Couple things to note:
- Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
- Slope can be calculated using any two points on a line and the formula y₁ - y₂ / x₁ - x₂.
For the first problem, we know the slope of Function A is 6 (refer to slope-intercept form above). To compare the slopes of Function A and Function B, first find the slope of Function B.
Use y₁ - y₂ / x₁ - x₂. Two points on the line are (0, 1) and (-1, -2). Plug these into the formula accordingly and solve for slope.
y₁ - y₂ / x₁ - x₂
1 - (-2) / 0 - (-1)
1 + 2 / 0 + 1
3 / 1
3
The slope of Function B is 3. This is half of 6 (the slope of Function A), so the correct answer to question 1 is the first option: Slope of Function B = 2 × Slope of Function A.
For the second problem, substitute m and b in y = mx + b according to the graph. b is the y-intercept (the point at which the line intersects the y-axis); it is (0, -4), or -4. This gives us
y = mx - 4
We must now find m. Follow the same steps above to find slope. Our two points are (-2, 0) and (0, -4).
y₁ - y₂ / x₁ - x₂
0 - (-4) / -2 - 0
0 + 4 / -2
4 / -2
-2
Substitute.
y = -2x - 4
The first option is the correct answer.
Answer:
To write repeated multiplication of the same number in exponential notation, first write the number being multiplied as the base. Then count how many times that number is used in the multiplication, and write that number as the exponent.
Step-by-step explanation:
Answer:
bottom one
Step-by-step explanation:
Because it's tall and if it was the same as the circumference it would have been wide
Answer:
-210 degrees.
Step-by-step explanation:
That is 150 - 360
= -210 degrees.
ANSWER
1. 3391680
2. 3876
EXPLANATION
1. We want to find the value of:
![P^{12}_7](https://tex.z-dn.net/?f=P%5E%7B12%7D_7)
This is called "12 permutation 7"
Permutation function is defined as follows:
![P^n_r\text{ = }\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=P%5En_r%5Ctext%7B%20%3D%20%7D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
Therefore, we have that:
![\begin{gathered} P^{12}_7=\frac{12!}{(12\text{ - 7)}!}\text{ = }\frac{12!}{5!} \\ P^{12}_7=\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!} \\ P^{12}_7=\text{ 12 }\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6 \\ P^{12}_7=3391680 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5E%7B12%7D_7%3D%5Cfrac%7B12%21%7D%7B%2812%5Ctext%7B%20-%207%29%7D%21%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B12%21%7D%7B5%21%7D%20%5C%5C%20P%5E%7B12%7D_7%3D%5Cfrac%7B12%5Ccdot11%5Ccdot10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%5Ccdot5%21%7D%7B5%21%7D%20%5C%5C%20P%5E%7B12%7D_7%3D%5Ctext%7B%2012%20%7D%5Ccdot11%5Ccdot10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%20%5C%5C%20P%5E%7B12%7D_7%3D3391680%20%5Cend%7Bgathered%7D)
2. We want to find:
![C^{19}_{15}](https://tex.z-dn.net/?f=C%5E%7B19%7D_%7B15%7D)
This is called "19 combination 15"
Combination function is defined as:
![C^n_r=\frac{n!}{(n-r)!\cdot r!_{}}](https://tex.z-dn.net/?f=C%5En_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%5Ccdot%20r%21_%7B%7D%7D)
Therefore, we have that: