In triangle ABC, AB = 6, BC = 8, and angle ABC = 90 degrees. Find the area of triangle ABC.
Answer:
24
Step-by-step explanation:
The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.
6 x 8 = 48
48 / 2 = 24
HELP ME PLS THIS IS A SCREENSHOT I WILL ADD MORE PONINTS
Answer:
Estimated difference: 88 - 6 = 82
Actual difference: 87.71 - 5.8 = 81.91
Dole Pineapple Inc. is concerned that the 466 mL can of sliced pineapple is being overfilled. The population standard deviation is 0.88 mL. The quality control department took a random sample of 50 cans and found that the arithmetic mean volume was 467.3 mL.
At the 0.10 level of significance, can we conclude that the mean volume is greater than 466 mL?
a. What is the decision rule? (Round the final answer to 3 decimal places.)
Reject H0: μ ≤ 466 and accept H1: μ > 466 when the test statistic is
(Click to select)
.
b. What is the value of the test statistic? (Round the final answer to 2 decimal places.)
Value of the test statistic =
a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).
b.The value of the test statistic is 3.75.
What is Null hypothesis?A null hypothesis is a statement that suggests there is no significant difference between two sets of data or that any observed difference is due to chance or random sampling error.
The alternative hypothesis is a statement that contradicts the null hypothesis and proposes that there is a significant relationship between two or more variables being studied.
According to the given information:
Dole Pineapple Inc. wants to know if their 466 mL cans of sliced pineapple are being overfilled. They took a random sample of 50 cans and found the average volume to be 467.3 mL, with a known population standard deviation of 0.88 mL.
To determine if the mean volume is greater than 466 mL at a significance level of 0.10, we use a one-tailed test and the following steps:
a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).
b. Value of the test statistic: Using the formula for the z-test, we find the test statistic to be 3.75.
Since the test statistic (3.75) is greater than the critical value (1.28), we can reject the null hypothesis and conclude that the mean volume is significantly greater than 466 mL.
To know more about Hypothesis, visit:
https://brainly.com/question/29519577
#SPJ1
a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).
b.The value of the test statistic is 3.75.
What is Null hypothesis?
A null hypothesis is a statement that suggests there is no significant difference between two sets of data or that any observed difference is due to chance or random sampling error.
The alternative hypothesis is a statement that contradicts the null hypothesis and proposes that there is a significant relationship between two or more variables being studied.
According to the given information:
Dole Pineapple Inc. wants to know if their 466 mL cans of sliced pineapple are being overfilled. They took a random sample of 50 cans and found the average volume to be 467.3 mL, with a known population standard deviation of 0.88 mL.
To determine if the mean volume is greater than 466 mL at a significance level of 0.10, we use a one-tailed test and the following steps:
a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).
b. Value of the test statistic: Using the formula for the z-test, we find the test statistic to be 3.75.
Since the test statistic (3.75) is greater than the critical value (1.28), we can reject the null hypothesis and conclude that the mean volume is significantly greater than 466 mL.
To know more about Hypothesis, visit:
https://brainly.com/question/29519577
#SPJ1
What fractions are close to 1 than to 0
The answer of the given question based on the fraction is , a value that is greater than 1/2.
What is Fraction?A fraction is mathematical expression that represents part of whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.
Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.
So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:
2/3 is closer to 1 than to 0 because it is greater than 1/2
7/8 is closer to 1 than to 0 because it is greater than 1/2
3/4 is closer to 1 than to 0 because it is greater than 1/2
On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:
1/4 is closer to 0 than to 1 because it is less than 1/2
3/10 is closer to 0 than to 1 because it is less than 1/2
2/5 is closer to 0 than to 1 because it is less than 1/2
To know more about Expression visit:
https://brainly.com/question/1859113
#SPJ1
The number of deer on an island is given by D=200+100sin( 2 π x), where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 150 ?
Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.
What are a leap year and a year?If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.
We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.
150=200+100sin(2πx)
Subtracting 200 from both sides, we get:
-50 = 100sin(2πx)
Dividing both sides by 100, we get:
-0.5 = sin(2πx)
To find the value of x that satisfies this equation, we can take the inverse sine of both sides:
sin⁻¹(-0.5) = 2πx
Using a calculator, we find that sin⁻¹(-0.5) = -π/6.
-π/6 = 2πx
Solving for x, we get:
x = -1/12
Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:
2000 + 1/12 ≈ 2000.1
To know more about Leap year visit:-
https://brainly.com/question/24068575
#SPJ1
Becky would like to retire with an amount of 200,000 she found a bank that offers 9% simple interest and assume she’ll be working for 40 years what is the initial amount that Becky would have to invest to be able to take the 200,000?
