By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle DEF.
Instructions to draw the routes:
Draw the x-axis and y-axis to create a coordinate plane.
Mark the starting point of Zari's run as (0,0) on the coordinate plane.
From (0,0), move 2 units north to reach (0,2).
From (0,2), move 4 units east to reach (4,2).
From (4,2), move directly back to the starting point (0,0) using the shortest route.
Mark the starting point of Taye's run as (0,0) on the coordinate plane.
From (0,0), move 2 units west to reach (-2,0).
From (-2,0), move 4 units south to reach (-2,-4).
From (-2,-4), move directly back to the starting point (0,0) using the shortest route.
Instructions to prove that the two triangles are congruent using ASA:
Label the vertices of Zari's triangle as A (0,0), B (4,2), and C (0,0).
Label the vertices of Taye's triangle as D (0,0), E (-2,-4), and F (0,0).
Show that angle A and angle D are congruent because they are both right angles (90 degrees).
Show that segment AB and segment DE are congruent because they both have a length of 4 units.
Show that segment AC and segment DF are congruent because they both have a length of 2 units.
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please help me quick! here is screenshot algebra
The function that is even is f(x) = 6x² - 8.
option C.
What is an even function?An even function is a function that satisfies the condition f(-x) = f(x) for all values of x in its domain. In other words, an even function is symmetric with respect to the y-axis.
The function that is even is calculated as follows;
f(x) = 5x² - x
f(-x) = 5(-x)² - (-x)
f(-x) = 5x² + x
f(x) ≠ f(-x)
f(x) = 3x³ + x
f(-x) = 3(-x)³ + (-x)
f(-x) = -3x³ - x
f(x) ≠ f(-x)
f(x) = 6x² - 8
f(-x) = 6(-x)² - 8
f(-x) = 6x² - 8
so f(x) = f(-x), this function is even.
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Each number in the first table represents the points scored by a player on the Ace Academy basketball team. Make a
frequency distribution, including relative frequency (percent of total: frequency)
total
1 5 8 10 10 13
369 10 11 13
379 10 12 14
4 7 10 10 12 14
For the relative frequencies below, round to the nearest tenth.
Score Frequency Relative Frequency
1
The most common point total scored was 10 with a frequency of 9 or 25% of the total frequency.
What is the frequency distribution of points scored?To create the score frequency distribution, we have to list the unique values in the data set and count how many times each value appears.
Element Frequency Relative frequency (percent)1 1 1/24 = 0.042 = 4.2%
3 2 2/24 = 0.083 = 8.3%
4 1 1/24 = 0.042 = 4.2%
5 1 1/24 = 0.042 = 4.2%
6 1 1/24 = 0.042 = 4.2%
7 2 2/24 = 0.083 = 8.3%
8 1 1/24 = 0.042 = 4.2%
9 2 2/24 = 0.083 = 8.3%
10 6 6/24 = 0.25 = 25%
11 1 1/24 = 0.042 = 4.2%
12 2 2/24 = 0.083 = 8.3%
13 2 2/24 = 0.083 = 8.3%
14 2 2/24 = 0.083 = 8.3 %
----------
24
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3 The circles in the model represent positive and negative units.
O O O
оо
Which equation is true based on the model?
A (-3) + 5 = -2
B (-3) + 5 = 2
C -3+ (-5) = -2
D 3+ (-5) = 2
KEY
= 1
=-1
The equation is true based on the model is B) (-3) + 5 = 2.
If we consider the circles on the left as negative units and the circles on the right as positive units.
Then we can see that there are 5 positive units and 3 negative units, so the sum is
= 5 - 3
= 2.
Therefore, the correct equation is: B) (-3) + 5 = 2.
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Find the slope of the line with a y-intercept = 4, passing through the point (2,8)
Answer:
8 = 2m + 4
2m = 4, so m = 2
So the equation of this line is y = 2x + 4.
D is the correct answer.
Ocarolyn and Abby
went camping and
caught a total of a fish.
How many fish
weighed 8 1/4 pounds
or less?
XX
XX
X X
x+
XX-
X
8 8
8
8 9
Weight of Fish in Pounds
1
The following table shows students’ test scores on the first two tests in an introductory calculus class.
Calculus Test Scores
First test, x 64
59
45
73
73
76
40
56
68
55
78
83
Second test, y 68
63
55
74
68
75
43
64
61
64
77
84
Step 2 of 2 : If a student scored a 69
on his first test, make a prediction for his score on the second test. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.
if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.
Students’ test scores on the first two tests in an introductory calculus class.
To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.
The regression equation for these data is
y = 0.6443x + 19.943
Where y is the predicted score on the second test and x is the actual score on the first test.
Substituting x = 69 into this equation, we get
y = 0.6443(69) + 19.943 ≈ 64.57
Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.
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Calculate, to the nearest cent, the Present Value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time.
3 years, at 1.3% per year, compounded weekly (52 times per year).
PV=?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1000\\ P=\textit{original amount deposited}\\ r=rate\to 1.3\%\to \frac{1.3}{100}\dotfill &0.013\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]1000 = P\left(1+\frac{0.013}{52}\right)^{52\cdot 3} \implies 1000=P(1.00025)^{156} \\\\\\ \cfrac{1000}{(1.00025)^{156}}=P\implies 961.76\approx P[/tex]
A framed picture has a total area y, in square inches. The thickness of the frame is
represented by x, in inches. The equation y = (8+2x)(10 + 2x) relates these two
variables.
1. What are the length and width of the picture without the frame?
2. What would a solution to the equation 100 = (8+2x)(10+2x) mean in this
situation?
The given total area including the frame is y = (8+2x)(10+2x).
As per the question the thickness of the frame is x.
The area of a rectangle is given by A=L*B
For a picture with frame it will be A=(L+2t)*(B+2t)
1. Comparing the above equation with the given equation it can be concluded that the Length is 10 and the width is 8.
2. The given equation is 100=(8+2x)(10+2x)
Upon solving it simplifies to [tex]x^2+9x-5=0[/tex]
x=0.525.
Thus the thickness x=0.525.
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A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time, walk toward each other, and meet in 5 hours. The turtle walks 10 meters per hour slower than the hedgehog. It the turtle had left home 4.5 hours earlier than the hedgehog, the two have me 150/ from the hedgehog's house. Find the distance between the garden and the woods.
If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.
How to find the distance?Let d represent the distance between the turtle's garden and the hedgehog's wood
Let h represent the speed of the hedgehog
Let the turtle's speed = h-10
Le the time it takes for the hedgehog to walk from the woods to the meeting point= t
Set up two equations
d = (h-10)(t+4.5) + ht (Equation 1)
d - 150 = ht (Equation 2)
Solve for d by substituting equation 2 into equation 1:
ht + (h-10)(t+4.5) = ht + 150
(h-10)t + 45h = 150
t = (150 - 45h) / (h-10)
Substitute t into equation 2:
d = ht + 150 - (h-10)(t+4.5)
d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)
d = 2250/(h-10) (distance between the garden and the woods)
Since the turtle and hedgehog meet in 5 hours
Thus,
d = ( h-10 ) (5) + h( 5- 4.5 )
d = 5h - 25
Substitute
5h - 25 = 2250/(h-10)
Multiplying both sides by h-10
5h² - 75h + 250 = 0
Dividing both sides by 5
h²- 15h + 50 = 0
Using the quadratic formula
h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)
h = (15 ± 5) / 2
So,
h = 10 or h = 5
Distance between the garden and the woods :
d = 2250/(h-10)
d= 2250/(5-10)
= 450 meters
Therefore the distance is 450m.
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Select the correct answer from each drop-down menu. f(x) = x2 − 8x + 15 g(x) = x − 3 h(x) = f(x) ÷ g(x) h(x) = . The domain of h(x) is U .
Answer:
f(x) = x²-8x+15
g(x) = x -3
h(x) = f(x) ÷ g(x)
= x²-8x+15 ÷ x-3
x-3√x²- 8x +15 | x-5
x² - 3x
-5x + 15
- 5x + 15
-----------
h(x) = x-5
Jamal is planning a conference. A local hotel rents a ballroom for $620 and charges $35 per guest for food.
Step 2 of 5: Determine the total charge if 138 guests attend the conference.
The total charge if 138 guests attend the conference is $5450
Determining the total charge if 138 guests attend the conference.From the question, we have the following parameters that can be used in our computation:
A local hotel rents a ballroom for $620 And charges $35 per guest for food.Using the above as a guide, we have the following:
Total = ballroom + food * number of guests
Substitute the known values in the above equation, so, we have the following representation
Total = 620 + 35 * 138
Evaluate
Total = 5450
Hence, the total charges is $5450
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what number is 8% larger than 230
Answer:
That number is 230 × 1.08 = 248.4.
To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.
How to solve for the numberTo find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.
Step 1: Calculate the 8% increase of 230:
8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4
Step 2: Add the 8% increase to 230:
230 + 18.4 = 248.4
Therefore, a number that is 8% larger than 230 is 248.4.
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There are two spinners. The first spinner has three same-sized sectors labeled 1, 2, and 3. The second spinner has four same-sized sectors labeled 3, 4, 5, and 6. The spinners are spun once. How many outcomes do not show an odd number on the first spinner and show a 3 on the second spinner?
Answer:
The first spinner has a 1/3 chance of not showing an odd number, and the second spinner has a 1/4 chance of showing a 3. The probability of both events happening is:
1/3 x 1/4 = 1/12
Therefore, there is a 1/12 chance of an outcome showing a 3 on the second spinner and not showing an odd number on the first spinner. Since there are a total of 3 x 4 = 12 possible outcomes, the number of outcomes that meet the criteria is:
12 x 1/12 = 1
So there is only one outcome that meets the criteria.
what is the range of the data set
Answer: 9
Step-by-step explanation:
Range = maximum number - minimum number (in a data set)
50-41 = 9 minutes
Imagine that two friends, Lola and Joni, each buy an iPod touch for $400, and pay with a credit card. When this happens, the credit card company pays Apple, and the friends become indebted to the credit card company. For every year they don't pay back the debt, the company charges them interest: a percentage of what they owe. The interest rate is called an annual percentage rate (APR), while the amount owed is called a balance.
Calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is calculated once per year.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%:
Joni 36%
In reality, credit card companies don't charge interest every year, they charge interest every month. To determine the monthly interest rate, divide the APR by 12.
Lola has an annual rate of 6%. So Lola has a monthly rate of
0.5%
Joni has an annual rate of 36%. So Joni B has a monthly rate of:
3%
Given that both Lola and Joni charge $400 initially calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is compounded monthly.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%
Joni 36%
Do you think it matters how often credit card companies charge interest? Explain.
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 10 years, how much would the $400 iPod end up costing in total (with monthly compounding)?
Lola's total cost (balance after 10 years): $
Joni's total cost (balance after 10 years): $
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
How to solveAmount = P = 340
Amy's interest rate = ra = 6% = 0.06
Mackenzie's interest rate = rm = 30% = 0.3
Amount is compounded yearly.
Amount at the end of the year is calulated as
Pn= P(1+r)
We will use Excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.40 382.02 404.95 482.30
Mackenzie 30% 340.00 442.00 574.60 746.98 1641.12
Amy has an annual rate of 6%. So Amy has a monthly rate of 6 /12 = 0.5% = 0.005
Mackenzie has an annual rate of 30%. So Mackenzie has a monthly rate of 30/12 = 2.5% = 0.025
Pn= P(1+r)
Here will be replaced by a number of months and r is relaced by monthly interest rate
We can modified this formula as
12n
Pn= P(1+)
Where n and r is same as in first part of question.
We will use excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.97 383.23 406.87 486.90
Mackenzie 30% 340.00 457.26 614.97 827.06 2011.86
From the above two tables, it is clear that it does matter how the company charges interest. When compounded monthly, the amount will more as compared to when compounded yearly. So,
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 12 years, we can add one more column to calculate for n = 12.
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
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How much would you need to deposit in an account now in order to have $2000 in the account in 15years? Assume the account earns 7% interest compounded monthly.
Answer:
To calculate the amount you would need to deposit in the account now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount you will have after 15 years, P is the principal amount (the amount you need to deposit now), r is the annual interest rate (7%), n is the number of times the interest is compounded per year (12 for monthly compounding), and t is the time in years (15).
Plugging in the values, we get:
2000 = P(1 + 0.07/12)^(12*15)
Simplifying the right side, we get:
2000 = P(1.00583)^180
Dividing both sides by (1.00583)^180, we get:
P = 2000 / (1.00583)^180
P = $775.80 (rounded to the nearest cent)
Therefore, to have $2000 in the account in 15 years with an annual interest rate of 7% compounded monthly, you would need to deposit $775.80 now.
