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3 years ago

Building a is 180 feet shorter than building

2 answers:

8 0

Here is the set up:

a = b - 180
a + b = 1520

We have a systems of linear equations in two variables.

b - 180 + b = 1520

2b = 1520 + 180

2b = 1700

b = 1700/2

b = 850

Plug b = 850 into either equation.

I will use a + b = 1520.

a + 850 = 1520

a = 1520 - 850

a = 670

Answer:

Building a is 670 feet. Building b is 850 feet.

Fofino [41]3 years ago

7 0

B= 850 ft
a= 670 ft

b + (b-80) =1,520
2b=1700
b=850 a=670 =(1,520-850)
850-670=180 ( difference between a and b)

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If the 4th and 7th terms of a GP are 250 and 31250 respectively. Find the two possible values of a and r

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Answer:

a = 2, r = 5

Step-by-step explanation:

Nth term of a GP = a×r^(n-1)

Where 'a' is the first term and 'r' is the common ratio

4th term = a×r^3 = 250

r^3 = 250/a

7th term = a×r^6 = 31250

a×r^6 = 31250

a×(r^3)^2 = 31250

a×(250/a)^2 = 31250

a×(62500/a^2) = 31250

62500/a = 31250

a = 62500/31250 = 2

a = 2

since r^3 = 250/a,

r^3 = 250/2 = 125

r = (125)^(1/3)

r = 5

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Use the properties of operations to determine if each pair of expressions is equivalent

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Using the properties of operations the given pair of expressions are not equivalent

Solution:

Given that, we have to use the properties of operations to determine if each pair of expressions is equivalent

And the two expressions are:

$\frac{1}{2}(4-2 x) \text { and } 2-2 x$

Now, we know that, there are four (4) basic properties of operations:

Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.

So, if we observe we can apply distributive property on 1st expression

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

$\begin{array}{l}{\frac{1}{2}(4-2 x) \rightarrow \frac{1}{2}(4)-\frac{1}{2}(2 x)} \\\\ {\rightarrow 2-x}\end{array}$

Here the resulting expression is 2 – x and it is not equivalent to 2 – 2x

Hence, the given two expressions are not equal.

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