1.5d + 3.25 = 1 + 2.25d ---What are the steps to find x?

We want to find the concentration (percentage of salt in volume) in a mix of 25 mL of water an 125 mL of a 20% salt solution.

We will find that the concentration is: 16.7%

Let's see how to get that.

The concentration will be given by the quotient between the amount of salt and the total volume.

The amount of salt will be given by:

s = 125mL*0.2

This is because a 20% of these 125 mL are salt.

And the total volume is just the sum between the volume of water (25 mL) and the volume of salt solution (125 mL)

v = 25 mL + 125 mL = 150 mL

Then the concentration will be:

s/v = 0.2*(125 mL)/(150 mL) = 0.167

Now we multiply this by 100% to get:

0.167*100% = 16.7%

The concentration of the mixture will be 16.7%, so when we mixed the solution with water the concentration decreased, as expected.

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Answer:

This is an example of inductive reasoning.

Step-by-step explanation:

You eat at several Mexican restaurants and decide that Mexican food is hot. This is an example of inductive reasoning.

Inductive reasoning is defined as the type of reasoning, where multiple premises are considered and all are believed to be true. These are combined to obtain a specific conclusion.

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

 [tex]|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}[/tex]

Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.

[tex]|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5 [/tex]

[tex]|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6 [/tex]

[tex]|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4 [/tex]

[tex]|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \ \sqrt{25}=5 [/tex]

[tex]|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4 [/tex]

Answer: B and D

Answer:  The correct option is (A) [tex]7\dfrac{1}{24}.[/tex]

Step-by-step explanation:  We are given to perform the following indicated operation :

[tex]E=1\dfrac{2}{3}+5\dfrac{3}{8}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following rule :

[tex]a\dfrac{b}{c}=\dfrac{ac+b}{c}.[/tex]

From (i), we get

[tex]E\\\\=1\dfrac{2}{3}+5\dfrac{3}{8}\\\\\\=\dfrac{5}{3}+\dfrac{43}{8}\\\\\\=\dfrac{40+129}{24}\\\\\\=\dfrac{169}{24}\\\\\\=7\dfrac{1}{24}.[/tex]

Thus, the required answer is [tex]7\dfrac{1}{24}.[/tex]

Option (A) is CORRECT.

Answer:

3/7

Step-by-step explanation:

Answer:  81/8 simplified form = 10 1/8 mixed form

Step-by-step explanation:

Hi, to answer this question we have to solve the expression:

First, we have to convert the mixed fractions into improper fractions:

-2 1/4 = -(2 x 4 +1) /4 = -9/4

-4 1/2 = -( 4 x 2 + 1 ) / 2 = -9/2

Next, we have to simply multiply both numbers:

-9/4 x -9/2 = 81/8 simplified form = 10 1/8 mixed form

Feel free to ask for more if needed or if you did not understand something.

Answer-

The sequences of transformations that maps △ABC to △A′B′C′ are

Solution-

The coordinates of the vertices of ΔABC are

A = (−4, 6)

B = (−2, 2)

C = (−6, 2)

The coordinates of the vertices of ΔA′B′C′ are

A′ = (2, 6)

B′ = (0, 2)

C′ = (4, 2)

As all the y-coordinates of all the function are same, so the triangle is neither translated up or down (∵ (x, y) → (x, y±k)), nor reflected over x-axis(∵ (x, y) → (x, -y)).

As the signs of x-coordinate is changed, it might be reflected over y axis,

Rule for reflection over y axis is,

(x, y) → (-x, y)

so,

A" = (4, 6)

B" = (2, 2)

C" = (6, 2)

As the x-coordinates of vertices of ΔA′B′C′ are 2 units less than that of ΔA"B"C"

So it is then translated 2 units left.

Therefore, the sequences of transformations that maps △ABC to △A′B′C′ are

Answer:

Here is my test answer

Step-by-step explanation:

Answer:

This is proved with two property of equality subtraction and multipication property.

Step-by-step explanation:

Given [tex]\frac{x}{6} + 2 = 15[/tex]

By subtraction property of equality

           [tex]\frac{x}{6} +2 - 2 = 15 - 2[/tex]

      ⇒  [tex]\frac{x}{6} = 13[/tex]

Now by multiplication property

          x = 13(6) = 78

Hence the result.

Given the statements, we cannot conclude whether Mike will or will not go to the bank; therefore, no conclusion is possible.

The statement 'If Mike gets paid today, then Mike will go to the bank' sets up a conditional relationship where Mike going to the bank is dependent on whether he gets paid or not. The second statement 'Mike did not get paid today' is a fact that allows us to draw a conclusion about the first conditional statement.

Since the condition for Mike going to the bank (getting paid) is not met, we cannot conclude that Mike will go to the bank based on the information given. However, this also does not mean that Mike will not go to the bank for some other reason. Therefore, the only valid conclusion we can draw here is option D: 'No conclusion is possible' about Mike's action related to going to the bank.

x - 32 = 73

 to get x add 32 to 73

32 +73 = 105

x = 105

Answer:

Step-by-step explanation:

First, we need to consider a few rules about transformation of functions, specifically about the negative sign and the division of the function by a number.

The negative sign indicates that the function has to be reflected regarding the vertical axis. The normal function is like the third option, and the reflect one is like the last graph.

On the other hand, the fraction presents a contraction of the function size, but this characteristics is not enough to select the right graph, because third and fourth options have the same size.

Therefore, according to the negative sign in the given function, the correct answer is the last graph.

We want to see which one of the given graphs is the graph of the function:

f(x) = (-1/2)*x^3

The correct graph is the last one, positive at the left, when x is negative, and negative at the right, when x is positive.

Let's analyze our function, first we know that the parent cubic function:

g(x) = x^3

Is negative for negative values of x and positive for positive values of x, then the graph is below the horizontal axis at the left, and above the horizontal axis at the right.

But our function multiplies this by a negative number, -1/2.

Then that is inverted, we should see that at the left, the graph is above the horizontal axis, and at the right the graph is below the horizontal axis.

Then the correct option is the last graph.

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