When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
how can we describe logarithm ?A log is a mathematical function used to calculate how many times the base, or initial value, must be increased by itself to produce the target value. In other terms, a logarithm is an exponent's negative action.
The base-10 logarithm is the most widely used type of logarithm, though there are other types as well. Some many mathematical and scientific tasks include the usage of logarithms, such as estimating the pH of a solution, gauging the volume of sound, and estimating population growth rates.
given
As we are aware that log x of y = 2, x2 = y.
We also understand that xy = 27.
When we change y in the second equation to x2, we obtain:
[tex]xx^{2} =7^{2} \\x^{3} = 27\\[/tex]
x = 3
When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
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d = 8 1/2 in., r = underline ? , underline C =?
Given: D = 8 1/2 in.
We know that the diameter of a circle is twice the radius. Therefore, we can find the radius by dividing the diameter by 2:
radius (r) = D/2 = 8 1/2 / 2 = 4 1/4 in.
To find the circumference (C) of the circle, we can use the formula:
C = 2πr
where π (pi) is a constant approximately equal to 3.14.
Substituting the value of r, we get:
C = 2π(4 1/4) = 2π(17/4) = 8.5π
Therefore, the radius is 4 1/4 in. and the circumference is 8.5π in.
Every day, people face problems at home, work, school, or in their community that they must solve. Think about your life from the past 2 weeks, when something did not work out the way you intended, such as your car breaking down, you running out of milk, or facing a scheduling conflict. A lot of them need you to use math to help solve the problem.
Share at least 1 problem that you encountered recently, and answer the following questions in your main post:
What was the problem, and why it was difficult for you?
How did you use math in trying to solve the problem, and what was the outcome?
How would you approach in the problem differently next time?
personal experience based .
why we use mathematics in daily life ?maths gives us a way to understanding patterns ,define relationships , and predict the future.
One of my friends wanted to host a dinner party at her house, and she asked me to help her plan the menu. She told me that she was expecting around 10 guests, and she wanted to make sure that she had enough food for everyone. The difficult part was that she had a limited budget and wanted to keep the cost of ingredients low.
Mathematical approach:
To help my friend plan the menu, I used math to estimate the amount of food we needed to buy. I researched online to find the average portion sizes for the dishes we were planning to serve and calculated the total amount of ingredients needed based on the number of guests. Then, I compared the cost of the ingredients at different grocery stores to find the best deals and estimated the total cost of the meal.
Outcome:
By using math, we were able to plan a menu that was within my friend's budget and had enough food for all the guests. We were also able to find the best deals on ingredients, which helped us save money.
Approach for next time:
Next time, I would try to involve my friend more in the mathematical calculations to make sure she understands how to plan a meal within her budget. I would also consider making a list of alternative dishes that we could serve in case we were unable to find a certain ingredient or if it was too expensive.
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A basketball team won a game by 22 points and then beat the same team by 12 points in a re-match. The total score of the winning team across both games was 190 points. What was the total score of the team that lost?
what is the answer to this question?
dy/dx=?
