1.### Evaluate for x = 11
x + 4

Answer:
15

Explanation:

To evaluate the expression x+4 for x=11:

x+4=11+4=15

So, the value of the expression when x=11 is 15.

x+4=11+4=15

So, the value of the expression when x=11 is 15.

2.### Evaluate for n = 0: 2 (4 + n) - 5

Answer:
3

Explanation:

To evaluate the expression 2(4+n)−5 for n=0:

Substitute n=0 into the expression: 2(4+0)−5

Simplify inside the parentheses: 2(4)−5

Multiply: 8−5

Subtract: 3

So, the value of the expression when n=0 is 3.

Substitute n=0 into the expression: 2(4+0)−5

Simplify inside the parentheses: 2(4)−5

Multiply: 8−5

Subtract: 3

So, the value of the expression when n=0 is 3.

3.### Evaluate for x = 8 and y = 10: 3x + 2y

Answer:
44

Explanation:

Substitute x=8 and y=10 into the expression: 3(8)+2(10)

Perform the multiplications:

3×8=24

2×10=20

Add the results: 24+20=44

So, the value of the expression when x=8 and y=10 is 44.

Perform the multiplications:

3×8=24

2×10=20

Add the results: 24+20=44

So, the value of the expression when x=8 and y=10 is 44.

4.### Write an algebraic expression for 77 more than the product of 2 and u

Answer:
2u+77

Explanation:

o write an algebraic expression for "77 more than the product of 2 and u":

Start with the product of 2 and u: 2u.

Add 77 to this product: 2u+77.

So, the algebraic expression is 2u+77.

Start with the product of 2 and u: 2u.

Add 77 to this product: 2u+77.

So, the algebraic expression is 2u+77.

5.### Determine the result of the expression: | -10 - (|4| + 1) |

Answer:
15

Explanation:

Let's break down the expression step by step:

Absolute Value of 4: The absolute value of 4 is simply 4 because the absolute value of a positive number is the number itself.

Absolute Value of -10: The absolute value of -10 is 10 because it's the positive distance from zero to -10 on the number line.

Now, we have the expression: | -10 - (|4| + 1) |

Inside the innermost parentheses, we calculate |4| + 1, which is 4 + 1 = 5.

Then, we have -10 - 5 inside the outer parentheses, which is -15.

Finally, we take the absolute value of -15, which is 15.

So, the absolute value of -10 minus the absolute value of 4 plus 1 is indeed 15.

Absolute Value of 4: The absolute value of 4 is simply 4 because the absolute value of a positive number is the number itself.

Absolute Value of -10: The absolute value of -10 is 10 because it's the positive distance from zero to -10 on the number line.

Now, we have the expression: | -10 - (|4| + 1) |

Inside the innermost parentheses, we calculate |4| + 1, which is 4 + 1 = 5.

Then, we have -10 - 5 inside the outer parentheses, which is -15.

Finally, we take the absolute value of -15, which is 15.

So, the absolute value of -10 minus the absolute value of 4 plus 1 is indeed 15.

6.### Which is bigger? -14 or 0

Answer:
-14 < 0

Explanation:

In the given question, we are comparing -14 with 0. 0 is bigger than any negative number. Thus, -14 is less than 0 and the correct answer is A.

7.### What is: 6 + (-4)

Answer:
2

Explanation:

To calculate 6+(−4):

Start with the number 6.

Add -4 to it.

6+(−4)= 6 − 4=2

So, the result is 2.

Start with the number 6.

Add -4 to it.

6+(−4)= 6 − 4=2

So, the result is 2.

8.### Evaluate for m = -5: m + 7

Answer:
2

Explanation:

To evaluate the expression m+7 for m=−5:

Substitute m=−5 into the expression: −5+7

Perform the addition: −5+7=2

So, the value of the expression when m=−5 is 2

Substitute m=−5 into the expression: −5+7

Perform the addition: −5+7=2

So, the value of the expression when m=−5 is 2

9.### What is: 8 - (-4)

Answer:
12

Explanation:

To calculate 8−(−4):

Start with the number 8.

Subtract -4 from it.

8−(−4)= 8 + 4=12

So, the result is 12.

Start with the number 8.

Subtract -4 from it.

8−(−4)= 8 + 4=12

So, the result is 12.

10.### Evaluate for m = -8: 9 - m

Answer:
17

Explanation:

To evaluate the expression 9-m for m=−58

Substitute m=−8 into the expression: 9 - (-8)

Perform the addition: 9+8=17

So, the value of the expression when m=−8 is 17

Substitute m=−8 into the expression: 9 - (-8)

Perform the addition: 9+8=17

So, the value of the expression when m=−8 is 17

11.### What is: -7 (-4) (3)

Answer:
84

Explanation:

To evaluate the expression −7×(−4)×3:

Multiply −7 by −4: −7×(−4)=28

Multiply the result by 3: 28×3=84

So, the value of the expression −7×(−4)×3 is 84.

