Correct Answer: First Option
Explanation:
There are two ways to find the actual roots:
a) Either solve the given quadratic equation to find the actual roots
b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.
Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:
This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.
Answer:
option C. Angle BTZ Is-congruent-to Angle BUZ
Step-by-step explanation:
Point Z is equidistant from the vertices of triangle T U V
So, ZT = ZU = ZV
When ZT = ZU ∴ ΔZTU is an isosceles triangle ⇒ ∠TUZ=∠UTZ
When ZT = ZV ∴ ΔZTV is an isosceles triangle ⇒ ∠ZTV=∠ZVT
When ZU = ZV ∴ ΔZUV is an isosceles triangle ⇒ ∠ZUV=∠ZVU
From the figure ∠BTZ is the same as ∠UTZ
And ∠BUZ is the same as ∠TUZ
So, the statement that must be true is option C
C.Angle BTZ Is-congruent-to Angle BUZ
Answer:
Number of Cucumbers = 12
Number of Tomatoes = 4
Step-by-step explanation:
Let number of cucumber be c and number of tomatoes be t
Since he has room for 16 plants, we can write:
c + t = 16
He wants to plant 3 times as many cucumbers as tomatoes. We can write:
c = 3t
We can substitute this in 1st equation and solve for t:
c + t = 16
3t + t = 16
4t = 16
t = 16/4 = 4
And c = 3t
c = 3(4) = 12
Number of Cucumbers = 12
Number of Tomatoes = 4
<h2>
Therefore he took 40 gram of 
type solution and 10 gram of 
type solution.</h2>
Step-by-step explanation:
Given that , A pharmacist 13% alcohol solution another 18% alcohol solution .
Let he took x gram solution of type solution
and he took (50-x) gram of type solution.
Total amount of alcohol =![[x\times\frac{13}{100}] +[(50 -x) \times\frac{18}{100} ]](https://tex.z-dn.net/?f=%5Bx%5Ctimes%5Cfrac%7B13%7D%7B100%7D%5D%20%2B%5B%2850%20-x%29%20%5Ctimes%5Cfrac%7B18%7D%7B100%7D%20%5D)
gram
Total amount of solution = 50 gram
According to problem
⇔![\frac{ [x\times\frac{13}{100}] +[(50 -x) \times\frac{18}{100} ]}{50}= \frac{14}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B%20%5Bx%5Ctimes%5Cfrac%7B13%7D%7B100%7D%5D%20%2B%5B%2850%20-x%29%20%5Ctimes%5Cfrac%7B18%7D%7B100%7D%20%5D%7D%7B50%7D%3D%20%5Cfrac%7B14%7D%7B100%7D)
⇔
⇔- 5x= 700 - 900
⇔5x = 200
⇔x = 40 gram
Therefore he took 40 gram of type solution and (50 -40)gram = 10 gram of type solution.
