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Lesechka [4]
3 years ago
9

Evaluate the expression you got in part f for d = 5.

Mathematics
1 answer:
Triss [41]3 years ago
8 0

Answer:

Before you get started, take this readiness quiz.

Is n÷5 an expression or an equation? If you missed this problem, review Example 2.1.4.

Simplify 45. If you missed this problem, review Example 2.1.6.

Simplify 1+8•9. If you missed this problem, review Example 2.1.8.

Evaluate Algebraic Expressions

In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Example 2.3.1: evaluate

Evaluate x+7 when

x=3

x=12

Solution

To evaluate, substitute 3 for x in the expression, and then simplify.

x+7

Substitute.

3+7

Add.

10

When x=3, the expression x+7 has a value of 10.

To evaluate, substitute 12 for x in the expression, and then simplify.

x+7

Substitute.

12+7

Add.

19

When x=12, the expression x+7 has a value of 19. Notice that we got different results for parts (a) and (b) even though we started with the same expression. This is because the values used for x were different. When we evaluate an expression, the value varies depending on the value used for the variable.

exercise 2.3.1

Evaluate: y+4 when

y=6

y=15

Answer a

Answer b

exercise 2.3.2

Evaluate: a−5 when

a=9

a=17

Answer a

Answer b

Example 2.3.2

Evaluate 9x−2, when

x=5

x=1

Solution

Remember ab means a times b, so 9x means 9 times x.

To evaluate the expression when x=5, we substitute 5 for x, and then simplify.

9x−2

Substitute 5 for x.

9⋅5−2

Multiply.

45−2

Subtract.

43

To evaluate the expression when x=1, we substitute 1 for x, and then simplify.

9x−2

Substitute 1 for x.

9⋅1−2

Multiply.

9−2

Subtract.

7

Notice that in part (a) that we wrote 9•5 and in part (b) we wrote 9(1). Both the dot and the parentheses tell us to multiply.

exercise 2.3.3

Evaluate: 8x−3, when

x=2

x=1

Answer a

Answer b

exercise 2.3.4

Evaluate: 4y−4, when

y=3

y=5

Answer a

Answer b

Example 2.3.3: evaluate

Evaluate x2 when x=10.

Solution

We substitute 10 for x, and then simplify the expression.

x2

Substitute 10 for x.

102

Use the definition of exponent.

Evaluate: 2x when x=6.

Answer

exercise 2.3.8

Evaluate: 3x when x=4.

Answer

Example 2.3.5: evaluate

Evaluate 3x+4y−6 when x=10 and y=2.

Solution

This expression contains two variables, so we must make two substitutions.

3x+4y−6

Substitute 10 for x and 2 for y.

3(10)+4(2)−6

Multiply.

30+8−6

Add and subtract left to right.

32

When x=10 and y=2, the expression 3x+4y−6 has a value of 32.

exercise 2.3.9

Evaluate: 2x+5y−4 when x=11 and y=3

Answer

exercise 2.3.10

Evaluate: 5x−2y−9 when x=7 and y=8

Answer

Example 2.3.6: evaluate

Evaluate 2x2+3x+8 when x=4.

Solution

We need to be careful when an expression has a variable with an exponent. In this expression, 2x2 means 2•x•x and is different from the expression (2x)2, which means 2x•2x.

2x2+3x+8

Substitute 4 for each x.

2(4)2+3(4)+8

Simplify 42.

2(16)+3(4)+8

Multiply.

32+12+8

Add.

52

exercise 2.3.11

Evaluate: 3x2+4x+1 when x=3.

Answer

exercise 2.3.12

Evaluate: 6x2−4x−7 when x=2.

Answer

Identify Terms, Coefficients, and Like Terms

Algebraic expressions are made up of terms. A term is a constant or the product of a constant and one or more variables. Some examples of terms are 7, y, 5x2, 9a, and 13xy.

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What is the solution to the equation <br> 13×3/4+x=7(1/4)
yan [13]
I'm going to assume you mean:

13 * (3/4) + x = 7 * (1/4)

Let's go ahead and simplify the right side.

7 * (1/4) = 1.75

So now we have:


13 * (3/4) + x = 1.75

Now let's take care of the right side. Multiplication before addition.

13 * (3/4) = 9.75

9.75 + x = 1.75

To isolate x, we subtract 9.75 from both sides.

9.75 - 9.75 + x = 1.75 - 9.75

x = -8

Hopefully I spaced this well. \('-')/
5 0
3 years ago
How do you factor 125-x^3?
xz_007 [3.2K]

Step-by-step explanation:

We have

125 - x {}^{3}

First, 125 is a perfect cube because

5 \times 5 \times 5 = 125

and

x^3 is a perfect cube because

x \times  x \times x = x {}^{3}

so we can use the difference of cubes identity

( {x}^{3}  -  {y}^{3} ) = (x - y)( {x}^{2}  + xy +  {y}^{2} )

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

64 - 27

we know that

64 - 27 = 37

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

(4 - 3)( {4}^{2}  + 4(3) + 3 {}^{2} )

1(16 + 12 + 9) = 1(37) = 37

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

(5 - x)( {5}^{2}  + 5x +  {x}^{2} ) =

(5 - x)(25 + 5x +  {x}^{2} )

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2 years ago
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It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide
kozerog [31]

If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

=1.167

=1.17 hour

Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

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Math question I need help with it please help me !
never [62]

Answer:

96 degrees

Step-by-step explanation:

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Maria has $11 to buy fish for her aquarium. Each goldfish costs $2. How many goldfish can she buy? Do not include units in your
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Answer:She can buy 5 goldfish.


Step-by-step explanation: If you divide the amount of money she has to spend by the cost of the goldfish;

$11/5 = 5.5

Since she can’t buy 5 and a half goldfish, she can only buy 5.


7 0
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