two runners on an east-west highway are 421.2 feet apart heading east. a hot air balloon is flying ahead of them. the angle of elevation to the balloon of the runner closet to the balloon is 24.5o. if the hot air balloon is 1500 feet directly above a point on the highway east of both runners, what is the angle of elevation to the balloon of the runner the greatest distance from the balloon?

The equation can be written as 6 + (-6y) = -6y - 1 + (7).

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given is an equation with missing parts.

The left hand side of the equation does not contain a term with variable, but the right hand side contains it.

Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.

So the right hand side must be equal.

So the expression in the right hand side is -6y - 1 + (7).

Hence the expressions are 6 + (-6y) on the left hand side and  -6y - 1 + (7) on the right hand side.

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Answer:

Small jet seat capacity: 73

Large jet seat capacity = 90

Step-by-step explanation:

Let x be the number of seats on the small jet

Let y be the number of seats on the large jet

From the word description for last week:

Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers

we can formulate the equation
1x + 2y = 253  .............(1)

For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers

5x + 4y = 725 ...............(2)

Equation (1)  x 2 ==>
2x + 4y = 2(253)

2x + 4y = 506  ..............(3)

So our two equations are:

5x + 4y = 725 . .............(2)
2x + 4y = 506  ..............(3)

Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506

5x + 4y - 2x - 4y = 219

5x -2x +4y - 4y = 219

3x = 219

x = 219/3

x = 73

Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253

73 + 2y = 253

2y = 253 - 73

2y = 180

y = 180/2

y = 90

Answer
Small jet seat capacity: 73

Large jet seat capacity = 90

It should be noted that the rate will be gotten by dividing the distance by the time taken.

A rate in mathematics is a ratio that contrasts two distinct quantities with dissimilar units. Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator

By reducing them to their simplest form, we can express the rate. By way of illustration, if a person walks 30 steps in 20 seconds, their walking speed is 30 steps/20 seconds, or 3 steps/2 seconds.

The information above was given as your information is incomplete. The table wasn't shown.

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

        so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

                fg(x)  = -x^4-4x^3

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

       so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

              fg(x)  = -x^4-4x^3

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Answer:1, 3, 9, 27

Step-by-step explanation:

When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

v = x /t

Where:

Information about the problem:

Applying the velocity formula, we get:

v = x /t

v = 5280 feet / 5 minutes

v = 1056 feet/ minutes

By converting the unit from feet to miles and from hours to minutes, we have:

1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour

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Answer: 90200

Step-by-step explanation:

9020 x 10 = 90200.

Just add one more zero when multiplying by ten.

The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.

There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

The equal sides of an isosimple triangle are longer than the base's length.

We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.

2a denotes the two identical sides: 2(6.3) + b = 15.7

The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.

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Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

Answer:

66?

Step-by-step explanation:

18+18= 36

15+15= 30

30+36= 66

The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

The following figure accurately depicts the table.

Experimental probability is the likelihood of a future event based on past happenings.

Experimental probability is equal to the ratio of good results to all possible results.

To calculate the likelihood that the Texas Sharpshooters will score precisely

Next hockey game: 1 goal

As displayed in the table:

a successful outcome is repeated four times.

So, positive results equal 4

8 total results

likelihood = 4/8 = 0.5

So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

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Answer:

0.50 (Choice C)

Step-by-step explanation:

Khan Academy told me.

The equivalent expression is (a)  1 + √5

From the question, we have the following parameters that can be used in our computation:

√5 + 1

The additive property of equality states that

a + b = b + a

using the above as a guide, we have the following:

√5 + 1 = 1 + √5

This means that the equivalent of √5 + 1 is 1 + √5

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Complete question

Which of the following is equivalent to √5 + 1

O A 1 + √5

OB. 1-√√5

O C. √5-1

OD √5-2

Answer:

4x+6y = 46

Step-by-step explanation:

you just add by column

2x+2x

y+5y

9+37

Answer:300 tires

Step-by-step explanation: I set it up like this 100:45

X : 135

Then I am trying to find x. I cross multiplied. (100 times 135) and (45 times x) which is 45x= 13500 then if you know simple algebra then you get x by itself so you divide 13500 and 45 which equals 300.

The original price of the house is 156,000

From the question,

The house was increased by 30% which leads to an increase to 156000

To get the original price of the house

Let the value of the house be x

We then multiply the original price of the house(x) by 30%

we have 0.30*x

0.30x = 156000

Divide both sides by 0.30

x = 520,000

Hence, 520000 is the original price of the house

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Answer:

a) the triangles are similar triangles because they are the same shape. The angles in both triangles have the same value.

b) The similarity ratio between the two triangles is 0.5, because the lengths of the sides of the triangle on the right are double the value of the lengths of the sides of the triangle on the left.

c) angle U = angle G. angle V = angle H. angle T = angle F.

UV/GH = VT/HF = TU/FG = 0.5

55 is the number of soda bottles the machine can make each minute.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, the graph shows the relationship between time and the number of soda bottles a machine can make. Use points ​(4​,220​) and ​(7​,385​)

Since this graph is a straight line graph and also it goes through the origin that means time is directly proportional to the number of soda can manufactures

To prove this theory

the ratio between cans to the time taken by machine = 220/4 = 385/7

Since the ratio is the same for two points.

Thus,

Soda machine makes in 4 hours = 220 cans

Soda machine makes in 1 hours = 220/4 = 55 cans

Therefore, the number of soda bottles the machine can make each minute is 55.

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The probability that  randomly selected costume needs both shortened and taken in is 9/33

There are a total of n(T) = 33 costumes. Of these n(A) = 17 require alteration. The two sorts of change are shortening and taking in. n(S) = 15 costumes require shortening, and n(I) = 11 costumers require being taken in.

We are to determine the probability that a randomly selected costume requires both shortening and taken in.

The following is the formula for the union of sets.

P(S ∪ I) = P(S) + P(I) - P(S ∩ I)

∴ S ∪ I = A

∴ P(A) = P(S) + P(I) - P(S ∩ I)

∴ [tex]\frac{n(A)}{n(T)} = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - P(S \cap I)[/tex]

∴ [tex]P(S \cap I) = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - \frac{n(A)}{n(T)}[/tex]

Substituting the values:

∴ [tex]P(S \cap I) = \frac{15}{33} + \frac{11}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{26}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{9}{33}[/tex]

Therefore the probability that randomly selected costume needs both shortened and taken in is 9/33

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The solution to the given inequality expression is; x < 5

We want to solve the inequality expression;

8 - 4x > -12

Add 4x + 12 to both sides using addition property of equality to get;

8 - 4x + 4x + 12 > -12 + 4x + 12

20 > 4x

Divide both sides by 4 using division property of equality to get;

20/4 > 4x/4

x < 5

That expression is what we will have as our final solution to the inequality expression .

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Answer: 3 dogs

Step-by-step explanation:

Each dog eats 1/6 cans of food

Stanley uses a total of 1/2 cans of food

[tex]\frac{1}{2}[/tex]  / [tex]\frac{1}{6}[/tex] = 1/2 * 6

= 3 dogs

Answer:

14sin(55) and

14cos(35)

Step-by-step explanation:

Greetings!!

just remember trigonometric ratios which are

[tex]sin = \frac{opposite}{hypotenus} \\ cos = \frac{adjecent}{hypotenus} \: and \\ tan = \frac{opposite}{hypotenus} [/tex]

following that substitute given values to solve for x.

[tex]sin55 = \frac{x}{14} [/tex]

solve for x

[tex]x = 14 \sin(55) [/tex]

And

[tex] \cos(35) = \frac{x}{14} [/tex]

solve for x

[tex]x = \cos(35) [/tex]

Hope it helps!!!

A line of symmetry is the reflections map the figure onto itself.

A line of symmetry is, in other words, a line that splits a figure into two mirror representations. This line's reflection maps the figure onto itself. While some figures lack symmetry, others do feature one or more lines of symmetry. An example of a form having reflection symmetry is a rectangle.

