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2 years ago

A stack of magazines is 4 2/5 inches high. Each magazine is 2/5 inch thick.

Mathematics

1 answer:

oee [108]2 years ago

7 0

Answer:

Equation:(4 2/5)/2/5=? ; estimate: a

little more than 10 magazines; answer:

11 magazines in the stack.

Step-by-step explanation:

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When salt and water are combined, they form a salt or saline solution. How much ml of water must be added to 150 mL of an 80% sa

Vinvika [58]

Answer:

We must add 400 ml of water.

Step-by-step explanation:

We can use the following equation:

$C_{i}V_{i}=C_{f}V_{f}$

Where:

C(i) is the initial concentration of the solution (80%)
C(f) is the final concentration of the solution (30%)
V(i) is the initial volume (150 ml)
V(f) is the final volume

Now, we just need to solve the equation for V(f).

$V_{f}=\frac{C_{i}V_{i}}{C_{f}}$

$V_{f}=\frac{80*150}{30}$

$V_{f}=400\: ml$

Therefore, we must add 400 ml of water.

I hope it helps you!

3 0

3 years ago

The first five terms of an arithmetic sequence are 8, 13/2, 5, 7/2, and 2. Which function, f(x), could be used to describe the x

juin [17]

Answer:

f(x) = 8 - 1.5x

Step-by-step explanation:

Here, we want to write a function that can be used to describe the x th term of the sequence

Mathematically, this can be calculated by looking at the numbers in the sequence

The difference between each successive term

is -1.5 ( 6.5-8, 3.5 -5)

So the formula for then x th term will be;

f(x) = 8 - 1.5x

where x refers to the number of the term , for example the 4th term

5 0

3 years ago

Read 2 more answers

Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$