Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?

x squared over 4 plus y squared over 1 equals 1
x squared over 1 plus y squared over 2 equals 1
x squared over 1 minus y squared over 4 equals 1
x squared over 1 minus y squared over 2 equals 1

Answer:

The line of the equation in the point-slope form of the line passing through the point (3, -1) and having slope 1/2 will be:

[tex]y +1 = \frac{1}{2} (x-3)[/tex]

Please check the attached graph.

Step-by-step explanation:

Given

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where

In our case:

m = 1/2

The point (x₁, y₁) = (3, -1)

substituting the values m = 1/2 and the point  (x₁, y₁) = (3, -1)  in the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - (-1) = \frac{1}{2} (x-3)[/tex]

[tex]y +1 = \frac{1}{2} (x-3)[/tex]

Thus, the line of the equation in the point-slope form of the line passing through the point (3, -1) and having slope 1/2 will be:

[tex]y +1 = \frac{1}{2} (x-3)[/tex]

Please check the attached graph.

Answer:

360000

Step-by-step explanation:

Answer: You will pay 360,000,000

Step-by-step explanation:

900,000 • 0.05 • 8 = 360,000

change 5 to a decimal

The expressions that are equivalent to each other will be 7⁴, 7 · 7 · 7 · 7, and 7 to the fourth power. Then the correct options are A, B, and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 7 to the fourth power

This can be mathematically expressed as,

⇒ 7⁴

⇒ 7 · 7 · 7 · 7

⇒ 2,401

The expressions that are equivalent to each other will be 7⁴, 7 · 7 · 7 · 7, and 7 to the fourth power. Then the correct options are A, B, and E.

More about the equivalent link is given below.

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Answer:

91

Step-by-step explanation:

11*8=88 +3=91

Answer: The answer would be 91

Step-by-step explanation: since it's originally f(x)=11x+3 and x=8

then you plug in for X.

f(8)=11(8)+3=91

BRAINLIEST PLS

Answer:

I believe it's 19u+72

Step-by-step explanation:

Hope this helps! ^^

Answer:

(u + 8)(u + 9)

Step-by-step explanation:

Assuming you require to factorise the expression

u² + 17u + 72

Consider the factors of the constant term (+ 72) which sum to give the coefficient of the u- term (+ 17)

The factors are + 8 and + 9, since

8 × 9 = 72 and 8 + 9 = 17, then

u² + 17u + 72 = (u + 8)(u + 9) ← in factored form

Answer:

try adding them togeher

Step-by-step explanation:

Answer:

Carole has $53.95 and washes cars for $8 each. Carole wants to attend a musical that costs $145.75.

a. Write and solve an inequality to determine the minimum number of cars Carole must wash to be able to buy the ticket to the musical.

b. Is the answer to the question that same as the solution to the inequality? Explain.​

2

SEE ANSWERS

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

We will first take a right triangle and we will apply the pythagorean theorem to it. First, the base of the right triangle will be 12/2 which is 6; then, we will just use the theorem.

a^2+b^2 = c^2 (pythagorean theorem)

8^2+6^2 = c^2

100 = c^2

c = 10 because the square root of 100 is 10

Answer:

B

Step-by-step explanation

5:1 means for every 1 table their is 5 chairs.

And for every 5 chairs there is 1 table.

Answer: 4-2.1x

Step-by-step explanation:

Answer:

2<5

Step-by-step explanation:

there u go hope it helps

Answer:

0.14

Step-by-step explanation:

To get this, you need to divide the number by a 100.

14/100 = 0.14

Therefore 14% is 0.14 as a decimal.

Hope that helped! :)

Answer:

It would be 90 miles/2, it's rate is 45 miles per hour

Answer:

90 miles/2 hours

Step-by-step explanation:

180/8 = 22.2mph

240/6 = 40mph

90/2 = 45 mph

30/1 = 30 mph

45 mph is faster than every other unit rate, therefore 90 miles/2 hours  is the fastest.

Answer:

Area of park = 650m ²

Cost of setting blocks = Rs.24,700

Step-by-step explanation:

Given:

Length of park L = 26 m

Width of park B = 25 m

Find:

Area

Cost of Paving = 38 per m square

Computation:

Area of park = L x B

Area of park = 25 x 26

Area of park = 650m ²

Cost of setting blocks = Area of park x 38

Cost of setting blocks = 650 x 38

Cost of setting blocks = Rs.24,700

Step-by-step explanation:

Given

No. of employees [tex]N(t)=500(0.02)^{0.7^{t}}[/tex]

(a)When the company opens i.e. at t=0

[tex]N(0)=500(0.02)^{1}=10[/tex]

There are 10 employees at the beginning

(b)when N=100

[tex]100=500(0.02)^{0.7^{t}}\\0.2=0.02^{0.7^{t}}[/tex]

Taking log both sides

[tex]\ln (0.2)=0.7^t \cdot \ln (0.02)[/tex]

[tex]0.7^t=\frac{\ln (0.2)}{\ln (0.02)}=0.4114[/tex]

again taking log

[tex]t\times \ln (0.7)=\ln (0.4114)[/tex]

[tex]t=\dfrac{\ln (0.4114)}{\ln (0.7)}=2.49[/tex]

(c)when t tends to [tex]\infty[/tex], [tex](0.7)^t\rightarrow 0[/tex]

So, [tex]N(\infty)=500\cdot(0.02)^0=500\times1=500[/tex]

i.e. there can be 500 employees at max

Given:

A figure is dilated by a factor of [tex]\dfrac{5}{6}[/tex].

To find:

The factor by which the area of the figure will change.

Solution:

We know that, if a figure is dilated by a factor k then the area of that figure is change by a factor of k² .

A figure is dilated by a factor of [tex]\dfrac{5}{6}[/tex].

So, [tex]k=\dfrac{5}{6}[/tex].

The area of the figure will change by a factor of k² .

[tex]k^2=\left(\dfrac{5}{6}\right)^2[/tex].

[tex]k^2=\dfrac{5^2}{6^2}[/tex]

[tex]k^2=\dfrac{25}{36}[/tex]

Therefore, the area of the figure will change by the factor of [tex]\dfrac{25}{36}[/tex].

Answer:

4x+3150-6x=2876

-2x=-274

x=137

y=525-137

y=388

Hence, about 137 childern tickets were sold and 388 gernal admission tickets were sold.

Paul.

The solution of the given situation is that about 137 childern tickets were sold and 388 admission tickets were sold.

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that school is selling tickets to their Spring theater production Student tickets cost $6 each and non-student tickets cost $9 each There are a total of 250 seats available in the auditorium.

Let s represent the number of student tickets sold and let n represent the number of non-student tickets sold then the equation is;

4x+3150-6x=2876

-2x=-274

x=137

Now,

y=525-137

y=388

Hence, about 137 childern tickets were sold and 388 admission tickets were sold.

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Answer: 6,924‬ votes

Step-by-step explanation:

The ratio of yes to no votes was 7 to 5.

This means that for every 7 yes votes, there were 5 no votes.

If there were 2,885 nos, the number of yeses can be gotten using direct proportion:

7 : 5

x : 2,885

Cross multiplying would give:

5x = ‭20,195‬

x = 20,195/5

x = ‭4,039‬ yes

Total votes would be:

= ‭4,039‬ + 2,885

= ‭6,924‬ votes

Answer:

well just cout

Step-by-step explanation:

los 1=-1 2=-2see easy

Answer:

$140

Step-by-step explanation:

Ryan put $160 in a bank account. After 2 months, the total in his account decreased by 25%.

Step 1

We calculate the Decrease

Original amount × Percentage Decrease

Original amount = $160

Percentage Decrease = 25%

Hence:

Decrease = $160 × 25%

= $40

Step 2

The amount in Ryan's account now is calculated as:

$160 - $40

= $140

Answer:

Step-by-step explanation:

The formula for Pythagorean theorem is [ a² + b² = c² ]. We are already given "a" and "c" for both problems, so, solve the theorem for b.

Question 1:

5² + b² = 12²

25 + b² = 144

b² = 119

√b = √119

b ≈ 10.9ft

Question 2:

6² + b² = 15²

36 + b² = 225

b² = 189

√b = √189

b = 13.7ft

Best of Luck!

Answer:

15/2 I think

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

4(5 + 16)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

[tex]c=\sqrt{a^{2} + b^{2} } \\14 = \sqrt{9^{2}+ b^{2} } \\14 = \sqrt{81 + b^{2} } \\14^{2} = 81+b^{2} \\196 = 81 + b^{2} \\81 + b^{2} = 196\\b^{2} = 196-81\\b^{2} = 115\\b = \sqrt{115} \\b = 10.72\\b = 11[/tex]

Answer:

To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: If each input has only one line connected to it, then the outputs are a function of the inputs.