if the gradient of a line,B,is -3, what is the gradient of the line which is perpendicular to B

Using an exponential function, the sound intensity of a noise that is 130 dB is of I = 10 watts/m².

The sound level, in dB, of a sound of intensity given by I is given according to the following equation:

[tex]B = 10\log{\left(\frac{I}{I_0}\right)}[/tex]

In which [tex]I_0[/tex] is the smallest sound heard by the human ear, which is of [tex]I_0 =  10^{-12}[/tex] watts/meter.

Hence, for a sound of 130 db, the intensity I is found as follows:

[tex]130 = 10\log{\left(\frac{I}{10^{-12}}\right)}[/tex]

Isolating the logarithm, the equation is:

[tex]\log{\left(\frac{I}{10^{-12}}\right)} = 13[/tex]

The power of 10 and the logarithm are inverse functions, hence the power of 10 is applied to both sides of the equation to isolate the intensity creating the exponential function given as follows:

[tex]10^{\log{\left(\frac{I}{10^{-12}}\right)}} = 10^{13}[/tex]

[tex]\frac{l}{10^{-12}} = 10^{13}[/tex]

[tex]l = 10^{-12} \times 10^{13}[/tex]

Multiplying two terms with the same base and different exponents, we keep the base and add the exponents, hence the intensity is given as follows:

I = 10 watts/m².

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Answer:

true

Step-by-step explanation:

3p^3-4p^2-13p+14 = (p-1)(3p-7)(p+2)

Using equation, the number of hours Ajay spent washing car and tutoring are 2 and 4 hours respectively.

Ajay is working two summer jobs working $8 per hour washing cars and $11 per hour tutoring.

Last week Ajay worked 2 more hours tutoring than hours washing cars and earned a total of $60.

The system of equation that could be used to determine the number of hours Ajay worked washing cars last week and the number of hours he worked tutoring last week can be calculated as follows:

let

x = number of hours washing cars

y = number of hours tutoring

Therefore,

y = 2 + x

Hence,

8(x) + 11(2 + x) = 60

8x + 22 + 11x = 60

19x  = 60 - 22

19x = 38

x = 38 / 19

x = 2

Therefore,

y = 2 + 2

y = 4

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Answer:

variables :

Let = w = The number of hours washing car.

let = t = The number of hours tutoring.

system of equations:

8w + 11t = 60

t = w + 2

Step-by-step explanation:

Answer:

a = 9 cm

Step-by-step explanation:

a = √(15²-12²)

a = √(225 - 144)

a = √81

a = 9 cm

(a) The equation of the parallel line is y = 3x - 11.

(b) The equation of the perpendicular line is y = - x/3 - 1.

Consider the line graphed,

The two points on the line are ( 1, - 4 ) and ( 2, - 1 ).

Now, the slope of the line with two points ( x₁, y₁ ) and ( x₂, y₂ ) is:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Then,

m = ( - 1 - (-4) ) / ( 2 - 1 )

m = 3

(a) The lines which are parallel have the same slope.

Now, the parallel line passes through ( 3, - 2 ).

Therefore, the equation of the line is y = mx + b where b is the y-intercept.

y = mx + b

- 2 = 3 × 3 + b

- 2 = 9 + b

b = - 11

Therefore, the equation of the line is y = 3x - 11.

(b) The slope of the line perpendicular to the line with slope m is equal to - 1/m.

Then the slope of the perpendicular line is - 1/3.

The line passes through the point ( 3, - 2 ).

y = mx + b

- 2 = ( - 1/3 ) × 3 + b

- 2 = - 1 + b

b = - 1

Then the equation of the perpendicular line is:

y = - x/3 - 1

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Answer:

x = 52°

Step-by-step explanation:

Exterior Angle Theorem

The interior angles of a triangle sum to 180°.  Angles on a straight line sum to 180°.  Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ x + 90° = 142°

⇒ x + 90° - 90° = 142° - 90°

⇒ x = 52°

Let us assume that,

→ x + y + 90° = 180°

Now the required value of y is,

→ y + 142° = 180°

→ y = 180° - 142°

→ [ y = 38° ]

Then the value of x will be,

→ x + 38° + 90° = 180°

→ x = 180° - 128°

→ [ x = 52° ]

Hence, the value of x is 52°.

Answer:

The answer will be 4/5

Step-by-step explanation:

25m^2-17=-1

25m^2=-1+71

√25m^2=√16

5m=4

m=4/5

The points to be graphed are (0, 1) and (-0.2, 0). The graph of the equation is shown in the attached image

Given y-2=1/5(x-5)

In order to graph the equation of the line:

First, find the value of x when y = 0:

y-2=1/5(x-5), when y = 0:

0 -2 = 1/5(x-5)

-2 = 1/5x - 1

1/5x = -2 + 1

1/5x = -1

-5x = 1

x = -1/5 = -0.2

Also, find the value of y when x = 0:

y-2= 1/5(x-5), when x = 0:

y-2= 1/5(0-5)

y-2 = 1/5(-5)

y-2 = -1

y = 1

Therefore,  the values to be plotted on our graph are (0, 1) and (-0.2, 0). The image of the graph is attached

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The coordinates of T are (13, -6) which s is the midpoint of rt r(-9,4) and s(2,-1).

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,

M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Assuming that S is the midpoint of the line segment RT, where point R's coordinates are (-9, 4) and S's coordinates are (2, -1).

We have to determine the coordinates of point T.

The midpoint is the average of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).

In this case, the midpoint is given by M = S(2, -1).

Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).

2 = (-9 + x₂)/2

-9 + x₂ = 4

x₂ = 13

-1 = (4 + y₂)/2

4 + y₂ = -2

y₂ = -6

Therefore, the coordinates of T are (13, -6).

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The question seems to be incomplete the correct question would be

Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T

We can tell if the components on each side of the equation are congruent when you see the equals sign with a squiggly line on top. Name the corresponding sides after that. Two triangles with corresponding sides have matching sides. Congruent triangles will have the same length.

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The least common multiple of the 3x and 3(x−2) is 9x(x - 2)

From the question, the expressions are given as

3x and 3(x−2)

The expressions do not have direct factors or multiples

So, we multiply both expressions to calculate the least common multiple

This above computation can then be represented as

Least common multiple = Product of the two expressions

Substitute the known values in the above equation

So, we have the following representation

Least common multiple = 3x * 3(x - 2)

Evaluate the product of 3x and x in the above equation

So, we have the following equation

Least common multiple = 9x(x - 2)

Hence, the least common multiple of the expressions is 9x(x - 2)

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The longest side of the other triangle is 37.8 cm

From the question, the sides of the triangle are given as

This means that

Ratio = Corresponding sides of the triangles

So, we have

Ratio = Longest sides : Shorters sides

Substitute the known values in the above equation

So, we have the following equation

18 : 7 = Longest side : 14.7

Multiply 18 : 7 by 2.1

So, we have

37.8 : 14.7 = Longest side : 14.7

So, we have

Longest side = 37.8

Hence, the longest side  is 37.8 cm

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The value of x = 7/2 and y = -2, Given equation are linear.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.

The equation are,

y=-4x+12                     --------(i)

6x+ 5y = 11                 --------(ii)

for eq(i),

y + 4x = 12

4x + y = 12

Now, put together both the equation and multiply with coefficient of x to make common value of x so that we can cut by opposite signs,

(4x + y = 12)  * 6

(6x+ 5y = 11)   * 4

After multiplying, we get

24x + 6y = 72

24x + 20y = 44

Now change the signs with + to - and - to +, like that

24x + 6y = 72

24x + 20y = 44

-      -            -

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

0  + 6y - 20y = 72 - 44

=> -14y = 28

=>  y = 28/(-14)

=>  y = -2

Put y = -2 in eq(i),

4x + y = 12

4x - 2 = 12

4x = 12 + 2

x = 14/4

x = 7/2

Hence, the values we get after solving given equation is x=7/2 and y= -2.

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Answer:

y>-7

Step-by-step explanation:

Answer:

the answer is option 3

Step-by-step explanation:

18+6y<42

6y<42-18

6y<24

y<4

Following a dilation with a scale factor of s, the coordinates of point C are 3.s +2,s. The line's equation is 3y = x - 2

When you know the slope of the line to be examined and the point given is also the y intercept, you can use the slope intercept formula

y = mx + b. (0, b).

The y value of the y intercept point is represented by b in the formula.

