Pythagorean Theorem is
a ²+ b ² = c ²
a and b are the shorter sides, while c is the hypotenuse, or longest side. Let’s say the side we are looking for is “b”.
Let’s first rearrange the equation, then sub in.
a ²+ b ² = c ²
b ² = c ²- a ²
b = √ (c ²- a ²)
b = √(17 ²- 15 ²)
b = √(289-225)
b = √ 64
b = 8
Answer:
20
Step-by-step explanation:
ƒ(x) = 3x² – 2
g(x) = 4x + 2
1. Add the functions
By definition,
(ƒ + g)(x) = ƒ(x) + g(x)
3x² - 2
<u> + 4x + 2
</u>
3x² + 4x
(ƒ + g)(x) = 3x² + 4x
2. Evaluate (ƒ + g)(2)
(ƒ + g)(2) = 3(2)² + 4(2) = 3(4) + 8 = 12 + 8 = 20
Answer:
Step-by-step explanation:
go from one point to the other. From the left point to the right point you are running across (to the right) three times. Then you are ¨rising¨ (going down) once. going to the right is positive. If you are going down its negative. Vise versa. The formula is Rise/Run. your answer would be -1/3. the one is negative because it went down.Then divide it and you have -0.333. I hope I helped!
Answer:
- You have to fill the blank squares to complete the table.
- See the figure attached and the explantion below.
Explanation:
The figure attached shows the three squares that you have to fill to complete the table to summarize the different <em>theorems</em> to <em>prove triangles are congruent.</em>
<u>1. SAS</u>
<u></u>
SAS stands for Side Angle Side. That means that whenever two sides and the included angle on one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.
Thick marks are used to mark the corrsponding parts, sides or angles that are congruent. That is why the two triangles to the first triangles on the image (on the upper square to the right) are marked:
- One thick straight mark for two sides that are congruent
- Two thick straight marks for the other two sides that are congruent
- On thick curved mark for the two angles that are congruent
In that way, the figures show two triangles, with two congruent sides and the included angle congruent, to prove that the two triangles are congruent by the SAS theorem.
<u>2. ASA</u>
<u></u>
ASA stands for Angle Side Angle.
The ASA congruency theorem states that if two angles of a triangle and the included side are congruent, then the two triangles are congruent.
Thus you have to add the legend "Two congruent angles with and included side", which means that if the two angles and the included side on one triangle are congruent to two angles and the included side of other triangles, then both triangles are congruent.
The rule to mark the sides and angles that are congruent is with the use of thick marks. This is how it was done in the drawing of the two triangles in the lower right square:
- One thick straight mark for two sides that are congruent
- One thick curved mark for two angles that are congruent
- Two thick curved marks for the other two angles that are congruent
Answer:
10.3
Step-by-step explanation:
When calculating the mean from a grouped frequency table, first you must estimate what the value is through finding the number halfway between the value that x is greater than and less than:
The number halfway between 8 and 9 is 8.5
The number halfway between 9 and 10 is 9.5
The number halfway between 10 and 11 is 10.5
The number halfway between 11 and 12 is 11.5
Next, you have to multiply the estimated value by its frequency:
8.5 x 3 = 25.5
9.5 x 11 = 104.5
10.5 x 17 = 178.5
11.5 x 9 = 103.5
Then, add up the values you calculated and divide them by the total frequency (all the frequencies added up).
total estimated length: 25.5 + 104.5 + 178.5 + 103.5 = 412
total frequency: 3 + 11 + 17 + 9 = 40
412/40 = 10.3