A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second.
Write an equation that shows the relationship between the elevation of the feather, y, and the number of seconds it has been falling, x.

Answer:

∠AFB

Step-by-step explanation:

Vertical angles are opposite to one another and share the same vertex or endpoint. ∠DFE is ∠AFE both share the point F, and they are opposite to each other, so they are also vertical to each other.

Answer:

$172,984.44 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=25000\left(1+\dfrac{0.065}{4}\right)^{4 \cdot 30}[/tex]

[tex]\implies A=25000\left(1.01625\right)^{120}[/tex]

[tex]\implies A=25000\left(6.9193776...\right)[/tex]

[tex]\implies A=172984.4404[/tex]

Therefore, if you deposit $25,000 now at 6.5% compounded quarterly,  you will have $172,984.44 (nearest cent) in 30 years.

Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

Let X be the number of hours it takes Paige to sort the toys alone.

It takes Madison X + 6 hours to sort the toys alone.

Together, it takes them X + (X + 6) = 4 hours to sort the toys.

Combining like terms, we get 2X = 4

Dividing both sides by 2, we get X = 2

Therefore, it takes Paige 2 hours to sort the toys alone.

It takes Madison 2 + 6 = 8 hours to sort the toys alone.

Answer:

m angle B = 27.54 degree

m angle C = 60.85 degree

Step-by-step explanation:

angle A is 90º so the other two angles must sum to 90º

2x+5x-8=90

7x-6=90

7x=96

x=13.77

therefore,

m angle B = 27.54 degree

m angle C = 60.85 degree

Answer: I believe 140

Step-by-step explanation: This is how I found my answer:

420 / 3

= 140

420-140

=  280

420= number of all tickets sold.

140= number of adult tickets sold

280= number of student tickets sold

You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:

"the number of student tickets sold was three times the number of adult tickets."

So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!

The required solutions are x = 2-i and x = 2+i to the given quadratic function.

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

-2x² + 8x - 10 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = -2, b = 8 and c = -10

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-8\pm \sqrt{8^2-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}[/tex]

[tex]x=\dfrac{-8\pm \:4i}{2\left(-2\right)}[/tex]

[tex]x=\dfrac{-8+4i}{2\left(-2\right)},\:x=\dfrac{-8-4i}{2\left(-2\right)}[/tex]

x = 2-i, x = 2+i

Thus, the required solutions are x = 2-i and x = 2+i to the given quadratic function.

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200 rides does it take to break even.

What are the many sorts of cost?

Fixed and variable costs are the two main categories of expenses incurred by enterprises. While variable costs fluctuate with output, fixed costs do not.

                 Sometimes, fixed costs are referred to as overhead costs. They must be paid whether a company produces 100 or 1,000 widgets.

The cost function is given by

C(x ) = 15x + 1000

It is also given that it costs $25 per ride.

so,

Revenue function for x number of rides be

 R(x) = 20x

For break even:-

The cost must be equal to the Revenue i.,e

       C(x) = R(x)

  15x + 1000 = 20x

     1000 = 20x - 15x

     1000 =  5x

        x = 1000/5

        x = 200

Therefore, 200 rides does it take to break even.

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answer:

step by step explanation:

(4,8); y = 2x — 4 = ?

Th length of the enclosed area of the scale model in inches is 32 inches.

Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet.

The enclosed area of the Alamo Mission was 480 feet long and 160 feet wide.

The length of the enclosed area of the scale model in inches can be calculated as follows:

30 feet = 2 inches

480 feet = ?

cross multiply

length of the enclosed area = 480 × 2 / 30

length of  the enclosed area = 960 / 30

length of the enclosed area = 32 inches

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Answer:1.44

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

k = 4-a

a (4-a) = 3

-a^2 +4a -3 = 0   ====> Quadratic Formula ===>  a =  1   and k = 3

1^3 + 3^3 = 28

Answer:D

beacuse it is correct  just trust me i have done this class and its correct

The 1 dollars found near the table by your friend is likely the money for the tickets.

You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.

let

x = number of individual ticket

y = number of couple tickets = 2x

Therefore, using equation,

2x(10) + 6x = 1075

2x + x = 195

Hence,

20x + 6x  = 1075

3x = 195

x = 195 / 3

x = 65

Hence,

26x = 1075

26(65) = 1690

Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.

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Answer:

Step-by-step explanation:

(2, 0), (3, 4)

(4 - 0)/(3 - 2)= 4/1 = 4

For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:

A less than sign, such as a, denotes that an is greater than b.

Given inequality is:

|2x+7|+9 >18.

