MATHEMATICS HIGH SCHOOL

1)simplify the expression (2x)^4

2)the perimeter of a rectangular is twice the sum of its length and its width. the perimeter is 16 meters and its length is 2 meters more then twice its width

3)Find the real numbers x and y that make the equation true.

-3 + yi = x + 6i

Answers

Answer 1
Answer: (2x)^4=16x^4
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2(l+w)=16\n l=2w+2\n\n 2(2w+2+w)=16\n 6w+4=16\n 6w=12\n w=2\n\n l=2\cdot2+2\n l=6
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-3+yi=x+6i\Rightarrow x=-3 \wedge y=6

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Identify the 42nd term of an arithmetic sequence where a1 = -12 and a27 = 66

Answers

The arithmetic formula is expressed as an = a1 + d *(n-1)where n is an integer. Substituting from the given a1 = -12 and a27 = 66, 66 = -12 + d *(27-1). hence  , d is equal to 3. a42 thus using the formula is equal to 111. The final answer to this problem is 111.

Answer:

42nd term is 111

Step-by-step explanation:

a_1=-12,a_(27)=66

Now, Using formula of nth term of an A.P. we have :

a_n=a+(n-1)* d\n\text{Take n=27}\n\implies a_(27)=-12+(27-1)* d\n\implies 66=-12+26\cdot d\n\implies 26\cdot d = 78\n\implies d = 3

Now, first term a = -12 , n = 42 and d = 3

So, 42nd term is :

a_(42)=-12+(42-1)* 3\n\implies a_(42)=-12+41* 3\n\implies a_(42)=-12+123\n\bf\implies a_(42)=111

Hence, 42nd term is 111

Help me with this question please thank you A ball is thrown downward from a window from a tall building. Its position at time t in seconds is s = 16t^2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 161 feet.

Answers

s=16t^2+32t;\ s=161\n\n16t^2+32t=161\n\n16t^2+32t-161=0\n\na=16;\ b=32;\ c=-161\n\n\Delta=b^2-4ac\to\Delta=32^2-4\cdot16\cdot(-161)=1024+10304=11328\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n√(11328)=√(64\cdot177)=8√(177)\approx106.4\n\nx_1=(-32-106.4)/(2\cdot16)< 0;\ x_2=(-32+106.4)/(2\cdot16)=(74.4)/(32)=2.325\approx2.3\ (ft)
if I understood correctly:
s = 16t^2 + 32t, s=161
16t^2 + 32t=161
16t^2 + 32t-161=0
t=(-32+8√177)/32=-1+√177/4≈2,326≈2,3

What is 1.4 as a decimal?

Answers

You meant 1.4 as a fraction (1.4 is already a decimal)

1.4 as a fraction is one and two fifths, or 1 2/5 (or 7/5).

Conevert 94500 hours to years

Answers

that's 1.084 calendar years
Hey, Yohanita!
1 hour=0.00011406844106464 years
94500 hours=10.787671 years
I hope this helps;)

Solve the inequality 2(x-3)-5x<9

Answers

Answer:

x > -5

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(x-3)-5x<9 expand left side

2x-6-5x<9. group like terms on left side

-3x-6<9. add 6 to each side

-3x<15. divide each side by -3 (reverse sign because of division by a negative)

x>-5

A statistician wants to determine the average annual Gross National Product for countries in Africa. He samples the 20 largest (in terms of population) African countries over 10 years, and gets their quarterly G.N.P results for each quarter of each year. Which one of the following is a true statement concerning the statistician's study?

Answers

Answer:

Step-by-step explanation:

The description provided offers information about the statistician's study. Let's analyze the given scenario and identify the true statement:

Sample Size and Selection:

The sample consists of the 20 largest African countries in terms of population, and data is collected quarterly for each year over a span of 10 years.

Scope:

The study focuses on African countries, particularly the 20 largest by population, providing insights into the continent's economic productivity.

Frequency of Data Collection:

Data is collected quarterly for each year over a period of 10 years, resulting in a substantial amount of data for analysis.

Based on this information, a true statement concerning the study could be:

True Statement:

"The study aims to analyze the quarterly Gross National Product (G.N.P) of the 20 largest African countries, focusing on economic productivity over a span of 10 years."

This statement accurately captures the objective, sample size, data collection frequency, and scope of the study.
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