An asteroid follows a hyperbolic path defined by the equation 16x2 − 9y2 = 576. If one of its foci is the sun's position, the minimum distance between the asteroid and the sun is AU. (Note that x and y are expressed in astronomical units, AU.)

Answer: 4 years

Step-by-step explanation:

144 + 8(4) = 176

108 - 5(4) = 88

88 x 2 = 176

Answer:

Step-by-step explanation:

To solve for k first multiply both sides by 3

That's

Next divide both sides by f in order to isolate k

We have

Simplify

We have the final answer as

Hope this helps you

Answer:

Coffees cost $2 each and bagels cost $4 each

Step-by-step explanation:

Let

Coffee=c

Bagels= b

2 coffees and 5 bagels for which he paid $24

2c + 5b= 24 (1)

he returned to buy 3 coffees and 4 bagels for

$22

3c + 4b = 22 (2)

2c + 5b= 24 (1)

3c + 4b = 22 (2)

Multiply (1) by 3 and (2) by 2

6c + 15b = 72 (3)

6c + 8b = 44 (4)

Subtract (4) from (3)

15b - 8b = 72 - 44

7b = 28

Divide both sides by 7

b= 28 / 7

= 4

b= $4

Substitute b=4 into (1)

2c + 5b= 24

2c + 5(4) = 24

2c + 20 = 24

2c = 24 - 20

2c = 4

Divide both sides by 2

c= 4 / 2

c= $2

Therefore,

Coffees cost $2 each and bagels cost $4 each

Answer:

The number is:

16

Step-by-step explanation:

2(a/2 + 4) = 24

2*a/2 + 2*4 = 24

a + 8 = 24

a = 24-8

a = 16

Check:

2(16/2 + 4) = 24

2*16/2 + 2*4 = 24

16 + 8 = 24

Answer:

34

Step-by-step explanation:

Answer:

5z

Step-by-step explanation:

Answer:

5z

Step-by-step explanation:

'The product of 5 and a number' would be 5 *  n.

Since the number in the question would be 'z', we will write it as '5 * z'.

However, the most ideal way to write this is '5z'. So,  "The product of 5 and a number z" would be '5z'.

Hope this helps.

It`s easy.

Real axis (-4) is the abscissa, the part with i (-8) is the ordinate. That`s why...  

Answer:

The correct answer is 12.8 J.

Step-by-step explanation:

To solve this problem, we must remember how to calculate the kinetic energy of an object.

The kinetic energy is represented by the formula K = 1/2 * m * v^2, where m represents the mass of the object and v represents the speed or velocity of the object.  If we plug in the given values into the formula, we get:

K = 1/2 * m * v^2

K = (1/2) * (0.40) * (8.0)^2

Our first step is to square the velocity.  After doing this step, we get the following:

K = (1/2) * (0.40) * (64)

Finally, we can perform the multiplication, to get:

K = 12.8

The unit for kinetic energy is joules, so the correct answer is 12.8 J.

Hope this helps!

Kinetic energy is the energy due to motion of an object

The kinetic energy of the bird is 12.5 joules

Reason:

The known parameter are;

The mass of the bird, m = 0.50 kg

The speed of the bird, v = 8.0 m/s

Required:

To find the kinetic energy of the bird

Solution:

[tex]Kinetic \ energy = \dfrac{1}{2} \cdot m \cdot v^2[/tex]

Therefore;

[tex]The \ kinetic \ energy \ of \ the \ bird = \dfrac{1}{2} \times 0.40 \ kg \times (8.0 \ m/s)^2 = 12.8 \ J[/tex]

The kinetic energy of the bird is 12.8 J

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Answer:

2k-8

Step-by-step explanation:

3k +9 -k-17

Combine like terms

3k -k    +9-17

2k         -8

Answer:Simplifying

3k + 9 + -1k + -17 = 0

Reorder the terms:

9 + -17 + 3k + -1k = 0

Combine like terms: 9 + -17 = -8

-8 + 3k + -1k = 0

Combine like terms: 3k + -1k = 2k

-8 + 2k = 0

Solving

-8 + 2k = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '8' to each side of the equation.

-8 + 8 + 2k = 0 + 8

Combine like terms: -8 + 8 = 0

0 + 2k = 0 + 8

2k = 0 + 8

Combine like terms: 0 + 8 = 8

2k = 8

Divide each side by '2'.

k = 4

Simplifying

k = 4

Step-by-step explanation:

Answer:

61/50

Step-by-step explanation:

1*a = a

1 = b/b

then:

23*25 * 1 = (23/25)(12/12) = (23*12)/(25*12) =276/300

9/30 *1 = (9/30)(10/10) = (9*10)/(30*10) = 90/300

then:

(23/25) + (9/30) = (276/300) + (90/300)

= (276+90)/300

= 366/300

= 122/100

= 61/50

The addition of the fraction 23/25 + 9/30 is equal to 61/50.

A fraction represents a part of a number or any number of equal parts.

'a/b' of a quantity means that quantity is first divided in 'b' parts, and then mutiplied by 'a', or,

Once the denominators become same, the numerators can add up directly, giving us the final result of addition.

1*a = a

1 = b/b

then:

23*25 * 1 = (23/25)(12/12)

= (23*12)/(25*12) =276/300

9/30 *1 = (9/30)(10/10)

= (9*10)/(30*10) = 90/300

Now add the terms;

(23/25) + (9/30) = (276/300) + (90/300)

= (276+90)/300

= 366/300

= 122/100

= 61/50

Therefore, the addition of the fraction 23/25 + 9/30 is equal to 61/50.

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Answer:

8x^2 + 5y + 1

Step-by-step explanation:

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

group like terms

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

add similar items

= 8x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 5y + 1 - 3 + 3

= 8x^2 + 5y + 1

f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)

To confirm that f(x) and g(x) are inverses.

f(g(x)) = x

g(f(x)) = x

f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)

f(g(x)) = (-15x² -15x)/(-15x² - 15)

f(g(x)) = -15x/-15

f(g(x)) = x

g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)

g(f(x)) = (-15x² - 105x)/(-15x²- 105)

g(f(x)) = -105x/-105

g(f(x)) = x

f(x) and g(x) are inverses.

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

[tex]a(2x + 3) = 9x + 15 + x \\ a = \frac{5(2x + 3) }{2x + 3} \\ a = 5 \\ [/tex]

Hoor it helps

The solution of the given expression a(2x+3) = 9x+15+x is 5.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

Given the expression,

a(2x+3) = 9x + 15 + x

Divide both sides by 2x + 3

a = (9x + 15 + x)/(2x + 3)

a = (10x + 15)/(2x + 3)

a = 5(2x + 3)/(2x + 3)

a = 5

Hence "The solution of the given expression a(2x+3) = 9x+15+x is 5".

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Answer:

A - B  =  [  -1  3  ]

             [ -6  2  ]

             [ -4 -10 ]

Step-by-step explanation:

Since Matrix A and Matrix B have the same size, then we can simply perform the operation of subtraction on each position within the matrices to get the resulting subtracted matrix.

A =  [  4  7  ]              B =  [  5  4  ]

      [ -3  8  ]                     [  3  6  ]

      [ -5 -2  ]                    [  -1  8  ]

A - B  =  [ (4 - 5)  (7 - 4) ]

             [ (-3 - 3) (8 - 6) ]

             [ (-5 - -1) (-2 - 8) ]

A - B  =  [  -1  3  ]

             [ -6  2  ]

             [ -4 -10 ]

