15. Given the following relation {(2, 1), (-4,5), (1,7), (2, -3), (-1,2)), determine if it is a function.
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By  -236 dB approximately the noise is reduced on imparting sound barrier.

Given that, the foreman of a construction team puts up a sound barrier that reduces the intensity of the noise by 50%. Let the intensity of the sound is I and it is reduced 50% then, new intensity of sound will be

new intensity after reduction = I-50% of I = I/2

Now, the Loudness is calculated by using the formula,

L = 10 log I/I₀

now, I = I/2 and I₀ = 10⁻¹² W/m²

So, we have to find out by how many decibels(dB) the noise is reduced after putting a sound barrier.

This will simply be calculated by subtracting the two noise before and after the sound barrier indulgence. Let's proceed to solve accordingly.

L = 10 log I/I₀ - 10 log I/2I₀

= 10(log I/I₀ - log I/2I₀)

By using the logarithmic property, log(a/b) = log a - log b

= 10(log I-log I₀-log I-log2I₀)

= 10(-log I₀ - log2I₀)

= -10(log I₀ + log2I₀)

Now, we know that, I₀ = 10⁻¹² W/m²

Put the value of I₀ and solve accordingly, we get

L = -236 dB approximately

Therefore, L = -236 dB approximately is the required answer.

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The slope is positive for the points (12,3),(-2,-5),(1,15)

The slope of a line is that the quantitative relation of quantity|the quantity|the number} that y will increaseas x will increase some amount.

Slope tells you ways steep a line is, or what quantity y will increaseas x will increase. The slope is constant (the same) anyplace on the road.

One way to think about the slope of a line is by imagining a roof or a side. each roofs and ski slopes may be terribly steep or quite flat. In fact, each ski slopes and roofs, like lines, may be utterly flat (horizontal). you'd ne'er realize a side or a roof that was utterly vertical, however a line may be.

formula of slope for 2 point line =y2-y1/x2-x1

for point (12,3). m=3+1/12 =4/12 =1/3 which is correct.

for point (-2,-5)m=-4/-2=2 which is correct

for point (-3,1) m=2/-3 which is not correct

for point (1,15)m=16/1 which is correct

for point (5,-2)m=-1/5 which is not correct.

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Hence, the complete the point-slope equation of the line through ( − 2 , 6 ) (−2,6) is y = 6 .

We have given two points ( − 2 , 6 )and  (−2,6) .

Using slope formula , we get

m = 6 - 6 / -2 -(-2)

m = 0

Putting m = 0 , x₁ = -2 and y₁ = 6 in equation (1) , we get

 y - 6 = 0

 y = 6

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The simplest form of the expression is determined by solving the fractional exponent.

If an exponent of the base (number) is expressed in a fraction, it is called a fractional exponent. In an expression say x^1/y, 1/y is the fractional exponent. Fractional exponent represents the power and root together.

In the given expression, the base term is -32y^15, while the exponent is 1/5.

Since, (ab)^m=a^mb^m

Hence, (-32y¹⁵)^¹/₅=(-32)^1/5*(y^15)^1/5

When a base number has a negative sign, and the power is an odd number, the negative sign is extracted.

(-32)^1/5*(y^15)^1/5=-(32)^1/5*(y^15)^1/5

Since, (a^m)^n=a^m*n

-(32)^1/5*(y^15)^1/5=-32^1/5y^15*1/5

As 32=2*2*2*2*2=2^5

The expression becomes.

-(2^5)^1/5*(y^15^)1/5

Multiplying the powers,

-(25)^1/5*(y^15)^1/5=-(2^5*1/5)(y^15*1/5)=-2y^3

The simplest form of expression is (-32y¹⁵)^¹/₅ is -2y^3.

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Answer:

Step-by-step explanation:

A=(1/2) x b xh

h=6

A = (1/2) x b x 6

24=3b

b=24/3

b=8

Answer:

Step-by-step explanation:

Step 1: we write 23% in decimal form: 23%=0.23.Step 2: we find the multiplier. Since we're increasing by 23%, we add 0.23 to 1: 1+0.23=1.23.Step 3: we multiply 80 by the multiplier 1.23: 80×1.23=98.4

So that means your answer is 1.23

The components of -5RS are {-20; 65}.

The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy). where V is a vector. These are part of the vectors generated along the axis.

Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).

Due to the trigonometric relationship

cos θ = adjacent side/hypotenuse = vx/V

sin θ = opposite side/hypotenuse = vy/V

where V is the magnitude of vector V.

So, the Component of -5RS is Given by:

-5RS = -5* {Sx - Rx; Sy - Ry} = {2 - (-2); -8 - 5} = -5*{4; -13}

-5RS = {-20; 65}

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log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.

Now,

log(5) - (log (2x)) =1

=> log (5) - [log (2) + log (x)] = 1 (as log(ab) = log(a) + log (b))

=>log (5) - log (2) - log (x) = 1

=> log ([tex]\frac{5}{2}[/tex]) - log (x) = 1

=> 0.3979 - log (x) = 1

=> log (x) = 0.3979 - 1

Since, generally the base of log is 10, raising them to 10

=> [tex]10^{log_{10}x} = 10^{-0.6021}[/tex]

=> x = 0.2499

Hence, log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.

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Answer: anwser is negative 6

Step-by-step explanation:

i hope you get i had it too and got it right if its not they are giving diffrent anwser then

The linear function slope, f(2)=-4, and f(3)=2 the equation for f(x) is y = 6x +6

This is the same as finding the line that goes through the two points (3,2) and (2,-4)

It has slope[tex]\frac{-6}{-1}[/tex] = 6 = [tex]\frac{(-4-2)}{(2-3)}[/tex] = m=6.  slope = rise/run.  or change in y coordinates/change in x coordinates

The y-intercept is given by(2,-4) as 6, b= 6. so plug that into the slope-intercept equation

y= MX + b

y = 6x +6

It's just a coincidence they both happened to = 6. m=b=6

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.  the web change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx. Where “m”  is the slope of a line. So, tan θ to be the slope of a line.

Pick two points on the road and determine their coordinates. Determine the difference in y-coordinates of those two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Whenever the equation of a line is written within the form y = MX + b,  it's called the slope-intercept form of the equation. The m  is the slope of the line. And b  is that the b in the point that is the y-intercept (0, b).  for instance, for the equation y = 3x – 7, the slope is 3,  and therefore the y-intercept is (0, −7).

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It should be noted that 5 groups of 2 hundredths will be 3.2e-9.

It should be noted that the information is simply about finding 5 groups of 2 hundredths.

In this case, this will be illustrated as:

= 5 × 2 hundredths

It should be noted that 2 hundredths simply means 0.02. Therefore, the information is to calculate 0.02 in 5 places. This will be illustrated thus:

= 0.02 × 0.02 × 0.02 × 0.02 × 0.02

= 3.2e-9.

Therefore, it should be noted that 5 groups of 2 hundredths will be 3.2e-9.

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The solutions to the equation (3x - 5)²= 19 are: - [tex]\frac{\sqrt{19} + 5}{3}[/tex] and [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

In this question we have been given an equation that is (3x - 5)²= 19

Now taking square root both sides

(3x - 5)² = 19

3x - 5 = ± [tex]\sqrt{19}[/tex]

Add 5 to both sides to make equation simpler

3x = ± [tex]\sqrt{19}[/tex]+ 5

Divide both sides by 3

x = ±[tex]\frac{\sqrt{19} + 5}{3}[/tex]

Now separating the solutions we get

x = [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

x = - [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

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Solution of log 6-log 3 x = -2 is , x =200

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log 6-log 3 x= -2

using formula of log a - log b, we can write the eq. as

[tex]log \frac{6}{3x} = -2[/tex]

=> [tex]6 / 3x = 10^{ -2}[/tex]

=> [tex]3x = 600[/tex]

=> [tex]x =200[/tex]

Thus solution of log 6-log 3 x=-2 is , x =200

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Answer:

38

Step-by-step explanation:

It is clear that the number of sweets that should be bought so that each child can get either 8 or 9 sweets should be divisible by both 8 and 9

This is called the LCM or least common multiple of 8 and 9
Since 8 and 9 have no divisors in common LCM of 8 and 9 is 72 so 72 is the minimum number of sweets to buy so that there are no leftovers if each child gets 8 or 9 sweets

Let's compute the number of sweets that were bought the first time. Let the number of children be X

Since each child got 8 sweets and 2 were left over, the total of sweets must be 8X + 2

If each child were to get 9 sweets each then there would be 2 sweets short

This can be written as 9X -2 for the total number of sweets

Since these have to be equal,
9X - 2 = 8X + 2

Add 2 to both sides:
9X - 2 + 2 = 8X +2 + 2
9X = 8X + 4

Subtract 8X from both sides
9X - 8X = 8X - 8X + 4
1X = 4
==> X = 4
So number of children is 4

Total number of sweets bought
= 8 x 4 + 2 = 34

or

= 9 x 4 - 2 = 34

Therefore number of extra sweets to be bought = 72 - 34 = 38

Hope that helps and if you don't understand and need more explanation, please post a comment

From the graph of a function over the interval [-4,4]. the following are found for each function

The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.

This would be through the points in the function. We are given  [-4,4]

-4 is the negative side while 4 is the positive. We have to write this out as

-4 ≤ x ≤ 4.

The positive part part of the function is at 4. This is because we can assume a +4 sign.

The negative part is the point -4.

Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively

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Answer:

Step-by-step explanation:

Given

By basic algebra, we can say that: the satellite to run for about 130 days if it requires 15W of power.

Given:

To find: t when P = 15.

Finding:

On substituting the given values in the given formula, by basic algebra, we get:

15 = 50 [tex]e^{\frac{-t}{250}}[/tex]

=> [tex]\frac{15}{50}=\frac{3}{10}[/tex] = [tex]e^{\frac{-t}{250}}[/tex]

=> log [tex]\frac{3}{10}[/tex] = [tex]\frac{-t}{250}[/tex]

=> - 0.522 = [tex]\frac{-t}{250}[/tex]

=> 130.5 = t

Hence, the satellite to run for about 130 days if it requires 15W of power, as solved by basic algebra.

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$600.

Given that

Profit per kg =  $4.

we find out the overall profit for 150 kg of rice.

Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses.

Total Revenue - Total Expenses = Profit.

for 1 kg profit is $4

then for 150 kg profit is =  (profit of 1 kg × total rice)

                                     = 4×150$

                                      = $600

Hence the overall profit on 150 kg of rice is $600 .

Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product.

Profit(P) - The amount gained by selling a product with more than its cost price.

Profit or Gain = Selling price – Cost Price

Profit percentage (P%) = (Profit /Cost Price) x 100

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Let the two points be given by:

[tex]P(x_{1},y_{1}) \\ Q(x_{2},y_{2})[/tex]

[tex]rate = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

If (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.

An expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power

We have,

(x + 1) is a factor of p(x) = x² + x + 2

We need to find x.

Since (x + 1) is a factor of p(x) it should satisfy p(x).

x + 1 = 0

x = -1

Thus if (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.

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The distance is √116.

The distance formula to calculate the distance between two points (x1,y1) ( x 1 , y 1 ) , and (x2,y2) ( x 2 , y 2 ) is given as,

D=√(x2−x1)²+(y2−y1)²

Given:

(10,0) (0,4)

Using Distance formula

=√(x2 - x1)² + (y2 - y1)²

=√(0-10)² + ( 4-0)²

=√100 + 16

=√116

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Answer:

4.5

Step-by-step explanation:

a^2+b^2=c^2

64+16=80=c^2

c=80^0.5

x^2+80=100

x^2=20

x=4.5

24units² is the area of the given triangle.

The formula of the area of a triangle using coordinates:

Now, substitute the values in the formula as follows:

Therefore, the area of the given triangle is 24units².

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Answer:

12-6 is the right answer

Step-by-step explanation:

Multiple 3 to 4 which is 12 and then then multiple it with two which is 6 so the answer is 12-6

The interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.

In the fields of finance and economics, interest is the payment of a sum over and above the principal amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. It is not the same as a fee that the borrower might pay to the lender or another entity.

Principal = $2560

Time = 17 months = 1.417 years

Rate = 5.125%

Therefore, the Interest will be:

= (Principal × Rate × Time) / 100

= (2560 × 1.417 × 5.125) / 100

= $185.9

Therefore, the interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.

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The value of the function f(-8) is -512

A function is defined as an expression, rule or law that shows the relationship between two variables;

Given the function:

f(x)= x × x²

To determine the function f(-8), we substitute the value of x  as -8 in the function

With this, we have;

f(-8) = (-8) × (-8)²

expand the bracket

f(-8) = -8 × 64

Multiply through

f(-8) = - 512

The value of the function is -512

Thus, the value of the function f(-8) is -512

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Answer:x=0

Step-by-step explanation:hope it helps, brainliest? i could really use it

The range of possible values of x from the given equation is 37.

The given equation is (x+20)=57.

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and the range is the possible output given by the function. Domain→ Function →Range.

The domain and range are defined for a relationship and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

Now,

Domain = the set of all x-coordinates

Range = the set of all y-coordinates

Here, x+20=57

⇒x=37

Verification:

Put x=37 in x+20=57 and verify.

37+20=57

⇒57=57

LHS=RHS

Therefore, the range of possible values of x from the given equation is 37.

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