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2 years ago

If one zero of the quadratic polynomial x²+3x+k is 2, then the value of k is. [ ]

Mathematics

2 answers:

Alex_Xolod [135]2 years ago

3 0

Answer:

b) -10

Step-by-step explanation:

x^2 + 3x + k = (x - 2)(x - a)

(x - 2)(x - a) = x^2 - 2x - ax + 2a = x^2 + [-2 - a)x] + 2a

-2 - a = 3

2a = k

a = -5

k = 2(-5) = -10

Answer: b) -10

yulyashka [42]2 years ago

3 0

Answer:

GET READY FOR FIGHT !!!!!

Step-by-step explanation:

*Intense music in background*

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How many servings of popcorn are in 5 1/2 cups of each person receives 3/4 cup of popcorn?

Reil [10]

Answer:

7.3333, so if you round down, 7.

Step-by-step explanation:

5 1/2 divided by 3/4 is 7.3333

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2 years ago

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zvonat [6]

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Step-by-step explanation:

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2 years ago

Find the two intersection points

bogdanovich [222]

Answer:

Our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

Step-by-step explanation:

We want to find where the two graphs given by the equations:

$\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1$

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

$\displaystyle y = -\frac{3}{4} x + \frac{1}{4}$

Substitute this into the first equation:

$\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16$

Simplify:

$\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16$

Square. We can use the perfect square trinomial pattern:

$\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16$

Multiply both sides by 16:

$(16x^2+32x+16)+(9x^2-54x+81) = 256$

Combine like terms:

$25x^2+-22x+97=256$

Isolate the equation:

$\displaystyle 25x^2 - 22x -159=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 25, b = -22, and c = -159. Substitute:

$\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}$

Evaluate:

$\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}$

Hence, our two solutions are:

$\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}$

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

$\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2$

And:

$\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}$

Thus, our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

6 0

2 years ago

Maria needs to be at the airport terminal at 15:20. It will take

bogdanovich [222]

Answer:

12:30

Step-by-step explanation:

6 0

2 years ago

There are 15 blueberry muffins in a large basket. This represents 5/9 of all the muffins that are in the basket. The equation 5/

noname [10]

The answer is 27 muffins.

5/9m=15

9/5*5/9 which cancels each other out leaving just m.

Then you multiply 15 by 9/5 which gives you 135/5 which reduces to 27.

7 0

3 years ago

Read 2 more answers