Find the simple interest on $900 for 18 months at a rate of 9.5% per year

1 answer:

6 0

To get the simple interest, we must use the formula: I= (p)(r )( t)
So, in this one we need to multiply $900x18x9.% and the answer will be $128.25. This is the amount of interest they are going to pay per year.

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If x2 + mx + m is a perfect-square trinomial, which equation must be true?

Volgvan

Your answer is x² + 2x + 1

7 0

3 years ago

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What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

3 years ago

You and your friend are selling tickets to a charity event. You sell 11 adult tickets and 8 student tickets for $158. Your frien

svetlana [45]

So what we have to do to solve this problem is to write down those values in 2 equations (one that represents what you sold and the other what your friend sold) compare them and find how much each ticket is worth.
First equation : 11x + 8y = 158
Where x = how much each adult ticket is
and y = how much each student ticket is

The second equation is : 5x + 17y = 152

Using the method of substitution , we can compare each equation side by side:
11x + 8y = 158
5x + 17y = 152
Now we need to set one of the variables of both equations so they are equal:
11(5)x + 8(5) = 158(5)
5(11)x + 17(11)x = 152(11)

55x + 40y = 790
55x + 187y = 1672

Then we subtract the second equation by the first one

55x-55x + 187y - 40y = 1672 - 790
147y = 882
y = 6
The we apply y to one of the equations to discover x :
11x + 8y = 158
11x + 8(6) = 158
11x + 48 = 158
11x = 110
x = 10

So the awnser is :
Each adult ticket (x) is $10
And each student ticket (y) is $8
I hope you understood my explanation,

7 0

3 years ago

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What are the dimensions of the simple shapes you obtained in part C? List dimensions for all your decompositions (sets of shapes

olasank [31]

Answer:

Option 1

Figure Length (feet) Width (feet)

small rectangle 14 6

large rectangle 20 7

Figure Base (feet) Height (feet)

triangle 6 6