Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?

Answer:

D. 20 + 2√10 units

Step-by-step explanation:

Perimeter is the distance all round a figure.

AB = 10. This is given in the question

AC = √((3-5)²+(4--2)²

= √(4+36)

=√40 = 6.32 units

BC = 5 - -5 = 10 units

Perimeter = AB+AC+BC

= 10+6.32+10

= 26.32 units

Answer:

Each player received 548/p dollars.

Answer: The measure of angle a is 90-25=65° and the measure of angle be is 25°.

Step-by-step explanation:

Let the two complementary angles be 'a' and 'b'.

So, the sum of two complementary angles is 90°.

So, it becomes,

[tex]a+b=90^\circ---------------(1)[/tex]

First angle is 15 less than twice the measure of the second angle.

So, it becomes,

[tex]a=2b-15-------------(2)[/tex]

Put the equation (2) in equation (1), we get

[tex]a+b=90^\circ\\\\2b-15+b=90^\circ\\\\3b+15=90^\circ\\\\b=90-15\\\\3b=75^\circ\\\\b=\dfrac{75}{3}\\\\b=25^\circ[/tex]

Hence, the measure of angle a is 90-25=65° and the measure of angle be is 25°

Answer:

Option A - [tex]W=\frac{P}{2}-L[/tex]

Step-by-step explanation:

Given : The formula for the perimeter of a rectangle is P=2(L+W).

To find : Solve for W ?

Solution :

The formula for the perimeter of a rectangle is

[tex]P=2(L+W)[/tex]

Multiply,

[tex]P=2L+2W[/tex]

Subtract 2L both side,

[tex]P-2L=2W[/tex]

Divide by 2 both side,

[tex]W=\frac{P-2L}{2}[/tex]

or [tex]W=\frac{P}{2}-L[/tex]

Therefore, Option A is correct.

I think the answer is C, since it is measured to 2 decimal places

The correct answer is: c. 4. In some cases, a fourth-degree polynomial with five terms could have at most 4 different linear factors.

To understand how many different linear factors a fourth-degree polynomial with five terms could have at most, let's consider the Fundamental Theorem of Algebra, which states that a polynomial of degree (n) has exactly (n) complex roots, counting multiplicity. For a fourth-degree polynomial, this means it can have at most 4 linear factors, as each linear factor corresponds to a root.

However, the polynomial could have repeated roots, reducing the number of distinct linear factors. If all four roots are distinct, then there will be 4 different linear factors. But if one or more roots are repeated, the number of different linear factors will decrease. The polynomial could have fewer than 4 distinct linear factors if it has repeated roots.

Complete Question:

A fourth degree polynomial with five terms could have, at most, how many different linear factors?

a. 3

b. 2

c. 4

d. 5

Answer:

20

Step-by-step explanation:

The requried measure of angle B is 25 degrees. Option A is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let A be one of the acute angles of the right triangle. Then, we have:

tan(A) = opposite/adjacent

Given that the tangent of angle A is 2.1445, we can write:

2.1445 = opposite/adjacent

Since angle B is also an acute angle of the same right triangle, we have:

tan(B) = opposite/adjacent

But since the sum of the angles of any triangle is 180 degrees, and one of the angles in this triangle is a right angle (90 degrees), we have:

A + B + 90 = 180

B = 90 - A

Substituting the expression for B into the equation for the tangent of angle B, we get:

tan(90 - A) = opposite/adjacent

tan(90 - A) = (1/tan(A)) x adjacent/opposite

tan(90 - A) = (1/2.1445) x adjacent/opposite

tan(90 - A) = 0.466

Taking the inverse tangent of both sides, we get:

90 - A = tan⁻¹0.466)

90 - A = 25.38

A = 90 - 25.38

A = 64.62

Therefore, the measure of angle B is,
B = 90 - A
  = 90 - 64.62 = 25.38 degrees

Thus, the requried measure of angle B is 25 degrees.

Learn more about triangles here:
https://brainly.com/question/2773823

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In the number 474, the 4 in the ones place is less than the value of the 4 in the hundreds place by a factor of 100 because each position to the left in the place value system is worth ten times more than the one to its right.

The question deals with the concept of place value in mathematics. Specifically, it requires understanding how the value of a digit changes based on its position within a number. In the number 474, the 4 in the ones place has a value of 4, whereas the 4 in the hundreds place has a value that is 100 times greater, since each move to the left in place value represents a multiplication by 10. Therefore, the 4 in the ones place is less than the value of the 4 in the hundreds place. Here's a simple breakdown of the place values in the given number 474:

Since 1 is less than 100, the 4 in the ones place is worth less than the 4 in the hundreds place by a factor of 100.

The value of the 4 in the ones place is 10 times the value of the 4 in the hundreds place.

The 4 in the ones place is 10 times the value of the 4 in the hundreds place.

The solution to the proportion 2/8 = -30/x is x = -120, found by cross multiplying and simplifying the resulting equation.

To solve the proportion 2/8 = -30/x, we will cross multiply to find the value of x. After cross multiplying, we obtain 2x = -30  imes 8. Simplifying this gives us 2x = -240, and dividing both sides by 2 yields x = -120. So the solution to the proportion is x = -120.