evaluate the following 7 = 5x+y÷3-3y​

Answer:

8x^3 + 4x^2 + 4x -7

Step-by-step explanation:

Add like terms.

Answer: everything is explained in the picture

Step-by-step explanation:

Given:

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]

We need to determine the equation of the line.

Slope:

Let us convert the equation to slope - intercept form.

[tex]-6 y=15-4x[/tex]

   [tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]

From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]

Since, the lines  are perpendicular, the slope of the line can be determined using the formula,

[tex]m_1 \cdot m_2=-1[/tex]

  [tex]\frac{2}{3} \cdot m_2=-1[/tex]

      [tex]m_2=-\frac{3}{2}[/tex]

Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;

[tex]y-9=-\frac{3}{2}(x-6)[/tex]

Simplifying the terms, we get;

[tex]2(y-9)=-3(x-6)[/tex]

[tex]2y-18=-3x+18[/tex]

[tex]3x+2y=36[/tex]

Thus, the equation of the line is [tex]3x+2y=36[/tex]

The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).

The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.

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Answer:

1200 cm is bigger. There are 100 cm in a meter. In 10 meters, there are 1000 cm. 1200 cm is longer than 1000 cm (10 meters)

Step-by-step explanation:

Gross profit is $44,000 and Net profit is $32,000

Step-by-step explanation:

Given :

Gross profit :

Gross Profit = Total income - Cost of goods sold

⇒ $86,000 - $42,000

⇒ $44,000

⇒ Gross profit is $44,000

Net profit :

Net profit = Gross profit – Total Expenses

⇒ $44,000 - $12,000

⇒ $32,000

⇒ Net profit is $32,000

Answer:

2x ÷ 4 = 8

Step-by-step explanation:

2x ÷ 4 = 8

2x/4 = 8

2x = 32

x = 16

Answer: A/5+30*5

Step-by-step explanation:

Answer: 24 cups.

Step-by-step explanation:

Let be "x" the amount of cups of peaches  that Fred will need to make 60 cups of  fruit salad.

According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:

[tex]2:3[/tex]

Which can also be written as a fraction:

[tex]\frac{2}{3}[/tex]

Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.

Knowing the above, you can set up the following proportion:

[tex]\frac{2}{5}=\frac{x}{60}[/tex]

Now you must solve for "x" in order to find its value. This is:

[tex](60)(\frac{2}{5})=x\\\\x=24[/tex]

Answer:

[tex]x=-2.6[/tex]

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

The linear function that models the data in the table is [tex]\( f(x) = 2x + 3 \)[/tex].

To find the linear function, we need two key pieces of information: the slope mn and the y-intercept b. In the given function f(x) = 2x + 3, the coefficient of x (2) represents the slope, and the constant term (3) represents the y-intercept.

The slope m indicates the rate at which the function is changing, and in this case, it is 2. This means that for every unit increase in x, y increases by 2 units. The y-intercept b is the value of y when x is zero, which is 3 in this case. Therefore, the linear function f(x) = 2x + 3 accurately models the relationship between x and y in the given dat x in a linear manner.

In summary, the general form of a linear function is [tex]\(f(x) = mx + b\)[/tex], where m is the slope and b is the y-intercept. The values of m and b can be determined from the data or information provided.

The linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex], where x represents the input and f(x) the output.

To find a linear function that models the data in the table, we can use the slope-intercept form of a linear equation: f(x) = mx + b, where m is the slope and b is the y-intercept.

Let's find the slope (m) first using the given data points (-4, -6) and (3, 7):

[tex]\[m = \frac{\text{change in } y}{\text{change in } x} = \frac{7 - (-6)}{3 - (-4)} = \frac{13}{7}.\][/tex]

Now that we have the slope, we can use any point from the table to find the y-intercept (b). Let's use the point (0, 1):

[tex]\[1 = m(0) + b \implies b = 1.\][/tex]

Now, we can write the linear function:

[tex]\[f(x) = \frac{13}{7}x + 1.\][/tex]

So, the linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex].

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x[/tex]

Answer:

11

Step-by-step explanation:

6 : 1

66 : X

X/66 = 1/6

X = 11

The range of the data set is 67 pounds.