First we have to rearrange all the variables to the left side of the given equation:

Then,

|2x+7|>18-9

|2x+7|>9

2x+7>9 or 2x+7< -9

S0, x>1 or x< -8

Therefore, x< -8 or x>1

Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

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Answer:

1/4

Step-by-step explanation:

1/2 divided by 2 would be 0.25, and since that's a quarter it would be 1/4.

Answer:

648

Step-by-step explanation:

An easy way to do this is to multiply all sides, then divide by 2.

8 × 9 × 18 = 1296

Now divide that by 2:

1296 ÷ 2 = 648

The area of the triangle is 648.

In linear equation,  162 is his new weight .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Mr. Miller weigh =  180pound

10% decrease =  180 * 10/100

                        = 18

new weight = 180 - 18

                   =   162

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Answer: 2x+y=5

Step-by-step explanation:

The standard form of a linear equation is

ax+by=c

Move all terms containing variables to the left side of the equation.

2x+y=5

Answer:

2x + y = 5

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y=-2x+5[/tex]

To write the given equation in standard form, collect the terms with variables on one side of the equation, ensuring the term in x is positive.

Add 2x to both sides:

[tex]\implies y+2x=-2x+5+2x[/tex]

[tex]\implies y+2x=5[/tex]

[tex]\implies 2x+y=5[/tex]

Answer:

[tex]x=59[/tex]

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\implies x=180-48-73=59[/tex]

The location of G is (3, 0).

Given question in that we have a number line.

A number line goes from negative 5 to positive 10.

Point D is at negative 2 and point F is at positive 7.

A line is drawn from point D to point F.

So we can write coordinate of point D as (-2,0) and point F as (7,0).

line segment from D to  F divides as point G as in ratio of 5:4

Consider two points P(x1, y1) and Q(x2, y2). We have to find the coordinates of the point R which divides PQ in the ratio m : n

x = [tex]m*x2+n*x1/(m + n)[/tex]

[tex]y = m*y2+n*y1/(m + n)[/tex]

so here in our question m =5 n=4

x1=-2 x2=7 y1=0 y2=0

x = 5*7+4*(-2)/9

x = 3

y = 5*0+4*0/9 = 0

So the location of G is (3, 0)

Given Question is incomplete complete question here.

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? A number line goes from negative 5 to positive 10. Point D is at negative 2 and point F is at positive 7. A line is drawn from point D to point F.

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The independent variable in the given function is h.

The Independent variables are those variable whose value does not depend on any other variable. And it causes the change in other variables.

The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.

Given the function p(h)=20h−50, which represents Lamont works for a company that pays him $20 per hour(h), but $50 each week is deducted from his pay for insurance.

Now, in the given function since the amount that Lamont will get depends upon the number of hours for which he is working.
Therefore, the h is the independent variable and p is the dependent variable.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x is 1.

The value of y is 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 = 5 is an equation.

We have,

-4.5x - 2y = -12.5 ____(1)

3.25x - y = -0.75 _____(2)

From (1) we get,

-4.5x + 12.5 = 2y

y = (-4.5x + 12.5) / 2 _____(3)

Now,

3.25x - y = -0.75

Putting (3) in (2) we get,

3.25x - (-4.5x + 12.5) / 2 = -0.75

6.5x + 4.5x - 12.5 = 2 x -0.75

11x - 12.5 = -1.5

11x = -1.5 + 12.5

11x = 11

x = 1

Now,

From (3) we get,

y = (-4.5x + 12.5) / 2

y = (-4.5 x 1 + 12.5) / 2

y = (-4.5 + 12.5) / 2

y = 8/2

y = 4

Thus,

The value of x is 1.

The value of y is 4.

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Answer:

The answer is B

Step-by-step explanation:

I took the test and got it right,(also i have a pic) brainiest pls!!

Answer:

27.3

Step-by-step explanation:

21 times 1.3 = 27.3 = original price

She paid 70% of the regular price of $30.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,

Percentage = 21 / 30

Percentage = 0.7 x 100

Percentage = 70%

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The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.

In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.

Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.

And we need to find the statement is true or not.

According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.

Here we have counts for two categorical or nominal variables.

So, there is no large value comparision take palce.

Therefore, the statement is false.

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Therefore the solution of this question is  the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Here,

The perimeter of the square drawn on the grid

The vertices given in the question are (3,3) & (7,7)

The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]

Thus at vertices  (3,3) & (7,7)

=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]

=>4[tex]\sqrt{2}[/tex]

Therefore the perimeter of the square = 4a

thus,

=>4*4[tex]\sqrt{2}[/tex]

=>16[tex]\sqrt{2}[/tex] units

Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

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