Graph △FGH with vertices F(2, 2), G(2,4) and H(4,4) and its image after the similarity transformation. Translation: (x, y) → (x-3, y-1) Dilation: scale factor of 2

The height of the triangle is h = 18.18 inches

Given data ,

In an equilateral triangle, all three sides are equal in length.

Let the length of each side be s

Now , the perimeter of the equilateral triangle is given as 63 inches, so we have:

Perimeter of the triangle = 3s = 63 inches

Dividing both sides by 3, we get:

s = 63/3 = 21 inches

Let's now plot an altitude from one of the equilateral triangle's vertex to the side's midway. As a result, two right-angled triangles will be formed, each with the hypotenuse "s" and sides "s/2" and "h"

From the Pythagoras theorem , we get

(h²) + ((s/2)^2) = s²

Substituting the values we found earlier for "s", we get:

(h²) + ((21/2)²) = 21²

Simplifying further, we have:

(h²) + (10.5²) = 21²

(h²) + 110.25 = 441

Subtracting 110.25 from both sides, we get:

h² = 330.75

On taking square roots on both sides , we get

h = √(330.75)

h ≈ 18.18 inches

Hence , the height of the equilateral triangle is 18.18 inches

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The two compositions give:

Here we have two functions:

f(x) = 3x + 5

g(x) = -7x + 6

And we want to fin the two compositions:

f(g(2))

g(f(2))

First, let's find g(2) = -7*2+  6 = -14 + 8 = -8

Then:

f(g(2)) = f(-8) =  3*-8 + 5 = -19

Now the other one:

f(2) = 3*2 + 5 = 11

Evaluating g in that:

g(11) = -7*11 + 6 = -77 + 6 = -71

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Answer:

r 0.6 kWh to run for 30 minutes.

Answer:

ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes

Step-by-step explanation:

The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.

This is because the water level is 15 inches from the bottom of the aquarium.

Hence, the volume of water in the aquarium up to the 15 inch mark is:

V = l × w × h

V = 21 × 11 × 15

V = 3465 cubic inches

Therefore, the volume of water in the aquarium is 3465 cubic inches.

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The graph of the function f(x) = 5(3)ˣ - 1 is represented as the diagram given in option C.

To find the main points of the function f(x) = 5(3)ˣ - 1, we can identify its key features such as the y-intercept, x-intercept, and any asymptotes.

Y-intercept:

To find the y-intercept, we set x = 0 and evaluate the function:

f(0) = 5(3)⁰ - 1 = 4

Therefore, the y-intercept is (0,4).

Asymptotes:

There are no vertical asymptotes for this function since the base of the exponential function, 3, is positive.

The graph of the function is given in the attached image.

Therefore, the correct option is C.

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Answer:

Step-by-step explanation:

tax

Answer:

x^2y^4

Step-by-step explanation:

b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2

Answer:

Step-by-step explanation:

5 and 15

5^2=25

15^2=225

225+25=250

Answer:

x=3/2

x=-2

Step-by-step explanation:

The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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The missing values from ratio table are 17 and 28.

We have table as

3      1

48    16

51      x

78    26

84     y

So, the ratio are in proportion then

48 / 16 = 51 /x

3 = 51/x

x= 51/3

x = 17

and, 3/1 = 84/y

y= 84/3

y= 28

Thus, the values are 17 and 28.

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After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.

The number of half-lives in 30 days is 30/5 = 6.

So, after 1 half-life, the amount remaining is 948/2 = 474 grams.

After 2 half-lives, the amount remaining is 474/2 = 237 grams.

After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.

After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.

After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.

After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.

Therefore, after 30 days, 14.8125 grams of the element remains

We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.

We also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.

Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.

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Answer:60 degrees

Step-by-step explanation: The three angles of a triangle add to 180, a right angle is 90 so 180-90-30= 60.

Answer:

45

Step-by-step explanation:

Answer:

$3.58

Step-by-step explanation:

Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.

Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:

[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]

The length of the arc FG is 12.56 units

Length of an arc is the distance that runs through the curved line of the circle making up the arc.

An arc is a cut out section of a circle. The circumference is the whole body of the circle.

The length of an arc is expressed as

(tetha))360 × 2πr

where r is the radius and tetha is the angle between the radii.

l = 72/360 × 2 × 3.14 × 10

l = 4521.6/360

l = 12.56 units

therefore the length of the arc FG is 12.56 units

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Answer:

The answer is D.

[tex] \frac{1}{5}(12x - 10)[/tex]

Answer:

The answer to your problem is, 6.1 inches

Step-by-step explanation:

So we know that 1 inch of there model in real life is 50 feet.

Divide:

305 / 50

= 6.1 but we are going to use 6

Since it is 6 there model is 6 inches.

But remember we still have that 0.1 which we need to full fill for that:

Note that 6.1 will be in inches.

So it is done.

Thus the answer to your problem is, 6.1 inches

Answer:

It's linear

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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If the graphs of the linear equations in a system are parallel: A. There is no solution.

The general form for the equation of a line is:

y = mx + c

where:

m is slope

c is y-intercept

Usually, for two equations to have a solution, they must intersect each other.

However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.

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Answer:

  42 units³

Step-by-step explanation:

You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.

The formula for the volume of a prism is ...

  V = Bh

where B is the base area and h is the height perpendicular to the base.

Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...

  V = (5 1/4 u²)(8 u) = 42 u³

The volume of the prism is 42 cubic units.

The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.

Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.

Let's begin by calculating the total cost of producing 400 brownies a day:

Cost per brownie = 25 cents = 0.25 dollars

Total cost = 400 × 0.25 = 100 dollars

To make a daily profit of at least $420, the total revenue should be:

Total revenue = Total cost + Minimum profit

Total revenue = 100 + 420 = 520 dollars

The minimum selling price per brownie to achieve this revenue can be calculated as:

Selling price per brownie = Total revenue / Number of brownies produced

Selling price per brownie = 520 / 400

Selling price per brownie = 1.3 dollars

Therefore, the minimum selling price is $1.30 per brownies.

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C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

====================================================

Explanation:

If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.

Count the dots over the x axis labels of "0.4" through "0.6"

That makes 5+1+1 = 7 dots total.

There are 7 instances where the difference of proportions is 0.4 or larger.

This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.

This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.

Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.

The measure of angle ABC is 30 degrees. Option B

It is important to note the properties of a circle, they include;

Also note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.

From the information given, we have that;

<ADC = 60 degrees

This is the angle at the circle

Then,

<ABC is the angle at the circumference

<ABC = <ADC/2 = 60/2 = 30 degrees

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The weekly benefit of the employees is A = £ 11.40

Given data ,

Let's calculate the weekly benefit for an employee who spends an average of £14 each weekday and £22 on each day of the weekend, considering the 10% discount they receive at Tesco stores.

First, we'll calculate the total amount spent on weekdays and weekends separately:

Amount spent on weekdays = £14/day x 5 days/week = £70/week

Amount spent on weekends = £22/day x 2 days/week = £44/week

Next, we'll calculate the total amount spent in a week by adding the amounts spent on weekdays and weekends:

On simplifying the equation , we get

Total amount spent in a week = £70 + £44 = £114

Now, we'll calculate the 10% discount on the total amount spent:

10% of £114 = £11.40

Hence , the weekly benefit to the employee who receives a 10% discount on their shopping at Tesco stores would be £11.40

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Step-by-step explanation:

Use the Ratio Test since Ratio Test guarantee absolutely convergence.

[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]

This simplifes to

[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]

[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

Take the absolute value

[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

In order for this series to be convergent,

the limit as k approaches infinity must be less than 1.

In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.

Why

If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity

Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.

So one of the answer is 3.

The t-statistic value of the hypothesis is 2.236

The population mean is equal to 6,500 (H0: μ = 6500)

Alternative hypothesis:

The population mean is greater than 6,500 (Ha: μ > 6500)

We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.

First, we need to calculate the t-statistic using the formula:

t = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (6,600 - 6,500) / (1,000 / √500)

= 2.236

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