An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?

The equation y = 11x + 1 is a linear equation. All three ordered pairs, (0, 1), (1, 12), and (-1, -10), satisfy this equation.

The equation y = 11x + 1 represents a linear equation. To determine which ordered pairs satisfy this equation, we substitute the x and y values into the equation and check if the equation holds true. Let's check each option:

Based on the calculations, we can see that all three ordered pairs are valid solutions for y = 11x + 1.

Answer:

[tex]P = 0.201[/tex]

Step-by-step explanation:

If the discrete random variable X represents the number of correct Colin responses then X can be represented by a binomial distribution with parameters p, n, x.

In this case p represents the probability that colin gets a correct answer, n represents the number of questions.

So the probability that Colin receives x correct questions is:

[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]

Where:

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

[tex]n=10[/tex]

[tex]x=3[/tex]

[tex]P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}[/tex]

[tex]P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}[/tex]

[tex]P = 0.201[/tex]

I think 5x represents 90 degrees.

5x = 90

x = 90/5

x = 18

ANSWER

[tex]x = 18 \degree[/tex]

EXPLANATION

A semicircle subtends an angle of 90° at the circumference.

From the diagram, the semicircle subtends an angle of (5x)° at the circumference.

We equate this angle to 90° and solve for x.

This implies that,

[tex]5x = 90 \degree[/tex]

Divide both sides by 5.

[tex]x = \frac{90}{5} [/tex]

[tex]x = 18 \degree[/tex]

Answer:

If "m" stands for meters, then thats not possible.

Step-by-step explanation:

if m is meters then i would say 0.075 meters i’m pretty sure

Answer:

2970

Step-by-step explanation:

2700+ 270

270 because that is 10% of 2700

2700 because that is 75 x 36

Answer:

True

Step-by-step explanation:

The numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

A triangle with sides of lengths 20, 21, and 29 is a right triangle.

Three numbers can be the sides of a triangle if the sum of two of them is greater than the third. So, since

20+21 > 29,

20+29 > 21, and

21+29 > 20

Are trivially true, they can be the sides of a triangle.

The given numbers are a Pythagorean triplet and can be the dimensions of a right triangle.

20,21 and 29 is a Pythagorean triplet, since

[tex]20^2+21^2=29^2[/tex]

So you also know that they form a right triangle.

Hence, the numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

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Answer:

59.5

Step-by-step explanation:

The middle number of the number set is 59.5 because the number in between 59 and 60 is 59.5

The median of the data set: 46, 88, 28, 73, 63, 55  is 59.

Arranging in ascending order :  28, 46,55, 63, 73,88,

A number of terms are odd, then the median is the middle number i.e., 59.

⇒(55+63)/2=59

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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The answer is:

The first option,

[tex]y=-\frac{1}{2}x-3;x<-2[/tex]

To answer the question, we need to look for an inequality that fits with the following description:

- Negative slope, since the segment "a" is decreasing.

- x- axis interception at x equal to -6

- One of its point is located at (-2,-2)

- The segment exists from -∞ to -2.

So, checking we have:

Firs option

[tex]y=-\frac{1}{2}x-3[/tex]

With,

[tex]x<-2[/tex]

- Finding the y-axis component when x is equal to -2, we have:

[tex]y=-\frac{1}{2}*(-2)-3\\y=1-3=-2[/tex]

We have that one of the points of the segments is located at (-2,-2)

- Finding the "x" intercept, we have:

[tex]0=-\frac{1}{2}x-3\\\\\frac{1}{2}x=-3\\\\x=2*-3=-6[/tex]

Also, (from the inequality and the graph) we know that, the given segment exists from the negative infinite numbers to -2.

Hence, we can know that the first option meets all the requirements:

[tex]Slope=-\frac{1}{2}[/tex]

[tex]x-axis_{interception}=-6[/tex]

[tex]Point(-2,-2)[/tex]

and from the inequality, we know that the segment exists from -∞ to -2.

Have a nice day!

