The ratio of dogs to cats at the pet store is 1:2. There are 15 dogs. How many cats are there?

The required expression is  x + 2y = 2 (3/2 + y) that gives the value 3.

An algebraic expression is consists of variables, numbers with various mathematical operations,

To write the algebraic expression with variable x that has a value of 3.

Let x is a variable and y is another variable,

The expression for the x equal to 3 can be written as,

x + 2y = 2 (3/2 + y)

The expression x + 2y = 2 (3/2 + y) gives the value 3.

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Answer:

If you graph the data points and the points lie along a straight line then the data is linear.

Final answer:

To evaluate 5/9(f-32) when f=50, substitute 50 into the expression, simplify the bracket (50 - 32 = 18), and then multiply the result by 5/9. This simplifies to 18/9 (which is 2), and then 2 x 5, yielding a final answer of 10 degrees Celsius.

Explanation:

To evaluate the expression 5/9(f-32) when f=50, you need to plug the value of f into the expression and then simplify it.

Here are the steps:

Substitute 50 for f in the expression: (5/9) × (50 - 32).

Calculate the bracket first: 50 - 32 = 18.

Multiply the result by 5/9: (5/9) × 18.

Divide 18 by 9, which gives you 2.

Finally, multiply 2 by 5, which gives you 10.

Therefore, 5/9(f-32) evaluated at f=50 is 10 degrees Celsius.

Answer:

$7500

Step-by-step explanation:

Answer: (3x1/3) x 42

Step-by-step explanation: trust me I took the test.

There are total 1638 marbles.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Number of jars = 3

Each bar contain = 42 marbles

Red marbles = 13

So, total number of marbles

= 3 x 13 x 42

= 1638.

Hence, there are total 1638 marbles.

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Answer:

k/2 − 3/5

Step-by-step explanation:

To simplify the expression 2/5k - 3/5k + 1/10k, we combine the like terms and simplify the fractions. The simplified expression is -1/10k.

To simplify the expression 2/5k - 3/5k + 1/10k, we can combine like terms. Like terms have the same variable raised to the same power. In this case, the variable is 'k'. So, combining the fractions, we get:

(2/5 - 3/5 + 1/10)k

Now, let's simplify the fractions:

Therefore, the simplified expression is -1/10k.

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Answer:

The rate of change in the function y=x+4 is _Equal_ the rate of change of the function represented in the table.

Answer: He would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.

Step-by-step explanation:

Since we have given that

Fraction of mashed potatoes he had to fill up a container = [tex]\dfrac{4}{5}[/tex]

Fraction of mashed potatoes he ended up using = [tex]2\dfrac{4}{6}=2\dfrac{2}{3}=\dfrac{8}{3}[/tex]

So, we need to find the number of pounds that he would need to fill the container all the way.

So, number of pounds would be

[tex]\dfrac{8}{3}\div \dfrac{4}{5}\\\\=\dfrac{8}{3}\times \dfrac{5}{4}\\\\=\dfrac{10}{3}\\\\=3\dfrac{1}{3}[/tex]

Hence, he would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.

Answer: C.2

Step-by-step explanation:

Given: Independent variable= Number of sides

To check how many of the remaining three columns represent a linear relationship, we need to check the rate of change of the three columns with respect to dependent variable.

For number of diagonals

The rate of change of diagonals w.r.t number of sides is constant and that is 1.

For Sum of all interior angles (degrees)

The rate of change of  Sum of all interior angles w.r.t number of sides is constant and that is 180°.

For measure of each angle (degrees)

The rate of change of  measure of each angle w.r.t number of sides is not constant and that is 180°.

Since for vertices 3 , measure of angle=60

vertices 4 , measure of angle=90

From vertices 3 to 4 change in measure of angle is 30

vertices 5 , measure of angle=108

From vertices 4 to 5 change in measure of angle is 18

Thus number of diagonals and Sum of all interior angles are the columns represent a linear relationship when compared with the independent variable.

Therefore there are 2 columns represent a linear relationship when compared with the independent variable.

Solution:

The equation of linear relationship is , y= k x

That is, [tex]\frac{y-value}{x-value}=k({\text{a constant})[/tex]

As, you can see that , ratio of

1.

[tex]\frac{\text{Sum of interior angles of a regular polygon}}{\text{number of sides of that polygon}}={\text{Measure of each interior angle of regular polygon}}[/tex]

2. Also, as number of sides increases, the smallest regular polygon is equilateral triangle(3 sides) , having 0, diagonal, the number of diagonal increases by 1.

→→Regular polygon having sides , n≥3=k, where k is number of diagonals=0,1,2,3,4,[ For example, for, n=3,k=1,n=4, k=2,...]

Column (2)

[tex]C_{4}-C_{3}=C_{3}-C_{2}=C_{2}-C_{1}=1[/tex]

Column (4)

[tex]C_{2}-C_{1}=90-60=30\\\\ C_{3}-C_{2}=108-90=18\\\\ C_{4}-C_{3}=120-108=12[/tex]

Column (3)

[tex]C_{4}-C_{3}=720-540=180\\\\ C_{3}-C_{2}=540-360=180\\\\ C_{2}-C_{1}=360-180=180[/tex]

In, Column (2) and Column(3) the difference between two consecutive values is same, while in column (4) difference between two consecutive values is not same.So, C(2) and C(3) shows linear relationship, column (4) do not.

Option (C) 2 is Right choice.

Answer:

Negative Slope

Step-by-step explanation:

The slope is the ratio of Change in height to the change in horizontal distance. It can also be define as tangent of angle made by that line and it is find by formula, [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

The slope is said to be a positive slope when a line is moving from left to right, the line rises.

The slope is said to be a negative slope when a line is moving from left to right, the line falls.

Here, Let the student earns be y marks in test

and let incorrect question be x

then y₁ = 98 , y₂ = 90 and x₁ = 1 , x₂ = 5

then [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

[tex]slope (m)= \frac{90 - 98}{5 - 1} [/tex]

⇒ m = -2

Hence, it has negative slope.