[tex] \:\:\:\:\: \:\:\:\:\:\:\star\longrightarrow \sf y = x^{x}{}^{²}\\[/tex]
Taking the logarithm on both sides -
[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf log y = log x^{x}{}^{²}\\[/tex]
[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf log y = x^2 log x\\[/tex]
[tex]\:\:\: \boxed{\sf\pink{\:\:\: loga^b = blog a }}\\[/tex]
Differentiating with respect to x-
[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \dfrac{d}{dx} logy = \dfrac{d}{dx} x^2 log x \\[/tex]
[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf \dfrac{1}{y} \times \dfrac{dy}{dx} = x^2 \dfrac{d}{dx} log x + logx \dfrac{d}{dx} x^2\\[/tex]
[tex] \:\:\:\:\boxed{\sf\pink{\dfrac{d}{dx} logx = \dfrac{1}{x}}} \\[/tex]
[tex] \:\:\:\:\boxed{\sf\pink{\sf\dfrac{d}{dx}\bigg[f(x)\:g(x)\bigg] = f(x) \dfrac{d}{dx} g(x) + g(x) \dfrac{d}{dx} f(x)}}\\[/tex]
[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf \dfrac{d}{dx} = y \bigg[ x^2 \times \dfrac{1}{x} + logx \times 2x \bigg]\\[/tex]
[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \dfrac{dy}{dx} = y \bigg[ \cancel{x}\: x \times \dfrac{1}{\cancel{x}} + 2x\:logx \bigg]\\[/tex]
[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{\dfrac{dy}{dx} = y \bigg[ x + 2x\:logx \bigg]}\\[/tex]
[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{\dfrac{dy}{dx} = \boxed{\sf x^{x}{}^{²}\bigg[ x + 2x\:logx \bigg]}}\\[/tex]
3.9+3.4+4.5+3.1+3.9+4.1+3.6+3.9
Answer: 30.4
Step-by-step explanation:
Find the greatest common factor of 3, 15, and 35.
the gcf of 3, 15, and 35 is 1.
Answer: 1
Step-by-step explanation:
GCF means greatest common factor.
And the greatest common factor of 3, 15 and 35 would be 1 since
no other number is common between them.
3 * 1 = 3
15 * 1 = 15
35 * 1 =35
64. A polyhedron has 4 vertices and 4 faces. How
many edges does the polyhedron have?
(F) 4
(G) 5
(H) 6
(J) 8
(K) 16
Answer:
(H)
Step-by-step explanation:
Recall that [tex]V-E+F=2[/tex].
Setting [tex]V=F=4[/tex] yields [tex]E=6[\tex].
The ratio of A to B is 1 : 2 and B to C is 3 : 4. If C has the value of 32, what is the sum of the three numbers?
Answer:
A + B + C = 68
Step-by-step explanation:
A : B = 1 : 2
B : C = 3 : 4
Find the LCM of 2 and 3. LCM = 6
Multiply A : B by 3 and B : C by 2
[tex]\dfrac{A}{B}=\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}\\\\\\\dfrac{B}{C }=\dfrac{3}{4}=\dfrac{3*2}{4*2}=\dfrac{6}{8}[/tex]
A : B = 3 : 6 & B : C = 6 :8
A : B : C = 3 : 6 : 8
A = 3x
B = 6x
C = 8x
It is given that C is 32.
8x = 32
Divide both sides by 8
x = 32÷ 8
x = 4
A = 3*4 = 12
B = 6 * 4 = 24
Sum of three numbers = 12 + 24 + 32
= 68
-2/3w=12 solve for w
Select the correct answer from each drop-down menu.
Brian and Leo are flying to their grandmother's house on an airplane where 50 out of the 150 seats are window seats and passengers are randomly
assigned seats on the plane for each flight.
which is
the probability that Brian is assigned a window seat on the flight to his grandmother's house and the flight home from his
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is
grandmother's house.
The probabilities of Brian and leo being assigned a window seat on each flight are 1/9
what is the probability that Brian is assigned?The probability that Brian is assigned a window seat on the flight to his grandmother's house is:
50/150 = 1/3
The probability that LEO is assigned a window seat on the flight home from his grandmother's house is also:
50 window seats/ 150 seats = 1/3
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is:
50 window seats/150 seats * 49 window seats/ 149 seats = 1/9
Take note that Brian and Leo's chances of getting a window seat on each flight are independent, so we can simply multiply the odds to determine the likelihood of both happening.
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On a 6 question multiple-choice test, where each question has 5 answers, what would be the probability of getting at least one question wrong?
Answer:
[tex]\frac{24}{5}[/tex]
Step-by-step explanation:
We Know
The test has 6 questions.
Each question has 5 answers.
What would be the probability of getting at least one question wrong?
Each question can only have one correct answer, so the probability of getting a wrong answer for each question is [tex]\frac{4}{5}[/tex]
There are 6 questions on the test, so we take
[tex]\frac{4}{5}[/tex] x 6 = [tex]\frac{24}{5}[/tex]
So, the probability of getting at least one question wrong is [tex]\frac{24}{5}[/tex]
help ASAP
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
The experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].
The answer is "three over twenty."
What is probability?The frequency of K and 6 in the table are 8 and 7 respectively. Therefore, the total number of times a K or 6 was drawn is [tex]8 + 7 = 15[/tex].
The total number of draws was 100, so the probability of drawing a K or 6 on any one draw is:
Probability of K or 6 =[tex](Frequency of K + Frequency of 6) / Total number of draws[/tex]
[tex]= (8 + 7) / 100\\= 15 / 100\\= 3 / 20[/tex]
So the experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].
Therefore, the answer is "three over twenty."
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Which of the following is a balance for a single $1856 deposit in an account with an APR of 2.42% that compounds interest quarterly and is invested for six
Answer:
Using the formula for compound interest: A = P(1 + r/n)^(nt) where: A = the balance after the investment period P = the principal amount (the initial deposit) r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = the time the money is invested (in years) We can plug in the values given in the problem: P = $1856 r = 0.0242 (2.42% expressed as a decimal) n = 4 (quarterly compounding) t = 6/12 (6 months expressed as a fraction of a year) A = $1856(1 + 0.0242/4)^(4 * 6/12) A = $1856(1.00605)^2 A = $1931.
There are three possible cases (or scenarios) for how many solutions that an absolute value equation could have. How many solutions are there for each case? Why are their differences in the number of solutions? Give a mathematical example in your explanation.
PLS HELP ASAP
Consider the equation |x-4| = 5. This equation has two solutions since the distance of x from 4 on the number line can be 5 units in either direction, giving x = 9 or x = -1.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
An absolute value equation is of the form |x| = a, where "a" is a positive number. The absolute value of a number is always non-negative, so the equation |x| = a has two possible solutions, x = a and x = -a.
However, there are three possible cases for how many solutions an absolute value equation could have:
One solution: This occurs when a=0. The only solution is x=0 because |0|=0.
Two solutions: This occurs when a > 0. The two possible solutions are x = a and x = -a, since |a| = a and |-a| = a. For example, the equation |x-3| = 2 has two solutions: x-3 = 2 or x-3 = -2, which gives x = 5 or x = 1.
No solutions: This occurs when a < 0. Since the absolute value of a number is always non-negative, an absolute value equation with a negative number on the right-hand side has no solutions. For example, the equation |x-3| = -2 has no solutions since -2 is negative.
The difference in the number of solutions is due to the nature of absolute values. The absolute value of a number represents the distance of the number from zero on the number line, so an absolute value equation can have two solutions when the distance is equal to a positive number, one solution when the distance is equal to zero, and no solution when the distance is less than zero.
For example, consider the equation |x-4| = 5. This equation has two solutions since the distance of x from 4 on the number line can be 5 units in either direction, giving x = 9 or x = -1.
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Answer: Absolute value equations are important in situations where values cannot be negative, like measuring distance. For example, if you forget which floor your friend lives on and he tells you he's on the fourth floor, and you say you're two floors away, you could be on either the second or sixth floor. Absolute value inequalities are important in determining margins of error or tolerance, especially in manufacturing.
Step-by-step explanation:
When solving an absolute value equation, three possible scenarios could occur. The first scenario is when the absolute value expression equals a positive number. In this case, there will be two solutions, one positive and one negative. The second scenario is when the absolute value expression equals zero. In this case, there will be only one solution, which is zero. The third and final scenario is when the absolute value expression equals a negative number. In this case, there are no solutions, as the absolute value of any number is always non-negative.
