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3 years ago

14

Herman saves 22% of his monthly paycheck so he can buy a new car. He earned $825 last month. How much money did Herman save for

his new car last month

1 answer:

djyliett [7]3 years ago

8 0

Answer:$181.5

Step-by-step explanation:

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Find the area of the regular polygon below and round your answer to the nearest tenth.

stira [4]

The 9-sided polygon will have a central angle between the vertex and the center of one side of 360°/(2*9) = 20°. Then the apothem is
a = (6 in/2)*cot(20°) ≈ 8.242432 in
The perimeter is 9*6 in = 54 in, so the area is
A = (1/2)Pa = (1/2)*(54 in)*(8.242432 in) ≈ 222.5 in²

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3 years ago

On Monday morning,there were 30 tickets available for a concert if 1/3 of the tickets were sold on Monday and 1/5 of those left

lianna [129]

I think the answer would be 16, Hope this helps

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3 years ago

I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$

$f'(x)=12x^2+26x-12$

$f''(x)=24x+26$

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here: x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

$24(-2.6)+25$

$-37.5$

So we have a maximum at x=-2.6.

$24(.4)+25$

$9.6+25$

$34.6$

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

$y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56$

I'm shoving this into a calculator:

$y=-58.4654411$

So the approximate relative minimum is (0.4,-58.5).

If you graph $y=4x^3+13x^2-12x-56$ you should see the graph taking a dip at this point.

3 0

3 years ago

Since you have 15% off of $24.99, you should have found (on the previous Slide) that you will have to pay 85% of $24.99. Using t

Ahat [919]

Answer: $21.24

Step-by-step explanation:

Well if you apply the discount you will have to pay 85% of the price which is already said .

So 85% of 24.99 will give you the cost of the shirt.

0.85 * 24.99 = 21.2415

TO the nearest penny will be 21.24

7 0

3 years ago

The girl went to the store at 10:45 and lasted 1 hour and 30 minutes . At what time did she come out of the store

mars1129 [50]

She left at 12:15. 10:45 plus 1 hour= 11:45 + 15 min +12 +15= 12:15

4 0

3 years ago