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3 years ago

Solve the quadratic equation by completing the square. 2x2 + 3x - 4 = 0

Mathematics

2 answers:

AfilCa [17]3 years ago

8 0

Answer: x = 0

Step-by-step explanation:

4 + 3x - 4= 0

3x=0 (divide both sides by 3)

x= 0/3

x = 0

iren [92.7K]3 years ago

4 0

Step-by-step explanation:

$2 {x}^{2} + 3x - 4 = 0 \\ 16 {x}^{2} + 24x - 32 = 0 \\ 16 {x}^{2} + 24x + 9 = 41 \\ {(4x)}^{2} + 2 \times 4x \times 3 + {(3)}^{2} = 41 \\ {(4x + 3)}^{2} = 41 \\ |4x + 3| = \sqrt{41} \\ 4x + 3 = + - \sqrt{41} \\ 4x = - 3 + - \sqrt{41} \\ x = \frac{ - 3 + - \sqrt{41} }{4}$

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For every 4 gallons of green paint he uses 3 gallons of blue paint. Drag the correct number of each type of paint into the box t

Inga [223]

Answer:

Amount of green color used =

$\dfrac{64}{7}\text{ gallons}$

Step-by-step explanation:

We are given the following in the question:

Every 4 gallons of green paint is mixed with 3 gallons of blue paint. to make a particular shade.

Ratio of green color to blue paint can be calculated as:

$=\dfrac{\text{Amount of green color}}{\text{Amount of blue color}}\\\\=\dfrac{4}{3}$

Amount of shade = 16

Amount of green paint = $4x$

Amount of blue paint = $3x$

Thus, we can write:

$4x + 3x = 16\\7x = 16\\\\x = \dfrac{16}{7}$

Amount of green color used =

$4x = 4\times \dfrac{16}{7} = \dfrac{64}{7}\text{ gallons}$

Amount of blue paint used =

$3x = 3\times \dfrac{16}{7} = \dfrac{48}{7}\text{ gallons}$

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3 years ago

Explain the distance formula. Then use it to calculate the distance between A(1,1) and B(7,-7).

Lena [83]

Answer attached, but more letters needed

4 0

4 years ago

Trig questions:

navik [9.2K]

Question 1
Because the period is 2π, and the amplitude is 1obtain
f(x) = sin(x)
Because the horizontal shift is π, obtain
f(x) = sin(x - π)
Because the vertical shift is -4, obtain
f(x) = sin(x - π) - 4

Answer: 1. f(x) = sin(x - π) - 4

Question 2
The radius is 36/2 = 18 in.
1 revolution (360°) is the circumference, which is
2π(18) = 36π in
When the revolution is 62°, the distance traveled is
(62/360)*(36π) = (31/5)π in

Answer: 3. (31π)/5

Question 3.
Consider f(x) = 3cos(2x-π) - 1
f(0) = 3cos(-π) - 1 = -4
f(π/2) = 3cos(0) - 1 = 2
Rate of change = (2+4)/(π/2) = 12/π

From the graph, the rate of change of g(x) is
3/(π/2) = 6/π

Consider h(x) = sin(x) - 4
h(0) = 0 - 4 = -4
h(π/2) = 1 - 4 = -3
Rate of change = (-3+4)/(π/2) = 2/π
Therefore h(x) has the smallest rate of change

Answer: h(x)

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4 years ago

Which one is the larger average rate, -3.142 or -0.5?

SOVA2 [1]

Answer:

-0.5 is the larger average rate

Step-by-step explanation:

-3.142 is less than -0.5

5 0

3 years ago

A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form

Over [174]

Answer:

$\vec{v}= \text{ or } \approx$

Step-by-step explanation:

Component form of a vector is given by $\vec{v}=$ , where $i$ represents change in x-value and $j$ represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector $\vec{v}=$ , the magnitude is $||v||=\sqrt{i^2+j^2$ .

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being $i$ , one leg being $j$ , and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

$\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}$

To find the other leg, $i$ , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

$\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}$

Verify that $(9\sin 10^{\circ})^2+(9\cos 10^{\circ})^2=9^2\:\checkmark$

Therefore, the component form of this vector is $\vec{v}=\boxed{}\approx \boxed{}$

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3 years ago