MATHEMATICS HIGH SCHOOL

What is the equation of the following graph in vertex form?the graph shows a positive parabola with the vertex at, (-1,0) and passes through (0,1) and (-2,1)
Answers
y = (x − 1)2
y = (x − 1)2 + 1
y = (x + 1)2 − 1
y = (x + 1)2

Answers

Answer 1

Answer:

Vertex form uses the following formula:

$a(x-h)^2 + k$

a determines the stretch of the parabola. h and k are the x and y values of the vertex (h, k), respectively.

The vertex is at (-1, 0). There is no a value indicated for any answer. Plug these values into the equation:

$\text{h = -1, k = 0}$

$(x - (-1))^2 + 0$

$\boxed{(x+1)^2}$

The answer is (x+1)^2.

Answer 2

Answer:

Answer:

(x+1)^2

Step-by-step explanation:

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the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9. write down the co-ordinates of A and B

Answers

Answer:

k = 3

Step-by-step explanation:

If the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9, then their slopes are equal

For coordinate AB;

slope m1 = 3 - 3k/k-(-1)

m1 = 3-3k/k+1

For the line 2y+3x = 9

2y = -3x + 9

y = -3/2 x + 9/2

Slope m2 = -3/2

Since m1 = m2

3-3k/k+1 = -3/2

Cross multiply

2(3-3k) = -3(k+1)

Expand

6 - 6k = -3k - 3

-6k+3k = -3 - 6

-3k = -9

k = -9/-3

k = 3

Hence the value of k is 3

The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?

Answers

Answer:

Equation used to solve for x is 2x + 2.1 = 7.5

The value equal sides of triangle is 2.7 m

Step-by-step explanation:

Given: The isosceles triangle has a perimeter of 7.5 m and the shortest side, y, measures 2.1 m.

We have to find the value of x.

Since y is shortest sides and the triangle given is isosceles thus the other two sides must be equal.

So, length of two equal sides is x.

Then equation becomes,

⇒ x + x + y = 7.5

⇒ 2x + y = 7.5

Substitute the values of y = 2.1 , and solve for x, we have

⇒ 2x + 2.1 = 7.5

Subtract 2.1 both side, we get,

⇒ 2x = 7.5 - 2.1

Divide both side by 2, we get,

⇒ x = 2.7

Thus, the value equal sides of triangle is 2.7 m.

An isosceles triangle has 2 sides of the same length and one side that's not the same length.

So it says the shortest side, y, is 2.1m, so that means it's the side that is not the same length as the other two sides.

But the other two sides will be the same length. Let's make those 2 sides x.

The equation would be
x + x + 2.1 = 7.5

And with that you can find x.

If x/yis rational, must x and y each be rational?
A) Yes; because the quotient of rationals is rational.
B) No; because x and y could have a common irrational factor.
C) No; because the quotient of irrationals is always irrational.
D) Yes; because x and y must be integers, and integers are rational.

Answers

The answer is B.

Consider the fraction $(6 √(5) )/(√(5))$ .

Both the numerator and denominator, when by themselves, are irrational.

However, when they are divided, they result in the rational number $(6 √(5) )/(√(5))=\boxed{6}$ .

When $p,q$ have the same irrational factor, the irrational factor will be cancelled from the fraction and (possibly) leave a rational number.

Answer: The answer is B.

Step-by-step explanation:

No; because x and y could have a common irrational factor.

Solve the equationin x =-3
A.x=?

(Round to five decimal places as needed. Use a comma to separate answers as needed.)

B.The solution is the empty set.

Answers

Answer:

x = 0.04979

Step-by-step explanation:

ln x = -3

x = e^(-3)

x = 1/e^3

x = 0.04979

Proof:
Given: Isosceles trapezoid TRAP with TR=PA
Prove: Angle RTA = angle APR

Answers

The answer is in the attachment

A bowling alley charges $3.50 per game plus $5 to rent shoes. A second bowling alley charges $5 per game plus $2 to rent shoes. Howmany games would a person have to play for the two bowling alleys to cost the same amount?