Euler's formula, V − E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. Solve Euler's formula for V

The expression can be simplified as follows:

a. (-4)(-2) -6(2 - 5) = 26

b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43

c. 23 - (17 - 3.4)² +  6 = -155.96

The expressions can be solved using PEMDAS rule,

P = Parenthesis

E = Exponential

M = Multiplication

D = division

A = addition

S = Subtraction

Hence,

a.

(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26

b.

12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43

c.

23 - (17 - 3.4)² +  6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96

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The value of the variable 'x' shown in th the geometrical figure is equal to 2cm

What is line bisector?

A line bisector divides the line into two equal parts. For a line of length ' L ', the bisector divides the line into two equal parts of length L/2 each.

Given is a geometrical figure in which RS is bisector of AB at point T and RS = 36.

RS bisects AB at point T. Therefore, we can say that T is the mid-point of AB. So, we can write -

AT = TB

25 - 3x = 2y - 5

- 3x - 2y = - 5 - 25

-(3x + 2y) = - 30

3x + 2y = 30             ...[1]

RS = 36

RT + TS = 36

2y - 6 + 18 = 36

2y + 12 = 36

2y = 24

y = 12

Substitute y = 12 in [1], we get -

3x + 2 x 12 = 30

3x + 24 = 30

3x = 6

x = 2

Therefore, the value of x = 2

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The four Quantities are a1 , r, n , [tex]S_{n}[/tex]

What is a Series:

A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

Arithmetic progression

     an = a1 + ( n-1) d

     a1 is the first term

    d =common difference

    an is the nth term

   an can be found out if we know the a1 , d and n

b)  Arithmetic progression

         a1 is the first term

        an is the nth term

        sn is the sum of the n terms of the series

        Sn = n/2 ( a1 + an)

       we can calculate sn if we know a1 , an and n

c)Geometric progression

  an = a1rn-1

a1 is the first term

an is the nth term

r is the common ratio

we can calculate an if we know a1 , r and n

d)Geometric progression

  Sn = a1( 1- rn) / 1 - r

 a1 is the first term

r is the common ratio

sn is the sum of the n terms of the series

If we know a1 , r and n we can calculate [tex]S_{n}[/tex].

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Answer:

n – p

x= –––––

m

Hope that helps! Have a good day :)

Answer:

Below in bold.

Step-by-step explanation:

The time you were driving = distance / average speed

= 1500/42

= 35.714 hours.

Required equation is

t = 42 - d/s          where t = time not driving, d = distance and s = average speed

Time not driving :

t = 42 - 35.714

 = 6.286 hours

That is about 6 hours 17 minutes.

The amount in the savings account after 2 years, 5 years and 8 years is respectively $13.6, $34, $54.4.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't really compound, therefore the creditor only has to pay more interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.

Principle=3400

Rate of interest=0.2

Time period=2, 5 and 8 years

To calculate simple interest I= PRT/100

=> To find the amount in the savings account after 2 years

=(3400×0.2×2)/100

=13.6

So the amount in the savings account after 2 years is $13.6.

=> To find the amount in the savings account after 5 years

=(3400×0.2×5)/100

=34

Therefore the amount in the savings account after 5 years is $34.

=> To find the amount in the savings account after 8 years

=(3400×0.2×8)/100

=54.4

Hence the amount in the savings account after 8 years is $54.4.

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Answer:

2 years: 3413.60 or 3,413.60

5 years: 3434, 3,434.00, 3,434, or 3434.00

8 years: 3454.40 or 3,454.40

(the other persons is wrong)

It should be noted that Zahraa saying that the first division to perform is determining how many whole times 289 divides into 5,437 is incorrect.

It should be noted that based on the information, Zahraa is calculating the quotient of 54,379÷289 and she set up the long division with the numbers in the correct places.

She said that first division to perform is determining how many whole times 289 divides into 5,437. This is incorrect.

It should be noted that the first thing to do is to find the number of times that 28 will go in 54 and then bring the remainder down and solve till she gets the final value.

In this case, 54,379÷289 will be 188 47/289

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The solution of the given equation  x/2 + x/3 = 15 is x = 18

In this question,

We have been given an equation.

x/2 + x/3 =15

We need to find the solution of given equation.

First we simplify the LHS of given equation.

x/2 + x/3

= (3x + 2x) / (2)(3)

= 5x / 6

So given equation  would be,

⇒ x/2 + x/3 = 15

⇒ 5x / 6 = 15

⇒ 5x = (15)(6)

⇒ 5x = 90

⇒ x = 18

We need to check above solution.

Substitute x = 18 in LHS of given equation.

= 18/2 + 18/3

= 9 + 6

= 15

= RHS

Therefore, the solution of the given equation  x/2 + x/3 = 15 is x = 18

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The probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

In this question,

We have been given a standard deck of 52 cards.

Three cards are selected from a standard deck of 52 cards.

Sample space n(S) = 52

We need to find the probability that all three cards are diamonds if neither the first nor the second card is replaced.

We know that, in a standard deck of 52 cards, there are 13 diamond cards.

The probability that the first card is diamond,

P1 = 13/52

The card is not replaced, so the total number of cards in a standard deck = 51

And the number of diamonds = 12

Now the probability that second card would be diamond,

P2 = 12/51

Similarly the probability that the third card is diamond,

P3 = 11/50

So, the probability that all three cards are diamonds if neither the first nor the second card is replaced:

⇒ P = P1 × P2 × P3

⇒ P = 13/52 × 12/51 × 11/50

⇒ P = 0.25 × 0.24 × 0.22

⇒ P = 0.0132

Therefore, the probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

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Myra's distance is increasing as time increases.

Given table showing the time (in minutes) and distance (in miles) :

Time (in minutes)    Distance (in miles)

 0                                        0.0

 2                                        0.4

 4                                        0.8

 6                                        1.2

 8                                        1.6

As we can see from the table, when there is an increase of 2 minutes in time, the distance is increasing by 0.4 miles.

So the distance covered by Myra is increasing with increase in time.

The question is incomplete. Find the complete question below:

The table shows the total distance that Myra runs over different time periods. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0. 0, 0. 4, 0. 8, 1. 2, 1. 6. Which describes Myra's distance as time increases? increasing decreasing zero constant.

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The slope of the line containing (-6,-11) and (-12,-10) is  (-1/6).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .

On substituting the values of variables in equation1, we will get

m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).

As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (-6,-11) and (-12,-10) is  (-1/6).

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The characteristic that justifies each assertion Property of substitution

The substitution property asserts that if a=b, then one can of replacing b in quite an expression or equation.

X Y+20=Y W and X Y+20=D T

then Y W=D T

The replacement property of equality states that "If a variable x is equal towards another variable y, then x may be substituted in place of y in whatsoever equation/expression and y can indeed be substituted throughout the place of x in any equation/expression."

Substitution connects many aspects of mathematics and hence aids in viewing mathematics as an entire discipline.

Three phases are involved in the substitution method: Solve this equation for a single of the variables. Substitute (plug-inin) this equation into a different equation and solve. Replace the value inside this original equation to obtain the equivalent variable.

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Answer:

X€R or x€(-&, +&)......

Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

The term triangular coordinates can refer to at least three related systems of coordinates in the Euclidean plane: a special case of barycentric coordinates for a triangle, also known as a ternary plot or areal coordinates, among other things.

Because this is a right triangle, two of its sides can be found on the axes. Placing the triangle's right angle at the origin will allow the two legs to be parallel to the x- and y-axis.

Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

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Step-by-step explanation:

Hope the pictures will help you

The equation of the circle (x + 5)^2 + y^2 = 18 has a radius of 3√2 and a center located at (-5 , 0).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 5)^2 + y^2 = 18, is in standard form, then

h = -5

k = 0

r = 3√2

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Answer: 6 and 27

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x+8= 4(x+2) and that should be the answer if not then i don't know what to do

The algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

Given

The word phrase

"The quotient of the sum of 2 and a number b and 3"

Sum off 2 and a number b = 2+b

Then the quotient of the sum of 2 and a number b and 3 = [tex]\frac{2+b}{3}[/tex]

Hence ,the algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

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Answer:

384, 576

Step-by-step explanation:

The surface area is

[tex]2(12 \cdot 6+12 \cdot 6+6\cdot 8)=384[/tex]

The volume is

[tex](12)(8)(6)=576[/tex]

The required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

Given that,
Osslyn is thinking of a number, n.
Her first clue is that eight less than two times her number is between two and six (inclusive).
To write a compound inequality that shows the range of numbers that Josslyn might be thinking of.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number be x,
According to the question,
Gusset number = 2x - 8,   where x is between 2 and 8 implies
2 < x < 6

Thus, the required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

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The sum of the given finite series is -1

The given series is:

     [tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]

The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.

Let us expand this summation notation:

n = 1  ⇒ a(1) = (-1)¹ = -1

n = 2  ⇒ a(2) = (-1)² = 1

n = 3  ⇒ a(3) = (-1)³ = -1

We can continue to expand until n = 9, but we can see the pattern. The series can be written as:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]

We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]

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Answer:

  204 °C

Step-by-step explanation:

You want the predicted temperature of a pizza that has cooled for 20 minutes, as predicted by the formula ...

  log(temp) = 2.39 -0.004·time

where temp is in degrees Celsius, and time is in minutes.

Using time = 20 in the formula, we find ...

  log(temp) = 2.39 - 0.004·20 = 2.39 -0.08 = 2.31

Taking the antilog, we find the temperature to be ...

  temp = 10^2.31 ≈ 204.2 . . . . . degrees C

The predicted temperature of the pizza is 204 °C.

Answer:

32,14 minutes

Step-by-step explanation:

5.6 calories per hour = 5.6 x 60 = 336 calories per hour
So in 1 hour, that person will lose 336 calories

To lose only 180 calories time he should walk = 180/336 hour = 180/336 x 60 = 32,14 minutes

We can figure out our answer is in the ballpark by noting that 336/2 = 168

So to lose 168 calories, the person should walk for 1/2 hour so since 180 is slightly greater than 168, the person should walk for slightly more than half-hour

Using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

Given,

The points =  O(-12,0) and P(-8,3)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance [tex]=\sqrt{(-8--12)^{2}+(3-0)^{2} }[/tex]

[tex]=\sqrt{4^{2}+3^{2} } \\=\sqrt{16+9} \\=\sqrt{25}[/tex]

= 5 units

Hence, using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

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The inverse of a function is a mirror image of a graph around y = x thus graph in (A) will be the inverse of a function y = m(x).

The inverse of a function is basically a reverse function or undo of the function.

It means in the inverse function we need to interchange x and y.

Let's consider a function y = 2x + 3

The inverse of y is ⇒ y = (x - 3)/2

Now,

If we draw both graphs, both are mirror images of each other about x = y (as shown below).

Therefore y = m⁻¹(x) will be the mirror image of y = m(x) about y = x.

In option (A) the graph is the only mirror image of graph y = m(x).

Hence "The graph in option (A) shows the inverse of function y = m(x)".

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The given infinite geometric series 150+30+6+ . . . is convergent and the sum is 187.5

The given geometric series is:

  150 + 30 + 6 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 150

a(2) = 30

a(3) = 6

Hence, the common ratio is

   r = a(2) / a(1) = 30/150 = 1/5

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 1/5, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 150 and r = 1/5 into the formula:

S = 150 / (1 - 1/5)

   = 150 / (4/5)

   =  187.5

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Answer:

10

Step-by-step explanation:

First write out the equation: 42 = 12 + 3x

42 - 12 = 12 - 12 + 3x

30 = 3x

30/3 = 3x/3

x = 10

Answer:

y = 4x - 4

Step-by-step explanation:

Slope intercept follows the form y = mx + b

m represents the slope

b represents the y intercept

To find the slope of a table you can find the constant change in y over the constant change in x. The y values 0, 4, 8, 12 are increasing by 4 every point meaning the change in y is 4. The x values 1, 2, 3, 4 are increasing by 1 every point meaning the change in x is 1. Making the slope 4/1 or just 4.

Now use what you know: y = 4x + b to find b, we can use any of the coordinate points to substitute. I'm going to use point (1,0) where 1 is the x value and 0 is the y value.

y = 4x + b

0 = 4(1) + b

Solve for b

b = -4

:)

The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width of the rectangle. The area is 85 yd², hence:

xy = 85

If both the length and the width of the rectangle are doubled:

new length = 2x; new width = 2y

new area = 2x * 2y = 4xy = 4(85) = 340 yd²

The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

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The simplification by combining like terms of 0.5g + g is 1.5g.

According to the given question.

We have an expression 0.5g + g .

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 0.5g + g.

Here 0.5g, and g both are the like terms.

So, we add coeffcients of g to simplify the given expression.

Therefore, the simplification of 0.5g + g  is given by

0.5g + g

= 1.5g

Hence, the simplification by combining like terms of 0.5g + g is 1.5g.

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