Solve the equation for z -9=z/7

I have 30 coins consisting of nickels, and quarters. The total value of the coins is $4.10. How many of each kind do I have?

Vedmedyk [2.9K]

A=#nickels, b=#quarters

5a + 25b = 410 total value

5(a + 5b) = 410

a + 5b = 82

a + b = 30 total no. of coins

subtracting . . . 4b = 52

thus b = 13 and a = 17

13 quarters and 17 nickels = 13*25 + 17*5 = 410 = $4.10

5 0

4 years ago

Solve the compound inequality for x and identify the graph of its solution. x + 7 < 3 or x - 52 -1 O A. Solution: x < -4 o

aleksley [76]

Answer:

D. x < -4 or x ≥ 4

Step-by-step explanation:

You can eliminate choices A and B because the graph and the inequalities do not agree.

__

You can eliminate choice C because the first inequality tells you ...

x < some value

That means the shading will be to the left of an open circle.

This is only shown in Choice D.

_____

Additional comment

You can work multiple choice questions several different ways. I like to choose the simplest, which often means you do not actually need to work the problem. You only need to be able to identify ...

answers that are self-consistent
answers that are consistent with problem requirements
answers that are consistent with numerical and geometric facts

Here, we can eliminate incorrect answers by throwing out those that are not self-consistent and that are not consistent with the problem statement.

__

If we were to solve the inequalities, we would subtract 7 from both sides of the first one:

x +7 < 3

x < -4 . . . . . . subtract 7 from both sides

and we would add 5 to both sides of the second one:

x -5 ≥ -1

x ≥ 4 . . . . . . add 5 to both sides

If you write these inequalities so the symbols point left, you have ...

x < -4 or 4 ≤ x

This tells you shading is "outside" the segment between -4 and 4, and that there is an open-circle at x=-4. This is consistent with the number lines of choices B and D. However, these inequalities are not consistent with what is written in choice B.

6 0

3 years ago

F(x) = 12 + x X f(x) -3 -1 0 4 6

katen-ka-za [31]

9514 1404 393

Answer:

(-3, 9), (-1, 11), (0, 12), (4, 16), (6, 18)

Step-by-step explanation:

The function definition tells you that adding 12 to the x-value will give you the value of f(x).

-3 +12 = 9, for example

The (x, f(x)) values for the table are shown above.

7 0

3 years ago

It is estimated that t-weeks into a semester, the average amount of sleep a college math student gets per day S(t) decreases at

goldenfox [79]

Answer:

s(15)= $\frac{-3}{2} e^{15^{2} } +9.6$

Step-by-step explanation:

Before to getting started ,we have to consider the function which represents sleep decline rate S'(t) = $-3te^{t^{2} } \\$

Since this function is interpreted in this case as a rate of change, we can deduce this funcion is the first derivative of the function of average amount of sleep (S(t)).

In order to find S(t), we will integrate S'(t)

$\int\limits^ {} -3t3e^{t^{2} } \, dx \\$

This case corresponds to intergration by substitution

Substituting u= $x^{2} \\$

Computting the differential of u

$\frac{du}{dt} =2tdt\\$

Now, let's go back to our integral and write it in terms of u, using both definition of u and its defferential.

$\int\limits^{}-3te^{u} \, \frac{1}{2t}du \\\\\int\limits^{}\frac{-3}{2} e^{u}du\\$

The integral of a exponential function is itself. So the result is:

$\frac{-3}{2} e^{u} +c$

Now substitute u back in:

$\frac{-3}{2} e^{t^{2} } +c$

This answer correspond to function of average amount of sleep.

We know that when the semester begins (t=0) , math students sleep an average of 8.1 hours per day so we will use this info in order to find the value of c.

$s(0)=\frac{-3}{2} e^{0^{2} } +c=8.1\\\\\frac{-3}{2} +c=8.1$

Solve this equation

c=8.1+ $\frac{3}{2}$

c=9.6

Replacing the value of c on S(t)

S(t)= $\frac{-3}{2} e^{t^{2} } +9.6$

Now, let's to find the average of amount of sleep when 15 weeks has elapsed since the start date of the semester.

s(15)= $\frac{-3}{2} e^{15^{2} } +9.6$

4 0

3 years ago

Mira has breakfast at a restaurant. She leaves a 20\%20%20, percent tip of \$1.80$1.80dollar

mojhsa [17]

Answer:

Price of Mira Breakfast = 9 $ before tip

Step-by-step explanation:

Let say Mira's breakfast Price = B $

Tip she left = 20 %

20 % Tip amount = (20/100) B = 0.2B $

Tip Amount She left = $ 1.8

Equating Tip Amount

0.2B = 1.8

=> B = 9

Price of Mira Breakfast = 9 $ before tip

Step-by-step explanation:

6 0

3 years ago