Answer:  12

Step-by-step explanation:

2/3  = 8/12

1/4 = 3/12

8/12 + 3/12 + 11/12

amy & anna ate 11 and david had 1

Answer:

There were 12 donuts in the box.

Step-by-step explanation:

We are given the following information in the question:

Let x be the number of donuts in the box.

Then, according to the question

Number of donuts eaten by Amy = [tex]\frac{2x}{3}[/tex]

Number of donuts eaten by Anna = [tex]\frac{x}{4}[/tex]

Number of donuts eaten by David = 1

Total number of donuts =

Number of donuts eaten by Amy + Number of donuts eaten by Anna + Number of donuts eaten by David

[tex]\Rightarrow \frac{2x}{3} + \frac{x}{4} + 1 = x[/tex]

Solving the above equation:

[tex]11x + 12 = 12x\\x =12[/tex]

Thus, there were 12 donuts in the box.

ANSWER

y=10

x=5

EXPLANATION

The base angles of an isosceles triangle are equal.

This implies that:

8y-7=73°

Add 7 to both sides:

8y=73+7

8y=80°

y=10°

Interior angles of a triangle sums up to 180°

73+73+6x+4=180

150+6x=180

6x=180-150

6x=30

Divide both sides by 6

x=5

Answer:

C

Step-by-step explanation

The mapping diagram which shows the inverse of R(x) is Option (C).

A function is a special type of relation in which each element of the domain is paired with exactly one element in the range . A mapping diagram shows how the elements are paired. Its like a flow chart for a function, showing the input and output values. A mapping diagram consists of two parallel columns.

To identify the mapping diagram for inverse of a function, we simply just change the values of first set of columns into the second set of columns.

This is because if [tex]f(x) = y[/tex] , then  [tex]f^{-1}(y) = x[/tex]

For the given function R(x) , values are 6,7,8,9 in first column and 9,10,11,12 in the second column . Thus for the inverse function,  6,7,8,9  will be in the second column and 9,10,11,12 will be in the first column.

From the given Options, Option (C) is the correct mapping of inverse of R(x).

Thus, the mapping diagram which shows the inverse of R(x) is Option (C).

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Answer:

the answer on e2020 is 12.

The required answer is,

f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

3f(x) = 3ax² + 3bx + 3c

3f(2) = 12a  + 6b + 3c

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.

Now let the function be,

f(x) = ax² + bx + c

To find,

f(x) + f(x) + f(x)

we have,

f(x) + f(x) + f(x) = (ax² + bx + c) +  (ax² + bx + c) +  (ax² + bx + c)

⇒ f(x) + f(x) + f(x) = 3(ax² + bx + c)

or, f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

Similarly,

3f(x) = 3(ax² + bx + c)

or, 3f(x) = 3ax² + 3bx + 3c

now to find f(2), put x =  2 in f(x). we get,

f(2) = a2² + b2 + c

or, f(2) = 4a + 2b + c

Therefore,

3f(2) = 3(4a + 2b + c)

or, 3f(2) = 12a  + 6b + 3c

hence, the required answer is,

f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

3f(x) = 3ax² + 3bx + 3c

3f(2) = 12a  + 6b + 3c

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Check the picture below.

Answer:

I'd say C Sets 2 and 3 contain outliers.

Step-by-step explanation:

Set 2 has an outlier of 90, while set 3 has an outlier of 40. 40 isn't as much of an outlier as 90 is, so I'm not absolutely sure. Cmakes the most sense though.

Answer: Third option.

Step-by-step explanation:

The standard deviation increases as we have more values that are far away from the mean.

For example, in data set 2, we can see that most of hour points are between 38 and 49, but we also have a point with a value of 90, so we may expect that this data set has a big standard deviation.

The data set 3 is similar, most of our points are between 24 and 31, and we have a value that is on 40, so again we have an outlier that increases the value of the standard deviation.

Noticing it we can conclude that data set 2 and data set 3 have a greater standard deviation than set 1.

