Form a polynomial with real coefficients having the given degree and zeros. Degree​ 4; ​ zeros: multiplicity 2 Question content area bottom Part 1 Let a represent the leading coefficient. The polynomial is . ​(Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your​ answer.)

We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

A parabola refers to the shape that traces the equation of the form ax² + bx + c.

A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.

The parabola created when the directrix is on the y coordinate called a vertical parabola.

If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.

If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.

From the given definition of the directrix, we can find the value of p;

2p = y coordinate of focus - equation of the directrix

2p = 1 - (-1)

2p = 2

p = 1

Vertex, v(h, k) compared with f(h, k + p), we will get;

k + p = 1

k = 0

Therefore, the vertex is (-8, 0).

Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

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Answer:

Step-by-step explanation:

ok  

The person that has a better performance is Puja Limbu.

From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:

= 8/10 × 100

= 80%

Raju Lama did 11 out of 15 similar math problem. This will be:

= 11/15 × 100

= 73%

Therefore, Puja has a better performance.

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Answer:

y + 8 = -3/11(x+7)

Step-by-step explanation:

What is the point-slope form formula?

y-y1=m(x-x1) -------> y+8=-3/11(x+7)

Answer:

2m/4m = 9m/xm

2m(xm) = 4m(9m)

2xm = 36m

Answer:

1. $5

2. $1 per mile

3.y=x+5

Step-by-step explanation:

1. If you look at the graph you can see that the cost for 0 miles with the Green Cab is $5

2.If you look at the graph, for each mile traveled, the cost is $1

3. Since for each increase 1 increase in x, y increases by the same amount, the slope is 1

y=mx+b is the slope intercept form

m=slope

b=y intercept

since we know the slope is 1 we can put it in

y=1x+b

=y=x+b

to find the y intercept we can look at the graph and see what y equals when x is 0.

the y intercept is (0,5)

we can put that in so the equation in slope intercept form is

y=x+5

Answer:

569.80

Step-by-step explanation:

The measure of non reflex angle DOB in degrees is 140°

From the given information, we are to determine the measure of the non reflex angle DOB

From the given information,

m reflex ∠ DOB = 3.5y

and

m ∠ AOD = y

First, we will determine the value of y

From Linear pair theorem, we can write that

3.5y + y = 180°

4.5y = 180°

y = 180°/4.5

y = 40°

Also,

y + m ∠ DOB = 180° (Linear pair theorem)

Thus,

40° + m ∠ DOB = 180°

m ∠ DOB = 180° - 40°

m ∠ DOB = 140°

Hence, the measure of ∠ DOB is 140°

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Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

f(x) = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then

f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line

Answer:

18 hours of footage.

Step-by-step explanation:

This is a LCM problem. The least common multiple of 6 and 9 is 18. The minimum amount of hours needed to see the sparrow and butterfly at the same time is 18.

The equation of the line in slope-intercept form is y = -5x

From the question, we have the graph that can be used in our computation

On the graph, we have the following points

(0, 0) and (-1, -5)

Start by calculating the slope using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where,

(x, y) = (0, 0) and (1, -5)

So, we have

Slope = (-5 - 0)/(1 - 0)

This gives

Slope = -5

The equation of the line is then calculated as

y= Slope * (x - X) + Y

So, we have

y = -5 * (x - 0) + 0

Evaluate

y = -5x

Hence, the equation is y = -5x

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The radius of the circle to the nearest 10th is 2.0537.

Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.

we know that,

radians = arc / radius

radius = arc/radians

= 19.1/9.3

= 191/10/93/10

= 191/93

≈ 2.0537

Therefore the radius of the circle to the nearest 10th is 2.0537.

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Graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f ( 6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

As given in the question,

Given function are as follow:

f(x) = ( 1 / 3 )x + 1

g ( x ) = f ( 6x )

Calculate the function g(x) for f ( 6x ) is given by,

g ( x ) = f ( 6x )

⇒ g ( x ) = ( 1 / 3 )6x + 1

⇒ g ( x ) = 2x + 1

Substitute the value of x to get value of f ( x ) and g ( x ) and put it on graph.

After putting all the values of f(x) and g(x) .

Graph intersect at ( 0, 1 )

Graph is attached.

Therefore, graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f (6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

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Answer:

The radius (in centimeters) is 18.9999, or roughly 19 centimeters.

Step-by-step explanation:

If you need a step-by-step explanation, please let me know and I will help you. Thanks!

The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

As per the given,

Principle amount P = $2800

Rate of interest = 6% = 0.06

Compound quarterly n = 4

Time period T = 5 yeras

a)

Total amount = P(1 + R/n)^(nT)

Total amount = 2800(1 + 0.06/4)^(4 x 5)

Total amount = 2800(1.015)^20

Total amount = $3771.19

b)

Let's say the equivalent annual interest rate is r.

n = 1

3771.19 = 2800(1 + r/1)^(1 x 5)

3771.19 = 2800(1 + r)^5

1.061 = 1 + r

r = 0.06136 = 6.136%

Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".

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If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer

19.50 x 40 = $ 780 a week.

I hope this helps!

