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3 years ago

Jacob leaves his summer cottage and drives home. After

Mathematics

1 answer:

krok68 [10]3 years ago

6 0

Answer:

A linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (a, b) and (c, d) then the slope can be written as:

a = (a - c)/(b - d)

Here y will represent the distance between Jacob and his house, and the variable x represents the time that he has ben driving.

In this case, we know that after driving for 5 hours, he is 112km from home.

Then we can write this point as (5h, 112km)

We also know that after 7 hours he is 15km from home.

Then we can write this point as (7h, 15km)

Then the slope of this function will be:

a = (15km - 112km)/(7h - 5h) = -48.5 km/h

Then the equation is:

y = -(48.5 km/h)*x + b

To find the value of b, we can replace the values of one of the points, for example in the point (7h, 15km)

This means that we need to replace x by 12h, and y by 15km, then we get:

15km = -( 48.5 km/h)*7h + b

15km + ( 48.5 km/h)*7h = b = 354.5 km

then the equation will be:

y = (-48.5 km/h)*x + 354.5 km

Now we want to answer: How long had Jacob been driving when he was 209 km from home?

Then we need to only replace y by 209km, and solve for x:

209km = (-48.5 km/h)*x + 354.5 km

209km - 354.5 km = (-48.5 km/h)*x

-145.5km = (-48.5 km/h)*x

-145.5km/( -48.5 km/h) = x = 3h

So he is 209km away from his home after driving for 3 hours.

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4 0

2 years ago

N/2 + 0.6 =2<br> PLS HELP

iogann1982 [59]

First, subtract 0.6 from both sides of the numbers and then simplify

Then multiply all terms by the same value to eliminate fraction denominators which gives us 2.8

So, n = 2.8

Hope it helps!

6 0

3 years ago

Explain how to solve 4|3x-1|+1=8

denis-greek [22]

4|3x - 1| + 1 = 8

4|3x - 1| = 8 - 1

4|3x - 1| = 7

|3x - 1| = 7/4

Now lets think, we have 3x - 1 in module, so either its 7/4 or -7/4, we will have 7/4 at the end because of it, so we may have 2 solutions in this case:

3x - 1 = 7/4

and

3x - 1 = -7/4

So let's see:

3x - 1 = 7/4

3x = 7/4 + 1

3x = 11/4

x = 11/12

3x - 1 = -7/4

3x = -7/4 + 1

3x = -3/4

x = -1/4

So we have two possible answers, x = 11/2 and x = -1/4

8 0

3 years ago

For the graph, identify the axis of symmetry, vertex, y-intercept, max/min, and domain and range

kirill [66]

In the present problem, it is presented a figure of a graph of a parabola with concavity facing up, what implies in that the graph will not have a Max., but a Min. value, and it is in the vertex.

Let us start with the A.O.S. (Axis Of Symmetry). For a parabola, it is the line that passes in the minimum point, that can be identified in the present figure as being in the x = - 1 point. And for this reason, we are able to answer the first part as:

A.O.S.: x = -1

Now, as mentioned above, the vertex lies in the minimum point, which is located in the x = -1 and with height y = 2. This allow us to answer the second part as:

Vertex: (-1, 2)

About the y-interception, it happens when the graph passes through the y-axis. It happens when x = 0, and the answer is just the value of Y where the graph assumes x=0, which is at:

Y-intercept: y = 4

Because the parabola has concavity facing up, the graph presents a value of minimum, but no maximum. And this is possible to be identified as the point where x = -1 and y = 2, which lead us to the following answer for the third part of the question:

Min.: (-1 , 2)

The domain for any second-order polynomial is the entire real number because there is no restriction for the value of x. And for this reason, the answer of the fourth part of the answer is:

Domain: All real numbers

About the range, for a parabola with the concavity facing up, it can be determined as all the real numbers bigger or equal to the minimum value of the function, which is y = 2. From this reason, we are able to answer the last part of the question as:

Range: All real numbers ≥ 2

8 0

1 year ago

Select the counterexample to this conjecture:

vredina [299]

The answer is .90º + 90º = 180º, <span>.90º is not an obtuse angle</span>

4 0

3 years ago