Writing/Reasoning Find the area of the square in Problem 1.
Explain how you found the area and the perimeter.
Area
square centimeters

Answer:

3780

Step-by-step explanation:

first divide 210 by 2 it's 105 now multiply that by 36

Answer:

The answer is d

Step-by-step explanation:

simplyfied into the simpiliest form possible

a and c are directly proportional to each other when a and b are directly proportional and b and c are directly proportional.

If a and b are directly proportional and b and c are directly proportional, it means that their ratios are equal. Direct proportionality implies that as one variable increases, the other also increases in proportion and as one variable decreases, the other also decreases in proportion.

Mathematically, this can be written as

a = kb and b = mc, where k and m are constants of proportionality.

Multiplying these two equations gives: a = kbm

Substituting the value of b from the second equation in the first equation, we get: a = kmc

Therefore, a and c are also directly proportional to each other with a constant of proportionality km.

Thus, if a increases by a certain factor, c will also increase by the same factor.

If a and b are directly proportional and b and c are directly proportional, then it can be concluded that a and c are directly proportional as well.

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Answer: y = (1/2)x + 8

Step-by-step explanation:

Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2

y = (1/2)x + b

7 = (1/2)-2 + b

7 = -1 + b

8 = b

y = (1/2)x + 8

Answer:

\(81^{108}=1.30732\dots E206\)

Step-by-step explanation:

\(81^{108}\)

\(\mathrm{Refine\:to\:a\:decimal\:form}\)

\(=1.30732\dots E206\)

\(81^{108}=1.30732\dots E206\)

The populations from which the samples are obtained must be normally distributed.

Sampling is done correctly. Observations for within and between groups must be independent.

The variances among populations must be equal (homoscedastic).

Data are interval or nominal.

Given:

The expenses for the past 2 weeks is as shown in the table

so, the total expenses =

Kelly bank statement says that she has an ending balance of $349

So, the starting balance = 478 + 349 = 827

So, the answer will be: the starting balance = $827

The points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.

In graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". In a graph the points are plotted using coordinates in the form of (x, y) or (x, y, z) or (r, Ф, z) or (r, θ, Φ) as per need on different types of coordinate graphs.

We have the following coordinates -

(1, 5) , (4.5, 1) , (3.5, 2.5)

The following points are plotted on the graph as shown in the image attached.

For any coordinate -

(x, y)

[x] is plotted along the [x] - axis

[y] is plotted along the [y] - axis

Therefore, the points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.

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Answer: (1, 5) , (4.5, 1) , (3.5, 2.5)

Step-by-step explanation:

The horizontal distance from the tower to the fire is 7 feet

The term "angle of depression" describes the angle created by a horizontal line and the line of sight from the observer's eye to a location below their horizontal line of sight. It is often calculated by descending from the horizontal line.

The angle of depression is a term that is frequently used in discussions of observations or measurements involving objects that are below the observer's location in geometry and trigonometry.

We know that;

Tan 3 = x/140

x = 140 Tan 3

x = 7 feet

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The system of equations are:

c + b = 1285

170c + 480b = 477,300

Two equations would be derived from the information provided in the question. The equations are known as simultaneous equations. The equations would have to be solved together in order to determine the required values.

The methods that can be used to solve simultaneous equations are:

The form of the equations is:

Number of catastrophic plan sold + number of bronze plans sold = total plans sold

Cost of the catastrophic plan x number of the plan sold) + (number of bronze plan sold x cost of the plan) = total cost of the plans

c + b = 1285

170c + 480b = 477,300

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Answer:

y = -1/2x - 7/2

Answer:

Selling Price = $147

Mark Up = 75%

------------------

The selling price of the skateboard is $84.

Answer: 25 ft per min.

Step-by-step explanation:

Time= 100 min.

Distance= 2500 ft.

Speed= 2500/100 = 25 ft per min.

By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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It will take 12.5 minutes by the printer to use all 100 sheets of paper as the function is p(t) = -8t + 100 where p is the number of sheets left after t minutes of printing.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Here,

p(t)=-8t+100

Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function .When all the 100 sheets printed , then the number of sheets will left to print =0.

Substitute p(t)=0 in the given function, to find the value of t,

0=-8t+100

8t=100

t=12.5 minutes

The function is p(t) = -8t + 100, where p is the number of sheets left after t minutes of printing, and it will take the printer 12.5 minutes to use all 100 sheets of paper.

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The rate at which R is changing when R1=55 ohms and R2=72 ohms is −0.086 ohm/sec.

The given equation is: R1= R1 + R2.

To find the rate at which R is changing, differentiate both sides of the equation with respect to time:

dR1/dt = d(R1+R2)/dt = dR/dt

Given, R1=55 ohms and R2=72 ohms

Then, R = R1R2/(R1+R2)

On substituting the given values, we get R = 29.0196 ohms

Now, dR1/dt = 0.6 ohms/sec and dR2/dt = 1.6 ohms/sec

Using the quotient rule of differentiation, we get:

dR/dt = (R2dR1/dt − R1dR2/dt)/(R1+R2)²

On substituting the given values, we get:

dR/dt = (72×0.6−55×1.6)/(55+72)² ≈ −0.086 ohm/sec

Thus, when R1 = 55 ohms and R2 = 72 ohms, the rate at which R is changing is approximately −0.086 ohm/sec.

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Based on the given function and its behavior as r approaches infinity, the ultimate fate of this subpopulation of plants is exponential growth without any limitations.

To determine the ultimate fate of the subpopulation of plants described by the function N(r), we need to analyze the behavior of the function as r approaches infinity (i.e., the long-term trend).

First, let's simplify the given function:

N(r) = 6e^(5r) - 4r + 1/(9 + 2e^(5r))

As r approaches infinity, the exponential terms, e^(5r), dominate the function. Exponential functions grow rapidly as their exponent increases. Therefore, we can disregard the other terms in the function because their contribution becomes negligible compared to the exponential term.

Simplifying further, we can write the function as:

N(r) ≈ 6e^(5r)

Now, let's analyze the behavior of the exponential term e^(5r) as r approaches infinity. As r increases, e^(5r) will become larger and larger, which means the population growth will be exponential.

Exponential growth means that the population size will continue to increase without bound. In this case, as r approaches infinity, the subpopulation will grow indefinitely larger. This suggests that the ultimate fate of this subpopulation of plants is unbounded growth, assuming no external factors limit their growth.

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Answer:

(6 / 5)²

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

(8x-4)+(6x-12)=180

14x-16=180

14x=196

x=14

If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

\(y = y0 * e^(rt)\)

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

\(y = y0 * e^(rt)\)

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is\(e^r\)).

So, the correct answers are: A), B), C), and D).

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The equation (2/(x+1)) = (1/x - 2) has two solutions: x = 1/2 and x = -1.

The equation (2/(x+1)) = (1/x - 2), we need to find the value of x that satisfies the equation.

Let's simplify the equation step by step.

First, let's eliminate the fractions by multiplying both sides of the equation by the common denominator, which is x(x+1):

x(x+1) × (2/(x+1)) = x(x+1) × (1/x - 2)

Simplifying the equation, we have:

2x = (x+1) - 2x(x+1)

Expanding the brackets, we get:

2x = x + 1 - 2x² - 2x

Rearranging the terms, we have:

2x + 2x² = x + 1

Combining like terms, we obtain a quadratic equation:

2x² + x - 1 = 0

To solve the quadratic equation, we can either factor it or use the quadratic formula.

The quadratic equation does not factor easily.

We'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, the coefficients are:

a = 2, b = 1, and c = -1.

Substituting these values into the quadratic formula, we have:

x = (-(1) ± √((1)² - 4(2)(-1))) / (2(2))

x = (-1 ± √(1 + 8)) / 4

x = (-1 ± √9) / 4

Taking the square root, we get two possible solutions:

x = (-1 + 3) / 4

= 2/4

= 1/2

x = (-1 - 3) / 4

= -4/4

= -1

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This figure and the given statements are important for understanding basic principles of geometry.

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Answer:

7*450*.5%

Step-by-step explanation:

Answer:

x - 6y - 2 = 0

Step-by-step explanation:

Let “m” be the slope of line AB

and “a” be the slope of the line that passes through C and is perpendicular to AB

Then

\(m = \frac{6-0}{1-2} =-6\)

The second line is perpendicular to AB

then

m × a = -1

then

-6 × a = -1

then

\(a=\frac{1}{6}\)

C(2,0) lies on the line of equation y=ax+b

⇔ C(2,0) lies on the line of equation y=(1/6)x+b

⇔ 0 = (1/6)×2 + b

Then b= -1/3

Therefore Our equation is :

y = (1/6)x - 1/3

⇔ 6y = x - 2

⇔ x - 6y - 2 = 0

The value of arccsc(-4.258), rounded to two decimal places, is approximately -0.23 radians.

The arccsc function, also known as the inverse cosecant function, returns the angle whose cosecant equals a given value. In this case, we need to find the angle whose cosecant is -4.258. To approximate this value, we can use a calculator.

First, we need to find the cosecant of -4.258. Since cosecant is the reciprocal of sine, we can calculate it by taking the reciprocal of the sine of -4.258. Using a calculator, we find that the sine of -4.258 is approximately -0.879. Taking the reciprocal of this value, we get the cosecant as approximately -1.137.

Now, we need to find the angle whose cosecant is -1.137. This is the value we are looking for, which is approximately -0.23 radians. Rounding it to two decimal places, we get the final result of -0.23 radians as the approximate value of arccsc(-4.258).

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The given relation is NOT a function. By definition, a function is a relation in which no two ordered pairs have the same first component and different second components. In your given table, the y = -2 has two corresponding x values: it is paired with x = -1 and x = 6. Therefore, it is not a function.

The area is 364 because the perimeter is 84 feet, the sides are 28 times two witch it 56 and 84-56 is 26 so the other sides are 13 and 13 times 28 is 364

Answer:

6 + z

20 - x

x/6 - 8

5x/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a.6+z

b.22-x

c.8-x÷6

d.x+15÷4