4.5/17 - x = 3/8 solve

We have

SinC/ c  = Sin A / a

Sin 71/ 26 = Sin A / 27

Sin A  = 27 Sin 71 /  26  = about .982

So°

Sin-1(.982)  = A  = 79. 08°

Then angle B = 180 - 71 - 79.08 = 29.92°

And b is given by

b/sin29.92  = 26/sin 71

b = 26sin29.92/sin71 =  about 13.72

But A could also be an obtuse angle = 180 - 79.08 =  100.92°

So we have

B = 180 - 71 - 100.92 = 8.08°

And we have

b / sin 8.08  = 26/sin71

b = 26sin8.08/sin 71 = 3.865

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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Final answer:

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. For example, 10¹, 10², 10³, and so forth are all different orders of magnitude.

Explanation:

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. For example, 10¹, 10², 10³, and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of 10 are said to be of the same order of magnitude. For example, the number 800 can be written as 8 x 10², and the number 450 can be written as 4.5 x 10². Thus, the numbers 800 and 450 are of the same order of magnitude: 10². Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10⁻⁹ m, while the diameter of the sun is on the order of 10⁹ m.

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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Answer:

[tex]\text{2 Dimes}< \text{2 Dollars}[/tex]      

Step-by-step explanation:

A dime has a value of 10 cents. It is a 10 cent coin.

So, the value of 2 dime = [tex]2\times10 = 20 \text{ cents}[/tex]

Now, 1 dollar consist of 100 cents.

1 dollar = 100 cents

so, the value of 2 dollars = [tex]2\times100 = 200\text{ cents}[/tex]

Comprinf, 2 dimes and 2 dollars, we have,

[tex]\text{2 Dimes}< \text{2 Dollars}[/tex]

as

[tex]\text{20 Cents}< \text{200 Cents}[/tex]

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

A system of linear equations can be used to model the given situation. The number of rows with exactly 2 passengers can be found by solving the equation 2x = 12, and the number of rows with exactly 3 passengers can be found by solving the equation 3y = 12.

To write a system of linear equations, we need to translate the given information into algebraic expressions.

Let n be the number of packets of crackers.

According to the problem:

To determine the number of rows with exactly 2 passengers and 3 passengers:

The system of linear equations is:

p = 2n + 9

pn = 3(2n + 9)

2x = 12

3y = 12

We can solve this system of equations to find the values of x and y.

6.5 gallons = 24.6052 liters

6.5 has 2 significant figures, so it would need to be 25 liters

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.

Answer:

3/7

Step-by-step explanation:

To find the measure of ANGLE AXC, we assume Angle AXB is supplementary to Angle AXC. Solving the supplementary angle equation with the given expressions, we find x = 16. Substituting x back into the expression for Angle AXC, we determine its measure to be 121 degrees.

The question asks to find the measure of ANGLE AXC given that the measure of Angle AXC is represented by the expression 8x-7 and Angle AXB is represented by the expression 3x+10. Without additional context, it is not clear whether Angle AXB is related to Angle AXC in a way that would allow us to solve for x. However, if we assume Angle AXC and Angle AXB are supplementary angles (which sum to 180 degrees), we could set up the equation 8x - 7 + 3x + 10 = 180. If we solve this equation, we get:

Once we have found that x = 16, we can substitute it back into the expression for Angle AXC:

Therefore, the measure of ANGLE AXC is 121 degrees.

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.

Answer:

The quotient is:

                    [tex]xy^6+2y-6[/tex]

Step-by-step explanation:

We are asked to find the quotient of the mathematical expression which is given in terms of variable x and y is represented as:

[tex]=\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}[/tex]

Here the numerator is:

[tex]6x^2y^8+12xy^3-36xy^2[/tex]

and the denominator is:

[tex]6xy^2[/tex]

We can also represent our numerator term by the method of factoring it as:

[tex]6x^2y^8+12xy^3-36xy^2=6xy^2(xy^6+2y-6)[/tex]

Hence, our expression gets converted by replacing the numerator term to:

[tex]\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=\dfrac{6xy^2(xy^6+2y-6)}{6xy^2}\\\\\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=xy^6+2y-6[/tex]

                 Hence, the quotient is:

                  [tex]xy^6+2y-6[/tex]

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.