The reason there are differences in the number of solutions for each case is due to the nature of absolute value. Absolute value always returns a non-negative value, regardless of the sign of the number inside the absolute value expression. Therefore, when the absolute value expression is positive, there are two possible solutions, one positive and one negative. When the expression equals zero, there is only one solution, which is zero. And when the expression is negative, there are no solutions, as there cannot be a negative absolute value.
Parallelogram DEFG is transformed to parallelogram VSTU.
Parallelogram D E F G is reflected diagonally to form parallelogram V S T U.
The True statement is parallelogram DEFG is the pre-image because it is not the result of the transformation.
What is Transformation?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
Parallelogram DEFG is transformed to parallelogram VSTU.
It changes from parallelogram DEFG to parallelogram VSTU.
According to how it is said, DFEG is the initial parallelogram or pre-image that is changed to create VSTU, VSTU is changed from DEFG.
The following is an accurate statement concerning the transformation:
As the parallelogram DEFG is not the outcome of the transformation, it is the pre-image.
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The correct Question attached here are as follow:
(Q). Parallelogram DEFG is transformed to parallelogram VSTU. Which statement about the transformation is true?
Parallelogram DEFG is the pre-image because it is not the result of the transformation.Parallelogram DEFG is the image because it is the result of the transformation.Parallelogram VSTU is the pre-image because it is the result of the transformation.Parallelogram VSTU is the image because it is not the result of the transformation.On a coordinate plane, trapezoid A B C D has points (negative 3, negative 2), (negative 1, 2), (3, 2), and (5, negative 2).
Figure ABCD is graphed on a coordinate plane.
ABCD is an isosceles trapezoid. What is the approximate perimeter of ABCD? Round to the nearest tenth.
16.5 units
18.9 units
20.9 units
24.0 units
16.5 I relllllllly hope this helps
If the prisms below are similar, what is the ratio of the height of the smaller prism to the height of the larger prism? V = 15 cm3 V = 405 cm3
The ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27).
what is prism?
A prism is a geometric solid that has two parallel and congruent polygonal bases, and the sides connecting the bases are parallelograms. These parallelograms are typically rectangles, but they can also be squares or rhombuses. A prism can be named based on the shape of its base, such as a rectangular prism, triangular prism, hexagonal prism, etc.
Since the prisms are similar, their corresponding sides are proportional. In particular, the ratio of the heights of the prisms is the same as the ratio of their volumes.
Let the height of the smaller prism be h1 and the height of the larger prism be h2. Let the volume of the smaller prism be V1 = 15 cm^3 and the volume of the larger prism be V2 = 405 cm^3. Then:
V1/V2 = (h1^2 * 5) / (h2^2 * 5)
V1/V2 = h1^2 / h2^2
sqrt(V1/V2) = h1 / h2
Substituting the given values, we get:
sqrt(15/405) = h1 / h2
sqrt(1/27) = h1 / h2
1/sqrt(27) = h1 / h2
Therefore, the ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27), or approximately 1:5.2.
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use the points (6,56) and (12,26) from the following data set to determine the point-slope form of an equation that represents the data set. x 5 6 7 8 10 11 12 12 14 y 58 56 53 46 37 33 26 23 13 answer
The point-slope form of the equation that represents the data set is y - 56 = -5(x - 6), or y = -5x + 86.
EquationsWe are given two points: (6,56) and (12,26) from the data set. We can use the point-slope form of a linear equation to find an equation that represents the data set.
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
To find the slope, we use the two given points:
m = (y2 - y1) / (x2 - x1)
m = (26 - 56) / (12 - 6)
m = -30 / 6
m = -5
Now that we have the slope, we can use one of the given points, say (6, 56), to write the point-slope equation:
y - y1 = m(x - x1)
y - 56 = -5(x - 6)
y - 56 = -5x + 30
y = -5x + 86
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What is the volume of the solid figure?
Answer:
[tex]625 \: {in}^{3} [/tex]
Step-by-step explanation:
This figure is formed from a cube and a rectangular prism
First, we can find the volume of the cube:
(l (side length) = 5 in)
[tex]v(cube) = {l}^{3 } = {5}^{3} = 125 \: {in}^{3} [/tex]
Now, let's find the volume of the rectangular prism:
(h = 5 in; a (base area) = 20 × 5 = 100 in^2)
[tex]v(prism) = a(base) \times h[/tex]
[tex]v(prism) = 100 \times 5 = 500 \: {in}^{3} [/tex]
In order to find the total volume of this figure, we have to add these two volumes together:
[tex]v(total) = v(cube) + v(prism)[/tex]
[tex]v(total) = 125 + 500 = 625 \: {in}^{3} [/tex]
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Neil is creating a computer game in which bubbles represented by circles collide, merge, and separate in different ways. A bubble with a radius of 8 centimeters separates into small bubbles, each of which has a radius of 2 centimeters. The area of the large bubble is equal to the sum of the areas of the small bubbles. How many small bubbles are there?
There will be 16 small circular bubbles.
What is circle?A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the centre.
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
The area of the large bubble is A = π(8cm)² = 64π cm².
The area of a small bubble is A = π(2cm)² = 4π cm².
Let's assume that the number of small bubbles is n. Then, the total area of the small bubbles is n times the area of a single small bubble:
n(4π) = 4nπ cm²
According to the problem, the area of the large bubble is equal to the sum of the areas of the small bubbles:
64π = 4nπ
Dividing both sides by 4π, we get:
n = 16
Therefore, there are 16 small bubbles.
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What happens to the surface area of a rectangular prism if you double one dimension? Let's create several examples and see if a pattern emerges.
Let's take a look at Karen's post.
My rectangular prism has sides of 8 units, 6 units, and 5 units. To find the total surface area of the prism, I have to find the area of each face of the prism. There are two faces that have an area of 8(5) = 40 units2, two that have an area of 6(5) = 30 units2, and two that have an area of 8(6) = 48 units2. Adding all the areas I get the surface area is 236 units2.
If the smallest side is doubled the dimensions would be 8 units, 6 units, and 10 units. There are two faces that have an area of 8(10) = 80 units2, two that have an area of 6(10) = 60 units2, and two that have an area of 8(6) = 48 units2. Adding all the areas I get the surface area is 376 units2.
The surface area increased by 140 units2 or a factor of about 1.6.
Now it's your turn.
Come up with a set of dimensions for a rectangular prism, and calculate its surface area.
Double one of the dimensions of your prism. List the new set of dimensions, and find the new surface area.
Describe how doubling one of the dimensions affects the surface area.
Look at your classmates' posts. Add a response to one of the posts stating any patterns you noticed in the calculations of all your classmates, and the effect of doubling on dimension on the surface area.
Use the discussion rubric to see how you will be graded.
Answer:
All you need to do now is plug the numbers in and use the right units.
Step-by-step explanation:
On December 4, 2016, Dan Johnson, delivery truck driver for Farmers Products Inc., ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other vehicle filed suit against Farmers Products for damages to the vehicle. Estimated damages to this vehicle were between $6,000 and $10,000 with no amount within the range more likely than any other amount. Farmers Products issued its 2016 financial statements on March 3, 2017.
Farmers Products Inc. should disclose a contingent liability in its 2016 financial statements for the lawsuit filed against them due to a collision caused by one of their delivery truck drivers.
Based on the information provided, it appears that as of the date of the financial statements (March 3, 2017), Farmers Products would need to disclose a contingent liability related to the lawsuit filed against them by the other driver.
A contingent liability is a potential liability that may arise from past events but the outcome is uncertain and will depend on future events. In this case, the lawsuit filed against Farmers Products by the other driver represents a potential liability that may result in damages being awarded against the company.
