Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.

(5,3) , (4,1)

The polynomial of p(x) is  -24 (x² + 15x + 54) with the satisfying's conditions degree 3.

Given,

An nth degree polynomial p meets the requirements listed below:

p is of degree 3.

-9 is a zero, with multiplicity 2, of p.

-6 is a zero, with multiplicity 1, of p.

p(-1) = -960

We have to determine an nth degree polynomial that satisfier the conditions.

Let the polynomial be p(x) whose zero are -9 and -6

a be the coefficient.

p(x) = a (x+9) (x+6)

p(x) = a(x² + 6x + 9x + 54)

p(x) = a(x² + 15x + 54)

Now, take x = -1

p(-1) = a (-1² + 15 x -1 + 54)

-960 = a ( 1 - 15 + 54)

-960 = a x 40

a = -960/40

a = -24

We get,

p(x) = -24 (x+9) (x+6)

p(x)= -24 (x² + 15x + 54)

Therefore, the polynomial of p(x) is  -24 (x² + 15x + 54) with the satisfying's conditions degree 3.

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They achieved 26.9 miles per gallon approximately with that car in this trip.

Given that the initial odometer reading is = 87236.2 miles

Final odometer reading after trip is = 87626.2 miles

So the distance of the total trip is = 87626.2-87236.2 = 390 miles

They used 14.5 gallons of gas on the tri[p.

So the mileage is = 390/14.5 = 26.9 miles per gallon approximately.

Their car achieved 26.9 miles per gallon approximately.

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Based on the given parameters about a carpenter cutting the top section of a window frame, the side pieces of the frame are not parallel.

Parallel lines are lines which are equally distant from one another at all points.

To show that the side pieces of the frame are parallel:

The interior angles are equal in measure and the sum of the interior angles must be equal to 180°

The two given side pieces of the window frame are also equal in measure.

If the sum of both side angles is equal to 180∘, then, the sides are parallel.

37∘ + 50∘ = 87∘

2(37∘ + 50∘)

= 2(87∘)

= 174∘

Hence,

174∘ < 180∘

So therefore, the sides pieces of the window frame cut by the carpenter are not parallel.

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El promedio de los números enteros 3, 8, 9 y 12 es igual a 8. (Opción correcta: Cierto)

En este problema tenemos un conjunto de cuatro números enteros positivos, del cual debemos comprobar si el promedio uniforme es igual a 8. El promedio uniforme es definido por la siguiente operación:

[tex]\bar {x} = \frac {1}{n} \cdot \sum \limits_{i = 1}^{n} x_{i}[/tex]

Donde:

Si sabemos que n = 4, x₁ = 3, x₂ = 8, x₃ = 9 y x₄ = 12, entonces el promedio uniforme del conjunto de datos es:

[tex]\bar {x}[/tex] = (3 + 8 + 9 + 12) / 4

[tex]\bar x[/tex] = 8

El promedio del conjunto de datos, correspondiente a los números enteros positivos 3, 8, 9 y 12, es igual a 8.

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The speeds when converted are 29.648 km/h and 8.24 m/s

From the question, we have the following parameters that can be used in our computation:

Speed = 16 knots

Also, from the question, we have

1 nautical mile to be 1853 m

This means that

Speed = 16 * 1853 m per hour

Convert meters to kilometers

So, we have

Speed = 16 * 1.853 km per hour

Evaluate the products

Speed = 29.648 km/h

Also, we have

Speed = 16 * 1853 m per hour

Convert hour to seconds

So, we have

Speed = 16 * 1853/3600 m/s

Evaluate

Speed = 8.24 m/s

Hence, the speed in m/s is 8.24 m/s

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Answer:The question is very brief, im not sure if i understand what your asking

Step-by-step explanation:

The number of attempts Vonna made is 80.

Given,

Vonna scored 48 goals in her scoccer kicking practice.

Her success to failure rate is 3:2

Vonna scored 48 goals" means that there were 40 successes,

= 48 goals

= 3:2

= 48:3

= 16

x = 6 positive integer

hence let 3x:2x

= 3(16) = 48

= 2(16) = 32

Total attempts = 48+32

= 80

Hence the total number of attempts Vonna made is 80.

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The cost of the sweater is $ 30 and

1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos.

Mathematical Operations are activities or mathematical processes used to solve given problems. The most used mathematical activities are adding, subtracting, multiplying, and dividing.

The basic operations and their symbols are given below
Addition (+); Subtraction (-); Division (÷);  and Multiplication (x).  

Here we have

Priya exchanged 250 dollars for 4250 pesos  

[Here we used division and multiplication to solve the problem ]

Then the value of 1 dollar in pesos = [tex]\frac{4250}{250}[/tex] = 17 pesos

⇒ 1 dollar = 17 pesos

⇒ 25 dollars = 25 × 17 = 425 pesos

⇒ 3 dollar = 3 × 17 = 51 pesos

Given the cost of the sweater = 510 pesos  

The cost of the sweater in pesos = [tex]\frac{250}{4250} \times510[/tex] = 30

Therefore,

The cost of the sweater is $ 30 and

1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos

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Answer:

x = 2

Step-by-step explanation:

8x - 6 = 10 ( add 6 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Answer:

x = 2

Step-by-step explanation:

8x-6 = 10

8x-6+6 = 10+6

8x = 16

8x/8 = 16/8

x = 2

It depends on how accurate you want to be, but two straight lines between 0° and 30° and 30° and 90° will not be too bad for Sine.

Thus for angles less than 30°

sinx≈x/60

and for angles greater than 30°

sinx≈(30+x)/120

For Cosine you use the identity

cosx=sin(90−x)

And for Tangent you use the identity

tanx=sinxcosx

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Answer:

Yes i the relationship linear,exponential,or neither

The gallons of water and premium antifreeze solution that must be mixed are equal to 60 gallons and 120 gallons respectively.

In order to calculate the gallons of water and premium antifreeze solution, we would assign variables to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:

Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:

x + y = 180      ....equation 1.

0.60y = 0.40(180)    ....equation 2.

From equation 2, we have:

0.60y = 0.40(180)

0.60y = 72

y = 72/0.60

y = 120 gallons of premium antifreeze.

For the gallons of water, we have the following:

x + y = 180

x = 180 - y

x = 180 - 120

x = 60 gallons of water.

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Answer: I think it’s the first one.

Step-by-step explanation:

The new price for the car when there's an increase of 6% is $35616.

Given that the dealership increased the price of a certain car by 6% and the original price was $33,600.

The new price will be:

= Original price + Increase in price

= $33600 + (6% × $33600)

= $33600 + $2016

= $35616

The new price is $35616.

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The amount of the monthly payments is $368.34, and the total interest on the loan is $5,100.

The initial amount of money that we borrow is $17,000. We borrow this amount for a total of five years. The interest charged is 6%. We borrowed the money for the purchase of a car. We need to find the monthly payments and the total interest for the loan.

Let the total amount to be paid and the interest be denoted by the variables "A" and "I", respectively.

I = P*R*T

I = $17,000*0.06*5

I = $5,100

The total amount of money to be paid is the sum of the initial amount and the interest charged.

A = P + I

A = $17,000 + $5,100

A = $22,100

The total number of months in five years is 12*5 = 60.

The amount of the monthly payment is the ratio of the total amount to be paid to the total number of months.

M = $22,100/60

M = $368.34

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Answer:

C= 31in

Step-by-step explanation:

First you must know the circumference equation. The circumference equation is C=2πr, with r being the radius. Since we are given the radius, we will fill in the radius given for r. So then we will fill in and solve:

C=(2)(π)(5in)

C=(10)(π)

C=31.4in...

C=31in

Hope this helps!

Answer: 11.74

Step-by-step explanation:

4.33+4.33+1.54*1.54+11.74

A rectangle has two pairs of equal sides.

Answer: they both go up in cents by 5s.  they may not be only five but five's.  Therefore, they are adding by 5s and that is the linear relationship

Step-by-step explanation:

Answer:

$6

Step-by-step explanation:

5 x 0.20=1

5+1=6

a) A vertical stretch happens for values of a such that |a| > 1.

b) A vertical compression happens for values of a such that |a| > 0.

c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.

d) A reflection across the x-axis takes place when a < 0.

The definition of the quadratic function is given as follows:

f(x) = a(x - h)² + k.

The transformations to the function are given as follows:

Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:

a < 0.

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The resulting equation of isolation and substitution is  9y⁴-466 y² + 5481 = 0

Given:

{x² + y² = 25

{x²/16 - y²/9 = 1

Zach isolated  x² in the first equation, we have:

x² + y² = 25

x² = 25- y²

Zach then substituted the x² into the second equation:

x²/16 - y²/9 = 1                           (put x² = 25- y²)

(25- y²)²/16 - y²/9 = 1                (Expand the bracket)

(625- 50y²+y⁴)/16 - y²/9 = 1      The LCM of 9 and 16 is 144

( 9(625- 50y²+y⁴) - 16 y² ) /144 = 1         Cross multiply

9(625- 50y²+y⁴) - 16 y² = 144

5625 - 450y² + 9y⁴-16 y² = 144

9y⁴-466 y² + 5625 = 144

9y⁴-466 y² + 5625-144 = 0

9y⁴-466 y² + 5481 = 0  

Therefore, the resulting equation is  9y⁴-466 y² + 5481 = 0

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The table to show the number of cups for the colors will be:

Red cups Blue cups

1. 8

2. 16

3. 24

Given that the person is making purple paint in the ratio of 2 cups blue paint to 1/4 cups of red paint.

