Part 1 : When solving systems of equations, how do you determine what method to use?

Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.

–y + 3x = 6
y = –6x + 12


6x – 4y = 54
–9x + 2y = –69


2y = x + 1
–2x – y = 7
...?

To make 20 cups of Jessica's favorite purple paint, she needs approximately 6.67 cups of blue paint and 10 cups of red paint.

To find the number of cups of blue and red paint Jessica needs to make 20 cups of her favorite purple paint, we need to set up a proportion based on the ratios of blue paint and red paint in her favorite shade.

Since Jessica uses 1/3 cup of blue paint and 1/2 cup of red paint to make her favorite shade, we can set up the proportion:

1/3 cup of blue paint / 1/2 cup of red paint = x cups of blue paint / 20 cups of purple paint.

To solve for x, we can cross multiply and divide:

x = (1/3 cup of blue paint)(20 cups of purple paint) / (1/2 cup of red paint) = 20/3 = 6.67 cups of blue paint.

So, Jessica needs approximately 6.67 cups of blue paint and 10 cups of red paint to make 20 cups of her favorite purple paint.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{13.6{\text{ units}}}[/tex]. Option (d) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

[tex]\boxed{{\text{Distance}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} }[/tex]

Given:

The coordinates of the vertices of the polygon are [tex]\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right).[/tex]

Explanation:

The coordinates of the vertices of the polygon are [tex]\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right).[/tex]

The distance between points [tex]\left( { -2, 7} \right)[/tex] and [tex]\left( {2, 5} \right),[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 - 2} \right)}^2} + {{\left( {5 - 7} \right)}^2}}\\&= \sqrt {16 + 4}\\&= \sqrt {20}\\&= 4.47\\\end{aligned}[/tex]

The distance between points [tex]\left( {2, 5} \right)[/tex] and [tex]\left( {- 1, 5} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 1 - 2} \right)}^2} + {{\left( {5 - 5} \right)}^2}}\\&= \sqrt {9 + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]

The distance between points [tex]\left( {- 1, 5} \right)[/tex], and [tex]\left( { - 1, 3} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 1} \right)}^2} + {{\left( {3 - 5} \right)}^2}}\\&= \sqrt {0 + 4}\\&= \sqrt4\\&= 2\\\end{aligned}[/tex]

The distance between point [tex]\left( { -2, 7} \right)[/tex] and [tex]\left( { - 1, 3} \right)[/tex] can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 2} \right)}^2} + {{\left( {3 - 7} \right)}^2}} \\&= \sqrt {1 + 16} \\&= \sqrt {17} \\&= 4.13\\\end{aligned}[/tex]

The perimeter of the polygon can be calculated as follows,

[tex]\begin{aligned}{\text{Perimeter}} &= 4.47 + 3 + 2 + 4.13\\&= 13.6\\\end{aligned}[/tex]

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{13.6{\text{ units}}}.[/tex] Option (d) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: perimeter, shape, perimeter of shape below, Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

The limit as x approaches negative infinity of (1.001)^x is 0, because as we raise a number slightly larger than 1 to increasingly negative exponents, the results get closer and closer to zero.

The student is asking about the limit of a function as x approaches negative infinity, specifically for the function (1.001)^x. When evaluating this limit, it is essential to understand how exponential functions behave as the exponent becomes very large or very negative. Since 1.001 is greater than 1, raising it to increasingly negative exponents will result in values that approach zero. Therefore, the limit as x approaches negative infinity of (1.001)^x is 0.

Understanding the behavior of functions at infinity can be connected to the general concept where, for example, the reciprocal of a number as it approaches zero from the positive side (1/x) goes to positive infinity and from the negative side (1/x) goes to negative infinity. However, when evaluating the limit at negative infinity for our function, we must consider the base of the exponential function, which dictates that the function's values descend towards zero.

Final answer:

After performing the multiplication 9/8*0.97, which equals 1.09125, we find that this number is closest to 1 as compared to the other options provided (0.5 and 2).

Explanation:

To determine which number 9/8x0.97 is closer to among the options 0.5, 1, and 2, we need to perform the multiplication. The fraction 9/8 can be converted to a decimal by dividing 9 by 8, which gives us 1.125. Next, we multiply 1.125 by 0.97 to find the result of the original expression.

Multiplying these two numbers gives us 1.125 x 0.97 = 1.09125. Comparing this result to the options provided, we can clearly see that 1.09125 is closest to 1.

Therefore, the answer to the question is (b) 1, since 1.09125 is very close to 1 and further away from 0.5 and 2.

Answer:11 chaperones

Step-by-step explanation:1st you do 99÷18=5.5

2nd you make 5 circles then put the number 2 in them

3rd you make a half circle and put the number 1

4th you add 2+2+2+2+2+1

Answer: B. $300

Step-by-step explanation: 3/5 * 500 = 300

Answer:

9.61 and 10.24

Step-by-step explanation:

The answer is D: Mark the points of intersection between circle A and line AB.

The solution is:

B. Create circle A with point B on the original circle., these is a step in constructing an inscribed square using technology.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

An equilateral triangle is one in which the three angles and sides are equal. And this can be inscribed in another given shape. Inscribed triangle implies constricting a given triangle within the boundaries of another given shape, e.g circle. In this case, the edges of the triangle touches internally the circumference of the circle.

Draw circle A with point B on the circumference of the circle

Put your compass at B with radius equal to the radius of circle A

Draw an arc to cut the circumference of the circle

Draw another arc to cut the circumference on the other segment of the circle

Join the points where the arcs cut the circumference to construct the equilateral triangle.

Hence, The solution is:

B. Create circle A with point B on the original circle., these is a step in constructing an inscribed square using technology.

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The data provided does not include specific information needed to calculate the empirical probability of a randomly selected single parent in the U.S. military being in the Army.

Unfortunately, the provided information does not give specific numbers for single parents actively serving in the different branches of the U.S. military, including the Army. Therefore, it is not possible to accurately calculate the empirical probability this question is asking for. However, if such data were available, you would calculate the empirical probability of a randomly selected single parent in the U.S. military being in the Army by dividing the number of single parents in the Army by the total number of single parents on active duty.

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The total income tax in the year is [tex]\boxed{\$ 15000}.[/tex]

Further explanation:

Given:

The total taxable income is [tex]\$75000.[/tex]

The rate of tax on the first [tex]\$25000[/tex] is [tex]10\%.[/tex]

The rate of tax on the next [tex]\$25000[/tex] is [tex]20\%.[/tex]

The rate of tax on the next [tex]\$25000[/tex] is [tex]30\%.[/tex]

Explanation:

The rate of tax on the first [tex]\$25000[/tex] is [tex]10\%.[/tex]

The income tax on the first [tex]\$25000[/tex] can be obtained as follows,

[tex]\begin{aligned}{\text{Income tax}}&=\frac{{10}}{{100}}\times 25000\\&= \$ 2500\\\end{aligned}[/tex]

The rate of tax on the next [tex]\$25000[/tex] is [tex]20\%.[/tex]

The income tax on the next [tex]\$25000[/tex] can be obtained as follows,

[tex]\begin{aligned}{\text{Income tax}}&= \frac{{20}}{{100}}\times 25000\\&=\$5000\\\end{aligned}[/tex]

The rate of tax on the next [tex]\$25000[/tex] is [tex]30\%.[/tex]

The income tax on the next \$25000 can be obtained as follows,

[tex]\begin{aligned}{\text{Income tax}}&=\frac{{30}}{{100}}\times 25000\\&=\$ 7500\\\end{aligned}[/tex]

The total income tax can be obtained as follows,

[tex]\begin{aligned}{\text{Total income tax}} &= \$ 2500 + \$ 5000 + \$ 7500\\&= \$ 15000\\\end{aligned}[/tex]

Hence, the total income tax in the year is [tex]\boxed{\$ 15000}[/tex].

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Income Tax

Keywords:Total taxable income, tax, $75000, rate, 10 percent, 20 percent, final, income tax, 30 percent, salary.

Answer: B (38m/s)

Explanation: The vertical component of a vector such as velocity is the magnitude of the vector multiplied by the sine of the angle.