Identify the type of conic section given by the polar equation below. Also give the equation of its directrix (in rectangular coordinates is fine.)
r = 8/4+ cos θ.

Step-by-step explanation:

see the attachment......

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We are given that:

[tex]CB=2x+5[/tex]

And that DE = 10. We want to determine the value of x.

Note that CB is the sum of CD and DB. In other words:

[tex]CB=CD+DB[/tex]

Similarly, DE is the sum of DB and BE. Thus:

[tex]DE=DB+BE[/tex]

From the second equation, we can subtract BE from both sides:

[tex]DE-BE=DB[/tex]

Substitute this into the first equation:

[tex]CB=CD+(DE-BE)[/tex]

We are given that CB is 2x + 5 and DE is 10.

From the diagram, we can also see that CD is 3x - 1 and BE is 8.

Substitute:

[tex](2x+5)=(3x-1)+((10)-(8))[/tex]

Solve for x:

[tex]\displaystyle \begin{aligned}(2x+5) & = (3x-1) + (2) \\ \\ 2x + 5 & = 3x + 1 \\ \\ -x + 5 & = 1 \\ \\ - x & = -4 \\ \\ x & = 4 \end{aligned}[/tex]

In conclusion, the value of x is 4.

Answer:

Mr. Grote: 29, Ms. Maitner: 45

Step-by-step explanation:

x = number of points Mr. Grote scored

x + 16 = number of points Ms. Maitner scored

x + x + 16 = 74

x + x = 58

2x = 58

x = 29

29 + 16 = 45

Answer:

Step-by-step explanation:

The Bessel function or order zero of the first kind may be defined by the solution - to Bessel's differential equation - which is a finite value at the origin X=0 for positive or negative whole numbers (integers) or positive alpha (α) values.

Answer:

D. (f - g)(x) = 4x^3 + 7x^2 - 6x + 1

Step-by-step explanation:

You need to subtract g(x) from f(x).

(f - g)(x) = f(x) - g(x) =

= 4x^3 + 7x^2 - 2x - 1 - (4x - 2)

Distribute the negative sign at the left of the parentheses as you would distribute a -1. Every sign inside the parentheses changes.

= 4x^3 + 7x^2 - 2x - 1 - 4x + 2

Combine like terms.

= 4x^3 + 7x^2 - 6x + 1

Answer: D. (f - g)(x) = 4x^3 + 7x^2 - 6x + 1

Answer:

4x^3+7x^2-6x+1

Step-by-step explanation:

f(x) = 4x^3 +7x^2 -2x-1

g(x) = 4x-2

f(x) - g(x) = 4x^3 +7x^2 -2x-1 - ( 4x-2)

Distribute the minus sign

                4x^3 +7x^2 -2x-1 - 4x+2

Combine like terms

                   4x^3+7x^2-6x+1

Answer:

m = 123°

k = 57°

h = 123°

p = 99°

q = 81°

f = 99°

g = 81°

s = 42°

r = 57°

u = 57°

v = 123°

Step-by-step explanation:

Using basic angle relationships, we should be able to tell these angles easily.

If the 57° is supplementary to m, then m will be [tex]180 - 57 = 123[/tex] degrees.

k is also supplementary to m, so k is [tex]180-123=57[/tex] degrees - we also know this because it is an alternate interior angle to the other 57°.

h is an alternate interior angle to m, so h is the measure of m : 123°.

q is the same measure as the 81° angle, since they are corresponding angles. q is also 81°.

p is supplementary to q, so p is [tex]180-81=99[/tex] degrees.

f is an alternate interior angle to p, so f is also 99°.

g is also an alternate interior angle to q, so g is 81°.

The measure of s will be [tex]180-k-g[/tex] since all 3 sides of a triangle add up to 180°: so [tex]180-57-81=42[/tex] degrees.

r will be supplementary to the 81° angle and s, 42, so r is [tex]180 - 81 - 42=57[/tex] degrees.

u is an alternate interior angle to r, so u is also 57 degrees.

v is supplementary to u, so v will be [tex]180-57=123[/tex] degrees.

Hope this helped!

Answer:

20.

Step-by-step explanation:

2x + x - y^2; x = 8 and y = 2.

2(8) + 8 - (2)^2

= 16 + 8 - 4

= 24 - 4

= 20.

Hope this helps!

Answer:

= 20

Step-by-step explanation:

2x + (x - y²)

x = 8

y = 2

then:

  2*8 + (8 - 2²)

= 16 + (8 - 4)

= 16 + 4

= 20

Answer:

x=6

Step-by-step explanation:

subtract the 2x from 4x and add 3 to 9. we would get 2x=12. divide by 2 on both sides and you get x=6!

Answer:(14.80-0.8)*6=84

Step-by-step explanation:

Answer:

71.04

Step-by-step explanation:

0.8×14.80=11.84

11.84×6=71.04

Answer: Total cost: $820.26      Paid in tax: $62.51

Step-by-step explanation:

First you have to get the Tax. Since the Tax is 8.25% MOVE the decimal 2 spots to the right so now it is 0.0825.

Multiply 0.0825 by 757.75 you will get 62.514375.

Dont get scared of the big number simply simplify and you get the tax.

if you want the total he paid add tax and original cost.

Answer:

width of the confidence interval decreases if the sample size is increased to 20.

Step-by-step explanation:

There are some factors which affect the width of the confidence interval such as:

The decrease in the sample standard deviation decreases the width of the interval .

The decrease the confidence level decreases the width of the interval .

The increase in the sample size decreases the width of the interval .

In the given question the previous sample size was 10 which was then increased to 20. So this increase in sample size causes the confidence interval to decrease. This is because when sample size increases, it decreases the standard error. This interprets that the sample size is getting closer to true population size.

Answer:

1) 14 by 21

2)7

Step-by-step explanation:

i Dint do the complete work i am not sure.

The side lengths of the scaled copy would be 14 by 21 and If you want to scale the copy back to its original size then you should use a scale factor that would be 1/7.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7 which is given in the question.

As we know scale factor is the ratio of sides in the original image and the image after dilation.

So the side lengths of the scaled copy would be 14 by 21

If you want to scale the copy back to its original size

Therefore, you should use a scale factor that would be 1/7.

Learn more about the Scale images here:

brainly.com/question/13194929

#SPJ5

Answer:

No, a regular pentagon does not tessellate.

In a tessellation, all the angles at a point have to add to 360 degrees, as this means there is no overlap, nor are there gaps. To find the interior angle sum of a pentagon, we use the following formula:

(n-2)*180 (where n is the number of sides)

We plug in the number of sides (5) and get:

Angle sum = (5–2)*180

Angle sum = 3*180

Angle sum = 540

Regular pentagons have equal sides and equal angles, so to find the size of the interior angle of a pentagon, we divide the angle sum by 5 and get 108 degrees for every angle.

As I said before, the angles at a point need to add up to 360, so we need to know if 108 divides evenly into 360. If it does, the shape tessellates, and, if it doesn’t, the shape does not.

360/108 = 3.33333…

This means that a regular pentagon does not tessellate.

Hope this helps!

Answer:

No solutions

Step-by-step explanation:

First, isolate the absolute value:

|x-2| + 5 = 2

|x - 2| = -3

An absolute value can never equal to a negative number

So, there are no solutions

Answer:

-5

Step-by-step explanation:

the slope is the variable in front of the x

Answer:

12.5 feet

Step-by-step explanation:

The distance in a coordinate geometry is calculated using: [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]. Jerome and Eric have hiked 12.4 miles when they stopped to eat.

To do this, we make use of distance formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

From the figure, we have the following points:

[tex]A = (4,4)[/tex]

The other points between A and W in counterclockwise are:

[tex]B=(6,2)[/tex]

[tex]C = (8,2)[/tex]

[tex]D = (8,4)[/tex]

[tex]E = (10,6)[/tex]

[tex]W = (8,8)[/tex]

Distance AB is:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]AB = \sqrt{(4 - 6)^2 + (4 -2)^2} =\sqrt{8} =2.8[/tex]

Distance BC is

[tex]BC = \sqrt{(6 - 8)^2 + (2 -2)^2} =\sqrt{4} =2[/tex]

Distance CD is

[tex]CD = \sqrt{(8 - 8)^2 + (2 -4)^2} =\sqrt{4} =2[/tex]

Distance DE is :

[tex]DE = \sqrt{(8 - 10)^2 + (4 -6)^2} =\sqrt{8} =2.8[/tex]

Distance EW is:

[tex]EW = \sqrt{(10-8)^2 + (6 -8)^2} =\sqrt{8} =2.8[/tex]

So, distance AW is:

[tex]AW = AB + BC + CD + DE + EW[/tex]

[tex]AW = 2.8 + 2+ 2 + 2.8 +2.8[/tex]

[tex]AW = 12.4[/tex]

Read more about distance in coordinate geometry at:

https://brainly.com/question/3715220

Answer:

6.75

Step-by-step explanation:

9x0.75=6.75

Answer:

Correct answer is 6.75

Step-by-step explanation:

75% x 9 = 6.75

Answer:

All of the functions required to transform inputs into outputs (goods and ... provide all of the materials and supplies required to create finished products and deliver ... System for determining the right quantity of various items to have on hand

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

slope: (y² - y¹) / (x² - x¹)

(3, 0) & (3, 1)

(1 - 0) / (3 - 3) = 1 / 0

undefined = vertical line

Answer:

Step-by-step explanation:

Considering that the question is a fun riddle, I will give a suitable fun answer.

The question says that the son goes to school, so we can assume that the boy is a young child. So, he is probably short.

So, while getting down the stairs, it is easy for him to press the button in the elevator to reach the ground floor as the button for ground floor is the on the bottom of the switch panel.

However, since he is short he cannot reach the button for the 10th floor after returning from school. He can only reach up to the button for the 5th floor. So, he travels up to the 5th floor by the elevator and from there he takes the stairs to reach the 10th floor.

Answer:

The principal is $4,150.

Step-by-step explanation:

We have to find the principal if the maturity value is $4,500 and the simple interest is $350.

As we know that the formula for calculating the final amount or maturity amount is given by;

Amount = Principal + Interest

Here, Simple interest = $350

Amount or Maturity value = $4,500

So, the Principal = Amount - Interest

Principal = $4,500 - $350

               = $4,150

Hence, the principal if the maturity value is $4,500 and the simple interest is $350 is $4150.

Answer:

65oz for 6.99 dollars

Step-by-step explanation

Answer:

The difference is 8.56 cm. ( the metre is longer than the yard).

Step-by-step explanation:

1 yard = 36 inches

= 36 * 2.54

= 91.44 cm

1 metre = 100 cm.

Answer:

EF + FG = EG   Plug in the given values

4x + 15 + 39 = 110   Combine like terms (15 and 39)

      4x + 54 = 110   Subtract 54 from both sides

               4x = 56   Divide both sides by 4

                 x = 14

Answer:

D. 2

Step-by-step explanation:

(1 - -5)/(4 - 1) = 6/3 = 2

Answer: 2

Step-by-step explanation:

The slope of a line through two points (x₁, y₁) and (x₂, y₂) is given by (y₂ - y₁)/(x₂ - x₁). In this case, x₁ = 1, y₁ = -5, x₂ = 4, and y₂ = 1. So the slope is:

(1 - (-5))/(4 - 1) = 6/3 = 2

Answer:

(a) 51

(b)  [tex]T_{n}=a+(n-1)d[/tex]

(c) 20th figure

Step-by-step explanation:

The diagram is attached below.

The first triangle is formed using 6 toothpicks.

The second triangle is formed using 11 toothpicks.

The third triangle is formed using 16 toothpicks.

So, there is an increases of 5 toothpicks every time.

We can say that the number of toothpicks used to form n triangles are following an arithmetic progression with the first term as 6 and the common difference as 5.

The nth term will be:

[tex]T_{n}=a+(n-1)d[/tex]

(a)

Compute the number of toothpicks required for the 10th figure as follows:

[tex]T_{n}=a+(n-1)d[/tex]

[tex]T_{10}=6+(10-1)\times5[/tex]

     [tex]=6+(9\times5)\\=6+45\\=51[/tex]

Thus, the number of toothpicks required for the 10th figure is 51.

(b)

Compute the number of toothpicks required for the nth figure as follows:

[tex]T_{n}=a+(n-1)d[/tex]

(c)

Compute the value of n for [tex]T_{n}=102[/tex] as follows:

                 [tex]T_{n}=102[/tex]

   [tex]a+(n-1)d=102\\\\[/tex]

[tex]6+(n-1)\times 5=102[/tex]

         [tex]5(n-1)=96[/tex]

             [tex]n-1=19.2[/tex]

                   [tex]n=20.2\\n\approx 20[/tex]

Thus, the 20th figure will require exactly 102 toothpicks.

Answer:

Rs. 4128.57

Step-by-step explanation:

Given:

Solving for x:

Answer:

(x − 1)² + (y − 2)² = 25

Step-by-step explanation:

Equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

Answer:

[tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i

Step-by-step explanation:

Given

[tex]\frac{8-i}{6+i}[/tex]

Multiply numerator/ denominator by the conjugate of the denominator.

The conjugate of 6 + i is 6 - i, thus

= [tex]\frac{(8-i)(6-i)}{(6+i)(6-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{48-14i+i^2}{36-i^2}[/tex] → substitute i² = - 1

= [tex]\frac{48-14i-1}{36+1}[/tex]

= [tex]\frac{47-14i}{37}[/tex]

= [tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i

Answer:

I believe that it is a line, since a line is infinite

Step-by-step explanation: