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ivolga24 [154]
3 years ago
11

Can someone solve point-slope lines and show work? I’m confused

Mathematics
1 answer:
Bad White [126]3 years ago
8 0

Answer:

Option (2)

Step-by-step explanation:

Equation of a line passing through a point (x', y') and slope 'm' is given by,

y - y' = m(x - x')

From the question in the picture attached,

Slope of the line 'm' = -\frac{7}{10}

Line passes through a point (80, -71).

Equation of the line will be,

y + 71 = -\frac{7}{10}(x-80)

y = -\frac{7}{10}x+56-71

y = -\frac{7}{10}x-15

Option (2) will be the answer.

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f of x equals 4 x over quantity x squared minus 16. Show all work to identify the asymptotes and zero of the function.
yuradex [85]

Given:

The function is

f(x)=\dfrac{4x}{x^2-16}

To find:

The asymptotes and zero of the function.

Solution:

We have,

f(x)=\dfrac{4x}{x^2-16}

For zeroes, f(x)=0.

\dfrac{4x}{x^2-16}=0

4x=0

x=0

Therefore, zero of the function is 0.

For vertical asymptote equate the denominator of the function equal to 0.

x^2-16=0

x^2=16

Taking square root on both sides, we get

x=\pm \sqrt{16}

x=\pm 4

So, vertical asymptotes are x=-4 and x=4.

Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0.

8 0
3 years ago
Tammy bought a nightstand that was marked down 60% from an original price of $50. If she paid 10% sales tax, what was the total
AURORKA [14]

Answer: the total cost of the nightstand is $22

Step-by-step explanation:

The original price of the night stand is $50. If the original price of the night stand was marked down by 60%, it means that the amount of money by which it was reduced would be

60/100 × 50 = 0.6 × 50 = 30

The new selling price would be

50 - 30 = $20

If she paid 10% sales tax,the amount of tax paid would be

10/100 × 20 = 0.1 × 20 = 2

Therefore, the total cost of the nightstand would be

20 + 2 = $22

7 0
3 years ago
Sonia's check at Aubrey's Kitchen is $14.25. In order to leave a 10% tip, how much should she pay? Round to the nearest cent.
Sidana [21]

Answer:

Nearest cent- $1.43

Step-by-step explanation:

14.25x0.10=1.425

7 0
3 years ago
Enzo is studying the black bear population at a large national park.
Naddik [55]

Answer:

2,973

Step-by-step explanation:

The black bear population B(t), in the park is modeled by the following function:

B(t) = 2500 \cdot 2^{0.01t}

Where t is the time(in years) elapsed since the beginning of the study.

We want to determine the black bear population in 25 years time, t=25.

B(25) = 2500 \cdot 2^{0.01*25}\\=2973.02\\\approx 2973

There will be 2,973 black bears in 25 years time.

4 0
3 years ago
A rectangle has a height of 4w^3 and a width of 5w^2-3w-4.
Thepotemich [5.8K]

Answer:

Step-by-step explanation:

Area of the entire rectangle = height * width

= 4w³ *( 5w²-3w-4)

= 4w³ * 5w²- 4w³ *3w - 4w³ *4

=20w⁵ - 12w⁴ - 16w³

6 0
3 years ago
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