Answer:
Reason SAS postulate
Step-by-step explanation:
The two triangles must be congruent.
Reason: SAS postulate
Answer:
y = 5(x - 3)^2 + 50
Step-by-step explanation:
The problem wants you to rewrite the quadratic equation in the vertex form y = a(x - h)^2 + k
You are given a quadratic equation in standard form (ax^2 + bx = c).
To convert from standard form to vertex form, there are two ways but I will show you the easier(?) way.
Use the formula x = -b/2a to find the x-value (h) of the vertex. Note that the vertex in "vertex form" is (h, k) which is virtually the same as (x, y).
In y = 5x^2 - 30x + 95, a = 5, b = -30, and c = 95. Substitute a and b into the formula -b/2a.
Two negative make a positive, so -(-30) becomes 30 and 2 times 5 is 10. Now we have:
- 30/10 which simplifies down to 3.
The x (h) value of the vertex is 3. To find the y-value, substitute 3 into the original standard form equation.
- y = 5(3)^2 - 30(3) + 95
- = 5(9) - (90) + 95
- 45 - 90 + 95
- 50
The y (k) value of the vertex is 50. Now we have: (h, k) ⇒ (3, 50).
Substitute the values for h and k into the vertex form.
We still need the a-value, and this is easy to find. You take the a value from the original standard for equation (remember: <u>a</u>x^2 + bx + c)
So our a-value is 5. Now we can substitute this value into the vertex form and complete the question.
y = 5(x - 3)^2 + 50
A. The ratio of lynx to mountain lions to wolverines is 2:3:1.
Thus, there are 2 lynx in the ratio. If there were 6 lynx, we would have to multiply all of the numbers in the ratio by 3 (because 6/2 = 3) to keep the ratio in the same proportion.
Therefore, because there is 1 wolverine in the ratio, and 1 * 3 = 3, if there were 6 lynx, there would be 3 wolverines.
b. We can use the same ideas that we had in part a to help us in part b.
There are 3 mountain lions in the ratio, but there are 15 mountain lions in the problem. Thus, the multiplier is 5, because 15/3=5.
Therefore, because there are 2 lynx in the ratio, and 2*5 = 10, if there were 15 mountain lions, there would be 10 lynx.
c. There is one wolverine in the ratio, but there are 10 wolverines in the problem. Thus, the multiplier is 10, because 10/1 = 10
Therefore, because there are 3 mountain lions in the ratio, and 3 * 10 = 30, if there were 10 wolverines in the park, then there would be 30 mountain lions.
d. The total number of lynx, mountain lions, and wolverines is 30.
To find out how many of each animal there should be, we must make an equation using the ratio and the variable x.
2x + 3x + 1x = 30
This equation means that the total number of animals together is 30, which is true. Now let's simplify by combining like terms.
6x = 30
Finally, we can simplify by dividing both sides by the coefficient of x, or 6.
x = 5
Thus, going back to our original equation, we know that the amount of lynx is 2x, mountain lions is 3x, and wolverines is 1x.
Lynx = 2x = 2(5) = 10 lynx
Mountain Lion = 3x = 3(5) = 15 mountain lions
Wolverines = 1x = 1(5) = 5 wolverines
Hope this helps! :)
Probability that one is hired ans one not:
P ( A ) = (2 C 1 * 4 C 4) / 6 C 5 =
= ( 2 * 1 ) / 6 = 2/9 = 1 / 3
Answer: 1/3 or 33.33%
The factors of the expression x³-5x²-2x+24 are: (x+2)(x-3)(x-4)
<h3>
What is a factor?</h3>
A factor is a number that completely divides another number.
In other words, since the result may be divided by the two whole numbers we are multiplying, they are factors of the result if multiplying two whole numbers produces a result.
The numbers that can divide a number exactly are called factors.
There is none left over after division as a result.
The numbers you multiply together to produce another number are called factors.
A factor is hence the division of another number.
So, we have the expression: x³-5x²-2x+24
Now, calculate the factors as follows:
x³-5x²-2x+24
We already know that: P(-2) = 0
Hence, x+2 is a factor.
Now, other factors are: x² - 7x + 12
x² + 4x + 3x + 12
(x - 3)(x - 4)
Therefore, the factors of the expression x³-5x²-2x+24 are: (x+2)(x-3)(x-4)
Know more about the factors here:
brainly.com/question/24351176
#SPJ4
Correct question:
What is the factor of x³-5x²-2x+24?
