The first five terms of the sequence whose general term is given as a_(n)=2n-8 are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
To explain this in more detail, the general term for a sequence is given by an equation in the form a_(n)= some expression. In this case, the expression is 2n-8, so it can be read as “2 times the term number minus 8”.
To calculate the first term, we substitute n=1 into the equation and solve, so a_1=2*1-8=-6. To calculate the second term, we substitute n=2 into the equation and solve, so a_2=2*2-8=-4. Continuing in this manner, we calculate the third term as a_3=2*3-8=-2, the fourth term as a_4=2*4-8=0, and the fifth term as a_5=2*5-8=2.
Therefore, the first five terms of the sequence are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.
In conclusion, to find the first five terms of a sequence given by a general term a_(n)= some expression, substitute the values n=1, n=2, n=3, n=4, and n=5 into the expression and solve to get the desired terms.
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use the point-slope form to write the equation of a line that passes through the point (17,-12) with slope -3
The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.
Explain about the point-slope form?Write the equation of a line with only a slope of 3 and then a y-intercept of 6 on a graph. Observe how Scenario A provides us with sufficient details straight away to formulate the equation in the form y=mx+b since we already understand the slope, m, and y-intercept, b. Here is how the equation can be expressed: y=3x+6equation of a line using point-slope form is-
y - y1 = m(x - x1)
Points: (17,-12) and slope -3.
Put the values:
y - (-12) = -3(x - 17)
y + 12 = -3x + 51
y = -3x + 51 - 12
y = -3x + 39
Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.
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tear production rate reduced normal none astigmatism no yes soft spectacle prescription myope hypermetrope hard none Decision trees for the labor data wage increase Ist year <= 2.5 > 2.5 bad statutory holidays >10 < 10 wage increase Ist year good wage increase 1st year <= 2.5 > 2.5 working hours per week statutory holidays bad good <= 36 > 36 > 10 <= 10 bad health plan contribution good wage increase Ist year none half full <%3D4 bad good bad bad good 17 2nd_Heart Attack Yes Yes Q1. Given the following data table, answer the questions: (5 Marks) Marital Weight Stress Trait Age Gender Cholesterol Status Category Level Anxiety 60 Yes Female Overweight 150 High 50 69 Yes Male Overweight 170 Normal 60 52 No Female Normal 174 High 35 66 Yes Male Overweight 169 Normal 60 70 Yes Female Overweight 237 Normal 65 52 No Female Normal 174 High 35 58 Yes Male Normal 140 Normal 45 No Yes Yes No No (a) Explain the table with respect to rows and columns. Also, explain what is the meaning of rows and columns in any data table. (b) Which problem can be solved using above data table? (c) Prepare decision table for the above table. NEED ITS ACCURATE SOLUTION. ONLY THEN I WILL UPVOTE IT.
(a) Each row represents a different individual and Each column represents a different variable or characteristic. (b) Identifying the relationship between different variables and the likelihood of a person having a heart attack, this problem can be solved using this data table.
(a) The table is organized into rows and columns. Each row represents a different individual and includes information about their age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait. Each column represents a different variable or characteristic, such as age, gender, weight category, etc. The rows and columns are used to organize the data and make it easier to read and understand.
(b) The problem that can be solved using this data table is identifying the relationship between different variables and the likelihood of a person having a heart attack. For example, the table can be used to determine if there is a correlation between age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait and the likelihood of a person having a heart attack.
(c) Decision table for the above table:
| Age | Gender | Weight Category | Cholesterol Level | Marital Status | Stress Level | Anxiety Trait | Heart Attack |
|-----|--------|-----------------|-------------------|----------------|--------------|---------------|--------------|
| 60 | Female | Overweight | 150 | Yes | High | Yes | Yes |
| 69 | Male | Overweight | 170 | Yes | Normal | Yes | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 66 | Male | Overweight | 169 | Yes | Normal | No | Yes |
| 70 | Female | Overweight | 237 | Yes | Normal | No | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 58 | Male | Normal | 140 | Yes | Normal | No | No |
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This morning the temperature was -5 °F. How much must the temperature change to reach 0 °F?
Answer:
5°
Step-by-step explanation:
because: -5°+5°=0° I think
Answer:
5 degrees
Step-by-step explanation:
-5+5=0
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
The expression can be expanded as a sum of three logarithms:
[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
What is the logarithms?
Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.
Using the properties of logarithms, we can expand the expression as follows:
[tex]log4(xy^5 Z^4) = log4(x) + log4(y^5) + log4(Z^4)[/tex]
Now, we can simplify each logarithm using the property that log[tex](a^b[/tex]) = b log(a):
[tex]log4(x) + log4(y^5) + log4(Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
Hence, the expression can be expanded as a sum of three logarithms:
[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
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120 rupees 5 paise = — ( 120. 50 / 120. 05) rupees
The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.
We have, 120 rupees and 5 paise and we will express as rupees using decimals.
We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1
=> 1 paisa = Rs. 1/100
so, here conversation factor is = 1/100
The required value is obtained by multiplying the observed values by conversion factor. Therefore,
5 paise = Rs. (5×1/100)
= 5/100
= Rs. 0.05
Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05
Hence, required value is Rs. 120.05.
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Complete question:
Express in form of rupees
120 rupees 5 paise = — rupees.
Alice drew a scale drawing of a swimming pool. She used the scale 1 centimeter : 4 meters. If the actual length of the pool is 32 meters, how long is the pool in the drawing?
The pool is 0.5 centimeters long in the drawing.
The ratio of 1 centimeter to 4 meters means that for every 4 meters in real life, Alice drew 1 centimeter in her drawing.
To find out how long the pool is in the drawing, we need to divide the actual length of the pool by the scale factor.
The scale factor is 4 meters : 1 centimeter, which is the same as 1 meter : 0.25 centimeters.
So to find the length of the pool in the drawing, we need to divide the actual length of the pool by 4 to get the length in meters, and then multiply by 0.25 to convert to centimeters:
Length in drawing = (32 meters / 4) x 0.25 = 2 x 0.25 = 0.5 centimeters
Therefore, the pool is 0.5 centimeters long in the drawing.
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If of a number is 4 more than of the same number, what is the number?
12
20
24
28
Answer:
please your question is incomplete
Step-by-step explanation:
if....... of a number
Assume 4 years of monthly data was used to create a seasonally-adjusted forecasting model. The trend equation for the 4 years was found to be: y = 65 + 6.7X.
Seasonal factors are reported. Compute a seasonally-adjusted forecast for quarter 4 of year 5.
QTR1 QTR2 QTR3 QTR4
0.12 0.35 0.42 0.1
a. 10.8
b. 98.5
c. 24.5
d. 17.2
The seasonally-adjusted forecast for quarter 4 of year 5 is 91.9
The seasonally-adjusted forecast for quarter 4 of year 5 can be calculated by using the following equation:
Seasonally Adjusted Forecast = Trend Equation + Seasonal Factors
= 65 + 6.7X + 0.1
= 65 + 6.7X + 0.1
= 65 + 6.7*4 + 0.1
= 65 + 26.8 + 0.1
= 91.9
Therefore, the seasonally-adjusted forecast for quarter 4 of year 5 is 91.9.
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(Written assignment) A student was asked to simplify the following rational expression:
(x^2+3x+2)/(x^2+6x+8)
Here is the student’s work, in which the expression was simplified incorrectly:
Questions for thought:
1. Please explain the student’s mistake and why it is incorrect.
2.This type of mistake is common in Algebra, why do you think it is so common?
3.Have you ever made a mistake like this?
4. If you have made a mistake like the one shown above, what helped make you stop making this mistake?
5.What advice would you give future Algebra 2 students to help stop them from making mistakes like this?
You do not have to answer all the questions in your response. As long as your answer has AT LEAST FIVE (5) COMPLETE SENTENCES you will get brainliest
Answer:
The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.
Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.
Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.
My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.
A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
1 gallon
=
1 gallon=
4 quarts
4 quarts
1 quart
=
1 quart=
2 pints
2 pints
1 pint
=
1 pint=
2 cups
2 cups
1 cup
=
1 cup=
8 fluid ounces
8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of servings for?
Step-by-step explanation:
How many cups of milk are in a gallon = 16
If a recipe uses 2 cups for 6 servings, then he will make 48 servings from a gallon.
1 quart is 4 cups of milk, a gallon contains 4 quarts
1 pint is 2cups, a gallon contains 8pints of milk
From the question 1 gallon is 4 quarts or 8pints or 48servings
Which equations represent functions that are non-linear? Select each correct answer. A. Y = x B. 2 y = 1 2 x C. Y = 8 + x D. Y − 6 = x 2 E. Y = 1 3 − 5 x F. Y = 2 x 2 + 5 − 3 x 3 I NEED HELP NOW!!!
The equations y-6=x² and y=2x²+5-3x³ are non linear. Therefore, options D and F are the correct answers.
What is linear function?A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.
Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.
A) y=x
Here, degree of the equation is 1, so the equation is linear.
B) 2y=12x
Here, degree of the equation is 1, so the equation is linear.
C) y=8+x
Here, degree of the equation is 1, so the equation is linear.
D) y-6=x²
Here, degree of the equation is 2, so the equation is quadratic.
E) y=13-5x
Here, degree of the equation is 1, so the equation is linear.
F) y=2x²+5-3x³
Here, degree of the equation is 3, so the equation is cubic.
Therefore, options D and F are the correct answers.
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This is the graph of a function in the form. f(x)=a*b^x. What is the function?
A = f(x)=3^x.
B = f(x)=2*3^x.
C = f(x)=3*(0.1)^x
D = f(x)=(0.2^x)
An equation of the function include the following: C. f(x) = 3×(0.1)^x.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the base value or y-intercept.x represents time.b represents the rate of change.By critically observing the graph of this exponential function, we can logically deduce that the base value of this exponential growth function is at (0, 3) and its domain includes all real numbers i.e -∞ < x < ∞.
Therefore, the required exponential function is given by:
f(x) = 3(0.1)^x
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2. A package of paper is 2" high and 1.5" wide. If a warehouse shelf is 1' 5" high and 2 yards
long, how many packages of paper can be put on the shelf?
Therefore, approximately 408 packages of paper can be put on the shelf.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units such as square meters, square inches, or square feet. The area of a shape can be found by multiplying the length of the shape by its width. The concept of area is used in many areas of mathematics and in a wide range of real-world applications, including architecture, engineering, physics, and geography. The ability to calculate the area of a shape is an important skill in many fields and is a fundamental concept in geometry.
Here,
To solve this problem, we need to find the number of packages of paper that can fit on the warehouse shelf by dividing the total shelf area by the area of each package.
First, we need to convert the height of the shelf from feet and inches to inches:
1 foot = 12 inches
1' 5" = 1 * 12 + 5 = 17 inches
Next, we need to convert the length of the shelf from yards to inches:
1 yard = 36 inches
2 yards = 2 * 36 = 72 inches
Now we can find the area of the warehouse shelf:
Area = length * height
Area = 72 inches * 17 inches
Area = 1224 square inches
The area of each package of paper is:
Area = height * width
Area = 2 inches * 1.5 inches
Area = 3 square inches
Now we can find the number of packages of paper that can fit on the warehouse shelf:
Number of packages = Shelf area / Package area
Number of packages = 1224 square inches / 3 square inches
Number of packages ≈ 408
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expand the expression log6x^2
Answer:
log(2)+log(3)+2log(x)
you should try downloading an app called math away
i don't know if it's right but I got the answer from a reliable source
What is the answer? Please help!
Answer:
the answer is 88 square inches
Step-by-step explanation:
[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]
I need help please, I dont know how to do this
m=2
because in the other equation, the digit next to x is 2 so m must be 2
find the slope of the equation -6x+3y=-12
Answer: m=2
Step-by-step explanation: First convert the equation to slope-intercept form; y=mx+b. This new equation would be 3y=6x-12. Because y must be singular, each side must be divided by 3, to isolate the variable y. After doing this, the equation is y=2x-4. In terms of y=mx+b, m is attached to x, making the slope of this equation 2.
At the grocery store Adrian spends $8 on food, plus $4 each for pumpkins. Which statements are true? Choose all that are correct. Responses If Adrian buys 3 pumpkins, his total cost is $12. If Adrian buys 3 pumpkins, his total cost is $12. If Adrian buys 5 pumpkins, his total cost is $44. If Adrian buys 5 pumpkins, his total cost is $44. If Adrian buys 4 pumpkins, his total cost is $24. If Adrian buys 4 pumpkins, his total cost is $24. Adrian’s total cost may be represented as 8+4x . Adrian’s total cost may be represented as 8 + 4 x . Adrian’s total cost may be represented as 4+8x . Adrian’s total cost may be represented as 4 + 8 x . Adrian’s total cost may be represented as 12x .
You must SHOW ALL YOUR WORK for full points. Write your answer as an (x,y) ordered pair.
2x + 3y = 7
-2 + 1y = -11
Must be done in both elimination method and substitution method.
The solution to the equation is (5, -1)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
2x + 3y = 7
-2x + 1y = -11
Add to eliminate x
So, we have
4y = -4
Divide both sides by 4
y = -1
Recall that 2x + 3y = 7
Substitute the known values in the above equation, so, we have the following representation
2x - 3 = 7
So, we have
2x = 10
Divide
x = 5
For the substitution method, we have
2x + 3y = 7
-2x + y = -11
The second equation becomes
y = 2x - 11
By substitution, we have
2x + 6x - 33 = 7
So, we have
8x = 40
x = 5
Recall that
y = 2x - 11
So, we have
y = 2 * 5 - 11
y = -1
Hence, the solution is (5, 2)
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Simplify the following expression
by combining like terms.
3y + 8 + 4y + 2
Answer:
Step-by-step explanation:
1. Figure out which terms are alike. I have separated the like terms using parenthesis for clarification, however, this is not necessary when solving by yourself.
(3y + 4y) + (8 + 2)
2. Combine both sets of like terms however the signs dictate. In this case, add all the signs.
3y + 4y = 7y
(solve as if there was no constant so if 3 + 4 = 7 then 3y + 4y = 7y)
8 + 2 = 10
3. Put it all together
Final answer: 7y + 10
Note: Understanding how to combine and simplify like terms will be very helpful when you eventually will have to solve for y. When solving an equation you will always want to start by combing and simplifying like terms first.
Research online about the applications of Sinusoidal (periodic)
Functions in real life and write an abstract of your reading. Your
abstract must be between 150 and 200 words
Sinusoidal (periodic) functions, also known as sine and cosine functions, are ubiquitous in our daily lives. They are used to model a wide range of phenomena in fields such as engineering, physics, and mathematics.
One of the most common applications of sinusoidal functions is in the field of electronics, where they are used to model alternating current (AC) circuits.
Sinusoidal functions are also used in signal processing, audio and image compression, and speech recognition. In addition, they are used in the design of various mechanical and electrical systems, such as engines, turbines, and power generators.
Sinusoidal functions also play an important role in wave motion, such as ocean waves and sound waves. They are used to model the behavior of waves and to predict their properties, such as wavelength and frequency.
Furthermore, sinusoidal functions are used in the field of optics to model the behavior of light waves. They are used to describe the properties of light waves, such as amplitude, frequency, and phase.
In conclusion, sinusoidal functions have a wide range of applications in various fields, from electronics and signal processing to mechanics and optics. Their versatility and accuracy make them an essential tool for modeling and predicting real-world phenomena.
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write a point slope form equation of the line that passes through the point (1, 7) with the slope 3/5
Answer:
y - 7 = 3/5 (x - 1)
Use The Compound Interest Formula \( A=P\Left(1+\Frac{R}{N}\Right)^{N T} \) To Solve. Round To Two Decimal Places. Find The Accumulated Value Of An Investment Of $ 20,000 At 6% Compounded Annually For 16 Years. A. $ 39,200.00 B. $ 38,000.00 C. $ 47,931.16 D. $50,807.04
The accumulated value of an investment of $20,000 at 6% compounded annually for 16 years is $50,807.04. The correct answer is D.
To find the accumulated value of an investment of $20,000 at 6% compounded annually for 16 years, we need to plug in the given values into the compound interest formula: A = P(1 + r/n)^nt
Given values:
P = $20,000 (principal amount)
R = 6% (annual interest rate)
N = 1 (number of times interest is compounded per year)
T = 16 (number of years)
Plugging in the given values into the formula:
A = 20000(1 + (0.06/1))^(1)(16)
Simplifying the equation:
A = 20000(1.06)^16
Using a calculator to find the value of A:
A = $50,807.04
Therefore, the accumulated value is D. $50,807.04.
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Andrew Albring purchases an inflatable shark for $12.99, 8 gallons of chlorine at $1.99 each, 2 gallons of
algaecide at $7.99 each, 1 thermometer for $12.99, and 2 sets of fins at $22.99 each. If the sales tax rate
is 7.5%, what is the total purchase price?
A)$63.37
B)$86.94
C)$111.13
D)$111.65
Option D is correct, the total purchase price is $111.65.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Lets find the price of each item
Inflatable shark: $12.99
8 gallons of chlorine at $1.99 each: 8 x $1.99 = $15.92
2 gallons of algaecide at $7.99 each: 2 x $7.99 = $15.98
1 thermometer for $12.99: $12.99
2 sets of fins at $22.99 each: 2 x $22.99 = $45.98
Now add the costs of all the items:
$12.99 + $15.92 + $15.98 + $12.99 + $45.98 = $103.86
we multiply the total cost by the tax rate to find the sales tax.
$103.86 x 0.075 = $7.79
Finally, we add the sales tax to the total cost to get the final purchase price:
$103.86 + $7.79 = $111.65
Therefore, the total purchase price is $111.65.Option D is correct.
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Kyler designed a pool with a diameter of 25 meters. What is the area of the bottom of the pool?
Answer:
962.084375 meters² or 306.25π
Step-by-step explanation:
A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.
The formula for the area of a circle is pi • r²
Since we know the radius (17.5), we can solve this expression:
pi • 17.5²
pi • 306.25
If we use 3.1415 for pi, we get962.084375 meters²
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use table a-3 to find the range of values for the p-value of a left tailed test with n = 38 and a test statistic of t = 2.714?
The range οf P-values wοuld be 0.01 < P-value < 0.02
What is the test statistic?In statistics, a test statistic is a numerical value that is calculated frοm a sample οf data and is used tο determine whether οr nοt tο reject a null hypοthesis in a hypοthesis test.
The chοice οf test statistic depends οn the specific hypοthesis test being perfοrmed and the nature οf the data being analyzed. Fοr example, in a t-test fοr the mean οf a nοrmally distributed pοpulatiοn, the test statistic is the t-value, which is calculated as the difference between the sample mean and the hypοthesized pοpulatiοn mean divided by the standard errοr οf the mean.
Using Table A-3 with n = 38 and a left-tailed test statistic t = 2.714, we find the cοrrespοnding P-value tο be between 0.01 and 0.02. Therefοre, the range οf values fοr the P-value is:
0.01 < P-value < 0.02
Sο the cοrrect respοnse is:
0.01 < P-value < 0.02
Hence, the range οf P-values wοuld be 0.01 < P-value < 0.02
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Complete Question:
1. in a survey of 290 university applicant, 181 applied ESUT. 142 applied for UNN, 117 applied for FUTO, and each admission into at least one of the three universities. If 75 applie and UNN, 60 applied for ESUT and FUTO, and 54 for UINN a a. Draw a Venn diagram to illustrate this information. b. How many applicant applied All three universities il Exactly two universities PLASU towns.
a Draw a Venn diagram to illustrate the information
b how many applicant applied
I all three universities
ii Exactly two universities
III plasu
Answer:
a. Here is a Venn diagram to illustrate the information:
markdown
ESUT
/ \
FUTO UNN
\ /
\ /
(X)
where (X) represents the number of applicants who applied to all three universities.
b. To find the number of applicants who applied to all three universities, we can use the formula:
scss
Total = ESUT + FUTO + UNN - (Exactly two) - (None) + (All three)
We know that:
makefile
ESUT = 60 + 54 + (All three)
UNN = 75 + (All three)
FUTO = 54 + 60 + (All three)
Total = 290
Substituting these values, we get:
scss
290 = (60 + 54 + All three) + (54 + 60 + All three) + (75 + All three) - (Exactly two) - (None) + (All three)
Simplifying, we get:
scss
290 = 249 + 2(All three) - (Exactly two) - (None)
We also know that:
scss
None = Total - (ESUT + FUTO + UNN) = 290 - (181 + 142 + 117) = -150
This negative value means that there are no applicants who did not apply to any of the universities. This is a contradiction, so we must have made an error in our calculations.
Therefore, we cannot find the number of applicants who applied to all three universities or exactly two universities.
Select the correct answer from each drop-down menu.
Consider quadrilateral EFGH on the coordinate grid.
-6
E
-4
1
LL
F
>+
Y
6-
2-
O
-4-
-6-
H
-N
G
05.
6
In quadrilateral EFGH, sides FG and EH are
are
X
because they
The area of quadrilateral EFGH is closest to
✓square units.
Sides EF and GH
First box ( not congruent, congruent).
Second box ( each have a length of 5.83, each have a length of 7.07, have different lengths)
Third box ( not congruent, congruent with lengths of 4.24, congruent with length of 5.83)
Fourth box (41, 34, 25, 30)
In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.
How to calculate the distance between the two points?For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance FG = √[(4 - (-1))² + (-1 - 4)²]
Distance FG = √[5² + (-5)²]
Distance FG = √50
Distance FG = 7.07 units.
Distance EH = √[(1 - (-4))² + (-4 - 1)²]
Distance EH = √[5² + (-5)²]
Distance EH = √50
Distance FG = 7.07 units.
For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance EF = √[(-1 - (-4))² + (4 - 1)²]
Distance EF = √[3² + (3)²]
Distance EF = √9
Distance EF = 3 units.
Distance HG = √[(4 - 1)² + (1 - (-4))²]
Distance HG = √[3² + (5)²]
Distance HG = √34 units.
Mathematically, the area of a rectangle can be calculated by using this formula:
Area of rectangle = length × width
Area of rectangle = √34 × 7.07
Area of rectangle = 41.22 square units.
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Find an equation of the line parallel to y = 3x - 3 and that passes through the point (3, 2)
The solution is, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The equation of the given line is,
y=3x-3 ....1
We have to find the equation of a line parallel to y=3x-3 and passing through the point (x1, y1)=(3,2).
The general equation of a line is,
y = mx+c ....2
Here, m is the slope of the line.
Comparing equations (1) and (2), we find that the slope of the line
y=3x-3 is m=3.
The slope of two parallel lines are always equal.
Hence, the slope of a line parallel to the line y=3x-3 is also m=3.
Now, the formula for the point slope form of the equation of a line can be written as,
y - y1 = m (x - x1)
Substitute m=3, x1=3 and y1=2 in the above equation to find the equation of a line parallel to y=3x-3 and passing through point (3,2) is,
y-2 = 3(x - 3)
Therefore, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.
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Mariah house sits on an irregular lot with a triangular shaped backyard. Most of the backyard will be grass, but Mariah would also like a rectangular garden plot. She plans to outline both the yard and the garden plot with bricks. How many square yards of brick will Mariah need to buy?
In order to outline the yard and the garden allotment with bricks and Using Pythagorean theorem, Mariah will need to buy about 69.4 yards³ of brick.
what is pythagoras theorem ?
According to the Pythagorean Theorem, the square of the length of the hypotenuse in a right triangle equals the total of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. In mathematics, it can be expressed as:
c² = a² + b²
where the lengths of the other two sides (the legs) of the right - angled triangle are a and b, and c is the length of the hypotenuse. Pythagoras, an ancient Greek mathematician, is attributed with discovering and proving this theorem, so it bears his name. Geometry, algebra, and other fields of mathematics and science all make extensive use of the Pythagorean Theorem.
given
The Pythagorean formula can be used to determine side C.
C² = A² + B²
C²= 30² + 50²
C² = 900 + 2500
C² = 3400
C ≈ 58.3
As a result, the triangle-shaped yard's circumference is:
30 + 50 + 58.3 ≈ 138.3 feet
We require information regarding the measurements of the rectangular garden plot. Let's assume it is 20 feet long and 15 feet wide.
Thus, the vegetable plot's perimeter is as follows:
2(20 + 15) = 70 feet
The perimeters must now be converted from feet to yards (since we are calculating square yards).
circumference of a triangular yard: 46.1 yards x 138.3 feet
Garden plot boundaries measured as 70 feet by 23.3 yards.
In order to calculate the overall number of bricks required, we add the two perimeters:
46.1 plus 23.3 equals 69.4 square yards.
In order to outline the yard and the garden allotment with bricks, Mariah will need to buy about 69.4 yards³ of brick.
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