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White raven [17]
3 years ago
12

You saved $300 to spend over the summer. You decide to budget $50 to spend each week.

Mathematics
1 answer:
Oduvanchick [21]3 years ago
4 0

Answer:

<u>Part c) </u>

The Slope of the line is: m=-50 and represents the amount of money spent per week.

<u>Part d) </u>

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

Step-by-step explanation:

To solve this question we shall look at linear equations of the simplest form reading:

y = mx+c    Eqn(1).

where:

y: is our dependent variable that changes as a function of x

x: is our independent variable that 'controls' our equation of y

m: is the slope of the line

c: is our y-intercept assuming an x⇔y  relationship graph.

This means that as x changes so does y as a result.

<u>Given Information: </u>

Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:

c=300

The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:

m=50

So finally we have the following linear equation of:

y= - 50x + 300    Eqn(2).

Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.

So with respect to Eqn(2), and different weeks thus various x values we have:

Week 1: x=1 we have y= -50 *1 + 300 = -50 +300 = 250 dollars.

Week 2: x=2 we have y= -50 *2 + 300 = -100 +300 = 200 dollars.

Thus having understood the above we can comment on the questions asked as follow:

<u>Part c) </u>

The Slope of the line is: m=-50 and represents the amount of money spent per week.

<u>Part d) </u>

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

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If the gradient of a line joining the points (-2, 6) and (5, b) is 14.<br> Find the value of b.
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Answer:

b = 104

Step-by-step explanation:

Slope is expressed as;

m = y2-y1/x2-x1

14 = b - 6/5-(-2)

14 = b - 6/5+2

14 = b-6/7

Cross multiply

b-6 = 14 * 7

b - 6 = 98

b  = 98 + 6

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3 years ago
Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find
densk [106]

Answer:

x=4

Step-by-step explanation:

<u>Step 1</u>:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

<u>step 2:-</u>

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=\frac{-70}{13}

we can not choose negative value so x value is 4

Final answer:- x = 4

<u>verification:-</u>

<u></u>AC^2 = AB^2 + BC^2<u></u>

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

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