Under accounting standards, a contingent liability should be disclosed in the notes to the financial statements if it is probable that a liability has been incurred and the amount of the liability can be reasonably estimated. In this case, it is probable that Farmers Products may be liable for damages resulting from the accident and the estimated damages fall within a reasonable range of $6,000 to $10,000.
Therefore, in the notes to its 2016 financial statements, Farmers Products should disclose the existence of the lawsuit and the potential liability that may result. The disclosure should also include an estimate of the potential damages, if any, and any other relevant information about the lawsuit.
The question is incomplete; please see below for the whole question -
On December 4, 2016, Dan Johnson, a Farmers Products Inc. delivery truck driver, ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other car filed a lawsuit against Farmers Products for vehicle damages. Damage to this vehicle was estimated to be between $6,000 and $10,000, with no value within that range being more likely than any other. Farmers Products' 2016 financial statements were released on March 3, 2017.
1. Prepare the disclosures and/or journal entries that Farmers Products should include in its financial statements for the fiscal year ending December 31, 2016.2. How would the disclosures and/or journal entries alter if Farmers Products employed IFRS versus US GAAP?
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A sample of students is taken from the school's A honor roll. The school estimates that there are actually 360 students on the A honor roll. Using this sample from the table, how many students on the A honor roll are 8th graders?
280 8th graders
172 8th graders
114 8th graders
126 8th graders
The estimated number of students on the A honor roll who are 8th graders is 126.
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It involves using letters and other symbols to represent numbers and quantities in equations and formulas.
The main goal of algebra is to find the value of an unknown quantity, called a variable, by using known quantities and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can be solved using various techniques, including simplification, factoring, and solving equations.
The total number of students on the A honor roll is given by adding the number of students in each grade:
Total = 15 (6th grade) + 11 (7th grade) + 14 (8th grade) = 40
To find the proportion of students who are in 8th grade, we can divide the number of 8th graders by the total number of students:
Proportion of 8th graders = 14/40 = 0.35
To estimate the number of students on the A honor roll who are 8th graders, we can multiply the proportion of 8th graders by the total number of students on the A honor roll:
Estimated number of 8th graders = 0.35 x 360 = 126
Therefore, the estimated number of students on the A honor roll who are 8th graders is 126.
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
The axis of symmetry for f(x) is x = 1 and h(x) is x=3.
What is axis of symmetry?The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part. When folded along the axis of the symmetry, the two parts get superimposed. The straight line is called the line of symmetry/the mirror line. This line can be vertical, horizontal, or slanting.
Equation:Assuming that f(x) and h(x) are quadratic functions, here's how to find the axis of symmetry for each function:
f(x) = 2x² - 4x + 1
To find the axis of symmetry for f(x), we first identify the coefficients a, b, and c:
a = 2, b = -4, c = 1
Then, we use the formula:
x = -b / (2a) = -(-4) / (2 * 2) = 1
Therefore, the axis of symmetry for f(x) is x = 1. This means that the graph of f(x) is symmetric with respect to the vertical line x = 1.
h(x) = -x² + 6x - 5
To find the axis of symmetry for h(x), we first identify the coefficients a, b, and c:
a = -1, b = 6, c = -5
Then, we use the formula:
x = -b / (2a) = -6 / (2 * -1) = 3
Therefore, the axis of symmetry for h(x) is x = 3. This means that the graph of h(x) is symmetric with respect to the vertical line x = 3.
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The complete question would be:
Two functions are given below: f(x)=2x² - 4x + 1 and h(x)=-x² + 6x - 5. State the axis of symmetry for each function and explain how to find it.
How would you solve this?
