To the nearest hundredth, what is the length of line segment AB ? The length of line segment AB is approximately ______ units.


A. 2.45

B. 2.16

C. 7.75

D. 8.25​

An equation in standard form for a hyperbola with center (0, 0), vertex (0, 17), and focus (0, 19) is;  y²/172 – x²/(6√2)² = 1

We are given that the hyperbola has;

Center (0, 0), Vertex (0, 17) and Focus (0, 19)

The general form of equation of the given hyperbola has a form of;

y²/a²  - x²/b² = 1

Where;

±a is the y- coordinates of the vertices of the parabola (or y-intercepts).

b determines the asymptotes of the hyperbola in the equation y = ± (a/b)x.

From the vertex coordinates of (0.17), we have that; a = ± 17.

From the focus coordinates (0, 19), the y-coordinate of it is; c = 19 .

b can be found from Pythagorean theorem;

c² = a² + b²

Thus;

192 = 172 + b²

b² = 192 – 172

b² = 361 – 289

b = √72 = 6√2

The equation of the hyperbola is;

y²/172 – x²/(6√2)² = 1

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The equation in standard form for a hyperbola with the given center, vertex, and focus is y² / 289 - x² / a² = 1.

The equation of a hyperbola in standard form is given by:

(x - h)² / a² - (y - k)² / b² = 1 or

(y - k)² / b² - (x - h)² / a² = 1

Given that the center is (0,0) and the vertex is (0,17), we can see that the hyperbola is vertically oriented. Therefore, we can use the form (y - k)² / b² - x² / a² = 1.

Since the center is (0,0), the value of (h, k) is (0,0).

The distance between the center and the vertex is 17 units, which corresponds to the value of b.

The distance between the center and the focus is 19 units, which corresponds to the value of c.

Substituting these values into the equation gives: (y - 0)² / 17² - x² / a² = 1

The equation in standard form for the hyperbola is therefore y² / 289 - x² / a² = 1

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The last dot to the right would be the total distance.

So at 6 pm he had traveled 45 km.

The answer is 45.

Answer:

he traveled 10 miles

Step-by-step explanation:

He took different routes to get to his place that he needed to be

Answer:

x = - 5

Step-by-step explanation:

Given

- 3x + 5 > 17 ( subtract 5 from both sides )

- 3x > 12 ( divide both sides by - 3 )

Remembering to reverse the inequality symbol when dividing/ multiplying by a negative quantity.

x < - 4 ← symbol reversed

The value of x that is in the solution set is x = - 5

Answer:

[tex]\large\boxed{(x-5)^2+(y-3)^2=5^2\to(x-5)^2+(y-3)^2=25}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the end points of a diameter (8, 6) and (2, 0). The midpoint of a diameter is a center of a circle. Half of a length of diameter is a length of a radius.

The formula of a midpoint of a segment:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

Substitute:

[tex]x=\dfrac{8+2}{2}=\dfrac{10}{2}=5\\\\y=\dfrac{6+0}{2}=\dfrac{6}{2}=3[/tex]

The center of a circle is (5, 3).

The formula of a length of a segment:

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

Substitute:

[tex]d=\sqrt{(2-8)^2+(0-6)^2}=\sqrt{(-8)^2-(-6)^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]

The length of a diameter is 10 units. The length of a radius r = 10 : 2 = 5 units.

Finally we have the equation of a circle:

[tex](x-5)^2+(y-3)^2=5^2[/tex]

Answer:

Option b $2,770.25

Step-by-step explanation

Chyra owned shares of stock, details are :

Name of Fund - CAH Group

NAV - $15.83

Offer Price - $16.27

Chyra redeemed stock = 175 shares

As we know shares can be redeemed on NAV price.

Chyra's proceeds = 175 × 15.83 = $2,770.25

Chyra's proceeds were $2,770.25.

Answer:

B

Step-by-step explanation:

$2,770.25

Answer:

3

Step-by-step explanation:

Find the value of x in the equation 4 + x = 7

Answer:

X=3

Step-by-step explanation:

4 +x =7

x =7-4

=3

Answer: 5>y

Step-by-step explanation:

Answer:

y + 5

Step-by-step explanation:

5 more than y

y + 5

Answer:

Wow just wow

Step-by-step explanation:

I have no clue sorry ;-;

The answer is B rhombus because you can split a rhombus in half twice and have the same shape for both half

the area of the trapezoid is 9

Answer:

A = 7.5 unit^2

Step-by-step explanation:

The area of a trapezoid is found by

A =1/2 (b1+b2) *h

b1 = 1 unit

b2 = 4 units  

h = 3 units

I found these by counting on the graph

A = 1/2(1+4) *3

A = 1/2(5)3

A = 7.5 unit^2

If her balance is below 10, Chris must pay a few.

b = balance

Her balance was -$3.46. Then, Chris made a deposit, d, in ample time, so she did not have to pay a fee.

b + d > 10

b = -3.46

d > 10 - -3.46

Based on the information you provided, we can write an inequality to represent the situation. Chris's balance was -$3.46 and she made a deposit of d dollars. To avoid paying a fee, her balance must be greater than or equal to $10 on the statement date. So the inequality is: -3.46 + d >= 10. Solving for d, we get d >= 13.46. So Chris must have deposited at least $13.46 to avoid paying a fee.

Answer:

108

Step-by-step explanation:

1 foot has 12 inches

9x12=108

Answer:

D

Step-by-step explanation:

When reflected across the Y it becomes B, but then across the X, it fits into D.

t = time

Multiply the acceleration by time and add to the height:

The equation becomes H(t) = -16 * t^2 + 90

set h(t) to 0

0 = -16*t^ +90

Subtract 90 from both sides:

-90 = -16*t^2

divide both sides by -16:

t^2 = -90 / -16

t^2 = 5.625

t = √5.625

t = 2.37 seconds, round to 2.4 seconds.

Answer: b

Step-by-step explanation: edge

Answer: [tex]421.56+20g+\frac{k}{4}[/tex]

Step-by-step explanation:

You have the following information given in the problem above:

- She had $421.56 in her checking account.

- She she deposited g $20 bills  (which you can rewrite: [tex]20g[/tex]) and k quarters (which you can rewrite as folllowing:[tex]\frac{k}{4}[/tex]).

Therefore, the amount of money in her account after the deposit is the sum of the amoun she had in her account plus the amoun of money she deposited.

Then, you can write the following expression:

[tex]421.56+20g+\frac{k}{4}[/tex]

Answer:

421.56 + 20g + 1/4 k

Step-by-step explanation:

Joby had $421.56, and she deposited g $20 bills, and k quarter:

We don´t know how many $20 bills she deposited but we know it is expressed by the letter g, so she deposited $20g, and we add to that how many quarters of a dollar she added, in this case, we know that she deposited k quarters or 1/4 k dollars.

To write an expression to know the amount of money she has after the deposit we have to add:

What she had before the deposit = $421.56

The Dollars in $20 bills, we know it is = 20g

The number of dollars in a quarter of a dollar = 1/4 k

So we write:

421.56 + 20g + 1/4k

Hello!

First, we need to find the unit rate.

72 divided by 2 = 36.

36 x 9 = 324.

There were 324 pieces of paper to start with.

Hope this helps, ~Pooch ♥

Bella used 2/9 of a paper pack, equaling 72 pieces. To find the total number, we solve the proportion (2/9) * x = 72 to deduce that the pack initially contained 324 pieces.

Bella used 2/9 of a paper pack, which amounts to 72 pieces of paper. To find out how many pieces of paper were in the pack to begin with, we need to calculate the total amount of paper in the pack.

Let's set up a proportion where the total number of sheets is x. Since 2/9 of the total is 72, we can write the equation as follows:

So, the paper pack originally contained 324 pieces of paper.

Answer:

96

Step-by-step explanation:

The area of a parallelogram is A = b*h. Substitute b = 8 and h= 6 to find the area.

A = 8*6 = 48

The area of a triangle is A = 1/2 b*h. Substitute h = 6 and b = 16 since the triangle has a length of 8 as well as the whole parallelogram.

A = 1/2 *16*6 = 48

Together the areas equal 48 + 48 = 96

ANSWER

C. 80

EXPLANATION

The longer diagonal is serving as the hypotenuse of the right triangles.

Let the longer side of the kite be x cm.

Then, from the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

This means that,

[tex] {x}^{2} + {60}^{2} = {100}^{2} [/tex]

[tex] {x}^{2} + 3600 = 10000[/tex]

[tex] {x}^{2} = 10000 - 3600[/tex]

[tex] {x}^{2} = 6400[/tex]

[tex]x = \sqrt{6400} [/tex]

[tex]x = 80cm[/tex]

Answer:c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Here's all the steps, let's just remove all this confusing garbage with the adding negatives first.

6-(-3-7)-(-1+5+8)

Remember, subtracting a negative makes it positive.

6-(-10)-(12)

6+10-12

16-12

4

The expression 6–[(−3)+(−7)]–[(−1)–(−5)–(−8)] simplifies to 2 after solving the operations inside the brackets and applying the order of operations correctly.

The question asks to simplify the expression 6–[(−3)+(−7)]–[(−1)–(−5)–(−8)]. Let's break it down step by step.

Therefore, the simplified expression is 2.

[tex]5(u + 5) + p(u + 5) = (p + 5)(u + 5)[/tex]

Step-by-step explanation:

2/5 is equal to 4/10, or 40 percent.

Therefore 40 percent of 120 is 120*.4, or 48

The solution to the equation a - 5 = -2 is a = 3. You solve it by adding 5 to both sides, which isolates the variable 'a'.

To solve the equation a - 5 = -2, you need to isolate the variable 'a' on one side of the equation. You can do this by adding 5 to both sides of the equation. Here's the step-by-step process:

Start with the original equation: a - 5 = -2.

Add 5 to both sides: a - 5 + 5 = -2 + 5.

Simplify each side: a = 3.

The answer to the equation is a = 3.

To solve the equation a - 5 = -2, add 5 to both sides which gives us a = 3 as the solution.

The question is asking us to solve the equation a - 5 = -2 for the variable a. To isolate a on one side of the equation, we need to undo the subtraction of 5. We can do this by adding 5 to both sides of the equation:

a - 5 + 5 = -2 + 5

Which simplifies to:

a = 3

Thus, the value of a that solves the equation is 3.

Answer:

5y + 10

Step-by-step explanation:

simply open the brackets by multiplying everything by 5;

5(y+2) = 5y + 10

5y + 10 is the expression that is equivalent to 5( y + 2)

Answer:

Step-by-step explanation:

5y+10

Answer:

The correct option is 2.

Step-by-step explanation:

From the given number line it is clear that there are 4 jumps of 2 units in opposite direction.

After first jump, the total covered distance is

[tex]-(2)\times (1)=-2[/tex]

After second jump, the total covered distance is

[tex]-(2)\times (2)=-4[/tex]

After third jump, the total covered distance is

[tex]-(2)\times (3)=-6[/tex]

After fourth jump, the total covered distance is

[tex]-(2)\times (4)=-8[/tex]

It means the product (-2)(4) is modeled by the given number line.

Therefore the correct option is 2.

Answer:

D

Step-by-step explanation:

Read the question carefully.

"how many one centimeter cubes will fit into a 10 cm by 8 cm by 12 cm box."

Volume is the amount in which how much can go in it.

Answer:

c. surface area because fit is the key word for surface area

Step-by-step explanation:

10% of $42.87 = 10/100 × 42.87

= 4.287

Ans = $4.29

Happy to help! Marking my answer as the Brainliest would really be aprreciated.

Answer:

Group A has 20 students

Group B has 30 students

Step-by-step explanation:

The mean score of 50 students is 54%, so the sum of 50 scores, divided by 50 is 54%.  That means that 50(0.54) = 27 points were scored between the 50 students.

Let x represent the number of students in Group A

Let y represent the number of students in Group B

We have

0.6x + 0.5y = 0.54(50)    (the points scored, times their averages is the total)

and

x + y = 50

Use substitution to solve...solve the second equation for one variable...

x = 50 - y

Now plug that into the first equation...

0.6(50 - y) + 0.5y = 27

     30 - 0.6y + 0.5y = 27

             -0.1y = -3

                   y =  30

So there are 30 students in group B, therefore there are 20 students in group A          

Answer:

i believe it is "5!"

Step-by-step explanation:

1x2x3x4x5=120

but the answer is "5!" ( include the exclamation point)

hope this helps (again)

Answer:

5! or 120.

Step-by-step explanation:

Think about this logically:

You have 5 players to start off with, so you have 5 players that can go in the first position.

That leaves you with 4 players. Any one of those 4 players can go in the second position.

And then there were 3 players. Any one of those 3 players can go in the third position.

2 to go! Pick your favorite player out of the 2 available to go in the fourth position.

And that leaves just one player who has to go last.

This can be modeled as: 5x4x3x2x1, or 5!, which equals 120 unique permutations.

Answer:

The answer is 200000000

Step-by-step explanation:

You take all the numbers and follow the order of operations.

1/20 x 2=

0.1 x 40=

4 x 1000000=

4000000/2=

2000000

Answer:

100²⁰⁰⁰⁰⁰⁰

Step-by-step explanation:

1/20 = .05 // .05*2 = .1 /// .1*40= 4 /// 4* 1000000 = 4000000 /// 4000000/2 = 2000000 so 100^ 1/20x2x40x1000000/2=100²⁰⁰⁰⁰⁰⁰