To simplify the expression 13 - 2(1 - 15) ÷ 4, first calculate the value inside the parentheses:
1 - 15 = -14.
Then, multiply -14 by 2:
-14 * 2 = -28.
Next, divide -28 by 4:
-28 ÷ 4 = -7.
Finally, subtract -7 from 13:
13 - (-7) = 13 + 7 = 20.
Therefore, the simplified expression is 20.
The correct response is D. 20.
Simplify the expression.
13−2(1−15)÷4
responses
A. -38.5
B. 7.25
C. -26
D. 20
52 answers
Solve for r. r5−6=−1
To solve for r in the equation r^5 - 6 = -1, we can follow these steps:
1. Add 6 to both sides of the equation to isolate the term with r:
r^5 = -1 + 6
r^5 = 5
2. Take the fifth root of both sides to eliminate the exponent of 5:
∛(r^5) = ∛5
r = ∛5
Therefore, the solution for r is the cube root of 5.
1. Add 6 to both sides of the equation to isolate the term with r:
r^5 = -1 + 6
r^5 = 5
2. Take the fifth root of both sides to eliminate the exponent of 5:
∛(r^5) = ∛5
r = ∛5
Therefore, the solution for r is the cube root of 5.
Solve for x. −3x−8=10
To solve for x in the equation -3x - 8 = 10, we can follow these steps:
1. Add 8 to both sides of the equation to isolate the term with x:
-3x = 10 + 8
-3x = 18
2. Divide both sides by -3 to solve for x:
x = 18 / -3
x = -6
Therefore, the solution for x is -6.
1. Add 8 to both sides of the equation to isolate the term with x:
-3x = 10 + 8
-3x = 18
2. Divide both sides by -3 to solve for x:
x = 18 / -3
x = -6
Therefore, the solution for x is -6.
Simplify the expression. (2x+2)−(3x+11)
To simplify the expression (2x + 2) - (3x + 11), we can distribute the negative sign to the terms inside the second parentheses:
(2x + 2) - (3x + 11) = 2x + 2 - 3x - 11
Next, combine like terms:
2x - 3x + 2 - 11 = -x - 9
Therefore, the simplified expression is -x - 9.
(2x + 2) - (3x + 11) = 2x + 2 - 3x - 11
Next, combine like terms:
2x - 3x + 2 - 11 = -x - 9
Therefore, the simplified expression is -x - 9.
What is the first step in solving the equation: 20=6x−4
The first step in solving the equation 20 = 6x - 4 is to isolate the term with x. To do this, we can add 4 to both sides of the equation.
Adding 4 to both sides:
20 + 4 = 6x - 4 + 4
This simplifies to:
24 = 6x
Now, the equation is in the form 6x = 24.
Adding 4 to both sides:
20 + 4 = 6x - 4 + 4
This simplifies to:
24 = 6x
Now, the equation is in the form 6x = 24.
Simplify the expression. 6(3x−5)+2(3x−5)−8(2x−5)
To simplify the expression 6(3x - 5) + 2(3x - 5) - 8(2x - 5), we can distribute the coefficients to the terms inside the parentheses:
6(3x - 5) + 2(3x - 5) - 8(2x - 5) = 18x - 30 + 6x - 10 - 16x + 40
Next, combine like terms:
(18x + 6x - 16x) + (-30 - 10 + 40) = 8x + 0 = 8x
Therefore, the simplified expression is 8x.
6(3x - 5) + 2(3x - 5) - 8(2x - 5) = 18x - 30 + 6x - 10 - 16x + 40
Next, combine like terms:
(18x + 6x - 16x) + (-30 - 10 + 40) = 8x + 0 = 8x
Therefore, the simplified expression is 8x.
Write an equation and solve for the unknown number. Twice a number, increased by 3 is 7.
To represent the given situation as an equation, we'll use the variable "x" to represent the unknown number. The equation can be written as:
2x + 3 = 7
Now, let's solve for x:
Subtracting 3 from both sides of the equation:
2x + 3 - 3 = 7 - 3
This simplifies to:
2x = 4
Next, divide both sides of the equation by 2 to solve for x:
2x / 2 = 4 / 2
This gives us:
x = 2
Therefore, the unknown number is 2.