The range of a data set is the difference between the maximum and minimum values. In this case, the weights of the 7 dogs are 66, 8, 12, 74, 36, 66, and 7 pounds. To find the range, we subtract the smallest value (7) from the largest value (74):

Range = 74 - 7 = 67

So, the range of the data set is 67 pounds.

Answer:

The GCF of 21 and 30 is 3.

Step-by-step explanation:

Find the prime factorization of 21

21 = 3 × 7

Find the prime factorization of 30

30 = 2 × 3 × 5

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 3

Answer:

3

Step-by-step explanation:

Factors of 21: 1, 3, 7, 21

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

The GCF is the largest factor they both have.

GCF = 3

Answer:

just complete the whole drawing

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

It equals 4 miles

Answer:

7

Step-by-step explanation:

to edge a lawn =10.he edged 4 lawn =10multiplied by 4=40

2nd. total -40=180-40=140

3rd. when he mows 1 lawn he is paid 20 what about when he is paid 140=140 divided by 20 =7

Makoto mowed 7 lawns to earn $180.

Let's denote the number of lawns Makoto mowed as m. Since he edged 4 lawns, that part of the income is 4 times $10, which sums up to $40. The total income from mowing is then $20 times the number of lawns he mowed, which is m. The equation representing Makoto's earnings is:

20m + 40 = 180

Subtracting 40 from both sides gives us:

20m = 140

Dividing both sides by 20 to solve for m gives us:

m = 7

Answer:

22 1/2 cakes

Step-by-step explanation:

1 cake = 1 1/3 hours

Number of cakes in 30-hour week

= 30 ÷ 1 1/3

= 30 ÷ 4/3

= 30 x 3/4

= 90/4

= 45/2

= 22 1/2

Answer: 22 1/2 cakes

Answer: 122.5 Miles.

Step-by-step explanation: This is because if you multiply 35 miles by 3.5 inches, you get 122.5 miles.

Hope this helps!

Answer: $7.665 each, approximately $7.67 each

Step-by-step explanation:

If cost is $15.33

To be sharedby two friends will be the cost/2

15.33/2= $7.665 each

Each person should pay $5.11 to equally split the total cost of the pizza and garlic bread, which is $15.33.

The student is asking how to divide the total cost of a pizza and garlic bread, which is $15.33, evenly among three people. To calculate this, we can use simple division.

Here is the step-by-step calculation:

First, identify the total cost of the food: $15.33.

Next, determine the number of people sharing the cost, which is three.

Divide the total cost by the number of people: $15.33 ÷ 3 = $5.11.

Therefore, each person should pay $5.11 to equally split the cost of the pizza and garlic bread.

Answer: [tex]x=12, -2[/tex]

Step-by-step explanation:

[tex](x-5)^{2}=49[/tex]

F.O.I.L the binomial

[tex]x^2-10x+25=49[/tex]

Set to 0

[tex]x^2-10x+25_{-49} =49_{-49}[/tex]

[tex]x^2-10x-24=0[/tex]

Factor the polynomial

[tex](x-12)(x+2)[/tex]

Set to 0 and Inverse operations

[tex](x-12)=0\\x=12[/tex]

Set to 0 and Inverse operations

[tex](x+2)=0\\x=-2[/tex]

Answer:

[tex]x=12, -2[/tex]

Answer:

x = 5 and x = -5

Step-by-step explanation:

Given x^2 = 25, we take the square root of both sides.  The two solutions are x = 5 and x = -5

The values for x in the equation x2 = 25 are 5 and -5. These solutions are represented on a number line at points 5 and -5.

The equation x2 = 25 can be solved by taking the square root of both sides of the equation. When we take the square root of a number, we get two possibilities: a positive and a negative value, since squaring a number always results in a positive number. Therefore, the values for x in the given equation would be x = 5 and x = -5.

On a number line, these points would be represented at the 5 and -5 positions. Therefore the number line that represents all the values of x for the equation x2 = 25 is the one that includes both -5 and 5. Keep in mind that no other numbers would satisfy the equation x2 = 25.

