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4 years ago

Find the line of symmetry for the parabola whose equation is y = 2x^2 - 4x + 1.

1 answer:

5 0

The line of symmetry of y = 2x^2 - 4x + 1.
the axis of symmetry of x= - b/2a, so the line of symmetry is x= - 4/2x2= -1
x=-1

the values of a, b, and c from the general form of the equation (2x + 1)(x - 2) =(2x + 1)(x - 2) = 2x²-4x+x-2=2x²-3x-2=ax²+bx+c=0
by identifying, a =2, b=-3 and c=-2

the line of symmetry for the graph of y = -3x^2 + 12x - 11 is x= -b/2a, so
x= -12/2x-3=2, x=2

The x-coordinate of the vertex of the parabola whose equation is y = 3x2 + 9x, x=-b/2a=-9/6=-3/2

The line of symmetry of the parabola whose equation is y = ax2 - 4x + 3 is x = -2. What is the value of "a"
y = ax2 - 4x + 3, x=-b/2a=-2, implies -b=-2x2a, -(-4)=-2x2a, 4= -4a, a=-1

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Find area of the shaded portion of the figure

Nikitich [7]

Answer:

$\sf C) \quad 57 \frac34 \:cm^2$

Step-by-step explanation:

To find the shaded area, subtract the area of the semicircle from the area of the rectangle.

Formulae

$\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}$

$\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}$

$\textsf{Diameter of a circle}=2r \quad \textsf{(where r is the radius)}$

Area of rectangle

Given dimensions of the rectangle:

width = 7 cm
length = 11 cm

Substituting these values into the formula:

$\implies \textsf{Area}=\textsf{7} \times \textsf{11}=77\: \sf cm^2$

Area of semicircle

Diameter of semicircle = 11 - 2 - 2 = 7 cm

⇒ Radius (r) = 7 ÷ 2 = 3.5 cm

$\textsf{let}\: \pi=\dfrac{22}{7}$

$\implies \textsf{Area}=\dfrac12 \left(\dfrac{22}{7}\right) (3.5)^2=19.25\: \sf cm^2$

Area of shaded region

= area of rectangle - area of semicircle

= 77 - 19.25

= 57.75

$\sf =57 \frac34 \:cm^2$

4 0

3 years ago

Any help is appreciated.

Bogdan [553]

Step-by-step explanation:

Hey there!

Now, let's look into figure.

angle ACB = 65° { Base angle of triangle ABC}

angle ACB + angle BAC + angle ABC = 180°

65° + 65° + angle ABC = 180°

angle ABC = 180°-130°

Therefore, angle 50°

angle EBD = 50° ( Vertically opposite angle)

Now;

angle EBD= angle DEB = 50° ( Base angle of triangle BDE )

angle BDE + angle DEB + angle EBD = 180° ( Sum of interior angle)

angle BDE = 180° -100°

Therefore, angle BDE = 80°.

Now, 80° + 14x + 2 = 180° { being linear pair}

14x = 180°-82°

14x = 98°

$x = \frac{98}{14}$

X = 7°

Hope it helps......

3 0

3 years ago

What is 12 5/25 as a mixed number in simplest form?

KIM [24]

12 5/25 = 12 1/5

hope it helps

4 0

3 years ago

Read 2 more answers

here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides

forsale [732]

Answer:

Step-by-step explanation:

This is a linear graph,

Let find the equation of the line

Equation of a line can be determine using

y = mx + c

Where m Is the slope of the graph and c is the intercept on y axis when x = 0

So,

Slope m can be calculated using

Let chose the two point on the x and y axis

P1 = (0,45) and , P2 = (18,0)

m = ∆y / ∆x = y2 - y1 / x2 - x1

m = 0 - 45 / 18 - 0

m = -45 / 18

m = -2.5

So, the intercept on the y axis when x = 0 is 45. Then, c = 45

So, the equation of the line becomes

y = -2.5x + 45

Multiply through by 2

2y = -5x + 90

Where

y is dollars on card, = output

x is the number of rides = input

A. So, we want to find the output when the input is 10, I.e when x = 10

Then,

y = -2.5x + 45

x = 10

y = -2.5 × 10 + 45

y = -25 + 45

y = 20

Then, the output is 20 dollars on card.

B. When the output is 5

I.e y = 5

Then,

y = -2.5x + 45

5 = -2.5x + 45

5-45 = -2.5x

-40 = -2.5x

x = -40 / -2.5

x = 16 rides

The input is 16 number of rides

C. Point P is (7,27.5)

This tells us that when the input is 7, I.e the number of rides is 7, then, the output is 27.5 I.e their are $27.5 dollars on card.

4 0

3 years ago

What is the sum of the opposite angles in a square

xxMikexx [17]

Answer: (The sides are therefore chords in the circle!) This conjecture give a relation between the opposite angles of such a quadrilateral. It says that these opposite angles are in fact supplements for each other. In other words, the sum of their measures is 180 degrees.

6 0

3 years ago