Katniss and Peeta find the sum of their ages which is 50 years. Peeta is five years older than Katniss. What are their ages?

Answer:

No

y = –3

Step-by-step explanation:

solution

–8 = 2y – 2

–8 + 2 = 2y

– 6 = 2y

[tex] \frac{ \\ - 6}{2 } = \frac{2y}{2} [/tex]

–3 = y

y = –3

The relationship between the interior and exterior angles of a polygon is they are supplementary.

What is a regular polygon?

If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

Here,

we have to show how the interior and exterior angles of a polygon relate to each other.

A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.

As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).

Hence, the relationship between the interior and exterior angles of a polygon is they are supplementary.

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Answer:m/s

Step-by-step explanation:

Answer:

To find the average speed of the passenger jet, we need to divide the distance traveled by the time it took to travel that distance.

Average speed = distance / time

In this case, the distance is 1,213 miles and the time is 2.7 h.

Average speed = 1213 miles / 2.7 h = 449.6 miles/h

So the average speed of the passenger jet is 449.6 miles per hour.

The quadratic equation with solutions of (4 + i) and (4- i) is,

⇒ x² - 8x + 17 = 0

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The solutions of the quadratic equation are,

⇒ (4 + i) and (4- i)

Now, We know that;

A quadratic equation with roots a and b is,

⇒ x² -  (a + b)x + a × b = 0

Hence,  A quadratic equation with roots (4 + i) and (4 - i) is,

⇒ x² - (4 + i + 4 - i)x + (4 + i) (4 - i) = 0

⇒ x² - 8x + (4² - i²) = 0

⇒ x² - 8x + 16 + 1 = 0

⇒ x² - 8x + 17 = 0

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We can rewrite one side of the given equation using distributive property.

What is distributive property?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each term enclosed in a bracket multiplies the number outside of it, and the results are added.

The given equation is: 3(x + 2) = 18

Simplifying this,

3*x + 3*2 = 18

3x + 6 = 18

Hence, we can rewrite one side of the given equation using distributive property.

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An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

Give nonfiction books an x-factor.

Since there are three times as many fiction books as nonfiction books, we have a 3x/5 ratio, according to the question.

Due to the fact that they initially only sold two of these sorts and the fact that there were 240 volumes overall,

Due to this, the equation will be framed.

3x/5+x=240

So 8x/5=240

x=150 ( Number of non fiction books) ( no of non fiction books)

90 novels are so required.

Right at the start, this was a number.

Allow the number of books sold to increase.

In light of this, the equation is

Since there were 5:9 books in each category (fiction and nonfiction),

(90-y)/(150-y)=5/9

y=15

Therefore, the answer is 15.

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In the above case which involves a Pythagorean Triangle, using the trigonometric function TOA to solve we get: 61.93°

TOA is the acronnum for:

Tangent (θ) = Opposite /Adjacent

Tangent (θ) = 8/15

θ = Tan⁻¹ 0.5333333333

Thus

θ =  61.93°

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Solving the triangle we found the distance between the gazebo and the dock is: 69.34 meters. The answer is explained below:

The first thing to know is that to solve any triangle you must know at least one side and two other elements that can be sides or angles, that is, at least three elements of the six that make up a triangle.

Now, in the problem we know the value of one side (90 m) and 3 angles (see attached image), therefore the calculation of the distance (one side) is very easy if we apply the law of sines:

According to the Law of Sines, the ratio of the length of the sides of a triangle (not a rectangle) and their respective opposite angle sines, is the same value. Then:

d / sen (46°) = 90 m / sen (69 °)  

After, we pass  sen (46°) to the second term of the equation.

d= sen(46°)*90 m / sen (69°)

d = 0,7193*90/ 0,9335

d = 69,34 m

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Using the concept of arithmetic progression , We have t(n) = a +(n-1)d formula, The answer is 3.

A number sequence is a series of numbers that are listed in a particular order. The numbers in a sequence may follow a specific pattern or rule. Examples of number sequences include the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc.), the Fibonacci sequence (1, 2, 4, 8, 16, 32, etc.), and the triangular number sequence (1, 3, 6, 10, 15, etc.). Number sequences are often studied in mathematics and have many applications in fields such as computer science, engineering, and physics.

An arithmetic progression (AP) is a type of number sequence in which the difference between any two consecutive terms is always the same. This common difference is known as the "common ratio" of the sequence. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic progression because the common difference is 3.

t(n) =  a + (n-1)d

n=5

t(5)=17

a=5

17 = 5 +(5-1)d

12=4d

d=12/4 = 3

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The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

a line equation that is perpendicular to the line 2xy=5 and passes through the point (6, 4)

The slope of the given equation 2x-y=5 is first determined.

