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2 years ago

Y=3x-2

Mathematics

1 answer:

Inessa [10]2 years ago

7 0

Answer:

a) $(x,y) = (3, 7)$ is a solution of the linear equation.

b) The rate of change of the equation is 3.

c) The y-intercept of the equation is -2.

d) Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?

Step-by-step explanation:

a) If $(x,y) = (3, 7)$ is a solution of the linear equation, then $f(3) = 7$ . If $x = 3$ , then the function evaluated at this value is:

$y = 3\cdot (3) -2$

$y = 7$

Hence, $(x,y) = (3, 7)$ is a solution of the linear equation.

b) The rate of change of the equation is represented by the slope of the function, which is the constant that multiplies the indepedent variable ( $x$ ). Hence, the rate of change of the equation is 3.

c) The y-intercept of the equation is the only constant of the equation. Hence, the y-intercept of the equation is -2.

d) A real-world scenario would be the following: Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?

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A circle is centered at J(3, 3) and has a radius of 12.

stealth61 [152]

Answer:

$(-6,\, -5)$ is outside the circle of radius of $12$ centered at $(3,\, 3)$ .

Step-by-step explanation:

Let $J$ and $r$ denote the center and the radius of this circle, respectively. Let $F$ be a point in the plane.

Let $d(J,\, F)$ denote the Euclidean distance between point $J$ and point $F$ .

In other words, if $J$ is at $(x_j,\, y_j)$ while $F$ is at $(x_f,\, y_f)$ , then $\displaystyle d(J,\, F) = \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}$ .

Point $F$ would be inside this circle if $d(J,\, F) < r$ . (In other words, the distance between $F\!$ and the center of this circle is smaller than the radius of this circle.)

Point $F$ would be on this circle if $d(J,\, F) = r$ . (In other words, the distance between $F\!$ and the center of this circle is exactly equal to the radius of this circle.)

Point $F$ would be outside this circle if $d(J,\, F) > r$ . (In other words, the distance between $F\!$ and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between $J$ and $F$ :

$\begin{aligned}d(J,\, F) &= \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}\\ &= \sqrt{(3 - (-6))^{2} + (3 - (-5))^{2}} \\ &= \sqrt{145} \end{aligned}$ .

On the other hand, notice that the radius of this circle, $r = 12 = \sqrt{144}$ , is smaller than $d(J,\, F)$ . Therefore, point $F$ would be outside this circle.

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3 years ago

Sin(60-theta)sin(60+theta)

ehidna [41]

Step-by-step explanation:

$\sin(60 - \theta) \sin(60 + \theta) \\ = \{ \sin(60) \cos( \theta) - \sin( \theta) \cos(60) \} \{ \sin(60) \cos( \theta) + \cos(60) \sin( \theta) \} \\ = \{ \frac{ \sqrt{3} }{2} \cos( \theta) - \frac{1}{2} \sin( \theta) \} \{ \frac{ \sqrt{3} }{2} \cos( \theta) + \frac{1}{2} \sin( \theta) \} \\ \\$

from difference of two squares:

${ \boxed{(a - b)(a + b) = ( {a}^{2} - {b}^{2} ) }}$

therefore:

$= \{ {( \frac{ \sqrt{3} }{2}) }^{2} { \cos }^{2} \theta \} - \{ {( \frac{ \sqrt{3} }{2} )}^{2} { \sin }^{2} \theta \} \\ \\ = \frac{3}{4} { \cos }^{2} \theta - \frac{3}{4} { \sin}^{2} \theta$

factorise out ¾ :

$= \frac{3}{4} ( { \cos }^{2} \theta - { \sin}^{2} \theta) \\ \\ = { \boxed{ \frac{3}{4} \cos(2 \theta) }}$

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3 years ago

Read 2 more answers

Two boats leave a port at the same time, one going north and the other traveling south. The northbound boat travels 18 mph fast

shutvik [7]

Answer:

10 hours

Step-by-step explanation:

Two boats leave a port at the same time, one going north and the other traveling south.

Southbound boat rate = 40 mph

The northbound boat travels 18 mph faster than the southbound boat.

Northbound boat rate = 40 + 18 = 58 mph

Two boats rate = 40 + 58 = 98 mph (this means they are apart 98 km after one hour)

Total distance = 980 miles

Total rate = 98 mph

Time $=980:98=10$ hours

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2 years ago

In a 3M Privacy Filters poll, 806 adults were asked to identify their favorite seat when they fly, and 492 of them chose a windo

Snowcat [4.5K]

Answer:

Step-by-step explanation:

If majority of adults prefer a window seat when they fly, it means that more than half or more than 0.5 of the population prefer a window seat when they fly.

We would set up the hypothesis test.

For the null hypothesis,

p = 0.45

For the alternative hypothesis,

p > 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 492

n = number of samples = 806

P = 492/806 = 0.61

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.61 - 0.5)/√(0.5 × 0.5)/806 = 6.24

From the normal distribution table, the p value < 0.00001

Since alpha, 0.01 < than the p value, then we would reject the null hypothesis. Therefore, at a 1% significance level, we can conclude that the majority of adults prefer a window seat when they fly.

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3 years ago

Nandeville and Henningsburg are 75 miles apart. On a map, the two cities are 5 inches apart. How many miles does 1 inch represen

soldier1979 [14.2K]

Answer:

5 miles

Step-by-step explanation:

because when u divide 10 and 2 you will get 5

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2 years ago