Solve for X under the assumption that X>0 Enter your answer in interval notation using grouping symbols.

1.) What is slope and how is it determined from an graph?

Daniel [21]

1) Slope tell about the steepness of the line.

To find slope we look at the rise and run between 2 points.

attached the graph of line with slope

slope = $\frac{change in y values ( rise)}{change in x value (run)}$

= $\frac{2}{1}$

So slope = 2

2) we have x and y intercepts

x intercept is the point where the line crosses x axis

x intercept at x= 3

y intercept is the point where the line crosses y axis

y intercept at y= 6

3) Linear equation is y= 3x+2

function is f(x) = 3x+2

We can graph it using slope and y intercept

In f(x)= 3x + 2 , slope =3 and y intercept = 2

slope = 3, rise = 3 and run =1

The graph of f(x)= 3x+2 is attached below.

8 0

3 years ago

Given the following function, find the output value when x=3 f(x)=4x-5

Klio2033 [76]

Answer:

x=2

Step-by-step explanation:

4x-5=3

4x=3+5

4x=8/:2

x=2

6 0

3 years ago

Paola and her sister are eating lunch at a restaurant in Miami, Florida. They order two iced teas for $2.49 each, nachos for $15

slavikrds [6]

Answer:

1.82

Step-by-step explanation:

Add the prices to get the subtotal:

Sweet Tea:

2.49 * 2 = 4.98

4.98 + 15.99 + 4.99 = $25.96

The subtotal is $25.96

The sale's tax in Miami is 7% (the base 6% for FL, and the extra 1% for Miami).

$25.96 * 0.07 = 1.817 ≈ 1.82

The tax should be 1.82.

Hope this helps.

7 0

3 years ago

A bird caught a fish on the waters surface and flew in a stralght line diagonal to the water for 100 yards. Then, it dropped the

Masja [62]

Answer:

60 86.6

Step-by-step explanation:

Plato

3 0

3 years ago

Read 2 more answers

Please answer the question below (ABOUT VECTORS AND MAGNITUDE)

coldgirl [10]

(a) v appears to have a fixed direction along the positive x-axis. If ||u|| = 150 N, ||v|| = 220 N, then when θ = 30°, you have

u = (150 N) (cos(30°) i + sin(30°) j ) ≈ (129.904 i + 75 j ) N

v = (220 N) (cos(0°) i + sin(0°) j ) = (220 i ) N

(i and j are the unit vectors in the positive x and y directions)

and their sum is

u + v ≈ (349.904 i + 75 j ) N

with magnitude

||u + v|| ≈ √((349.904)² + (75)²) N ≈ 357.851 N ≈ 357.9 N

and at angle φ made with the positive x-axis such that

tan(φ) ≈ (75 N) / (349.904 N) → φ ≈ 12.098° ≈ 12.1°

(b) Letting θ vary from 0° to 180° would make v a function of θ :

u = (150 N) (cos(θ) i + sin(θ) j ) = (150 cos(θ) i + 150 sin(θ) j ) N

Then

u + v = ((220 + 150 cos(θ)) i + (150 sin(θ)) j ) N

→ M = ||u + v|| = √((220 + 150 cos(θ))² + (150 sin(θ))²) N

M = √(48,400 + 66,000 cos(θ) + 22,500 cos²(θ) + 22,500 sin²(θ)) N

M = 10 √(709 + 660 cos(θ)) N

(c) As a function of θ, u + v makes an angle α with the positive x-axis such that

tan(α) = (150 sin(θ) / (220 + 150 cos(θ))

→ α = tan⁻¹((15 sin(θ) / (22 + 15 cos(θ)))

(d) Filling in the table is just a matter of evaluating M and α for each of the given angles θ. For example, when θ = 0°,

M = 10 √(709 + 660 cos(0°)) N = 370 N

α = tan⁻¹((15 sin(0°) / (22 + 15 cos(0°))) = 0°

When θ = 30°, you get the same result as in part (a).

When θ = 60°,

M = 10 √(709 + 660 cos(60°)) N ≈ 323.3 N

α = tan⁻¹((15 sin(60°) / (22 + 15 cos(60°))) = 23.8°

and so on.

4 0

3 years ago