The line's equation is y=mx+b. where'm' represents the slope

Hence, The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

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The code is 4321.

A = 4

B = 3

C = 2

D = 1

The value of GL is 161.We can find by using supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees. For example angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.There are a total of two supplementary quantities and their units.

The sum of two angles is equal to 180° then they are supplementary angles. Each of the angles is said to be a supplement of another angle. Hence we can determine the supplement of an angle by subtracting it from 180°.

Now

According to supplementary angles

GL + LK =180

GL         =180- LK

GL         = 180 -19

GL      = 161

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The expression that is equal to 89.7 ÷ 10 is 897.5/100

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that an expression 89.7 ÷ 10

89.7 ÷ 10 = 8.97

1. 897.5/100

= 8.97

2. 8.975/100

= 0.08975

3. 8.975/1

= 8.975

4. 8.975/1000

= 0.008975

5. 89.750/1000

= 0.08975

Hence, the expression that is equal to 89.7 ÷ 10 is 897.5/100

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The surface area of the triangular prism is 55.8 units²

A triangular prism is a three-dimensional shape with two triangular faces and three rectangular faces. It is also known as a tetrahedron, which is a type of polyhedron with four faces. The triangular prism has a total of six faces and nine edges.

The formula of surface area of triangular prism is given as;

S.A = 2A + PH

The base area of the prism is given as;

A = 1/2 (b * h)

A = 1/2 * (9 * 14)

A = 63 units²

The perimeter of the triangle is the sum of all the sides.

This is calculated as P = a + b + c

P = perimeter = 9 + 9 + 12.7 = 30.7 units

Surface Area = 2(63) + 30.7 * 14

Surface Area = 55.8 units²

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Complete Question:

A triangular prism has a base that is an isosceles right triangle with sides 9 ft, 9 ft, and 12.7 ft. The height of the prism is 14 ft. What is the surface area of this prism.

Therefore , the solution of given problem of equation comes out to be

P is equal to 12 pounds per square foot.

Comparable to a balance scale, an equation. The equation (or scale) is out of balance if we add or subtract variable from one side. We also Must keep the "scale" (or equation) balanced while solving math equations such that both parts are always equal as expression are equal.

Here,

P= p = 12 + 4/9d is the equation that describes the relationship between the pressure,

p, of sea water in some deep ocean regions and the depth, d, below the surface.

Where

In pounds per square foot, p.

in feet is d

1) At a depth, seawater has a pressure of 85 pounds per square foot.

85 = 12 + 4/9d

4.9d/9 = 85 - 12 = 73

By xing it out, it becomes

4.9d = 73 × 9 = 657

d = 657/4.9

d = 134.1 feet

2) At 85 feet just below water's surface, the pressure of saltwater is

p = 12 + 4/9 × 85 = 12 + 4/765

P is equal to 12 pounds per square foot.

Therefore , the solution of given problem of equation comes out to be

P is equal to 12 pounds per square foot.

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The explicit formula for this geometric sequence 3, 15, 75, 375... is aₙ = 3(5)ⁿ⁻¹.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Note: The nth term of a geometric sequence is equal to the explicit formula for the geometric sequence.

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 15/3

Common ratio, r = 5.

Now, we can calculate the nth term (explicit formula) of this geometric sequence as follows:

aₙ = a₁rⁿ⁻¹

aₙ = 3(5)ⁿ⁻¹

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Complete Question:

Find an explicit formula for the geometric sequence 3, 15, 75, 375...

If Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour,  the standard deviation is 2.191.

Using this formula to find the Standard deviation

Standard deviation = √ Sample size  × Estimated drivers × (1 - Estimated drivers)

Let plug in the formula

Standard deviation = √ 30 × 0.20 × (1- 0.20)

Standard deviation = √ 30 × 0.20 × 0.80

Standard deviation = √ 4.8

Standard deviation = 2.191

Therefore we can conclude that the standard deviation is 2.191.

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Answer:

Step-by-step explanation:

uhh

Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.

Absolute advantage refers to the ability of a country or firm to produce a good or service at a lower cost than another country or firm. It is a concept in international trade and economic theory.

A country or firm has an absolute advantage in a good or service if it can produce that good or service more efficiently than another country or firm.

An individual has a comparative advantage in production if it produces at a lower opportunity cost when compared with other individuals.

The opportunity cost of Michael in the changing of oil = 10/ 8 = 1.25

Opportunity cost of Michael in changing tyres = 8 / 10 = 0.8

The opportunity cost of Martha in the changing of oil = 14 / 7 = 2

The opportunity cost of Martha in the changing of tyres = 7 / 14 = 0.5

Michael has an opportunity cost in changing of oil and Martha has an opportunity cost in changing of tyres.

Absolute advantage is when an individual produces more quantity of a good or service when compared to others.

So, Michael changes more oil (8) than Martha (7). Martha changes more tyres (14) than Michael (7)

Therefore, Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.

The complete question is:

Michael and Martha run a mechanic shop. In one hour Michael can perform eight oil changes or change ten tires. In one hour Martha can perform seven oil changes or change fourteen tires. Given this information which of the following is true?

A) Martha has a comparative advantage in changing oil.

B) Martha has an absolute advantage in changing oil.

C) Michael has a comparative advantage in changing tires.

D)Michael has an absolute advantage in changing tires.

E.) Michael has an absolute and a comparative advantage in changing oil

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Part 1: Where x is: time in hours. Where y is: distance in miles.

Part 2: The table is filled for the values of time and distance.

Part 3: y/x is fixed equation is proportional.

Total distance refers to the actual travel distance between the origin and destination locations of the material.

The formula for the distance is:

Distance = speed * time

Part 1:

The equation formed for the stated condition is:

y = 3x.

Where x is: time in hours.

Where y is: distance in miles.

Part 2: The table is filled for the values of time and distance.

Part 3:

For the equation.

y = 3x.

x = 1, y = 3 : y/x = 3

x = 2, y = 6 ; y/x = 3

As, y/x is fixed equation is proportional.

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The complete question with table is attached.

Answer: it is not a function

Step-by-step explanation: occurs when there was an attempt to call a value from a function, but the value is not actually a function.

Consider units digit as u and tens digit as t, so t=1/2 u is the right equation.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

given : t + u=9

1/2u+u=9 by substituting the value of t

3u=18

u=6.

t=1/2*6=3.

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On solving the question we can say that  slope intercept form of the equation is y = -1/4x +1/2

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (-2,1)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

1 = -1/4 *(-2) + c

⇒ c = 1/2

So the slope intercept form of the equation is

y = -1/4x +1/2

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Answer:

A) 1 to 2

Step-by-step explanation:

Total number of people: 623

Successes: 216

Failures: 623 - 216 = 407

Ratio of successes to failure = 216/407

Since 216 is approximately half of 407, the ratio is approximately 1/2.

Answer: A) 1 to 2

Answer:

28

Step-by-step explanation:

28 groups of 1/4 goes into 7

Answer:

28

Step-by-step explanation:

This is a division problem.

7 ÷ 1/4 =

= 7/1 ÷ 1/4

= 7/1 × 4/1

= 28/1

= 28

Answer: 28

You can also solve it this way.

There are 4 1/4's in 1.

In 7, there must be 7 times as many 1/4's.

7 × 4 = 28

Answer: 28

(1-0.2)C expression represents the cost after the discount

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Answer: B

Step-by-step explanation:

b is 64 because exterior angles are congruent

The horizontal tangents at x=3 and x=6 on the graph of the function f are shown in the given image. If [tex]g(x)=\int\limits^{2x}_0 {f(t)}\;dt[/tex], then g'(3) is -2. Then, option (C) is correct.

A function's zero slopes is indicated by a horizontal tangent line that runs parallel to the x-axis. The given graph of function f has horizontal tangents at x =3 and x = 6. Then, the given function is [tex]g(x)=\int\limits^{2x}_0 {f(t)}\;dt[/tex]. Then, we have to find g'(3). It is clear from the graph that f(3) = -3 and f(6) = -1.

Then, applying the Leibnitz rule for differentiation of the given function, we get,

[tex]\begin{aligned} g(x) &= \int^{2x}_0 f(t)\;dt\\g'(x)&=f(2x)\cdot\frac{d}{dx}(2x)-f(0)\cdot\frac{d}{dx}(0)\\&=2f(2x)\end{aligned}[/tex]

Now, substituting x = 3 in the above equation, we get,

[tex]\begin{aligned}g'(3)&=2f(2\times3)\\&=2f(6)\\&=2\times -1\\&=-2\end{aligned}[/tex]

The required answer is -2.

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According to the information, the sets of ingredients that have a proportional relationship with the original recipe are: option A, C and D.

To check the proportional relationship of the ingredients with the recipe we must carry out the following procedure.

Option A.

First, we need to establish how many times 6 is in 12 because this recipe includes 6 parts oil and the original recipe includes 12 parts oil.

Once we identify this number, we must divide the amounts of the original recipe by 2 to identify if the other values are correct.

In accordance with the above, option 1 would be proportional to the main recipe. For the other options we must perform the same procedure:

In the case of case C. we identify that 24 is twice 12, so we would have to multiply each ingredient by 2 to check the proportional relationship

In the last case (option D), we identify that the proportion is 3/4 with respect to the original recipe, so we must carry out the same procedure keeping this proportion in mind.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Attached image

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