The area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²
How to find the area of a rectangle?Suppose that the two adjacent sides of a rectangle be of 'a' units and 'b' unit lengths.
Then, we get the area of that rectangle as:
[tex]S = a \times b \: \rm unit^2[/tex]
For this case, we're specfied that:
One of the side of the considered rectangle is of 'a' units length.The perimeter of the considered rectangle = 24 unitsLet the other side (adjacent) be of 'b' units length
Then, as perimeter of a rectangle = 2(sum of lengths of one pair of adjacent sides of the rectangle)
Therefore, we get:
[tex]24 = 2(a+b)\\\text{Dividing both the sides by 2}\\12 = a + b\\b = 12 - a[/tex]
We expressed 'b' in terms of 'a' so that we can represent the area of the considered rectangle in terms of 'a' alone.
The area of the rectangle is:
[tex]S =a \times b = a \times (12 - a) \: \rm unit^2[/tex]
Thus, the area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²
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Dwayne used 12 centimeters of tape to wrap 6 presents. How much tape will Dwayne need in all if he has to wrap 9 presents?
Answer:
18cm
if it takes 12cm to wrap 6 presents, it means it takes 2cm to wrap one present.
9 individual presents will take 2 wraps, so Dwayne needs 18cm of wrapping paper.
What is the mean of the following set of numbers?
20, 14, 8, 28
20 + 14 + 8 + 28 = 70
70/4(we're dividing by 4 cause the no.of characters is 4)
and = 17.5
hope it really helps...!!!
help pls MATH IS HARD!!! :((
The y-intercept is the b term in slope intercept form (y = mx + b) or in the form of a point (0, y).
Function 1 is in slope-intercept form, and the b term is 5.
Function 2 is given in a table, but it is easy to find the point (0, y) and y is 5.25.
5.25 > 5
Function 2 has the greater y-intercept.
Hope this helps!
what is the value of 2x to the 3rd power + x to the 2nd power -x when x+3?
Answer:
I am unsure of the wording of this question, so I will answer both ways I see it.
When x = x + 3, the value of 2x³ + x² - x is 2x³ + 19x² + 59x + 66.
When x = 3, the value of 2x³ + x² - x is 60.
Step-by-step explanation:
x = x + 3 solution:
It is given that:
f(x) = 2x³ + x² - x
We are trying to find this when x = x+3. Substitute this value in for every x in the function.
f(x + 3) = 2(x + 3)³ + (x + 3)² - (x + 3)
Expand the first part.
f(x + 3) = 2(x + 3)(x + 3)(x + 3) + (x + 3)² - (x + 3)
Multiply pairs together.
f(x + 3) = 2(x + 3)(x² + 6x + 9) + (x + 3)² - (x + 3)
Multiply the remaining pairs together.
f(x + 3) = 2(x³ + 9x² + 27x + 27) + (x + 3)² - (x + 3)
Distribute the two inside the parenthesis.
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x + 3)² - (x + 3)
Evaluate (x + 3)².
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x² + 6x + 9) - (x + 3)
Remove all parenthesis and start simplifying.
f(x + 3) = 2x³ + 18x² + 54x + 54 + x² + 6x + 9 - x - 3
Combine all terms ending in x².
f(x + 3) = 2x³ + (18x² + x²) + 54x + 54 + 6x + 9 - x - 3
f(x + 3) = 2x³ + 19x² + 54x + 54 + 6x + 9 - x - 3
Combine all terms ending in x.
f(x + 3) = 2x³ + 19x² + (54x + 6x - x) + 54 + 9 - 3
f(x + 3) = 2x³ + 19x² + 59x + 54 + 9 - 3
Last, combine the final numbers to get:
f(x + 3) = 2x³ + 19x² + 59x + 60
x = 3 solution:
It is given that:
f(x) = 2x³ + x² - x
Substitute 3 in for every value of the function.
f(3) = 2(3)³ + (3)² - 3
Evaluate 3 cubed and then multiply it by 2.
f(3) = 2(27) + 3² - 3
f(3) = 54 + 3² - 3
Evalute 3 squared.
f(3) = 54 + 9 - 3
Add 54 and 9.
f(3) = 63 - 3
Subtract 3 from 63 to get:
f(3) = 60
A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?
The bank should not use the data from this survey because this is an observational study.
The bank can use the result of this survey to prove that working for the bank causes employees to participate in volunteer activities,
The bank did not select a random sample of employees, so the survey will not provide the bank with useful information
D
The bank would have to use the survey data to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities.
The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all
employees
DELL
The true statement about the bank survey is (e) The bank does not need to use an inference procedure to determine the participant proportion
How to determine the true statement?The population and the sample size are given as:
N = 60
This is so because the bank surveyed all her staff.
Since all the bank staffs participated in the survey, it means that the proportion of the study is 1 or 100%.
So, the bank do not need to determine the proportion that participates
Hence, the true statement is (e)
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Write an equation for the line in point-slope and slope-intercept forms.
Passes through (3, 5) and has a slope of 5/3.
point-slope form: y-y₁ = m(x-x₁)
=============
[tex]\rightarrow \sf y - 5 = \dfrac{5}{3} (x-3)[/tex]
slope-intercept form: y = mx + b
============
[tex]\rightarrow \sf y - 5 = \dfrac{5}{3}(x)+ \dfrac{5}{3}(-3)[/tex]
[tex]\rightarrow \sf y - 5 = \dfrac{5}{3}(x)-5[/tex]
[tex]\rightarrow \sf y = \dfrac{5}{3}(x)-5+5[/tex]
[tex]\rightarrow \sf y = \dfrac{5}{3}(x)[/tex]
point slope form:-
y-y_1=m(x-x_1)y-5=5/3(x-3)3(y-5)=5(x-3)3y-15=5x-15Slope intercept form
y=mx+b
3y=5xy=5/3x+0Which of the following is equal to ? (In the picture)
Answer:
2^1/6
Step-by-step explanation:
either find the result of all equations or
times square root(2) by cube root (3) and put it over 1
... 1/6 and put this as the power to the number in the question
Helppppp!!! What is the area of the trapezoid shown below?
Answer:
The area of T is equal to sum of area of R and Triangle
Step-by-step explanation:
[tex]area = 12 \times 2[/tex]
Area)= 24
[tex]area = \frac{1}{2} \times 12 \times 15[/tex]
Area= 90
Area of T = 90 PLUS 24
AREA == 114
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEBrett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20. his sample data has a mean of 295 and a sample size of 50. which of the following correctly depicts the z-statistic for brett’s data? –5.30 –0.11 4.28 6.27
The z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).
How to find the value of z-statistic for population mean?Suppose we're specified that:
The sample mean = [tex]\overline{x}[/tex]The population mean = [tex]\mu[/tex]The population standard deviation = [tex]\sigma[/tex]The sample size = nThen the z-statistic for this data is found as:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}[/tex]
For this case, we've got:
The sample mean = [tex]\overline{x}[/tex] = 295The population mean = [tex]\mu[/tex] = 310The population standard deviation = [tex]\sigma[/tex] = 20The sample size = n = 50Thus, we get:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{295 - 310}{20/\sqrt{50}} \approx -5.30[/tex]
Thus, the z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).
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According to the given data and applying it's formula, the z-statistic is of z = -5.30.
What is the z-statistic formula?It is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In this problem, the values of the parameters are given by:
[tex]\overline{x} = 295, \mu = 310, \sigma = 20, n = 50[/tex]
Hence, the z-statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{295 - 310}{\frac{20}{\sqrt{50}}}[/tex]
z = -5.30.
The z-statistic is of z = -5.30.
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Juan and two of his friends are going to share of a pizza. How much will each person get?
(A) 2/3 of the pizza (B) 1/4 of the pizza (C) 1/3 of the pizza (D) 1/6 of the pizza
Answer:
[C] 1/3 of the pizza
Step-by-step explanation:
Given that:
Juan and two of his friends are going to share of a pizza.
Thus, we know that:
Juan + two of his friend = 3 people
Hence, each person gets
1/3 of the pizza
Check Answer
1/3 × 3 =1 whole {whole pizza}
or we can do
1/3 + 1/3 + 1/3 = 1 whole.
We can also do this:
Numerator = how many each person gets
Denominator = Total people
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Kavinsky
Yvonne’s age, in years, is represented by y. Rebekah’s age is one year less than three times Yvonne’s age. What expression represents Rebekah’s age in years?
The expression that can be used to represent Rebekah's age in years given Yvonne's age is 3y - 1.
What expression represents Rebekah’s age?Mathematical expressions are statements that contain a combination of numbers and variables.
Given that Yvonne's age is y.
Rebekah's age = one less than 3 times y. 'less' means subtraction and 'times' means multiplication.
(3 x y) - 1
3y - 1
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What is 1/6 x 1/7 x 588 = ???
Answer:
14
Step-by-step explanation:
Because I looked it up
need some help with the question in the image
Cheers
Answer:
22%
Step-by-step explanation:
formula for percentage increase:
increase/original number x 100
increase is $66 (366-300)
66/300 x 100
= 22/100 x 100
= 22
hope this helped :)
Please Help!!! 100 Points!!! Will Mark Brainliest If Correct!!!
Make sure everything is spaced out and easy to understand. Please show all of your work(if needed).
Task 1
Nonlinear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
Part 1. Show all work in solving your system of equations algebraically.
