MATHEMATICS HIGH SCHOOL

F(x) = 4x^2 - 3x + 2kx + 1 What's the value of k for which the function has two zeros?? 
Can someone show me step by step?

Answers

Answer 1
Answer: f(x)=4x^2-3x+2kx+1=4x^2+(2k-3)x+1\n\na=4;\ b=2k-3;\ c=1\n\nfunction\ has\ two\ zeros\ when\ \Delta=b^2-4ac > 0\n\n\Delta=(2k-3)^2-4\cdot4\cdot1=4k^2-12k+9-16=4k^2-12k-7 > 0\n\na_k=4;\ b_k=-12;\ c_k=-7\n\n\Delta_k=(-12)^2-4\cdot4\cdot(-7)=144+112=256\n\nk_1=(-b_k-√(\Delta_k))/(2a_k);\ k_2=(-b_k+√(\Delta_k))/(2a_k)

√(\Delta_k)=√(256)=16\n\nk_1=(12-16)/(2\cdot4)=(-4)/(8)=-(1)/(2);\ k_2=(12+16)/(2\cdot4)=(28)/(8)=(7)/(2)\n\na_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\n\nAnswer:k\in(-\infty;-(1)/(2))\ \cup\ ((7)/(2);\ \infty)

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Help with number 11? Please

15 is 2 1/2 of what number?

Answers

15 is 2 1/2 of a number 6.

We need to find that 15 is 2 1/2 of what number.

What is the meaning of 'of' in maths?

In math, 'of' is also considered one of the arithmeticoperations which means multiplication within the brackets.

Let the unknown number be y.

Now, 2 1/2 of y=15

⇒5/2 ×y=15

⇒y=6

Therefore, 15 is 2 1/2 of 6.

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▪ Answer:

n = 6

▪ Step-by-step explanation:

n × 2 1/2 = 15

n × 5/2 = 15

n × 5 = 30

n = 30 ÷ 5

n = 6

Question 2: SQUARE ROOTS

Answers

Answer:

A) 15 and 16

Step-by-step explanation:

The square root of 250 is 15.8, so it falls between:

15 and 16

Help with distance between points in geometry.Two equations given

y=-5/4x+3.5
4y+10.6=-5x

Answers

rearrange equations so they look nicer:
y = -5/4x + 7/2
4y = -4x + 14

make both equations equal 4y:
4y + 10.6 = -5/x
4y = -5/x -10.6

this means that:
-4x + 14 = -5/x - 10.6

rearrange to find x:
[multiply by x]
-4x^2 +14x = -5 - 10.6x
4x^2 - 14x + 10.6x + 5 = 0
4x^2 -3.4x + 5 = 0

use the quadratic equation: x = (-b ± √(b^2 - 4*a*c)) / 2a
for this equation, a = 4, b = -3.4 and c = 5
write the answer in the form (x - answer one) (x - answer two)
this will give either two answers. Input these into the equation 4y = -4x +14 to find the coordinates.

To find the distance between these two points:

distance = √(change in x) + (change in y)

Final answer:

To find the distance between two points using given equations, solve the equations simultaneously to find the coordinates of the points and then use the distance formula.

Explanation:

To find the distance between two points using the given equations, we first need to find the points of intersection. We can do this by solving the given equations simultaneously to find the values of x and y. Once we have the coordinates of the two points, we can use the distance formula to find the distance between them.

  1. First, solve the given equations simultaneously to find the values of x and y.
  2. Substitute the values of x and y into the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2).
  3. Calculate the distance using the given formula.

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If 75 pairs of jeans are sold, what is the company’s profit?

Answers

Revenue: 2x² + 17x - 175
Cost: 2x² - 3x - 125
Profit: 20x - 50

Profit = Revenue - Cost
Profit = 2x² + 17x - 175 - (2x² - 3x - 125)
Profit = 2x² - 2x² + 17x + 3x - 175 + 125
Profit = 20x - 50

x = 75

profit = 20(75) - 50
profit = 1500 - 50
profit = 1450

Answer:

1450

Step-by-step explanation:

Terrance has 24 eggs to divide into equal groups. what are all possible numbers of eggs that Terrance could put in each group?

Answers

3 groups of 8. 8 groups of 3. 4 groups of 6. 6 groups of 4.
it depends on how many groups one thing that helps is if you draw circle as the group and add one tally to each of them till you hit 24 then you habe your answer

A bird feeder 24 times using 6 cups each time. A bag of seeds holds 32 cups. How many bags of seed did he use?

Answers

First, let's find how many cups the bird feeder uses 24 times.

24 x 6 = (20 x 6) + (4 x 6) = 120 + 24 = 148 cups.

Now, let's divide 148 by 32.

148 ÷ 32 = 4.625 bags of seed.

I hope this helped!
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