The symmetry axes are shown and given the letters m and n. The figure will map to itself when reflected across either (or both) of the symmetry axes. It seems like you want to call those reflections...

Ra, where

a = m, and

Rb, where

b = n

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The length of string will be used to hang each pennant is 3.9 meters.

The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.

Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.

And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.

the length of the string needed for 5 pennants is calculated as,

=> 0.65 x (5 + 1)

=> 3.9 meter.

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}[/tex]

Answer:

I think it is y=1/3x -7

Step-by-step explanation:

Answer:

(2,4)

Step-by-step explanation:

The point that's on the origin (0,0) goes to the right by 2 which is your x-axis and goes up 4 which is your y-axis.

Answer:

Translation: (2,4)

Step-by-step explanation:

The dot/point that's in the middle which is always (0,0) goes to the right by 2 (x-axis) meaning that the first coordinate would be 2. It then goes up 4   (y-axis) meaning that the second coordinate would be 4.

As per the concept of fraction, the amount time spend for each test is 1.67 hours

In math the term called fraction is known as  the number is expressed as a quotient in which the numerator is divided by the denominator.

Here we have know that Jordan spent 5 hours over the weekend studying for 3 tests.

In order to find the amount of time spend for each test, we have to divide the total number of subject by the time spend by him.

Here the value of total subjects = 5 and the amount of time spend by him is 3.

Then the amount of time time spend for each test is calculated as,

=> 5/3

=> 1.67 hours

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Answer:

The function rule for this set of ordered pairs is y = 2x + 1.

This can be determined by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) can be calculated by using the formula:

m = (change in y) / (change in x)

For the ordered pair (1, 3) and (3, 7), we can see that change in x = 3 - 1 = 2 and change in y = 7 - 3 = 4, so m = 4/2 = 2.

Then, using any of the point we can find the b which is y-intercept. let's take the point (-2, -3) and substitute the values in the function y = 2x + b

-3 = 2(-2) + b

-3 = -4 + b

b = 1

So, the function rule is y = 2x + 1

well, let's find the equation of the line through those points then, and let's see

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]

The percent of the gas in the tank remaining is equals to the 53.6..

The capacity of Wilon's car's gas tank

= 15 gallons

The amount of gas in Wilon's car's tank

= 8.4 gallon

The amount of gas in tank used on a recent trip = 3.9 gallons

The remaining amount of gas in tank

= amount of gas in Wilon's car's tank before trip - amount of gas in tank used on a recent trip.

= 8.4 gallons - 3.9 gallons

= 4.5 gallons

Percent is calculated as the value diving by total value and then multiply with hundred. Now, the percent of the gas in the tank remaining = (4.5/8.4)× 100

=( 45/84)100

= 4500/84

= 53.57 ~ 53.6 %

Hence, the percent of the gas in the tank remaining is 53.6 .

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Complete question:

Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He used 3.9 gallon on a recent trip. What is the percent of the gas in the tank remaining?

The error is that the student did not distribute the -3 to the x and 2 inside the parentheses.

The correct answer is 3x - 6

Simplification of an algebraic expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The student's error is that the student did not distribute the -3 to the x and 2 inside the parentheses when simplifying the expression.

The correct simplification of the expression is:

-3(x + 2) + 6x = -3x - 6 + 6x = -3x + 6x - 6 = 3x - 6

Therefore, the student's answer is 3x + 2, but the correct answer is 3x - 6.

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The student made error when removing the bracket. The correct simplification of the expression is 3x - 6

We can spot the error of the student by carefully observing the student's answer. This is illustrated below:

-3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2

From the student's work, we can see that the student made an error when removing the bracket.

We can correct the student's error by carefully removing the bracket as shown below:

-3(x + 2) + 6x

Remove bracket by multiplying through by -3

-3x - 6 + 6x

Rearrange by bring the numbers with x variables together

-3x + 6x - 6

3x - 6

Thus, the correct answer to the simplification is 3x - 6

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