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3 years ago

Given the equation f(x) = 2x² + 4x - 1, what is axis of symmetry? a. 1 c. -1 b. 2 d. 0

Mathematics

1 answer:

Irina-Kira [14]3 years ago

4 0

Answer: x=-1

Step-by-step explanation:

the x value of the vertex = -b/2a if the equation is in "ax^2+bx+c" for

you are in luck

x value of the vertex = -4/4 = -1

the line of symmetry is a vertical line, and since it must pass through the vertex

line of symmetry: x=-1

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1,380 people

Step-by-step explanation:

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2 years ago

1 1/5 divided by 3 4/5

Nana76 [90]

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6 /19

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Gary's car travel 30 miles on 1 1/5 gallon of gas. Gary wants to travel 90 miles. How many gallons of gas will his car use?

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3 years ago

Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =

Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0

3 years ago

A jar contains 6 yellow marbles, 4 black marbles, and 2 purple marbles. Two marbles are picked at random, without replacement. W

ludmilkaskok [199]

Answer:

The probability of selecting both yellow is 5/22.

Step-by-step explanation:

Given the number of yellow marbles = 6

Black marbles = 4

Purple marble = 2

Now find the total number of marbles in the jar.

Thus total marbles = Yellow marbles + Black marbles + Purples marble

Now insert the values in the above formula.

Total marbles = 6 + 4 + 2

Total marbles = 12

The probability of 2 yellow marble:

$= \frac{6}{12} \times \frac{5}{11} \\= \frac{5}{22}$

Thus, the probability of selecting both yellow is 5/22.

3 0

3 years ago