6x^2+12x+63=0 solve by factor

The observation of the graphing speed versus time is given below.

The rate at which the speed is changing is known as acceleration.

From the graph, the line segment OA and DE have linear acceleration which increases the velocity.

Similarly, from the graph, the line segment BC and EF have linear deacceleration which decreases the velocity.

From the graph, line segment AB has constant acceleration which increases the velocity.

And from the graph, the line segment CD has zero acceleration which makes the velocity to be constant.

More about the acceleration link is given below.

https://brainly.com/question/12550364

#SPJ1

The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).

Given the equation in the question;

To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.

y = −2x + 5

y = −2( 6 ) + 5

Multiply -2 and 6

y = -12 + 5

y = -7

Hence, the output value is -7, this forms an ordered pair of (6,-7).

To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.

y = −2x + 5

1 = −2x + 5

Add 2x to both sides

1 + 2x = −2x + 2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, the input value is 2, this forms an ordered pair of (2,1).

Learn more about functions here: brainly.com/question/28780365

#SPJ1

Answer:

y=3x+25

Step-by-step explanation:

we need start by making slope intercept form

lets move the 12x after moving it we get

-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4

we get y=3x-1

now we can create an equation to get the parallel line

y+2=3(x+9) now distribute

y+2=3x+27 and subtract the two

y=3x+25

Answer:

B. After the booking fee the party will cost $20 per person

The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Paula makes purses and the materials cost $2.25 per purse.

She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.

Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.

The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.

learn more about functions here :

https://brainly.com/question/12431044

#SPJ1

Answer: 5.00x - 2.25x = 5000

Step-by-step explanation:

The value after 11 years with annual compounding is $11,389.79

The value after 11 years with quarterly compounding is $11,552

The value after 11 years with monthly compounding is $11,589.68

The value after 11 years with continous compounding is $70,080.78.

When an amount is compounded annually, it increases in value once a year. When an amount is compounded quarterly, it increases in value four times a year. When an amount is compounded monthly, it increases in value twelve times a year. When an amount is compounded continuously, it increases continuously over the investment period.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Value after 11 years with annual compounding: $6,000 x (1.06)^11 = $11,389.79

Value after 11 years with quarterly compounding: $6,000 x (1 + 0.06 /4)^(11 x 4) = $11,552

Value after 11 years with monthly compounding: $6,000 x (1 + 0.06 /12)^(11 x 12) = $11,589.68

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

Value after 11 years: 6,000 x (2.718^0.06) x 11 = $70,080.78

To learn more about continuous compounding, please check: https://brainly.com/question/26476328

#SPJ1

There are 855 cockroaches crawling on the front of the building

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

The population density is given as:

Population density = total animals / area occupied

Given that, the population density of the cockroaches is 5 cockroaches per square meter.

The area of the building = area of triangle + area of square

Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²

Population density = total animals / area occupied

5 cockroaches per square meter = Total cockroaches / 171 m²

Total cockroaches = 855

There are 855 cockroaches

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The largest multiple of 30 that is less than the number, 520, can be found to be 510.

To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:

= 520 / 30

= 17.333

Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.

The multiple of 30 that is the largest and below 520 is then:

= 30 x Rounded down result of division of 520

= 30 x 17

= 510

Find out more on the largest multiple at https://brainly.com/question/13712343

#SPJ1

The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.

The perimeter of a shape is the distance of the path or boundary that surrounds the shape.

The formula for the perimeter of a semicircle is πr + 2r

π(pie)=3.14

r(radius)=2 yards (∴ radius=1/2diameter)

∴ the perimeter of a semicircle = πr + 2r

                                                    = 3.14×2+2×2

                                                    =10.28 yards.

∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.

To know more about perimeter:

https://brainly.com/question/27591380

The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

Learn more about ocean on;

brainly.com/question/1145641

#SPJ1

The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The given triangle is a right-angled triangle

As Z² = X²+Y²

So sin (x) = 60/68=0.88

and sin(y) = 32/68=0.47

Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.

Learn more about  Trigonometric Functions, by the following link.

brainly.com/question/24349828

#SPJ1

Answer in multiple forms depending on what needed

Answer:

c = 3

Step-by-step explanation:

48- (3c+4)=4(c+5)+3

48-3c-4=4(c+5)+3 Distributed the - sign

48 -3c -4= 4c+20 +3 Distributed the 4

44-3c =4c+23 Combined like terms

21-3c=4c Subtract 23 from both sides

21=7c Add 3c to both sides

3=c

Answer: Rise is 5 and run is 1 and now that is equal 5

Step-by-step explanation:

The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value given will be expressed thus:

= 24 - (5 + 3)^2 + 4 × 2^3

= 24 - (8)² + 4 × 8

= 24 - 64 + 32

= -8

The value is -8.

Learn more about exponents on:

brainly.com/question/13669161

#SPJ1

The perimeter of the shape is 38 total unit.

The perimeter of a shape is a measure of the distance round the boundary or edge of the shape.

The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.

Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.

Know more about perimeter of plane shapes here: https://brainly.com/question/24571594

#SPJ1

Order of operation to simplify this expression as follows:

   [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]

⇒ [tex](1.125\times 1)\div2[/tex]

⇒ [tex]1.125\div 2[/tex]

⇒ [tex]0.5625[/tex]

What is order of operation?

The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.

The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.

PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.

Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])

Here, division is the highest priority ,

[tex]((0.25+7\div 8)\times 1)\div 2[/tex]

[tex]((0.25+0.875)\times 1)\div2[/tex]

and then we solve parathesis,

[tex](1.125\times 1)\div2[/tex]

now we do multiply,

[tex]1.125\div 2[/tex]

and the final answer will be [tex]0.5625[/tex]

Learn more about order of operation :

https://brainly.com/question/550188

#SPJ13

Answer:

the change is in %age of decrease of 10%

Step-by-step explanation:

original value = 20

new value = 18

decrease = 2

%age decrease = decrease/original value * 100

                         =  2/20 * 100

                         =  10%

The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

The equation to find the roots, is a quadratic equation.

Hence,

2x² + 7x + 6

2x² + 3x + 4x + 6

x(2x + 3) + 2(2x + 3)

Hence,

(x + 2)(2x + 3) = 0

Therefore,

x + 2 = 0    or 2x + 3 = 0

x = -2 or x = -3 / 2

The roots of the equation is x = -2 and x = -3 / 2

learn more on roots of equation here: https://brainly.com/question/12404751

#SPJ1

The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

Learn more about the distance visit:

brainly.com/question/24386522

The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;

(a) The path is; y = -1.09375×10²·x² + 1.75·x

(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70

(c) The angle at the start is approximately 60.3°

A quadratic equation is a single variable polynomial equation of the second degree.

The points in the path which is a path of a projectile and has a shape of a parabola are;

(0, 0), (80, 70), and (160, 0)

The equations are;

y₁ = a·x₁² + b·x₁ + c

y₂ = a·x₂² + b·x₂ + c

y₃ = a·x₃² + b·x₃ + c

Plugging in the coordinates of the three points in the path gives;

The matrix becomes;

[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]

[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

We have;

A·X = Y, which gives;

[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]

Where;

A⁻¹ = The inverse of the matrix A

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]a = -\dfrac{7}{640}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

c = 0

The equation for Gunter Money's path is therefore;

[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]

(b) The vertex of the path is (h, k) = (80, 70)

The vertex form of a quadratic equation is; y = a·(x - h)² + k

The equation of Gunter Money's path in vertex form is therefore;

[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]

(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;

[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]

At the point Gunter Money takes off,  (0, 0), we have;

[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]

[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]

The angle is approximately 60.3°

Learn more about projectiles here:

https://brainly.com/question/14960116

#SPJ1

Answer:

557.143

Step-by-step explanation:

195 / 35% = 557.14

Answer:

L = 6 feet ; W = 4 feet

Step-by-step explanation:

l = 2 + w

perimeter/2 = 8

l + w > 8

2 + w + w > 8

2 + 2w > 8

2w > 8-2

2w > 6

2/2 w > 6/2

w > 3

smallest integer > 3 = 4

W= 4

L = 4 + 2 = 6

The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE

Complementary angles are two angles that sum up to 90°

For example 60° and 30° are complementary.

Either angle is called the complement of the other angle.

∠FED, ∠FDE and ∠DFE are in a triangle.

so,

∠FED + ∠FDE  +  ∠DFE = 180°

16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)

18x +36 = 180

18x = 180 - 36

18x = 144

x = 144/18

x = 8

so ∠FED = 16x - 8

Substitute x = 8 into the equation above we have

16(8) - 8 = 128 - 8 = 120°

∠FDE = 2x + 9

∠FDE = 2(8) + 9 = 25°

∠BED = 6x + 12

∠BED = 6(8) + 12

∠BED = 48 + 12

∠BED = 60°

∠CBD = -2x + 81

∠CBD = -2(8) + 81

∠CBD = 65°

so since ∠CBD = 65° and 90 - 65 = 25°

∠CBD is complementary to ∠FDE

In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE

learn more about complementary angles: https://brainly.com/question/151826

#SPJ1

Answer:

c. 7/12

Step-by-step explanation:

There are 36 possible outcomes when you roll a die twice.

11, 12, 13, 14, 15, 16

21, 22, 23, 24, 25, 26

31, 32, 33, 34, 35, 36

41, 42, 43, 44, 45, 46

51, 52, 53, 54, 55, 56

61, 62, 63, 64, 65, 66

The desired outcomes are the ones whose first number is greater than or equal to the second number. They are shown in bold and underline above.

There are 21 desired outcomes.

p(first number ≥ second number) = 21/36 = 7/12

Answer: c. 7/12

The system of equations has no solutions, meaning that the two lines never intersect, as shown by the image at the end of the answer.

A system of equations is a set of equations in the context of a problem, and these equations are solved to find the numeric value of each variable of the problem.

When the system involves linear equations, such as is the case in this problem, the solution is given by the intersection point between these two lines.

In this problem, the equations are given as follows:

From the second equation, it is found that:

x = 8 + 2y.

Replacing on the first equation, the solution for y can be obtained as follows:

2(8 + 2y) - 4y = 4

16 + 4y - 4y = 4

0y = -12

Which is a contradiction, hence the system has no solutions and the two lines do not intersect.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

The average monthly increase in net worth for the 6-month period is $1832.16.

Given:

A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.

Six months net worth = 15,866 - 4873

= 10,993

Average monthly increase in net worth =  six month net worth / 6

= 10,993/6

= $1832.16.

Therefore The average monthly increase in net worth for the 6-month period is $1832.16.

Learn more about the average monthly here:

https://brainly.com/question/20775093

#SPJ1

Answer:

The height of the flagpole is about 25.6 feet.

Step-by-step explanation:

The figure is omitted--please sketch it.

Put your calculator in degree mode.

Let h be the height of the flagpole.

[tex] \tan(52) = \frac{h}{20} [/tex]

[tex]h = 20 \tan(52) = 25.6[/tex]