2x + 3 = 7
Now, let's solve for x:
Subtracting 3 from both sides of the equation:
2x + 3 - 3 = 7 - 3
This simplifies to:
2x = 4
Next, divide both sides of the equation by 2 to solve for x:
2x / 2 = 4 / 2
This gives us:
x = 2
Therefore, the unknown number is 2.
Solve for x. 3x−7−2x+5=6
To solve for x in the equation 3x - 7 - 2x + 5 = 6, we can combine like terms:
Start by simplifying 3x - 2x:
3x - 2x = x
Next, simplify -7 + 5:
-7 + 5 = -2
Now, substitute the simplified terms back into the equation:
x - 2 = 6
To isolate x, we can add 2 to both sides of the equation:
x - 2 + 2 = 6 + 2
This simplifies to:
x = 8
Therefore, the solution for x is 8.
Start by simplifying 3x - 2x:
3x - 2x = x
Next, simplify -7 + 5:
-7 + 5 = -2
Now, substitute the simplified terms back into the equation:
x - 2 = 6
To isolate x, we can add 2 to both sides of the equation:
x - 2 + 2 = 6 + 2
This simplifies to:
x = 8
Therefore, the solution for x is 8.
In Atlanta, the temperature was −2 °F in the morning in the winter. There was a winter storm, and the temperature dropped 10 degrees. What is the temperature now?
To find the temperature after the temperature dropped by 10 degrees, you can subtract 10 from the initial temperature of -2 °F.
-2 °F - 10 = -12 °F
Therefore, the temperature now is -12 °F.
-2 °F - 10 = -12 °F
Therefore, the temperature now is -12 °F.
Shawn is solving the equation x/7−47=−6 One of his steps is to multiply both sides of the equation by 7. Why?
Shawn multiplied both sides of the equation x/7 - 47 = -6 by 7 in order to eliminate the denominator (7) from the left side of the equation. By multiplying the entire equation by 7, the fraction x/7 becomes x, resulting in a simplified equation that is easier to solve.
A mountain climber starts a climb at an elevation of 380 ft. above sea level. At his first rest stop he has climbed 182 ft., and by his second rest stop he has climbed another 208 ft. It is getting late in the day, so the climber starts his way down the mountain. If the climber descends 235 ft, how much does he need to descend to return to his original starting point?
To determine how much the climber needs to descend to return to his original starting point, we need to calculate the net change in elevation.
First, let's calculate the total distance climbed by adding the elevations at each rest stop:
182 ft + 208 ft = 390 ft.
Therefore, the climber has climbed a total of 390 ft.
Next, to find the total change in elevation, we need to subtract the net increase in elevation from the net decrease in elevation:
Total change in elevation = Total climb - Total descent
= 390 ft - 235 ft
= 155 ft.
The climber would need to descend an additional 155 ft to return to his original starting point.
First, let's calculate the total distance climbed by adding the elevations at each rest stop:
182 ft + 208 ft = 390 ft.
Therefore, the climber has climbed a total of 390 ft.
Next, to find the total change in elevation, we need to subtract the net increase in elevation from the net decrease in elevation:
Total change in elevation = Total climb - Total descent
= 390 ft - 235 ft
= 155 ft.
The climber would need to descend an additional 155 ft to return to his original starting point.
Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, how much is the regular price of each ticket?
Let's represent the regular price of each ticket as x.
Since Dea buys 6 tickets at a discount of $1.50 off the regular price, the cost of each ticket after the discount is x - $1.50.
The total cost of 6 tickets would be 6 times the cost of each ticket after the discount:
6(x - $1.50) = $51
Now, we can solve for the regular price of each ticket by solving the equation.
First, distribute the 6 to the terms inside the parentheses:
6x - 9 = $51
Next, isolate the variable term by adding 9 to both sides:
6x = $51 + $9
6x = $60
Finally, divide both sides by 6 to solve for x:
x = $60 / 6
x = $10
Therefore, the regular price of each ticket is $10.
