On this question, we can use the order of operations. ( pemdas )
First, we must fill in the missing numbers.
9*21 + (3*3)21 + 12
Start in the parentheses.
(3*3)21 = 9*21 = 189
189+189+12
The rest is just addition now!
189+189+12=390
390 is the correct answer.
Another example you can use is P:trees provide air, Q: 7 is an odd number. Write pq as a sentence. Then construct a truth table for this conditional. Solution: The conditional pq represents " If trees provide air, then 7 is an odd number." Trees provide air is the hypothesis, and 7 is an odd number is the conclusion. Note that the logical meaning of this conditional statement is not the same as its intuitive meaning. In logic, the conditional is defined to be true unless a true hypothesis leads to a false conclusion.
The implication of pq is that: since trees provide air, this makes 7 an odd number. However, intuitively, we know that this is false because the trees and the number 7have nothing to do with one another! Therefore, the logical conditional allows implications to be true even when the hypothesis and the conclusion have no logical connection
Answer:
Vertex: ![(-\frac{1}{3},-\frac{25}{3})](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B3%7D%2C-%5Cfrac%7B25%7D%7B3%7D%29)
Y-intercept: ![(0,-8)](https://tex.z-dn.net/?f=%280%2C-8%29)
Step-by-step explanation:
The x-coordinate of the vertex would be
and the y-coordinate of the vertex is whatever the output is given the value of x.
Therefore, the x-coordinate of the vertex is ![x=\frac{-b}{2a}=\frac{-2}{2(3)}=\frac{-2}{6}=-\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D%3D%5Cfrac%7B-2%7D%7B2%283%29%7D%3D%5Cfrac%7B-2%7D%7B6%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
This means the y-coordinate of the vertex is ![y=3x^2+2x-8=3(-\frac{1}{3})^2+2(-\frac{1}{3})-8=3(\frac{1}{9})-\frac{2}{3}-8=\frac{1}{3}-\frac{2}{3}-8=-\frac{1}{3}-8=-\frac{1}{3}-\frac{24}{3}=-\frac{25}{3}](https://tex.z-dn.net/?f=y%3D3x%5E2%2B2x-8%3D3%28-%5Cfrac%7B1%7D%7B3%7D%29%5E2%2B2%28-%5Cfrac%7B1%7D%7B3%7D%29-8%3D3%28%5Cfrac%7B1%7D%7B9%7D%29-%5Cfrac%7B2%7D%7B3%7D-8%3D%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B2%7D%7B3%7D-8%3D-%5Cfrac%7B1%7D%7B3%7D-8%3D-%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B24%7D%7B3%7D%3D-%5Cfrac%7B25%7D%7B3%7D)
So, the vertex is ![(-\frac{1}{3},-\frac{25}{3})](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B3%7D%2C-%5Cfrac%7B25%7D%7B3%7D%29)
The y-intercept of a function is the y-value at which x=0, or the y-value when the function crosses the y-axis. Therefore, if we plug x=0 into the function, we see that
, so our y-intercept is -8 or (0,-8).
I attached a graph below to help you visualize the vertex and y-intercept given the function.
See https://web2.0calc.com/questions/can-someone-help-please_7.
Given:
In ΔABC, AB = 5 unit, BC = 2 unit and ∠C = 90°
To find the The value of ∠B.
Formula
By Trigonometric Ratio we know,
![cos \ \theta=\frac{adj}{hyp}](https://tex.z-dn.net/?f=cos%20%5C%20%5Ctheta%3D%5Cfrac%7Badj%7D%7Bhyp%7D)
Let us take ∠B = θ
With respect to θ, BC is the adjacent side and AB is the hypotenuse.
So,
![cos \ \theta=\frac{BC}{AB}](https://tex.z-dn.net/?f=cos%20%5C%20%5Ctheta%3D%5Cfrac%7BBC%7D%7BAB%7D)
![cos \ B=\frac{2}{5}](https://tex.z-dn.net/?f=cos%20%5C%20B%3D%5Cfrac%7B2%7D%7B5%7D)
![B=cos^{-1} (\frac{2}{5} )](https://tex.z-dn.net/?f=B%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B5%7D%20%29)
![B = 66.42^{\circ}](https://tex.z-dn.net/?f=B%20%3D%2066.42%5E%7B%5Ccirc%7D)
Hence, the value of ∠B is 66.42°.