If Elon and Jeff work together, they can finish the work in 3 hours. If Jeff works together with Bruce, they can make this work done in 6 hours. Elon and Bruce can finish this work in 4 hours. How much time would it take to finish the work if all three worked together?

The equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)

Given a linear function that contains the coordinate point on its line (5, 7) and (9, 11)

The equation of its reciprocal can be determine by finding the equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)

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The information given about the probability shows that the cardinality of D is 18.

From the complete information, the number of red-colored cards is 26.

Also, the number of red-colored number cards will be 18.

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

Here, the cardinality of set D is 18.

Here is the complete question:

Take a deck of playing cards. Form following sets out of those:

A = Set of Face Cards

B = Set of Red Coloured Face cards

C = Set of Black Coloured Face Cards

D = Set of Red Coloured Number Cards

Find the Cardinality of set D

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The [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the series is evidently

[tex]\dfrac{2n-1}{(2n-1)!} = \dfrac{2n-1}{(2n-1)(2n-2)!} = \dfrac1{(2n-2)!}[/tex]

By the ratio test, the infinite series converges, since

[tex]\displaystyle \lim_{n\to\infty} \left| \frac{\frac1{(2(n+1)-2)!}}{\frac1{(2n-2)!}}\right| = \lim_{n\to\infty} \frac{(2n-2)!}{(2n)!} = \lim_{n\to\infty} \frac1{2n(2n-1)} = 0 < 1[/tex]

Answer: 28.78

Step-by-step explanation:

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}\\\\ \sin A=\frac{a \sin B}{b}\\\\\sin A=\frac{12 \sin 37^{\circ}}{15}\\\\\sin A=0.481452...\\\\A \approx 28.78^{\circ}, 151.21^{\circ}[/tex]

However, we disregard the second case, giving 28.78 degrees.

In the given diagram, the value of x is 15

From the question, we are to determine the value of x

From one of the circle theorems, we have that

Opposite angles of a cyclic quadrilateral are supplementary.

Thus, in the diagram

5x + 7x = 180°

12x = 180°

x = 180°/12

x = 15

Hence, the value of x is 15

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(-∞,8) is interval is the solution to set 0.35x – 4.8 < 5.2 – 0.9x.

0.35x - 4.8 < 5.2 - 0.9x

Adding 0.9x to both sides of equation.

0.35x - 4.8 + 0.9x < 5.2 - 0.9x + 0.9x

1.25x - 4.8 < 5.2

Adding 4.8 to both sides of equation.

1.25x - 4.8 + 4.8< 5.2 + 4.8

1.25x < 10

Dividing both sides of equation by 1.25

x < [tex]\frac{10}{1.25}[/tex]

Hence x < 8

Thus, (-∞,8) interval is the solution to given set 0.35x – 4.8 < 5.2 – 0.9x.

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Answer:

3

Step-by-step explanation:

If we write it out, the equation will be 3x-5/7 = 4/7. So first, we can multiply 7 by both sides to get 3x - 5 = 4. Next, we can add 5 to both sides to get 3x = 9. Lastly, we'll divide 3 by both sides to get x = 3.

Answer:

f is sometimes positive and sometimes negative on the interval

Step-by-step explanation:

So if you were to expand out the x's you would have x^2 * x * x * x which will result in x^5. and because the leading coefficient is positive, it will be going towards positive infinity as x goes towards positive infinity, and because the degree is odd the end behaviors will be opposite, so as x goes towards negative infinity the value of f(x) will be going towards negative infinity. One other thing to note is that because x^2 technically is two zeroes, with the same value, the zero at x=0 has a multiplicity of 2, meaning that it will not cross the x-axis, but rather have a turning point, once it intersects the x-axis, because the zero has an even multiplicity. Given this information we can draw a graph. So as you can see in the graph, it will sometimes be negative and sometimes positive

Answer:

62

Step-by-step explanation:

1. To find the total area, we must find the area of the three individual gardens and sum them together

2. Since the gardens are square, the area is equal to the side length squared

3. Therefore, square the sides and sum:

3^2 = 9

7^2 = 49

2^2 = 4

4+9+49 = 62

The time when movie finished was 21 : 38.

It is given that Theodore started watching movie at 19:30 and length of movie was 1 hour and 56 minutes.

We have to find the time when the movie finished if there was a break of 12 minutes also between movie.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations and the symbols are called variables.

As per the question ;

Theodore started watching movie at 19:30.

The length of movie = 1 hour and 56 minutes

Break = 12 minutes

So ;

Total length of running of movie = 2 hours and 8 minutes

The time when movie finished will be ;

= 19 :30 + 2:08

= 21 : 38

Thus , the time when movie finished was 21 : 38.

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Answer:

===================

a) Use the distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates and calculate:

[tex]d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]

The distance is AB = 10 units

b) Use midpoint formula and find x and y- coordinates of this point:

[tex]x= \cfrac{x_1+x_2}{2}[/tex]    and    [tex]y= \cfrac{y_1+y_2}{2}[/tex]

Substitute coordinates and find the midpoint:

[tex]x= \cfrac{-1+5}{2} =2[/tex]  and  [tex]y= \cfrac{10+2}{2}=6[/tex]

The midpoint is (2, 6)

Answer:

Length of line segment AB = 10 units

Midpoint of line segment AB = (2, 6)

Step-by-step explanation:

To find length, apply the distance formula :

To find the midpoint :

Answer:

104

Step-by-step explanation:

women = 8/8

men = 5/8

all workers = 8/8 + 5/8 = 13/8

extra women workers = 8/8 - 5/8 = 3/8

so...

3/8 = 24

13/8 = x

( cross multiplication method)

3/8 x = 39

x = 104

Hence, there are 104 workers

Answer:

104 workers

Step-by-step explanation:

w = women

m = men = 5/8 w

w - 5/8 w = 24

w = 64      then m = 5/8 * 64 = 40        total = 104

A pair of points which is perpendicular to line L is: D. (3, -5),(-6, 3).

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For points A, we have:

[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-9)}\\\\Slope = \frac{9}{12}[/tex]

Slope = 9/12.

For points B, we have:

[tex]Slope = \frac{6\;-\;(-2)}{-6\;-\;(-9)}\\\\Slope = \frac{8}{-3}[/tex]

Slope = -8/3.

For points C, we have:

[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-5)}\\\\Slope = \frac{9}{8}[/tex]

Slope = 9/8.

For points D, we have:

[tex]Slope = \frac{3\;-\;(-5)}{-6\;-\;3}\\\\Slope = \frac{-8}{9}[/tex]

Slope = -8/9.

In Mathematics, the condition for perpendicularity of two lines is:

m₁ × m₂ = -1

9/8 × 8/9 = -1

Thus, points (3,−5) and (−6,3) are perpendicular to line L.

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Complete Question:

Line L has a slope of 9/8. The line through which of the following pair of points is perpendicular to L?

A. (−9,−6),(3,3)

B. (9,−2),(−6,6)

C. (−5,−6),(3,3)

D. (3,−5),(−6,3)

Step-by-step explanation:

Let assume that

Cost of 1 burger = $ x

Cost of 1 doughnuts = $ y

According to statement, 9 burgers and 1 doughnut cost $ 31.30

[tex]\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}[/tex]

According to statement again, 3 doughnuts and 6 burgers cost $ 26.70

[tex]\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}[/tex]

On substituting the value of y from equation (1), we get

[tex]\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}[/tex]

So,

Cost of 2 burgers = 3.2 × 2 = $ 6.4

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

We need to make linear equations, to solve this problem.

let the cost of each burger be x, and that of each doughnut be y.

[tex] \qquad❖ \: \sf \:9x + y = 31 .30[/tex]

[tex] \qquad❖ \: \sf \:y = (31 . 30 - 9x)[/tex]

put value of y in other equation.

[tex] \qquad❖ \: \sf \:6x + 3y = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x + 3(31.3 - 9x) = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x + 93.90 - 27x = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x - 27x = 26.70 - 93.90[/tex]

[tex] \qquad❖ \: \sf \:27x - 6x = 93.90 - 26.70[/tex]

[tex] \qquad❖ \: \sf \:21x =67 .20[/tex]

[tex] \qquad❖ \: \sf \:x = 67.20 \div 21[/tex]

[tex] \qquad❖ \: \sf \:x = 3.20[/tex]

So, cost of each burger is x = $ 3.20

[tex] \qquad \large \sf {Conclusion} : [/tex]

Therefore, cost of two burgers is :

=========================================================

Explanation:

The floor is a 7 meter by 5 meter rectangle. The perimeter is

P = 2(L+W)

P = 2(7+5)

P = 2(12)

P = 24

The perimeter of the floor is 24 meters.

Multiply this perimeter by the unknown height h to get 24h

This expression represents the lateral surface area. This is the combined wall area. Set this equal to 120 and solve for h.

24h = 120

h = 120/24

h = 5

-----------------

Check:

One pair of walls is 7 meters by 5 meters, giving an area of 7*5 = 35 square meters each. So far that's 2*35 = 70 square meters for these two walls combined.

The other pair of walls is 5 by 5. Each has an area of 5*5 = 25 which doubles to 2*25 = 50

The total wall area is 70+50 = 120 to confirm the answer.

m<A = 28

m<B = 96

m<C = 56

Answer:

Step-by-step explanation:

Amy = x years

Ben = x + 2  (years)

Alice = x - 6 (years)

Answer:

a)

Amy's age is x.

• Ben's age is 2 more than Amy's age.

∴ Ben's age = x + 2

• Alice's age is 6 less than Amy's age.

∴ Alice's age = x - 6

Answer:

p = 3

q = 4

Step-by-step explanation:

Rotation by +90° (clockwise) about the origin:  (x, y) → (y, -x)

Therefore, (p, 4) rotated by +90° about the origin:

(p, 4) → (4, -p)

Therefore:

(4, -p) = (q, -3)

⇒ p = 3

⇒ q = 4

Therefore, (3, 4) is mapped into (4, -3) under a rotation by +90° about the origin.

The surface area of the composite shape is: 315 in.².

Surface area = surface area of square pyramid + surface area of square prism - 2(base area)

Surface area of square pyramid = Area of base + 1/2(perimeter of base × slant height) = 9² + 1/2[4(9) × 7] = 207 in.²

Surface area of square prism = 2a² + 4ah = 2(9²) + 4(9)(3)

Surface area of square prism = 2(9²) + 4(9)(3) = 270 in.².

Base area = 9² = 81 in.².

Surface area of the composite shape = 207 + 270 - 2(81) = 315 in.².

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Answer:

315 in.²

Step-by-step explanation:

Recall:

area of rectangle = length × width

area of triangle = base × height / 2

Base of prism: 9 in. × 9 in. = 81 in.²

4 sides of prism: 4 × 9 in. × 3 in. = 108 in.²

Lateral area of pyramid: 4 × 9 in. × 7 in. / 2 = 126 in.²

Total area = 81 in.² + 108 in.² + 126 in.² = 315 in.²

Answer:

2u^5+5

Step-by-step explanation:

Drop parenthesis and add like terms.

[tex]7u^{5}-5u^{5}+5=2u^{5}+5[/tex]

Hope this helps!

If not, I am sorry.

Answer : I think 3rd is the answer

Answer:

a b f would all be the correct answers

Step-by-step explanation:

Less than looks to the left

Greater than looks right

Anna should use the following equation,

[tex]a_{15} = 4(3)^{15}[/tex]

Equation for Determining the Number of Bacterial Cells

Initially, the count of bacterial cells = 4

It is given that the bacterial cell triples every month.

Hence, the equation for the count of bacterial cells after first month is,

a₁ = 4(3)

This count of 4(3) triples again in the second month.

So, after the second month, the equation for the count of bacterial cells is given by,

a₂ = 4(3)(3) = 4(3)²

Calculating the Count of Bacterial Cells For Each Month

Again, this count triples in the third month.

Therefore, the  equation for the count of bacterial cells after the third month becomes,

a₃ = 4(3)(3)(3) = 4(3)³

This count triples again in the fourth month and this process continues till 15 months.

Hence, the equation for determining the number of bacterial cells comes out to be as follows,

a₁₅ = 4(3)¹⁵

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Answer:

25

Step-by-step explanation:

un carro tiene 4 ruedas, entonces divide 100 por 4

100÷4=25

Answer:

Step-by-step explanation:

Answer:

The answer is

5/2x^2+11/30x+2

[tex] \frac{5}{2}x ^{2} + \frac{11}{30} x + 2[/tex]

Answer:

1. y ax

|
A-------------------------------B

|

------------C---------------------

|

|__________________x ax

for this, your A might be (0,5), B (5,5), C (2,2).

parallel means railroad tracks: same slope, different intercepts.

line AB in this case has a slope of 0, intercept (0,5), so y₁=0x+5 or just y₁=5

the line passing through C also has slope 0, but intercept (0,2), so y₂=0x+2 or just y₂=2

2. perpendicular means that the slopes of two lines multiply out to -1. If line AB has, for example, a slope of 2/3, then the line passing through C would have slope -3/2 (negative reciprocal). To make things easier have either point A or B be on the x or y axis

khan academy has some helpful videos :)

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/perpendicular-lines

The range of a function are the dependent variables for which the function exists. The range of the function will be y ≥ 5

The range of a function are the dependent variables for which the function exists

Given the function below;

f(x) = √x+7 + 5

The function can only exist for values less than or equal to -7 that is x ≤ -7.

Substitute

f(-7) =  √-7+7 + 5

f(-7) = 5

The range of the function will be y ≥ 5

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The volume of the rectangular box is 12 cubic inches

The formula for measuring the volume of a rectangular box is expressed as:

V = lwh

l is the length

w is the width

h is the height

Given the following

l = 2in

w = 3in

h = 2in

Substitute

V = 2* 3 * 2

V = 12 cubic inches

Hence the volume of the rectangular box is 12 cubic inches

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