Therefore, for every 1 cup of red paint, the number of blue paint will be:

= 2 ÷ 1/4

= 2 × 4

= 8 cups

Therefore, to get other values, you simply have to multiply by 8.

2 red paint will be:

= 2 × 8

= 16 blue cups.

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The value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.

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

We have to find the values of the variable in the given ordered pairs: (1,y) and (x,3).

Equation is 6x + 1.2y = −2.4

For ordered pairs: (1,y)

6(1)+1.2y =-2.4

1.2y=-8.4

y=-7

For Pair (x,3)

6(x)+1.2(3) =-2.4

6x = -6

x=-1

Hence, the value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.

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Answer:

[tex]P(x)=x^3-3x^2+16x-48[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial with real coefficients, and 4i is a root of f(x)=0, then its complex conjugate -4i is also a root of P(x)=0.

Therefore, the polynomial in factored form is:

[tex]P(x)=1(x-3)(x-4i)(x-(-4i))[/tex]

[tex]P(x)=(x-3)(x-4i)(x+4i)[/tex]

Expand the polynomial:

[tex]P(x)=(x-3)(x^2+4ix-4ix-16i^2)[/tex]

[tex]P(x)=(x-3)(x^2-16(-1))[/tex]

[tex]P(x)=(x-3)(x^2+16)[/tex]

[tex]P(x)=x^3+16x-3x^2-48[/tex]

[tex]P(x)=x^3-3x^2+16x-48[/tex]

The sentence that represents this equation 8 3/4 = 17 - x is B) 8 3/4 is the same as 17 decreased by a number.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, 8 3/4 is the same as 17 decreased by a number will be 8 3/4=17−x.

Therefore, the correct option is B.

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Complete question

What sentence represents this equation?

8 3/4 = 17 - x

A) A number is the same as the difference of 17 and 8 3/4.

B) 8 3/4 is the same as 17 decreased by a number.

C) 17 decreased by 8 3/4 is the same as a number.

D) 8 3/4 is the same as a number decreased by 17.

Answer:

y = 5x + 1

y = 5x + [tex]\frac{-3}{2}[/tex]

When the slopes are the same (5) the equations are parallel.

Step-by-step explanation:

You can look at the graph of the two equaions attached to see that there paralle.

2y - 10x +3 = 0  Add 10 to both sides of the equation

2y -3 = 10x  Add three to both sides of the equation

2y = 10x -3  Divide all the way through by 2

y = 5x + [tex]\frac{-3}{2}[/tex]

Answer:

hope this helps!!!

what the question............

Kinetic energy is defined as the work required to accelerate a body of a given mass from rest to its stated speed. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

Mass - (Measured in Kilogram) - Mass is the amount of matter in a body, regardless of its volume or the forces acting on it.

Velocity - (Measured in Meters per Second) - Velocity is a vector quantity (has both magnitude and direction) and is the rate of change of an object's position with respect to time.

We have that the data is:

The formula to calculate kinetic energy is:

             Ec = m * v²/2

Since it only asks us to calculate the kinetic energy, it is not necessary to clear the formula.

[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*\left(0.42 \ \frac{m}{s}\right)^2 }{2} }}[/tex]

[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*0.1764 \ \frac{m^2}{s^2} }{2} }}[/tex]

[tex]\boldsymbol{\sf{Ec=13.9356 \ kg*\dfrac{m^2}{s^2} }}[/tex]

We work with the units, in this case with m^2 = m*m.

[tex]\boldsymbol{\sf{Ec=13.9356 \boxed{\boldsymbol{\sf{Kg*\frac{m}{s^2} }}}*m }}[/tex]

Newton's units are: Kg*m/s^2.

[tex]\boldsymbol{\sf{Ec=13.9356 \ N*m \longmapsto Joule \ units=N*m}}[/tex]

[tex]\boldsymbol{\sf{Ec=13.9356 \ J}}[/tex]

But if you need the rounded answer, then 13.94 Joules.

The series as represented in the task content is divergent and hence; diverges.

It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.

It is noteworthy to know that;

If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.

Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.

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