Can someone check over these problems for me?
1. The width of a rectangle is fixed at 28 cm. What lengths will make the perimeter greater than 70 cm?
A: the length must be greater than 7 cm.
2. 7x=-63
A: x=-9
3. Is (-8.-9)a solution of 2x+4y=12
A: No
4. -1/2x=-9/10
A: 9/5
5. Solve the system of equations
x+3y=7
x=8-3y
A: No solution
6. find slope
(9,8)
(10,-7)
A:-15
correct.
thank you!
pls solve 3x10=(2x10)+(1x_)
To check over these problems, we can go through each one and explain the steps to arrive at the correct answer.
1. The width of a rectangle is fixed at 28 cm. What lengths will make the perimeter greater than 70 cm?
To find the perimeter of a rectangle, we add twice the length and twice the width. In this case, the width is given as 28 cm. So, the perimeter equation becomes: 2(length) + 2(28) > 70. Simplifying this, we get 2(length) + 56 > 70. Next, we subtract 56 from both sides, which gives us 2(length) > 14. Finally, dividing both sides by 2, we get length > 7 cm. Therefore, any length greater than 7 cm will make the perimeter of the rectangle greater than 70 cm.
2. 7x = -63
To solve for x in this equation, divide both sides by 7: x = -63/7. Simplifying, x = -9. Therefore, the solution to this equation is x = -9.
3. Is (-8, -9) a solution of 2x + 4y = 12?
To check if (-8, -9) is a solution, substitute the x and y values into the equation and see if it holds true. Plugging in -8 for x and -9 for y, we get: 2(-8) + 4(-9) = 12. Simplifying this equation, we have -16 - 36 = 12, which results in -52 = 12. Since this is not true, the answer is no, (-8, -9) is not a solution to the equation.
4. -1/2x = -9/10
To solve for x, we want to isolate the variable x. Multiply both sides of the equation by the reciprocal of -1/2, which is -2/1 or -2. This gives us: -2/1 * -1/2x = -2/1 * -9/10. Simplifying, we have x = 9/5. Therefore, the solution to this equation is x = 9/5.
5. Solve the system of equations:
x + 3y = 7
x = 8 - 3y
To solve this system, we can substitute the second equation into the first equation. Substituting x in the first equation with (8 - 3y), we get (8 - 3y) + 3y = 7. Simplifying, we have 8 - 2y = 7. Next, subtract 8 from both sides to isolate the variable: -2y = -1. Finally, divide both sides by -2 to solve for y: y = 1/2. Plugging the value of y back into the second equation, we have x = 8 - 3(1/2) = 8 - 3/2 = 13/2. Since we have different values for x and y, there is no solution to this system of equations.
6. Find the slope given two points: (9, 8) and (10, -7).
The slope between two points can be found using the formula (y2 - y1) / (x2 - x1). Let's substitute the values into the formula: (-7 - 8) / (10 - 9) = -15 / 1 = -15. Therefore, the slope between the two points is -15.