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2 years ago

Solve each equation with the quadratic formula. (Show work please)

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

3 0

Answer:

Let b=x

Such that b^2 =8b-8 will x^2=8x-8

Using the almighty quadratic formula

x1={-b+sqrt (b^2-4ac)}/2a

x2={-b-sqrt (b^2-4ac)}/2a

From the question

a=1

b=8

c=-8

x1={-8+sqrt (8^2-4(-8))}/2

x1=(-8+5.66)/2

x1=-1.17

x2={-8-sqrt (8^2-4(-8))}/2

x2=(-8-5.66)/2

x2=-6.83

:.(x1,x2)=(-1.17,-6.83)

Step-by-step explanation:

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3 years ago

8. What is the distance around the clock?

Elan Coil [88]

Answer:

The clock face is divided into sixty equal parts, each minute. The minute hand is located on the 20 minute mark at 6:20, the hour hand located between the 30 minute mark and the 35 minute mark. When the minute hand goes all sixty minutes, the hour hand only moves five, so to figure out the location of the hour hand, we look at how much the hour has progressed, in this case 20 minutes, or one third of the hour. So the minute hand has moved one third of the way through the hour, so has the hour hand moved one third of the way through the five minutes, or, five thirds of a minute, which is one and two thirds minute, one minute forty seconds. That puts the hour hand at thirty minutes plus one minute and forty seconds—at 31min 40sec—which is 11min 40sec farther than the minute hand.

Step-by-step explanation:

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1 year ago

Find A and B. Using the image above.

NeX [460]

Answer:

a = 7, b = $\frac{7\sqrt{3} }{3}$

Step-by-step explanation:

Using the sine ratio in the left right triangle and the exact value

sin45° = $\frac{1}{\sqrt{2} }$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{a}{7\sqrt{2} }$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

a × $\sqrt{2}$ = 7 $\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

a = 7

--------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan60° = $\sqrt{3}$ , then

tan60° = $\frac{opposite}{adjacent}$ = $\frac{a}{b}$ = $\frac{7}{b}$ = $\sqrt{3}$ ( multiply both sides by b )

b × $\sqrt{3}$ = 7 ( divide both sides by $\sqrt{3}$ )

b = $\frac{7}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{7\sqrt{3} }{3}$

7 0

2 years ago

Write an equation in point-slope form of the line having the given slope that contains the given point. then graph the line

RSB [31]

Answer:

$y=-x-4$

Step-by-step explanation:

$y-3=-1(x+1)$

$y=-x-1-3$

$y=-x-4$

4 0

2 years ago

A ball is thrown upward from ground level. Its height h, in feet, above the ground after t seconds is h-48t -16t^2.

Marat540 [252]

Answer:

36 feet.

Step-by-step explanation:

We have been given that a ball is thrown upward from ground level. Its height h, in feet, above the ground after t seconds is $h(t)=-48t -16t^2$ . We are asked to find the maximum height of the ball.

We can see that our given equation is a downward opening parabola, so its maximum height will be the vertex of the parabola.

To find the maximum height of the ball, we need to find y-coordinate of vertex of parabola.

Let us find x-coordinate of parabola using formula $x=-\frac{b}{2a}$ .

$x=-\frac{-48}{2(-16)}$

$x=-\frac{48}{32}$

$x=-\frac{3}{2}$

So, the x-coordinate of the parabola is $-\frac{3}{2}$ . Now, we will substitute $x=-\frac{3}{2}$ in our given equation to find y-coordinate of parabola.