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algol13
2 years ago
8

The equation of line fis - 3y + 4x = 9 write the equation of a line that is parallel to line and passes through the point (- 12,

6)
Mathematics
1 answer:
ollegr [7]2 years ago
3 0

Answer:

y =  - 4x - 42

Step-by-step explanation:

The equation of the line that is parallel to the line we are trying to find is

- 3y + 4x = 9 \\ or \\  - 3y =  - 4x + 9 \:(standard form) \\ \\therefore \: the \: slope \: of \: the \: line \\  \: is \:  - 4

We can recall that when two lines are parallel it means that they have the same slope. Therefore the slope of the line we are trying to find is also -4. We now know that:

y = 6 \:  \:  \: x =  - 12 \:  \:  \: slope =  - 4

Therefore the equation of the line is:

y = mx + c \\  6= ( - 4)( - 12) + c \\ 6 = 48 + c \\ 6 - 48 = c \\  - 42 = c

y = mx + c \\ y =  - 4x - 42

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Anna is a teacher at an elementary school. She purchased 73 tickets to take the first-grade children and some parents on a field
Svetllana [295]

She bought 54 child tickets and 19 adult tickets.

Step-by-step explanation:

No. of tickets purchased = 73

Cost of tickets = $771

Cost of one child ticket = $9

Cost of one adult ticket = $15

Let,

Child ticket = x

Adult ticket = y

According to given statement;

x+y=73   Eqn 1

9x+15y=771   Eqn 2

Multiplying Eqn 1 by 9;

9(x+y=73)\\9x+9y=657\ \ \ Eqn\ 3\\

Subtracting Eqn 3 from Eqn 2;

(9x+15y)-(9x+9y)=771-657\\9x+15y-9x-9y=114\\6y=114\\

Dividing both sides by 6;

\frac{6y}{6}=\frac{114}{6}\\y=19

Putting y=19 in Eqn 1

x+19=73\\x=73-19\\x=54\\

She bought 54 child tickets and 19 adult tickets.

Keywords: linear equations, subtraction

Learn more about linear equations at:

  • brainly.com/question/3227215
  • brainly.com/question/3269852

#LearnwithBrainly

4 0
3 years ago
Coffee: A popular chain of cafes has been receiving online complaints about one store location. Regular customers complained tha
hammer [34]

Answer:

The test statistic is z=2.5.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that more than 10% of the 16 ounce cups are underfilled.

Then, the null and alternative hypothesis are:

H_0: \pi=0.1\\\\H_a:\pi>0.1

The significance level is assumed to be 0.05.

The sample has a size n=100.

The sample proportion is p=0.18.

p=X/n=18/100=0.18

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.001}=0.03

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.18-0.1-0.5/100}{0.03}=\dfrac{0.075}{0.03}=2.5

This test is a right-tailed test, so the P-value for this test is calculated as:

P-value=P(z>2.5)=0.006

As the P-value (0.006) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

7 0
3 years ago
A nutritionist planning a diet for a rugby player wants him to consume 3,650 Calories and 650 grams of food daily. Calories from
Tcecarenko [31]

Answer:

300

Step-by-step explanation:

because when multiply then divide all of them then find a percent 300 is your answer

8 0
3 years ago
Read 2 more answers
A campus club held a bake sale as a fund raiser, selling coffee, muffins, and bacon and eggs sandwiches. The club members charge
OLEGan [10]

Answer:

The number of  bacon and egg sandwiches sells are 2 .

Step-by-step explanation:

Let us assume that the number of coffee cups campus club sells be x .

Let us assume that the number of muffins  cups campus club sells be y .

Let us assume that the number of bacon and eggs sandwiches campus club sells be z .

As given

Campus club sold a total of 55 items .

Thus the equation becomes

x + y + z = 55

Of the club members sold 5 more muffins than cups of coffee .

Thus

Number of muffins = 5 + Number of cups of coffee

y = 5 + x

Putting the value of y in the equation x + y + z = 55 .

x + 5 + x + z = 55

2x + z = 55- 5

2x + z = 50

As given

The club members charged $1 for a cup of coffee, 3$ for a muffin , and $4 for a bacon and egg sandwich and earns $119 .

Thus the equation becomes

x + 3y + 4z = 119

Putting the value of y in the above

x + 3 × (x + 5) + 4z = 119

x + 3x + 15 + 4z = 119

4x + 4z = 119 - 15

4x + 4z = 104

Simplify the above

x + z = 26

Thus the two equations are

2x + z = 50

x + z = 26

Multiply x + z = 26 subtracted from 2x + z = 50.

2x -x + z - z = 50  - 26

x = 24

Put the value of x in x + z = 26 .

24 + z =26

z = 26 - 24

z = 2

Therefore the number of  bacon and egg sandwiches sells are 2 .

7 0
3 years ago
X+2>7 write the solution set in interval notation
REY [17]

Answer:

(5, infinitysymbol)

Step-by-step explanation:

First solve the inequality. Subtract 2 from both sides.

x + 2 > 7

x > 5

So that is one way of writing the answer and it is hopefully kind of understandable. X>5 means all the numbers greater (bigger) than 5, forever to infinity.

Interval notation is a way of writing a set or group of numbers. Interval notation uses ( ) parenthesis or [ ] square brackets. Then two numbers go inside with a comma in between. The first number is where the set of numbers start and the second number is where the set ends. You always put parenthesis around the infinity symbol or negative infinity symbol. You only use a square bracket if the inequality symbols have the "or equal to" underline under the > or <.

So x > 5 in interval notation is:

(5, infinitysymbol)

This shows that 5 is not included in the solution; and all the numbers forever bigger than five are solutions as well.

5 0
1 year ago
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