for a pendulum with a length of l meters, the time in seconds that it takes the pendulum to swing back and forth is 2L^1/2. how long does it take a pendulum that is 9 meters long to swing back and forth

Answer: The two numbers are $x = 5$ and $y = 7.5$.

Step-by-step explanation:

Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:

$$2y = 3x + 15$$

$$\frac{1}{5}x + \frac{1}{9}y = 10$$

We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get

$$10y = 15x + 75$$

$$9x + y = 90$$

Subtracting these equations, we get

$$8y - 9x = 15$$

Multiplying this equation by 8, we get

$$64y - 72x = 120$$

Adding this equation to 5 times the first equation, we get

$$69y - 72x = 120 + 75$$

$$69y - 72x = 195$$

Dividing both sides by 3, we get

$$23y - 24x = 65$$

Subtracting this equation from 4 times the second equation, we get

$$96y - 36x = 360 - 260$$

$$96y - 36x = 100$$

Dividing both sides by 60, we get

$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$

Substituting the expression for $y$ from the first equation, we get

$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$

This simplifies to

$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$

Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.

Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

The ratio of cats to all animals is 5:14

the ratio of dogs to cats is 9:5

Given-

Cats = 5

Dogs = 9

Total animals = cats+ Dogs

     5+9=14

so  the ratio of cats to all animals  = 5: 14

and dogs to the cats= 9:5

Ratio give the relation between quantities of to identies.

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Answer:

67/153

Step-by-step explanation:

Answer:

the quotient of g and 25 is g/15.

Answer:

7/8

Step-by-step explanation:

Step 1: Count the total number of letters in the word FOOTBALL

There are 8 letters in the word FOOTBALL.

Step 2: Count the number of letters that are not L

There are 7 letters that are not L.

Step 3: Calculate the probability

The probability that the letter chosen is not an L is 7/8.

Step-by-step explanation:

{x : x < 100}

means all numbers smaller than 100. but that includes all negative numbers. so, NO.

{y|y > -0.1}

while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001

so, NO

{x|x in N}

N is the set of all natural numbers. that is the set of all positive integers.

so, YES

{y : 0 < y < 1}

that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.

so, YES

{x|x in Z}

Z is the set of all integer numbers (including the negative ones). so, NO

{y : 3 <= y < 22}

ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.

so, YES.

The unknown angle of the triangle is as follows:

∠BCE =  65 degrees

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, the angle ∠BCE can be found as follows:

∠BAC = 70 degrees

∠ABC = 60 degrees

∠ACB = 180 - 70 - 60

∠ACB = 180 - 130

∠ACB = 50 degrees

Hence, using exterior angle theorem,

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

∠BCD = 60 + 70 = 130 degrees

Hence,

∠BCE = 130 / 2 = 65 degrees

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From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))

We are given the engineers formula as;

F = (¹¹/₃₀₀)d(F - 13)

Where;

F is the strength of the steel in kilopound per square inch.

d is the diameter of the rocker in millimeters.

From the given formula, we can start by;

Multiply both sides by 300 to get;

300F = 11d(F - 13)

Divide both sides by 11(F - 13) to get;

d = 300F/(11(F - 13))

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Answer: 7x+10

Step-by-step explanation:

combine like terms

x+3x+x+2x+2+5+3

7x+10

Answer:

Step-by-step explanation:

Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

First: find the (x) and collect them, put them in the bracket (to ensure the + or -)

(x + 3x + x + 2x) + 2 + 5 + 3

=  7x + 2 + 5 + 3

Then we add up the numbers

= 7x + 10

This is the end result.

x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

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Answer: Her total earnings would be $28+$54=$82.

Step-by-step explanation:

Lori's base salary is calculated by multiplying her hourly rate by the number of hours she works. If Lori works 4 hours on a Tuesday and earns $7/hr, her base salary would be 4*$7=$28.

Lori's tips are calculated as 18% of her food sales. If Lori has $300 of food sales on a Tuesday, her tips would be 18%*$300=$54.

Lori's total earnings for the day would be the sum of her base salary and her tips. In this case, her total earnings would be $28+$54=$82.

Answer: The equation y = 53+2x relates the variables x and y, where x represents the number of days the crew has worked and y represents the total length of the road.

The change per day in the road's length is given by the coefficient of x in the equation, which is 2. Thus, the change per day in the road's length is 2 miles.

The road's length when the crew started working is given by the constant term in the equation, which is 53. Thus, the road's length when the crew started working was 53 miles.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the slopes of the lines parallel and perpendicular to 7x -6y = -3.

The slope is the x-coefficient when the equation is in slope-intercept form:

  y = mx +b

Solving for y gives ...

  -6y = -7x -3

  y = 7/6x +1/2 . . . . . divide by -6

The slope of the given line is 7/6.

A parallel line will have the same slope: 7/6.

A perpendicular line will have opposite reciprocal slope: -6/7.

