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3 years ago

Solve the equation 6w2 – 7w – 20 = 0.

Mathematics

1 answer:

Irina-Kira [14]3 years ago

4 0

Answer:

$\large\boxed{B.\ w=-\dfrac{4}{3},\ w=\dfrac{5}{2}}$

Step-by-step explanation:

$6w^2-7w-20=0\\\\6w^2-15w+8w-20=0\\\\3w(2w-5)+4(2w-5)=0\\\\(2w-5)(3w+4)=0\iff2w-5=0\ \vee\ 3w+4=0\\\\2w-5=0\qquad\text{add 5 to both sides}\\2w=5\qquad\text{divide both sides by 2}\\\boxed{w=\dfrac{5}{2}}\\\\3w+4=0\qquad\text{subtract 4 from both sides}\\3w=-4\qquad\text{divide both sides by 3}\\\boxed{w=-\dfrac{4}{3}}$

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SOLVE THE QUESTION BELOW ASAP

qwelly [4]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have

$h(t)=-16t^{2}+98$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts, and the axis of symmetry

<em>Find the vertex</em>

The function is written in vertex form

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98$

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

$-16t^{2}+98=0$

$t^{2}=\frac{98}{16}$

square root both sides

$t=\pm\frac{\sqrt{98}}{4}$

$t=\pm7\frac{\sqrt{2}}{4}$

therefore

The t-intercepts are

$(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)$

$(-2.475,0), (2.475,0)$

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

$x=0$ ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point $(0,98)$

The y-intercept is the point $(0,98)$

The t-intercepts are $(-2.475,0), (2.475,0)$

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98\ ft$

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

Find the difference

$98\ ft-82\ ft=16\ ft$

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

For t=2

$h(t)=-16(2)^{2}+98$

$h(2)=34\ ft$

Find the difference

$82\ ft-34\ ft=48\ ft$

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1

8 0

3 years ago

Consider the sequence:

Vera_Pavlovna [14]

Answer:

a_n = 2^n + 3

Step-by-step explanation:

The first differences have a geometric progression, so the explicit definition will be an exponential function. (It cannot be modeled by a linear or quadratic function.) The above answer is the only choice that is an exponential function.

First differences are ...

(7-5=)2, 4, 8, 16

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3 years ago

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01.01 LC)Which number line best shows how to solve −2 − ( −6)?

liraira [26]

Answer:

-6 - (-8) = 2.

Your number line might have a bubble at 2. Or it may show movement 8 units to the right of -6. Whatever it is, you should end up at the value of 2.

Step-by-step explanation:

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3 years ago

one vertex of a triangle is located at (0,5) on a coordinate grid after a transformation the vertex is located at(5,0) which tra

Alik [6]

Answer:

It's a rotation clockwise of 90 degrees about the origin.

Step-by-step explanation:

The given point moves from y = 5 to x = 5 so it has passed through 90 degrees about the origin.

It's a rotation clockwise of 90 degrees about the origin.

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3 years ago

The gandhara region is the home of many portrayals of ____.

Alexandra [31]

BUDDHA. It is a cold climate region where many BUDDHA carvings, with simplistic garments and appearance can be seen. This also exemplifies Gandhara art work that is usually influenced by roman empire.

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