Cheers.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 74 in

The statement

The length of a rectangle picture is 5 inches more than three times the width is written as

l = 5 + 3w

Substitute the expression into the above formula and solve for the width

That's

74 = 2(5 + 3w) + 2w

74 = 10 + 6w + 2w

8w = 64

Divide both sides by 8

w = 8

Substitute this value into l = 5 + 3w and find the length

That's

l = 5 + 3(8)

l = 5 + 24

l = 29

The dimensions of the rectangle are

length = 29 inches

width = 8 inches

Hope this helps you

Answer:

hope it helps

Step-by-step explanation:

2x+y=10

x-2y=12

2x+y=10

2x-4y=24

y=-14/5

2x=10+14/5

2x=64/5

x=32/5

Number one:

-4c - 6d + 9c + 2d

~Combine like terms

(-4c + 9c) + (-6d + 2d)

~Simplify

5c - 4d (Option A)

Number two:

2(-y + 9) + 8y

~Distribute

-2y + 18 + 8y

~Combine like terms

(-2y + 8y) + 18

~Simplify

6y + 18 (Option C)

Number three:

-3(-4y + 5) - 8y

~Distribute

12y - 15 - 8y

~Combine like terms

4y - 15 (Option C)

Number four:

6c - 8d + 3c + 4d

~Combine like terms

(6c + 3c) + (-8d + 4d)

~Simplify

9c - 4d (Option A)

Best of Luck!

The individuals in this set are C) Basketball players

This is because it's listing all the player names with their associated stats.

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

The data contains B) 3 variables, 2 of which are quantitative

The variables are

The first two variables are quantitative as they deal with numeric values, and it makes sense to do things like find the average. The last variable is qualitative. It is also an ordinal variable because we can order the labels from freshman to senior.

This data on the statistics from the basketball game contains 3 variables, 2 of which is quantitative.

A quantitative variable is a variable that can be used to show the degree of magnitude. This means that quantitative variables can be represented with numbers.

The quantitative variables are free throw percentage and the number of assists.

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Answer:

work shown and pictured

Answer:

w = y - x is the equation to find w

Where,

w = Weight of the liquid

x = Weight of the empty can

y = Weight of the can with liquid

Step-by-step explanation:

Let

Weight of the empty can = x

Weight of the liquid = w

Weight of the can with liquid = x + w = y

x= 30 grams

w = ?

y= 47.3 grams

y = x + w

w = y - x

= 47.3 - 30

= 17.3

w= 17.3 grams

Therefore, the weight of the liquid is 17 .3 grams

Answer:

[tex]x\geq 1[/tex]

B

Step-by-step explanation:

For square root functions, the domain is the restrictions on the x-variable.

Recall that you cannot take the square root of a negative. Thus, all values under the square root must be greater than or equal to 0. Thus, to find the domain, set the expression under the radical sign to greater than or equal to 0 and solve for x:

[tex](x-1)\geq 0[/tex]

Add 1 to both sides.

[tex](x-1)+1\geq 0+1\\x\geq 1[/tex]

Thus, the domain is:

[tex]x\geq 1[/tex]

All real numbers such that x is greater than or equal to 1.

Answer:

[tex]\huge \boxed{x \geq 1}[/tex]

Step-by-step explanation:

The domain of a function is all possible values for x.

There are restrictions on the value of x.

The number in the square root has to be greater or equal to 0 to be defined. Since the square root of a number lesser than 0 will be undefined.

[tex]x-1\geq 0[/tex]

Adding 1 to both sides.

[tex]x-1+1 \geq 0+1[/tex]

[tex]x\geq 1[/tex]

The domain of the function is [tex]x\geq 1[/tex]

All real numbers greater or equal to 1.

Answer:c

Step-by-step explanation:

Answer:

1. Two segments are MC and AX

2. Point N

3. Three collinear points are points A, point N and point X

4. Two other names for V are quadrilateral and rectangle

5. No N, M, and X are in a different plane from R

6. Two rays are ray NR and ray NA

7. The pair of opposite rays with end point N are ray NA and ray NX and ray NM and ray NC

8. Three lines are shown in the figure

Step-by-step explanation:

1) A segment is a line portion with two end points

2) A point marks a position

3) Collinear points are points on the same line

3) A quadrilateral is a four sided figure while rectangle has 90° interior angles

4) A ray is an line extending from a point without ending

5) Opposite rays are rays extending from the same point but in opposite directions

6) A line is a straight one dimensional geometric figure  that has no width but infinite number of points extending without end in both directions

Answer:

b

Step-by-step explanation:

Answer:

parallell

Step-by-step explanation:

Answer:

collinear points

Step-by-step explanation:

A line is defined by two points and is written as shown below with an arrowhead. Two lines that meet in a point are called intersecting lines. A plane extends infinitely in two dimensions.

Answer:

[tex]\frac{1}{15^{6}}[/tex]

Step-by-step explanation:

If you see a negative sign in the power, you will place the number and power over 1:

15^-6 = 1/(15^6)

[tex]\frac{1}{15^{6}}[/tex]

Simplify. Solve 15^6:

15^6 = 15 * 15 * 15 * 15 * 15 * 15 = 11,390,625

1/11,390,625 is your simplified answer.

However, note that you are solving for a positive exponent. Your answer will be:

[tex]\frac{1}{15^{6}}[/tex]

Answer:

ΔDEF is similar to ΔPQR by SAS similarity rule

Step-by-step explanation:

ΔDEF, with details:  

ΔPQR , with details:

As we see, the ratio of corresponding sides is:

And corresponding angles are:

Therefore,  ΔDEF is similar to ΔPQR by SAS similarity rule

Answer:

-7

Step-by-step explanation:

2p-9=5p+12

2p-9-12=5p

-21=5p-2p

-21=3p

p= -21/3

p= -7

Answer: P=51

--

Steps for Solving Linear Equation: 20−9=5p+12

--

Subtract 9 from 20 to get 11.

[tex]11=5p+12[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]5p+12=11[/tex]

Subtract 12 from both sides.

[tex]5p=11-12[/tex]

Subtract 12 from 11 to get −1.

[tex]5p=1[/tex]

Divide both sides by 5.

[tex]p=5-1[/tex]

Fraction 5−1​≈−0.2 can be rewritten as −51​=−0.2 by extracting the negative sign.

[tex]p=-51[/tex]

Answer:

El área del terreno B es 2000 m.

Step-by-step explanation:

Tenemos que el terreno A es:

[tex]L_{A}[/tex]: largo = 120 m

[tex]A_{A}[/tex]: ancho = 200 m

Y que el terreno B es:

Largo:

[tex] L_{A} = 3L_{B} [/tex]

[tex] L_{B} = \frac{L_{A}}{3} = \frac{120 m}{3} = 40 m [/tex]

Ancho:

[tex] A_{A} = 4A_{B} [/tex]

[tex] A_{B} = \frac{A_{A}}{4} = \frac{200}{4} = 50 m [/tex]

Entonces, asumiendo que el terreno es un rectángulo, el área del terreno B es:

[tex] a_{B} = L_{B}*A_{B} = 40 m*50 m = 2000 m [/tex]

Por lo tanto, el área del terreno B es 2000 m.

Espero que te sea de utilidad!

Answer:

JK = 72

Step-by-step explanation:

JL = JK + KL = (4x+8) + (6x-6) = 10x + 2 = 162

--> x = (162-2)/10 = 16

JK = 4x + 8 = 4 . 16 + 8 = 72

Answer: The value of x is = 5.

Step-by-step explanation:

So we are given the equation:

3x + 7 = 22​

We just have to isolate 3x and move 7 to the other side:

3x = 22 -7

3x = 15

Now divide:

x = 15/3

x = 5

There you go!

Answer:

5

Step-by-step explanation:

22-7=15 and 15 divided by 3 =5