A mountain on a tropical island experiences changes in its height due to volcanic activity. Its current height is 2,827 meters, which is 10% taller than it was when the mountain was last measured. How tall was it then?

The third side of a triangle can be calculated using the Pythagorean Theorem.

This theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite the right angle.

Formula:

[tex]a^2 + b^2 = c^2[/tex]

Determine the two side lengths of the triangle

Calculate the sum of the squares of the two side lengths.

Calculate the square root of the sum of the squares of the two side lengths. This is the length of the third side (the hypotenuse).

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ4

Answer:

120

Step-by-step explanation:

90÷6=15×8=120

[tex]b = 5, \: g = 3, \: r = 8[/tex]

[tex]total = 5 + 3 + 8 = 16[/tex]

[tex]p(b) = \frac{5}{16} [/tex]

[tex]p(g |without \: replacement|) = \frac{3}{16 - 1} = \frac{3}{15} = \frac{1}{5} \\ [/tex]

[tex]p(b \: and \: g) = \frac{5}{16} \times \frac{1}{5} = \frac{1}{16} [/tex]

Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.

Here,

we can rationalize a radical-containing fraction's denominator by doing the following:

Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.

Verify in step two that all radicals have been streamlined.

Step three is to simplify the fraction, if necessary.

Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

To know  more about fraction , visit

brainly.com/question/10708469

#SPJ1

Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.

Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.

An inequity of 3R + 7B 1000 has been handed to us.

We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.

Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.

Guliskhan moves at a steady pace of 3 meters per second because of this.

B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.

C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.

=>3*60 + 7*90 ≥ 1000

=>180 + 630 ≥ 1000

=>810 ≠> 1000

Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

To know more about inequality , visit

brainly.com/question/28823603

#SPJ4

Answer:

the lateral area of the regular prism is 30 cm².

Step-by-step explanation:

Given;

the base of the regular prism, b 4cm

height of the prism, h = 2.5 cm

The lateral area of the regular prism is calculated as the product of the base perimeter and height of the prism.

L.A = P x h

where;

P is the perimeter of the base = 3 x 4cm (equilateral triangle has equal sides)

P = 12 cm

L.A = 12 cm x 2.5 cm

L.A = 30 cm²

Therefore, the lateral area of the regular prism is 30 cm².

Answer:

30 cm2

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

60 divided by 15=4

90 x 4 =360

Answer:

720 miles

Step-by-step explanation:

This is assuming the train continues to move at the same speed.

You can think about the problem in the following way:

The 2 hour journey is split up into x number of 15 minute segments.

2 hours = 120 minutes

120/15 = 8

Therefore, x = 8.

If the journey can be split into 8 15 minute segments, and each 15 minute segment carries it 90 miles, the total distance traveled is given by:

8 * 90 miles = 720 miles

Atlernatively, you can calculate the average speed of the train.

Speed = Distance/Time

So: Speed = 90 miles/15 minutes = 6 miles/minute.

Reusing the above formula, substituting in speed = 6 miles/minute and time = 120

Answer:

50.24

Step-by-step explanation:

The formula for solving circumference is 2 x pi x r

first the radius is 8 (divide 16 by 2 and get radius)

( pi can be 22/7 or 3.14. but I’m taking 3.14 )

second, we have all values, now we just have to substitute them!

Pi = 3.14

R = 8

so when we do 2x 3.14 x 8 = 50.24

I hope this helped!

Answer: The area of the circle is 64π cm

Step-by-step explanation:

d=16→r=8

A= π⋅8 ^2

A= π⋅64

A=64π

A system that has no solution is classified as inconsistent.

A system that has one and only one solution is classified as  independent

The system of equation graphed is consistent and independent.

The equations given by the graph are expressed as;

3x - 4y = 32

3x + 5y = 24

Now, if we subtract eq 1 from eq 2, we will get;

5y - (-4y) = 24 - 32

9y = -8

y = -8/9

Put 8/9 for y in eq 2 to get;

3x + 5(8/9) = 24

3x = 24 - 40/9

3x = 176/9

x = 176/27

Now, to classify solution to equations, we say that;

1) When there is no solution, it is inconsistent.

2) When there is one and only one solution, it is independent

Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.

Read more about Graph of Linear Equations at; https://brainly.com/question/14323743

#SPJ1

Answer: 36 are red

Step-by-step explanation:

3 out of every 5

5*12 = 60

so do 3*12 which = 36

36/60

Answer: I believe is the first one

Step-by-step explanation:  It says animal in hundreds right. so looking at it 200 animals is right. But also x = 2 and y = 12

Hope this helps I'm sorry if it does not help

Answer:

0.26.  This is the fraction of states that do not use wind energy.  

Step-by-step explanation:

There are 50 states total.  If 37 use wind energy, then 50 - 37, or 13, do not.

13/50 = 0.26.  This is the fraction of states that do not use wind energy.  

Answer: A perimeter is the total length of all the sides of a polygon. It is calculated by adding up the lengths of all the sides of the polygon. For a polygon with distinct and non-overlapping sides, each side length contributes exactly once to the perimeter. So in such case, a side length of a polygon can never produce two different perimeters.

However, it's worth mentioning that, one side length of a function could be a side of a polygon and the other could be a side of another shape. Also, it's possible that a single side length of an object is connected to a different set of side length, generating different perimeters.

For example, the length of an arc of a circle can be considered as a "side length" of the circle and it can be used to calculate both the perimeter of the arc and the circumference of the full circle, which are different measurements.

Also, a circular pool has a radius, but it's perimeter is the circumference, and this length is produced by the same radius but it's a different perimeter from the length of the radius.

In summary, a side length can produce different perimeter if we are talking about different shapes and measurements.

Step-by-step explanation:

Answer:

1) The stars are not constant in their position.

2) No. The stars aren't in original position because of apparent movement of stars in the sky.

3) Due to rotation of earth on its axis , the stars appear to move from west to east in the sky. Actually stars don't move as they are constant in their position but they appear to move with respect to earth.

4) Both the motion of stars & motion of sun are similar because both are an example of apparent motion. Both appear to change their respective positions but in reality , sun & stars are constant in their positions. But as earth is rotating , it appears like sun & stars are changing their positions.

The reasonable solutions for this situation is (1, 3.5) and (2, 2)

A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.

Audrey has x pounds of red grapes and y pounds of green grapes.

She has less than 5 pounds of grapes in all, hence:

x + y < 5

Also, x ≥ 0, y ≥ 0

a) The option (–1, 2) is wrong because x = -1 < 0

b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5

c) The option (2, 2) is correct because 2 + 2 = 4 < 5

d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.

e) The option (5, 0) is wrong because 5 + 0 is not less than 5

To learn more about Graphs visit:

https://brainly.com/question/17267403

#SPJ4

The process to find the asymptote and zeros of the function is explained below.

The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.

Here we need to find the way to identify the asymptotes and zeros of a function.

The process of finding the asymptote is defined as,

If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.

Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.

Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.

The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.

To know more about asymptote here.

https://brainly.com/question/2303876

#SPJ4

Answer:

x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

Step-by-step explanation:

Given the expression x/x²-1 + 4/x²-6x-7

Factorize x²-6x-7

x²-6x-7

= x²-7x+x-7

= x(x-7)+1(x-7)

= (x+1)(x-7)

Replace back into the expression given

x/x²-1 + 4/x²-6x-7

= x/x²-1 + 4/ (x+1)(x-7)

= x/(x+1)(x-1) + 4/(x+1)(x-7)

Find the LCM

=  x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

This gives the required expression

Answer:

45.7 inches

Step-by-step explanation:

The perimeter uses 3 sides of the square, so 3 x 10 = 30. We'll add that later.

Then we need to find the circumference of the half-circle. We know the diameter is 10, because that's the side of a square.

Circumference = pi x diameter

C = 3.14 x 10 = 31.4

But that's for the whole circle. We only have a half.

31.4 /2 = 15.7 is the perimeter for the half circle. Add this to the 3 sides of the square

30 + 15.7 = 45.7

The company is likely to sell 3,120 copies of rock music per week.

