MATHEMATICS HIGH SCHOOL

Write a compound inequality that represents the situation. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour.A. 20 > x > 50

B. 20 ≤ x ≤ 50

C. 20 ≥ x ≥ 50

D. 20 < x < 50

Answers

Answer 1
Answer:

Answer:

B. 20 ≤ x ≤ 50

Step-by-step explanation:

If the maximum speed is 50 miles per hour, that means it cannot go above 50 miles per hour, it has to be 50 miles per hour or less, which is expressed like this

x\leq 50

Now, if the minimum speed is 20 miles per hour, that means the speed can only be 20 miles per hour or more, that's represented as

x\geq 20

If we unit both expression, we would have the following compound inequality

20\leq x\leq 50

This means that the speed has to be 20 miles per hour or more, but 50 miles per hour or less.

Therefore, the right answer is

Answer 2
Answer: The correct answer is b. Hope that helps!

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Uncle Percy and the ratiolas are donating 75% of $84 where does the $84 fit in to proportion

Answers

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x-----> amount corresponding to 75%

we know that

using proportion

(100)/(84)(\%)/(\$) =(75)/(x) (\%)/(\$)\n \n x=84*75/100\n \n x=\$63

The image of the point (9,0) under a translation is (7,4). Find the coordinates ofthe image of the point (0,8) under the same translation.

Answers

Answer:

(-2, 12)

Step-by-step explanation:

How much interest will be paid in 1 year for a loan of $4500 at 7 1/2% simple interest?

Answers

The answer is $337.50 paid. We would change 7 1/2% (7.5%) to its decimal form which is .075. Then we would multiply that by $4,500 which would get $337.5 or $337.50 which is the same thing. Hope this helped! 

Say that the economy is in a recession, which is causing the value of gold to fall by three percent. If you have gold reserves which were previously worth $8,590, how much value have you lost as a result of this recession, to the nearest cent?

Answers

Answer:

value we have lost as a result of this recession, to the nearest cent is:

 257 dollars and 70 cents

Step-by-step explanation:

We have a gold which was worth $8590.

The value of gold fell by three percent.

Value we have lost as a result of this recession is:

      3% of $8590

  = (3)/(100)*8590

  =  $ 257.7

1 dollar= 100 cents

257.7 dollars           =    257 dollars and 70 cents  

                       

hence,  value we have lost as a result of this recession, to the nearest cent is:

 257 dollars and 70 cents
Given:
Value of gold = 8,590
decrease in value = 3%

8,590 * 3% = 257.70 amount lost due to recession.

8,590 - 257.70 = 8,332.30 new value of gold.

If the domain of the function F = {(x, y) | 2x + y = 7} is {1, 2, 3}, what is the range?

Answers

Answer:

The range of the function is {1,3,5}.

Step-by-step explanation:

The function is defined as

F=\{(x,y)|2x+y=7\}

The set of all possible inputs is called domain and the set of output is called range.

In other words the possible values of x are elements of domain and the values of y are the elements of range.

Since the domain is {1,2,3} and the function is

2x+y=7

Put x=1

2(1)+y=7

2+y=7

y=7-2

y=5

Put x=2

2(2)+y=7

4+y=7

y=7-4

y=3

Put x=3

2(3)+y=7

6+y=7

y=7-6

y=1

Since the possible values of y are 5,3 and 1, therefore the range of the function is {1,3,5}

Using the graph of f(x) = log10x below, approximate the value of y in the equation 10y = 6

Answers

The given function is

f(x)= log 10 x

Taking base as 10

y=\log_(10)10 +\log_(10)x→→Using the property of, log a b= log a + log b

→y = 1 + \log_(10)x as, \log_(10)10=1

we have to approximate the value of y in the equation

→10 y = 6

→y=(6)/(10)

(6)/(10)= 1 + \log_(10)x  

\log_(10)x =  (-4)/(10)

x= (10)^{(-4)/(10)}=(10)^(-0.4)=0.398

Solving graphically,

we get , x= 0.398 for , y= (6)/(10)=.6
f(x) = ㏒(10x)
f(x) = ㏒₁₀(10x)

10y = 6
 10    10
    y = 0.6

f(x) = ㏒₁₀(10x)
0.6 = ㏒₁₀(10x)
10^(0.6) = 10x
10^{(3)/(5)} = 10x
\sqrt[5]{10^(3)} = 10x
\sqrt[5]{1000} = 10x
\frac{\sqrt[5]{1000}}{10} = x
(3.98)/(10) \approx x
0.398 \approx x
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