Since Dea buys 6 tickets at a discount of $1.50 off the regular price, the cost of each ticket after the discount is x - $1.50.
The total cost of 6 tickets would be 6 times the cost of each ticket after the discount:
6(x - $1.50) = $51
Now, we can solve for the regular price of each ticket by solving the equation.
First, distribute the 6 to the terms inside the parentheses:
6x - 9 = $51
Next, isolate the variable term by adding 9 to both sides:
6x = $51 + $9
6x = $60
Finally, divide both sides by 6 to solve for x:
x = $60 / 6
x = $10
Therefore, the regular price of each ticket is $10.
Solve for x. 1/3 (6x − 9) = −33
To solve for x in the equation 1/3(6x - 9) = -33, we can follow these steps:
1. Distribute 1/3 to the terms inside the parentheses:
(1/3)(6x - 9) = -33
(2x - 3)/3 = -33
2. Multiply both sides of the equation by 3 to eliminate the fraction:
3 * (2x - 3)/3 = -33 * 3
2x - 3 = -99
3. Add 3 to both sides to isolate the term with x:
2x - 3 + 3 = -99 + 3
2x = -96
4. Divide both sides by 2 to solve for x:
(2x)/2 = (-96)/2
x = -48
Therefore, the solution for x is -48.
1. Distribute 1/3 to the terms inside the parentheses:
(1/3)(6x - 9) = -33
(2x - 3)/3 = -33
2. Multiply both sides of the equation by 3 to eliminate the fraction:
3 * (2x - 3)/3 = -33 * 3
2x - 3 = -99
3. Add 3 to both sides to isolate the term with x:
2x - 3 + 3 = -99 + 3
2x = -96
4. Divide both sides by 2 to solve for x:
(2x)/2 = (-96)/2
x = -48
Therefore, the solution for x is -48.
wrong
Apologies for the mistake. Let's start over and solve the equation correctly:
To solve for x in the equation (1/3)(6x - 9) = -33, we can follow these steps:
1. Distribute 1/3 to the terms inside the parentheses:
(1/3)(6x - 9) = -33
2x - 3 = -33
2. Add 3 to both sides to isolate the term with x:
2x - 3 + 3 = -33 + 3
2x = -30
3. Divide both sides by 2 to solve for x:
(2x)/2 = (-30)/2
x = -15
Therefore, the solution for x is -15.
To solve for x in the equation (1/3)(6x - 9) = -33, we can follow these steps:
1. Distribute 1/3 to the terms inside the parentheses:
(1/3)(6x - 9) = -33
2x - 3 = -33
2. Add 3 to both sides to isolate the term with x:
2x - 3 + 3 = -33 + 3
2x = -30
3. Divide both sides by 2 to solve for x:
(2x)/2 = (-30)/2
x = -15
Therefore, the solution for x is -15.
Solve for x. −3/5(15x−30)=198
To solve for x in the equation (-3/5)(15x - 30) = 198, we can follow these steps:
1. Distribute -3/5 to the terms inside the parentheses:
(-3/5)(15x - 30) = 198
(-3/5)*15x - (-3/5)*30 = 198
-9x + 6 = 198
2. Subtract 6 from both sides to isolate the term with x:
-9x + 6 - 6 = 198 - 6
-9x = 192
3. Divide both sides by -9 to solve for x:
(-9x)/-9 = 192/-9
x = -192/9
We can further simplify -192/9 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
-192/9 = -64/3
Therefore, the solution for x is -64/3.
1. Distribute -3/5 to the terms inside the parentheses:
(-3/5)(15x - 30) = 198
(-3/5)*15x - (-3/5)*30 = 198
-9x + 6 = 198
2. Subtract 6 from both sides to isolate the term with x:
-9x + 6 - 6 = 198 - 6
-9x = 192
3. Divide both sides by -9 to solve for x:
(-9x)/-9 = 192/-9
x = -192/9
We can further simplify -192/9 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
-192/9 = -64/3
Therefore, the solution for x is -64/3.
