The bedroom of our house is 1,200 cubic meters. We know there are 3.4 x 10⁹ particles of dust per cubic meter. Write how many particles of dust are present in the bedroom of our house.

Answer:Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Step-by-step explanation:

Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Answer:

Median

Step-by-step explanation:

The best measure of center in this case would be the median, as the presence of a few outliers (first-graders who were behind in language acquisition) would greatly affect the mean, while the median would provide a better representation of the typical vocabulary knowledge of first-graders in the group.

The required solution of the given system of equations is x = 5 and y = -1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x+4y=8 - - - - - (1)

x-4y=4 - - - - (2)

Put x from equation 2 to equation 1
12y + 12 + 4y = 8
16y = -4
y = -1/4

Now,
Put y in equation 2
x - 4 {1/4} = 4

x = 5

Thus, the required solution of the given system of equations is x = 5 and y = -1/4.

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The equation of the line that runs through the point (0,-1) and (1,2) in slope-intercept form is y = 3x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the diagram, the line runs through the point (0,-1) and (1,2).

First, we determine the slope of the line

Slope m = change in y / change in x

Slope m = (2 - (-1)) / (1 - 0)

Slope m = (2 + 1) / (1 - 0)

Slope m = 3/1

Slope m = 3

Next, plug the slope m = 3 and point (0,-1) into the point slope formula.

y - y₁ = m( x - x₁ )

y - (-1) = 3( x - 0 )

y + 1 = 3x - 0

y + 1 = 3x

Subtract 1 from both sides

y + 1 - 1 = 3x -1

y = 3x - 1

Therefore, the equation of the line is y = 3x - 1.

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If Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. her boat speed in still water is;3 km/h.

Let's x represent the  Jane's boat speed in still water

Upstream, her speed was x - 2 km/h.

Downstream, her speed was x + 2 km/h.

Let's d represent the distance between the start and end point

Let the  time it takes to cover d at a speed of x - 2 km/h=  30 min.

Let the  time it takes to cover d at a speed of x + 2 km/h=  10 min.

So we have:

d / (x - 2) = 30 min and

d / (x + 2) = 10 min.

Multiplying both sides of each equation

d * x - 2d = 30 * (x - 2)

d * x + 2d = 10 * (x + 2).

Adding the two equations and solve for x

2d * x = 40 * x + 20

20 * x = 40 * x + 20

20 * x = 60 * x

x= 3 km/h

Therefore Jane's boat speed in still water is 3 km/h.

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Answer: x=3

Step-by-step explanation:

3(x+6)-10=17

3x+18-10=17

3x+8=17

3x=17-8

3x=9

x=3

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

The equation of the horizontal asymptote of f(x) is given as follows:

x = 5/4.

The rational function f(x) in the context of this problem is defined as follows:

f(x) = (-4x² + 54x - 47)/(4x - 5).

The horizontal asymptote of a function happens at a value of x which is outside the function's domain.

For a rational function, the denominator cannot be zero, hence the value of x that represents the horizontal asymptote of f(x) is obtained as follows:

4x - 5 = 0

4x = 5

x = 5/4.

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Answer:

9 and 6

Step-by-step explanation:

7x - x + 9 ← collect like terms

= (7x - x) + 9

= 6x + 9

the constant term is the numeric term, with no variable ( letter) attached

the constant term is + 9

the coefficient of x is the numeric value before x

the coefficient of x is 6

The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the cost of each cappuccino and y represent the cost of each house lattes.

Two cappuccinos and three house lattes was $14.55, hence:

2x + 3y = 14.55   (1)

Also:

One cappuccino and two house lattes was $8.77, hence:

x + 2y = 8.77    (2)

From both equations:

x = 2.79, y = 2.99

The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

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Step-by-step explanation:

If you write down the amount of time Bryant spends sleeping every night, you will see a sequence of numbers between 6 and 9 hours inclusive.

Answer:

70 * 12 = 840

1400 + 840 = 2240

$2,240 monthly

Step-by-step explanation:

Hope it helps! =D

Answer:

2170

Step-by-step explanation:

Write out the first 3 terms:

a 1 = 1400 ← rent in 1st year

a 2 = 1470 ← rent in 2nd year

a 3 = 1540 ← rent in 3rd year

Arithmetic Sequence: d=70

Explicit Formula:

an = a 1+(n−1)d

a 12 = 1400+(12−1)(70)

a 12 = 2170

Answer:

C) AB, AC, AD

Step-by-step explanation:

All of the line segments stem from point A and connect to a point on the circle.

Hope this helped! :)

Answer:

third option

Step-by-step explanation:

the radius of a circle is a line segment from the centre of the circle A to a point on the circumference of the circle.

the circle shown here with centre A has 3 segments to the circle.

AB , AC and AD

Answer:

C

Step-by-step explanation:

Converting 40% into a decimal would be .40

Since you want to find 40% of 35, we would multiply

(35)(.40) = 14

Answer:

To find the GCF of 2^5·5·11 and 2^3·5^2·7, we first prime factorize each number:

2^5·5·11 = 2^5 x 5 x 11

2^3·5^2·7 = 2^3 x 5^2 x 7

Next, we look for the highest power of each prime factor that they both have in common:

2^3 is the highest power of 2 that both numbers have.

