An airplane is 45 miles from the end of the runway, AB, and 9 miles high, AC, when it approaches the airport. What is the distance from the airplane to the end of the runway?

The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

The problem can be solved by using a system of equations.

We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.

From the problem, we know:

x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)

We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:

(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles

Now we have a system of two equations with two variables (x and y):

x + y = 55

(30)x + (40)y = 1850

We can solve this system of equations using any method of solving such as substitution or elimination.

x = 55 - y

and substitute it in the second equation

(30)(55-y) + (40)y = 1850

1650 - 30y + 40y = 1850

-14y = -200

y = 14.28

x = 55 - 14.28 = 40.72

So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

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The product of (7x - 6)² is  49x² - 84x + 36.

Equation is (7x - 6)²,

⇒ We will solve the given problem using the algebraic identity

(a - b)² = a² + b² - 2ab

Here a = 7x and b = 6

⇒ (7x - 6)² = (7x)² + 6² - 2(7x)(6)

⇒ (7x - 6)² = 49x² + 36 - 84x

⇒ 49x² - 84x + 36

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied.

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Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

a) The minimum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7 +6

=> 13

b) The maximum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7+6+4

=> 17

Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

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Answer:

x^2-23

Step-by-step explanation:

This means that the solution to the equation x is 6.

An equation is a mathematical statement that expresses the relationship between two values. It typically consists of an equal sign (=) and two expressions that are related to each other. Equations are used to describe how one value depends on another, or how two values are related to each other.

To solve this equation, use the Quadratic Formula,
which states that for an equation of the form ax2 + bx + c = 0,
the solution is x = [-b ± √(b2 - 4ac)] / 2a.
Plugging in the given equation,
we have a = 5, b = -3, and c = 45.
This means that the solution to the equation is x = [-(-3) ± √((-3)2 - 4*5*45)] / 2*5, or x = 6.

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It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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Answer:

X

[tex] \frac{y2 - y1}{x2 - x1} - \frac{y - y1}{x - x1} [/tex]

Step-by-step explanation:

in every point given put one as (x1, y1) and the other is (x2, y2)

simplify the formula and you'll get you linear equation

The result of addition and subtraction is

The directions to solve these problems are to round each fraction to the nearest whole number and then add or subtract. We have to round each fraction into the nearest whole number.

1. 5 (2/3) - 1 (1/4) = (5 + 1) - 1 = 6 - 1 = 5

2. 8 (5/12) + 31 (1/6) = 8 + 31 = 39

3. 3 (1/4) + 3 (3/5) = 3 + (3 + 1) = 3 + 4 = 7

4. 9 (1/10) - 6 (7/10) = 9 - (6 + 1) = 9 - 7 = 2

5. 7 (5/8) + 2 (1/7) = (7 + 1) + 2 = 8 + 2 = 10

6. 20 (9/11) - 18 (3/10) = (20 + 1) - 18 = 21 - 18 = 3

7. 10 (3/7) + 22 (2/9) = 10 + 22 = 32

8. 1 (5/6) + 5 (1/6) = (1 + 1) + 5 = 2 + 5 = 7

9. 113 (1/13) + 86 (9/11) = 113 + (86 + 1) = 113 + 87 = 200

10. 65 (17/20) + 19 (3/25) = (65 + 1) + 19 = 66 + 19 = 85

11. 71 (41/50) + 25 (5/24) = (71 + 1) + 25 = 72 + 25 = 97

12. 12 (13/15) + 18 (2/5) = (12 + 1) + 18 = 13 + 18 = 31

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The product is 3x * 4x^(3/2) = 12x^(5/2)

How to do the product of root?

When multiplying two terms with the same base and different exponents, you can add their exponents.

For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)

The product of 3√(x^2) * 4√(x^3) is equal to:

12x^(5/2)

This is because when you multiply two terms with the same base, you can add their exponents:

3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)

This is because

√(x^2) = x^(2/2) = x

√(x^3) = x^(3/2) = x^(3/2)

so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)

Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)

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To find out how much Kim spent in total with the 8% sales tax included, we first need to add up the cost of all 4 items: $32.45 + $46.78 + $12.91 + $52.38 = $144.52

Next, we'll multiply that total cost by the sales tax rate as a decimal (8% expressed as 0.08) to find out how much tax Kim had to pay: $144.52 x 0.08 = $11.56

Finally, we'll add the total cost of the items and the tax to find out how much Kim spent in total: $144.52 + $11.56 = $156.08

Answer:

the answer 112

Step-by-step explanation:

hope this helps

Answer :

The first one

Step-by-step explanation:

A cube root is a number that, when cubed, is equal to the given number.