First part

The scale factor of dilation = 2

Given that the center of dilation is the point (2, 0) on the preimage, we have;

The coordinates of the image are;

(2, 0), (2 ×(5 - 2) + 2, (2 × (1 - 0)), (2 × (5 - 2) + 2, 0)

Which gives;

The coordinates of the vertices of the image are; (2, 0), (8, 2), (8, 0)

Please find the drawing of the image of the dilation of triangle ΔABC with a scale factor of 2 attached.

Second [part;

The scale factor = 3

Center of dilation = (2, 0)

The coordinates of the image are therefore;

(2, 0), (3 × (5 - 2) + 2, (3 × (1 - 0)), (3 × (5 - 2) + 2, 0)

Which gives;

(2, 0), (11, 3), and (11, 0)

Please find attached the drawing of the image of the dilation of triangle ΔABC with a scale factor of 3

Third part;

The scale factor = 12

Center of dilation = (2, 0)

The coordinates of the image are;

(2, 0), (12 × (5 - 2), 12 × (1 - 0)), (12 × (5 - 2), 0)

Which gives;

(2, 0), (36, 12), (36, 0)

Please discover connected the drawing of the image of ΔABC having a scale factor of 12

Fourth part

Center of dilation = (2, 0)

Scale factor of dilation = s

The coordinates of the image are;

A(2, 0), C(s × (5 - 2) + 2), s × (1 - 0)), B(s × (5 - 2) + 2, 0)

Which gives;

The coordinate of point C is  3.s +2,s.

Fifth part

The slope of the line is m, which is equal to the slope of the side AC  of Δ A B C, which is given as follows;

[tex]$m=\frac{1-0}{5-2}=\frac{1}{3}[/tex]

The equation of the line in point and slope form is therefore;

[tex]$y=\frac{1}{3} \times(\mathrm{x}-2)[/tex]

Which gives;

3y = x - 2

- The equation of the line is 3y = x - 2

The complete question is:

Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 2. Draw the dilation of triangle ABC with center (2,0) and scale factor 3. Draw the dilation of triangle ABC with center (2,0) and scale factor 12. What are the coordinates of the image of point C when triangle ABC is dilated with center (2,0) and scale factor s? Write an equation for the line containing all possible images of point C.

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Answer:

The correct answer is C.

Step-by-step explanation:

I got the answer by plotting the points on a graph. Then count how many places you have to go from one point to the other to find the slope. To find the y - intercept, look at where the point passes or is on the y-intercept. Sorry if this isn't a good explanation.

After solving the arithmetic sequences, he lengths of the first four segments will be 20 cm.

Arithmetic sequences take the following format: a, a+d, a+2d, a+3d, etc. up to n terms. A is the first term; d is a frequent difference; and n is the total number of terms.

Find the AP, the number of terms, and the common difference for the calculation using the arithmetic sequence formulas. To determine the nth term, sum, or common difference of a given arithmetic sequence, various arithmetic series formulas are used.

To find the lengths of the first four segments we use the Arithmetic progression formula that is

[tex]a_n =[/tex] a₁ + (n - 1)d

Where

an = the nᵗʰ term in the sequence

a₁ = the first term in the sequence

d = the common difference between terms

We have a₁ as 5 cm and as it is being duplicated the common ration d is 5

and we have been asked the length of the first four segments, so n = 4

Lets substitute the given information

[tex]a_n =[/tex] 5 + (4 - 1)5

    = 5 +(3)5

    = 5 + 15

    = 20

Thus, after continually duplicated segment ab, the lengths of the first four segments will be 20Cm

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The slope of the linear graph is - 4 / 3.

The slope of a linear graph is the change in the dependent variable with respect tot he change in the independent variable.

The slope is describe as rise over run.

Therefore, the slope can be represented mathematically, as follows;

Hence,

slope = y₂ - y₁ / x₂ - x₁

Therefore, using (0, -2) and (- 3 / 2, 0)

x₁ = 0

x₂ = - 3 / 2

y₁ = - 2

y₂ = 0

Therefore,

slope = 0 + 2 / - 3 / 2  - 0

slope = 2 ÷ - 3 / 2

slope = 2 × 2 / -3

Therefore,

slope = - 4 / 3

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There is nothing more we can do with these binomials, so we break them up and combine like terms.

