Need help please!
14. Write an equation of a line that is parallel to the line 2x – 3y = 6. Explain how you know that the graph of
your equation is parallel to 2x – 3y = 6.

15. A student drew the line y = 2x + 3
a. Write equations for two lines that are perpendicular to this line. Justify your answer.
b. What do you notice about the slopes of these two lines? What generalization can you make about two lines
that are both perpendicular to the same line?

The equation to represent the situation is y = 15 + 30x.

The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.

Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.

The equation that can be used to represent the given situation is as follows:

let

x = number of hours used for the training

y = total cost

Therefore,

y = 15 + 30x

Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.

Therefore,

75 = 15 + 30x

75 - 15 = 30x

60 = 30x

divide both sides by 30

x = 60 / 30

x = 2

Therefore, she used 2 hours for the training.

learn more on equation here:https://brainly.com/question/14373070

#SPJ1

Answers:

1st box:  [tex]\boldsymbol{90}[/tex]

2nd box:  [tex]\boldsymbol{90}[/tex]

3rd box:  [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]

===============================================

Explanation:

Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.

By "corner", I refer to a 90 degree angle.

Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.

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

Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]

We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.

That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]

After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.

Answer:

$67.50

Step-by-step explanation:

27(2) = 54

27/2 = 13.5

54+13.5 = 67.5

Answer:

67.5

explanation:

27/2= 13.5

5*13.5= 67.5

According to the Pythagoras theorem, the value of ED is 8.4 cm

Pythagoras theorem:

Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

A, B, C, D, E, F, G and H form a cuboid.

AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.

Now, we need to find the value of Ed and round off it into 1 decimal place.

Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.

Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.

Because, BG and ED are opposite to each other.

Which means both have the same hypotenuse value.

So, according to the Pythagoras theorem,

=> BG² = BC² + CG²

=> BG² = (2.3)² + (8.1)²

=> BG² = 5.29 + 65.61

=> BG² = 70.9

So, the value of BG is 8.42.

Therefore, the value of ED is 8.4 When we round off this into one decimal place.

To know more about Pythagoras theorem here.

https://brainly.com/question/343682

#SPJ1

The GCF: 2x³y

answer: 2x³y2x³y(9y³+1)

All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.

A square is a term to refer to a geometric figure that is characterized by the following characteristics:

One key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.

Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.

Learn more about angles in: https://brainly.com/question/13954458

#SPJ1

To cover the area of floor, we will spend $0.65 for the entire 0.23 squared feet

Perimeter of Rectangle could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. A rectangle is a quadrilateral that has two pairs of parallel sides equal and all the four angles at the vertices are right angles.

The formula of perimeter of a rectangle is given as

P = 2(L + W)

But the width the rectangle is 6 feet more than half it's length.

W = 6 + 1/2L

If the perimeter is 313 times the length;

P = 2(L + W)

P = 2(L + 6 + 1/2L)

But P = 313L

313L = 2(L + 6 + 1/2L)

313L = 2L + 12 + L

313L = 3L + 12

310L = 12

L = 12 / 310

L = 0.039 ft

The length of rectangle is 0.039ft

The width of the rectangle is 6 + 1/2(0.039) = 6.0195ft

The perimeter of the rectangle = 2(L + w)

Perimeter = 2 (0.039 + 6.0195)

Perimeter = 12.117ft

The area of the rectangle is L * w

A = L * W = 0.039 * 6.0195

A = 0.234ft^2

The cost of the materials will be 2.75 * 0.234 = $0.65

Learn more on perimeter of rectangle here;

https://brainly.com/question/19819849

#SPJ1

Step-by-step explanation:

it is a parallelogram.

that means both pairs of opposite sides are parallel and the sides of each pair are equally long.

the sum of all internal angles is 360°.

the opposing angles are equal.

and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.

so,

76 = 4x - 8

84 = 4x

x = 21

-3z + 8 + 76 = 180

-3z + 84 = 180

-3z = 96

z = -32

-3z + 8 = -6y - 10

-3×-32 + 8 = -6y - 10

96 + 8 = -6y - 10

104 = -6y - 10

114 = -6y

y = -19

The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.

