Figure FGH has vertices located at F(1, 3), G(–1, 2), and H(2, 1). The figure is rotated using the origin as the center of rotation. The image has vertices located at F’(3, –1), G’(2, 1), and H’(1, –2). Which rotation could have taken place?
a 45° clockwise rotation
a 90° clockwise rotation
a 90° counterclockwise rotation
a 180° counterclockwise rotation

After 45 hours, approximately 46.375 mg of the isotope will be left, given its half-life is 15 hours. This was determined by calculating the amount remaining after each of three half-lives. Each half-life reduces the amount by half.

To determine how much of the isotope is left after 45 hours, we need to use the concept of half-life. The half-life of the isotope is 15 hours. This means that every 15 hours, half of the isotope decays. We start with 371 mg.

First, calculate how many half-lives have passed:

After each half-life, the amount of isotope remaining is halved:

Therefore, after 45 hours, approximately 46.375 mg of the isotope will be left.

Answer:

224 cars.

Step-by-step explanation:

We have been given that Jen has 1568 orange cars and 448 blue cars. she wants to line up the cars in groups so that each group has the same number of cars and contains only orange cars or only blue cars.

To solve our given problem, we will find greatest common factor of 1568 and 448.

Prime factorization of 1568: [tex]2\times 2 \times 2\times2\times2\times7\times7[/tex]

Prime factorization of 448: [tex]2\times 2 \times 2\times2\times2\times2\times7[/tex]

We can see that  448 and 1568 is [tex]2\times 2 \times 2\times2\times2\times7=224[/tex]

Therefore, each group will have 224 cars.

Answer:

it take 31.53 minutes to run the entire race

it take 6.3 minutes to run the 1 km

Step-by-step explanation:

A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.

[tex]\frac{2}{3} \cdot 5= \frac{10}{3}[/tex]

3.33 km is covered in 21 minutes

So 5 km is covered in [tex]\frac{5 \cdot 21}{3.33}=31.53[/tex]minutes

it take 31.53 minutes to run the entire race

[tex] \frac{10}{3}[/tex] km is covered in 21 minutes

1 km is covered in [tex]\frac{21}{\frac{10}{3} } =6.3[/tex]

It takes to run the entire race is 31 minutes and 30 seconds and it takes to run 1 kilometer is 6 minutes and 18 seconds.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

[tex]\rm speed = \dfrac{distance}{time}[/tex]

A runner ran 2/3 of a 5 kilometers race in 21 minutes. They ran the entire race at a constant speed.

2/3 of 5 km is given as x

[tex]x = \dfrac{2}{3}* 5 = \dfrac{10}{3}[/tex]

Then the speed will be

[tex]\rm speed = \dfrac{\frac{10}{3}}{21} = \dfrac{10}{3*21} = \dfrac{10}{63}[/tex]

a. It takes to run the entire race will be

[tex]\rm Time = \dfrac{5}{ \frac{10}{63}} = \dfrac{63* 5 }{10} =31.5[/tex]

It takes to run the entire race is 31 minutes and 30 seconds.

B.  It takes to run 1 kilometer will be

[tex]\rm Time = \dfrac{1}{ \frac{10}{63}} = \dfrac{63* 1}{10} = 6.3[/tex]

It takes to run 1 kilometer is 6 minutes and 18 seconds.

More about the speed link is given below.

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Answer:

[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]

Step-by-step explanation:

The given expression is

[tex]f(x)=x^{3}-9x^{2} +26x-24[/tex]

First, we need the divisors of the independent term, which is 24.

24 divisors: 1, 2, 3, 4, 6, 8, 12, 24.

Now, we replace each divisor in the function, and those which gives zero as result, those are gonna be the roots of the equation.

For [tex]x=1[/tex]

[tex]f(1)=(1)^{3}-9(1)^{2} +26(1)-24=1-9+26-24=-6[/tex]

This means [tex]x=1[/tex] is not a solution.

For [tex]x=2[/tex]

[tex]f(2)=(2)^{3}-9(2)^{2} +26(2)-24=8-36+52-24=0[/tex]

So, [tex]x=2[/tex] is the first solution.

For [tex]x=3[/tex]

[tex]f(3)=(3)^{3}-9(3)^{2} +26(3)-24=27-81+78-24=0[/tex]

It's solution.

For [tex]x=4[/tex]

[tex]f(4)=(4)^{3}-9(4)^{2} +26(4)-24=64-144+104-24=0[/tex]

Therefore, all roots are

[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]

The height of the fountain is 43.20m

Data;

The circumference of a circle is given as

[tex]c = 2\pi r[/tex]

Let's calculate the radius of the circle

[tex]c=2\pi r\\r=c/2\pi \\r=190/(2*3.14)\\r=30.25m[/tex]

Assuming the radius of the pool makes a right angle triangle with the top of the fountain;

[tex]tan\theta=\frac{opposite}{adjacent}\\tan55=\frac{x}{30.25}\\ x= 30.25tan55\\x=43.20m[/tex]

From the calculations above, the height of the fountain is 43.20m

Learn more on right-angle triangles here;

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Answer:

118

Step-by-step explanation:

The speed of tortoise with the given distance and time is 2.5 meters per minute.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, distance =12.5 meters and time =5 minutes.

We know that, Speed =Distance/Time

= 12.5/5

= 2.5 meters per minute

Hence, the speed of tortoise is 2.5 meters per minute.

To learn more about the speed, distance, and time visit:

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Answer:

z+1 , 6 + w and [tex]2x^{4}+4[/tex] are polynomials.

Step-by-step explanation:

Given  : Expressions.

To find: Which expressions are polynomials.

Solution : We have given expression

Polynomial : A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer.

So, z + 1  having variable z and contact 1 so, it is a polynomial.

6 + w is also a polynomial.

[tex]2x^{4}+4[/tex] is also a polynomial that has degree 4 .

But expression [tex]y^{2}-\sqrt[1]{y}+4[/tex] is not a polynomial because it has fractional exponent.

Therefore, z+1 , 6 + w and [tex]2x^{4}+4[/tex] are polynomials.

To get the probability of two individual events both occurring, you have to multiply the probabilities of their individual events occurring. Therefore in this problem, the probability that a student selected at random will pass both French 101 and French 102 is 0.683 (.75 x .91). The answer is already rounded to three decimal places.

25 candles

What is profit and loss ?

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

According to the given question,

Candles sold must cover the expenses = 100

Let x be the no. of candles that needs to be sold to cover the expenses

rent = 100

Cost price of 1 candle = CP = 1

Cost price of x candles = CP = 1x

Selling price of 1 candle = SP = 5

Selling price of x candles = SP = 5x

Therefore, from the above statements we can infer that the profit generated must be equal to the expenses,

So, SP - CP = Profit = 100

5x - x  = 100

4x = 100

x = 25

Therefore, we need 25 candles that needs to be sold to cover the expenses

Read more about SI units at:

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