Two bikers leave the same shopping center at the same time traveling in
opposite directions. If the first biker travels 2 mph faster than the second,
how fast is each riding if after 3 hours they are 78 miles apart?
The faster biker travels
mph
The slower biker travels
mph​

Answer:

Step-by-step explanation:

get rid of the denominator by multiplying by x

Answer:

The equation is y=-x+6.

Step-by-step explanation:

To find the slope of this equation, we use the equation m=y2-y1/x2-x1, where m is the slope. Take one y coordinate and subtract it from the other and do the same with the x coordinates. Then, divide the difference of the y coordinates by the difference of the x coordinates. For example, 6-2/0-4. This gets us 4/-4. You can also do 2-6/4-0 which gets us -4/4. No matter what, we get -1 for each (we don't include the 1 in front of the x). To find the y-intercept, plug in the coordinates. For example, do 6=0(-1)+b or 2=4(-1)+b. No matter which you use, you get an answer of b=6. This gives you an equation of y=-x+6. Hope this helps :)

The equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

To determine the equation for the line that passes through the points (4,2) and (0,6),

We will use the formula for the determining the equation of a line with two given points

The formula for the determining the equation of a line with two given points is

[tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The given points are (4,2) and (0,6)

Therefore,

x₁ = 4

y₁ = 2

x₂ = 0

y₂ = 6

Now, putting these into the formula,

We get

[tex]\frac{y-2}{x-4}=\frac{6-2}{0-4}[/tex]

This becomes

[tex]\frac{y-2}{x-4}=\frac{4}{-4}[/tex]

[tex]\frac{y-2}{x-4}=-1[/tex]

Then, the equation becomes

[tex]y-2 = -1(x-4)[/tex]

[tex]y-2 = -x +4[/tex]

[tex]y = 4+2-x[/tex]

[tex]y = 6-x[/tex]

Hence, the equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

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Answer:

c = -2

Step-by-step explanation:

The two functions are given as:

f(x) =  x^2 - 2x

g(x) = 6x + 4

To find:

(f+g)(x) = 0

We can evaluate (f+g)(x) using the given functions.

We know that:

(f+g)(x) = f(x) + g(x)

= x²- 2x + 6x + 4

= x² + 4x + 4

Now, we have for x = c:

c² + 4c + 4 = 0

x² + 2c + 2c + 4 = 0

c(c+2) + 2(c+2) = 0

(c+2)² = 0

c+2 = 0

c = -2

Answer:

‭1.267650600228229401496703205376e+130‬

Step-by-step explanation:

√400 =20

20¹⁰⁰ = ‭1.267650600228229401496703205376e+130‬

Hope this helps!

Answer: X^4 you just subtract or add with exponents

Step-by-step explanation:

In mathematics, when you multiply variables that have the same base, you add their exponents. The solution to the problem X^-3•x^7 is x^4.

To multiply the variables with the same base, you need to add their exponents. In this case, x-3 multiplied by x7 would be equal to x-3+7 or x4. Therefore, the answer is x4.

The problem given is X^-3•x^7. This problem involves the multiplication of two variables with exponents. In mathematics, when you multiply variables with the same base, you keep the base and add the exponents. This is called the 'Laws of Exponents'. Therefore, for X^-3•x^7, our base is X, so we add the exponents -3 and 7 to get 4. Hence, the result is x^4.

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Answer:

Step-by-step explanation:

Rewrite X^2+22x=31, leaving space after the "22x:"

X^2+22x                          = 31

The coefficient of x is 22.  Take half of that, obtaining 11.  

Square this result:  11^2 = 121.

Write in "+121      -121" after the x term:

X^2+22x  + 121 - 121 = 31

Rewrite X^2+22x + 121 as

          (x + 11)^2  -121 =  31

Add 121 to both sides:

           (x + 11)^2 = 152

Take the square root of both sides:

            x + 11 = ±√152 = ±2√38

Finally, x = -11 ±2√38.

This is "solution by completing the square"

Answer: OPTION A

Step-by-step explanation:

We have this quadratic equation: [tex]x^2+22x=31[/tex]

In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:

[tex](\frac{22}{2})^2=11^2[/tex]

Now we must add 11² to both sides of the equation:

[tex]x^2+22x+11^2=31+11^2[/tex]

Therefore, after complete the square and factor, we get:

[tex](x+11)^2=152[/tex]

This matches with the option A.