Solve for x. 3(4x−12)=84
To solve for x in the equation 3(4x - 12) = 84, we can follow these steps:
1. Distribute 3 to the terms inside the parentheses:
3(4x - 12) = 84
12x - 36 = 84
2. Add 36 to both sides to isolate the term with x:
12x - 36 + 36 = 84 + 36
12x = 120
3. Divide both sides by 12 to solve for x:
(12x)/12 = 120/12
x = 10
Therefore, the solution for x is 10.
1. Distribute 3 to the terms inside the parentheses:
3(4x - 12) = 84
12x - 36 = 84
2. Add 36 to both sides to isolate the term with x:
12x - 36 + 36 = 84 + 36
12x = 120
3. Divide both sides by 12 to solve for x:
(12x)/12 = 120/12
x = 10
Therefore, the solution for x is 10.
Solve for x. 20(2x−8)=440
To solve for x in the equation 20(2x - 8) = 440, we can follow these steps:
1. Distribute 20 to the terms inside the parentheses:
20(2x - 8) = 440
40x - 160 = 440
2. Add 160 to both sides to isolate the term with x:
40x - 160 + 160 = 440 + 160
40x = 600
3. Divide both sides by 40 to solve for x:
(40x)/40 = 600/40
x = 15
Therefore, the solution for x is 15.
1. Distribute 20 to the terms inside the parentheses:
20(2x - 8) = 440
40x - 160 = 440
2. Add 160 to both sides to isolate the term with x:
40x - 160 + 160 = 440 + 160
40x = 600
3. Divide both sides by 40 to solve for x:
(40x)/40 = 600/40
x = 15
Therefore, the solution for x is 15.
Solve for x. 0.72=0.4(x+1.4)
To solve for x in the equation 0.72 = 0.4(x + 1.4), we can follow these steps:
1. Distribute 0.4 to the terms inside the parentheses:
0.4(x + 1.4) = 0.72
0.4x + 0.56 = 0.72
2. Subtract 0.56 from both sides to isolate the term with x:
0.4x + 0.56 - 0.56 = 0.72 - 0.56
0.4x = 0.16
3. Divide both sides by 0.4 to solve for x:
(0.4x)/0.4 = 0.16/0.4
x = 0.4
Therefore, the solution for x is 0.4.
1. Distribute 0.4 to the terms inside the parentheses:
0.4(x + 1.4) = 0.72
0.4x + 0.56 = 0.72
2. Subtract 0.56 from both sides to isolate the term with x:
0.4x + 0.56 - 0.56 = 0.72 - 0.56
0.4x = 0.16
3. Divide both sides by 0.4 to solve for x:
(0.4x)/0.4 = 0.16/0.4
x = 0.4
Therefore, the solution for x is 0.4.
Solve for x. 2(1.5x−7)=6
To solve for x in the equation 2(1.5x - 7) = 6, we can follow these steps:
1. Distribute 2 to the terms inside the parentheses:
2(1.5x - 7) = 6
3x - 14 = 6
2. Add 14 to both sides to isolate the term with x:
3x - 14 + 14 = 6 + 14
3x = 20
3. Divide both sides by 3 to solve for x:
(3x)/3 = 20/3
x = 20/3
Therefore, the solution for x is 20/3 or 6.67.
1. Distribute 2 to the terms inside the parentheses:
2(1.5x - 7) = 6
3x - 14 = 6
2. Add 14 to both sides to isolate the term with x:
3x - 14 + 14 = 6 + 14
3x = 20
3. Divide both sides by 3 to solve for x:
(3x)/3 = 20/3
x = 20/3
Therefore, the solution for x is 20/3 or 6.67.
Solve for x. 5x−2x+4=−5
To solve for x in the equation 5x - 2x + 4 = -5, we can follow these steps:
1. Combine like terms on the left side of the equation:
5x - 2x + 4 = -5
3x + 4 = -5
2. Subtract 4 from both sides to isolate the term with x:
3x + 4 - 4 = -5 - 4
3x = -9
3. Divide both sides by 3 to solve for x:
(3x)/3 = (-9)/3
x = -3
Therefore, the solution for x is -3.
