\displaystyle \lim_{x \to 16} \left( \frac{ \cancel{(x - 16)}( \sqrt{x} + 4)}{ \cancel{x - 16} } \right)$

$\displaystyle \lim _{x \to 16} \left( \sqrt{x } + 4\right)$

now it's safe enough to substitute 16 thus

substitute:

$\displaystyle = \sqrt{16} + 4$

simplify square root:

$\displaystyle = 4 + 4$

simplify addition:

$\displaystyle = 8$

hence,

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) = 8$

6 0

3 years ago

Which expression has a base with an exponent of 4?

m_a_m_a [10]

Answer:

The expression that has a base is 3m⁴

Step-by-step explanation:

I hope it helps!!!

7 0

3 years ago

Can someone help me out

Likurg_2 [28]

False i think, i did it in my head so it might be wrong, but im pretty sure its false. hope it helped

8 0

3 years ago

Read 2 more answers

Help me plzzzzzzzzzzzzzzzzzzz

4vir4ik [10]

Answer:

5.5; 11.00; 16.50

$E = 5.5h$

Step-by-step explanation:

Given

The attached table

Solving (a): Complete the table

First, calculate the slope (m)

$m = \frac{E_2 - E_1}{h_2 - h_1}$

So:

$m = \frac{27.5- 22.00}{5-4}$

$m = \frac{5.50}{1}$

$m = 5.50$

So, the equation of the table is:

$E = m(h - h_1) + E_1$

$E = 5.5(h - 4) + 22$

$E = 5.5h - 22 + 22$

$E = 5.5h$

When h =1,2,3

$E = 5.5 * 1 = 5.5$

$E = 5.5 * 2 = 11.00$

$E = 5.5 * 3 = 16,50$

6 0

3 years ago

Which value or values for the variable c from the set below will make 5.6 + 0.4c

konstantin123 [22]

<span>a. only 2.5
By plugging in all three values, we will find that only 2.5 will create a correct solution of the choices.
</span>5.6+0.4(2.5) < 6(2.5) True
6.6 < 15
5.6+0.4(1) < 6(1) False
6 < 6
5.6+0.4(0.875) < 6(0.875) false
5.95<5.25

4 0

3 years ago