-3x^{2}-21x-54 what are the zeros? (Solutions)

Answers

Answer 1

Answer: the only way to solve if it is equal to something
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54

remember if we can do
xy=0 then assume x and y=0

so factor

0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is

if you have
ax^2+bx+c=0 then
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

x^2+7x+18
a=1
b=7
c=18

x= $\frac{-7+/- \sqrt{7^(2)-4(1)(18)} }{2(1)}$
x= $(-7+/- √(49-72) )/(2)$
x= $(-7+/- √(-23) )/(2)$
i=√-1
x= $(-7+/- i√(23) )/(2)$

the zerose would be
x= $(-7+ i√(23) )/(2)$ or $(-7- i√(23) )/(2)$

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At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height , x of the tree ?

Answers

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of $x-49$ meters and the distance from the top of the tree to the end of the shadow is $x+1$ meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

$x^(2)+(x-49)^(2)=(x+1)^(2)$

Expanding, we get,

$2 x^(2)-98 x+2401=x^(2)+2 x+1$

$2 x^(2)-98 x+2400=x^(2)+2 x$

$2 x^(2)-100 x+2400=x^(2)$

$x^(2)-100 x+2400=0$

Solving the equation using the quadratic formula $x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}$ , we get,

$x=\frac{-(-100)\pm\sqrt{(-100)^(2)-4 \cdot 1 \cdot 2400}}{2 \cdot 1}$

Simplifying, we have,

$x=(100\pm√(10000-9600))/(2)$

$x=(100\pm√(400))/(2)$

$x=\frac{100\pm{20}}{2}$

Thus,

$x=(100+20)/(2) \nx=(120)/(2) \nx=60$ and $x=(100-20)/(2) \nx=(80)/(2) \nx=40$

where the value $x=40$ is not possible because substituting the value $x=40$ in $x-49$ results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

Ava is 23 cm taller than Olivia,and Olivia is half the height of Lucas. If Lucas is 1.78 m tall,how tall are Ava and Olivia? Express their heights in centimeters.

Answers

Ava's height is 89 cm
Olivia's height is 112 cm

Further explanation

Given:

Ava is 23 cm taller than Olivia
Olivia is half the height of Lucas
Lucas is 1.78 m tall

Question:

How tall are Ava and Olivia?

Express their heights in centimeters.

Problem solving:

From the information above, only Lucas's tall has known at 1.78 m.

Because Olivia is half the height of Lucas, then we must multiply Lucas's height with ¹/₂ to get Olivia's tall.

$\boxed{ \ Olivia's \ height = (1)/(2) * 1.78 \ m \ }$

Or, we can halve Lucas's height as follows:

$\boxed{ \ Olivia's \ height = 1.78 \ m / 2 \ }$

Thus, Olivia's height is $\boxed{ \ 0.89 \ meters \rightarrow 89 \ cm \ }$

Next, we find out Ava's height.

Because Ava's is 23 cm taller than Olivia’s, then we must add Olivia’s height with 23 cm to get Ava's height.

Ava's height = 89 cm + 23 cm

Thus, Ava's height is $\boxed{ \ 112 \ cm \rightarrow 1.12 \ meters \ }$

We have to express their height in centimeters. Recall that 1 m = 100 cm.

Conclusion

Ava's height is 0.89 m or 89 cm
Olivia's height is 1.12 m or 112 cm
Lucas's height is 1.78 m or 178 cm

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Keywords: Ava is 23 cm taller than Olivia, half the height of Lucas, 1.78 m tall, multiply, express their heights in centimeters.

Thus, the height of ava and olivia is $\boxed{112\text{ cm}\text{ and }89\text{ cm}}$ respectively.

Further explanation:

It is given that height of ava is $23\text{ centimeter}$ more than the height than the height of olivia and the height of olivia is half of the height of lucas.

Consider the height of ava, olivia and lucas as $x,y$ and $z$ .

The height of the lucas is given as $1.78\text{ meter}$ .

This implies that the value of $z$ is as follows:

$\boxed{z=1.78}$

Since, the height of lucas is given in meter so, it is necessary to convert the unit into centimeter.

The height of lucas is converted into centimeter unit as follows:

$\begin{aligned}1\text{ meter}&\rightarrow 100\text{ centimeter}\n1.78\text{ meter}&\rightarrow 1.78*100=178\text{ centimeter}\end{aligned}$

Since, the height of olivia is half of the height of lucas so, the equation formed is as follows:

$\boxed{y=(z)/(2)}$

Substitute $178$ for the $z$ in the above equation.

$\begin{aligned}y&=(178)/(2)\n&=89\end{aligned}$

Therefore, the value of $y$ is $89$ .

This implies that the height of olivia is $89\text{ centimeter}$ .

It is given that height of ava is $23\text{ centimeter}$ more than the height than the height of olivia so, the equation formed is as follows:

$\boxed{x=23+y}$

Substitute $89$ for $y$ in the above equation.

$\begin{aligned}x&=23+89\n&=112\end{aligned}$

This implies that the height of ava is $112\text{ centimeters}$ .

Thus, the height of ava and olivia is $\boxed{112\text{ cm}\text{ and }89\text{ cm}}$ respectively.

Learn more:

1. Learn more about problem on coordinate of the graph brainly.com/question/1286775

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Answer details:

Grade: Middle school

Subject: Mathematics

Topic: Problems on Ages

Keywords: Age, height, ava, olivia, lucas, tall, meter, centimeter, unit, conversion, 1.78, value, half of height, taller than olivia, ava is 23 cm.

You roll a standard number die. What is the probability of rolling a number less than 5?

Answers

probablity is (desired outcomes)/(total possible outcomes)

less than 5
therea er 1,2,3,4
4 number

total possible is 6 since 6 faces
probablity is 4/6=2/3

look at it this way. it is originally 6. you take away 2 (cause you can only roll 1 through 4,) then you have 4/6, which simplifies to 2/3.

What does it mean by this, Write an expression for: Seven hundred and two more

Answers

this means you ave to do an equation but without a equal sign. So this is going to be 700+2.
~JZ

What is the slope of these two points: (2,2) and (8,8)

Answers

Answer:

m=1

Step-by-step explanation:

x1,y1 (2,2) x2,y2 (8,8)

m=8-2/8-2

m=1

the slope of (2,2) and (8,8) is 1.

The dragonfly is the fastest flying insect it can move at a speed of about 50 feet per second find the approximate time for a dragonfly to travel 400ft

Answers

Answer:

8 seconds

Step-by-step explanation:

400 divided by 50 is 8

Answer: 8 sec

Step-by-step explanation

50 = 1sec

50 + 50 = 100

50 + 50 + 50 + 50 = 200

You keep adding 50 until you reach 400

Every 50 you add is 1 sec so if you add eight 50’s it would be 400 and that would mean it takes him 8 seconds to travel 400ft

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