In the triangle below, what is the length of the side opposite the 60 angle?
Answers
c = 2√3
a = √3
b² = c² - a²
b² = ( 2√3 )² - ( √3 )² = 12 - 3 = 9
b = √9 = 3
Answer:
The length of the side is A ) 3.
Related Questions
After lunch, you need to buy new shoes. You bought a pair last year and they cost $79.00. Now, the same shoes cost $86.00. By what percent has the price increased? Write your answer to 2 decimal places. *
The set of integers contains whole numbers and their _____.
Andrew has a new 3 ft wide bookcase with two shelves, each 15 in. in high. he plans to store his CD’s on the shelves, using new CD racks. Each CD rack is 17 in. wide and 7 in. high, and holds three stacks of 12 CDsWill Andrew have enough room for his 250 CD’s in the bookcase if he uses the two shelves inside the book case it doesn’t put any CDs on top of it? how many CDs will he be able to store?
What multiplies to -240 and adds to 8
Answers
x 3(x 2 + 5x + 1)
Answers
The required product of expression x³(x² + 5x + 1) is x⁵ + 5x⁴ + x³.
What is the distributive property of a product?
The distributive property of multiplication (also known as the distributive property of product over addition) is a fundamental property of arithmetic that helps simplifyexpressions involving multiplication and addition. It states that for any three numbers a, b, and c:
a * (b + c) = a * b + a * c
Here,
We can use the distributive property of multiplication to expand the product:
x³(x² + 5x + 1) = x³x² + x³5x + x³*1
Simplifying each term, we get:
x³x² = x³⁺² = x⁵
x³5x = 5x¹⁺3 = 5x⁴
x³*1 = x³
Setting it all together, we have:
x³(x² + 5x + 1) = x⁵ + 5x⁴ + x³
Therefore, the product is x⁵ + 5x⁴ + x³.
Learn more about the distributive property here:
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x (18x+15x+3)
x(33x+3)
(33x^2)+3x
y = (x + 3)^2
y = x^2 - 3
y = x^2 + 3
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
We need a parabola with a vertex at (0,-3)
If we select the equation:
When we put x = 0, we get
And similarly, when we put y = -3, we get
Hence, third option is correct.
Answers
Answer:
Graph
Step-by-step explanation:
The simplest way to graph a linear equation is to make an x, y chart.
Plug in values for x ( 3 values for x works ), then find the y values and graph the cordinates.
Another way to graph the above line is to identify the slope and the y-intercept. Because the function is in slope-intercept form, we can readily see both ( slope intercept form is y= mx + b where m= slope and b= y-intercept )! So b= 75 and m= 15. So to graph the y-intercept, it is ( 0, b ) and just count the slope from that point!
Final answer:
To graph the equation y = 15x + 75, start by plotting the y-intercept (0,75). Then move 15 units up and 1 to the right from the intercept. Connect the points to create the graph.
Explanation:
To graph the equation y = 15x + 75, you need to recognize it as the linear equation in slope-intercept form, y = mx + b. In this equation, m (slope) is 15 and b (y-intercept) is 75.
Start by plotting the y-intercept which is at the point (0, 75) on the y-axis. Then, from that initial point, use the slope or 'rise over run,' to find the next points. Given the slope is 15 (or 15/1), you will go up 15 units and right 1 unit from the intercept to plot your next point. Continue this process until you have enough points to produce a straight line.
By connecting these plotted points, you create the graph of y = 15x + 75.
Learn more about Graphing Linear Equations
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Answers
Answer:
The risk premium is positive, indicating a preference for certainty over risk.
Step-by-step explanation:
The risk premium is a measure of how much someone is willing to pay to avoid a risky situation or to insure against potential losses. It is the difference between the expected value of a gamble (or lottery) and the guaranteed (certain) outcome.
In this case, you're dealing with a decision maker who has initial wealth of 4 and faces the following lottery:
Option A: A loss of 2 with a probability of 1/2
Option B: A gain of 2 with a probability of 1/2
Let's calculate the expected value of this lottery:
Expected Value (EV) = (Probability of Option A) * (Value of Option A) + (Probability of Option B) * (Value of Option B)
EV = (1/2) * (-2) + (1/2) * (2)
EV = -1 + 1
EV = 0
The expected value of this lottery is 0. This means that, on average, the decision maker doesn't expect to gain or lose wealth; it's a fair game in terms of expected value.
Now, to calculate the risk premium, we compare this lottery to a certain outcome. In this case, the certain outcome is keeping the initial wealth of 4.
Risk Premium = Guaranteed Outcome - Expected Value of Lottery
Risk Premium = 4 - 0
Risk Premium = 4
The risk premium is 4, which means that the decision maker is willing to pay up to 4 to avoid taking this lottery. This is because the lottery is a risky proposition, and the decision maker values the certainty of keeping their initial wealth at 4 over the gamble, even though, on average, the gamble doesn't result in a gain or loss. Therefore, the risk premium is positive, indicating a preference for certainty over risk.
Answers
This is what the equation looks like then 4+2(35)
Since the 2 is next to the ( ) that means you multiply. So 35*2 = 70
Then the last part is 70+4 = 74 !