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4 years ago

Can someone please answer this quickly and correctly? 20 points!

Mathematics

1 answer:

Marysya12 [62]4 years ago

5 0

The missing side is 7 in

Explanation:
The information we have to know in order to solve this is that the formula of area of trapezoid is
a = 1/2h (b1 + b2)

We can fill in the information we know from the picture into the equation
15 = 1/2(3.4) (1.8 + b2)

The dimension we are solving for is b2, or base 2. To make it easier, let's replace b2 with n. Now we can solve this equation

1) Multiply 1/2 by 3.4, which is 1.7
15 = 1.7 (1.8 + n)

2) Distribute by doing 1.7 x 1.8 + 1.7 x n
15 = 17n + 3.06

3) Subtract 3.06 from both sides of the equation
15 - 3.06 = 17n + 3.06 - 3.06
11.94 = 17n

4) To isolate n, since we want one n instead of 17, we divide both sides by 17
11.94/17 = 17n/17
7 = n

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If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

Solution:

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

Use the following log rules

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

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3 years ago

Sonny has $75 to spend the night the new Nintendo switch game that he wants to buy requires $93 his parents had they will lend h

Verdich [7]

Answer:

he needs 18 more dollars from his parents

Step-by-step explanation:

93-75=18 therefore he is missing 18 dollars

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3 years ago

Another question! A piece of fabric costs $5.29 a yard, which is an estimate cost of 16.3

lbvjy [14]

Answer:

B.)$80

5.29 times 16.3 is 86.227 but it is not close to 21 not 165 and not a 800 so the answer would be 80

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3 years ago

Read 2 more answers

Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the

Dmitry_Shevchenko [17]

Answer:

Meghan should use positive integers to represent income. Income is money that flows into the business, and it is always positive. The higher the income, the more money a business will have.

On the other hand, expenses must be represented by negative integers. Expenses are money that flows out of a business, and is always negative. The higher the expenses, the less money the business will have. Expenses reduce a business's net income.

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3 years ago

What is the coordinate of the midpoint of segment AC

Aloiza [94]

Answer:

-5.5

Step-by-step explanation:

$\frac{-7+-4}{2}\\\\\frac{-11}{2}\\\\-5.5$

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3 years ago