An accountant drives 50 miles a day to work. Write an expression that represents the total number of miles he drives after x days
Answer:
It is 50x or 50*x or 50(x).
The Question is inside of the picture
Answer:
it is the opposite way around
Step-by-step explanation:
Is it an integer?
19/20 - yes or no
32/4 - yes or no
74 - yes or no
23 - yes or no
5.95 - yes or no
Answer:
19/20--no
32/4--yes (32/4 = 8)
74--yes
23--yes
5.95--no
Compare these distributions.
Both distributions of exam scores are and there are clear outlier(s) in each distribution of exam scores.
The center of the distribution of exam scores earned by students who completed homework is the center of the distribution of exam scores earned by students who did not complete homework.
The variability in scores of those who completed homework is that of the students who did not complete homework.
The comparison data is shown below.
Based on the information provided, we can infer that:
Both distributions have outliers.The center of the distribution of exam scores is the same for both groups, meaning that the average score of students who completed homework is the same as the average score of students who did not complete homework.The variability (spread) of exam scores of those who completed homework is the same as the variability of exam scores of those who did not complete homework.Without more information about the specific data and the context of the study, it is difficult to make further comparisons or draw any conclusions about the relationship between completing homework and exam scores. However, it is interesting to note that completing homework did not seem to have an impact on the average exam score or the variability of exam scores.
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Please help me with this
a)There is higher variability of Y with larger values of X.
b) There is non linear relation between X and Y.
a) Based on the given figure, we can make the following observations:
The scatterplot shows an upward trend, indicating a positive relationship between X and Y.The points appear to be spread out in a fan-like shape, suggesting increasing variability of Y with larger values of X. This means that as X increases, the values of Y become more spread out.The scatterplot does not provide clear information about the variability of X with larger values of Y.Therefore, the correct statement is There is higher variability of Y with larger values of X.
b) Based on the features, it is likely that a linear model may not be suitable for these data, and a non-linear model or other regression techniques may be more appropriate to capture the relationship between X and Y accurately.
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A company knows that 32% of their customers order their product in Black and 26% in White and 22% in Grey.
2 orders are made, Find the probability that at least 1 is Grey.
bacteria in a culture is given by function n(t)=920e^0.35t
A) The continuous rate of growth of this bacterium population = 0.35
B) The initial population of the culture = 920
C) The number of bacteria at time t=5 are 5294
Here, the function [tex]n(t)=920\times e^{(0.35\times t)}[/tex] represents the number of bacteria in a culture at time t
A) We know that in exponential function f(x) = [tex]ae^{kx}[/tex], k is the rate of growth
Here, in this function n(t) = [tex]920\times e^{(0.35\times t)}[/tex], the continuous rate of growth is 0.35
B) To find the initial population of the culture
Substitute t = 0, in n(t)
n(0) = [tex]920\times e^{(0.35 \times 0 )}[/tex]
n(0) = 920 × e⁰
n(0) = 920
This is the initial population.
C) Now we find the number of bacteria at time t=5
[tex]n(t)=920\times e^{(0.35\times t)}[/tex]
Substitute t = 5 in above equation.
n(5) =[tex]920 \times e^{(0.35 \times 5)}[/tex]
n(5) = 5294.23
n(5) ≈ 5294
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The number of bacteria in a culture is given by the function
n(t) =920e^0.35t Where t is measured in hours
A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent
B) what is the initial population of the culture (at t=0) your answer is __
C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria
-3x+6y-2z=5 7x+2y+9z=19 -x+y-z=0
Answer:
x = 7, y = 3, z = -4
Step-by-step explanation:
Help please!!!!
Whoever answers right gets brainliest!
Answer:
its 112.7
Step-by-step explanation:
x+2x=3x. 3x = 338
divide 3x and 338 by 3 three is cancelled and x equals to 112.7
[tex]\sf x=13.[/tex]
Step-by-step explanation:1. Formula for area.Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.
2. Form an equation.We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.
Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:
[tex]\sf (x)(2x)=338(in^{2} )[/tex]
3. Solve the equation.a) Solve the product.
[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]
b) Divide by "2" on both sides of the equation.
[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]
c) Take the square root of both sides.