1. Combine like terms on the left side of the equation:
5x - 2x + 4 = -5
3x + 4 = -5
2. Subtract 4 from both sides to isolate the term with x:
3x + 4 - 4 = -5 - 4
3x = -9
3. Divide both sides by 3 to solve for x:
(3x)/3 = (-9)/3
x = -3
Therefore, the solution for x is -3.
Solve for x. 9x+9x−21=33
To solve for x in the equation 9x + 9x - 21 = 33, we can follow these steps:
1. Combine like terms on the left side of the equation:
18x - 21 = 33
2. Add 21 to both sides to isolate the term with x:
18x - 21 + 21 = 33 + 21
18x = 54
3. Divide both sides by 18 to solve for x:
(18x)/18 = 54/18
x = 3
Therefore, the solution for x is 3.
1. Combine like terms on the left side of the equation:
18x - 21 = 33
2. Add 21 to both sides to isolate the term with x:
18x - 21 + 21 = 33 + 21
18x = 54
3. Divide both sides by 18 to solve for x:
(18x)/18 = 54/18
x = 3
Therefore, the solution for x is 3.
Solve for x. 14x−3x+11=−22
To solve for x in the equation 14x - 3x + 11 = -22, we can follow these steps:
1. Combine like terms on the left side of the equation:
14x - 3x + 11 = -22
11x + 11 = -22
2. Subtract 11 from both sides to isolate the term with x:
11x + 11 - 11 = -22 - 11
11x = -33
3. Divide both sides by 11 to solve for x:
(11x)/11 = (-33)/11
x = -3
Therefore, the solution for x is -3.
1. Combine like terms on the left side of the equation:
14x - 3x + 11 = -22
11x + 11 = -22
2. Subtract 11 from both sides to isolate the term with x:
11x + 11 - 11 = -22 - 11
11x = -33
3. Divide both sides by 11 to solve for x:
(11x)/11 = (-33)/11
x = -3
Therefore, the solution for x is -3.
At Mariah's birthday party, 9 of her friends ate 34 of her chocolate cake. How much of the cake did each friend eat?
To find out how much of the cake each friend ate, we need to divide the total amount of cake eaten (34) by the number of friends (9).
34 / 9 ≈ 3.7778
So, each friend ate approximately 3.7778 pieces of the chocolate cake.
34 / 9 ≈ 3.7778
So, each friend ate approximately 3.7778 pieces of the chocolate cake.
as a fraction
To represent the amount of cake each friend ate as a fraction, we can write it as 34/9.
Therefore, each friend ate 34/9 of the chocolate cake.
Therefore, each friend ate 34/9 of the chocolate cake.
its wrong
Apologies for the mistake. Let's recalculate the amount of cake each friend ate as a fraction.
To determine the fraction, we need to divide the total amount of cake eaten (34) by the number of friends (9).
34 / 9 = 3 remainder 7
Since each friend cannot eat a fraction of a cake, we can say that each friend ate 3 whole pieces of the cake.
Therefore, each friend ate 3/9 or 1/3 of the chocolate cake.
To determine the fraction, we need to divide the total amount of cake eaten (34) by the number of friends (9).
34 / 9 = 3 remainder 7
Since each friend cannot eat a fraction of a cake, we can say that each friend ate 3 whole pieces of the cake.
Therefore, each friend ate 3/9 or 1/3 of the chocolate cake.
The product of 9 and the sum of a number and 8 is 180. What is the number?
Let's represent the unknown number as x.
The equation can be written as:
9(x + 8) = 180
Now, let's solve for x:
1. Distribute 9 to the terms inside the parentheses:
9x + 72 = 180
2. Subtract 72 from both sides to isolate the term with x:
9x + 72 - 72 = 180 - 72
9x = 108
The equation can be written as:
9(x + 8) = 180
Now, let's solve for x:
1. Distribute 9 to the terms inside the parentheses:
9x + 72 = 180
2. Subtract 72 from both sides to isolate the term with x:
9x + 72 - 72 = 180 - 72
9x = 108
Wrong the answer is 12