The correct option is the third option.

Answer:

10/24 and 15/36, more answers possible

Step-by-step explanation:

if you multiply both the numerator and denominator by the same number, it will always be equivalent to 5/12, as you can simplify it back to that fraction.

5/12, multiply both by two, and you have 10/24

5/12, multiply both by three, and you have 15/36

10/24 and 15/36 are fractions equivalent to the given fraction.

10/24: This is equivalent to 5/12 because it can be reduced to 5/12 by dividing both the numerator and the denominator by 2.

15/36: This is another fraction equivalent to 5/12 since it can be reduced to 5/12 by dividing both the numerator and denominator by 3.

Answer:

4

Step-by-step explanation:

a linear function is

y = ax + b

so, for the first pair of x, y

8.5 = 2a + b

b = 8.5 - 2a

the second pair

15.25 = 5a + b

let's use the substitution information from the first pair :

15.25 = 5a + 8.5 - 2a

6.75 = 3a

a = 2.25

b = 8.5 - 2×2.25 = 8.5 - 4.5 = 4

so, we get as linear function

y = 2.25x + 4

that means the y-intercept (x = 0) is at y = 4

y = 2.25×0 + 4 = 4

The y-intercept of this function will be at (0, 4).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In the table below, x represents miles traveled and y represents the cost to travel by train.

Miles (x)    Cost (y)

   2            8.50

   5           15.25

   8          22.00

  12          31.00

Then the linear equation will be

y - 8.50 = [(31.00 - 8.50) / (12 - 2)] (x - 2)

y - 8.50 = 2.25(x - 2)

y - 8.50 = 2.25x - 4.5

          y = 2.25 + 4

The graph of the equation is given below.

Then the y-intercept of this function will be at (0, 4).

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Answer:

Step-by-step explanation:

[tex]METHOD\ \#1\\\\\text{Put b = 3 to each equation and check equality:}\\\\A.\ 3-24b=75\\L_s=3-24(3)=3-72=-69\\R_s=75\\L_s\neq R_s\\\\B.\ 65+9b=38\\L_s=65+9(3)=65+27=92\\R_s=38\\L_s\neq R_s\\\\C.\ -2b+30=24\\L_s=-2(3)+30=-6+30=24\\R_s=24\\L_s=R_s\\\\D.\ 102b-21=-55\\L_s=102(3)-21=306-21=285\\R_s=-55\\L_s\neq R_s[/tex]

[tex]METHOD\ \#2:\\\\\text{Solve each equation:}\\\\A.\\3-24b=75\qquad\text{subtract 3 from both sides}\\-24b=72\qquad\text{divide both sides by (-24)}\\b=-3\neq3\\\\B.\\65+9b=38\qquad\text{subtract 65 from both sides}\\9b=-27\qquad\text{divide both sides by 9}\\b=-3\neq3\\\\C.\\-2b+30=24\qquad\text{subtract 30 from both sides}\\-2b=-6\qquad\text{divide both sides by (-2)}\\b=3\\\\D.\\102b-21=-55\qquad\text{add 21 to both sides}\\102b=-34\qquad\text{divide both sides by 102}\\b=-\frac{1}{3}[/tex]

x=1/4 because, 1/4 will multiply with 4 to cancel out to have an exponent of 1

[tex]\bf (9^4)^{?}=9^1\implies 9^{4\cdot ?}=9^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{4?=1\implies ?=\cfrac{1}{4}}[/tex]

Answer:

36g + 81

Step-by-step explanation:

9 is your multiplier.  Multiply each of the two terms inside the parentheses by this 9, one at a time:  

36g + 81

Answer:

9 (4g + 9) = 9*(4g) + 9* (9) = 36g + 81

Step-by-step explanation:

Answer:

8/15

Step-by-step explanation:

Well to add fractions you have to have the same denominator so you would multiply your 1/3 by 5 to be 5/15 then you can add.