5^2 is the highest power of 5 that both numbers have.

So, the GCF of 2^5·5·11 and 2^3·5^2·7 is 2^3 x 5^2 = 180.

Step-by-step explanation:

If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

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the equation of the tangent line to the curve y = 2 sin x at the point (π/6, 1) will be y = √3 x + 0.093.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

y = mx + b

1) m = slope of the tangent line = derivative at the point (pi/6, 1)

Function: y = 2sinx

Derivative: y ' = 2cosx

evaluate at x = pi/6=> y ' = 2cos(pi/6) = √3

2) equation using the slope and the point (pi/6, 1)

y - 1 = √3 ( x - pi/6 )

y = √3 x - √3(pi/6) +1 =√3 x + 0.093

y = √3 x + 0.093

m = √3, b = 0.093

Therefore, y = √3 x + 0.093 will be the equation of the tangent line to the curve y = 2sin x at point (π/6, 1).

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Answer: 3 3/8 or 3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

Answer:

working on a answer hold up

Step-by-step explanation:

The unit rate of Jana's ride is 0.3 Miles per minutes

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The unit rate of Jane's ride is

= 15miles/50minutes

= 0.3miles per minute

therefore the unit rate of Jane's ride is 0.3 miles per minute.

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The rate of increase is 150%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Desk were on sale for $200 the sale is over,

and they have gone back up to the full price of $300.

The rate of increase,

= 300 x 100 / 200

= 150%

Therefore, the rate is 150%.

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Proportionately, if Hayden uses 4 cups of flour and 5 cups of sugar to make cupcakes, he will eat 20 cupcakes.

Proportion refers to the relative size or ratio of one value compared to another quantity.

Proportions are represented as fractional values with decimals, percentages, or fractions.

The quantity of flour for 1 cupcake = 1/5 cups

The quantity of sugar for 1 cupcake = 1/4 cups

The quantity of flour Hayden uses = 4 cups

The number of cupcakes from 4 cups = 20 (4 ÷ 1/5)

The quantity of sugar Hayden uses = 5 cups

The number of cupcakes from 5 cups of sugar = 20 (5 ÷ 1/4)

Thus, according to the proportion of cupcake ingredients to the available quantities of ingredients, Hayden will make and eat 20 cupcakes.

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A cupcake requires 1/5 cup of flour and 1/4 cup of sugar to make.

The greatest number of biscuits Habib can make is 25

From the question, we have the following parameters that can be used in our computation:

Habib has 400 g of butter

150 g of sugar

675g of flour

Factor each number to determine the GCF

So, we have

400 = 2 * 2 * 2 * 2 * 5 * 5

150 = 2 * 3 * 5 * 5

675 = 3 * 3 * 3 * 5 * 5

So, we have

GCF = 5 * 5

Evaluate

GCF = 25

Hence, the number of biscuits is 25

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Answer:

Option B

Step-by-step explanation:

Answer:

6561m^4

Step-by-step explanation:

(9m)^4 =

(9 * m)^4 =

9^4 * m^4 =   ==> distribute the power 4 to 9 and m

6561 * m^4 = ==> simplify

6561m^4

Part 1

E. There is a pair of congruent angles and a pair of congruent right triangles, so the triangles are similar by the AA [tex]\sim[/tex] postulate.

Part 2

Note that 4 ft 6 in = 4.5 ft. Using the fact that corresponding sides of similar triangles have proportional side lengths,

[tex]\frac{x}{14}=\frac{4.5}{4} \implies \boxed{x=15.75 \text{ ft}}[/tex]

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

The length of time it will take Rachel to pay off her credit card balance can be calculated by dividing the outstanding balance by the monthly payment amount and then adding the number of months needed to pay off the balance.

Balance = $8,281

Monthly payment = $250

Annual interest rate = 16%

To calculate the length of time it will take to pay off the balance, we would first need to calculate the monthly interest rate, which can be done by dividing the annual interest rate by 12:

Monthly interest rate = 16% / 12 = 1.33%

Next, we can calculate the monthly payment amount, including the interest:

Monthly payment amount = $250 + ($8,281 * 1.33%)

By continually subtracting the monthly payment amount from the balance and adding the monthly interest, we can determine the length of time it will take to pay off the balance.

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

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The total charge for the month is given as follows:

$123.93.

The total charge for the month is obtained applying the proportions in the context of the problem.

The costs are given as follows:

For a customer with 7 lines, the charges are given as follows:

Hence the total charge is then calculated as follows:

3 x 19.99 + 4 x 15.99 = $123.93.

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Answer: 3 , 4 and 5 are correct options

Step-by-step explanation:

We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.

[tex]50 = w * (3w-5)[/tex]

Expand the multiplication

[tex]50 = 3w^{2}- 5w[/tex]

Subtract 50 from both sides.

[tex]0 = 3w^{2} - 5w - 50[/tex]

We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.

Finally, we can plug this solution into the length formula we found earlier to solve for length.

[tex]l = 3w - 5[/tex]

Plug in the solution to w.

[tex]l = 3(5) - 5[/tex]

Multiply 3 and 5.

[tex]l = 15-5[/tex]

Subtract 5

[tex]l = 10[/tex]

Therefore the width is 5 and the length is 10.