what is the slope of the line if it is y=4x+12

*30 points*

The equation for x is,

⇒ x = 3/2y + 3

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

2x - 3y = 6

We can simplify the equation as,

2x - 3y = 6

Divide 2 both side,

x - 3/2 y = 3

Add 3/2y both side,

x - 3/2 y + 3/2 y = 3 + 3/2 y

x = 3/2 y + 3

Hence, The equation for x is,

⇒ x = 3/2y + 3

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

4 pieces of candy

Step-by-step explanation:

36÷8=4.5

If you can't have half a candy, then each kid would get 4 pieces.

Answer:

D is your answer

Step-by-step explanation:

Just did it and it was right : )

Also for anyone else who needs the other answers they are as follows:

1. D. \(6x^4\)  then  C. \(3x^4\)

2. B. \(-30x^2 \sqrt{2x}\)  then  C. \(4x^4^3 \sqrt{2x^2}\)

3. D. \(2x\sqrt{10x} - 2x \sqrt{5}\)

4. B. \(32x^2 \sqrt[3]{2x} -8x^3\)

5. A. \(-22\)  then  C. \(4x^4 \sqrt{5} +2x^2 \sqrt{3x} + 4x^3 \sqrt{30} +6x \sqrt{2x}\)

6. B. \(x^\frac{2}{12}* y^\frac{9}{12}\)  then  C. \(\sqrt[12]{x^2*y^9}\)

NC Math 2 -22092x0

Multiplying Radicals

Assignment

Due March 11

Multiplying radicals with like indices.

The solution of the given equation will be 2√5x(√2-1).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The expression will be solved as below:-

= √5x ( √8x² - 2√x)

= √5x ( 2√2x - 2√x)

= √5x(√2-1)(2√x)

= 2√5x(√2-1).

Therefore the solution of the given equation will be 2√5x(√2-1).

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Answer:

The balance of the account is $64,190.

Step-by-step explanation:

The amount of money after t years of continous compounding is given by the following equation:

\(P(t) = P(0)e^{rt}\)

In which P(0) is the initial deposit and r is the interest rate, as a decimal.

$60,000 deposited for 6 years at 1.125% interest compounded continuously.

This means that \(P = 60000, r = 0.01125, t = 6\)

So

\(P(6) = 60000e^{0.01125*6} = 64190\)

The balance of the account is $64,190.

Answer:

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

Step-by-step explanation:

Mai biked 5 1/4 miles today

So he biked, in miles:

\(5 + \frac{1}{4} = \frac{5*4 + 1}{4} = \frac{20+1}{4} = \frac{21}{4}\)

Noah biked 2 1/2 miles.

So, in miles, he biked:

\(2 + \frac{1}{2} = \frac{2*2 + 1}{2} = \frac{4+1}{2} = \frac{5}{2}\)

How many times the length of Noah’s bike ride was Mai’s bike ride?

We divide the Mai distance by Noah's distance. In a division of fractions, we multiply the numerator by the inverse of the denominator. So

\(\frac{\frac{21}{4}}{\frac{5}{2}} = \frac{21}{4} \times {2}{5} = \frac{21*1}{2*5} = \frac{21}{10} = 2.1\)

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

The given expression is

1. The expression has three terms. 3y, -5x, and 4. Remember that terms are those expressions separated by a sign.

2. The coefficients of the expressions are 3, and -5. Remember that a coefficient is a number that multiplies a variable.

1) If the 10 kg sugar is Rs. 880 . Find the cost of 15 kg sugar.....

Solution,

let the required cost be Rs x

Here , the quantities of sugar and their cost are direct proportion

So, 10 : 15 = 8: x

\( \: \frac{10}{15} = \frac{880}{x} \\ x = \frac{880 \times 15}{10} \\ x = Rs1320\)

Hence , the cost of sugar is Rs.1320

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2) 50 students in a hostel have provisions for 21 days . How long would it last for 75 students?

Solution,

Let the required number of a day = x

Here , the number of student and the number of days are in inverse proportion.

