Please explain in simple language how to complete the square.

The factors 2t - 3 represent the time it takes for the mountain lion to reach its highest point and return back to the ground.

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Given that,

The equation h = -16t² + 24t represents the height (h) of the mountain lion above the ground at any given time (t) in seconds.

Now, By factoring the equation as,

h = -16t² + 24t

h = -8t × (2t - 3)

Here, Factor 2t - 3 indicates the time it takes for the height (h) to reach zero, which corresponds to the mountain lion being on the ground.

So, when 2t - 3 equals zero, the height is zero, indicating that the mountain lion has returned to the ground.

Therefore, factors 2t - 3 help us determine the point in time when the mountain lion reaches its peak height and when it returns back to the ground.

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Answer:

Let $y$ be the younger turtle's age today. Then the older turtle's age today is $11y.$ So $24$ years from now, the younger turtle's age will be $y+24$ and the older turtle's age will be $11y+24.$ However, we know the older turtle's age will be $7$ times that of the younger turtle then, which tells us that

\[11y+24=7(y+24).\]Distributing, we get $11y+24=7y+168.$ Subtracting $7y+24$ from both sides of this equation, we get $4y=144,$ so $y=36.$

This is the younger turtle's age today, but that's not what we're looking for in this problem - we're looking for the number of years from today that the older turtle's age will be triple that of the younger turtle. Let $k$ be this number of years. Since the younger turtle's age today is $y=36$ and the older turtle's age today is $11 \cdot 36=396,$ it follows that $k$ years from now my turtles' ages will be $36+k$ and $396+k$ respectively. Since we want to know when the older turtle's age will be triple that of the younger turtle, we want to know for what $k$ this equation will be true:

\[3(36+k)=396+k.\]Distributing, we get $108+3k=396+k.$ Subtracting $k+108$ from both sides of this equation, we get $2k=288.$ Therefore, $k=\boxed{144}.$

Step-by-step explanation:

A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Answer:

Center: ( -6,5) Radius: 7

Step-by-step explanation:

I hope this helps!

Answer:

radius =  9

C:(9,3)

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

1/2x - 5 = 10 - 3/4x ---> move like terms to the same side

1/2x + 3/4x = 10 + 5 ---> calculate

5/4x = 15 ---> multiply both sides by 4/5

x = 12

Answer:

(a) AC = 12.565 m

(b) bearing of C from A is 90°

(c) BT = 9.373 m

Step-by-step explanation:

(a) extend North line down & perpendicular to AC.

Call that perpendicular intersection "P".

∠BAC = 90° - 53° = 37°

cos 37° = AP/15

0.7986 = AP/15

AP = 11.979 m

∠PNC = 180° - 161° = 19°

∠BCP = 90° - 19° = 71°

18 cm = 0.18 m   (red flag note: 18 cm looks very out of scale for the picture)

cos 71° = CP/0.18

0.3256 = CP/0.18

CP = 0.586 m

AC = 11.979 + 0.586 = 12.565 m

(b) The bearing to C from A is 90°

(c) tan 58° = 15/x

1.6003 = 15/x

x = 9.373 m

Answer:

alternate exterior: 2 and 7

corresponding: 1 and 5

alternate interior: 3 and 6

Step-by-step explanation:

Answer:

a= 8 and 1

b= 7 and 3

c= 6 and 3

Step-by-step explanation:

Answer: A, D

Step-by-step explanation:

For number 7 the answer is A

For number 8 since you are only moving it is the same size, therefore, producing a congruent image for all 3 of those translation. So for 8 the answer is d.

Answer:

Look Below

Step-by-step explanation:

1) The answer is A. It is A because if you want a reflected images across the Y-Axis, you want just the X value to change. Not the Y. So since the Y is positive and the X is positive, if you want a reflected image you want the X to be negative and the Y to be positive.

2) The answer is D. It is D because those are all forms that will produce a Congruent Image.

If you find any faults in my answer please let me know. Thanks! Have a Good Day!

Answer:

The diameter of a billiard ball is approximately 6 cm. what is the volume? round your answer to the nearest whole number.

A. 113 cm3

B. 903 cm3

C. 25 cm3

D. 38 cm3

Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

6

centimeters

...................................................................................................................................................

For this case we have that by definition, the volume of a sphere is given by:

Where:

r: It is the radius of the sphere

According to the data we have to:

Substituting we have:

The option that best fits is option B.

Answer:  v=113cm3

The option that best fits is option B.