[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]
4) Final answer.[tex]\sf x=13.[/tex]
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ACTIVITY 1: Solve the following rational equation.
The solutions to the rational equations are
(1) x = 14/3 (2) x = -2/3 (3) x = 4(4) x = 0 or x = 3(5) x = 0 or x = -2(6) x = 4/5(7) x = √(17/5)(8) x = 11/9(9) x = -1 or x = 2 (10) x = 1 or x = 2Solving the rational equationsThe rational equations can be solved as follows
(1)
(x - 2)/(2x + 4) = 1/5
This gives
5x - 10 = 2x + 4
So, we have
3x = 14
x = 14/3
(2)
For equation (2), we have
(x + 3)/2 - x/4 = 4/3
So, we have
[2(x + 3) - x]/4 = 4/3
[x + 6]/4 = 4/3
So, we have
3x + 18 = 16
x = -2/3
(3)
For equation (3), we have
3/(x + 1) - 2/(x - 1) = 1/(x² - 1)
So, we have
3(x - 1) - 2(x + 1) = 1
This gives
3x - 3 - 2x - 2 = 1
x = 4
(4)
For equation (4), we have
18/(x² - 3x) = 2x/(x - 3) - 6/x
So, we have
18 = 2x² - 6(x - 3)
This gives
x = 0 or x = 3
(5)
For equation (5), we have
3x/(x + 2) + 6/x + 4 = 12/(x² + 2x)
Multiiply through by x² + 2x
3x² + 6(x + 2) + 4(x² + 2x) = 12
Evaluate
x = 0 or x = -2
(6)
For equation (6), we have
1/(x - 2) + 4/(x + 9) = 3/(x² + 7x - 18)
Multiiply through by (x² + 7x - 18)
x - 9 + 4x + 8 = 3
So, we have
5x = 4
Evaluate
x = 4/5
(7)
For equation (7), we have
3/5x² - 1/5 = 2/25x²
Multiiply through by 25x²
15 - 5x² = 2
So, we have
5x² = 17
Evaluate
x = √(17/5)
(8)
For equation (8), we have
9/(x + 1) = 2/(x² - 1)
Multiiply through by 25x²
9x - 9 = 2
So, we have
9x = 11
Evaluate
x = 11/9
(9)
For equation (9), we have
3/(x³ - 8) = 1/(x - 2)
Cross multiiply
(x³ - 8) = 3(x - 2)
Evaluate
x = -1 and x = 2
(10)
For equation (10), we have
x²/2 - 3x/2 + 1 = 0
Multiiply through by 2
x² - 3x + 2 = 0
Factoize
(x - 1)(x - 2) = 0
So, we have
x = 1 and x = 2
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To the nearest megawatt, what is the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010?
The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
The data for this question can be found in the following table:
Year Electricity Generated (Megawatts)
2007 4,353
2008 7,113
2009 9,403
2010 10,089
To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.
Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts
Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
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pleaseeeeeeeeeeeeeeeeeeeeeeee
Answer:
congruent to each other cause their measurements are same.
congruent means if 2 shapes have same measurements they are called congruent
Given that f (x) = StartFraction 2 Over x squared EndFraction, What is the value of f(x) when x = 2? a. 2.5 c. 1 b. 2 d. 0.5
For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.
The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.
The given function is:
f(x) = 2 ÷ x²
We are asked to find the value of f(x) when x = 2.
Substituting x = 2, we get:
f(2) = 2 ÷ 2²
= 2 ÷ 4
= 1/2
= 0.5
Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:
f(x) = 2 ÷ x²
= 2 ÷ 4
= 1/2
Then, substituting x = 2, we get the same result:
f(2) = 1/2
f = 0.5
Hence, option (d) is correct.
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True or False
This is a Quadratic Equation y=5x+2
The equation is not a quadratic equation. Statement is false.
What is quadratic equation ?A second-order polynomial equation with just one variable, x, is referred to as a quadratic equation. with a ≠ 0 . The fundamental theorem of algebra guarantees that it has at least one solution since it is a second-order polynomial equation. The arrangement might be genuine or complex.
According to question:This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 5 and the y-intercept is 2. A quadratic equation is an equation in the form y = ax^2 + bx + c, where a, b, and c are constants and x is the variable.
Thus, given equation is not a quadratic equation. Statement is false.
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