Answer:

( 7,-1 )

Step-by-step explanation:

Answer: 22 times

Step-by-step explanation: divide 137 by 6

The rate of change of the end points of the line is 32/10

What is slope?

Slope is defined as the rate of change of y with respect to x.  Also it is defined as increase in y over increase in x or decrease in y over decrease in x

slope is denoted by the formula = Δy/Δx

Where Δy = change in y

Δx= change in x

The given points are (-9, -2) and (5, 119/5)

The slope of the end points   (119/5 + 21)/(5+9)

The slope is (119+105)/5

M= 44.8/14

The slope is 3.2 = 32/10

Therefore the rate of change is given as 32/10

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The values of A and B are 2 and 4 respectively.

Given is the equation as -

(x + A)² - 3 = x² + 4x + B

We can write the given equation as -

(x + A)² - 3 = x² + 4x + B

x² + A² + 2Ax = x² + 4x + B

A² + 2Ax = 4x + B

A² + 2Ax = B + 4x

Equating both sides, we get -

A² = B

and

2A = 4

A = 2

Then B will be equivalent to 4.

B = 4

Therefore, the values of A and B are 2 and 4 respectively.

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The Value for x and y as follow:

A) x=2 and y=-8

B) x = -2 and y = 5

C) x = -9/4 and y= -5/2

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Given:

A) 9x- 2y = 34...............(1)

5x+ 2y = -6..............(2)

Adding equation (1) and (2) we get

9x -2y = 34

5x + 2y = -6

_____________

14x = 28

x= 28/14

x= 2

and, 5x +2y= -6

5(2) + 2y= -6

2y = -6 -10

y = -8

B) x+ 6y = 28.....................(3)

2x -3y = -19................(4)

Multiply equation (2) by 2 we get

4x - 6y = -38.......................(5)

Adding equation (3) and (5), we get

x + 6y = 28

4x- 6y = -38

___________

5x = -10

x= -2

and, x+ 6y= 28

-2 +6y= 28

6y= 30

y=5

C) 8x -6y = -3................(6)

6x -5y = -1......................(7)

Multiply equation (6) by 5 and equation by (6), we get

40x - 30 y = -15

36 x - 30y = -6

-       +           +

____________

4x = -9

x= -9/4

and, 8x - 6y = -3

8(-9/4) - 6y = -3

-18 - 6y= -3

-6y = 15

y = -5/2

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By solving an expression we will see that the total cost for the tickets is $192.

We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:

6*2 = 12 adults in total.

6*4 = 24 children in total.

We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:

12*$8 + 24*$4

That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.

The total cost is then:

12*$8 + 24*$4 = $192

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[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]

A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The line going through the origin equation is also y=2x.

A line that crosses the origin is symbolized by the equation y=mx.

Also, y=2x satisfies the point (0,0)

A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

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Answer:

$50.25

Step-by-step explanation:

7.5% as a decimal is 0.075.

So, the fee is [tex](0.075)(670)=\$50.25[/tex].

Step-by-step explanation:

hope this is right hehe.....

Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

The average like for each minute of the video that he uploads will be 2,000 likes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The total number of likes is calculated as,

Like / View = 1 / 5

Like / 9,000,000 = 1 / 5

Like = 1,800,000

The total number of minutes is calculated as,

Time length = (9,000,000 / 150,000) x 15

Time length = 60 x 15

Time length = 900 minutes

The average like for each minute of the video that he uploads will be given as,

⇒ 1,800,000 / 900

⇒ 2,000

The average like for each minute of the video that he uploads will be 2,000 likes.

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The complete question is given below.

Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1: 5. Dagogo wants to reach a total of 9,000,000 views on his channel.

Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of the video he uploads?

Using equations, the weights of the four fish are as follows:

Equations are mathematical statements showing the equality of two mathematical expressions.

Using the equation sign (=), equations depict that expressions are equal or equivalent.

The total weight of the four fish = 1,032

Let the weight of the Amberjack = x

Weight of the Tarpon = 2x

Weight of the White Marlin = 4x (2 x 2x)

Weight of the Tuna = 5x

x + 2x + 4x + 5x = 1,032

12x = 1,032

x = 86

Amberjack = 86 pounds (x)

Tarpon = 172 pounds (2x)

White Marlin = 344 pounds (4x)

Tuna = 430 pounds (5x)

Total weight = 1,032 pounds (86 + 172 + 344 + 430)

Thus, we solved the weight of each fish using equations.

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How much did each fish weigh?

Answer:

4/15

Step-by-step explanation:

find common denominators, which is 15

multiply 2/3 by 5 and and 2/5 by 3

2 x 5 = 10 and

3 x 5 = 15

10/15

2 x 3 = 6 and

5 x 3 = 15

6/15

subtract numerators

10 - 6

 15

= 4/15

Step-by-step explanation:

that means the current value of $117,000 is 100 - 35 = 65% of the original price.

65% = $117,000

1% = 65%/65 = 117000/65 = $1,800

100% = 1%×100 = 1800×100 = $180,000

the original (100%) purchase value was $180,000.