...............................................................................................................................................

Answer:

V ≈ 904 cm³

Step-by-step explanation:

Let r denotes radius

r = 6cm (given)

As it a sphere of radius 6cm,

Volume of a sphere,

V = 4/3 π r³

V = 4/3 (3.14) (6)³

V = 4/3 (3.14) x 216

V = 4 (3.14) x 72

V = 12.56 x 72

V = 904.32 cm³

Rounding off,

V ≈ 904 cm³

...............................................................................................................................................

Answer:

113 cm

Step-by-step explanation:

Unknown, This is physically impossible to answer.

You need to give more information than that, or an image.

also what type of triangle is it obtuse acute right e.t.c.

Please put more information so i can answer this the correct way.

Answer:

11

Step-by-step explanation:

sorry if I got it wrong but from what I understand it is 11

Answer:

Length of rectangle = 16 cm

Width of rectangle = 4 cm

Step-by-step explanation:

Given:

Area of rectangle = 64 cm²

Find:

Length and width

Computation:

Assume;

Length of rectangle = a

So,

Width of rectangle = a -12

Area of rectangle = l x b

So,

a(a-12) = 64

a² - 12a - 64 = 0

a² - (16-4)a - 64 = 0

a² - 16a+ 4a - 64 = 0

a (a-16) + 4(a-16)= 0

(a-16)(a+4) = 0

a= 16 , a = -4

So,

Length of rectangle = 16 cm

Width of rectangle = a -12

Width of rectangle = 16 -12

Width of rectangle = 4 cm

Step-by-step explanation:

7+2x-2 = 4x -3

5= 2x -3

2x = 8

x = 4

Answer:d

Step-by-step explanation:

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]

[tex] \frac{ {x}^{12} - {6x}^{10} + {15x}^{8} - {20x}^{6} + {15x}^{4} - {6x}^{2} + 1 }{ {x}^{6} } [/tex]

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]

[tex](x - 1 \div x) {}^{6} [/tex]

Arrange the powers

[tex] \frac{x {}^{12} - {6x}^{10} + {15x}^{8} - {20x}^{6} + {15x}^{4} - {6x}^{2} + 1 }{ {x}^{6} } [/tex]

Answer:

y = -1/5x + 3

Step-by-step explanation:

y=mx+b

Answer:

if those measurements are degrees, then yes. If those measurements are the side lengths, then no.

Step-by-step explanation:

all angles on a triangle must had up to 180 degrees.

the two smaller sides of the triangle must add up to be larger than the largest side.

Answer:

D

Step-by-step explanation:

At least Im Sure lol

Answer:

essentially the answer is 33

Answer:

2(x – ½)(x + ½)

Step-by-step explanation:

2x² – ½

The above expression can be factorised as follow:

2x² – ½

2 is common to both 2 and ½. Thus,

2x² – ½ = 2[x² – ¼]

Recall

(½)² = ¼

Thus,

2[x² – ¼] = 2[x² – (½)²]

Difference of two squares

2(x – ½)(x + ½)

Therefore,

2x² – ½ = 2(x – ½)(x + ½)

Answer:

9

Step-by-step explanation:

Range = Max value - min value

Max value = 6

Min value = -3

Range:

6 - (-3)

6 + 3

9

Answer:

9

Step-by-step explanation:

there are 9 numbers between -3 and 6 ;)

Answer:

$500

Explanation:

If Joe saved 60% of the cost, given that the amount he saved was $300, to find the total cost of the computer, we need to know 100% of the cost.

60% = $300

[Set the percentage to a fraction and let x be the total cost]

(60/100) x = $300

60x / 100 = $300

_____________

60 → 30 × 2 → 15 × 2 × 2 → 5 × 3 × 2 × 2

______________________________

100 → 50 × 2 → 10 × 5 × 2 → 5 × 2 × 5 × 2

_______________________________

5 × 3 × 2 × 2 / 5 × 2 × 5 × 2 =

3 / 5.

_____________________________

3x / 5 = 300

3x / 5 × 5 = 300 × 5

3x = 1500

÷3 ÷3

x = $500

We can easily silve it by splitting the middle term or by using the discriminate method *

x 2 +3x -70

x2 + 10x - 7x -70

x(x + 10) -7(x +10)

(x / 7) ( x + 10)

x = 7 or -10

Answer:

Step-by-step explanation:

As per picture we see two pairs of opposite sides marked as congruent

Correct choice is the last one: