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love history [14]
3 years ago
9

Match each expression to another expression with the same value. 24 ÷ 3 53 × 7 56 − 21 4 − 3 40 × 2 8 × 50 8 × (5 × 12 − 10) (8

× 7 − 3) × 7 8 × 3 ÷ (6 − 3)
Mathematics
1 answer:
FrozenT [24]3 years ago
6 0

Answer:

a. 24 ÷ 3  = 8                       ⇒              i. 8 × 3 ÷ (6 − 3)  = 8

b. 53 × 7 = 371                     ⇒             h. (8 × 7 − 3) × 7 = 371

g. 8 × (5 × 12 − 10) = 400    ⇒             f. 8 × 50 = 400

Step-by-step explanation:

Given:

We have to match the equivalent expressions:

a. 24 ÷ 3                 f. 8 × 50

b. 53 × 7                 g. 8 × (5 × 12 − 10)

c. 56 − 21               h. (8 × 7 − 3) × 7

d. 4 − 3                   i. 8 × 3 ÷ (6 − 3)

                e. 40 × 2          

             

Solution:

a. 24 ÷ 3 = 8                

b. 53 × 7 = 371            

c. 56 − 21 = 35            

d. 4 − 3 = 1  

e. 40 × 2 =80                            

f. 8 × 50 = 400                      

g. 8 × (5 × 12 − 10)  <em>Using PEMDAS rule.</em>

⇒ 8\times (60-10)

⇒ 8\times 50

⇒ 400

h. (8 × 7 − 3) × 7

⇒ (56-3)\times 7

⇒ (53)\times 7

⇒ 371

i. 8 × 3 ÷ (6 − 3) = 8

⇒ \frac{8\times 3}{3}

⇒ \frac{24}{3}

⇒ 8

Answers:

a. 24 ÷ 3  = 8                       ⇒              i. 8 × 3 ÷ (6 − 3)  = 8

b. 53 × 7 = 371                     ⇒             h. (8 × 7 − 3) × 7 = 371

g. 8 × (5 × 12 − 10) = 400    ⇒             f. 8 × 50 = 400

c,d and e didn't have any match    

a is equivalent to i,b equivalent to h and g is equivalent to f.

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|1/2b-8|=|1/4b-1|<br> b=____ and ____
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Answer:

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Step-by-step explanation:

The absolute value equation |1/2b-8| = |1/4b-1| resolves to a piecewise linear function with three pieces. There are two solutions.

<h3>Domains</h3>

The absolute value function on the left has a turning point where its value is zero:

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The absolute value function on the right has a turning point where its value is zero:

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For b > 16, both absolute value functions are identity functions. In this domain, the equation is ...

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For 4 < b < 16, the function on the left negates its argument, so the equation in this domain is ...

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For the purpose of finding the value of b, this is effectively identical to the equation for b > 16. (The value of b does not change if we multiply both sides of the equation by -1.)

<h3>Solutions</h3>

<u>Domain b < 4 ∪ 16 < b</u>

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<u>Domain 4 < b < 16</u>

  -(1/2b -8) = 1/4b -1 . . . . equation in this domain

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  36 = 3b . . . . . . . . . . . add 2b+4 to both sides

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This solution is in the domain of the equation, so is the other solution to the original equation.

<h3>Graph</h3>

For the purposes of the graph, we have define the function g(b) to be the difference of the two absolute value functions. The solutions are found where g(x) = 0, the x-intercepts. The graph shows those to be ...

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<em>Additional comment</em>

Defining g(b) = |1/2b-8| -|1/4b-1|, we can rewrite it as ...

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