Answer:

82%

Step-by-step explanation:

Answer: x = 6, x = -4

Step-by-step explanation:

Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):

0 = x² - 2x - 24

                    ∧

                   1 -24

                   2 -12

                   3  -8

                   4  -6 = -2    This works!

0 = (x + 4)(x - 6)

Apply the Zero-Product Property (set each factor equal to zero and solve)

0 = x + 4      0 = x - 6

-4 = x            6 = x

The solutions are x = 6 and x = -4. Therefore, the zeros of the function are 6 and -4.

Finding the Zeros of the Function p(x) = x^2 – 2x – 24

To find the zeros of the function p(x) = x^2 – 2x – 24, we need to determine the values of x that make the function equal to zero. This means we solve the equation:

x^2 – 2x – 24 = 0

This is a quadratic equation and can be solved using factoring. We look for two numbers that multiply to -24 and add to -2. These numbers are 4 and -6:

(x - 6)(x + 4) = 0

Setting each factor equal to zero gives us the solutions:

So, the zeros of the function p(x) = x^2 – 2x – 24 are 6 and -4.

Answer:

x^2 +8x+12

Step-by-step explanation:

(X+2)(x+6)

Foil

first: x*x = x^2

outer: x*6 = 6x

inner : 2*x = 2x

last: 2*6 = 12

Add them together:  x^2 +6x+2x+12 = x^2 +8x+12

Answer:

6/7

Step-by-step explanation:

One way of doing this problem is to find the square root of numerator separately (it is 6) and the square root of the denominator likewise (it is 7).  Then the value of the given expression is 6/7.

The value of the given expression is [tex]\frac{6}{7}[/tex].

What is a mathematical expression?

"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."

The given mathematical expression is

[tex](\frac{36}{49})^{\frac{1}{2}} \\= (\frac{6^{2} }{7^{2} })^{\frac{1}{2}}\\= [(\frac{6}{7})^{2}]^{\frac{1}{2}}\\= \frac{6}{7}[/tex]

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For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -2)\\(-3,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 2)} {- 3-0} = \frac {2} {- 3} = - \frac {2} {3}[/tex]

So, the equation is of the form:

[tex]y = - \frac {2} {3} x + b[/tex]

We substitute a point to find "b":

[tex]-2 = - \frac {2} {3} (0) + b\\-2 = b[/tex]

Finally, the equation is:

[tex]y = - \frac {2} {3} x-2[/tex]

Answer:

Option C

For this case we have that from 2:16 am until 2:16 pm exactly 12 hours have passed. On the other hand, from 2:16 p.m. until 8:16 p.m., exactly 6 hours have elapsed.

If we add, we have that from 2:16 am to 8:16 pm have elapsed: 12 + 6 = 18 hours.

As we ask for the time elapsed between 2:16 am until 8:10 pm we must subtract 6 minutes. So, we have:

18 hours with 54 minutes

Answer:

18 hours with 54 minutes

Answer: The y-intercept would be 10

Step-by-step explanation:

(-2, 15), (1, 6), (2, 3), (4, -3), (7, -12) are the coordinate points, you can graph it to find the intercept. I used the graphing calculator desmos.

Answer:its 9

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The digit in the tenths place of 25.391 is 3.

Answer: [tex]3[/tex]

Step-by-step explanation:

It is important to know that, in order to find the digit in the tenth place of a decimal number, you need to indentify the first digit located to the right of the decimal point.

Therefore, knowing this and having the decimal number provided in the exercise:

 [tex]25.391[/tex]

You can observe that the  first digit to the right of the decimal point is 3.

Therefore, the digit in the tenths place of ths decimal number is: [tex]3[/tex]

when a graphed line is vertical, it indicates that the relation is not a function

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

We can visually identify functions by their graphs using the vertical line test. If any vertical line intersects the graph more than once, then the graph does not represent a function.

The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds.

As we can see, any vertical line will intersect the graph of y=|x|−2 only once.

Therefore, it is a function.

A vertical line can cross the graph of x=|y|+1 more than once.

therefore, it is not a function.

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Answer:

If one factor is (x-10) then the other factor is (x+2).

Step-by-step explanation:

We need to factorize the term x^2-8x-20

For factorization we need to break the middle term.

Middle term : -8x

Product of first and last term: -20x^2

Factors: -10x, +2x

Solving:

x^2-8x-20

x^2-10x+2x-20

x(x-10)+2(x-10)

(x-10)(x+2)

So, if one factor is (x-10) then other factor is (x+2)

Answer:

4,444097208657794

Step-by-step explanation:

c = 20ft

b = 19.5ft

just use the pythagorean theeorem

Answer:

slope = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3-2}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

1/5

Step-by-step explanation:

Answer:

Third week, 15 words per minute

Step-by-step explanation:

First week: 10 words per minute

Second week

10 * 20% = 10*.2 = 2

It is an increase, so we add the 2 to the original amount

10+2 = 12 word per minute

Third week

12 * 25% = 12 *.25 = 3

It was an increase, so we add the 3 to the amount in week 2

12+3 = 15 words per minute

The number of wheels on a group of buses involves mathematical calculations and can be analyzed using multiplication, probability, and physics, particularly when combined with other factors such as passenger capacities or mechanical variables like angular velocity of a flywheel within the bus.

The question about the number of wheels on a group of buses relates to mathematical calculations, specifically pertaining to multiplication and potentially to probability and combinatorics if one were analyzing how to most efficiently deploy a fleet of buses for transportation or which bus to take based on passenger load and capability.

A practical example of a bus-related math problem would be: if a bus has 6 wheels, then a fleet of 10 buses would have a total of 60 wheels. This is a straightforward multiplication problem (10 buses x 6 wheels per bus = 60 wheels).

In the context of probabilistic analysis, considering a situation where buses have different passenger capacities, we might use the expected value formula E(X) = Σx₁p(x₁) to calculate the best option for transportation based on various factors, including the number of passengers each bus can transport.

Moreover, buses also have a place in physics problems. For instance, calculating the angular velocity a bus's flywheel must have to achieve a certain speed involves understanding the concepts of rotational kinetic energy and its transformation into translational energy. This more complex application lies within the realm of physics but has roots in mathematical computation.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation y = 6x + 8. Therefore

m = 6

b = 8

Answer: A: (0,8)

Step-by-step explanation:

Hello There!

The number of adult tickets sold in the school play = 225

Total Number Of Tickets = 505

Number Of Student Tickets = x + 55

Number of adult tickets sold can be represented by X

Number of student tickets = X + 55

X+X+55=505

2x+55=505

2x=505-55

2x=450

X=225

Answer:

225

Step-by-step explanation:

x+x+55 = 505

2x + 55 = 505

2x = 505-55

2x = 450

x = 225

GOOD LUCK ! ;)

Answer:

Option 1

Step-by-step explanation:

Before answering the question, we should define what the like radicals are.

The radicals which have the same expression under the root and same root number. There can be numerical multiples outside the radical but we have to compare the root number and same expression under the root.

In the given question, only option one has the same root number to the radical given in the question and the same expression under the root ..

Answer with explanation:

→Draw a Line segment of any length on a piece of paper.Measure the length of segment with the help of Straightedge.

→Now if it is a number divisible by 3,with the help of compass divide the length of segment by 3 and by placing the compass on the straightedge open the compass starting from 0 up to that length.

→If the number is not divisible by 3, round the number to nearest rational number.

→And then Mark arc with the help of Compass from starting of line segment the length being equal to the number obtained after dividing by 3,and after obtaining the first point taking the same width mark second arc from the point obtained.

This is required trisected line segment.

⇒The Statement is True which is we can trisect a line segment using only a straightedge and a compass.

Answer:

True

Step-by-step explanation:

Just did the test :)

Answer:

Assuming your asking what is 4.82 hours to minutes, the answer to this is 289.2 minutes

Answer:

40 students play all three games .

Step-by-step explanation:

You have universal and it says everyone likes all three games so your union is same as universal and there is no complement or any one who didn't like any games so use formule of universal = n A + n B + n C - n only interaction or who likes any two .Solve it and you will get your answer

Answer:

156 sq in

Step-by-step explanation:

If you have a rectangle measuring 13 inches by 12 inches, you will consider the side with 13 inches as the length of the rectangle and the one with 12 inches as the width of the rectangle.

The area of a rectangle is obtained by multiplying the length by the width... so, you'll get:

A = 13 in x 12 in = 156 square inches

Answer:

the first option

a = -2

b = 3

Step-by-step explanation:

See photo attached. (: