1. Two boats A and B depart from a port at the same time, travels to the north at 15 miles per hour, while B travels eastward at 20 mph. How fast boats are separated two hours after they left the port?

[tex]\left\{\begin{array}{ccc}-5x-3y=12&(**)\\y=x-12&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\-5x-3(x-12)=12\qquad\text{use distributive property}\\-5x+(-3)(x)+(-3)(-12)=12\\-5x-3x+36=12\qquad\text{subtract 36 from both sides}\\-8x=-24\qquad\text{divide both sides by (-8)}\\\boxed{x=3}\\\\\text{Put the value of x to}\ (**):\\\\y=3-12\\\boxed{y=-9}\\\\Answer:\ \boxed{x=3\ and\ y=-9\to(3,\ -9)}[/tex]

The subset of real numbers that the number 1/3 belongs is to the rational numbers. These numbers  is a number that can be written as a ratio. The numerator and the denominator of the fraction are both integers.

Step-by-step explanation:

[tex]\dfrac{1}{3}[/tex]   belongs to the subset "Rational number( [tex]\mathbb Q[/tex] )" of Real numbers [tex]\mathbb R[/tex].

Or

[tex]\dfrac{1}{3} \in \mathbb{Q} \subset \mathbb R[/tex]

To find in which subset of real numbers does  [tex]\dfrac{1}{3}[/tex]   belong.

In technical terms, there can be infinite subsets of real numbers in which  [tex]\dfrac{1}{3}[/tex]  can belong to.

But, the set of real numbers is divided into some special subsets viz. rational numbers. irrational numbers, integers, non integers etc..

Since the given number is expressed in the form of  [tex]\dfrac{m}{n}[/tex] which are called rational numbers, thus given number  [tex]\dfrac{1}{3}[/tex] belongs to rational numbers.

The set of rational numbers is denoted by [tex]\mathbb Q[/tex]

The set of real numbers is denoted by [tex]\mathbb R[/tex].

Thus, we can express our result symbolically as:

[tex]\dfrac{1}{3} \in \mathbb{Q} \subset \mathbb R[/tex]

Learn more about rational numbers here:

https://brainly.com/question/2563850

To find the perpendicular slope, we simply flip the fraction (aka reciprocal) and flip the sign (go from positive to negative, or vice versa)

So for problem 1a) we flip the fraction to go from 4/3 to 3/4. Then we flip the sign to go from +3/4 to -3/4. The final answer to problem 1a) is -3/4

The answer to problem 1b) is 7/3 following the same basic steps: -3/7 ---> -7/3 ---> 7/3

The answer to problem 1c) is -1/4. You can think of 4 as 4/1 which flips to 1/4 and it becomes -1/4

I'll let you try out the rest 1d and 1e. Tell me what you get so I can check your answers.

Answer:

2 solutions

Step-by-step explanation:

Since the equations are not equal, they provide two solutions. Negative numbers provide no solutions. If they are equal to zero, they have one solution.

Answer:

Eliphat is right, 2

Step-by-step explanation:

Answer:

B: integer and rational number

Step-by-step explanation:

whole numbers: 0, 1, 2, 3, 4, ...

integer: ..., -4, 3, -2, 1, 0, 1, 2, 3, 4, ...

rational number: any number that can be written as a fraction of integers

Answer: B: integer and rational number

Answer:

B and C.

Step-by-step explanation:

-20 is a negative integer.

It is also rational.

Answer:

There seems to be a typo error but still this has solution.

Let the number be = x

A positive real number is 6 less than another. Means the second will be [tex](x+6)[/tex]

The sum of the square of the two numbers is 38.

[tex]x^{2} +(x+6)^{2} =38[/tex]  

=> [tex]x^{2} +36+12x+x^{2} =38[/tex]

=> [tex]2x^{2}+12x+36 =38[/tex]

=> [tex]2x^{2}+12x=2[/tex]

=> [tex]2x^{2}+12x-2=0[/tex]

Taking out 2 common;

=> [tex]x^{2}+6x-1=0[/tex]

Solving this quadratic equation, we get;

[tex]x=-3+\sqrt{10}[/tex] and [tex]x=-3-\sqrt{10}[/tex]

As positive number is needed, we have [tex]-3+\sqrt{10}[/tex]

or x = [tex]\sqrt{10}-3[/tex]

x = 0.162277

And other number is 6.162277.

Given:

Question:

Find out the numbers.

Problem-solving:

Let us use [tex]\boxed{ \ x \ }[/tex] to represent the positive real number.

This positive real number is 6 less than another. The other number is [tex]\boxed{ \ x + 6 \ }[/tex]

The sum of the square of the two numbers is 38, i.e., [tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]

Let us work on expanding it.

[tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]

Recall that [tex]\boxed{ \ (a + b)^2 = a^2 + 2ab + b^2 \ }[/tex]

[tex]\boxed{ \ x^2 + x^2 + 12x + 36 = 38 \ }[/tex]

[tex]\boxed{ \ 2x^2 + 12x + 36 - 38 = 0 \ }[/tex]

[tex]\boxed{ \ 2x^2 + 12x - 2 = 0 \ }[/tex]

Both sides are divided by two.

[tex]\boxed{ \ x^2 + 6x - 1 = 0 \ }[/tex]

Let us solve the equation by using the quadratic formula.

[tex]\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-1)}}{2(1)} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{36 + 4}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{40}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm 2\sqrt{10}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6}{2} \pm \frac{2\sqrt{10}}{2} \ }[/tex]

[tex]\boxed{ \ x = -3 \pm \sqrt{10} \ }[/tex]

[tex]\boxed{ \ x_1 = -3 + \sqrt{10} \ . \ . \ . \ x_1 > 10 \ }[/tex] this is fulfilled.

[tex]\boxed{ \ x_2 = -3 - \sqrt{10} \ . \ . \ . \ x_2 < 10 \ }[/tex]

[tex]\boxed{ \sqrt {10} = 3.162 \ }[/tex]

Notes:

[tex]\boxed{ \ ax^2 + bx + c = 0, \ \ \ \ \  a \neq 0 \ }[/tex] is a quadratic equation in standard form.

Methods of solving quadratic equations include:

Keywords: a positive real number is 6, less than another, if the sum of the square, 38, then finds, quadratic equation, methods, factoring, the zero product property, the square root, completing, the quadratic formula

In a parallelogram, opposite angles are the same.

Because you are given angle C is 70 degrees, angle R is also 70 degrees.

An exterior angle of a triangle is equal to the sum of the two opposite inside angles.

Angle KSO is an exterior angle to the triangle made from ORS,

So angle KSO would equal the sum of angle O and angle R.

Angle KSO = 65 + 70 = 135 degrees.

Answer:

20 is the answer.

Step-by-step explanation:

Substitute 3 in for x and -2 in for y.

4(3) - (-2 to the third power)

12 - -8 = 12 + 8

The answer is 20

Please mark brainliest as that would really help out :3

[tex]-8x^3-2x^2-12x-3\\\\=-2x^2(4x+1)-3(4x+1)\\\\=(4x+1)(-2x^2-3)\\\\=\boxed{-(4x+1)(2x^2+3)}[/tex]

Answer:

Sometimes

Step-by-step explanation:

Answer:

Two lines that lie in parallel planes are sometimes parallel.

Step-by-step explanation:

Two lines that lie in parallel planes are sometimes parallel. It is not necessary that they are always parallel.

Rather two parallel lines are always coplanar.

There is always a plane which contains two parallel lines.

The equation of line passes through the point (1, 2) will be;

⇒ y = 7x - 5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (1, 2).

And, The slope is,

⇒ m = 7

Now,

Since, The equation of line passes through the point (1, 2).

And, Slope of the line is,

⇒ m = 7

Thus, The equation of line with slope 7 is,

⇒ y - 2 = 7 (x - 1)

⇒ y - 2 = 7x - 7

⇒ y = 7x - 7 + 2

⇒ y = 7x - 5

Therefore, The equation of line passes through the point (1, 2) will be;

⇒ y = 7x - 5

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ5

Answer:

9.8 percent decrease

Step-by-step explanation:

To find the percent decrease, we take the original value and subtract the new value and divide by the original value.

percent decrease = (original - new)/ original

                                = (23.5 - 21.2)/ 23.5

                                =2.3/23.5

                                =.09787234

This is in decimal form.  Multiply by 100 to put it in percent form

9.787234 percent

Round to the nearest tenth so we look at the 8 and round up.

9.8 percent decrease

Answer:

The answer is 9.8%

Step-by-step explanation:

Also, only two people can answer a question.

Answer:

I think it would be linear because its really easy?!

Step-by-step explanation:

Answer:

Country A won 78 medals

Country B won 26 medals

Country C won 15 medals

Step-by-step explanation:

We have been given with :-

A+B+C=119  _____equation(1)

B=C+11  ____equation(2)

A=B+C+37 ____equation(3)

1) Starting with the 3rd equation,

A=B+C+37

2) Subtract 37 from both sides

A-37=B+C+37-37

3) Cancelling out +37 and -37 from the right side we get,

A-37 = B+C

or

B+C = A-37

4) Plugin B+C= A-37 in the equation 1,

A+B+C = 119

=> A+(A-37) = 119

=> 2A-37 = 119

5) Add 37 to both sides

2A-37+37=119+37

6) Cancelling out -37 and +37 from the left side, we get

2A = 156

7) Divide both sides by 2

[tex]\frac{2A}{2} =\frac{156}{2}[/tex]

8) Cancelling out the 2's on the left side, we get

A = 78

9) Now, we plugin A=78 in the equation 1

A+B+C=119

=> 78+B+C=119

10) Subtract 78 from both sides

78+B+C-78 = 119 -78

11) Cancelling out +78 and -78 from the left side, we get

B+C= 41 ____let it be equation (4)

12) Subtracting C from both the sides of the equation 2, we get

B=C+11

=> B-C = C+11 - C

13) Cancelling out +C and -C from the right side, we get

B-C= 11 _____let it be equation (5)

14) Adding the equations 4 and 5, we get

B+C+B-C=41+11

15) Cancelling out the +C and -C, we get

2B = 52

16) Divide both sides by 2

[tex]\frac{2B}{2}=\frac{52}{2}[/tex]

17) Cancelling out the 2's on the left, we get

B =  26

18) Substituting A= 78 and B= 26 in the equation (1), we get

A+B+C=119

=> 78+26+C=119

=> 104+C=119

19) Subtracting 104 from both the sides, we get

104 + C - 104 = 119 -104

20) Cancelling out +104 and -104 from the left side, we get

C = 15

The problem is a basic algebra problem where we assign variables to the number of medals each country won. We then use given equations related to these variables to solve for each unknown.

In this problem, we are trying to solve for the number of medals each country won, so let's start by assigning variables for the number of medals for each country. Let's say, Country A = A, Country B = B, and Country C = C.

According to the problem, we know that Country A won 37 more medals than the sum of the other two countries, that's expressed by this equation: A = B + C + 37.

It's also stated that Country B won 11 more medals than Country C, so we have this equation: B = C + 11.

Further, we know that the total number of medals is 119, so we have this equation: A + B + C = 119.

Now, solve these equations systematically. First, substitute the value of A and B from first and second equation into the third equation and solve the variable C, then substitute the obtained value of C in second equation to find B and finally substitute the obtained values of B and C in first equation to find A.

This is a basic algebraic problem-solving situation. It involves the use of equations and variables to find the solution.

https://brainly.com/question/11315620

#SPJ3

Answer:

p < 7

Step-by-step explanation:

To isolate the p, subtract 3 from both sides to get p < 7.

The correct answer is p < 7

Explanation:

To get your answer you need to first set out you equation, 3 + p < 10. Next, you need to subtract 3 from both sides of the equation, 3 + p - 3 < 10 - 3 =      p < 7. Finally, we have our answer of p < 7.

Hope This Helps!!!

-AnimeDabGirl

Answer:

The answer would be x=2

Step-by-step explanation:

Answer:

The box plot will have its left tail longer than the right tail becuase a few exceptionally low prices make the distribution skewed to the left.                                              

Step-by-step explanation:

As seen in the attached file, the box plot has its left tail longer than the right tail because of the exceptionally low prices that is :$2

Firstly arranging the data in increasing order:

$2,$2,$25,$25,$26,$26,$27,$27,$28,$28,$30

Median of the data = 26 (since there are odd numbers)

Lower quartile (Q1) = 25

Upper quartile (Q2) = 26

By plotting the box plot we conclude that the left tail is longer than the right tail.

Answer:

The Answer is C. The box plot will have its left tail longer than the right tail because a few exceptionally low prices make the distribution skewed to the left.

Hope This Helps?

Answer:

m∡J = 110°, m∡L = 45°, m∡K = 25°

Step-by-step explanation:

Similar means they have the same angles. F corresponds with K, G with J, and  E with L.

m∡J = 110° because it corresponds with m∡G.

m∡L = 45° because it corresponds with m∡E.

To get m∡K, we have to remember all triangles add to 180. Add J and L together, and subtract that sum from 180° to get m∡F, which is equal to m∡K.

110 + 45 = 155

180 - 155 = 25

m∡K = 25°

Answer:

8x¹²y³

Step-by-step explanation:

The answer is D you move the decimal over 1 then add 2 0

Answer:

D

Step-by-step explanation:

Answer:

$55.20

Step-by-step explanation:

What is the brokerage fee

.15 * 48 = 7.2

The total cost of his ticket is the price of the ticket plus the brokerage fee

total cost = 48 + 7.2

               = $55.20

Marcus had to pay a total of $55.20 for the concert ticket, which includes the 15% brokerage fee on top of the original ticket price.

Marcus bought a concert ticket for $48. The online ticket broker charged a 15% brokerage fee on top of the ticket price. To calculate the total amount Marcus had to pay, we first need to calculate the brokerage fee. The brokerage fee is found by multiplying the ticket's price by the brokerage fee rate. So, $48 multiplied by 15% (or 0.15) gives us the brokerage fee of $7.20. This brokerage fee is then added back to the original ticket price, so Marcus paid a total of $48 + $7.20 = $55.20 for the concert ticket.

https://brainly.com/question/32197511

#SPJ12

Answer:

The answer is 1.2

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

You can use a calculator... Or you can ask google this, "What is 0.324 divided by 0.27?"

0.324 divided by 0.27 is 1.2

Explanation: For questions 4-11, plug in the values of the variables into the equations. Ex no. 8: 7.8 + 3.5(w) where w=6.8. Plug 6.8 into the equation: 7.8 + 3.5(6.8) = 7.8 + 23.8 = 31.6 is the answer.

For questions 12-15, the order of operations is Please Excuse My Dear Aunt Sally: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. In other words, solve each equation according to the arrangement of the operations. Ex no. 15: y² - 10 ÷ 5 + x where x = 2.5 and y = 4. Plug these numbers into the equation: 4² - 10 ÷ 5 + 2.5. The order of operations says that parenthesis should be solved first. Since there are no parenthesis, we can skip this operation. The next operation is exponents. 4² has an exponent of 2, which means that we multiply 4 by itself 2 times to get 16 (4 x 4 = 16). We now have 16 - 10 ÷ 5 + 2.5. The next operation is multiplication. There is no multiplication in this equation, so we skip this operation. Next is division. We can divide -10 by 5 to get -2. We now have 16 - 2 + 2.5 (Do not change an addition sign unless you are dividing a negative number by a positive number). The next operation is addition. We can add -2 and 2.5 to get 0.5. Lastly, we can also add 16 by 0.5: 16 + 0.5 = 16.5 is the answer.

25(x-y) simplified using the distributive property gives us 25x - 25y.

WE are given the expression as 25x-25y

WE know that distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

To use the distributive property to simplify 25(x-y), we need to distribute the 25 to both x and y separately.

So,

25(x-y) = 25(x) - 25(y)

= 25x - 25y

Therefore, 25(x-y) simplified using the distributive property gives us 25x - 25y.

Learn more about distributive property here;

https://brainly.com/question/5637942

#SPJ6

Final answer:

The expression 25(x-y) is simplified using the distributive property by multiplying 25 by each term inside the parentheses, resulting in 25x - 25y.

Explanation:

To use the distributive property to simplify the expression 25(x-y), you should multiply each term inside the parentheses by 25.

This is what it looks like when we apply the distributive property:

25 × (-y) = -25y

So, the simplified expression is 25x - 25y.

When we evaluate expressions, we are typically trying to express them in a way that shows the multiple or product terms explicitly. This process is like reversing distributive law and turning it back into factors (multiples). Here, the distributive law helps us see that the expressions 25x and -25y, when combined, produce the same value as the original expression 25(x-y).

[tex]2x-y=12\\\\y=2x-12\\\\[/tex]

Answer:

23 buns

Step-by-step explanation:

The dog ate 5 buns.

The Owen gave the dog 18 more buns

5+18 = 23

Answer:

It can be written that way, but the functions are not the same. The numbers the would be plugged in would not produce the same answer.

Answer:  " 86 words per minute "

______________________________________________

Step-by-step explanation:

______________________________________________

We are looking for the "unit rate" ; or "rate per [single] unit" ;

in this case, "words per [single} minute" ; that is "words per minute"

Given:   "301 words per 3.5 minutes" ;

or:   " 301 words / 3.5 min. " ;

      =  " (301 / 3.5)  words/ min.

      =  " 86 words / min. "

_______________________________________________

The answer is:  " 86 words per minute " .

_______________________________________________

Hope this helps!

    Best wishes!

_______________________________________________

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{3-2}{4-2}=\dfrac{1}{2}[/tex]

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

[tex]m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}[/tex]

We have the equation:

[tex]\dfrac{-3}{x-2}=\dfrac{1}{2}[/tex]        cross multiply

[tex](1)(x-2)=(-3)(2)[/tex]

[tex]x-2=-6[/tex]           add 2 to both sides

[tex]x=-4[/tex]