The scale factor is 3. The original rectangle has side lengths of 3 and 6. What are the side lengths of the new figure after the scale factor is applied?

Answer:

you don't

Step-by-step explanation:

this is at it's simplest form, tell your teacher that or if its online answer, talk to your tutor or teacher

Answer:

Number is 19

Step-by-step explanation:

denote the number by x.

the line says:

5x - 20 = 18 + 3 x

Subtracting 3x form both sides

2x - 20 = 18

adding 20 to both sides

2x = 38

dividing both sides by 2

x = 19

Answer:

19

Step-by-step explanation:

let n = the number

5n - 20 = 18 + 3n

combine like terms in one of four different ways

2n = 38

n = 19

Answer:We want to write and solve a system of equations to model the given situation.

g = 2*d - 8

g + d = 46

The first thing we need to do, is define the variables we will be using.

g = number of songs that the guitarist wrote.

d = number of songs that the drummer wrote.

From "The guitarist wrote 8 fewer than twice the number of the songs that the drummer wrote."

We can write:

g = 2*d - 8

And we know that in total they wrote 46 songs, so we can also write:

g + d = 46

Then the system of equations is:

g = 2*d - 8

g + d = 46

Step-by-step explanation:

\(\large\boxed{Formula: A= P(1+ \frac{R}{100}{)}^{T}}\)

Let's substitute according to the formula.

\(A= 50000(1+ \frac{10}{100}{)}^{5}\)

A= $80525.5

Now, we can find the interest paid

\(\large\boxed{I= A-P}\)

We'll have to deduct the total amount from the principal amount.

Let's substitute according to the formula.

\(I= 80525.5-50000\)

I= $30525.5

Hence, the total amount paid after 5 years is $80525.5 and $30525.5 was paid as interest.

As x approaches 0, the limit of p(x) does not exist.

To determine the limit of p(x) as x approaches 0, we can evaluate the behavior of the function from both sides of x = 0.

If we approach from the left side (negative values of x), the expression cos²2(x)/sin(2x) approaches positive infinity as sin(2x) approaches 0 and cos²(x) remains positive.

However, if we approach from the right side (positive values of x), the expression cos²(x)/sin(2x) approaches negative infinity as sin(2x) approaches 0 and cos²(x) remains positive.

Since the function has different limits from the left and right sides, the limit of p(x) as x approaches 0 does not exist.

Therefore, the statement "As x approaches 0, the limit of p(x) does not exist" accurately describes the behavior of the function.

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Let g be the integral function defined by g(x) = ∫x-1 (-1/2 * cos (t³ / 2t)) dt for x = 0, g is g(x) = -1/2(x-1 * sin(t³/2t) - x-1 * cos(t³/2t)).

To solve this integral, we need to use the substitution method. We will let u = t/2t, du = 3t/2 dt.

Thus, the integral becomes:

g(x) = -1/2 * ∫x-1 cos(u) du

Using integration by parts, we get:

g(x) = -1/2(x-1 * sin(u) + ∫x-1 sin(u) du).

After integrating the second part, we obtain the final result:

g(x) = -1/2(x-1 * sin(u) - x-1 * cos(u))./2t

we subtitute the value of u to get:

g(x) = -1/2(x-1 * sin(t³/2t) - x-1 * cos(t³/2t)).

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Answer:

\(\displaystyle J'(3) = -1\)

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Rule [Chain Rule]:                                                                                       \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)

Derivative:                                                                                                                     \(\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle J(x) = e^{f(x)}\)

Step 2: Differentiate

Step 3: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

The answer is T = - 7.5 Cos π/12( t - 4 ) + 10.5

Given the fact that

The maximum temperature is 18 degrees Celsius.

Minimum temperature = 3 degrees Celsius

4 a.m. is the midpoint between 10 a.m. and 10 p.m.

Temperature changes may be modeled using the sine and cosine functions throughout the year. The following equation can be used to represent these data:

T = A cos B(t - C) + D, where A,B,C,D, are constants, T is the  temperature in °C and t is the hour (1–24

A = amplitude = (Tmax - Tmin)/2

A = (3 - 18)/2 = - 15/2 = -7.5 ( note : after midnight)

B= 2π/24 = π/12

C = units translated to the right

C = 4

D = ymin + amplitude = units translated up

D = 7.5 + 3 = 10.5

The trigonometric function formula that mimics the temperature T in Johannesburg t hours after midnight

T = - 7.5 Cos π/12( t - 4 ) + 10.5

What is temperature?

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Answer:

19/28 or about 68%

Step-by-step explanation:

7 + 12 + 9 = 28

7 + 12/28

19/28

Answer:

|-2| < 6

Step-by-step explanation:

|-2| < 6

The absolute value of -2 is 2

2 < 6

So |-2| < 6

Answer:

The question is not clearly stated, but I can correctly infer that you wanted to ask the question below:

Out of 150 members, 120 took part, what is the percentage of the total that took part:

Answer:

80%

Step-by-step explanation:

The question is asking us to find what percentage of 150 is 120

Let the percentage of 150 that is 120 be x

x % of 150 = 120

x/100 × 150 = 120

0.01x × 150 = 120

0.01x = 120 ÷ 150 = 0.8

x = 0.8 ÷ 0.01 = 80

∴ 120 = 80% of 150

Answer:

A triangle has an area of 30cm². The base and height are scaled by a factor of 3. What is the area of the resulting triangle? _cmA triangle has an area of 30cm². The base and height are scaled by a factor of 3. What is the area of the resulting triangle? _cm²²

Answer:

A. -0.875

Step-by-step explanation:

Find where the points are located

A=-4.25

B=2.5

Add the points

-4.25+2.5=-1.75

-1.75/2=-0.875

The dollar was worth more than today in 1960 and 1880. In those years, inflation-adjusted values of the dollar were higher.

To determine when the dollar was worth more than it is today, we need to consider the historical context and inflation rates. Inflation erodes the purchasing power of a currency over time. Comparing the given years, 1960 and 1880, with today, we find that the dollar had higher purchasing power in both those periods.

In 1960, the dollar had a higher value due to lower inflation rates compared to today. Similarly, in 1880, the dollar's purchasing power was even higher due to significantly lower inflation rates during that time. Therefore, in both 1960 and 1880, the dollar was worth more than it is today, considering inflation-adjusted values.

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Answer:

it's going to be the first one, (x+7,-y)

Step-by-step explanation:

take one point, A for example and count how far it moved left and right. left is negative, right is positive, do the same for y

When multiplying integers, the rules for determining the sign of the product are as follows:

1. If both integers have the same sign (either both positive or both negative), the product will be positive.

2. If one integer is positive and the other is negative, the product will be negative.

3. When multiplying zero by any integer, the product is always zero.

Remember to always multiply the absolute values of the integers and then determine the sign of the product based on the rules above.

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\( \large \mathfrak{Solution : }\)

According to formula :

\( \boxed{ \boxed{simple \: \: interest = \frac{p \times r \times t}{100} }}\)

Answer:

Step-by-step explanation:

BD = 100.8

AB² = BC×BD = 2096.64

AC = \(\sqrt{AB^{2}- BC^{2} }\) = \(8\sqrt{26}\)

Answer:

exact form -108/5, decimal form -21.6, and mixed number form -21 and 3/4

We can then compare those values to determine the global maximum and minimum.

Find the derivative of f(x) using the chain rule: f'(x) = (3/x) - 1For a critical point, f'(x) = 0: (3/x) - 1 = 0 ⇒ 3 = x.

So x = 3 is the only critical point in the domain x>0. We can check that this is a local maximum point by looking at the sign of the derivative on either side of x = 3:When x < 3, f'(x) is negative.

When x > 3,

f'(x) is positive.

So f(x) has a local maximum at x = 3.

To find the values of f(x) at the endpoints of the domain, we can evaluate the function at x = 0 and x = ∞:f(0) is undefined.

f(∞) = -∞.

Therefore, f(x) has no global maximum but it has a global minimum, which occurs at x = e. To show this, we can compare the values of f(x) at the critical point and the endpoint:

e ≈ 2.71828, which is the base of the natural logarithm.

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Answer:

power of ten

Step-by-step explanation:

x3 would be the answer

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }\)

The frequency table for the lengths of the 25 earthworms is shown in the image attached below.

A frequency table is a type of table that is used to graphically represent the frequencies or relative frequencies associated with a categorical variable.

In this exercise, you're required to complete the frequency table for the lengths of the 25 earthworms as follows:

In conclusion, the frequency table for the lengths of the 25 earthworms is shown in the image attached below.

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The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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(i) The slope of the curve at t = 0 is undefined.
(ii) The slope of the curve at t = m is given by -sin(m) / (1 - m^2).
(iii) The slope of the curve at t = 1 is e / (1 - e).


(i) To find the slope of the curve, we need to differentiate the given equations with respect to t and then substitute t = 0. However, after differentiating the equations, we find that the resulting expressions involve dividing by √t, which is not defined when t = 0. Therefore, the slope of the curve at t = 0 is undefined.

(ii) Differentiating the given equations with respect to t and substituting t = m, we obtain expressions for the slopes of the curve at t = m. The slope is given by -sin(m) / (1 - m^2).

(iii) By differentiating the equations with respect to t and substituting t = 1, we find the slope of the curve at t = 1. The slope is given by e / (1 - e).

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The unit rate of blue beads to red beads in Kyle's bag is 1(1/15).

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Blue beads = 1/3

Red beads = 5/16

The unit rate of blue beads to red beads.

= 1/3 ÷ 5/16

= 1/3 x 16/5

= 16/15

= (16/15) / 1

= 1(1/15) / 1

Thus,

The unit rate is 1(1/15).

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Answer:

5

Step-by-step explanation: