The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?


A. The skaters’ paths intersect once, but that point is outside the rink.

B. The skaters’ paths intersect once, and that point is inside the rink.

C. The skaters’ paths intersect twice, but only one of those points is inside the rink.

D. The skaters’ paths intersect twice, and both points are inside the rink.

Answer:

Step-by-step explanation:

The correct answer is, "a divided by 5"

Answer:

c

Step-by-step explanation:

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Answer:

C, A, D, B

Step-by-step explanation:

(a) We need to compare the sum of this series to 3/4 and 31/36.  So we just need to find the sum within 1/36.

1 / (n + 1 + 1)² ≤ 1/36

(n + 2)² ≥ 36

n + 2 ≥ 6

n ≥ 4

So we just need to find the partial sum of the terms from n=0 to n=4.

1 − 1/4 + 1/9 − 1/16 + 1/25 ≈ 0.839

We can use this to approximate the actual sum within 1/64.

(b) 1 − 1/7 + 1/49 − 1/343 + ...

We can rearrange this as the difference between two geometric series:

(1 + 1/49 + 1/2401 + ...) − (1/7 + 1/343 + 1/16807)

∑₀°° (1/49)ⁿ − ∑₀°° 1/7 (1/49)ⁿ

1 / (1 − 1/49) − (1/7) / (1 − 1/49)

(6/7) / (48/49)

7/8

So from smallest to largest, the answer is C, A, D, B.

Answer: left, down

Hope this helps.

Answer:

y=arcsinx and y=arctanx

Step-by-step explanation:

The functions that are symmetric with respect to the origin will be y = arcsin x and y = arctan x. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Simply put, inverse trigonometric operations are the opposites of the fundamental trigonometric parameters sine, cosine, secant, cosecant, tangent, and cotangent.

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

The functions that are symmetric with respect to the origin will be y = arcsin x and y = arctan x. Then the correct option is D.

The diagram is given below.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Answer: the answer is the second one

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The "associative property" can apply to any number of operations. The ones we're usually concerned with are multiplication and addition.

Basically, the associative property says you can regroup elements that have the same operation being performed on them. Effectively, that regrouping lets you perform the sequence of operations in whatever order you may choose.

For multiplication, the associative property can be written:

  (ab)c = a(bc)

This form matches the first of the choices shown:

  3(ab) = (3a)b

__

For addition, the associative property can be written:

  (a+b)+c = a+(b+c)

This form matches the second of the choices shown:

  (3 + a) + b = 3 + (a + b)

__

If you must select one answer, you need to know which associative property you're talking about.

In this triangle the three interior angles are = ∠82° , ∠54° and ∠x .

Then ;

∠82° + ∠54° + ∠x = 180° ( under angle sum property which says that the sum of the three interior angles of a triangle is equal to 180° )

= 136 ° + x = 180

= x = 180 - 136

∠x and ∠y will sum up to 180° as they are a linear pair .

= 44° + y = 180

= y = 180 - 44

Since ∠y and ∠z are vertically opposite angles their angle measure will be equal . Which means ;

= ∠y = ∠z

= 136° = ∠z

Therefore :-

Answer:

A triangle with side lengths 4 cm, 5 cm, and 6 cm

A triangle with side lengths 4 cm, 5 cm, and 15 cm

A triangle with side lengths 4 cm and 5 cm and a 50∘ angle

A triangle with angle measures  30 ∘ and 60 ∘ , and a 3 cm side length

Step-by-step explanation:

A triangle measuring 60 ∘, 80∘ and 80∘ is more than sum of angles of a triangle (180∘). This cannot be constructed as triangle because it is more than 180∘.

A triangle can be constructed, If the sum of any two sides is greater than third side,

Thus, a triangle with side lengths 4 cm, 5 cm, and 6 cm can be constructed because;

4 cm + 5cm > 6 cm

A triangle with side lengths 4 cm, 5 cm, and 15 cm can be constructed as well, because;

5 cm + 15 cm > 4 cm

A triangle with side lengths 4 cm and 5 cm and a 50 ∘ angle can be constructed ( two sides and an angle between them)

A triangle with angle measures  30 ∘ and 60 ∘ , and a 3 cm side length can be constructed ( two angles and a side between them)

Answer:

[tex] \frac{ - 2 {x}^{2} + 19x + 3 }{3 {x} (4x^{2} - 9 )} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6 {x}^{2} + 9x} + \frac{1}{2x - 3} - \frac{2}{3x} \\ \\ = \frac{5}{3x(2 {x} + 3)} + \frac{1}{2x - 3} - \frac{2}{3x} \\ \\ = \frac{5(2x - 3) + 1 \times 3x(2x + 3)}{3x(2 {x} + 3)(2x - 3)} - \frac{2}{3x} \\ \\ = \frac{10x - 15 + 6 {x}^{2} + 9x}{3x((2 {x} ) ^{2} - {3}^{2} )} - \frac{2}{3x} \\ \\ = \frac{6 {x}^{2} + 19x - 15}{3x(4x^{2} - 9 )} - \frac{2}{3x} \\ \\ = \frac{3x(6 {x}^{2} + 19x - 15) - 2 \times 3x(4x^{2} - 9 )}{3x(4x^{2} - 9 ) \times 3x} \\ \\ = \frac{18{x}^{3} + 57 {x}^{2} - 45x - 24x^{3} + 54x }{3x(4x^{2} - 9 ) \times 3x} \\ \\ = \frac{ - 6 {x}^{3} + 57 {x}^{2} + 9x }{9 {x}^{2} (4x^{2} - 9 )} \\ \\ = \frac{ 3x(- 2 {x}^{2} + 19x + 3) }{9 {x}^{2} (4x^{2} - 9 )} \\ \\ \huge \orange{ \boxed{= \frac{ - 2 {x}^{2} + 19x + 3 }{3 {x} (4x^{2} - 9 )} }}[/tex]

Answer:B

Step-by-step explanation:

=========================================

Explanation:

n = some unknown number

2n = twice a number

4+2n = four more than twice a number

4+2n = 8 since the "is" means "equals"

Below is a diagram showing the word problem broken up in a table form

Answer:

Step-by-step explanation:

2g=7h-3f

g=[tex]\frac{7h-3f}{2}[/tex]

Answer:

g= [tex]g=\frac{7}{2}h- \frac{3}{2}f[/tex], f∈R, h∈R

Step-by-step explanation:

3f+2g=7h

2g=7h-3f

g=[tex]\frac{7}{2}h - \frac{3}{2} f[/tex]

Answer:

i think its c but it could also be d sorry if im wrong T-T

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

-9|-x+5|=0

Divide by -9

|-x+5|=0

The are normally two solutions, one positive and one negative, but +0=-0=0

-x+5 =0

Add x to each side

-x+5+x =0+x

5 =x

Answer:

C

Step-by-step explanation:

Non proportional graphs are non-linear and don’t go (necessarily) through 0,0

Proportional graphs are linear and always (eventually) cross through with 0,0

Answer:

34

Step-by-step explanation:

16+18 34 should help

Answer:

34

Step-by-step explanation:

2*8=16

9*2=18

16+18=34

Answer:

12.2 12.3 12.4 12.5

Step-by-step explanation:

Let's create an equation to find the # of weeks until Chad learns 937 pieces.

x = # of weeks

937 = 2x + 805

Subtract 805 from both sides.

132 = 2x

Divide both sides by 2

66 = x

Chad will need 66 weeks of lessons to learn 937 pieces.

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°

Answer: 80 = 20 + 5v

Step-by-step explanation:

This equation allows you to find out how many visits would create an even rate for both gyms.

Answer:

What is the question?

Step-by-step explanation:

Answer:

the second option

Step-by-step explanation:

hope this helps

Answer:

555052

Step-by-step explanation:

Answer: $5

Step-by-step explanation: $75 divided by 15 burgers is $5 per burger

Answer:

5

Step-by-step explanation:

we paid $75 for 15 hamburgers.

so 15 hamburges = $75

so 1 hamburges = 75/15 =$5

therefore ,The rate per hamburger is $5

ANSWER:

1.3/2

2.4/27

3.2/25

4.3/25

5.4

Answer:

1.3/2

2.4/27

3.2/25

4.3/25

Step-by-step explanation: