vertex represents a maximum or minimum point for the function. Explain your
answer.
b. Rewrite f(x) in vertex form by completing the square.
2. A cannonball is shot from the top of an ocean cliff as shown. The height (in meters) of the cannonball above th
water is given by h(t) = -5t2 + 15t + 8, where t is the number of seconds after the shot. Determine
whether each statement is true according to the graph. Select True or False for each statement.
Statement
True
Fal
The cannon is 8 meters above the water.
The cannonball reaches its maximum height at 1.5
seconds after it is shot.
The cannonball hits the water 8 seconds after it is
shot.

Answer:

3

Step-by-step explanation:

The minimum distance would be when there would be a horizontal line connecting the point (-5,1) with the line x=-2. So there would be a line from (-5,1) to (-2,1) which would be a straight line of 3 since -2 +5 = 3.

Answer:

a) 5xy + 9yz + 3zx + 5x - 4y

Step-by-step explanation:

→ (7xy + 5yz - 3zx) + (4yz + 9zx - 4y) + (-3xz + 5x - 2xy)

→ (7xy - 2xy) + (5yz + 4yz) + (-3zx + 9zx - 3xz) + (5x) + (-4y)

→ 5xy + 9yz + 3zx + 5x - 4y

Hence, option (a) is the correct answer.

Answer:

[tex]\textsf{A)}\quad \sf 5xy+9yz+3zx+5x-4y[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf (7xy+5yz-3zx)+(4yz+9zx-4y)+(-3xz+5x-2xy)[/tex]

Remove the parentheses:

[tex]\implies \sf 7xy+5yz-3zx+4yz+9zx-4y-3xz+5x-2xy[/tex]

Collect like terms:

[tex]\implies \sf 7xy-2xy+5yz+4yz+9zx-3zx-3xz+5x-4y[/tex]

Combine like terms:

[tex]\implies \sf (7-2)xy+(5+4)yz+(9-3-3)zx+5x-4y[/tex]

[tex]\implies \sf 5xy+9yz+3zx+5x-4y[/tex]

I suppose it's going to look like this, you just need to continue the graph for other figure numbers and numbers of circles

Answer:

radius = 12 cm

Step-by-step explanation:

al - Arc Length

[tex] \alpha \: - Central \: Angle ( in \: \: radians)[/tex]

r - Radius

[tex]al \: = 8\pi \: cm[/tex]

[tex] \alpha \: = \frac{2\pi}{3} [/tex]

[tex]al \: = \alpha \times r[/tex]

[tex]r \: = \frac{al}{ \alpha } [/tex]

[tex]r = \frac{8\pi}{( \frac{2\pi}{3} )} [/tex]

[tex]r = 12 \: cm[/tex]

Answer:

Step-by-step explanation:

The equation of a circle:

(a, b) - the center of a circle

r - the radius of a circle

x² - 8x + 16 + y² + 10y + 25 = 81

(x² - 2(x)(4) + 4²) + (y² + 2(y)(5) + 5²) = 81

use: (a - b)² = a² - 2ab + b² and (a + b)² = a² - 2ab + b²

(x - 4)² + (y + 5)² = 9²

Therefore

the radius: r = 9

the center: (4, -5)

The radius is 9 and the center of the circle  (4, -5)

A circle's center is a point throughout the circle that is equally spaced from every other point on the circumference. The line of refraction symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry surrounding the centre.

The equation of a circle:

(x - a)² + (y - b)² = r²

The center of a circle will be (a, b)

The radius of a circle will be r

x² - 8x + 16 + y² + 10y + 25 = 81

Solving the above equation on the basis of the Equation of a circle.

(x² - 2(x)(4) + 4²) + (y² + 2(y)(5) + 5²) = 81

Using the identity in the above-given equation.

(a - b)² = a² - 2ab + b² and (a + b)² = a² - 2ab + b²

(x - 4)² + (y + 5)² = 9²

The center of the circle will be at coordinates 4 and 5. And the radius of the circle derived is 9.

Learn more about the center of a circle, here

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Answer:

We know that,

★ Area of Square = ( Side )² ★

Given:

Area of Squared garden is 1764 m².

To Find:

➛ Side = √1764

➛ Side = 42

We know,

★ Perimeter of Square = 4 × Side ★

Given:

➛ Perimeter = 4 × 42

➛ Perimeter = 168

Answer:

0.267

Step-by-step explanation:

:)

Answer:

the dryer costs $450

step-by-step explanation:

w + d = 831

w = d-69 (they told us we will have to take $69 from the cost of the dryer to determine the cost of the washer)

(d-69) + d = 831

Let's combine like terms

2d - 69 = 831

add 69 to both sides to solve for d

2d = 900

divide both sides by 2 to solve for d

d = 450; the dryer costs $450

Answer:

koalas

Step - by - step explanation:

because they're so cute and cuddly

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

[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

a+(-5)=-9

What is a equal to?

[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

First, a+(-5)=-9 can be written as follows:-

⇒a-5=-9

Now, add 5 to both sides:-

⇒a=-9+5

And finally,

⇒a=-4

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

Answer:

a = -4

Step-by-step explanation:

We have to,

Find the required value of a,

→ a + (-5) = -9

→ a - 5 = -9

→ a = -9 + 5

→ [ a = -4 ]

Hence, the value of a is -4.

Answer:

24t

Step-by-step explanation:

Multiply 8 by 3t
Since 8 is outside of the bracket, while 3t is inside the bracket
8 * 3t
= 24t

Answer:

Step-by-step explanation:

Formula Development

Let the width = w

Let the Length = 5*w

P = 72

P =2w + 2L

Area = 5w * w

Solution

Start with the Perimeter. Solve for w.

P = 2w + 2L                  Substitute the givens

72 = 2w + 2*5w            Combine

72 = 2w + 10w              Combine   Combine again

72 = 12 w                       Divide by 12

72/12 = 12w/12

w = 6

Now for the area

Area = 5w * w

w = 6

Area = 5*6*6

Answer: Area = 180 cm^2

Step-by-step explanation:

The goal is to isolate that given variable. The process is the same process that you use to solve linear equations; the only difference is that you will be working with a lot more letters, you also prob will not be able to simplfy as much as linear equations

Answer:

it is more than one step so it takes longer to solve

Step-by-step explanation:

the process of isolating a variable in these literal equations is similar to solving a one-step equation because after isolating a variable you solve the rest of the equation,it is different from solving a one-step equation because it is more than one step so it takes longer to solve

Answer:

hope this helps:)

Step-by-step explanation:

the thousands place is right before the first comma therefore it is in bold here:

69581.491337

since 5 is [tex]\geq[/tex] 5 you round 9 up to a 10

once you round, the numbers below it all turn into zeros.

giving the number to be 70,000

hope this helps:)

Answer: Heyaa!~

Your Answer Is... 70,000

Step-by-step explanation:

Hopefully this helps you!~

Answer:

2x² + 6x + 8

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 6x + 8 + 2x²

= 2x² + 6x + 8

Answer:

[tex]\frac{1}{3}[/tex](9) = 3

[tex]\frac{1}{4}[/tex](16) = 4

[tex]\frac{2}{5}[/tex](25) = 10

[tex]\frac{3}{5}[/tex](25) = 15

[tex]\frac{1}{5}[/tex] x = 10    x=50

[tex]\frac{1}{4}[/tex]x= 10      x=40

The linear equations of the candles are y = 0.5x + 8 and y = 0.4x + 8. And both relationships are the function.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A candle burns down at the rate of 0.5 inches per hour.

The original height of the candle was 8 inches.

Let y be the height of the candle and x be the number of hours.

Then the linear equation will be given as

[tex]\rm y = mx + c[/tex]

where m is the rate and c is the initial value. Then the linear equation of the candle will be

y = -0.5 x + 8

The function is a linear function.

If the value of m is replaced by 0.4. Then the linear equation will be

y = 0.4x + 8

And this will also be a linear function.

More about the linear system link is given below.