-2x - 13 + 19 + 5x
5x - 2x + 19 - 13
3x + 19 - 13
3x + 6

Answer:

[tex]\boxed{\sf 3x+6}[/tex]

Step-by-step explanation:

[tex]\sf \left(-2x-13\right)+\left(19+5x\right)[/tex]

Simplify:-

[tex]\sf -2x-13+19+5x[/tex]

Combine like terms/Add numbers:-

[tex]\sf -2x+5x-13+19[/tex]

[tex]\sf (-2x+5x)=\bf 3x[/tex]

[tex]\sf (-13+19)=\bf 6[/tex]

[tex]\boxed{\sf 3x+6}[/tex]

Therefore, your answer is D. 3x + 6!!

_______________________

Hope this helps!

Have a great day!

To find the probability, we will need to first find the area of the whole circle and the area of the shaded part.

Area of the Big Circle

Given that the radius, R, is 20cm, the area is

Area of the Shaded Part

We can find the area of the shaded part by calculating the area of the small circle (r = 10cm) and subtract it from the big circle.

Hence

The area of the shaded portion is

Probability of landing on the shaded portion:

The probability is calculated by

Therefore, the probability that the ball will land on the shaded area is 3/4.

The FOURTH OPTION is correct.

The value of the composite function (f - g)(x) is x² - 3x + 1

The functions are given as

f(x) = x² + 1

g(x) = 3x

The composite function definition is given as

(f - g)(x)

This composite function is calculated using the following composite function formula

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation

So, we have the following equation

(f - g)(x) = x² + 1 - 3x

Evaluate the like terms

(f - g)(x) = x² - 3x + 1

Hence, the composite function is (f - g)(x) = x² - 3x + 1

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Answer: The quotient of (30 x 10^-24)/(5 x 10^-24) is 6, which means that in scientific notation, it’s written as 6 x 10^0.

Answer:

12

Step-by-step explanation:

bla bla bla is not 12 and I know that thanks for my points is not 12 thanks

The slope of the line h is 3

Let m1 be the slope of line g and m2 be the slope of line h.

Line g passes through points (2, 3) and (5, 2).

Using the formula of slope,

m1 = (2 - 3)/(5 - 2)

m1 = -1 / 3

Line h is perpendicular to line g.

We know that the product of slopes of the perpendicular lines is -1.

m1 * m2 = -1

(-1/3) * m2 = -1

m2 = 3

Therefore, the slope of the line h is 3

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Solution:

Given:

Account 2 details:

Assume a year is 365 days;

Using the compound interest formula to get the amount;

Hence, substituting the values;

Therefore, the balance in account 2 will be $9633.55

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The total amount earned in a week including the commission is $605 working for 40 hours.

The hourly rate is $15.125.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

The amount earned in a week = $350

Amount earned in commission = 3% of $8,500

= 3% of 8500

= 3/100 x 8500

= 3 x 85

= $255

The number of hours worked = 40 hours.

The hourly rate for the week:

= (350 + 255) / 40

= 605 / 40

= $15.125

Thus,

The hourly rate is $15.125.

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it is True that the division law of exponents says that if b is a non zero number and n and m are any numbers in the exponents of b then b^m/b^n = b^(m-n)

This is the law that governs numbers that are have exponents or power.

According to the question b is the number while m and n represents the value of the exponents or the numbers for which number b is raised to their power say: b^m and b^n

The division law of exponents holds as:

=  b^m ÷ b^n

= b ^ ( m - n )

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Answer:

8

Step-by-step explanation:

Hello, no worries! It's a pleasure to meet and help you out today.

Median refers to the number that is in the middle of a data set.

The data set you provided has the numbers listed in order, which is great! However, if it's not listed in order, then you must list it in order by yourself.

Data Set: 4, 5, 5, 8, 8, 8, 9, 12, 13

As I said previously, we must find the middle value in the data set.

Data Set: 4, 5, 5, 8, 8, 8, 9, 12, 13

Clearly, the middle value in the data set is 8, so that's the median.

I hope my work has helped you in a way, and I wish you the best of luck with the rest of your assignment! (:

Answer:

He bought 2 notebooks

Step-by-step explanation:

Add up the cost of the pens, pencils, sharpeners, and the change.

This will give you £4.80, subtract that from £7.00 and you get £2.20

Since the notebooks are only £1.10, he could've only bought 2.

Please mark brainliest!!!

Given:-

To find the volume of the cone.

From the given image it is clear,

So now we substitute the known values. so we get,

So the required volume is 125ft^3.