A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

From the given values and conditions, We need to form a equations and equate both sides to solve for the miles, The answer is 300 miles.

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.

x= miles

60+0.6x=0.8x

0.8x-0.6x=60

0.2x=60

x=60/0.2

=300 miles

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Please provide your question with a math problem in the form of an image or text.

Answer:

9:15

Step-by-step explanation:

Time needed to deliver 100 letters: 100 : 40 = 2,5 hours = 2:30min
Your break: 6:45 + 2:30 = 9:15

Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.

Step-by-step explanation:

The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]

this would cancel out on the right hand side such that we would have:

[tex]\frac{2n}{(d + g)} =a[/tex]

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The length of y in the triangle is 18.55 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The side y of the triangle can be found using sine law.

Therefore,

a / sin A = b / sin B = c / sin C

Applying the sine law,

y / sin 106 = 15 / sin 51

cross multiply

y sin 51° = 15 sin 106°

divide both sides by sin 51°

y sin 51° / sin 51° = 15 sin 106° / sin 51°

y = 15 sin 106° / sin 51°

Therefore,

y = 15 × 0.96126169593 / 0.77714596145

y = 14.4189254391 / 0.77714596145

y = 18.5536589719

Hence,

y = 18.55 units

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Answer:

The answer would be the second and fourth options.

Step-by-step explanation:

This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!

Answer:

  -9447840

Step-by-step explanation:

You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.

The n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

where a1 is the first term and r is the common ratio.

Using the given values, we have ...

  -160 = a1·(-1/3)^(11 -1)

  a1 = (-160)·(-3)^10 = -9447840

The first term is -9447840.

The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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The given equation is a second order differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

Isaac Newton listed three kinds of differential equations given -

[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]

Given is a differential equation as follows -

d²a/db² + a = 4b + 10sin(b)

The given equation is -

d²a/db² + a = 4b + 10sin(b)

Let y = a and x = b, then we can write -

d²y/dx² + y = 4x + 10sin(x)

A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -

d²y/dx² + P(x) dy/dx + Q(x) y = f(x)

For the equation given -

d²y/dx² + y = 4x + 10sin(x)

On comparing, we get -

P(x) = 0

Q(x) = 1

f(x) = {4x + 10sin(x)}

Therefore, the given equation is a second order differential equation.

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Check the picture below.

3(5 - 12) + 4 ÷ 2 = - 19

A must be the answer

The required ratio is 1:2.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given that, A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions, it can be a shorter time between the first and second flashes than between the second flash and the third flash,  One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. The beacons are set 120 degrees apart along the rotation

If the second beacon is 120° after the first, then the first is 360° -120° = 240° after the second.

Therefore, the ratio of the times between beacons is =

120° : 240° = 1 : 2

Hence, the ratio is 1 : 2

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Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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The expression 1.7 x 5.5  can be an area model of the rectangle where the length is 1.7 and the width is 5.5

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The expression 1.7 x 55 is an area model.

Area of rectangle = length x width

Now,

Length = 1.7

Width = 55

Area = 1.7 x 5.5

Thus,

The expression 1.7 x 5.5 can be an area model.

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Answer:

-5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

negative times negative equals positive

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 6

The equation of the line that is parallel to the line y = - 5x + 6 is written as,

y = - 5x + c

The equation passes through (-4, -1), then we have

- 1 = - 5 (-4) + c

- 1 = 20 + c

- 21 = c

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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Total Liabilities  + Equity = $220,000.

Total Assets = $220,000.

What is Ratio Analysis and Balance Sheet?

The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.

One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.

Here we are given in the Question,

Assets

Cash = $45,000

Inventory = $41,000

Property = $134,000

Liabilities

Notes  = $55,000

Wages  = $56,000

and

Equity

Stock = $50,000

Investment = $59,000

Total Liabilities  + Equity = ( Notes + wages ) + (stock + Investment)

Total Liabilities  + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)

Total Liabilities  + Equity = $220,000.

Total Assets = Cash + Inventory + Property

Total Assets = $45,000 + $41,000 + $134,000

Total Assets = $220,000

Therefore,

Total Liabilities  + Equity = Total Assets.

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Answer:

-3,950

Step-by-step explanation:

First -5,000(1-0.21)

Then multiply -5,000 x 0.79 = -3,950

The probability that the team will win more than 9 games this season, given the average number of wins for the team, is 4 %

The Z-score formula is:

Z = (x - mean) / standard deviation

Where x is the number of wins we're interested in (9), mean is the average number of wins (7.6), and standard deviation is the standard deviation of the number of wins (1.3)

Z = (9 - 7.6) / 1.3

= 2.3 / 1.3

= 1.77

This means that 9 wins is 1.77 standard deviations above the mean. The result is the probability of a team winning more than 9 games this season, which is around 0.04 or 4% from the standard normal distribution table.

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The product of given numbers is 60x³(x−3)²(x+2)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra,

Multiply the numbers:

6x²x(x−3) * (x−3)10(x+2)

Multiply 6 and 10

60x²x(x−3) (x−3)(x+2)

Multiply x terms

60x³(x−3) (x−3)(x+2)

Multiply (x-3) terms

60x³(x−3)²(x+2)

So, the product of given numbers is 60x³(x−3)²(x+2)

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The solution to the equation 8z = 4x - 32 is z = -4 and x = 8.

An equation is a mathematical statement that states that two expressions are equal. It consists of an equals sign and two expressions, one on each side of the equals sign. Equations are used to solve for the value of the unknown expressions, and can be used to solve problems in various fields such as physics, chemistry, engineering, and mathematics.

1. Start by isolating the z variable by subtracting 4x from both sides of the equation. This will give us: 8z = -32.
2. Divide both sides of the equation by 8. This will give us: z = -4.
3. Finally, substitute z = -4 into the original equation and solve for x. This will give us: 4x = 32, so x = 8.

Therefore, the solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
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Complete questions as follows-
8z = 4x - 32
Please explain step by step how to solve 8z = 4x - 32.

Answer:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For:

x

=

0

(

3

⋅

0

)

+

2

y

=

6

0

+

2

y

=

6

2

y

=

6

2

y

2

=

6

2

y

=

3

or

(

0

,

3

)

For:

y

=

0

3

x

+

(

2

⋅

0

)

=

6

3

x

+

0

=

6

3

x

=

6

3

x

3

=

6

e

d

)

(

3

)

x

=

2

or

(

2

,

0

)

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}

Step-by-step explanation:

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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957÷3=319 this divide answer i hope help you

Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b.  For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).

Given the equation 17v = 62, we can take the logarithm base 17 of both sides:

log(17^v) = log(62)

v*log(17) = log(62)

Dividing both sides by log(17) gives us:

v = log(62) / log(17)

This is the solution for v, the unknown variable in the equation.

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The perimeter and the area of the fountain is calculated to be

94.25 feet and 625.32 square feet respectively

The perimeter of the fountain consisting of two semicircles and a quarter circle is

= perimeter of semicircle * 2 + perimeter of circle * 1/4

= π d + 2 π r * 1/4

for semicircle, diameter, d = 20 ft

for circle, radius r, = 20 ft

substituting the values

= 20π + 2 * π * 20 * 1/4

= 20π + 10π

= 30π

= 94.25 feet

Area of the fountain

= area of semicircle * 2 + area of circle * 1/4

area of semicircle * 2 = area of circle of radius 10 ft

for semicircle, radius, r = 10 ft

for circle, radius r, = 20 ft

= π 10² + π 20² * 1/4

= 100π + 100π

= 200π

= 625.32 square feet

The area of the fountain is 625.32 square feet

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