what is the resultant image of point A(-12,3) , after a scale factor 1/3 and a rotation of 270 degrees?

The scale factor of the dilation of the given object is 4.

The scale factor of dilation:

The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.

Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.

The basic formula to find the scale factor of a dilated is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

[tex]SD=\frac{32cm^2}{4cm^2}[/tex]

SD=4

Thus, the scale factor of the dilation of the given object is 4.

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I think "E" it's the most close answer for me

Answer:

X>3

Step-by-step explanation:

So we're solving for X

Since it's an inequality, let's make it = 27 instead

4x+15=27

Now we can subtract 15

4x = 12

x = 3

Now that it's saying > 27, that means the same for x, it's has to be > too, concluding x>3... all x's greater than 3

C(x) = 16x – 63, where x is the number of thousands of bottles, gives the cost of producing bottled spring water.

The formula R(x) = - x2 + 326x – 7463 calculates the total amount (revenue) from the sale of these bottles.

Bottles sold will yield the highest profit.

Profit maximization

Profit after selling 245 thousand bottles

C(x) = 16x – 63

R(x) = – x² + 326x – 7463.

Revenue – Cost = Profit

P(x) = R(x) – C (x)

= – x² + 326x – 7463 – (16x – 63) (16x – 63)

= – x² + 310x – 7400

Choice c)

Profit = x2 minus 310x minus 7400

P(x) = – x² + 310x – 7400

P’(x) = -2x + 310

P’(x) = 0 => -2x + 310 = 0 => x = 155

P’’(x) = - 2 < 0

As a result, profit is greatest at x = 155.

The highest profit will be generated if 155 bottles are sold.

Alternative b)

Profit maximization at x = 155

P(x) = – x² + 310x – 7400

= -(155)² + 310(155) – 7400

= Rs 16625

The highest possible profit is Rs 16625.

Alternative b)

Profit after selling 245 thousand bottles

X = 245

−(245)2 + 310(245) – 7400 = profit

= 8525

Alternative (a) Rs 8525

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Answer:

Second choice : -3, 11, -45, 179

Step-by-step explanation:

First term: a₁ =  - 3

Second term a₂ = -4a₁ -1 = (-4)(-3) - 1 = 12 - 1 = 11

There are only two options with 11 as the third term, Options 2 and 4 look the same but the fourth option has curly braces around the numbers making it a set rather than a sequence

If you wanted to be sure and compute the third term to see if it matches

a₃ = -4a₂ - 1 = -4(11)- 1 = -44 - 1 = -45

well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°,  now, we also know that there are 180° in π radians, so

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians[/tex]

Answer:

C

Step-by-step explanation:

Hi there and welcome to brainly!

By looking at the number line, we want to identify which point represents the approximate value of 5π

We know that π has an approximate value of 3.14 so the approximate value of 5π = 5 × 3.14 = 15.7

Looking at the number line, 15.7 falls in between 15 and 16 which correlates to point C

The average rate of change from x = -2 to x = 0 of the function f(x) = 3x² - 2x + 5 is -8.

The average rate of change from -2 to 0 is;

f(0) - f(-2) / 0 - (-2)

Given the quadratic equation in question;

f(x) = 3x² - 2x + 5

Plug in the values;

[ ( 3(0)² - 2(0) + 5 ) - ( 3(-2)² - 2(-2) + 5  ) ]/ 0 - (-2)

[ ( 0 - 0 + 5 ) - ( 12 + 4 + 5  ) ]/ 0 - (-2)

[  5 - 21 ] / 0 - (-2)

[  -16 ] / 2

-16/2

-8

Therefore, the average rate of change is -8.

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Answer:

The answer assumes that the density of glass is 3 g/cm^3, not 3 g/cm^2.

The mass of the paperweight is 270 grams.

Step-by-step explanation:

Lets calculate the volume of a sphere having a radius of 3.5cm, and then divide that by 2 to get the volume of the hemisphere (half a sphere).  The sphere has a diameter of 7cm (therefore, a radius of 3.5cm).

Vol (sphere) = (4/3)πr^3

Vol = (4/3)(3.14)(3.5cm)^3

Vol = 180 cm^3

Half of this (the hemisphere) will be 90 cm^3

We know the volume, and we know the density of glass (3 g/cm^3), so multiply the two to obtain the mass of the paperweight.

 (90 cm^3)*(3g/cm^3) = 270 grams

The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Rita the mentor has two independent exercise designs that she offers her clients: Plan An and Plan B. Every client does it is possible that either (not both). On Friday there were 5 clients who arranged A and 3 who arranged B. On Saturday there were 2 clients who arranged A and 6 who arranged B. Rita prepared her Friday clients for a sum of 10 hours and her Saturday clients for a sum of 10 hours.

