In a right triangle, the measures of the two smaller angles are (3X+6) and (2X-1) . Find the measure of the smallest angle in the triangle.

Answers

Answer 1

Answer: In a right triangle the biggest angle is 90°.

Then the two smaller angles sum up 180° - 90° = 90 °.

Now you can use this equation: 3x + 6 + 2x - 1 = 90 and solve for x:

5 x + 5 = 90
5x = 85
x = 85/5
x = 17

Then, the smallest angle is 2(17) - 1 = 33°

Answer 2

Answer:

Then, the smallest angle is 2(17) - 1 = 33°

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Please help quickly!Mr. Brownwood invests a certain amount of money at 9% interest and $1,800 more than that amount in another account at 11% interest. At the end of one year, he earned a total of $818 in interest. How much money was invested in each account?

$3,500 at 9%; $4,300 at 11%

$3,400 at 9%; $3,200 at 11%

$3,100 at 9%; $4,900 at 11%

Answers

Answer:

The answer is $3,100 at 9%; $4,900 at 11%

Step-by-step explanation:

You can solve this problem with a system of equations, that is, a system that can contain 2 or more equations. In this case, arms 2 linear equations with two variables: x and y. So first you define what your variables are:

x: amount of money invested in the account with 9% interest
y: amount of money invested in the account with 11% interest

Now you can define the system of equations. On the one hand you know that in the account that has 11% interest Mr. Brownwood deposited $1800 more than in the other account. In an equation and according to the previously defined variables this means: y=x+1800 Equation (A)

On the other hand, you know Mr. Brownwood earned $ 818 in interest. This means that the sum between the interest generated in the account deposited with 9% interest plus the interest generated in the account deposited with 11% interest is $ 818. And to calculate the amount of money generated by interest you multiply the percentage of interest by the amount deposited. Remember that to convert from percentage to decimal you must divide the number by 100. Then 9% is 0.09 and 11% is 0.11. In summary, considering this, you get the equation: 0.09*x+0.11*y=818 Equation (B)

Now you have both equations with the two variables to solve the system. There are several ways to solve the system. One of the most used ways is substitution, which consists in isolating one of the variables from one of the equations and replacing it in the other equation.

In this case you isolate the variable "y" from equation A, and you get: y=1800+x

Now replace it in equation (B): 0.09*x+0.11*(1800+x)=818

First you apply distributive property, which consists of distributing the multiplication by the terms within the parenthesis:

0.09*x+0.11*1800+0.11*x=818

0.09*x+198+0.11*x=818

Now, we leave the variable x on one side of the equality, in this case the left, and the numbers without the variable on the other side, in this case the right. To pass the numbers from one side of the equality to the other, you must keep in mind that you must use the opposite operation, that is, if the number 198 is adding on one side of the equality, the other side is subtracted:

0.09*x+0.11*x=818-198

Now you perform the corresponding operations. Then you isolate the variable and, and as in the previous case, you pass the number that accompanies the variable on the other side of equality with the opposite operation. In this case it is multiplying and its opposite operation is the division:

0.2*x=620

$x=(620)/(0.2)$

x=3100

Now you replace this value in either of the two equations, A or B, and solve that equation to get the value of y. So: y=4900

Remembering that x was amount of money invested in the account with 9% interest and y was amount of money invested in the account with 11% interest, you can say that $3100 was the amount invested at 9% and $4900 was the amount invested at 11%

Answer:3100 with 9%

Step-by-step explanation:

108 is 36% of what number? Write and solve a proportion to solve the problem

Answers

We set up a proportion: 108/?= 36/100

Cross multiply: 36*?= 108*100
⇒ ?= 108*100/36= 300

108 is 36% of 300.

4. You have a deck of 40 number cards: five of each number 2 to 9. You shuffle the deck, pick a card, look at it, return it to the deck, and then repeat for a second card. Determine each theoretical probability. a) sum is 12 b) difference is less than 5 c) product is odd

Answers

To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.

Total number of cards = 40 (5 cards for each number from 2 to 9)

a) Sum is 12:

There are several combinations of cards that can result in a sum of 12:

3 and 9
4 and 8
5 and 7
7 and 5
8 and 4
9 and 3

Total favorable outcomes = 6 (since there are 6 possible combinations)

Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600

Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)

Probability (sum is 12) = 6 / 1600 = 0.00375

b) Difference is less than 5:

There are several combinations of cards that can result in a difference less than 5:

2 and 3
3 and 2
3 and 4
4 and 3
4 and 5
5 and 4
5 and 6
6 and 5
6 and 7
7 and 6
7 and 8
8 and 7
8 and 9
9 and 8

Total favorable outcomes = 14

Total possible outcomes = 1600

Probability (difference is less than 5) = 14 / 1600 = 0.00875

c) Product is odd:

For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.

Total possible outcomes = 1600

Probability (product is odd) = 25 / 1600 = 0.015625

To summarize: