Find the error. A student was finding the measure angle 5 in the figure below. She concluded that m angle 5=86
Answers
The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
What is a supplementary angle?An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.
From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
Hence, option 2 is correct.
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The complete question is:
Related Questions
An Internet provider is trying to gain advertising deals and claims that the mean time online per day is than minutes. You are asked to test this claim.
(a) How would you write the null and alternative hypotheses if you represent the Internet provider and want to support the claim?
(b) How would you write the null and alternative hypotheses if you represent a competing advertiser and want to reject the claim?
Answers
a. Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
b. Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
What is null hypothesis?A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
a) The following is how you can write the null and alternative hypotheses if you are the Internet service provider and want to back up your claim that people spend less than 30 minutes online on average per day:
Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
(b)If you address a contending promoter and need to dismiss the case that the interim online each day is not exactly or equivalent to 30 minutes, the invalid and elective speculations can be composed as follows:
Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
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elem algebra
I tried doing a question on my own, I didn't get it right :(
ANY HELP WILL BE GREAT, THANKSS
Answers
Answer:
the missing y coordinate is 2/5
Step-by-step explanation:
You are basically solving for y since you are missing the y coordinate
Since x=5 plug that in and you will get 5+5y=7
subtract 5 on both sides and you will get 5y=2
divide 5 on both sides and you will get 2/5
Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Answers
Yes, we can solve Curious Georgia's math problem using the concept of combinations.
There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.
We have,
Yes, we can solve Curious Georgia's math problem using the concept of combinations.
Since we cannot backtrack or go out of our way, we need to take exactly 6 blocks to the north and 6 blocks to the east to reach the math classroom.
This means that we need to choose 6 out of the 12 blocks to go north, and the remaining 6 blocks will be used to go east.
The total number of paths we can take is the number of ways we can choose 6 blocks out of the 12 blocks.
This can be calculated using the combination formula:
[tex]^nC_r[/tex] = n! / r!(n-r)!
where n is the total number of objects, r is the number of objects to choose, and ! represents the factorial function
In this case,
we have n = 12 and r = 6.
The number of paths.
= [tex]^{12}C_6[/tex]
= 12! / 6!(12-6)!
= 924
Therefore,
There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.
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HELP ME PLEASE! And I already did the first part I need help on the second. (Give me a full explanation NO DECIMALS! Just fractions.)
Answers
The amount of chalk that is greater is yellow.
Michelle is correct because more than 1/2 the chalk in the bucket is blue.
How to determine which amount of chalk is greater?In order to determine the amount of chalk that is greater between the amount of yellow chalk and amount of green chalk, we would have to find the difference between them as follows;
Difference = 2/6 - 3/12
Difference = (4 - 3)/12
Difference = 1/12 (positive value)
Similarly, we can determine the greater amount of chalk as follows;
2/6 × 2/2 = 4/12
4/12 > 3/12
Total number of chalks = 2/6 + 5/12 + 3/12
Total number of chalks = (4 + 5 + 3)/12
Total number of chalks = 12/12
Total number of yellow and green chalks = 2/6 + 3/12
Total number of yellow and green chalks = (4 + 3)/12
Total number of yellow and green chalks = 7/12 chalks.
1 - 7/12 = 5/12
7/12 - 1/2 = 6/12 (Michelle is correct).
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determine the area of the shaded region of a wooden patch in a circular park if the radius of the circle is: a. 8m b. 12
Answers
Answer:
22.88
Step-by-step explanation:
O/360 * π r squared
90/360 * 8 squared
1/4 * π (64)
4 π
Next:
b*h/2
8*12/2 = 48
8π - 48
8π = 25.12
48-25.12 = 22.88
Aaron writes an algebraic expression to represent the product of 14 and the difference of 18 and 3x. What are the factors in this expression
Answers
The factors in this algebraic expression are:
14 And (18 - 3x)
How to find he factors in the algebraic expression ?An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.
Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:
Factorization using common factors
Factorization by regrouping terms
Factorization using identities
The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:
14 * (18 - 3x)
The factors in this expression are:
14
(18 - 3x)
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Company A charges a $125 annual fee plus $7 per hour car share fee.
Company B charges $110 plus $10 per hour. What is the minimum number of
hours that a car share needs to be used per year to make company A a better
deal?
OA. 9
B. 6
O C. 5
D. 11
Answers
Cost of Company A = $125 + $7x
The cost of using Company B is given by:
Cost of Company B = $110 + $10x
We want to find the minimum number of hours of car sharing per year such that Company A is a better deal than Company B. In other words, we want to find the value of x such that:
Cost of Company A < Cost of Company B
125 + 7x < 110 + 10x
15 < 3x
5 < x
So the minimum number of hours of car sharing per year to make Company A a better deal is 6 hours. Therefore, the answer is B!!
help this is due today!!!
Answers
Answer:
46
Step-by-step explanation:
46 (ve had this problem before)
As our scientific and technical knowledge has increased, so has our need for ever-smaller and ever-larger units of measure. The prefixes used to denote some of these units of measure are listed in the table below.
These new units of measure are quickly working their way into our everyday lives. For example, it is quite easy to purchase a 1-terabyte hard drive. One terabyte (TB) is equal to 1012 bytes. As another example, many computers can do multiple operations in 1 nanosecond (ns). One nanosecond is equal to 10−9 s.
In the 1980s, it became possible to measure optical events in nanoseconds and picoseconds. Express 1 ps as a decimal.
Answers
The expression of 1 picoseconds as a decimal would be = 0.000000000001 picoseconds.
What is a scientific notation representation of figures?The scientific notation of representation of figures is a systematic way of representation of too large or too small figures encountered in everyday arithmetics.
From the table above, the larger figures are represented with 10 ^ X without a negative sign.
But the smallest figures are represented with 10 ^ -X with a negative sign.
The scientific notation for 1 picoseconds = 10^-12
When converted to decimal
= 0.000000000001 picoseconds.
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20
Answers
A statement which could be true for g is that: D. g(-13) = 20.
What is a domain?In Mathematics and Geometry, a domain can be defined as the set of all real numbers for which a particular function is completely defined.
How to determine the true statement?Since the domain of this function is given by -20 ≤ x ≤ 5, it simply means that the value of x must between -20 and 5. Also, with a range of -5 ≤ g(x) ≤ 45, the value of x must between -5 and 45.
By extrapolating the function, we can deduce that:
g(0) = -2
g(-9) = 6
g(-13) = 20
In this context, we can reasonably infer and logically deduce that based on the answer options provided, g(-13) = 20 is the only statement that could be true for the function g.
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For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
Answers
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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evaluate the expression 8 - 12 - (-6)
Answers
Answer:
2
Step-by-step explanation:
(4+sqrt -20i)+(5+sqrt -30i)
Answers
The sum of the two complex numbers is 9 - √30) + 2√(5)i.
Explain complex numbers
Complex numbers are numbers that consist of a real part and an imaginary part, expressed as a+bi, where a and b are real numbers and i is the imaginary unit. They are used in mathematics to represent solutions to equations that cannot be solved using only real numbers.
According to the given information
To add complex numbers (4+√(-20i)) and (5+√(-30i)), we add their real parts separately and their imaginary parts separately:
Real parts: 4 + 5 = 9
Imaginary parts: √(-20i) + √(-30i)
We can simplify each of the square roots using the fact that:
√(-1) = i
Therefore:
√(-20i) = √(20) * √(i) = 2√(5) * i
√(-30i) = √(30) * √(i) = √30) * i * √(-1) = √(30) * i^2 = -√(30)
So the imaginary parts simplify to:
2√(5)i - √(30)
Putting it all together, we get:
(4+√(-20i)) + (5+√(-30i)) = 9 + (2√(5)i - √(30)) = 9 - √(30) + 2√(5)i
Therefore, the sum of the two complex numbers is 9 - √(30) + 2√(5)i.
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EASY ALGEBRA 2 !! PLEASE HELP
Answers
according to the question the balance in the account earning compound interest after 6 years is $4,156.22.
what is interest ?Multiply the principal with the rate of interest, the time period, and various other factors to determine simple interest. Simple returns = money + interests + hours is the marketing formula. This approach makes calculating interest the simplest. The approach to calculating interest that is most usually employed is as a percentage over the principal sum. For instance, he will just pay his share of the interest at 100% when he borrows $100 with a friend and agrees to shell out it back with 5% interest. $100 has been reduced to $5 (0.05). Every time you borrow money, you must pay interest, which is applied to whatever loans you make. On the loan balance, interest is typically calculated using an annual percentage.
given,
To calculate the balance in the account earning compound interest after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the sum of money at the end of the period of time
P stands for the principle (beginning sum).
the decimal representation of the annual interest rate (r).
n represents how many times the interest rate is compounded annually.
t is the duration (in years).
In this case, we have:
P = $3500 (the principal)
r = 2.16% = 0.0216 (the annual interest rate)
Since interest is compounded four times a year (quarterly), n is equal to four.
t = 6 (the time period is 6 years)
With these values entered into the equation, we obtain:
A = 3500(1 + 0.0216/4)^(4*6)
A = $4,156.22
Therefore, the balance in the account earning compound interest after 6 years is $4,156.22.
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The balance in the account earning compound interest after 6 years when the principal is $3500 at an annual interest rate of 2.16% compounded quarterly is approximately $4,029.53.
What is compound interest?Compound interest is the term used to describe the interest that is calculated on both the initial investment and any accumulated interest. It is interest on top of interest, to put it another way.
We can use the formula for compound interest to find the balance in the account after 6 years:
A = P(1 + r/n)^(nt)
where:
A = balance after 6 years
P = principal = $3500
r = annual interest rate = 2.16%
n = number of compounded times per year = 4 (quarterly)
t = time in years = 6
Plugging in the values, we get:
A = 3500(1 + 0.0216/4)^(4×6)
A ≈ $4,029.53
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A theatre contains 457 seats and the ticket prices for a recent play were $54 for adults and $17 for children. If the total proceeds were $14,984 for a sold-out matinee, how many of each type of ticket were sold?
Answers
Answer: 195 adult tickets and 262 children tickets
Step-by-step explanation:
Let a be adult tickets and c be children tickets.
We know there are 457 seats.
a + c = 457
We also know the cost of the tickets and how much money was made.
$54a + $17c = $14,984
Now, we have a system of equations we can use to solve.
a + c = 457
$54a + $17c = $14,984
Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.
195 adult tickets and 262 children tickets.
Answer:
Chidden tickets were 262 and adult tickets were 195 tickets
Step-by-step explanation:
Let x = the number of children tickets
Let y = the number of adult tickets.
x + y = 457
17x + 54y = 14984
Use substitution
x + y = 457 Solve for y
y = 457 -x Substitute 457 -x for y in the equation 17x + 54y = 14984
17x + 54y = 14984
17x + 54(457 -x) = 14984 Solve for x Distributer the 54
17x + 24678 - 54x = 14984 Combine like terms
-37x = -9694 Divide both sides by -37
x = 262
The number of children tickets.
x + y = 457 Substitute 262 for x and solve for y
262 + y = 457 Subtract 262 from both sides
y = 195
The number of adult tickets.
Helping in the name of Jesus.
You have invested in a plot of land and have turned it into a campground
to rent out space to campers. You need to decide what to charge your
customers. You will charge somewhere between $40 and $150 per
campsite. If you charge dollars per day, it has been found that the
number, , of campsites rented per day can be modeled by the function
() = −0.01^2 − 2x + 600. How much should you charge to maximize your
revenue, ?
Answers
Answer:
Step-byeat -step explanation:
I want to know the claim ___ which corresponds to ____
And the opposite ___ which corresponds to ____
Answers
The correct values to fill in the missing information are:
Claim: p ≠ 0.5 which corresponds to H0: p = 0.5 (two-tailed test)Opposite: p = 0.5 which corresponds to H1: p = 0.5 (two-tailed test)The test is: two-tailedThe test statistic is: 0.55 (to 2 decimals)The p-value is: 0.5823 (to 4 decimals)Based on this we: Fail to reject the null hypothesisConclusion: There does not appear to be enough evidence to support the claim that the proportion of American adults who eat salad once per week is different from 50% at a significance level of 0.05.What is the sentences about?Claim: The claim is that the proportion of American adults who eat salad once per week is different from 50%, which corresponds to the null hypothesis H0: p = 0.5.
Opposite: The opposite of the claim is that the proportion of American adults who eat salad once per week is equal to 50%, which corresponds to the alternative hypothesis H1: p = 0.5 (Note that in this case, the alternative hypothesis is the opposite of the claim since we are testing for a difference from 50% in the claim).
Therefore, the claim is H0: p ≠ 0.5 (two-tailed test), and the opposite is H1: p = 0.5 (two-tailed test).
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Drag each number to the correct location on the table.
Complete a two-way frequency table using the given probability values.
Answers
The complete table as determined from the given probabilities is given below:
X Y Total
A 40 28 68
B 38 54 92
Total 78 82 160
What is the probability P(A|B)?P(A|X) means the conditional probability of A given X has occurred. In this case, 40/92 means out of 92 times X occurred, A occurred 40 times.
P(B) means the marginal probability of B, which is the total probability of B occurring regardless of whether A occurred or not. In this case, 78/160 means out of 160 trials, B occurred 78 times.
The row and column totals are calculated by adding up the corresponding values.
The grand total is the sum of all the values in the table.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See the attached image.
Solve for m 5(20 - m) = 40
Answers
Answer: 12
Step-by-step explanation: distribute 5 to 20 and -m which gives you
100 - 5m = 40. Subtract 100 on both sides which gives you -5m = -60. Divide both sides by -5 which gives you m = 12
I don't know this I've tried but I just don't know.
Answers
Answer:the median is Q2 aka 105
Step-by-step explanation:
what is the cosine of angle b
Answers
For the given right angled triangle cosine of angle B is 5√89/89.(option A).
What is right angled triangle?
It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.
The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.
In the given figure base= 5 inches and perpendicular = 8 inches
By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches
For any right angled triangle,
(perpendicular)² +(base)²= (hypotenuse)²
⇒ (8)² + (5)² = (c)²
⇒ 64+ 25 = c²
⇒ c² =89
⇒ c= ±√89
As hypotenuse cannot be negative
So hypotenuse = √89 inches.
Now to find cosine of angle B that is cos B we will use the trigonometric function.
cos B= Adjacent side/ hypotenuse
= 5/√89
= 5√89/89 [ Multiplying the numerator and the denominator by √89 ]
Hence, cosine of angle B is 5√89/89.
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Correct answer gets brainliest!!!!
Answers
Option B
One dimensional objects
Answer:
B. One-dimensional objects
A line segment can "grow" from one-dimensional objects. A line segment is a one-dimensional figure that has two endpoints and connects them with a straight path. One-dimensional objects include lines and curves, and a line segment can be a part of a longer line or curve.
Three-dimensional objects (A) are made up of length, width, and height and cannot "grow" into a line segment, but a line segment can be a part of a three-dimensional object, such as an edge or a diagonal.
Zero-dimensional objects (C) are points, which do not have any length, width, or height. A line segment cannot "grow" from a point, but a point can be one of the endpoints of a line segment.
What is the linear equation for your line of best fit? What does the slope of this line mean? What does the y-intercept of this line mean? (It's scattered plot points)
Answers
Answer:
need better photos
Step-by-step explanation:
Answer: Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
Step-by-step explanation:
Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
The diagram represents two statements:p and q Which represents regions a,b,c
Answers
The statement for regions A, B, C are "Elements in P but not in Q." "Elements in both P and Q." and "Elements in Q but not in P." respectively
Describing the statements of the regions of A, B and CThe descriptions of the regions A, B and C from the Venn Diagram that complete the question are as follows:
Region A:
This region represents the set of elements that belong only to P, but not to Q i.e. A is the set of elements that are in P but not in Q.