The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:

(-20, y) = [tex](x_1, y_1)[/tex]

(-11, 15) = [tex](x_2, y_2)[/tex]

m = 0

Substitute the values into the slope formula:

0 = (15 - y) / (-11 -(-20))

0 = (15 - y) / 9

Multiply both sides by 9

0 = 15 - y

0 + y = 15 - y + y

y = 15

The answer is: a. 15.

Learn more about the slope on:

https://brainly.com/question/16949303

#SPJ1

The equation which is correct is :

n + q = 104

Since we have given that:

Number of nickels and quarters = 104

Total amount from them = $22

Let the number of nickels be 'n'

Let the quarters be 'q'

So, the equation will be

n + q = 104           -------------------------------------------- (1)

Since we know that

value of nickels = 0.05 dollars

Value of quarters = 0.25 dollars

So, the equation will be

0.05n + 0.25q = $22       ------------------------------------ (2)

So, there are two system of linear equation can be used to find the number of nickels and the number of quarters. i.e.

n + q = 104

0.05n + 0.25q = $22

Using elimination we can find the value of n and q :

0.05( n + q =104 )

⇒0.05n+0.05q=5.2-----------(3)

Now, from equation (2) and (3), we get,

0.05 n + 0.05q = 5.2

0.05 n + 0.25q = 22

(-)       (-)           (-)

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

0          + 0.2q = 16.8

q = 16.8 ÷ 0.2

q = 84

Putting the value of q = 84 in equation (1),

   n + q = 104

⇒ n + 84 = 104

⇒ n = 104 - 84

⇒ n = 20

Hence,  n +q =104 equation is correct.

Learn more about Linear Equation:

https://brainly.com/question/11897796

#SPJ4

The solution of the given equation is x = 10/3

The replacement value is 10/3.

This is incorrect question

Correct question is :

What is the solution to the equation 6x−5=15, given the replacement set {5/6, 5/3, 10/3}

Given,

In the question:

The equation is given as:

6x - 5 = 15

To find the solution of the given equation.

Now, According to the question:

The equation is:

6x - 5 =15

Combine the like terms:

6x = 15 + 5

6x = 20

x = 20 /6

x = 10/3

Hence, The solution of the given equation is x = 10/3

The replacement value is 10/3.

Learn more about Equation at:

https://brainly.com/question/17149704

#SPJ4

Answer: m1=2 and m2=88

Step-by-step explanation:

90=x-9+8x

99=9x

x=11

Answer:

============================

Use equation for continuous compound:

Plug in the values and calculate:

Answer:

$5,252.53 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]

[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]

[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]

[tex]\implies \sf A=5252.53457...[/tex]

Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).

It is possible to multiply or divide an equation by the same number on each side of the equation without changing the answer, according to the "multiplication property" of the equation.

How can you use the properties of operations to multiply linear expressions?

According to the equation's "multiplication property," it is possible to multiply or divide an equation by the same number on each side of the equation without changing the equation's outcome. The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same sign will be positive. If a and b are positive integers and x is a variable, then (xa * xb) = x(m + n). The identity, commutative, associative, and distributive properties of multiplications are four properties that can facilitate the process. They offer guidelines for solving multiplication problems quickly using properties that always hold true for particular equations.

To know more about equation,

https://brainly.com/question/10413253?referrer=searchResults

#SPJ1

The pounds of chocolate chips that were left is B. eleven-twelfths pounds

Given that Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins

The fraction left will be:

= Total pounds bought - The amount used

= 7 1/2 - (3 3/4 + 2 5/6)

= 7 1/2 - (3 9/12 + 2 10/12)

= 7 1/2 - 6 7/12

= 11/12

In conclusion, the correct option is B.

Learn more about fractions on;

brainly.com/question/17220365

#SPJ1

the 60th percentile of breaking strength for this type of fishing line is

k= 6.64

assume that k pounds is the both percentile of breaking strength for this type of finishing line

p( x<k) = 0.60

p( x- 6.44/0.75 < k- 6.44/0.75)= 0.60

then k-6.44 /0.75 = 0.26

thus k= 6.64

Hence , the 60th percentile of breaking strength for this type of fishing line is 6.64

learn more about of percentile here

https://brainly.com/question/15210125

#SPJ4

Answer: option 2

Step-by-step explanation:

The leading coefficient is positive and the degree is odd, so the correct answer is option 2.

The standard deviation of the monthly amount charged is 346.41

Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.

Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:

a = 300

b = 1500

Step 2: Calculate the variance using the formula Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]

Using the formula for the variance and the values identified in step 1

(a = 300 , b = 1500), we have:

Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]

         = [tex]\frac{(1500 - 300)^{2} }{12}[/tex]

         = 1440000/12

         = 120,000

the variance is 120,000

Step 3: Calculate the standard deviation by taking the square root of the variance. σ = [tex]\sqrt{Var(x)}[/tex]

The standard deviation is the square root of the result from step 2 (variance = 120,000)

σ = [tex]\sqrt{Var(x)}[/tex]

σ = [tex]\sqrt{120000}[/tex]

   = 346.41

The standard deviation of the monthly amount charged is 346.41

To learn more about  standard deviation:

https://brainly.com/question/16555520

#SPJ4

Answer:

A = 64 m²

Step-by-step explanation:

Step 1: What is the question asking

Step 2: What is known

Step 3: Conversion

Step 4: Answer the question/solve for the area

Heidi earned $30 in commission.

The amount of money that the store made from Heidi's sales is equal to $720.

In this exercise, you're required to determine the amount of money earned by the salesperson as commission based on the price at which she sold a jewelry.

Mathematically, the amount of commission earned on the sales of a product can be calculated by using this mathematical expression:

Commission = Percent commission × Sales price

Given the following data:

Percent commission = 4%

Sales price = $750.

Substituting the given parameters into the formula, we have;

Commission = 4/100 × 750

Commission = 0.04 × 750

Commission = $30.

Next, we would determine the amount of money that the store made from her sales:

Sales = $750 - $30.

Sales = $720.

Read more on commission here: https://brainly.com/question/24951536

#SPJ1

Answer:

a = -1
b = -9

Step-by-step explanation:

when x = -2 put -2 for x in the equation:

a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b

then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5

Answer:

slope and x-intercept is -1/2

y-intercept is 5

Answer:

Step-by-step explanation:

Estimated line of best fit added to the graph (see attached).

The most reasonable value of y corresponding to x = 3 is approximately 18 gallons.

The matching answer choice is D.

Answer:

(D) 17 gallons

Step-by-step explanation:

The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup

to-go containers to sell to customers.

Let y represent the number of cups of potato salad remaining,

And x represents the number of to-go containers Isaac has filled,

As per the given situation, we can write the equation as:

y = 30 - x  ....(i)

Substitute the value of x = 2.5 in the above equation,

y = 30 - 2.5

y = 27.5

Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1

The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

Given that,

The equation is (2x-3)(2x+1)

We have to find the differentiative equation.

Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.

Differentiation is the rate at which one quantity changes in relation to another.

Take the equation

(2x-3)(2x+1)

We can do in two ways

1st way

Multiply

4x²+2x-6x-3

Subtraction

4x²-4x-3

Differentiation

8x-4

The equation is 8x-4.

2nd way

We have a formula in differentiation that is

u.v=uv'+vu'

Take u as 2x-3 and v as 2x+1

(2x-3)(2)+(2x+1)(2)

4x-6+4x+2

8x-4

Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

To learn more about differentiation visit: https://brainly.com/question/24898810

#SPJ1

The unit rate of Ricky purchase is $3.75 per pizza.

The unit rate of William purchase is $8 per pounds of blackberries.

Unit rate is the ratio of two different units, with denominator as 1.

In other words, a unit rate is a rate where the second quantity is one unit , such as $10 per pound, 30 miles per hour, 22 Indian Rupees per Nigerian naira, etc.

Let's find the unit rate of the situations.

Ricky spent $15.00 on 4 pizzas

unit rate = 15 / 4

unit rate = 3.75 dollars per pizza

William paid $20.00 for 2 1/2 pounds = 5 / 2 pounds of blackberries.

Therefore,

unit rate = 20 ÷ 5 / 2

unit rate = 20 × 2 / 5

unit rate = 40 / 5

unit rate = 8 dollars per pounds of blackberries

learn more on unit rate here; https://brainly.com/question/19165812

#SPJ1

Answer:

B

Step-by-step explanation:

Answer: $28.89

Step-by-step explanation: 2% of 1,444.50 is $28.89