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lesantik [10]
3 years ago
12

A mixture of alcohol and water contains a total of 36 oz of liquid. There are 9 oz of pure alcohol in the mixture. What percent

of the mixture is water? What percent is alcohol?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
7 0

First, we can start off with a fraction:

9/36 = 1/4

Now that we have this fraction, we multiply by 25:

25/100

This can be changed into a percent:

25%

100 - 25 = 75

25% is alcohol and 75% is water

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Part A- Create a fourth degree polynomial in standard form. How do you know it is in standard form?
Alexeev081 [22]

Answer:

(a)2x^4-9x^3+x^2+x-5

Step-by-step explanation:

(a)The degree of a polynomial is the highest power of the unknown variable in the polynomial.

A polynomial is said to be in standard form when it is arranged in descending order/powers of x.

An example of a fourth degree polynomial is: 2x^4-9x^3+x^2+x-5

We know the polynomial above is in standard form because it is arranged in such a way that the powers of x keeps decreasing.

(b)Polynomials are closed with respect to addition and subtraction. This is as a result of the fact that the powers do not change. Only the coefficients

change. This is illustrated by the two examples below:

(2x^5-3x^2+x)+(3x^5-5x^2)\\=2x^5-3x^2+x+3x^5-5x^2\\=5x^5-8x^2+x\\$Similarly\\(2x^5-3x^2+x)-(3x^5-5x^2)\\=2x^5-3x^2+x-3x^5+5x^2\\=-x^5+2x^2+x

The degrees do not change in the above operations. Only the number beside each variable changes. Therefore, the addition and subtraction of polynomials is closed.

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3 years ago
((10 - 3)2 + 7)- 4 + 62
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Step-by-step explanation:

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If 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible v
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3 years ago
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
AveGali [126]

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing  a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-4-0}{0-1}=4

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4)  in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-1.5-0}{0-1.5}=1

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5)  in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

6 0
3 years ago
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