Region B:
This region represents the set of elements that belong to both circle P and circle Q. i.e. B is the intersection of sets P and Q.
Region C:
This region represents the set of elements that belong only to circle Q, but not to circle P. i.e. C is the set of elements that are in Q but not in P.
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A rectangle has a length of x + 4 cm and a width of 2x − 7 cm.
(a) If the perimeter is 36cm, what is the value of x?
(b) What is the area of this rectangle
Answers
Answer:
See below!
Step-by-step explanation:
Given data:Length = x + 4 cm
Width = 2x - 7 cm
Part a)Perimeter:
Sum of all sides of a shape is called perimeter.Perimeter of rectangle = 2(length) + 2(width)Put the given data.
36 = 2(x + 4) + 2(2x - 7)
Distribute36 = 2x + 8 + 4x - 14
Combine like terms36 = 2x + 4x + 8 - 14
36 = 6x - 6
Add 6 to both sides36 + 6 = 6x
42 = 6x
Divide both sides by 642/6 = x
7 = x
OR
x = 7Part b)Area of rectangle = length × widthArea = (x + 4)(2x - 7)
Put x = 7
Area = (7 + 4)(2(7) - 7)
Area = 11(14 - 7)
Area = 11(7)
Area = 77 cm²[tex]\rule[225]{225}{2}[/tex]
Answer: (a) x=7
(b) area of this rectangle = 77[tex]cm^{2}[/tex]
Step-by-step explanation:
(a) the perimeter of a rectangle = 2 * [ l + b ]
36 = 2 * [ (x + 4) + (2x - 7) ]
36 / 2 = x + 4 + 2x - 7
18 = 3x -3
18 + 3 = 3x
21 = 3x
x = 7
(b) the area of a rectangle = l * b
l = x + 4 = 11cm
b = 2x -7 = 7cm
therefore, 11cm * 7cm = 77[tex]cm^{2}[/tex]
guys someone help me asap!!!! tell me all that apply for this!
Answers
The sequences that show that the two figures are similar, but not congruent, are:
Triangle MNO is translated 3 units to the right, and then dilated about the origin by a scale factor of 0.5, then translated 5 units down, and then reflected across the y-axis to obtain triangle M'NO'. Pentagon EFGHI is dilated about the origin by a scale factor of 2 to obtain pentagon E'F'G'H'I'. Triangle JKL is dilated about the origin by a scale factor of 3 to obtain triangle J'K'L.How to explain the sequenceThis sequence includes a dilation with a different scale factor for each figure and reflections, which preserve the shape of the figures but not their size or orientation.
In conclusion, the correct options are A and C
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Look at the key below the map that shows the color-scaled performance range. What is the range for 1 Year performance? How does it compare to the 1 Dat performance range? Why do you think this is the case?
1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%
1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%
Answers
The range of 1 year performance is more than 1 Day performance.
We have,
1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%
1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%
Now, the range of 1 year performance
= Highest - lowest
= 30 - (-30)
= 60
and, the range of 1 Day performance
= Highest - lowest
= 30 - (-3)
= 33
Thus, the range of 1 year performance is more than 1 Day performance.
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Find the minimum or maximum of the function y=x^2-9
Answers
I will be finding the minimum of this parabolic function.
The function y = x^2 - 9 is a parabola that opens upwards, since the coefficient of the x^2 term is positive. Therefore, the minimum value of the function occurs at the vertex of the parabola.
To find the x-coordinate of the vertex, we can use the formula -b/2a, where the quadratic function is in the form y = ax^2 + bx + c. In this case, a = 1 and b = 0, so the x-coordinate of the vertex is -b/2a = -0/(2*1) = 0.
To find the corresponding y-coordinate of the vertex, we can substitute x = 0 into the function, which gives y = 0^2 - 9 = -9.
Therefore, the minimum value of the function y = x^2 - 9 is -9, which occurs at x = 0.
~~~Harsha~~~
The minimum point of this function is located at (0, -9).
Step-by-step explanation:1. Determine whether it's a minimum or maximum.So from plain sight we can tell we're looking for a maximum point, because the coefficient of x² is positive, it's 1. If the function was y=-x²-9, we would be looking at a minimum point.
2. About the minimum...The vertex if the exact point where a quadratic or any pair exponent function will start to either decay or increase, therefore, it will be the minimum or maximum point.
Formula for "x" value of vertex: [tex]\sf x_{Vertex} =\dfrac{-b}{2a}[/tex].
In this equation, a and b are coefficients extracted when the formula is expressed on its standard form.
Standard form of a quadratic equation: ax² + bx + c = 0
➔ You need to substitute the "y" by a "0", and the formula should look like this:
[tex]\sf 0=x^2-9[/tex]
➔ Reorganizing...
[tex]\sf x^2-9=0[/tex]
3. Extracting the coefficients.Let's expand the previous expression:
[tex]\sf x^2+0x_{} -9=0[/tex]
The coefficients are:
a= 1, beacuse "x²" is being multiplied by 1, which is implicit.
b= 0, because "x" doesn't really exist on the simplified equation.
c= -9.
4. Calculate the "x" and "y" locations of the vertex.Now let's calculate the "x" position of the vertex using the formula from step 2:
[tex]\sf x_{Vertex} =\dfrac{-b}{2a}=\dfrac{-(0)}{2(1)}=0[/tex]
Now, the "y" value can be obtained just by substituting "x" by 0 on the argument of the function:
[tex]\sf y=(0)^2-9\\ \\y=-9[/tex]
Therefore, the vertex, or minimum point of this function is located at (0, -9).
Check out the attached image to verify this information with the graph.
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A rectangular room is 2 feet
longer than it is wide. Its area is 168 square feet. Set this up as a quadratic equation
Answers
Answer:
x = -14 and x = 12
Step-by-step explanation:
Let x be the width of the rectangular room in feet. Then, according to the problem, the length of the room is 2 feet longer than the width, or x + 2 feet.
The area of a rectangle is given by the formula A = length × width, so we have:
A = (x + 2) × x = x^2 + 2x
We are also given that the area of the room is 168 square feet, so we set A = 168 and get:
x^2 + 2x = 168
This is a quadratic equation in standard form, where 1x^2 + 2x - 168 = 0. We can solve this equation by factoring or using the quadratic formula. This will give us the value(s) of x, which represents the width of the room. Once we have the width, we can find the length by adding 2 feet to it.
And x is : -14 and 12
how does cot^2(x)-tan^2(x)=csc^2(x)-sec^2(x)
Answers
The proof of cot²(x) - tan²(x) = csc²(x) - sec²(x) is the help of trigonometry
identity and Pythagorean identity .
what is trigonometry identity ?A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are trigonometric functions such as sine, cosine, tangent, cotangent, secant, or cosecant.
The Pythagorean identity is a fundamental trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent, in terms of the unit circle or right triangle.
Proof of cot²(x) - tan²(x) = csc²(x) - sec²(x)The identity you provided, cot²(x) - tan²(x) = csc²(x) - sec²(x), is a trigonometric identity that can be derived from the Pythagorean identity and the reciprocal identities. Here's one way to prove it:
Start with the Pythagorean identity:
sin²(x) + cos²(x) = 1
Divide both sides by sin²(x):
1 + cos²(x)/sin²(x) = 1/sin²(x)
Recall that cot(x) = cos(x)/sin(x) and tan(x) = sin(x)/cos(x):
1 + cot²(x) = csc²(x)
Subtracting sec²(x) from both sides:
cot²(x) - tan²(x) = csc²(x) - sec²(x)
Therefore, cot²(x) - tan²(x) = csc²(x) - sec²(x) is a valid trigonometric identity.
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