It is denoted with an exponent of "1/3".

Example, the cube root of 27 is 27^1/3 = 3.

Now,

[tex]24^{ \frac{1}{3} } \: is \: the \: same \: as \: \sqrt[3]{24} [/tex]

From there, we can simplify

[tex] \sqrt[3]{24} \\ \sqrt[3]{2 \times 2 \times 2 \times 3} \\ \sqrt[3]{ {2}^{3} \times 3} \\ 2 \sqrt[3]{3} [/tex]

Linear equations in two variables can be relatively easy to understand and work with, as they represent straight lines in the xy-plane. The slope-intercept form of a linear equation, y = mx + b, is a simple way to represent a line with a specific slope and y-intercept.

Graphing linear equations is also straightforward, as you can find the x-intercept and y-intercept and plot the line using these points.

However, solving linear equations in two variables can become more challenging when the equations involve multiple terms or are presented in a different form. Also, understanding the concept of slope, y-intercept, and how to graph the line can be challenging for some students.

Overall, linear equations in two variables can be considered as a fundamental concept in algebra and mathematics and it requires practice to gain mastery over it.

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The slope of the equation is 42, and it represents the $42 the artist earns, on is true after analyzing data from recent sales.

Sales in mathematics is the process of exchanging goods or services for money. It is a vital part of the economy and involves the transfer of ownership from the seller to the buyer. In mathematical terms, sales can be expressed as a function where the input is the amount of money paid for goods or services and the output is the goods or services received. Sales can also be expressed as an equation in which the variables are the cost of goods or services, the number of goods or services sold, and the total sale amount.

The slope of the equation is 42, and it represents the $42 the artist earns, on average, for every piece of pottery sold.

The constant -200 represents the cost of renting the booth.

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=> 999 is not a perfect cube.

Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .

Now, According to the question:

A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).

It is the real solution of the equation [tex]x^3[/tex] = 999.

The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.

The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].

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Answer:$917.58.

Step-by-step explanation:

The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.

So, we can plug in the values into the formula:

A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585

The final amount in her account after 12 years is $917.58

To round to the nearest cent, we can use the following method:

If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.

If the digit in the thousandths place is greater than 5, we round up the hundredths digit.

In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.

So, the final amount in her account after 12 years is $917.59.

Answer: $800.516

Step-by-step explanation:

We use the equation

A = P(1 + )^nt

P = principal

r = rate of interest

t = times

Now let's solve

P = $500

r = 4% = 0.04

t = 12 years

A = $500(1 +[tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516

Multiply the hypotenuse of triangle by sinθ to determine the length of the side opposite the angle (θ). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos(θ).

Scalene triangles are typically described as triangles with no two sides that are equal. Isosceles triangles are those triangles whose two sides are equal. An equilateral triangle is one with equal lengths on each of its three sides. Clearly, all equilateral triangles are isosceles, but not the opposite.

The side across from the right angle is always the hypotenuse of a right triangle. The opposite and neighboring sides are the other two sides.  

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y = 8/3x + 100 exists the equation of the line in slope-intercept form.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

A line's slope and y intercept are represented in the slope intercept form as y = mx + b.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) contains

m = y₂-y₁/x₂-x₁

At two of the points the line passes through in the accompanying graph.

Let the two points be (0, 100) and (42, 148)

Let the equation be m = y₂-y₁/x₂-x₁

substitute the values in the above equation, we get

Slope = 148-100/42

= 48/42 = 8/3

To find y intercept, we get

100 = 8/3(0) + b

b = 100

So slope intercept form exists y = 8/3x + 100

Therefore, y = 8/3x + 100 exists the equation of the line in slope-intercept form.

The complete question is:

Examine the linear graph. Determine the y-intercept and write the y-intercept in coordinate form. Then write the equation of the line in slope-intercept form.

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Equivalent 7/8 is equals to 56/64 in fractions.

In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.

The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

= 7/8 is equivalent to:

= 7/8 * 8/8

= 56/64

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Correct Question:

What is 7/8 equivalent to in fractions?.

The designs that meet the condition have leg lengths that are in the ratio of 1: 12.

Two ramps that meet the Americans Disabilities Act are;

The needed measure of the angle of a ramp according to the Americans with Disability Act is θ ≤ 4.8°.

Given, the ratio of the leg lengths is 1: 12, we have;

Expressed as a fraction, we have;

The required ratio of leg lengths = [tex]\frac{1}{12}[/tex]

Probable leg lengths are seen by multiplying the numerator and denominator of the above fraction by a constant as follows;

Possible leg length for the ramp = [tex]\frac{1 * 3}{12 * 3} = \frac{3}{36}[/tex]

A second possible combination of leg length for the ramp = [tex]\frac{1 * 5}{12 * 5} = \frac{5}{60}[/tex]

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The complete question is:

The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8-degree angle in a right triangle has a 1: 12 ratio for the legs. Design 2 ramps that meet the Americans with Disabilities Act requirements.

The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °

Because Cos (±37° +360k) = 0.8

0≤2X ≤ 360°

0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°

50 2x+45° = 360°-37° or 2x+45° = 360° + 37°

{list the equation} 397° -45°=2X = 323-45°

2X = 323-45°. 2x=397° -45°

2x= 278°.         2x= 352°

X = 139°.          X=176°

So , x = 139° or x = 176°

To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!

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Answer: ratio of 1:   10mins

               ratio of 5:   50mins

Step-by-step explanation:

The ratio of 1:

[tex]\frac{1}{6}[/tex] x 60 (hours should be converted to minutes therefore it is 60 mins and

            the denominator seen here is taken by adding the two values in the

             given ratio and since we're still finding 1 you should divide 1 by the

          added denominator and the same applies when finding the ratio 5)

Answer= 10mins

The ratio of 5:

[tex]\frac{5}{6}[/tex] x 60 (refer to the underlined explanation above)

answer= 50mins

so if you want to verify you add the two values you got to see if you got 60 as 60mins in hours was divided in ratio so when you add it will be 60 which means your answer is correct!

Answer: 12:60

Step-by-step explanation: To find the ratio, we must take 1 h and turn it into minutes. So as we know, it's 60 minutes. So next, we shall change the ratio into fraction form (don't worry it's the same basic format)

[tex]\frac{1}{5} = \frac{?}{60}[/tex]

So with that given information, we know that 60 would be our denominator. So, we need to divide both denominators, and then whatever we get from that, multiply that by the given numerator. So, we would do:

60 / 5

= 12

12 * 1

= 12

Therefore we now know that 1/5 = 12/60 as a ratio. I hope this helped :)

(Attachment included)

Answer:34xt25

Step-by-step explanation:

Answer:awnsers below

Step-by-step explanation:

a. The probability of selecting 2 red balls is (5/8) * (5/8) = 25/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a red ball on the second draw is also 5/8, since the ball is replaced after each draw.

b. The probability of selecting 1 red ball and then 1 white ball is (5/8) * (3/8) = 15/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a white ball on the second draw is 3/8, since the ball is replaced after each draw.

Answer:

Step-by-step explanation:

a)

P(Red)=5/8

(5/8)^2=25/64

b)

P(Red)=5/8    P(White)=3/8

5/8*3/8=15/64

Answer:

c)31

Step-by-step explanation:

The goal of this exercise is to determine the total savings by paying the debt early at

�

)

a)

19

19th payments

�

)

b)

25

25th payments and

�

)

c)

31

31st payments.

The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.

It follows from the task content that the solution of the given equation for variable, x is to be determined.

Since the given equation is; 13x = 6y.

It follows that the equation can be solved as follows;

13x = 6y

Divide both sides of the equation by 13 so that we have;

x = 6y / 13.

Ultimately, the formula for x is; x = 6y / 13.

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Step-by-step explanation:

x²-8x+7=0

x²-7x-x+7=0

x(x-7) -1(x-7)=0

(x-7) (x-1)=0

Either, x-7=0 i.e x=7

or, x-1=0 i.e x=1

The First Class Mail (1 oz.) letter rate for postage purchased at the Post Office will increase two cents to $0.60 from $0.58.

Domestic shipping refers to shipping a package via a carrier within a country's borders.

Now, According to the question:

The “Metered Mail” rate for First Class Mail (1 oz.) letters which includes online postage and postage meters, will increase 4 cents to $0.57 from $0.53.

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