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3 years ago

How are the formulas for the area of a rectangle and the area of a triangle alike and different?

Mathematics

1 answer:

rodikova [14]3 years ago

5 0

Answer:

A diagonal of a rectangle separates the rectangle into two congruent triangles. The area of each triangle is one-half the area of the rectangle. So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

Step-by-step explanation:

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Evaluate 9(x + 5y) for x = 2 and y = 5.

Orlov [11]

Answer:

243

Step-by-step explanation:

STEP 1: Evaluate the variables

9(2 + (5)(5))

STEP 2: Then from there you can multiply the equation

18 + 225 = 243

6 0

3 years ago

3 coffees and 4 donuts cost $10.05. In the same cafeteria, 5 coffees and 7 donuts cost $17.15. How much do you have to pay for 4

MakcuM [25]

Answer

You need to pay $14.20 to get 4 coffees and 6 donuts.

Explanation

Let's say that the price of one coffee and x and the price of one donut is y.

In the first instance, 3x+4y=10.05.

In the second instance, 5x+7y=17.15.

You can use these equations to find the value of a coffee and the value of a donut.

We can find x and y using elimination. To do this, you should add or subtract one equation from another to "get rid" of a variable (I'll "get rid" of x). We can't just add or subtract the equations right now, since that wouldn't lead to 0x.

Multiply the first equation by 5, and the second equation by 3. After this, both equations will have 15x. Make sure to multiply each term by 5 and 3.

15x+20y=50.25. This means that 15 coffees and 20 donuts is $50.25.

15x+21y=51.45. This means that 15 coffees and 21 donuts is 51.45.

Now since there are an equal number of coffees, we can subtract these equations.

(15x+21y=51.45)-(15x+20y=50.25) equals y=1.20 (a donut costs $1.20).

Plug the price of the donut into y to find x; 3x+4(1.20)=10.05. The value of x is 1.75. The price of a coffee is 1.75.

You can multiply 1.75 by 4 to find the price of 4 coffees and 1.20 by 6 to find the price of 6 donuts.

1.75*4 is 7.00 and 1.20*6 is 7.20.

You can add those to find the total price; 7.00+7.20=14.20.

5 0

3 years ago

Find the length of the third side. If necessary, write in simplest radical form.

Mazyrski [523]

Answer:

$\boxed {\boxed {\sf 8}}$

Step-by-step explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

$a^2+b^2=c^2$

Where a and b are the legs of the triangle and c is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

$a= 7 \\b= \sqrt{15}$

Substitute these values into the formula.

$(7)^2+(\sqrt{15})^2=c^2$

Solve the exponents.

(7)²= 7*7=49

$49+ (\sqrt{15})^2=c^2$

(√15)²=√15*√15=15

$49+15=c^2$

Add.

$64=c^2$

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

$\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c$

The third side length is 8.

6 0

3 years ago

Read 2 more answers

Does (lnk)/(k^3), where as k starts at one and continues on to infinity, converge? ...?

max2010maxim [7]

Yes. The numerator does not increase as fast as the denominator increases, causing the function's value to decrease with every subsequent increase in the value of k. This causes the function to converge at a point.

7 0

3 years ago

What is 310,763,146 in expanded form

lesya [120]

In expanded form, the number would look like this:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 40 + 6

When you add the value of all of these digits, it'll get you the number: 310,763,146. Adding all of these values up and getting the number you originally started with is a great method of making sure you got the right answer.

6 0

3 years ago