Answer:
<u>52% of Ms. Green's class has a pet.</u>
Step-by-step explanation:
So, I did this as simple as possible. First, I changed 25 to 100 to represent 100%. I multiplied 25 by 4 to get 100, so I then multiplied 13 by 4 to get 52.
25 → 100
13 → 52
So, this means that the answer is 52%.
A way to check, is by looking at the answer and seeing if it looks correct. Most of the time, you will be able to see if your answer is correct just by looking at it.
<u>Given:</u>
Polynomial = P(x) = 3x² + kx + 6
Factor of the ablove polynomial = (x+3)
<u>To </u><u>Find</u><u>:</u>
Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6
<u>Solu</u><u>tion</u><u> </u><u>:</u>
Now,
x + 3 = 0
⇒x = (-3)
So,
As (x+3) is a factor so x = (-3) is one root of the polynomial.
Therefore,
P(-3) = 0
→ P(-3) = 3(-3)² + k(-3) + 6 = 0
→ 3(9) - 3k + 6 = 0
→ 27 - 3k + 6 = 0
→ 27 + 6 - 3k = 0
→ 33 - 3k = 0
→ - 3k = -33
→ k = -33 ÷ -3
→ k = 11
- <u>Hence,For the value of k = 11, (x+3) is a factor of 3x²+ kx + 6</u>
<h2><u>V</u><u> </u><u>E</u><u> </u><u>R</u><u> </u><u>I</u><u> </u><u>F</u><u> </u><u>I</u><u> </u><u>C</u><u> </u><u>A</u><u> </u><u>T</u><u> </u><u>I</u><u> </u><u>O</u><u> </u><u>N</u><u> </u><u>:</u></h2>
3x²+ kx + 6, by putting the value of k = 11 and taking -3 as root the remainder should be zero
→ 3x²+ 11x + 6
→ 3(-3)² + 11(-3) + 6
→ 3(9) - 33 + 6
→ 27 - 33 + 6
→ 27 + 6 - 33
→ 33 - 33
→ 0
<u>Hence verified</u><u> </u><u>!</u>
1. If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle. A prudent auxiliary line is a chord connecting points of intersection of the sides of the angle with the circle as shown at the right.<span>
</span><span>2. Inscribed angle theorem. The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.
</span>
According to 2. : measure of arc RT = 2 m (angle S) = 60
Apply 1. : m(angle U) = (arc RS - arc RT )/2 = (84 - 60)/2 = 12
Answer:
![c = 1](https://tex.z-dn.net/?f=c%20%3D%201)
Step-by-step explanation:
The given expresion is
![2 {x}^{2} + 3x + c](https://tex.z-dn.net/?f=2%20%7Bx%7D%5E%7B2%7D%20%20%2B%203x%20%2B%20c)
For this expression to be factorable using integers, we must find factors of 2c, that will sum up to 3.
We know 2,c are factors of 2c
Their sum should be 3.
![c + 2 = 3](https://tex.z-dn.net/?f=c%20%2B%202%20%3D%203)
This implies that:
![c = 3 - 2 \\ c = 1](https://tex.z-dn.net/?f=c%20%3D%203%20-%202%20%5C%5C%20c%20%3D%201)