Answer:
average rate of change = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the average rate of change of h(x) in the interval a ≤ x ≤ b , is
[tex]\frac{h(b)-h(a)}{b-a}[/tex]
here the interval is - 2 ≤ x ≤ 2 , then
h(b) = f(2) = [tex]\frac{1}{8}[/tex] (2)³ - 2² = [tex]\frac{1}{8}[/tex] (8) - 4 = 1 - 4 = - 3
h(a) = h(- 2) = [tex]\frac{1}{8}[/tex] (- 2)³ - (- 2)² = [tex]\frac{1}{8}[/tex] (- 8) - 4 = - 1 - 4 = - 5
then average rate of change
= [tex]\frac{-3-(-5)}{2-(-2)}[/tex]
= [tex]\frac{-3+5}{2+2}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
−2x + 1 ≥ 5. show work inequality
Answer:
x≥ -2
Step-by-step explanation:
−2x + 1 ≥ 5
-1 -1
-2x ≥ 4
x≥ -2
Make a new triangle
B
15
Ch
17
8
The Finale! All trig ratios for a right triangles
Complete the table below using what you know about
trigonometric ratios for right triangles.
LA
Write your ratios as fractions. A message will appear
when you are correct.
angle
LB
opp
adj
hyp
sin
COS
8
17
15
17
tan
15
8
15
8
Angle A is the right angle, so the trigonometric ratio we get is sin(LA) = 8/17, cos(LA) = 15/17, tan(LA) = 8/15, sin(LB) = 15/17, cos(LB) = 8/17, tan(LB) = 15/8
What is the trigonometric ratio?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios. (sec). A branch of mathematics called trigonometry in geometry works with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
The right triangle with sides that are 8, 15, and 17 in length needs to be labeled as follows in order to use trigonometry ratios.
B
/|
17/ |
/ |
/___|__
A C 15
where the right angle A is. The chart can then be filled out as follows:
angle opp adj hyp sin cos tan
LA 8 15 17 8/17 15/17 8/15
LB 15 8 17 15/17 8/17 15/8
The tangent is opposite/adjacent, the sine is adjacent/hypotenuse, and the cosine is opposite/hypotenuse.
The trigonometry ratios for the right triangle with sides that are 8, 15, and 17 in length are as follows.
sin(LA) = 8/17
cos(LA) = 15/17
tan(LA) = 8/15
sin(LB) = 15/17
cos(LB) = 8/17
tan(LB) = 15/8
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Which of the following statements is NOT true? (graph in the picture)
The slope of the line of best fit is 4,744.
The y-intercept of the line of best fit is 9,994.
The slope of the line of best fit means that the value of the house increased
$4,744 each year.
The y-intercept of the line of best fit means that it cost $9,994 to build the house.
The statement that is NOT true is: "The y-intercept of the line of best fit means that it cost $9,994 to build the house."
Hi! Based on the given information and without a visual of the graph, I will provide a general answer using the terms provided. Please note that an accurate response may require additional information or context.
The slope of the line of best fit indicates the rate of change in the value of the house over time, and a positive slope signifies that the value has increased. However, the y-intercept of the line of best fit does not necessarily mean that it cost $9,994 to build the house.
The y-intercept represents the estimated value of the house when the independent variable (usually time) is zero, but it does not account for factors like construction costs, inflation, or changes in the real estate market.
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Cubie Corporation has provided the following data concerning its only product: Selling price $ 87 per unit Current sales 13,000 units Break-even sales 11,700 units What is the margin of safety in dollars?
The margin of safety in dollars is $113100
The margin of safety is the value of sales or sales in units that are in excess of the break-even sales or units. The break-even point is where the firm is neither making a profit nor a loss and its total revenue is equal to its total expenses.
The margin of safety can be calculated by deducting the break-even sales value from the budgeted/actual sales value.
The margin of safety in dollars = budgeted/actual sales value - break-even sales value
Margin of safety in dollars = (87 * 13000) - (87 * 11700) = $113100
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0.85 divided by 3 2/5 divided by 3/4
Answer: 1/3
Step-by-step explanation: To do complex equations like this try using a calculator