•°• 50 : 75. = x : 21

\( \frac{50}{75} = \frac{x}{21} \\ x = \frac{50 \times 21}{75} \\ x = 14 \: days \\ \)

Hence, the provisions last for 14 days for75 students

~nightmare 5474~

1) The cost of 15 kg sugar is; Rs. 1320

2) The number of days that it would take the provisions to last for 75 students is; 14 days

1) Cost of 10 kg = Rs. 880

Thus, by proportion the cost of 15 kg sugar will be;

(15 × 880)/10

>> 13200/10

>> Rs. 1320

2) We are told that;

50 students = provisions for 21 days

Thus for 75 students the number of days the provisions would last them is gotten by proportion;

(50 × 21)/75

>> 1050/75

>> 14 days

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Answer:

An increase of $0.94

Step-by-step explanation:

Answer:

594.1

Step-by-step explanation:

87÷15=5.1

672-83=589

so then you add those to together and get 594.1

Answer:    It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.

Step-by-step explanation:

\(5.\)

Step-by-step explanation:-

\(8 + k\)

If k = -3. Then,

\(8 + ( - 3)\)

\( = 8 - 3\)

\( = 5.\)

I learned this so many times but I forgot how to do it exactly.

But looking at this, you can already determine that y is equal to -3 so couldn't you use that as an answer.

Answer:

Step-by-step explanation:

First what you want to do is find the slope.

-3+3/1+3

0/4

slope=0

now you want to write the equation in point-slope form

y+3=0(x-1)

simplify

y+3=0

subract 3 from each sides

y=-3 is the answer

whatever x is, y is equal to -3

Answer:

This is a ssa situation, no triangle is possible.

Step-by-step explanation:

"SSA" means "Side, Side, Angle".

In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.

In triangle ABC:

Given:

The angle that is between the sides a and b is angle C.

Therefore, as angle A is not the angle between the given sides, ΔABC is an SSA triangle.

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 44^{\circ}}{12.6}=\dfrac{\sin B}{19}\)

\(\implies \sf \sin B=\dfrac{19\sin 44^{\circ}}{12.6}\)

\(\implies \sf \sin B=1.0475007...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, although this is an SSA situation, no triangle is possible.

Answer:

=2x-4

Step-by-step explanation:

Answer:

The fully simplified form is2x-4

Step-by-step explanation:

Use Distributive property

5(x-2)=5x-10

3(2-x)=6-3x

5x-10+6-3x

Combine like terms

2x-4

Answer:

3 x

x + y

Step-by-step explanation:

(think about it with a horizontal line between the two numbers)

When using fractions and whole numbers turn the whole numbers into fractions like ---> 3/1

and if their like 3 5/6 (for example) you would multiply the denominator by the whole number ---> 3*6=18 then add what's on the numerator with it. so 18+5=23 which would make it 23/6

Just some tips for making it easier!

Hope it helps! :)

Given data:

The first given number is a=6.15x10^7.

The given number can be written as,

a=61,500,000

Thus, the given number can be expressed as 61,500,000.

Answer:

j=30

Step-by-step explanation:

Answer: 48

Step-by-step explanation:

In using quarterly time series data, Quarter two  can serve as the base period for interpretation of dummy variables.

What do you mean by interpretation?

The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.

                           Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.

What are examples and variables?

A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.

                                 The two primary categories of variables are categorical and numeric.

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Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

The coefficient of 8.2N1602 is 8.2N.

The given number is 8.2N1602, and you're required to find the coefficient of the number. The coefficient is the numerical factor that a term is multiplied by in an algebraic expression.

It is usually a number, but it may also be a letter that represents a number. The coefficient is the number that appears before the variable or term. For instance, in 3xy, 3 is the coefficient.In the given number, the coefficient is 8.2N, which is a decimal number.

A decimal is a number that uses place value and a decimal point to show the value of digits to the right of the decimal point.In general, decimals are a method of writing fractions that have a denominator of 10 or a power of 10.

The decimal 8.2 is 8 and 2 tenths, or 8.2/10. To convert a decimal number to a fraction, multiply the decimal by the appropriate power of 10 to make the decimal whole. In this case, we have 8.2N, which is already in decimal form.

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Answer:

8730

Step-by-step explanation:

It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.

We have to:

At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.

¡Hope this helped!