The length of each Plan A workout is given as,

Rate = (5 + 2) / 10

Rate = 7 / 10

Rate = 0.70 per hour

The length of each Plan B workout is given as,

Rate = (3 + 6) / 10

Rate = 9 / 10

Rate = 0.90 per hour

The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

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Answer:

C and D

Step-by-step explanation:

3x + 1 and 1 + 3x are the phrase for 'Thrice a number more than 1.

they can simplify to get the same answer.

If he bake 3 loave pf banana bread. Since 23 1/3 wants a lot of bread, Erin's banana bread is not enough.

These are the specified parameters:

Erin's number of guests = 20 people.

Each guet to have 1 1\6 of a loaf.

If he bake 3 loave pf banana bread.

Much to be desired bread

= number of guests × bread per guest

= 20 × 1 1/6

= 20 × 7/6

= 70/3

= 23 1/3

He baked 3 banana loaves, whereas the desired number of loaves was 23 1/3.

Thus Erin's banana bread is not enough for the guest.

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The area of the cylinder is 3, 399. 74 square centimeters

The formula for calculating the area of  a cylinder is expressed with the equation;

A = 2πrh + 2πr²

Given that the parameters are;

From the information given, we have that;

Radius, r = 13.4 centimeters

Height, h = 27 centimeters

Now, subsitute the values, we get;

Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²

expand the bracket

Area = 2272. 104 + 1127.64

Add the values

Area = 3, 399. 74 square centimeters

Hence, the value is 3, 399. 74 square centimeters

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The concept is Data Analysis,  which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.

To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.

Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.

Limitations include:

Question

You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.

A) exclude the outliers

B) Understand the strengths and sins of the tools

C) Critically dissect the correlations

D) Look at the environment

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Answer:

52

Step-by-step explanation:

Using the exterior angle theorem, [tex]112+x=164 \implies x=52[/tex]

The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

What is a function ?

Function can be defined as which relates an input to output.

Given,

Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms.

Height = b

Volume V = 6³-6b²+9b.

Length of each side (s) :

V = 6³-6b²+9b.

s^2 b  = b (b^2 - 6b + 9 )

s^2 = b^2 - 6b + 9

(a - b ) ^2 = a^2 + b^2 -2ab

s^2 = (b-3) ^2

s = b-3

height is 18 inches and height is given as b

Hence, b = 18

s= b-3 (from i)

= 18 - 3

s = 15

Therefore volume:

volume of rectangle = l x b x h

V= 18 x15 x15= 4,050

(If height = 15

then, b = 15

b -15 = 0

Definition of remainder theorem:

we divide a polynomial P(x) by a factor ( x – a); to find a smaller polynomial along with a remainder. The factor doesn't have to be a part of the polynomial.

b^3 - 6b^2 + 9b  /  b-15  = 2160

Therefore Volume with b = 15 is 2160

Therefore, The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

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The total sound level at the point is 100 dB (10 dB x 10 speakers).

The formula for calculating the sound level emitted by each speaker is 10 * log (100 / 10) = 10 dB. This means that each speaker emits a sound level of 10 dB.

To calculate this, we first need to understand the principle of the logarithmic addition of sound levels. The logarithmic addition of sound levels states that when two sound waves with different amplitudes overlap, the resulting amplitude is the sum of the logarithms of the individual amplitudes.

For example, let's say we have two sound waves with amplitudes of 10 dB and 20 dB. The resulting amplitude will be 10 * log (10 + 20) = 10 * log (30) = 10 dB + 20 dB = 30 dB.

Therefore, in our example, the 10 speakers each emit a sound level of 10 dB. This means that when all 10 speakers play simultaneously, the total sound level at the point is 100 dB (10 dB x 10 speakers).

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a. The percentage of GMAT scores is 647 or higher approximately 15.9%

b. The percentage of GMAT scores that are 747 or higher (to 1 decimal) is approximately 2.3%.

c. The percentage of GMAT scores between 447 and 547 is approximately 84.1%.

d. The percentage of GMAT scores between 347 and 647 (to 1 decimal) is approximately 98.0%.

a. The GMAT score of 647 is 100 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 647-547/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are 647 or higher is approximately 15.9%.

b. The GMAT score of 747 is 200 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 747-547/100 = 2.

