Find the solution to the system of equations.

Westkost [7]

Answer:

A=10 cm

B=5 cm

Area of square = 25 cm

Step-by-step explanation:

Since that is an equilateral triangle based off the fact that all the sides are the same variable (a) then that means 30 divided by 3 which equals 10. So now we know that a = 10. Lets input that information for the rectangle. Since there are 2 a's that equals 20 and the perimeter is 30 so b has to be 5 since 5 times 2 is 10 plus 20 equals 30. so now we know that a=10 and b=5 so our squares sides are all 5. The area of the square is 25

7 0

2 years ago

a triangle garden is being formed with stones. the three sides measure 4 meters by 6 meters by 7 meters. which of the following

postnew [5]

all sides of a triangle are equal

3 0

2 years ago

A car dealer offers 6 different models, 4 colors, and 3 kinds of transmissions. How many unique cars could you choose from at th

Mkey [24]

6 × 4 × 3 = 72 cars.

72 different type of cars.

8 0

2 years ago

Read 2 more answers

While standing on top of a hill at a ski resort, Alexa Latour spots the ski lodge below. If the vertical height of the hill is 1

alexira [117]

Answer: The distance to the lodge is 1514 ft

Step-by-step explanation: Please refer to the diagram attached.

The point where Alexa is standing at the top of the hill is marked as point A. The vertical height of the hill is from point A to point B which has been given as 1209 ft. Also, when Alexa looks down, she does that at an angle of depression measuring 53 degrees. Therefore while looking at the lodge, she forms an angle between her line of sight and the height of the hill. That angle is calculated as 90 degrees minus 53 degrees and that equals 37 degrees (as shown in the diagram). Note that her line of sight is AC since the ski lodge is at point C. Therefore the distance she must ski in order to get to point C (which shall be represented by X) shall be calculated using trigonometric ratios.

Note that we have a reference angle which is 37. We also have an adjacent which is 1209 (the side that lies between the reference angle and the right angle). And then we want to calculate the hypotenuse, yet unknown, (which is the side facing right angle). Since we have an adjacent, a hypotenuse and the reference angle, X can be calculated as

Cos A = Adjacent/Hypotenuse

Cos A = AB/AC

Cos 37 = 1209/X

By cross multiplication we now have X = 1209/Cos 37

By using our calculator or checking the table of values, Cos 37 = 0.7986

X = 1209/0.7986

X = 1513.899

Approximated to the nearest feet,

X = 1514 ft

8 0

3 years ago

Is the statement (3^5)^4 = (3^4)^5 true? Explain your reasoning.

Evgesh-ka [11]

Answer:

We use the power rule of exponents to find out that both sides of the equation equal 3^20 (or 3486784401).

Step-by-step explanation:

For this example, we can just use a calculator and find out that both (3^5)^4 and (3^4)^5 are the same value. But how do we know this algebraically?

When dealing with exponents, we must have a good understanding of the properties of exponents before doing any calculations.

For this example, I recognize that the power rule of exponents is being used:

$(a^{m})^{n} = a^{m*n}$

So let's apply this rule to the given equation.

(3^5)^4 = (3^4)^5

3^(5*4) = 3^(4*5)

3^20 = 3^20

Now we know both sides of the equation equal 3^20 (or 3486784401).

3 0

2 years ago