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marissa [1.9K]
3 years ago
12

lass="latex-formula">
​
Mathematics
1 answer:
andriy [413]3 years ago
6 0
A would equal 24 because 17+7 is 24
You might be interested in
Evaluate the expression you got in part f for d = 5.
Triss [41]

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.

8 0
3 years ago
Generally those who are less active have no opportunities to exercise
Alex777 [14]
What is this question?
8 0
3 years ago
Read 2 more answers
A pharmacist has 30% and 60% iodine solutions on hand. How many liters of each iodine solution will be required to produce 6 lit
kkurt [141]

Answer:

4 liters of 60% solution; 2 liters of 30% solution

Step-by-step explanation:

I like to use a simple, but effective, tool for most mixture problems. It is a kind of "X" diagram as in the attachment.

The ratios of solution concentrations are 3:6:5, so I've used those numbers in the diagram. The constituent solutions are on the left; the desired mixture is in the middle, and the numbers on the other legs of the X are the differences along the diagonals: 6 - 5 = 1; 5 - 3 = 2. This tells you the ratio of 60% solution to 30% solution is 2 : 1.

These ratio units (2, 1) add to 3. We want 6 liters of mixture, so we need to multiply these ratio units by 2 liters to get the amounts of constituents needed. The result is 4 liters of 60% solution and 2 liters of 30% solution.

_____

If you're writing equations, it often works well to let the variable represent the quantity of the greatest contributor—the 60% solution. Let the volume of that (in liters) be represented by v. Then the total volume of iodine in the mixture is ...

... 0.60·v + 0.30·(6 -v) = 0.50·6

... 0.30v = 0.20·6 . . . . subtract 0.30·6, collect terms

... v = 6·(0.20/0.30) = 4 . . . . divide by the coefficient of v

4 liters of 60% solution are needed. The other 2 liters are 30% solution.

6 0
3 years ago
Write two linear expressions that have a sum of 3x-8
irakobra [83]
1. (5x + 2 )
2. ( -2x -10 ) 
5 0
3 years ago
Read 2 more answers
URGENT: I need these problems answered and steps :/ Will give the first person BRAINLIEST and please show the steps and please p
hjlf

Answer:

1) -15/32

2) 2/15

3) -203.5

4) -3/2 = -1.5

5) 10/3 = 3 1/3

Step-by-step explanation:

For 1, you just multiply the numerators and denominators together (3 by 5, 4 by 8) and then because it is negative, add the negative sign.

For 2, you multiply again, but because there are 2 negative signs, it becomes positive.

For 3, you divide 81.4 by 0.4, you could also divide 814 by 4.

For 4, you keep change flip, so the equation would become -9/4 (-2 1/4=-9/4) and 3/2 would become 2/3. The equation would be (-9/4 * 2/3). Then, you would get -18/12 which is -3/2.

For 5, you just multiply 4/3 by 5/2 which is 20/6 and because 2 negatives, it becomes positive.

3 0
3 years ago
Read 2 more answers
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