Chandra has 2 liters of a 14% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of a 34% solution?

Answer:

A: (-2,4)

Step-by-step explanation:

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The domain of the given relation includes the set of all x-values in the relation, which is: {–4, −2, 3}.

The domain of a relation is the set of all possible x-values (input), while the y-values are the range.

Given the relation, {(−4, 3), (3, 6), (−2, 1), (3, 6)}:

Domain of the relation is: {–4, −2, 3}.

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Final answer:

The system of equations 9x - 3y = 3 and 3x + 8y = -17 is solved using elimination. By multiplying the second equation by 3 and subtracting the first from the resulting equation, y is eliminated and found to be -2. Substituting y into one of the original equations then gives x as -1/3.

Explanation:

Solving a System of Equations by Elimination

To solve the system by elimination, we aim to eliminate one of the variables by combining the equations. We have the equations 9x - 3y = 3 and 3x + 8y = -17. Let's multiply the second equation by 3 to align the coefficients of x.

After multiplication, our system looks like this:

Now, subtract Equation 1 from Equation 2, which eliminates the x variable:

-3y - 24y = 3 - (-51)

-27y = 54

To find the value of y, divide both sides by -27:

y = -2

Now that we have y, we can substitute it back into one of the original equations to find x:

3x + 8(-2) = -17

3x - 16 = -17

3x = -1

x = -1/3

So the solution to the system is x = -1/3 and y = -2.

To cover 348 tiles when one bottle can cover 20 tiles, you divide 348 by 20 which equals 17.4, and then round up to 18 bottles since you can't buy a fraction of a bottle.

To determine how many bottles of paint are needed to cover 348 tiles when one bottle covers 20 tiles, you should divide the total number of tiles by the number of tiles that can be covered by one bottle. The calculation is as follows:

Divide 348 (the total number of tiles) by 20 (the number of tiles one bottle of paint can cover).

348 \/ 20 = 17.4

Since you can't buy a fraction of a bottle, you would need to round up to the next whole number. Therefore, you need 18 bottles of paint to cover all 348 tiles.

On Saturday, 285 hamburgers were sold.

A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. And an equation system is a simultaneous equation.

Given, a local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday.

Let x represents the number of hamburgers sold and y represents the number of cheeseburgers sold.

So, x + y = 510     {equation 1}

According to the question,

there were 60 more cheeseburgers sold than hamburgers.

x = y+ 60

We have a system of equations,

Substituting the value of x to the equation 1,

y+60+ y = 510

2y = 510 - 60

y = 450 / 2

y = 225

Then, x = 285

Therefore, 285 hamburgers were sold on Saturday.

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The line y = 4x + 2 is graphed and attached with the answer.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have a equation that represents a line as -

y = 4x + 2

We can graph the given equation as shown in the figure attached.

Therefore, the line y = 4x + 2 is graphed and attached with the answer.

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Answer:

A

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given that

sin 48° cos 15° - cos 48° sin 15°

As we know that,

[tex]\sin A\cos B-\cos A\sin B=\sin(A-B)[/tex]

So, we get that

[tex]A=48\textdegree\\B=15\textdegree[/tex]

Now, put it in the above expression.

[tex]\sin (A-B)=\sin(48-15)=\sin 33\textdegree[/tex]

Hence, Option 'D' is correct.

The volume of the prism is 927 cubic Inches.

This is defined as the measure of how much space there is within a three-dimensional object.

Area of Octagon A = 1/2 x apothem x perimeter

A= 1/2 x 4.83 x 4(8) = 77.28

Volume  = Area of the base × height

                = 77.28 x 12 = 927 cubic inches.

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Answer:

Paul is 70 kg, John is 62 kg and David is 65 kg.

Step-by-step explanation:

Let x the mass for each person.

Paul = x

John is lighter than Paul, so John = x-8

David's mass is 5 kg less than John's, so David = x-5

Solution:

Make an equation.

x + (x-8) + (x-5) = 197

3x -13 = 197

3x = 197 + 13

3x= 210, then divide both side by 3, to get 70.

Do substitution to get a correct answer.

70+62+65= 197

197= 197

To subtract[tex]\(\frac{11}{12} - \frac{5}{8}\), find a common denominator (24), then subtract numerators: \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex] in simplest form.

To subtract the fractions [tex]\(\frac{11}{12} - \frac{5}{8}\[/tex]), we need to find a common denominator.

The least common multiple (LCM) of 12 and 8 is 24.

Now, rewrite both fractions with the denominator 24:

[tex]\[\frac{11}{12} \times \frac{2}{2} = \frac{22}{24}\]\[\frac{5}{8} \times \frac{3}{3} = \frac{15}{24}\][/tex]

Now, subtract:

[tex]\[\frac{22}{24} - \frac{15}{24} = \frac{22 - 15}{24} = \frac{7}{24}\]So, \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex]

erform a simple calculation to match the screen size of a standard TV to that of a widescreen TV. If you currently have a 4:3 TV and you want to continue watching 4:3 on a widescreen TV, multiply the diagonal length of the older TV model by 1.22. The result would be the diagonal screen size that the widescreen TV would have to be to match the old model.

The value of 'm' in the equation y=mx represents the slope of the line. However, without specific 'x' or 'y' values or a complete equation like y=mx+b, it is impossible to determine the value of 'm'.

The formula y=mx is the slope-intercept form of a linear equation where y is the dependent variable, m is the slope, and x is the independent variable. However, in this particular case, the equation provided is not complete in this form because there is no specific 'x' or 'y' value provided, and so it's not possible to calculate 'm' directly from this equation. Instead, in a more complete example, like y = 3x, you could identify 'm' as 3 by simply looking at the coefficient of 'x'. In order to clarify your equation, please provide either specific values of 'x' and 'y', or a complete equation in the format y = mx + b, where b is the y-intercept.

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