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4 years ago

The graph of the piecewise function is shown.

Mathematics

2 answers:

aivan3 [116]4 years ago

7 0

Answer:

Range of f(x) is:

B) { f(x)| –∞ < f(x) ≤ 4}

Step-by-step explanation:

The range of a function is the set of all those values which that function takes. i.e. The range is the resulting y-values or f(x)-values we get after substituting all the possible values of x.

Here, we can see that f(x) takes all the values between -∞ and 4

Hence, range of f(x) is:

B) { f(x)| –∞ < f(x) ≤ 4}

motikmotik4 years ago

6 0

Range, from -inf to 4

4 >= f(x) > - inf B

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What is the answer??

Dovator [93]

Answer:

y₂ = 3

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - $\frac{3}{4}$

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (7, - 6) and (x₂, y₂ ) = (- 5, y₂ )

m = $\frac{y_{2}+6 }{-5-7}$ , that is

$\frac{y_{2}+6 }{-12}$ = - $\frac{3}{4}$ ( cross- multiply )

4(y₂ + 6) = 36 ( divide both sides by 4 )

y₂ + 6 = 9 ( subtract 6 from both sides )

y₂ = 3

8 0

3 years ago

While Mike was visiting his sister in Arlington, he bought an aquarium that was marked down 60% from an original price of $100.

Ymorist [56]

Answer:

$42

Step-by-step explanation:

100 - 60% * 100 = $40

Since tax is 5%, therefore:

40 + 5% of 40 = $42

Thenks and mark me brainliest :))

6 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Clim_%7Bh%20%5Cto%20%5C116%7D%20x-16%2F%5Csqrt%7Bx%7D%20-4" id="TexFormula1" title="\lim_{h

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

What does the value 40 in the equation y=7.5+40 represent in the context of this situation?

vodka [1.7K]

Answer:

40 is an addend in an addition

40 is the y-intercept if the question really is y = 7.5x + 40.

Step-by-step explanation:

40 is just a number in a sum of 2 numbers.

Perhaps you meant

y = 7.5x + 40

If that is the case, then 40 is the y-intercept.

6 0

3 years ago

The count in a bacteria culture was 800 after 15 minutes and 1200 after 40 minutes. Assuming the count grows exponentially,

Maslowich

Answer:1) bacteria size = b(initial) * e^(r * t)

initial size = 300

final size = 1600.

Substituting the values into the main equation:

1600 = 300 * e^(r * 35 - 20)

solving for 'r'.

1600 = 300 * e^(r * 15)

1600/300 = e^(r * 15)

taking natural log on both sides to eliminate the power

ln(16/3) = ln[e^(r * 15)]

ln(16/3) = r * 15

r = ln(16/3) / 15

= 0.11159843

= 11.16%

To find the initial bacteria size,

Given: t = 20

300 = b * e^(0.1116 * 20)

Solving for b:

300 = b * e^2.232

b = 300/e^2.232

b = 32

Step-by-step explanation:

3 0

3 years ago