Solve for x: 3x − 5 = 2x + 6.
1
−1
11
−11

-5/2 (3x+4)<6-3x          distribute

-15/2 x-10<6-3x                move -15/2 to the other side by adding it to 3x

-10<6+9/2 x                       move 6 over by subtracting it from -10

-16<9/2 x                          divide 9/2 by 16 (or multiply 2/9)

-32/9<x

Answer:

combining like terms

Step-by-step explanation:

After solving the system of linear equations, Malik has 123 domestic stamps and 89 foreign stamps.

Given the following system of equations:

[tex]x - y = 34\\\\x + y = 212[/tex]

To solve the system of linear equations, we would use the elimination method:

Adding the two equations together, we have:

[tex]2x = 246[/tex]

Dividing both sides by 2, we have:

[tex]x = \frac{246}{2}[/tex]

x = 123 domestic stamps

To find the value of y:

[tex]x + y = 212\\\\y = 212 - x\\\\y = 212 - 123[/tex]

y = 89 foreign stamps

Read more: https://brainly.com/question/3600420

To solve this problem, we use algebraic equations to represent the situation. By setting up an equation for the total sales and solving for the number of pens, we can then calculate the number of pencils sold based on the given information. In this case, 34 pens and 42 pencils were sold.

Let's solve this problem using algebra. Let the number of pens sold be x. According to the problem, the number of pencils sold is x + 8. Now we can set up an equation to represent the total sales:

0.20x + 0.05(x + 8) = 8.90

Simplifying the equation, we get:

0.20x + 0.05x + 0.40 = 8.90

Combining like terms,

0.25x + 0.40 = 8.90

Next, we can subtract 0.40 from both sides of the equation to isolate x:

0.25x = 8.90 - 0.40

Subtracting, we find that

0.25x = 8.50

Finally, we can divide both sides of the equation by 0.25 to solve for x:

x = 8.50 / 0.25

Calculating, we find that x = 34. This means that 34 pens were sold. Since 34 pens were sold and there were 8 more pencils sold than pens, there must have been 34 + 8 = 42 pencils sold.

https://brainly.com/question/32183344

#SPJ2

Final answer:

The standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3 is x² = -12y.

Explanation:

To find the standard form of the equation of a parabola with a given focus and directrix, we use the definition of a parabola: the locus of points equidistant from the focus and the directrix. Since the focus is at (0, -3) and the directrix is y = 3, the vertex is halfway between the focus and directrix, at (0, 0). The distance from the vertex to the focus (and to the directrix) is 3 units. The standard form of the parabola opening downwards is

(x - h)² = -4p(y - k)

where (h, k) is the vertex and p is the distance from the vertex to the focus, when the parabola opens upwards or downwards.

Substituting the values for the vertex and p, we get

(x - 0)² = -4(3)(y - 0)

which simplifies to

x² = -12y

This is the standard form of the parabola with the given focus and directrix.

Both Table A and Table B in the question represent functions, as each x value corresponds to exactly one y value in both tables. The operation of replacing the graph of f(x) with f(x) + 4 results in a vertical shift of the graph 4 units upward.

The subject of the question involves interpreting the data sets presented in Table A and Table B and understanding the behavior of functions. According to the definition, a function is a mathematical relationship wherein each input (x) corresponds to exactly one output (y).

Now, let's determine which tables represent functions. Table A: each 'x' corresponds to exactly one 'y', so this represents a function.

For Table B, each 'x' also corresponds to exactly one 'y', so this also represents a function.

This means both Table A and Table B represent functions.

As for the second question, the operation of replacing the graph of f(x) with f(x) + 4 will result in the graph shifting 4 units upward. The vertical shift is a result of adding 4 to the entire function f(x).

Learn more about Functions and Graphs here:

https://brainly.com/question/40116062

#SPJ3

Translations are part of rigid motions which also include reflection and rotation. For these three, we can then assume that neither the perimeter nor the area of an object would change. This means that, once an object is translated it is not biased or distorted (either enlarged or diminished). Thus, making the perimeter of the original and the image are equal. So for this problem, the perimeter of the image would be the same as the pre-image, and that would be 44 units. 

In the context of geometric transformations, the shape and size do not change, only position. Therefore, if the trapezoid's pre-image has a perimeter of 44 units, the image, as a result of translation, will have the same perimeter of 44 units.

In the context of geometric transformations like translations, rotations, or reflections, the shape and size of the object do not change--only its position does. The pre-image and the image are congruent, so their perimeters are the same.

In the situation described in your question, Penny's trapezoid is translated so that one of its vertices is at the origin. Because a translation is a type of isometry (a transformation that preserves distance), the shape of the trapezoid and the lengths of its sides will not change in the translation process. As a result, if the perimeter of the pre-image is 44 units, then the perimeter of the image will also be 44 units, regardless of where the vertices are located.

https://brainly.com/question/29987040

#SPJ3

Final answer:

Rodney sold 16 cars and Greg sold 8 cars in March.

Explanation:

Let's start by representing the number of cars sold by Rodney and Greg in March as variables. Let R represent the number of cars sold by Rodney and G represent the number of cars sold by Greg.

Given that Rodney sold twice as many cars as Greg in March, we have the equation R = 2G.

In April, Rodney sold 5 fewer cars than he did in March, so we have the equation R - 5.

Greg sold 3 more cars than he did in March, so we have the equation G + 3.

Lastly, we know that they sold the same number of cars in April, so we can set R - 5 = G + 3.

Now, we can solve the system of equations to find the values of R and G. Substituting R = 2G into the last equation, we get 2G - 5 = G + 3. Solving for G, we find G = 8. Substituting this value back into the equation R = 2G, we get R = 16.

Therefore, Rodney sold 16 cars and Greg sold 8 cars in March.

Rodney: 16 cars

Greg: 8 cars

Simply C Because well Nowadays You Have To Have Credit For Everything And Its Crazy When Your A Teenager Living On Your Own Without Any Credit. I Had To Buy Things For Around The House And Eventually Bought A $5,000 Bed Set

Answer:

A. $4.29

B. $1.44

Step-by-step explanation:

A. We have been given that Larry goes to gym twice a week for 13 weeks. Let us multiply 13 by 2 to find the number of times Larry visited the gym for first 3 months.

[tex]\text{The number of Larry's visits to gym for the first 3 months}=13\times 2=26[/tex]

Since there are 12 months in a year, then Larry has gone to gym only 9 times for rest of month as 12-3=9.

Now let us add 26 and 9 to get the total number of Larry's visits to gym.

[tex]\text{Larry's total visits to gym}=26+9[/tex]

[tex]\text{Larry's total visits to gym}=35[/tex]

Now let us divide total cost (150) by total number of visits (35) to get the each visit's cost.

[tex]\text{Each visit's cost}=\frac{150}{35}[/tex]

[tex]\text{Each visit's cost}=4.2857142857142857\approx 4.29[/tex]

Therefore, each visit to the center costs $4.29 to Larry.

B. If Larry continued going twice a week all year, then total number of Larry's visits to center will be 52 times 2.

[tex]\text{Larry's total visits to center}=52\times 2[/tex]

[tex]\text{Larry's total visits to center}=104[/tex]

Now let us divide total cost (150) by total visits (104) to find the cost of each visit.

[tex]\text{Each visit's cost}=\frac{150}{104}[/tex]  

[tex]\text{Each visit's cost}=1.4423076923076923\approx 1.44[/tex]

Therefore, If Larry continued going twice a week all year, it would cost  him $1.44 for each visit.