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Answer:

Step-by-step explanation:

we know that If two angles are complementary, then their sum is equal to 90 degrees

Letx -----> the measure of an angle

 y-----> the measure of he other angle

we know thatx+y=90 -----> y=90

-x -----> equation

Ax=y+54 ----> equation

Bsubstitute equation B in equation A and solve for yy=90-(y+54)

y=90-y-542y=36y=18°

Find the value of xx=y+54 -----> x=18+54=72°

thereforeThe measure of the angles are 72 degrees and 18 degrees

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

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

           An angle measures 54º more than the measure of its supplementary angle. What is the measure of each angle?

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

Angle Measurements:- 63º and 117º

[tex]\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}[/tex]

                        Supplementary angles add up to 180º.

Now, let the unknown angle be n.

Set up an equation:-

[tex]\bigstar[/tex] [tex]\textsf{n+n+54=180}[/tex] (remember, supplementary angles add up to 180)

Add the n's :

[tex]\textsf{2n+54=180}[/tex]

Subtract 54 on both sides:

[tex]\textsf{2n=126}[/tex]

Divide by 2 on both sides:

[tex]\textsf{n=63\textdegree}[/tex]

Now, add 54 to find the other angle:

63+54=117

Check:-

We can easily check our work by adding the two angles together and seeing whether or not we end up with 180º.

[tex]\textsf{63+117=180}[/tex]

[tex]\textsf{180=180}\LARGE\checkmark[/tex]

LHS=RHS (Left-Hand Side = Right-Hand Side)

Hence, the angles are 63 and 117.  [tex]\checkmark[/tex]

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

Work Shown:

E = exterior angle = 60 degrees

n = number of sides of the regular polygon

n = 360/E

n = 360/60

n = 6

The regular polygon has 6 sides.

The area of the planned school garden have dimensions of g + 4 and g + 10 respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the area of the planned school garden as:

A = g² + 14g + 40

A = g² + 10g + 4g + 40 = g(g + 10) + 4(g + 10)

A = (g + 4)(g + 10)

The area of the planned school garden have dimensions of g + 4 and g + 10 respectively.

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Answer:

Less than

Step-by-step explanation:

4 and 1/4 is basically equal to 4 and 2/8

Answer: less becuase 4 1/4 x 4=17 and 4 1/8 x 4=16.5

Step-by-step explanation:

Answer:

269.12

Step-by-step explanation:

Answer:

4 twenty dollar bills = 20 x 4

                                = 120

Thus, the answer is 120 dollars.

Step-by-step explanation:

From the information given, it is correct to state that M = - 3; while c = 26. This problem relates to a Rhombus. See the definition of a Rhombus below.

A Rhombus is a 2-dimensional quadrilateral whose sides have equal length.

It is given that ABCD is a Rhombus. This means that

Hence, the slope of AC = -3.

This is arrived at as follows:

Given that the diagonals of Rhombus' are perpendicular, hence

I/3 x m = -1 ⇒ -3

⇒ Line y-11 = -3 (x-5)

⇒ Line AC thus ⇒ y = -3x + 26

Recall that the coordinates are (5, 11). Thus let y = -3x + b

Hence, -3 x 5 + b = 11
b = 11 + 15

b = 26.

Therefore the equation is given as:

y = -3X + 26 were:

m = -3; and

c = 26

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Answer:

Step-by-step explanation:

Remark

There are 6 faces on a cube.

Each face has an area of s^2

s = 5

One face is s^2

One face is 5^2 = 25 cm^2

6 faces are 6*25 cm^2

6 faces are 150 cm^2

Answer

150 cm^2

Answer:

(9,0)

Step-by-step explanation:

8 + 1 = 9

3 - 3 = 0

(9,0)

Answer: Choice C

[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}0 & 1\\\cline{1-2}2 & 2\\\cline{1-2}4 & 3\\\cline{1-2}6 & 4\\\cline{1-2}\end{array}[/tex]

=========================================================

Explanation:

There are four marked points on the line.

Each point is of the form (x,y)

Each of these points is then listed in the table format as shown above.

There are infinitely many other points on the line; however, we only select a few of them to make the table (or else we'd be here all day).

Extra side notes:

Answer:

the anwser is c

Step-by-step explanation:

trust me

Answer:

Your answer will be 38cm...