Multiply −7 by −4: −7×(−4)=28

Multiply the result by 3: 28×3=84

So, the value of the expression −7×(−4)×3 is 84.

12.### What is: [-3 (4) (2)]/-8

Answer:
3

Explanation:

To evaluate the expression [-3 x 4 x 2]/-8

Multiply −3 by 4: −3×4=−12

Multiply the result by 2: −12×2=−24

Divide the result by −8:

−24/−8 = 3

So, the value of the expression [-3 x 4 x 2]/-8 is 3.

Multiply −3 by 4: −3×4=−12

Multiply the result by 2: −12×2=−24

Divide the result by −8:

−24/−8 = 3

So, the value of the expression [-3 x 4 x 2]/-8 is 3.

13.### Is x equal to 10, 12, or 25?: x + 6 = 18

Answer:
12

Explanation:

To determine if x is equal to 10, 12, or 25 for the equation x+6=18:

Start with the equation: x+6=18

Subtract 6 from both sides to solve for x: x=18−6 x=12

So, x is equal to 12.

Start with the equation: x+6=18

Subtract 6 from both sides to solve for x: x=18−6 x=12

So, x is equal to 12.

14.### Solve. 1785 = t - (-836)

Answer:
949

Explanation:

To solve the equation 1785=t−(−836):

Rewrite the equation to simplify the double negative: 1785=t+836

Subtract 836 from both sides to solve for t: 1785−836=t

Perform the subtraction: 949=t

So, t=949.

Rewrite the equation to simplify the double negative: 1785=t+836

Subtract 836 from both sides to solve for t: 1785−836=t

Perform the subtraction: 949=t

So, t=949.

15.### Solve. -7x = 105

Answer:
-15

Explanation:

To solve the equation -7x=105

Divide both sides of the equation by −7 to solve for x:

-7x/7=105/7

Perform the division

x=-105/7

x=-15

So, the solution to the equation −7x=105 is x=−15.

Divide both sides of the equation by −7 to solve for x:

-7x/7=105/7

Perform the division

x=-105/7

x=-15

So, the solution to the equation −7x=105 is x=−15.

16.### Translate: The quotient of a number t and 7, plus 2, is -4.

Answer:
T/7 + 2 = -4.

Explanation:

To translate the given statement "The quotient of a number t and 7, plus 2, is -4," we need to find the correct algebraic expression that matches this description.

The statement can be broken down as follows:

"The quotient of a number 𝑡t and 7" means t/7

"plus 2" means we add 2 to the quotient.

"is -4" means the expression equals -4.

Putting it all together, we get:

t/7+2=-4

The statement can be broken down as follows:

"The quotient of a number 𝑡t and 7" means t/7

"plus 2" means we add 2 to the quotient.

"is -4" means the expression equals -4.

Putting it all together, we get:

t/7+2=-4

17.### Write as a fraction. Simplify!: 0.4

Answer:
2/5.

Explanation:

To write 0.40.4 as a fraction and simplify it:

Write 0.4 as a fraction:

0.4=4/10

Simplify the fraction by finding the greatest common divisor (GCD) of 4 and 10, which is 2:

4÷2/10÷2=2/5

So, 0.4 as a simplified fraction is 2/5

Write 0.4 as a fraction:

0.4=4/10

Simplify the fraction by finding the greatest common divisor (GCD) of 4 and 10, which is 2:

4÷2/10÷2=2/5

So, 0.4 as a simplified fraction is 2/5

18.### Write as a fraction. Simplify!: 0.55555...

Answer:
5/9

Explanation:

To express the repeating decimal 0.55555... as a fraction and simplify it, we can set up the following equation:

x = 0.55555...

Now, we'll subtract this repeating decimal from 10x, which should eliminate the repeating part:

10x - x = 5.55555... - 0.55555...

9x = 5

Now, divide both sides by 9 to solve for x:

x = 5/9

So, the repeating decimal 0.55555... is equal to the fraction 5/9.

x = 0.55555...

Now, we'll subtract this repeating decimal from 10x, which should eliminate the repeating part:

10x - x = 5.55555... - 0.55555...

9x = 5

Now, divide both sides by 9 to solve for x:

x = 5/9

So, the repeating decimal 0.55555... is equal to the fraction 5/9.

19.### Which is greater?: -3/7 or -0.375

Answer:
-3/7 < -0.375

Explanation:

To determine which is greater, −3/7 or -0.375 we need to compare the two values. We can convert -3/7 to a decimal for an easier comparison.

Convert -3/7 to a decimal

-3/7 ≈ 0.4286

Compare the two decimals:

−0.4286 (approximate value of −3/7)

−0.375

Since −0.4286 is less than −0.375, −0.375 is greater.

Therefore, −0.375 is greater than −3/7

Convert -3/7 to a decimal

-3/7 ≈ 0.4286

Compare the two decimals:

−0.4286 (approximate value of −3/7)

−0.375

Since −0.4286 is less than −0.375, −0.375 is greater.

Therefore, −0.375 is greater than −3/7

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