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
Task 2
Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
Answer:
Step-by-step explanation:
Part A, the system of equation is, presented here as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Part B; The graph of the system of equation is attached
The reason for the above answers is as follows;
Part A
A system of equations are a given number of equations from which a common solution of the system can be found
A linear equation is an algebraic equation in which the maximum exponent of the variables is one and the graph of the equation is a straight line which is of the form y = m·x + c
A maximum value of the exponents of the variable quadratic equation is 2, and the general form of the quadratic equation is y = a·x² + b·x + c, where a, b, and c are real numbers
Therefore, the system of equation that can be created is as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Method for solving;
Divide equation (1) by 2, and equate both values of y to find the common solution as follows;
2·y/2 = (3·x + 2)/2 = 1.5·x + 1
∴ y = 1.5·x + 1
Equating both values of y gives;
y = 1.5·x + 1
y = 2·x² - 3·x + 2
Therefore;
1.5·x + 1 = 2·x² - 3·x + 2
2·x² - 3·x - 1.5·x + 2 - 1 = 0
2·x² - 4.5·x + 1 = 0
Using the quadratic formula, we get;
x = (4.5 ± √((-4.5)² - 4×2×1))/(2 × 2)
x = 2, or x = 0.25
From which we get;
y = 1.5 × 2 + 1 = 4, or y = 1.5 × 0.25 + 1 = 1.375
The points where the line graph and the quadratic graph intersect are;
(2, 4), and (0.25, 1.375)
Part 2
Chang bought a pad of paper for $1.50, a pen for $.80, and a ruler for $0.90 at the school store.
How much did Chang spend?
O A. $2.70
B. $3.20
C. $10.40
D. $18.50
Add the prices together:
1.50 + 0.80 + 0.90 = 3.20
Answer: B. $3.20
Answer:
$ 3.20 (Answer B)
Step-by-step explanation:
Add up the three prices given:
$1.50
0.80
0.90
-------------
$ 3.20 (Answer B)
Select all pairs of complementary angles in the diagram.
Answer:
Step-by-step explanation:
Complementary angles sum to 90 degrees.
< BAF and < BFA
<CDE and < CED.
Supplementary ( sum to 360):
< FBC and <BFE
<BCE and < FEC.
jacob poured 5/6 cup of orange juice and a cup 5/8 of cranberry juice into a pitcher . He drank 1/2 cup of the juice in the pitcher. How many cups of juice are left in the pitcher?
Alvarez has $650 deposited into his bank account. The account earns simple interest of 5. 5% per year. No other money is added or withdrawn from the account for a period of four years. What is the total amount of money in the account after four years?
Answer:
$793
Step-by-step explanation:
The amount of money in an account earning simple interest is given by the formula ...
A = P(1 +rt)
where P is the principal invested at rate r for t years.
__
Using the values given in the problem statement, the account balance can be found to be ...
A = $650(1 +0.055×4) = $650×1.22 = $793
There will be $793 in the account after 4 years.
Find the value of x
please help!!!
Sum of the interior angles of any n-side shape must equals to :
[tex](n - 2) \times 180[/tex]
Thus ;
[tex](5 - 2) \times 180 = [/tex]
[tex] 3\times 180 = [/tex]
[tex]540 \: \: degrees[/tex]
So :
[tex]x + 122 + 100 + 90 + 144 = 540[/tex]
[tex]x +456 = 540[/tex]
Subtract both sides 456
[tex]x + 456 - 456 = 540 - 456[/tex]
[tex]x = 84[/tex]
There u go...
Have a great day ♡♡♡♡♡Quadrilateral wxyz is a paralelogram if w=50
what is wzy
HELP PLSS HAHAHAHHAHA
Sam buys 6 pencils and 5 erasers for a total cost of $1. 60. Sally buys 3 pencils and 3
erasers for a total cost of $0. 90. How much does one ERASER cost?
Which weight occurs most often? Which weight occurs least often? How can you tell from the line plot?
sorry about the lines lol
the question is not visible lol
Table 2. Hybrid Car Sales in the USA Year 2005- 205,828 Year 2007-352,852 Year 2012-432,798. By What percent did tje sales of hybrid cars increase from 2005 to 2012? Rnter your answer rounded to the nearest whole percent
The percentage increase in the sales of hybrid cars from 2005 to 2012 is 10%.
What are percentages?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency.
What is the increase in the percentage of hybrid cars?Percentage increase = (number of cars sold in 2012 / number of cars sold in2005)^(1/n) - 1
(432,798/ 205,828)^(1/8) - 1 = 10%
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A 2-yard piece of linen costs $18.54. What is the price per foot?
Answer:
3.09 per ft
Step-by-step explanation:
1 yd = 3ft
so 2 yd = 6ft
6ft = 18.54
18.54 /6ft
3.09 per ft
Write the equation of the line that passes through the points (4,8) and
(1,8). Put your answer in fully reduced point-slope form, unless it is a
vertical or horizontal line.
Answer:
y=8
Step-by-step explanation:
vertical lines parallel to x axis
y= 45(1.6)^2
I need help with this, thanks!
An isosceles triangle MNP has one angle, N, with a measure of 20". The
angles M and Pare congruent. Which is the measure of angle P?
P=80º
Start by doing 180-20 since N=20
M and P are congruent, so P = 160/2
P=80
Please help me please please I need it so bad
Answer:
A i= 44. B i= 44. C i= 40.