2x+3y=-5
3x-5y=21

The value of y that satisfies the system of the equations above is
A) 2
B)7
C) -3
D)There is no solution

Final answer:

The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.

Explanation:

To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.

Using the formula, we get:

A = (1/2) × (18 inches + 22 inches) × 8.5 inches

A = (1/2) × 40 inches × 8.5 inches

A = 20 inches × 8.5 inches

A = 170 square inches

So, the area of the trapezoid is 170 square inches.

The equation will have infinitely many solutions.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

This equation has infinitely many solutions.

3x - 3x - 2 = - 2

3x - 3x = 0

3x = 3x

This equals each other meaning infinite solutions.

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Point O is the center of the circle passing through points D, E, and F because it is equidistant from all these points. This is proven by the construction of the perpendicular bisectors of DE and EF and their intersection at point O.

The point O is the center of the circle that passes through the three points D, E, F because it is equally distanced from each of them. Here's why: When you draw perpendicular bisectors of lines DE and EF, you're effectively finding the midpoint of each line. Then, when these bisectors intersect at point O, point O is equidistant from points D and E (due to being on the bisector of DE), and from points E and F (due to being on the bisector of EF).

By definition, the center of a circle is a point that is equidistant from all points on the circle's circumference. Hence, because points D, E, and F are on the circumference and are equidistant from O, O is the center of the circle passing through points D, E, and F.

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Point O is the center of the circle passing through points D, E, and F because it is equidistant from the vertices of triangle DEF, which is confirmed by the properties of the perpendicular bisectors of line segments DE and EF that intersect at point O.

To determine that point O is the center of the circle passing through points D, E, and F, we use the properties of perpendicular bisectors in a triangle. When we draw the line segments DE and EF, we are essentially drawing two sides of the triangle DEF. Constructing the perpendicular bisectors of these sides involves finding the midpoint of each side and then drawing a line that is perpendicular to that side at its midpoint.

The point where these two perpendicular bisectors intersect, point O, is equidistant from the vertices of the triangle (D, E, and F). This is because the perpendicular bisector of a line segment has the property that every point on the bisector is equidistant from the two endpoints of the segment. In the case of triangle DEF, point O is equidistant from D and E, since it lies on the bisector of DE, and is also equidistant from E and F, since it lies on the bisector of EF.

Since point O is equidistant from all three vertices of the triangle, it can serve as the circle's center, with the radii to the vertices being equal. This circle that we have created by using this method is also known as the circumcircle of triangle DEF, and point O is referred to as the circumcenter.

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Answer:

Option D. 20 minutes.

Step-by-step explanation:

It has been given in the question that distance between the shore of a lake is 3 miles.

Speed of Jim is 4 mph and speed of John is 5 mph.

Let they meet after time t hours.

Therefore distance traveled by Jim in t hours = 4×t miles

and distance traveled by John in t hours = 5×t miles

Total distance they cover = 3 miles.

Now 4t + 5t = 3

9t = 3

t = 3/9 hours.

t = (3×60)/9 minutes.

t = 20 minutes.

Answer is they will meet after 20 minutes.

The probability that the first winner is from Pike and the second from Wells is 1/6, found by multiplying the individual probabilities of each event happening in sequence.

The question asks for the probability that the first winner comes from Pike and the second from Wells in a random drawing. With 10 customers in total, 3 from Pike and 5 from Wells, the probability of drawing a Pike resident first is 3/10. If that happens, one less customer is available, leaving 9, with 5 still from Wells.

So, the probability for the second draw is 5/9. Multiplying these probabilities gives the combined probability for both events happening in sequence. Therefore, the required probability is (3/10) * (5/9), which simplifies to 1/6.

The probability that both customers selected are Pike residents is [tex]{\frac{28}{153}}[/tex]

To find the probability that both customers selected are Pike residents, follow these steps:

1. Calculate the probability that the first customer is a Pike resident:

  - There are 18 customers in total.

  - There are 8 Pike residents.

  - So, the probability that the first customer is a Pike resident is:

  [tex]\[ \frac{8}{18} = \frac{4}{9} \][/tex]

2. Calculate the probability that the second customer is also a Pike resident, given that the first one was a Pike resident:

  - After selecting the first Pike resident, there are now 17 customers left.

  - There are now 7 Pike residents remaining.

  - So, the probability that the second customer is a Pike resident, given the first was a Pike resident, is:

  [tex]\[ \frac{7}{17} \][/tex]

3. Calculate the combined probability:

  - Since the selections are dependent events (one customer is selected after another without replacement), multiply the probabilities of each step:

  [tex]\[ \left( \frac{4}{9} \right) \times \left( \frac{7}{17} \right) \][/tex]

4. Simplify the multiplication:

  - Multiply the numerators: [tex]\(4 \times 7 = 28\)[/tex]

  - Multiply the denominators: [tex]\(9 \times 17 = 153\)[/tex]

  - So, the combined probability is:

    [tex]\[ \frac{28}{153} \][/tex]

Final answer:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes.

Explanation:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes. In payroll, taxable earnings refer to the portion of an employee's wages or salary that is subject to various taxes, such as income tax and Social Security tax.

For example, if an employee earns $1,000 per week and the income tax rate is 20%, the taxable earnings would be $800 ($1,000 - $200).

It's important to note that not all earnings may be taxable. Some types of income, such as certain reimbursements or non-taxable fringe benefits, may be excluded from taxable earnings.

Answer:

55555555555555555555

Step-by-step explanation:

The degree is 5.

The degree of a polynomial is the highest power of the variable in a polynomial expression.

Given function:

6x5 - 4x2 + 2x3 - 3 + x

as, the function have powers 2, 3  and 5.

Among which the highest power is 5.

So, degree of the polynomial is highest power of the variable present in an equation.

Hence, the degree of polynomial is 5.

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Answer:

y=6

Step-by-step explanation:

If angle A of a rhombus decreases, angle C must also decrease and the side length of the rhombus must remain the same for it to still be a rhombus.

When angle A of a rhombus decreases, there are two changes that need to happen in order for the rhombus to still be a rhombus.

Therefore, if angle A decreases, angle C must also decrease by the same amount, and the side length of the rhombus must remain the same in order for ABCD to still be a rhombus.

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Answer:

A

Step-by-step explanation:

In 16 days will they have an equal amount of money.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raul has $640 saved, and jaime has $320 saved.

Raul earns $180 per day and jaime earns $200 per day.

let the be number of days they both have same amount

640 + 180x = 320 + 200x

320 = 20x

x= 16

Hence, 16 days will they have an equal amount of money.

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I think by 1-5 you mean 1/5??

1/5 = 0.20 = 20%

50% + 20% = 70%

100-70 = 30

 so 30% were sponge cakes

5x-16 = 4(x-8)-3x

first expand what is in parenthesis

4(x-8) = 4x-32

 so now you have 5x-16 = 4x-32-3x

subtract 3x from 4x on the right side of equation 4x-3x = x

5x-16 = x -32

subtract 1x from each side to get

4x-16 = -32

add 16 to both sides to get 4x=-16

x = -16/4 = -4

x=-4

Answer: [tex]6\sqrt{2}\ in[/tex]

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 6 in.

Let h be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,Moreover in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 6 in.

Thus by Pythagoras theorem, we get

[tex]h^2=6^2+6^2=36+36\\\\\Rightarrow\ h^2=72\\\\\Rightarrow h=\sqrt{72}\\\\\Rightarrow h=6\sqrt{2}\ in[/tex]

Hence, the length of its hypotenuse = [tex]6\sqrt{2}\ in[/tex]