1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bezzdna [24]
2 years ago
11

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) <em>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?</em>

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: <em>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?</em>

You might be interested in
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.

5 0
2 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) }}

3 0
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.

<u>Southbound boat rate</u> = 40 mph

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

<u>Northbound boat rate</u> = 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

3 0
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.

8 0
2 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

6 0
2 years ago
Other questions:
  • Y = a(b)*
    8·1 answer
  • I need Geometry help!!!!
    9·1 answer
  • Write the equation of a line that is parallel to y = -0.75x and that passes through the point (8,0).
    13·1 answer
  • Please help question in the picture
    6·1 answer
  • Find the values of a and b such that x² - 4x+9 = (x+a)² + b
    15·1 answer
  • Are the tables proportional why and why not
    13·1 answer
  • Cung Pí simplifies
    13·1 answer
  • A marching band is performing in a rectangular arrangement, with a width of $w$ people. The length consists of seven less people
    6·1 answer
  • Please I need help with this ASAP
    11·1 answer
  • Long division 1,755 divided by 27
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!