Three years after purchase, a car is estimated to be worth

1 answer:

7 0

Y - value
x - year

$24000=a\cdot3+b\\
19000=a\cdot5+b\\\\
24000=3a+b\\
-19000=-5a-b\\
---------\\
5000=-2a\\
a=-2500\\\\
b+3\cdot(-2500)=24000\\
b-7500=24000\\
b=31500\\\\
\boxed{y=-2500x+31500}

$

a)
$f(x)=-2500x+31500\\
f(x+1)=-2500(x+1)+31500\\
f(x+1)=-2500x-2500+31500\\
f(x+1)=-2500x+29000\\\\
f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\
f(x)-f(x+1)=-2500x+31500+2500x-29000\\
f(x)-f(x+1)=\boxed{2500}$

b)
$f(0)=-2500\cdot0+31500=\boxed{31500}$

c)
$f(10)=-2500\cdot10+31500\\
f(10)=-25000+31500\\
f(10)=\boxed{6500}$

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A radio station ordered hats and coffee mugs to give away as prizes. A total of 1,000 of these items were ordered, and 3 times a

marshall27 [118]

Answer:

The options are not shown, so i will answer in a general way.

Let's define the variables:

h = number of hats

m = number of mugs.

We know that a total of 1000 items were ordered, then:

h + m = 1000

We also know that we have 3 times more mugs than hats, this can be written as:

m = 3*h

Now we have the system of equations:

h + m = 1000

m = 3*h

To solve these, we usually start by isolating one of the variables in one equation and then replace that in the other equation, but in this case, we already have m isolated in the second equation, then we can replace that in the first equation to get:

h + m = 1000

h + (3*h) = 1000

Now we can solve this equation for h, and find the number of hats ordered.

4*h = 1000

h = 1000/4 = 250

There were 250 hats ordered.

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Which equation below represents a line with a slope of - 2/3 that passes through the point (-4.5 , 10)?

Lostsunrise [7]

Answer:

Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.

Let's try this with option C. To make things easier, convert -4.5 into decimal form: $-4\frac{1}{2}$ . Substitute $-4\frac{1}{2}$ for x and 10 for y in the equation, then solve: