How do you simplify 6 by the power of negative 2 multiplied by 6 by the power of 3

There are 50-50 chances that you will get a head or a tail

The equation of the hyperbola with foci (-2, 0), (2, 0), and vertices, (-1, 0), (1, 0) is [tex] \underline{\frac{ {x}^{2} }{ {1}^{2} } - \frac{ {y}^{2} }{ 3} } = 1[/tex]

The general form of the equation of an hyperbola is presented as follows;

[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

Where a is obtained from the vertex written as (-a, 0), (a, 0)

The given vertex are (-1, 0), (1, 0), which gives;

a = 1

The general form of the foci of a hyperbola are; (-c, 0), (c, 0)

The given foci of the hyperbola are; (-2, 0), (2, 0)

Where;

Therefore;

By comparison, we have;

c² = 2²

Which gives;

The equation of the hyperbola is therefore;

[tex] \underline{\frac{ {x}^{2} }{ {1}^{2} } - \frac{ {y}^{2} }{ 3} } = 1[/tex]

Learn more about the equation of a hyperbola here:

https://brainly.com/question/13003184

#SPJ1

The system of linear equations that represents this scenario is: q + d = 16

0.25q + 0.10d = 3.10

To represent the scenario described, we can set up a system of linear equations using the given variables:

Let q represent the number of quarters.

Let d represent the number of dimes.

We are given two conditions:

1) The total number of coins is 16:

q + d = 16

2) The total value of the coins is $3.10:

0.25q + 0.10d = 3.10

Therefore, the system of linear equations that represents this scenario is:

q + d = 16

0.25q + 0.10d = 3.10

Learn more about Linear equations here:

https://brainly.com/question/32634451?

#SPJ2

The measure of each interior angle of a regular polygon is [tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides.

Question 1

[tex]144=\frac{180(n-2)}{n}\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}[/tex]

Question 2

[tex]\frac{180(n-2)}{n}=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}[/tex]

Answer:

3/25

Step-by-step explanation:

0.12=12/100

12/100 can be simplified 6/50 = 3/25

The chocolate will last for 1 day, if she gets 4 more dragons

The expression can be represented using the following ratio:

Ratio = Dragons : Days : Chocolate

For the 2 dragons she has, we have:

Ratio = 2 : 12 : 300

When she gets 4 more dragons, we have:

Ratio = 6 : days : 300

Equate both ratios

6 : days = 12 : 2

Express as fraction

days/6 = 2/12

Multiply both sides by 6

days = 6 * 2/12

Evaluate

days = 1

Hence, the chocolate will last for 1 day

Read more about ratios at:

https://brainly.com/question/2328454

#SPJ1

Current year's debt ratio is 2.50

Last year's debt ratio is 2.44

Compute Dan's Dependable Delivery debt ratio for two consecutive years?

The debt ratio is the total liabilities divided by the total assets

The debt ratio for the current year =  2.50

The debt ratio for last year =2.44(find attached excel file and formula sheet)

Debt ratio means the portion of the firm's total assets funded using borrowing(external funding), the lower the ratio, the better since having a higher debt means a higher interest would be paid, the higher the debt, the higher the chance of the firm defaulting on paying interest and repaying the principal borrowed.

The fact that the debt ratio has increased in the current year, means that the ratio has worsened because more debt has been taken.

https://brainly.com/question/21406342

#SPJ1

the quadratic equation is:

y = 0.2*x*(x - 28)

If we know that the roots are J and K, and the leading coefficient is a, then the quadratic equation is:

y = a*(x - K)*(x - J)

Here we know that the roots are at x = 0 and x =28, then:

y = a*(x - 0)*(x - 28).

We also know that the vertex is a minimum, so a is positive, and we know that the vertex is (14, -40), then we have:

-40 = a*(14)*(14 - 24) = -a*196

a = 40/196 = 0.20

Then the quadratic equation is:

y = 0.2*x*(x - 28)

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The diameter of the milky way is given as 4.3 x 10¹¹m while the diameter of the radius of the earth is 0.00276

The transformed system is given as 23.18 x 10⁸ in real length

Hence the diameter is

10 x 10²⁰ / 23.18 x 10⁸

= 4.3 x 10¹¹ m

Distance from the sun to the earth = 1.496 x 10¹¹m

Transformed system = 1.496 x 10¹¹m/23.18 x 10⁸

= 64.5 m

Actual radius = 6.4 x10⁶ / 23.18 x 10⁸

= 0.00276

read more on the milky way here

https://brainly.com/question/13485795

#SPJ1

Answer:

78.5

Step-by-step explanation:

pi(r^2)

3.14(5^2)

3.14(25)

78.5

pls kindly see the attached picture for the answer and explanation thank you

The y-intercept of the line is 0.75 or 3/4

The given parameters are:

Slope, m = 1/4

Point (x, y) = (0.2, 4/5)

A linear equation is represented as:

y = mx + b

This gives

4/5 = 1/4 * 0.2 + b

Evaluate the product

4/5 = 0.05 + b

Subtract 0.05 from both sides

b = 0.75

Hence, the y-intercept of the line is 0.75 or 3/4

Read more about linear equations at

https://brainly.com/question/1884491

#SPJ1

Answer:

b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).

Step-by-step explanation:

See attached image.

The side of the edge of the cube is 9. 9cm

Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm

To find the edge of the face, we know that the face of the cube is a square

Formula for diagonal of a square = [tex]\sqrt{2a}[/tex]

Where is the side of the square

We then have,

[tex]\sqrt{2a} = 14[/tex]

Make 'a' the subject

a = [tex]\frac{14}{\sqrt{2} }[/tex]

Simplify the surd

a = [tex]\frac{14}{\sqrt{2} }[/tex] × [tex]\frac{14}{\sqrt{2} }[/tex]

a = [tex]\frac{14\sqrt{2} }{2}[/tex]

a = [tex]7\sqrt{2}[/tex]

a = 9. 9cm

Therefore, the side of the edge of the cube is 9. 9cm

Learn more about a cube here:

https://brainly.com/question/1972490

#SPJ1

Answer: Its 9.8 cm

Step-by-step explanation: I said so

Answer:

-70x, 26y^3, -3z

Step-by-step explanation:

The way to solve this is by combining like terms. The terms we have given to us include x, y^3, and z. As a result, we will group terms based on these variables.

1. Find all the terms with each variable.

* -35x, -35x

* 23y^3, 3y^3

* -3z

2. Combine like terms.

* -35x + (-35x) = -35x - 35x = -70x

* 23y^3 + 3y^3 = 26y^3

* -3z + 0 = -3z

Answer:

Hello! The answer is: [tex]-70x - 3z + 26y^3[/tex]

Step-by-step explanation:

First, rearrange to combine like terms:

[tex]-35x - 35x - 3z + 23y^3 + 3y^3[/tex]

Now, combine like terms:

[tex]-70x - 3z + 26y^3[/tex]

Answer:

<C = 45 degrees.

Step-by-step explanation:

This is a right triangle (indicated by the square representing <A). All angles in a triangle add up to 180 degrees

180 - 90 is 90. Knowing that there are only two angles left, you can divide 90 by 2, resulting in 45.

<C = 45.

Answer:

185 when we subtract 212-127 it gives 185 thanks for the seeing image

[tex]m = \frac{ - 5 - 4}{3 - 0} = \frac{ - 9}{3} = - 3[/tex]

[tex]g(x) = - 3x + 4[/tex]

[tex]g(x) \: ha s \: a \: steeper \: slope[/tex]

Answer:

∠ 3 = 105°

Step-by-step explanation:

∠ 3 and ∠ 6 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 6 = 180°

∠ 3 + 75° = 180° ( subtract 75° from both sides )

∠ 3 = 105°

Answer:

probably c

Step-by-step explanation:

The multiplicative rate of change of the function will be 0.5. Then the correct option is C.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

The missing table is attached below.

For x = 2, y will be 0.125

0.125 = ab²  ...1

For x = 3, y will be 0.0625

0.0625 = ab³   ...2

Divide equation 2 by equation 1, we have

b = 0.0625 / 0.125

b = 0.5

Then the correct option is C.

More about the exponent link is given below.

https://brainly.com/question/5497425

#SPJ1

Answer:

4 units

Step-by-step explanation:

Answer:

a=223.57

c=181.43

Step-by-step explanation:

a=405-c

substitute for a in the equation :

12a+5c=3590

12(405-c)+5c=3590

4860-12c+5c=3590

-7c=3590-4860

-7c=-1270

c=1270/7=181.43

a=405-1270/7

a=1565/7=223.57

Answer:

The number of ways in which the digits can be assigned in the color wheel can be determined by the permutation of 8 taken 4 since it is in circular formation and whichever comes first is not important.

number of ways = 9P4 = 3024 ways

Answer:

angle angle theorem.

Step-by-step explanation:

If you want to determine whether a few angles are similar you can use formulas such as SAS AAA ASA etc.

this means

side angle side

angle angle anlge

angle side angle

Hello!

d₁ = distance covered in Part 1

d₂ = distance covered in Part 2

d₃ = distance covered in Part 3

Distance in Part 2 :

⇒ d₃ = 15 x 300 = 4500 m

⇒ d₂ = 2/5d₃

⇒ d₂ = 2/5 x 4500

⇒ d₂ = 1800 meters

Speed in Part 2 :

⇒ v₂ = 1800 m / 12 min

⇒ v₂ = 150 meters per minute

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[ b ] is the Correct one

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:4 \: log_{3}(y) - 6 \: log_{3}(x) + 7 \: log_{3}(z) [/tex]

[tex] \qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) - \: log_{3}(x {}^{6} ) +\: log_{3}(z {}^{7} ) [/tex]

[tex] \qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) + \: log_{3}(z{}^{7} ) - \: log_{3}(x {}^{6} ) [/tex]

([tex] \sf a\: log (b) = log {b}^{a}[/tex])

[tex] \qquad❖ \: \sf \: log_{3}( {y}^{4} {z}^{7} ) - log_{3}( {x}^{6} {}^{} ) [/tex]

([tex] \sf{log (a) + log (b) = log (ab)} [/tex])

[tex] \qquad❖ \: \sf \: log_{3} \bigg( \dfrac{y {}^{4} {z}^{7} }{ {x}^{6} } \bigg ) [/tex]

([tex] \sf{log (a) - log (b) = log (a/b)} [/tex])

[tex] \qquad \large \sf {Conclusion} : [/tex]

[ b ] is the Correct choice

Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

Answer:

Step-by-step explanation:

Argument

I think the answer is A = N or D. It that is true, then M = C because all three angles are equal which gives similarity. But there is a side involved. OM = CB. Therefore the two triangles are congruent by ASA

Answer

ASA

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

m = (y2 - y1)/(x2 - x1)

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

Read more about linear equations at:

https://brainly.com/question/13763238

#SPJ1