All categories

3 years ago

Directions: Tables, graphs (use grid points!), and stories are provided. For each case:

Mathematics

1 answer:

castortr0y [4]3 years ago

5 0

Answer:

See explanations below

Step-by-step explanation:

Using the coordinate points in the table (0, 4) and (2, 9)

Slope m = y2-y1/x2-x1

m = 9-4/2-0

m = 5/2

slope = 5/2

Get the y-intercept

Substitute m = 5/2 and (0,4) into y = mx+c

4 = 5/2(0) + c

4 = 0+c

c = 4

y-intercept is 4

Get the equation

Recall that y = mx+c

y = 5/2x + 4

Using another 2 points (2,9) and (4, 14)

Slope = 14-9/4-2

Slope = 5/2

Since the slope is the same for the coordinates, hence the the equation is correct

You might be interested in

1. Emmanuel bought 28 lb of potting soil this week. This amount is 4 lb more than twice the amount of potting soil he bought las

fiasKO [112]

What do you have so far?

4 0

4 years ago

How do you do these questions?

Lady bird [3.3K]

Answer:

(e) csc x − cot x − ln(1 + cos x) + C

Step-by-step explanation:

(e) ∫ (1 + sin x) / (1 + cos x) dx

Split the integral.

∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx

Multiply top and bottom of first integral by the conjugate, 1 − cos x.

∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx

Pythagorean identity.

∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx

Divide.

∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx

Integrate.

csc x − cot x − ln(1 + cos x) + C

= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx

The error function is odd (erf(-x) = -erf(x)), so:

= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx

= 0

7 0

3 years ago

A department store sells a pair of shoes with an 87% markup. If the store bought the pair of shoes for $55.25, what is the selli

kolbaska11 [484]

Markup means they sell it for that percentage more than they bought it for. First let's calculate how much they will mark it up for:

$\sf 55.25\cdot 87\%$

Convert 87% into a decimal(87/100):

$\sf 55.25\cdot 0.87$

Multiply:

$\sf\approx 48$

This is how much they'll mark it up, now let's add it to how much they bought it for to find out the selling price:

$\sf 48+55.25\approx\boxed{\sf \$ 103}$