Find a polar equation r for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)
Conic: Parabola Eccentricity: e = 1 Directrix: y = 4

Answer:

-16

Step-by-step explanation:

-5-(3^2+2)

Parentheses first

-5-(9+2)

-5-(11)

Subtract

-16

Answer:

x = 3, y = -2

Step-by-step explanation:

Since y=y

then, -3x +7 = 2x-8

7+8 = 3x+2x

15 = 5x

x=3

substitute

y = 2(3) - 8

y = -2

Hope that helped!!! k

Answer:

y = -2

x = 3

Step-by-step explanation:

Solve using elimination

1. Rearrange the equations to make it easier to solve

y = -3x + 7 → 3x + y = 7

y = 2x - 8 → 2x - y = 8

2. Multiply the equations to have a matching coefficient

2(3x + y = 7) = 6x + 2y = 14

3(2x - y = 8) = 6x - 3y = 24

3. Subtract

 6x + 2y = 14

- 6x - 3y = 24

  0 + 5y = -10

4. Solve for y

5y = -10

y = -2

5. Substitute y in any equation to solve for x

-2 = -3x + 7

-3x = -9

x = 3

Answer:

2m^3 + 3m^2

Step-by-step explanation:

8m^4+12m^3

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

4m

2m^3 + 3m^2

Check

4m(2m^3+3m^2)

8m^4 + 12 m^3

Answer:

B) C and G

Step-by-step explanation:

The radius is equal to 1/2 the diameter

r = 1/2 d

G has a diameter of 45

1/2 (45) = 22.5

C and G are the same

Answer:

c and g!

Step-by-step explanation:

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

Slope = 5/1 = 5

Slope = 10/2 = 5

Slope = 15/3 = 5

Slope = 20/4 = 5

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

Read more about Linear function at; https://brainly.com/question/15602982

Answer:

Three angles measuring 40°, 70° and 65°

Step-by-step explanation:

Because they don't add up to 180°

Answer:

The correct answer is 10° 25° 145°

Step-by-step explanation:

It's because the two smallest angles added up must be greater than the largest angle to create a triangle. Your welcome.

Answer:

Option  A

Step-by-step explanation:

2001 can be divided by 3, 23, and 29 without remainders. This means that the three numbers are prime divisors of 2001.

2001/3 = 667

2001/23 = 87

2001/29 = 69

The sum of the prime divisors is 55.

3 + 23 + 29 = 55

Option A should be the correct answer.

Hope this helps.

Answer:

The answer is 90+0+0.1+0.02+0.005.

Step-by-step explanation:

The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.

Answer:

Below

Step-by-step explanation:

Suppose that m and n are both even numbers.

So we can express them as the product of 2 and another number.

● n = 2×a

● m = 2×b

● m-n = 2b-2a

● m-n = 2(b-a)

m-n is an even number since it is divisible by 2.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Suppose that both n and m are odd numbers.

● n = 2a+1

● m = 2b+1

● m-n = 2b+1-(2a+1)

● m-n = 2b+1-2a-1

● m-n = 2b-2a

● m-n = 2(b-a)

So m-n is even since it is divisible by 2.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Suppose that m is odd and n is even ir vice versa

● n = 2a or n= 2a+1

● m = 2b+1 or m = 2b

● m-n = 2b+1-2a or m-n = 2b-2a-1

● m-n = 2(b-a) +1 or m-n = 2(b-a)-1

In both cases m-n isn't even.

■■■■■■■■■■■■■■■■■■■■■■■■■■

So m-n is even if and only if m and n are odd or m and are even

Answer:

Case 1

both m and n are even

Therefore m/2 and n/2 are integers

Then,

m-n

=2(m/2 - n/2)

Since m/2 and n/2 are integers

Then m/2 - n/2 will be an integer

Therefore,

m-n = 2(Z)

Where Z is an integer

Since 2 is a factor of m-n

Therefore m -n is even

Case 2

Both m and n are odd

m-n

= 2(½m - ½n)

When an odd number is divided by 2 it gives an integer and a remainder of 1

Therefore

½m = Y + ½

And

½n = Z + ½

Where Y and Z are integers

Then

m-n = 2(Y+½-Z-½)

= 2(Y-Z)

Y-Z will also be an integer

m-n= 2A

Therefore m-n is even

Case 3

One is odd and the other even

m-n = 2(m/2 - n/2)

Assume m is even and n is odd

From the discussions above

m-n = 2(Y - Z - ½)

m-n = 2(A - ½)

Hence m-n is not even because when is divided by two it doesn't give an integer.

Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.

Answer:

2  1/5

Step-by-step explanation:

2 3/4 * 4/5

Change the mixed number to an improper fraction

( 4*2+3)/4 * 4/5

11/4 * 4/5

The 4 in the numerator and denominator cancel

11/5

Changing back to a mixed number

5 goes into 11 2 times with 1 left over

2 1/5

Answer:

[tex]2\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]2\frac{3}{4}*\frac{4}{5}\\\frac{11}{4}*\frac{4}{5}\\\frac{11}{5}\\ 2\frac{1}{5}[/tex]

Answer:

$106

Step-by-step explanation:

You have 100$ in savings account

Interest rate =3%

Time = 2 years

Total in 2 years:

The interest formula is as follows:

Amount Invested · Rate = Interest Earned

If we invest $100 at 3% interest per year,

how much do we earn that year?

Well based on our formula, we can simply multiply 100 · 3%.

Think of the 3% as 3/100.

So we have 100 · 3/100 and the 100's cancel and we're left with 3.

So $3 is earned in 1 year.

So after two years, you will have double that or $6.

Answer:

2:3

Step-by-step explanation:

It’s easy

Answer:

2.5

Step-by-step explanation:

i think

━━━━━━━☆☆━━━━━━━

▹ Answer

80%

▹ Step-by-Step Explanation

20/25 = 0.8 → 80%

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer: B

Step-by-step explanation:

Why did historians choose to study this topic?

Answer:

1978.2 or 630π feet

Step-by-step explanation:

The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.

Answer:

Hello,

Step-by-step explanation:

Area of the sphere:

[tex]S=4*\pi *r^2[/tex]

Volume of the sphere:

[tex]V=\dfrac{4*\pi *r^3}{3}[/tex]

[tex]\dfrac{S}{3} =\dfrac{V}{7} \\\\\dfrac{4*\pi *r^2}{3} =\dfrac{4*\pi *r^3}{3*7} \\\\1=\dfrac{r}{7} \\\\\\r=7\\\\great \ circle: 2*\pi* r=14*\pi\\[/tex]

[tex]Volume=\dfrac{4*\pi *7^3}{3} =\dfrac{1372*\pi }{3} \approx{1436,7550...(cm^3)}[/tex]

Answer:

See Attachment for graph

Charges = $200 when number of she works for 3 hours

Step-by-step explanation:

Given

Charges = $25 per hour + $125 (c = 25n + 125)

Required

Graph the equation.

From the graph, determine c when n = 3

To plot the graph; first, we have to determine the points to use;

When n = 1

[tex]c = 25 * 1 + 125[/tex]

[tex]c = 25 + 125[/tex]

[tex]c = 150[/tex]

When n = 2

[tex]c = 25 * 2 + 125[/tex]

[tex]c = 50 + 125[/tex]

[tex]c = 175[/tex]

When n = 3

[tex]c = 25 * 3 + 125[/tex]

[tex]c = 75 + 125[/tex]

[tex]c = 200[/tex]

When n = 4

[tex]c = 25 * 4 + 125[/tex]

[tex]c = 100 + 125[/tex]

[tex]c = 225[/tex]

Plotting n on the x axis and c on the y axis; we have

c   ||   n

1    ||   150

2   ||   175

3   ||    200

4   ||    225

(See attachment)

From the attachment;

When she works for 3 hour; This implies that n = 3

And c = $200 when n = 3

See Proof

[tex]c = 25n + 125[/tex]

Substitute 3 for n

[tex]c = 25 * 3 + 125[/tex]

[tex]c = 75 + 125[/tex]

[tex]c = 200[/tex]

The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :

The stem and leaf plots are given below:

Rounding the data to the nearest 10;

The values obtained are :

630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870

Ordering the data allows for easier generation of the plot.

Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960

The stem plot without splitting :

STEM __ LEAF

6 ___ 00, 30, 50, 50, 70

7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90

8 ___ 10, 10, 30, 60, 60, 70

9 ___ 00, 60

KEY :  6 | 00 = 600

The stem plot WITH splitting :

STEM __ LEAF

6 ___ 00, 30

6 ___ 50, 50, 70

7 ___ 00, 10, 20, 40, 40

7 ___ 80, 80, 90, 90, 90

8 ___ 10, 10, 30

8 ___ 60, 60, 70

9 ___ 00

9 ___ 60

KEY :  6 | 00 = 600

The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.

Learn more on stem and leaf plot : https://brainly.com/question/12857419?

Answer:

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

[tex]P= 2*(L + B)[/tex]

Substitute 80 for P

[tex]80 = 2 * (L + B)[/tex]

Divide through by 2

[tex]40 = L + B[/tex]

[tex]L + B = 40[/tex]

Make L the subject of formula

[tex]L = 40 - B[/tex]

Area of a rectangle is calculated as thus;

[tex]Area = L * B[/tex]

Substitute 40 - B for L

[tex]Area = (40 - B) * B[/tex]

Express this as a function

[tex]A(B) = (40 - B)* B[/tex]

[tex](40 - B)* B = A(B)[/tex]

Set A(B) = 0 to determine the roots

Hence;

[tex](40 - B)* B = 0[/tex]

[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]

[tex]40 = B[/tex] or [tex]B = 0[/tex]

[tex]B = 40[/tex] or [tex]B = 0[/tex]

The maximum area of a rectangle occurs at half the sum of the roots;

So;

[tex]B= \frac{B_1 + B_2}{2}[/tex]

[tex]B= \frac{40+0}{2}[/tex]

[tex]B= \frac{40}{2}[/tex]

[tex]B = 20[/tex]

Recall that [tex]L = 40 - B[/tex]

[tex]L = 40 - 20[/tex]

[tex]L = 20[/tex]

Hence the lengths of the sides are 20 cm and 20 cm

Answer:

Answer=53,800

Step-by-step explanation:

just add the two zero behind the number

Answer:

Philomena would make more than $14.06 interest in the second month

Step-by-step explanation:

We are not told how much Philomena put initially, but what we are told is that she has more now as she has been making interests.

This means that if the percent interest remains the same, the amount will definitely have to be more.

For example, let's say we had $10 and we had 10% interest that means we now add $1 to make $11. Since we now have $11, 10 percent of that is $1.1. so now we have $11 + $1.1 = $12.1 which is more than $11.

Thus,Philomena would make more than $14.06 interest in the second month.

Answer:

More than 14.06

Step-by-step explanation:

apesex

Answer:

C

Step-by-step explanation:

this is a "translation" - a shift of the object without changing its shadow and size.

this shift is described by a "vector" - in 2D space by the x and y distances to move.

we have here (1, 0) - so, we move every point one unit to the right (positive x direction) and 0 units up/down.

therefore, C is the right answer (the x coordinates of the points are increased by 1, the y coordinate are unchanged).

Answer:

( x-2)^2 + ( y +8) ^2 =121

Step-by-step explanation:

The equation of a circle can be written as

( x-h)^2 + ( y-k) ^2 = r^2

where ( h,k) is the center of the circle and r is the radius

( x-2)^2 + ( y- -8) ^2 = 11^2

( x-2)^2 + ( y +8) ^2 =121

Answer:

(x - 2)² + (y + 8)² = 11²

Step-by-step explanation:

General equation for a circle

( x - h )² + ( y - k )² = r², where (h,k) is the center and r ,radius..

with center ( 2,-8 ) and radius 11

(x - 2)² + (y + 8)² = 11²

Answer:

The answer is option D

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question to calculate the radius we use the formula

radius = diameter / 2

diameter =70mm

radius = 70/2 = 35 mm

So the volume of the sphere is

[tex]V = \frac{4}{3} \pi \times {35}^{3} [/tex]

[tex]V = \frac{171500\pi}{3} [/tex]

We have the final answer as

Hope this helps you

Answer:

Lowering the level of significance, α increases the probability of making a Type II error, β.

Step-by-step explanation:

Lowering the level of significance, α increases the probability of making a Type II error, β.

This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.

Answer:

300

Step-by-step explanation:

1100 = 900 [tex]e^{k*20}[/tex]

1.222222 =  [tex]e^{k*20}[/tex]

ln(1.222) = 20k ln(e)

k = ln(1.222)/20

k = .2004

900 = x [tex]e^{15* .20004}[/tex]

900/x =    [tex]e^{15* .20004}[/tex]

 [tex]e^{15*.2004} = 900/x[/tex]

x = 900/   [tex]e^{15*.2004}[/tex]

x = 300

Answer:

0.30924

Approximately ≈ 0.3092

Step-by-step explanation:

To solve for this question, we use the formula:

z = (x - μ)/σ

where x is the raw score

μ is the sample mean

σ is the sample standard deviation.

From the question,

x is the raw score = 260

μ is the sample mean = population standard deviation = 258

σ is the sample standard deviation

= σ/√N

N = 76 samples

σ = Population standard deviation

= 35/√76

= 4.0146919966

Hence,

z = (x - μ)/σ

= 260 - 258/ 4.0146919966

= 0.4981702212

Approximately = 0.498

We find the Probability using z score table for normal distribution

P(x = z) = P( x = 260)

= P( z = 0.498)

= 0.69076

The probability that a random customer will have more than $260 in his or her wallet is calculated as:

P(x>Z) = 1 - P( z = 0.498)

P(x>Z) = 1 - 0.69076

P(x>Z) = 0.30924

Approximately ≈ 0.3092

Answer:

c

Step-by-step explanation:

12/18 = 2/3

Answer:c

Step-y-step explanat:c