Using a standard normal table, we can find that the percentage of GMAT scores that are 747 or higher is approximately 2.3%.

c. The GMAT scores between 447 and 547 are 100 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (447-547)/100 = -1 and (547-547)/100 = 0.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -1 and 0 is approximately 84.1%.

d. The GMAT scores between 347 and 647 are 200 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (347-547)/100 = -2 and (647-547)/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -2 and 1 is approximately 98.0%.

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The complete question is -

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

a. What percentage of GMAT scores are 647 or higher?

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

c. What percentage of GMAT scores are between 447 and 547 ?

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

Span {u1, u2} = P, and we have found two vectors in u1 = (1, 0, -a/c) and u2 = (0, 1, -b/c) in R3 that span the plane P.

Given: "Find two vectors in u1 and u2 in R3 so that span {u1, u2} = P", where P is a plane in R3.

To find the vectors u1 and u2, we need to find two linearly independent vectors that lie in the plane P.

One possible method to find these vectors is to choose a point on the plane and find a normal vector to the plane. We can then use the point and the normal vector to parameterize the plane.

For example, let's choose a point on the plane as (x0, y0, z0) and a normal vector to the plane as n = (a, b, c).

Then, the equation of the plane can be written as:

ax + by + cz = d

where d = a * x0 + b * y0 + c * z0

We can then choose two linearly independent vectors in the plane by taking partial derivatives with respect to x and y, respectively.

Let's choose u1 = (1, 0, -a/c) and u2 = (0, 1, -b/c). These two vectors lie in the plane and are linearly independent.

Therefore, span {u1, u2} = P, and we have found two vectors in u1 and u2 in R3 that span the plane P.

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The probability that the sum of the numbers on the dice facing up add up to 3 is 1/18 and VAR(A)= 1

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

A 6-sided dice has numbers 1, 2, 3, 4, 5, 6 at each of the 6 sides.

The event of rolling two fair 6-sided dice, which the numbers on the dice facing up add up to 3, is by having (1, 2) or (2, 1).

probability = desired outcome / total outcomes

probability = 2 / (6 x 6)

probability = 2 / 36

probability = 1/18

VAR(A)= 1

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Answer:
The solution to the system of linear inequalities x <= 8 and y > -3, represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x=8 and above the line y=-3 .

Step-by-step explanation:

The solution to the system of linear inequalities x <= 8 and y > -3 can be represented on a coordinate plane as a region that satisfies both inequalities.

To graph the solution, we first plot the line x = 8 on the coordinate plane. Since x <= 8, this line represents the boundary of the solution. Everything to the left of the line x = 8 is included in the solution.

Next, we plot the line y = -3. Since y > -3, everything above the line y = -3 is included in the solution.

The final graph will be a half-plane formed by the line x=8 and above the line y=-3 .

The graph shows that f is not continuous at x=-4 and x=4. This is because the graph does not have a continuous line at those points.

A graph is a visual representation of data that uses dots, lines, or bars to show how different elements of a set of data are related. Graphs are typically used to show patterns or trends in data over time, or to compare different sets of data. Graphs can also be used to show the relationships between different variables.

At x=-4, there is a large gap between the left side and the right side of the graph. At x=4, the graph has a sharp corner, which shows that the graph is not continuous.

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Answer

percentage= 100

a. 10% of 70

10/100 × 70 = 7

b. 10% of 110

10/100 × 110 = 11

c. 25% of 160

25/100× 160 = 40

d.25% of 48

25/100 × 48 = 12

e. 50% of 90

50/100 × 90 = 45

f. 50% of 350

50/ 100 × 350 = 175

g.75% of 300

75/100 × 300 = 225

h. 75% of 48

75/100 × 48 = 36

Answer:

$29

Step-by-step explanation:

Since the gifts are matching, the cost of each gift be equal, say $x
Now, Total cash - cash leftover = cost of both gifts
which is, 75 - 17 = 2x
or $58 = 2x
Thus, x would be 58/2 = $29
Or each gift would cost $29

Answer:

[tex]5 \leqslant 20 - 1.3x < 10[/tex]

Answer: The initial amount (a) in the exponential function is 5, and the decay factor (b) is 0.5.

Step-by-step explanation: :D

When 0.36 is expressed as a common fraction in lowest terms, the numerator is 9 and the denominator is 25. The sum of the numerator and denominator is 34.

To calculate the sum of the numerator and denominator when 0.36 is expressed as a fraction in lowest terms, follow these steps:

In this case, 0.36 can be expressed as 9/25. The greatest common factor of 9 and 25 is 1, so the fraction is already in its lowest terms. The sum of the numerator and denominator is 9 + 25 = 34.

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