If the company estimates sales of 6,000 copies a week at its online store, it is likely that 78/150 x 6,000 = 3,120 copies will be from the rock genre.

To find this, we first need to calculate the proportion of visitors that preferred rock music by dividing the number of visitors who preferred rock (78) by the total number of visitors surveyed (150). This gives us 78/150 = 0.52.

Next, we multiply this proportion by the estimated number of weekly sales at the online store (6,000) to find the number of sales that are likely to be from the rock genre. 0.52 x 6,000 = 3,120.

So, the company is likely to sell 3,120 copies of rock music per week.

To learn more about the multiply, visit:

brainly.com/question/23536361

#SPJ4

Answer:

B. 64 cubic meters

Step-by-step explanation:

The first rectangle has the dimensions 7 x 2 x 4. 2 x 4 is 8, and 8 x 7 is 56. The square has the dimensions 2 x 2 x 2, which is 8. 56 + 8 is 64, so the answer is 64.

Answer:

ITS B HOPE THIS HELPS

Step-by-step explanation:

Answer:

x = A/7

Step-by-step explanation:

Given that the screen is rectangular, recall that the area A of a rectangle whose length is L and width is W is given as

A = L * W

Hence if the width is 7 inches and the length is x inches then the area which is A square inches is connected to both sides as

A = x * 7

Divide both sides by 7

x = A/7 inches

Answer:

Isosceles trapezoid has congruent base angles:

∠A ≅ ∠D and ∠B ≅ ∠C

Answer:

x = 16 degrees

y = 28 degrees

Step-by-step explanation:

1.) ∠A ≈ ∠D since they are base angles: so;

5x = 80

=> divide 5 on both sides:

x = 16 degrees

2.) Now Substitute 16 in for the x-value

5x ⇒ 5(16) = 80,

3.) Since we know the measure of the sum of interior angles is 360° we can say that:

(4y - 12) + 100 + 5(16) + 80 = 360

=> 4y - 12 + 100 + 80 + 80 = 360

=> 4y + 248 = 360

Subtract 248 on both sides of "="

=> 4y = 112

Divide 4 on both sides of "="

=> y = 28

Hope this helps!

The inverse of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.

So the correct answer is  f ^ - 1 * (x) = 3/x - 1

The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.

Given the function f(x) = 3/(x + 1), we can find its inverse by:

y = 3/ (x + 1)

Multiply with (x + 1) and divide by y

y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y

x + 1 = 3/ y

x = 3/ y - 1

Switching the roles of x and y:

y = 3/ x - 1

Thus f^(-1)(x) = 3/ x - 1

It's worth noting that in order for a function to have an inverse function it must be a one-to-one function. This means that for every y value there is only one x value.

To know more on inverse function

https://brainly.com/question/12253920

#SPJ4

Answer:

Step-by-step explanation:

Answer:

ITS 64 degrees

Step-by-step explanation:

Answer:

116

Step-by-step explanation:

hope this helps:)..........

Answer:

6 Passwords

Step-by-step explanation:

718, 781, 817, 871, 178, 187

(Hope this helped! Please comment any questions) :)

Answer:

The idiot that sent the link just got taken down so I'll just answer with my comment.

Step-by-step explanation:

"I believe it is 6"

Answer:

the amount spent on petrol is Rs 9,676

Step-by-step explanation:

Given that

The tax driver filled the car petrol with 54 liters on Saturday

On sunday, he filled his tank with 64 liters

And, the petrol cost is Rs 82 per liter

We need to find out the amount of money spent

SO,

= (54 liters + 64 liters) × Rs 82

= Rs 9,676

Hence, the amount spent on petrol is Rs 9,676

The answer choice which represents a number line for the intersection of the given intervals is; (4, ∞).

The answer choice which represents a number line for the union of the given intervals is; (-3, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-3, ∞) and (4, ∞)

It follows that the intersection of both intervals is the interval; (4, ∞).

Also, the interval which represents the union of both intervals is; (-3, ∞).

Hence, the image which represents both scenarios is attached.

Read more on intersection and union of sets;

https://brainly.com/question/28278437

#SPJ1