Given: HF || JK; HG ≅ JG Prove: TriangleFHG ≅ TriangleKJG Triangles F H G and K J G connect at point G. Sides F H and J K are parallel. Sides H G and G J are congruent. To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof? AngleFGH ≅ AngleKGJ because vertical angles are congruent. AngleJKG ≅ AngleHFG because vertical angles are congruent. AngleFHG ≅ AngleJKG because right angles are congruent. AngleHFG ≅ AngleKJG because alternate interior angles are congruent.

Answer: there you go

Step-by-step explanation:

According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.

To calculate the surface area of the composite solid we have to perform the following procedure:

Sides (a) area

Sides (b) area

Face (c) area

Base area

4 * 7 = 28

Total surface area

To calculate the total surface area we have to add the value of each face as shown below:

According to the above, the surface area of this solid would be 127.

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We have found the unit vector u in the direction of v and verified that ||u|| = 1. The values are: u = (-9/√85, -2/√85) and ||u|| = 1.

To find a unit vector u in the direction of v and to verify that ||u|| = 1, where v = (-9, -2), we can follow these steps:

Step 1: Calculate the magnitude of v. Magnitude of v is given by:

||v|| = √(v₁² + v₂²)

Substituting the given values, we get: ||v|| = √((-9)² + (-2)²) = √(81 + 4) = √85 Step 2: Find the unit vector u in the direction of v. Unit vector u in the direction of v is given by:

u = v/||v||

Substituting the given values, we get:

u = (-9/√85, -2/√85)

Step 3: Verify that ||u|| = 1.

The magnitude of a unit vector is always equal to 1.

Therefore, we need to calculate the magnitude of u using the formula:

||u|| = √(u₁² + u₂²) Substituting the calculated values, we get: ||u|| = √((-9/√85)² + (-2/√85)²) = √(81/85 + 4/85) = √(85/85) = 1

Hence, we have found the unit vector u in the direction of v and verified that ||u|| = 1. The values are: u = (-9/√85, -2/√85) and ||u|| = 1.

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Answer:

where is the question i do not see a question but if you provide me with one i will be more than happy to help you!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It is A because A can type 50 words in a minute and B only types 40 words in a minute and 50 words > 40 words

Answer:

1 4 5

Step-by-step explanation:

Answer:

The second box

The forth box

And

The sixth box

Step-by-step explanation:

Answer:

The ratio of this number to the rectangle’s area is 9:32.

Step-by-step explanation:

The information provided are:

The area of the square is:

A = (side)²

  \(=(8\ \text{feet})^{2}\\\\=64\ \text{feet}^{2}\)

The number of people standing insider the square is:

n = 18

Compute the ration of n to A as follows:

\(n:A=18:64\)

        \(=\frac{18}{64}\\\\=\frac{9}{32}\\\\=9:32\)

Thus, the ratio of this number to the rectangle’s area is 9:32.

If the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

Number of boys in the class = 15 boys

Number of girls in the class = 20 girls

The ratio can be defined as the a number that can be used to express one quantity as a fraction of the other ones. That means we are comparing them by dividing those numbers

Here the ratio will be

Number of boys in the class : Number of girls in the class

Substitute the values in the ratio

= 15 : 20

Divide both numbers by 5

= (15/5) : (20/5)

= 3 : 4

Hence, if the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

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Answer:

A) x+5=x+3

B) x+5=5+x

Step-by-step explanation:

A) If an equation has no solutions then when it is algebraically solved it will be an untrue statement.

For example, x+5=x+3. To solve subtract x from both sides. This becomes 5=3, which is not a true statement. Therefore, there are no solutions.

B) If an equation has infinite solutions then when it is algebraically solved it will be a statement that is always true.

For example, x+5=5+x. To solve first subtract x from both sides. This equals 5=5, which is always true. Therefore, there are infinite solutions.

Answer:

4

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

i think of a number multiply it by 3 and add 4 i get 22.

x = a number

x is being multiplied by 3 (3*x or 3x), thening add 4 is equal to 22.

3x + 4 = 22

    - 4    - 4

3x = 18

/3      /3

x = 6

Therefore, the unknown number is 6.

Hope this helps!

The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Their sum is 55 .

Their mean (average) is (55/10).

That's 5.5 . (Choice b).

Answer:

60

Step-by-step explanation:

30 pages per 6 hours

300/30 = 10

10*6 = 60 hours

Answer:

21. Same Line

22. Same Line

23. Perpendicular

24. Neither

25. Parallel

26. Neither

27. Neither

28. Neither

29. Perpendicular

30. Perpendicular

31. Neither

32. Perpendicular

33. Parallel

34. Perpendicular

35. Perpendicular (?)

36. Neither

37. Neither

38. Parallel

39. Neither

40. Parallel

Answer:

2.7

Step-by-step explanation:

you can do sin17 * 9.3, because sin = opp/hyp = x/9.3

use your calculator for sin17 and multiply it by 9.3

Answer:

x=4/3 .   x=2/5

Step-by-step explanation:

The ratio can be written as a fraction as $5/25 reduced to 1/5 by dividing with 5.

A fraction is written as a ratio of two numbers, separated by a fraction bar. The number above the fraction bar is the numerator and the bottom number is the denominator.

This fraction can then be reduced.

To reduce a fraction, we must find the greatest common factor (GCF) of the numerator and denominator.

Here the GCF of 5 and 25 is 5.

When we divide the numerator and denominator by the GCF, we get the reduced fraction 1/5.

The ratio of $5 to $25 can be written as a fraction by expressing the values as $5/25 and reduced to 1/5 by dividing the numerator and denominator by the greatest common factor of 5.

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Answer:

probably of a head= 1/2

probably of a multiple of 3 (either 3 or 6)= 2ways*1/6 as 1/6 is the prob of any one side

Step-by-step explanation:

Answer:

1/12 or 8.3%

Step-by-step explanation:

To find probability, mark the how many sides you are testing in your probability over the possible outcomes.

Die: 1 side out of 6 sides is the test = 1/6 probability abt. 16%

Coin: 1 side out of 2 sides is the test = 1/2 probability 50%

To find total probability of getting a 5 on the die and a heads on the coin is found by multiplying the two fractions together.

1/6 x 1/2 = 1/12

abt. 16% x 50% = abt. 8%

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Ordered pair{(−6,−1),(−8,4),(−5,4),(3,−9)} from the given set of ordered pairs represents the function.

As given in the question,

Given set of ordered pairs following is the one which represents the function :

In the given set of ordered pair for input value 3 there are two outputs 3 and -4 , therefore it is not a function.

In the given set of ordered pair for input value -5 there are two outputs 7 and 8 , therefore it is not a function.

In the given set of ordered pair each input has unique single output. Therefore it is a function.

In the given set of ordered pair for input value -1 there are two outputs 0 and -4 , therefore it is not a function.

Therefore, ordered pair{(−6,−1),(−8,4),(−5,4),(3,−9)}  from the given set of ordered pairs represents the function.

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The answer option that matches the graph I drew include the following: D. graph D.

In Mathematics, the following rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph:

In this context, we can logically deduce that the most appropriate graph to represent the solution to the given inequality y ≤ - 2x is graph D because the solid boundary lines must be shaded below.

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The range of a particular artillery piece in miles, which has a range r of 8260 yards is 4.7 miles (approximately).

It is given in the question that 1 mile is equal to 5280 ft and 1 yard is equal to 3 ft.

Hence, according to the question,

1 yard = 3ft

1/3 yard = 1 ft

Hence,

5280 ft = 1/3 * 5280 yards

5280 ft = 1760 yards

As 1 mile = 5280 ft

So,

1 mile = 1760 yards

Hence,

1/1760 mile = 1 yard

We have to find the range of 8260 yards in miles.

Hence,

8260*1/1760 miles = 8260 yards

8260 yards ≈ 4.69 miles ≈ 4.7 miles

8260 yards ≈ 4.7 miles

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The probability that the first student chosen is a boy and the second is a girl is 7/30.

We are given that there are 3 girls and 7 boys in a class with a total of 10 students.

Let us find the probability of selecting a boy first, and then a girl second.

To find the probability of the first event occurring followed by the second, we use the multiplication principle of probability.

This states that the probability of two independent events occurring together is the product of the probability of each event occurring separately.

The probability of selecting a boy first is 7/10.

If a boy is selected first, there are 3 girls and 6 boys left to choose from, so the probability of selecting a girl second is 3/9 (since there are 9 students left in total).

Therefore, the probability of selecting a boy first and then a girl is:7/10 × 3/9 = 21/90

Simplifying this fraction gives the answer in reduced form:21/90 = 7/30

Therefore, the probability that the first student chosen is a boy and the second is a girl is 7/30.

The answer is represented as a fraction in reduced form.

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The probability that the first student chosen is a boy and the second is a girl is 7/15.

To calculate the probability of the first student chosen being a boy and the second being a girl, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since there are 10 students in total, the teacher can choose any two students out of the 10. Therefore, the total number of possible outcomes is given by the combination formula:

C(10, 2) = 10! / (2!(10 - 2)!) = 45

Number of favorable outcomes:

The first student chosen must be a boy, and there are 7 boys in the class. Once a boy is chosen, there are 3 girls left, and the second student chosen must be a girl. Therefore, the number of favorable outcomes is given by:

Number of favorable outcomes = Number of ways to choose a boy (7) * Number of ways to choose a girl (3) = 7 * 3 = 21

Probability:

The probability is then calculated as the number of favorable outcomes divided by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = 21 / 45

To reduce this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 3:

Probability = (21 / 3) / (45 / 3) = 7 / 15

Therefore, the probability that the first student chosen is a boy and the second is a girl is 7/15.

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Answer:

x=-28/3

28/x=1-4

28/x=-3

28=-3x

-28/3=x

switch them around and that's your answer.

Answer:

x = 4

Step-by-step explanation:

28÷x+4=11

28/x  + 4 = 11

Subtract 4 from each side

28÷x+4-4=11-4

28 / x = 7

Multiply each side by x

28/x * x = 7x

28 = 7x

Divide each side by 7

28/7 = 7x/7

4 =x

The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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It will take approximately 15.9 years from now for the water treatment plant to reach its design capacity, assuming an arithmetic rate of population growth.

To determine the number of years from now when the water treatment plant will reach its design capacity, we need to consider the population growth rate and the projected population increase over the next 20 years.

Currently, the population of the community is 20,000, and the average water consumption is 4200 m3/day. The existing water treatment plant has a design capacity of 6000 m3/day.

To estimate the future population, we can assume an arithmetic rate of population growth. This means that the population will increase by a constant amount each year. We can calculate the rate by dividing the projected population increase (44,000 - 20,000 = 24,000) by the number of years (20). So the growth rate is 24,000 / 20 = 1200 people per year.

To estimate when the plant will reach its design capacity, we need to consider both population growth and water consumption. The water consumption per person remains constant at 4200 m3/day.

Initially, the water treatment plant has a surplus capacity of 6000 m3/day - 4200 m3/day = 1800 m3/day.

The surplus capacity can accommodate an additional number of people, given that each person consumes 4200 m3/year (4200 m3/day * 365 days/year). So, the surplus capacity can accommodate 1800 m3/day / 4200 m3/year ≈ 0.43 people per day.

To determine the number of years it will take for the plant to reach its design capacity, we divide the remaining population increase (24,000) by the surplus capacity per year (0.43 people/day * 365 days/year):

Years = 24,000 / (0.43 * 365) ≈ 15.9 years.

Therefore, it will take approximately 15.9 years from now for the water treatment plant to reach its design capacity, assuming an arithmetic rate of population growth.

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The closest measurement to the circumference of the parachute in feet is 78.54 feet. The calculation was done by multiplying the radius by 2π (the constant pi, approximately equal to 3.14), which gives the circumference of a circle is 78.54 feet.

The circumference of the parachute can be calculated using the formula

C = 2πr

where r is the radius of the parachute.

Given that the radius of the parachute is 12.5 feet, we can substitute this value in the formula and calculate the circumference

C = 2πr

C = 2π(12.5)

C ≈ 78.54 feet

Therefore, the circumference of the parachute is closest to 78.54 feet.

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--The given question is incomplete, the complete question is given

" Which measurement is closest to the circumference of circumference of the parachute in feet if radius is 12.5.  "--

Answer:

18

Step-by-step explanation:

for f(3), x = 3

We should use the one where x ≥ 3

f(x) = 2x²

f(3) = 2 * 3²

= 2*9

=18

No, Kareem is not correct because the ratio of 4:1 can never be equal to the ratio of 12:9.

Here,

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.

Because 4+8=12 and 1+8=9.

We have to find that Kareem is correct or not.

What is a ratio?

Ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Now,

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.

Calculate the ratio as;

12 / 9 = ( 3 x 4 ) / ( 3 x 3 ) = 4/3

So,

12 / 9 = 4 / 3

Hence, Kareem is incorrect because the ratio of 4:1 can never be equal to the ratio of 12:9.

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