Becky would have to invest 43,478 to be able to take the 200,000. The solution has been obtained by using the simple interest.
What is simple interest?
Simple interest is the cost of borrowing that is determined by utilising only the original principle and a constant interest rate.
We are given the following information:
Amount = 200,000
Interest rate = 9%
Time = 40 years
Let the principal be x.
So, we get
⇒ Amount = Principal + Interest
⇒ 200,000 = x + (9% of x) * 40
⇒ 200,000 = x + 0.09x * 40
⇒ 200,000 = x + 3.6x
⇒ 200,000 = 4.6x
⇒ x = 43,478
Hence, Becky would have to invest 43,478 to be able to take the 200,000.
Learn more about simple interest from the given link
https://brainly.com/question/25793394
#SPJ1
50 Points! Multiple choice algebra question. Use synthetic substitution to find f(3) for f(x)=x²-9x+5. Photo attached. Thank you!
By using synthetic substitution on f(x)=x²-9x+5, f(x) = -13. Hence option C is the correct answer.
How to use synthetic substitution?Synthetic substitution is a method used to evaluate a polynomial function for a specific value of the independent variable. This method involves setting up a table with the coefficients of the polynomial and the value we are substituting. Then, we use synthetic division to perform the substitution and find the corresponding value of the function.
1) To use synthetic substitution, we first write the coefficients of the polynomial in descending order of their powers.
2) Next, we set up a table with the coefficients and the value we are substituting, which is typically denoted by a vertical line.
3) Then, we use synthetic division to perform the substitution. To do this, we bring down the first coefficient, multiply it by the substitution value, and write the result underneath the next coefficient. We then add this result to the next coefficient, and repeat the process until we reach the last coefficient. The final value is the result of the substitution, which is the value of the function for the given argument.
To use synthetic substitution, we first set up a table with the coefficients of the polynomial f(x) and the value we are substituting, which is 3 in this case:
x \ f(x) 1 -9 5
3
Then, we bring down the first coefficient, which is 1, and multiply it by the substitution value, 3, to get 3. We write this value underneath the second coefficient:
x \ f(x) 1 -9 5
3 3
Next, we add the 3 and the -9 to get -6, and multiply this value by the substitution value, 3, to get -18. We write this value underneath the third coefficient:
x \ f(x) 1 -9 5
3 3 -6
Finally, we add the -18 and the 5 to get -13, which is the value of f(3):
x \ f(x) 1 -9 5
3 3 -6 -13
Therefore, f(3) = -13.
To know more about synthetic substitution visit:
brainly.com/question/29161764
#SPJ1
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.
Answer: 205.031(nearest thousandth)
or 205.03125
Step-by-step explanation:
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.
His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.
x = 14.2
s²= 0.9867
s= 0.9933
t α2, n-1 = 3.7074
The margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
Know more about the confidence interval here:
https://brainly.com/question/15712887
#SPJ1
Correct question:
Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
Let g(x)=x^5+x^4. On which intervals is g decreasing
g(x) is decreasing function on the interval (-4/5, 0).
What is calculus?Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes to find the overall effect. It provides a framework for modeling and analyzing a wide range of phenomena, from the motion of objects to the behavior of complex systems.
Calculus is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the study of rates of change, slopes of curves, and the computation of derivatives. Integral calculus deals with the study of accumulation of small changes, computation of areas, and the computation of integrals.
To determine where g(x) is decreasing, we need to find where its derivative is negative.
The derivative of g(x) is:
g'(x) = 5x⁴ + 4x³
To find where g'(x) < 0, we can factor out a common term of x³ to get:
g'(x) = x³(5x + 4)
So, g'(x) < 0 when:
x³ < 0 and 5x + 4 < 0
This condition is not possible, as x³ is never negative.
x³ > 0 and 5x + 4 < 0
This condition is satisfied when -4/5 < x < 0.
Therefore, g(x) is decreasing function on the interval (-4/5, 0).
To learn more about decreasing function from the given link
https://brainly.com/question/26111694
#SPJ1
A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?
Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.
The nth term of an arithmetic sequence can be found using the formula:
an = a1 + (n-1)d.
The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:
(7/10) ÷ 7 = (7/10) × (1/7) = 1/10
Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
To learn more about arithmetic sequence from the given link:
https://brainly.com/question/15412619
#SPJ1
Antoni Gaudi purchased a bedroom set with an installment loan that has an APR of 12%. The bedroom set sells for $2,650. The store financing requires a 15% down payment and 42 monthly payments. What is the finance charge?
The finance charge for Antoni Gaudi's bedroom set purchase is $731.08.
What is an installment?An installment refers to a sum of money that is paid back in parts over a period of time, typically with interest.
Define loan?A loan is a financial agreement between a lender and a borrower, in which the lender provides the borrower with a specific amount of money or assets, which the borrower agrees to pay back with interest over a predetermined period of time. Loans can be used for a variety of purposes, such as purchasing a home, starting a business, or paying for education.
Based on the given information, the bedroom set sells for $2,650, and the financing requires a 15% down payment, which is $397.50 ($2,650 x 0.15).
Therefore, the amount financed is $2,252.50 ($2,650 - $397.50).
To calculate the finance charge, we need to know the total amount of payments Antoni Gaudi will make over the 42-month period. Each monthly payment can be calculated using the following formula:
Monthly Payment = (Amount Financed x (APR/12)) / (1 - (1 + APR/12)^-n)
Where:
APR is the annual percentage rate (12% in this case)
n is the total number of payments (42 in this case)
Plugging in the values, we get:
Monthly Payment = ($2,252.50 x (0.12/12)) / (1 - (1 + 0.12/12)^-42)
= $70.99 (rounded to the nearest cent)
Therefore, the total amount of payments Antoni Gaudi will make over the 42-month period is $2,983.58 ($70.99 x 42).
The finance charge can be calculated as follows:
Finance Charge = Total Payments - Amount Financed
= $2,983.58 - $2,252.50
= $731.08
Therefore, the finance charge for Antoni Gaudi's bedroom set purchase is $731.08.
Learn more about down payment here:
https://brainly.com/question/31293332
#SPJ1
Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
Learn more about Discounts at
https://brainly.com/question/30814332
#SPJ9
What is
22.50 x 15 Steph by step
Answer: 337.5.
Step-by-step explanation:
Answer:
337.5
Step-by-step explanation:
What is 8% of 425 coins?
Answer: 34
Step-by-step explanation:
To find 8% of 425 coins, multiply 425 by 0.08 (which is the decimal equivalent of 8%).
425 * 0.08 = 34
So, 8% of 425 coins is 34 coins.
answer these questions in detail
Answer:
5. x = 60
6. F' (1, 4)
Step-by-step explanation:
5. The angles shown are same side exterior angles, so they are supplementary (add to 180)
(x + 85) + 35 = 180
x + 120 = 180
x = 180 - 120 = 60
x = 60
6. The line x = 1 is a vertical line, passing through the x=axis at (1, 0). All x coordinates on this line equal 1.
The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)
Janna's health class measures the heart rates of students after they walked for five minutes. The heart rates, in beats
per minute, were as follows.
102, 74, 86, 74, 96, 95, 103, 102 Find the median of the data set. What does the median tell you? (Hint: If the data set has an even number of values,
the median is the mean of the two middle values.)
The median of the data set is: 95.5
What is median?
median is the number at the middle of the given data.
To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:
74, 74, 86, 95, 96, 102, 102, 103
Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.
Therefore, the median of the data set is: (95 + 96) / 2 = 95.5
To know more about median visit,
https://brainly.com/question/26177250
#SPJ1
yara said that the vertical distance between two points is -5 units how do you know that yara's statement is incorrect
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
Find the Taylor Polynomial 3P x (up to3
x ) for( ) x
f x e , centered at0x ?
We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.
The Taylor Polynomial is given by:
(x)=∑
k=0
n
k!
f
(k)
(a)
(x−a)
k
where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.
Using this formula, we can find the Taylor Polynomial as follows:
\begin{align*}
f(x) &= e^x \
f'(x) &= e^x \
f''(x) &= e^x \
f'''(x) &= e^x \
\end{align*}
Evaluating each derivative at $x=0$, we get:
\begin{align*}
f(0) &= e^0 = 1 \
f'(0) &= e^0 = 1 \
f''(0) &= e^0 = 1 \
f'''(0) &= e^0 = 1 \
\end{align*}
Substituting these values into the formula for the Taylor Polynomial, we get:
\begin{align*}
P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \
&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}
\end{align*}
Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.
What is the measure of Za?
Angles are not necessarily drawn to scale.
After calculation, we can conclude that the required angle x is 56° respectively.
What are angles?A pair of rays (half-lines) with a shared terminal are combined to form an angle.
The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located.
So, we can calculate inner angle A because it will result in a 180o angle.
180º - 116º = 64º = Angle A
Now multiply angle A by angle C.
64º + 60º = 124º
Take it away from 180°.
180º - 124º = 56º
Consequently, angle X is measured at 56°.
Therefore, after calculation, we can conclude that the required angle x is 56° respectively.
Know more about angles here:
https://brainly.com/question/25716982
#SPJ1
Write the absolute value equation that has the following solutions.
One solution: x = 15
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
Learn more about absolute value:
https://brainly.com/question/1782403
#SPJ1
There is a sale at khols, and tennis shoes are 30% off. How much are you saving if the shoes originally cost $62
Answer: $18.6
Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off
721.60 divided by 80
Classify the following polynomial by its degree and the number of terms:
9x 3+4x 2 −7
We can classify the polynomial as a "trinomial" with a degree of 3.
How to Classify the following polynomial by its degreeThe given polynomial is:
9x^3 + 4x^2 - 7
The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the degree of the polynomial is 3, because the highest power of x in the polynomial is 3.
The number of terms in a polynomial is the number of individual expressions added or subtracted together. In this case, the polynomial has three terms: 9x^3, 4x^2, and -7.
Therefore, we can classify the polynomial as a "trinomial" with a degree of 3.
Learn more about polynomial at https://brainly.com/question/2833285
#SPJ1
Leon is building a square picture frame. The side of the frame is 335 millimeters long. If a meter of wood costs $8, how much will the wood he needs cost?
Answer: $9.66
Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380
We need 1380 millimeters which is equivalent to 1.38 meters.
We can multiply the number of meters by the cost of meters to find the total
i don't understand this question please help me answer it :)
(2x^2+6x-11)-(5x^2-x+7)
Answer:
-3x² +7x - 18
Step-by-step explanation:
Subtraction of expression:
Multiply each term of 5x² - x + 7 by (-1)
2x² + 6x - 11 - (5x² - x + 7) = 2x² + 6x - 11 - 5x² + x - 7
Combine like terms. Like terms have same variable with same exponent.
2x² and (-5x²) are like terms. 2x² - 5x² = -3x²
6x and x are like terms. 6x + x = 7x
-11 and (-7) are constants. -11 - 7= -18
= 2x² - 5x² + 6x + x - 11 - 7
= -3x² + 7x - 18
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
7 and 31 it asks
the 3rd and 6th is
The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.
How to find the Fibonacci sequence terms ?Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:
F(n) = F(n-1) + F(n-2)
We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:
F3 = F2 + F1 = 7
F6 = F5 + F4 = 31
We can also express F4 and F5 in terms of F1 and F2:
F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2
F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2
Now, let's substitute equation (4) into equation (2):
F6 = 2F1 + 3F2 + F1 + 2F2 = 31
3F1 + 5F2 = 31
By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:
F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)
F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)
The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.
Find out more on Fibonacci sequence at https://brainly.com/question/29764204
#SPJ1
The area of a figure in the shape of a
parallelogram is 74.4 m2 . If the height of
the parallelogram is 6 m, then what is the
length?
The area of a figure in the shape of a parallelogram is 74.4 m2 . If the height of the parallelogram is 6 m, the length of the parallelogram is 12.4 meters.
Describe Parallelogram?A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. It is a special type of quadrilateral, which is a polygon with four sides.
The opposite sides of a parallelogram are parallel, which means they have the same slope and never intersect. The opposite sides are also equal in length, which means they have the same distance between them.
The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. This property is known as the parallelogram law, which states that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.
The area of a parallelogram can be calculated by multiplying the base by the height. The base is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite side.
The area (A) of a parallelogram is given by the formula:
A = base x height
where the base is the length of one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.
In this problem, we are given the area of the parallelogram as 74.4 m² and the height as 6 m. Let the length of the parallelogram be denoted by b. Then, we can use the formula for the area of a parallelogram to write:
74.4 m² = b x 6 m
Solving for b, we get:
b = 74.4 m² / 6 m
b = 12.4 m
Therefore, the length of the parallelogram is 12.4 meters.
To know more about height visit:
https://brainly.com/question/872767
#SPJ1
the perimeter of rectangle is 76m if one side is 16m what is the other side?
Answer: 22
Step-by-step explanation:
The formula for perimeter of a rectangle is side 1 + side 1 + side 2 + side 2. Side one is 16. This means that 16x2 is 32. Then, you realize there are 44 meters remaining. 44/2=22. The other side is 22.