FG is perpendicular to DM, if DF = 4R, FM = r + 21, and DF = FM, what is the value of R?

Step-by-step explanation:

use fog

3(1/3x-3)+9

=x

use gof

1/3(3x+9)-3

=x

we can see that both results give us x hence they are inverse

Answer: -4/7

Step-by-step explanation:

the formula for the slope is rise/run

or (y-y1)/(x-x1)

we can apply this concept like this:

7-(-7)=7+7=14

-4-4=-8

since -8 is the rise and 14 is the run, the slope is -8/14

simplify to -4/7

Answer:

9

Step-by-step explanation:

because 8 gallons of lemonade will stand on charge $1.00 will add and answer will be 9

Answer:

the gcf of 41 and 48 would be 1

Answer: 1

Step-by-step explanation:

41      48

 /\       /\

1 * 41  1 * 48

If we assume that I = E(R + r), then I/I = R/E + r/E​.

The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.

Here, we are given that I = E/(R + r)

Taking reciprocals of both sides we get-

Reciprocal of I will be- 1/I

Reciprocal of E/(R + r) will be- (R + r)/ E

Thus,

1/I = (R + r)/ E

Simplifying the equation further, we get-

1/I = R/E + r/E

Hence, proved

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Taking into account the definition of a system of linear equations, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{xa + xb=47} \atop {4xa + 5xb=200}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable xa from the first equation, you obtain:

xa= 47 - xb

Substituting this expression in the second equation you get:

4×(47 -xb) + 5xb= 200

Solving:

4×47 - 4xb + 5xb= 200

188 - 4xb + 5xb= 200

- 4xb + 5xb= 200 - 188

xb= 12

Remembering that xa= 47 - xb. you get: xa=47 - 12 → xa= 35

Finally, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

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If a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40, then the fan expects the red team to win 9 matches less than the blue team in a season of 180 games.

As per the question statement, based on the records for the past several​ seasons, a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40.

We are required to calculate the number of games, the fan expects the red team to win, lesser than the blue team in a season of 180 games.

As per the probability record, maximum number of games, the fan believes that the blue team can win all over the season of 180 games = [tex](0.40*180)=(\frac{40}{100}*180)=(4*18)=72.\\[/tex]

Similarly, maximum number of games, the fan believes that the red team can win all over the season of 180 games = [tex](0.35*180)=(\frac{35}{100}*180)=(7*9)=63.\\[/tex]

Hence, the fan expects the red team to win [tex][(72-63)=9][/tex] matches less than the blue team in a season of 180 games.

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Answer:

(2,3)

Step-by-step explanation:

[tex]y=(2)^{2}-1=4-1=3[/tex]

when x = 2, y = 3

Hope this helps

If a > b then;

a + -b = a positive number

If b > a then;

a + -b = a negative number

If both addends are positive or if the positive addend has a greater absolute value than the negative addend, the sum will be positive. If both addends are negative or if the negative addend has a greater absolute value than the positive addend, the sum will be negative.

Answer:

6

Step-by-step explanation:

ya it of course sachi ta

Answer:

False.

Step-by-step explanation:

Whole numbers can be described as the integers greater than and including zero. 56 has no fractional or decimal part, and is positive, so it is a whole number and an integer!

Answer:

0.43repeating

Step-by-step explanation:

You simply divide 30 by 13, and you get 0.43333333333333333

3 is repeating

Answer:

10

Step-by-step explanation:

Ordered pairs are listed in this format: (x,y).

In the pair (10,5):

10 = x

and 5 = y

Answer:

In an ordered pair you will find (#,#) number one equals x and number two is y. So the answer is 10.

Step-by-step explanation:

(x,y)

The 95% confidence interval for p is (0.333, 0.480).

If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.

The formula for calculating the confidence interval is expressed as shown below;

CI = p±Z * √p(1-p)/n±0.5/n

Where Z is the z-score at 95% confidence

p is the sample proportion

n is the sample size

Given that n = 144, p = 0.7 and z-score at 95%  

CI = 1.645 (from z table)

Now Substituting this values;

CI = p ± 1.645*√0.7(1-0.4)/144 ±0.5/n

CI = 0.4 ± 1.645*√0.7(0.6)/144 ± 0.5/144

CI = 0.4 ±1.645 * √0.24/144 ± 0.00347

CI = 0.4 ±1.645 * 0.04087± 0.00347

CI = 0.4±0.06723±0.00347

CI =(0.333, 0.480)

Hence, The 95% confidence interval for p is (0.333, 0.480).

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Answer:

3.1kg

Step-by-step explanation:

4.7+5.6+6.4+2.8+3.5+4.4+4.5 = 31.9

4.375 x 8 = 35

35 - 31.9 = 3.1

The least natural number that has exactly 6 factors and is not divisible by 2 is 75.

It should be noted the factors of 75 include 1, 3, 5, 15, 25, and 75.

Therefore, it should be noted that 2 isn't among the factors based on the information given in the question.

Therefore, the least natural number that has exactly 6 factors and is not divisible by 2 is 75.

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Answer:a

a

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

According to the given question.

We have a equation of a line y-3= 4(x+8).

Here, we have to find the slope of a line y-3= 4(x+8) and a point on the line.

Since we know that, the equation of a lines through a point (x1, y1) is given by y - y1  = m(x - x1), where m is the slope of the line.

And the equation of slope intercept form for a line is y = mx + c.

So, compare the given equation of line y-3= 4(x+8) with the standard equation of line y - y1  = m(x - x1)  which passes through the point (x1, y1), we get

point ( -8, 3) on line y-3= 4(x+8).

Now, the slope intercept form of the line y-3= 4(x+8) is

y - 3 = 4x + 32

⇒ y = 4x + 32 + 3

⇒ y = 4x + 35

Thereofore, the slope of the line y-3= 4(x+8) is  4.

Hence, the  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

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Answer:

it cannot be simplified anymore

Answer:

0.648148

Step-by-step explanation:

it is already in its simplest form but in decimal it is 0.648148(rounded up to six decimal places.

Answer:

-1/9

Step-by-step explanation:

Using Descartes's Rule of Signs:

There are four positive real zeros P can have.

There are zero negative real zeros P can have.

Descartes' rule of sign is used to determine the number of positive and negative real zeros of a polynomial function.

We have,

P(x) = 2[tex]x^{4}[/tex] - 7x³ + x² - 18x + 3

We have to look at the sign of the coefficient

Here,

  2[tex]x^{4}[/tex] - 7x³  +  x²  -  18x + 3

(+)---(-)(-)---(+)(+)--(-)(-)---(+)

There are 4 variations so there are 4 positive real zeroes.

For finding negative real zeroes we Put x = -x.

P(-x) =  2[tex]x^{4}[/tex] + 7x³ + x² + 18x + 3

   2[tex]x^{4}[/tex]  +  7x³  +  x²  +  18x  +  3

(+)---(+)(+)----(+)(+)--(+)(+)-- --(+)

There are no variations so there are zero negative real zeroes.

Thus,

a) Using Descartes's Rule of Signs, we know that there are four positive real zeros P can have.

b) Using Descartes's Rule of Signs, we know that there are zero negative real zeros P can have.

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Complex fraction 4²/₃ + 1/3 – 4¹/₃ = 2/3

A fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.

Some steps to solve a fraction -

Step 1: Write the factors of numerator and denominator.

Step 2: Determine the highest common factor of numerator and denominator.

Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.

For example -

4²/₃ + 1/3 – 4¹/₃

= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3

= 14/3 + 1/3 – 13/3

= (14 + 1 - 13)/3

= (15 - 13)/3

= 2/3

Hence , in the mathematics problem can be solved by using the fractions.

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Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

Answer: 5/8 + 3/4 = 11/8 = 1 3/8 = 1.375

Step-by-step explanation:5/8+ 3/4= 5/8+ 3 · 2/4 · 2 = 5/8+ 6/8= 5 + 6/8 = 11/8

Answer: Incorect answer

Step-by-step explanation:

5/8X3/4 =11/8 =1 3/8=1.375

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Step-by-step explanation:

Answer:

Function 3 is less steep.

Step-by-step explanation:

The steepness of a linear function is determined by its coefficient of x.

Since the coefficient of x in [tex]f_3(x)[/tex], 0.5, is smaller than that of [tex]f_1(x)[/tex], 2, function 3 is less steep than function 1.

Significance of the coefficient of x

We can think of the function as an equation of a line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Steepness and value of x

The larger the numerical value of m, the steeper the line is.

Significance of the sign of x

The sign (positive or negative) of m tells us the direction in which the line is sloping towards. A positive m value gives us a line sloping upwards from left to right, while a negative m value gives us a line that is sloping downwards from left to right.

Additional:

For a similar question on the steepness of functions, do check out the following!

Answer:

This is a one to one function

Step-by-step explanation:

From the function, we know that f(x) = x - 7 is a linear graph.

Using horizontal line test

the graph is one to one if the horizontal line only cross the graph at one point

Answer:

{x|x>5}

Explanation:

4(x-3)-2(x-1)>0

4x-12-2x+2>0

2x-10>0

2x>10

x>5