All categories

3 years ago

Which equation represents a line which is parallel to the line y=-3/4 x -2

2 answers:

8 0

Answer: Any equation that is of the form y = -3/4x + b, where b is a real number, will be parallel to y = -3/4x - 2.

Step-by-step explanation:

A parallel line has the same slope as the original line. Therefore, if the equation of the original line is y = mx+b, m (the slope) will remain the same, while b can change.

garri49 [273]3 years ago

6 0

Answer:

Any equation with the same slope: for example y=-3/4x+10

Step-by-step explanation:

You might be interested in

Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x? f(x) = (x – 8)2 – 56 f(x) = (x – 4)2 + 0 f(x) = (x + 8)2 – 7

kkurt [141]

Answer:

f(x) = x² + 8 - 16x

= x² - 16x + 8

= (x² - 16x + 64) - 64 + 8

= (x + 8)² - 56

4 0

3 years ago

Read 2 more answers

the graph shows the speed of a vehicle during the final 50 seconds of a journey at the start of the 50 seconds the speed is k me

Simora [160]

Answer:

a) 27 m/s

b) 30 m/s

c) i) 3

ii) Deceleration

Step-by-step explanation:

The question is not complete, the correct question is given as:

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

(a) Work out the average speed of the vehicle during the 50 seconds

(b) Work out the value of k.

(ii) Describe what this gradient represents

Answer:

The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m

a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:

$Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s$

b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.

$Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s$ c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time

$Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3$

ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²

6 0

3 years ago

The time needed to complete a final examination in a particular college course is normallydistributed with a mean of 80 minutes

Artist 52 [7]

Answer:

a) 0.023

b) 0.286

c) 10 students will be unable to complete the exam inthe allotted time.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 80 minutes

Standard Deviation, σ = 10 minutes

We are given that the distribution of time to complete an exam is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(completing the exam in one hour or less)

P(x < 60)

$P( x < 60) = P( z < \displaystyle\frac{60 - 80}{10}) = P(z < -2)$

Calculation the value from standard normal z table, we have,

$P(x < 60) =0.023= 2.3\%$

b) P(complete the exam in more than 60 minutes but less than 75 minutes)

$P(60 \leq x \leq 75) = P(\displaystyle\frac{60 - 80}{10} \leq z \leq \displaystyle\frac{75-80}{10}) = P(-2 \leq z \leq -0.5)\\\\= P(z \leq -0.5) - P(z < -2)\\= 0.309- 0.023 = 0.286= 28.6\%$

c) P(completing the exam in more than 90 minutes)

P(x > 90)

$P( x > 90) = P( z > \displaystyle\frac{90 -80}{10}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,

$P(x > 90) = 1 - 0.8413 = 0.1587 = 15.87\%$

15.87% of children of class will require more than 90 minutes to complete the test.

Number of children =

$\dfrac{15.87}{100}\times 60 = 9.52\approx 10$

Approximately, 10 students of class will require more than 90 minutes to complete the test.

4 0

3 years ago

Suppose you average 69mi/h traveling on the highway. If you drive for 5 hours, how far will you travel?

Mariulka [41]

345 mi; if you travel 69 miles per hour, and drive 5 hours, you have to multiply 69 and 5 to find how far you travel in 5-- 69 times 5 is 345.

7 0

3 years ago

Find m<1 and m<2 in the diagram below.

cluponka [151]

The equation to solve for angle 1 is reliant upon the fact that the measure of an exterior angle is equal to the sum of its interior angles. In our case, angle 1 = 38 + 70 which is 108. Now to find angle 2 we have to rely upon the fact that angles 1 and 2 are supplementary, or angle 2 = 180 - angle 1. We have angle 1 is 108 so angle 2 = 180 - 108 and angle 2 = 72

7 0

3 years ago