All categories

3 years ago

How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from

Mathematics

1 answer:

dexar [7]3 years ago

3 0

Answer:

6.04 km

Step-by-step explanation:

From the image attached, both triangles form are similar to each other because their corresponding angles are equal, therefore they are equiangular triangles. equiangular triangles have the same shape but different sizes and the ratio of their corresponding sides are equal.

Therefore since their corresponding sides are equal we can calculate the distance from the main gate to Manatee Springs. It is given by:

$\frac{3500\ yards}{2000\ yards} = \frac{4200\ yards}{x}\\ x= \frac{4200\ yard*2000\ yards}{3500\ yards}=2400\ yards$

x = 2400 yards.

The distance from the main gate to Manatee Springs = x + 4200 yards = 2400 + 4200 = 6600 yards

The distance from the main gate to Manatee Springs = 6600 yards = (6600 * 0.0009144) km = 6.04 km

The distance from the main gate to Manatee Springs = 6.04 km

You might be interested in

The scale of the room design shows that 1" = 3 feet. How big is the actual room if the design shows a square that is 6 inches wi

adoni [48]

Answer:

arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:

1 inch=30 feet.

If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?

In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.

Using Proportions to Find Dimensions

A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.

A scale drawing is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.

Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as

1 in4 ft

(Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)

A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.

First, create a proportion using equivalent ratios. Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the variable x.

1 in.4 ft.=4 in.x ft.

Then, cross multiply and simplify the equation to find the value of x.

xx==4(4)16

The sculpture will be 16 feet tall.

Let’s make a scale drawing. Use the scale 1′′=2′. Draw a room that is 8′×12′.

First, write a proportion to find the measurement of the width.

1′′2′=x′′8′

Next, cross multiply and simplify the equation to find the value of x.

2x2xx===1(8)84

The drawing will be 4

4 0

3 years ago

P (D) = .42, P (E) = .27, and P (D ∩ E) = .15 P (D U E)

Paul [167]

We know that $P(D\cap E)=P(D)P(E)=\boxed{0.1134}$ .

And $P(D\cup E)=P(D)+P(E)-P(D\cap E)=\boxed{0.5766}$ .

Hope this helps.

6 0

3 years ago

In your own words, explain how to find the incenter and the circumcenter of a triangle and what the Circumcenter Theorem and Inc

LekaFEV [45]

Circumcenter is where three perpendicular bisectors intersect and incenter is where the three angle bisectors intersect.

Way to find them and the theorems are mentioned below.

Step-by-step explanation:

To find Incenter :

Construct angle bisectors of each angle of the triangle and their intersection point gives the incenter.

To find Circumcenter:

Construct perpendicular bisectors of all sides of triangle and their intersection point gives the circumcenter.

Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.

Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.

5 0

3 years ago

Stacy owes $40 on her credit card. After she made a payment, her new balance was $10. What was the amount of her

Yakvenalex [24]

Answer:

Step-by-step explanation:

x + 40 = 10

x = -30

She paid $30 on her credit card

6 0

3 years ago

Read 2 more answers

Square root of 3x^4 times square root of 5x^2 times square root of 10.

Cloud [144]

Answer:

Step-by-step explanation:

As long as the indices are the same for all the radicals, you can multiply them together. Our index for each of these is 2 (square root) so we multiply them all together and put it under 1 square root sign (radical):

$\sqrt{150x^6$ The largest perfect square in 150 is 25, and the 6th power on the x needs just to be rewritten in terms of an exponent of 2 to give us:

$\sqrt{25*6*(x^3)^2}$ and pull out the perfect squares to get

$5x^3\sqrt{6}$

5 0

3 years ago

Read 2 more answers