The population for 2015 is 1,640,000 ,so option A is correct.

Given:

The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.

where x is the number of years since 2005.

x = 2015 - 2005

x = 10

P(x) = x³ + 2x² - 8x + 520.

= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]

= 1000 + 2*100 - 80 + 520

= 1520 + 200 - 80

= 1720 - 80

= 1640.

Given the projected population in thousands so = 1640 * 1000

= 1640000.

Therefore The population for 2015 is 1,640,000 ,so option A is correct.

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Answer:

a

Step-by-step explanation:

f(x) = y, so y=1-x. the slope is always infront of the x, so if there is nothing infront of x then it'll be a 1. so in this cas slope is a -1 and the y intercept is 1.

If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

In the question ,

it is given that ,

the length of the shadow of the flag pole = 18m

the angle of "elevation" of the sun = 54°

let the height of the flagpole be = "x" ,

The flagpole and the shadow form a right triangle ,

So , tan(54°) = (height of flag pole)/(shadow of flagpole)

Substituting the values from above ,

we get ,

tan(54°) = x/18

on cross multiplication ,

x = 18 × tan(54°)

x = 18 × 1.3763

x = 24.7734

x ≈ 24.8

Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

The given question is incomplete , the complete question is

A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?

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a) The general equation is:

y = m*(x - h) + k

b) The slope is -3

c) the point-slope form is: y = -3*(x - 6) + 1

d) The standard form is: y + 3x = 19

We will write a linear equation that relates two variables x and y, and the slope-point form is given by:

y = m*(x - h) + k

Where m is the slope, and (h, k) is a point on the line.

Particularly, if a line passes through two points (a, b) and (c, d), then the slope of that line is:

m = (d - b)/(c - a)

In this case, the line passes through (6, 1) and (5, 4), then the slope is:

m  = (4 - 1)/(5 - 6) = 3/-1 = -3

Now  we can use one of the given points to write the line in the point-slope form, I will use (6, 1) to get:

y = -3*(x - 6) + 1

Now we want to write this in standard form.

Expanding the right side we get:

y = -3x + 18 + 1

y = -3x + 19

Adding 3x in both sides we get:

y + 3x = 19

This is the standard form.

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Answer:26

Step-by-step explanation:

According to the Pythagoras theorem, the value of the other leg is, 15.7 cm

Pythagoras theorem:

Pythagoras theorem defines that  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.

Here we need to find the measure of the other leg and round off it to nearest tenth.

Though the given question, we know that the value of

Hypotenuse = 16 cm

one leg = 3cm,

Then let us consider the length of the other leg as x.

So, according to the Pythagoras theorem,

It can be calculated as,

=> hypotenuse² = one leg² + other leg²

=> 16² = 3² + x²

=> 256 = 9 + x²

Here we need the value of x, so it can be rewritten as,

=> 247 = x²

=> x = √247

When we take square root for 247, then we get the value of x as,

=> x = 15.716

When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.

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The value of 'E' in the algebraic equation is -2

Algebraic equation is a mathematical statement in which two expressions are set equal to each other.

Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e

Use 0.75 to open the bracket

6 + 0.75e = 2 -1.25e

Collect the like terms

0.75e+1.25e = 2-6

2e = -4

Divide both sides by 2

2e/ 2 = -4/2

e =-2

Therefore, the value of 'E' in the equation is -2

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The value of the unknown variable in the ordered pair is 8

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

(r, 3), (5, 9)

Also, we have

m = 2

The meaning of the above notations are

Ordered pairs (x, y) = (r, 3), (5, 9)

Slope, m = 2

The slope of points is calculated using the following slope equation

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (r, 3), (5, 9) and m = 2

Substitute the known values in the above equation, so, we have the following representation

(9 - 3)/(r - 5) = 2

Evaluate the difference

This gives

6/(r - 5) = 2

Divide both sides by 2

So, we have

3/(r - 5) = 1

Cross multiply

r - 5 = 3

So, we have

r = 3 + 5

Evaluate the sum

r = 8

Hence, the value of r is 8

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Possible question

What is the value of r using the following points and slope

(r, 3), (5, 9), m=2

Answer:

The number is 27.

Step-by-step explanation:

Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.

Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.

3 (1 + 6) = 21 does not work because 16 isn't the same as 21.

3 (2 + 7) = 27 does work because 3 * 9 is 27.

3 (3 + 8) = 33

3 (4 + 9) = 39

By evaluating The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1) the value calculated is 7/60.

Given:

= ∫∫∫7[tex]x^{2}[/tex] dV

T(x,y,z) : 0≤x≤1; 0≤y≤1-x; 0≤z≤1-x-y]

apply limits and solving we get:

= 7/2([tex](x^{3} /3+x^{5} /5-x^{4}/2)[/tex]

= 7/2(1/3+1/5-1/2)

= 7/2(1*5+1*3/15 - 1/2)

= 7/2(8/15 - 1/2)

= 7/2(16 - 15/30)

= 7/2*1/30

= 7/60

Therefore after evaluating the value of triple integral is 7/60.

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Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + (4√3)^2 = c^2

16 + 48 = c^2

64 = c^2

√64 = c

8 = c