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Answer:

5x=-15

Step-by-step explanation:

8x-6x=4-10

2x=-6

x=-3

5x=-15

Answer:

T-shirts

Step-by-step explanation:

First, find the unit price for caps. Divide 25 by 4, which equals $6.25. Then, divide 20.25 by 3, which equals $6.75. Next, divide 30 by 4, which equals $7.50. Finally, divide 32.50 by 5, which equals $6.50. To t-shirts have a unit rate of $6.50

i think the answer is t-shirts , hope this helps

Answer: 2 tons.

Step-by-step explanation:

1 pound = 0.0005 tons.

4,000*0.0005=2

Jasmine's rhino weighs 2 tons

Answer:

2 tons

Step-by-step explanation:

Since 1 ton is 2000 pounds, we can make a proportion:

2000lbs/1ton=4000lbs/xtons

4000lbs=2000lbs*xtons

2=tons

So Jasmine's pet rhino weighs 2 tons

Answer: The probability is 1/52 or .0192.

Step-by-step explanation:

A standard deck of cards has 52 so the probability of picking 1 card would be 1/52.

(a) The probability of drawing a spade is 1/4.

(b) The probability of drawing a face card (jack, queen, or king) is 3/13.

(c) The probability of drawing a red card is 1/2.

(d) The probability of drawing a card that is not an ace is 12/13.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

(a) The probability of drawing a spade.

There are 13 spades in a standard deck of 52 cards, so the probability of drawing a spade is:

P(spade) = 13/52 = 1/4

(b) The probability of drawing a face card (jack, queen, or king).

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck of 52 cards, so the probability of drawing a face card is:

P(face card) = 12/52 = 3/13

(c) The probability of drawing a red card.

There are 26 red cards (13 hearts and 13 diamonds) in a standard deck of 52 cards, so the probability of drawing a red card is:

P(red card) = 26/52 = 1/2

(d) The probability of drawing a card that is not an ace.

There are 48 cards that are not aces in a standard deck of 52 cards (there are 4 aces), so the probability of drawing a card that is not an ace is:

P(not ace) = 48/52 = 12/13

Thus,

(a) The probability of drawing a spade is 1/4.

(b) The probability of drawing a face card (jack, queen, or king) is 3/13.

(c) The probability of drawing a red card is 1/2.

(d) The probability of drawing a card that is not an ace is 12/13.

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The complete question:

A card is randomly chosen from a standard deck of cards. Find each probability.

(a) The probability of drawing a spade.

(b) The probability of drawing a face card (jack, queen, or king).

(d) The probability of drawing a card that is not an ace.

Answer:

v > -1

Step-by-step explanation:

1/3(v-2) < v

Multiply both sides by 3(from 1/3) to equalize both sides.

This is equal to:

v-2 < 3v

Simplify equation:

v-2 < 3v =

-2 < 3v - v =

-2 < 2v

-1 < v

Swap sides:

v > -1

Therefore v is greater than -1.

Answer:

v > -1

Step-by-step explanation:

Simplify the left side.

Apply the distributive property.

13v+13⋅−2<v

Combine 13 and v

v3+13⋅−2<v

Combine 13 and −2

v3+−23<v

Move the negative in front of the fraction.

v3−23<v

Move all terms containing v to the left side of the inequality.

Subtract v from both sides of the inequality.

v3−23−v<0

Simplify the left side of the inequality.

−2(v+1)3<0

Multiply each term in −2(v+1)3<0 by −1

2(v+1)3>0

Multiply both sides of the equation by 3

2(v+1)>0⋅(3)

and again Simplify the left side.

Apply the distributive property.

2v+2⋅1>0⋅(3)

Multiply 2 by 1

2v+2>0⋅(3)

Multiply 0 by 3

2v+2>0

Subtract 2 from both sides of the inequality.

2v>−2

Divide each term by 2 and simplify.

Getting the conclusion where V is greater than 1

v>−1

Hope this helps

Answer:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

4

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

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Answer:

C Both relation and function.

Step-by-step explanation:

This would pass the vertical line test so it is both a relation and a function