3/15 + 5/15 = 8/15

1 over 3 would change to 5 over 15 to make the denominators equal then you add the numerators and you get 8 over 15

Answer:

18x-30-10x-35=25

8x-65=25

8x-65+65=25+65

8x=90

Divide by 8 for 8x and 90

x=90/8 or 45/4 or 11 1/4 ( Answers)

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We know that the following are the coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, we are to find the coordinates of its image?

If a point is reflected through y-axis, the sign of the x coordinate is changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

Answer:

B [tex]log_{2} 42[/tex]

Step-by-step explanation:

Due to the product rule of logarithms, we can combine them as such. Then it will simplify to our answer.

[tex]log_{2} 6+log_{2} 7=log_{2} (6*7)\\\\log_{2} 42[/tex]

The single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex]  is [tex]log_{2} 42[/tex]. The correct answer is option B.

To express [tex]log_2^{6} + log_2^{7}[/tex] as a single logarithm, we can use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

Simplifying the expression within the logarithm, we get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex]. The correct answer is option B.

Logarithms are used to simplify complex mathematical calculations involving large numbers. They allow us to break down a number into its constituent parts and perform operations on those parts more easily. In this problem, we are asked to express the sum of two logarithms as a single logarithm. To do this, we use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

We simplify the expression on the right-hand side of the equation to get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex].

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Answer:

x = (8.75 - 2 5/6) / 7.1 + (4 1/2 + 2 2/3) / 4 3/10

x = 2.5

Answer:

2  1/2

Step-by-step explanation:

Order of operations rules require that we do any work within parentheses first.  Thus, calculate (8.75 - 2  5/6); it is (5  11/12).  Next, calculate (4  1/2 + 2  2/3); it is ( 7  1/6).  So what we have now looks like:

(5  11/12) / 7.1  + (7  1/6) / (43/10)    (Note that 4  3/10 = 43/10)

Performing the two indicated divisions, we get:

5/6 + 1  2/3.

Since the LCD here is 6, we add:    5/6 + 1  4/6, which comes out to

                                                          1  9/6, or 1 + 1  1/2, or    2  1/2 (answer)

Step-by-step explanation:

[tex]8^{2x-4}=8^{5x+1}\iff2x-4=5x+1\qquad\text{add 4 to both sides}\\\\2x=5x+5\qquad\text{subtract 5x from both sides}\\\\-3x=5\qquad\text{divide both sides by (-3)}\\\\\boxed{x=-\dfrac{5}{3}}\\\\================================[/tex]

[tex]2^{x+6}=16^{3x+4}\\\\2^{x+6}=(2^4)^{3x+4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{x+6}=2^{4(3x+4)}\iff x+6=4(3x+4)\qquad\text{use the distributive property}\\\\x+6=(4)(3x)+(4)(4)\\\\x+6=12x+16\qquad\text{subtract 6 from both sides}\\\\x=12x+10\qquad\text{subtract 12x from both sides}\\\\-11x=10\qquad\text{divide both sides by (-11)}\\\\\boxed{x=-\dfrac{10}{11}}\\\\================================[/tex]

[tex]\left(\dfrac{1}{2}\right)^x=2^{x+3}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^{-1})^x=2^{x+3}\\\\2^{-x}=2^{x+3}\iff -x=x+3\qquad\text{subtract x from both sides}\\\\-2x=3\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{3}{2}}\\\\================================[/tex]

[tex]36^{2x}=216^{3x-1}\\\\(6^2)^{2x}=(6^3)^{3x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\6^{(2)(2x)}=2^{3(3x-1)}\iff(2)(2x)=3(3x-1)\qquad\text{use the distributive property}\\\\4x=(3)(3x)+(3)(-1)\\\\4x=9x-3\qquad\text{subtract 9x from both sides}\\\\-5x=-3\qquad\text{divide both sides by (-5)}\\\\\boxed{x=\dfrac{3}{5}}\\\\================================[/tex]

[tex]p\%=\dfrac{p}{100}\\\\100\%-12.6\%=87.4\%=\dfrac{87.4}{100}=0.874\\\\8\ years\to(0.874)^4\approx0.584\to58.4\%\\\\\text{After 8 years, the car will be worth 58.4}\%\ \text{of the initial price.}[/tex]

Answer:

7:2:8.

Step-by-step explanation:

The income form the raffle = £350

Income from the quiz = 14*4 = £56 + £44 = £100

Income from membership fees = 20*20 = £400.

The ratio of raffle : quiz : fees

= 350:100:400

Dividing each number by 50:

= 7:2:8   in simplest form.

Answer:

A ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Step-by-step explanation:

Given : The table shows a darts club's income in 2017 from a raffle, a quiz and membership fees.

To find : Express as a ratio the income from the raffle to the income from the quiz to the income from membership fees ?

Solution :

The raffle amount is £350.

Quiz, entry fees is 14 at £4 each and refreshment is £44.

The quiz amount is £[tex]14\times 4[/tex]+£44=£56+£44=£100

Membership fees=20 at £20 each.

The membership amount is £[tex]20\times 20[/tex]=£400

Now, the ratio of income from the raffle to the income from the quiz to the income from membership fees is

The ratio of raffle : quiz : membership

[tex]R= 350:100:400\\\\R= 35:10:40\\\\R=7:2:8[/tex]

Therefore, a ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

I'm pretty sure that question 1 is 254.5 m but i'm not entirely sure about my answer to question 2. sorry i couldn't be more help to you :( good luck!

The answer is:

The correct options are:

A)  [tex]y-2=-0.75(x-3)[/tex]

and

D) [tex]y-5=-0.75(x+1)[/tex]

To find the correct answers, we need to find a equation that meet the following charactheristics:

From the graph we can se that the function:

- Has a negative slope (is decreasing)

- Pass throught the points: (-1,5) and (3,2)

Now, discarding from the given options, we have:

[tex]y-2=-0.75(x-3)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-2=-0.75(-1-3)[/tex]

[tex]3=-0.75(-4)[/tex]

[tex]3=3[/tex]

Evaluating (3,2):

[tex]2-2=-0.75(3-3)[/tex]

[tex]0=-0.75(0)[/tex]

[tex]0=0[/tex]

We have that the equation is satisfied, so,  the line pass  through the given points.

Hence, we have that the equation A is an equation of the line shown.

[tex]y-5=-0.75(x-1)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-5=-0.75(-1-1)[/tex]

[tex]0=-3.5[/tex]

Hence, we have that since the equation is not satisfied, the line shown is not passing  through the point (-1,5) meaning that the equation is not an equation of the line shown.

So,  we have that the equation B is not equation of the line shown.

[tex]y-3=-0.75(x-2)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-3=-0.75(-1-2)[/tex]

[tex]2=-0.75(-3)[/tex]

[tex]2=2.25[/tex]

Hence, we have that since the equation is not satisfied, the line shown is not passing  through the point (-1,5) meaning that the equation is not an equation of the line shown.

So, we have that the equation B is not equation of the line shown.

(assuming you committed a mistake writing the options and the equality sign is missing)

[tex]y-5=-0.75(x+1)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-5=-0.75(-1+1)[/tex]

[tex]0=-0.75(0)[/tex]

[tex]0=0[/tex]

Evaluating (3,2)

[tex]2-5=-0.75(3+1)[/tex]

[tex]-3=-0.75(4)[/tex]

[tex]-3=-3[/tex]

We have that the equation is satisfied, so,  the line pass  through the given points.

Hence, we have that the equation B is an equation of the line shown.

Finally, we have that the correct options are:

A)  [tex]y-2=-0.75(x-3)[/tex]

and

D) [tex]y-5=-0.75(x+1)[/tex]

Have a nice day!

Answer:

The answer is 48pi

Step-by-step explanation:

what you have to do is you have to do 8*6=48 and there you go your answer

Answer:

48pi

Step-by-step explanation: