In this context, the x-intercepts of the graph of the function d(t) = 1 - 8 |t - 40| represent the times at which you are exactly one mile from the water stop. These intercepts occur when d(t) = 0, which means that you are at the water stop. Solving the equation d(t) = 0, we find that the x-intercepts are t = 20 and t = 60.
The y-intercept of the graph represents the distance in miles that you are from the water stop at time t = 0. In this case, the y-intercept is d(0) = 1 - 8|0 - 40| = 1 - 8|-40| = 1 - 8(-40) = 1 + 320 = 321. This means that at time t = 0, you are 321 miles from the water stop.
In summary, the x-intercepts represent the times at which you are exactly one mile from the water stop, and the y-intercept represents the distance in miles that you are from the water stop at time t = 0.
The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.
To establish if a graph reflects a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line crosses it at more than one location.
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a risk matrix/heat map plots threats on a two-dimensional grid to assess qualitative risk. it has what two factors as its x and y axes?
The answer is that a risk matrix/heat map has two factors namely, likelihood and Potential Impact on its x-axis and y-axis respectively.
What is a Risk map ?
A risk heat map is a tool used to present the results of a risk assessment process visually and in a meaningful way. Risk assessment is a critical step in risk management. It involves evaluating the likelihood and potential impact of identified risks.
Risk maps are a way of representing the resulting qualitative and quantitative evaluations of the probability of risk occurrence and the impact on the organisation in the event that a particular risk is experienced.
Organisations generally map risks on a heat map using a ‘residual risk’ basis that considers the extent to which risks are reduced by risk response strategies.
So, a risk matrix/heat map plots threats on a two-dimensional grid to assess qualitative risk. it has two factors as its x and y axes , Likelihood and Potential Impact respectively.
Please find the attached image.
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Chloe has xx dimes and yy nickels. She has at least 15 coins worth a maximum of $1 combined. Solve this system of inequalities graphically and determine one possible solution.
The system of inequalities that describes this scenario is presented as follows:
x + y ≥ 15.0.1x + 0.05y ≤ 1.x ≥ 0.y ≥ 0.One possible solution is given as follows:
(2,15).
Meaning that she has 2 dimes and 15 nickels.
How to describe the system of inequalities?The variables for the system of inequalities are given as follows:
Variable x: amount of dimes that Chloe has.Variable y: amount of nickels that Chloe has.The amounts cannot be negative, hence:
x ≥ 0.y ≥ 0.She has at least 15 coins, hence the first constraint is given as follows:
x + y ≥ 15.
A dime is worth $0.1, while a nickel is worth $0.05. The coins are worth a maximum of $1, hence:
0.1x + 0.05y ≤ 1.
The solution set of the inequality is composed by the shaded region on the graph given at the end of the answer.
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Question 61 point)
Write an Equation for each scenario using Mx+b, (Do not use any spaces or any dollar signs)
1. A Plain Medium Pizza Costs $8.00. Additional toppings costs $0.85 each
The equation when the plain medium pizza costs $8.00 and additional toppings costs $0.85 each is 8 + 0.85x.
Hot to illustrate the equation?In Mathematics, an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, we want to write an equation for the Plain Medium Pizza Costs $8.00 and additional toppings costs $0.85 each using Mx+b.
Let additional toppings be given as x.
Based on the information, the equation will be;
= 8 + (0.85 × x)
= 8 + 0.85x
The equation is 8 + 0.85x.
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Katrin estimated that she sold 40 sandwiches at her food truck during lunch. Later, a count showed that she actually sold 44. Find Katrin's percent error to the nearest tenth.
Answer:
10%
Step-by-step explanation:
percent error: p
44 - 40 = 4
4/40 × 100 = p
p = 0.1 × 100
p = 10%
Percent error is 10%
A play company is having two shows. In the morning show, chairs are set up in rows of 11 chairs. For the afternoon show, the number of chairs in each row was 4 more than the original number of rows. Then, 8 more rows are set up. If r represents the original number of rows set up for the morning show, which of the following functions will give the total number of chairs set up for the afternoon show?
A.
C(r) = r2 + 19r + 88
B.
C(r) = 11r2 + 88r
C.
C(r) = 15r2 + 120
D.
C(r) = r2 + 12r + 32
Word puzzles that need two operations to solve them are known as two-step problems.
What are two-step and multi-step problems?A word problem is a short passage that describes a situation from "real life" in which a mathematical calculation is required to resolve a problem.Word or story problems are regarded as an essential component of learning in the primary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations. Because of this, math teachers make a point of including word problems in as many of their lessons as they can.Word puzzles also assist kids in becoming more familiar with the language and concepts of mathematics, such as the words reduced, altogether, difference, more, share, multiply, and more.Word problems that must be solved in two steps include the following:In addition to a 45p pencil, I also purchase an 83p magazine. I purchase the items I want using a voucher that saves me 20p. I spend how much.
Addition (83p + 45p = £1.28) would be the initial operation in this scenario.
(£1.28 - 20p = £1.08) is the second procedure.
The Complete Question is two-step problems.
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An ice cream shoppe makes $15 for every 4 milkshakes they sell. If they made $71.25 in one hour on milkshakes, how many did they sell ? 15/4 = 71.25/ X
Answer:
57.5 milkshakes
Step-by-step explanation:
To find the number of milkshakes the ice cream shoppe sold in one hour, you can use the given information to set up the following equation: 15/4 = 71.25/X. Solving for X, we get X = 71.25 * 4/15 = 57.5. Therefore, the ice cream shoppe sold 57.5 milkshakes in one hour.
19
Step-by-step explanation:
15/4= 3.75
71.25 / 3.75=19
write 26:30 as a fraction in simplest form
Answer: 13/15
Step-by-step explanation:
26/30
Simple by 2
13/15
Answer:
26/30 = 13/15
Sin 30° x tan 60° in simplest form
The simplest form of Sin 30° x tan 60° is √3/2 or sin 60° or cos 30°.
What are trigonometry ratios?
Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).
Given that the trigonometry function is
sin 30° x tan 60°
Putting sin 30° = 1/2 and tan 60° = √3
= (1/2) ×√3
= (1/2) ×(√3/1)
Now multiply the denominators and numerators:
= √3/2
Putting √3/2 = sin 60°
= sin 60°
Again sin 60° = cos 30°
= cos 30°
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A music store marks up the instruments it sells by 50%. If the mark up price on the trumpet was $120, what was the ORIGINAL PRICE of the instrument?
The original price of the instrument is $60.
Discount Price:
50% of 120 = 50/100 * 120
= 0.5 * 120
= 60
Original Price = Sale Price - Discount Price
= 120 - 60
= 60
Therefore, the original price of the instrument is $60.
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Find the circumference of a circle with an area of 676πsquare millimeters. Leave your answer in terms of pi,
Answer:
Below
Step-by-step explanation:
Area = pi r^2
r = sqrt ( area/pi) = sqrt( 676 ) = 26
Circumference = pi d = 2 pi r = 2 pi (26) = 163.4 mm
what does a z-score tell us about an individual observation in a data set? it is the number of standard deviations an observation is away from the mean. the midpoint of the sorted sample data set the sum of all data values divided by the number of data items. the average. the most frequently occurring data value in the set. none of the above
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.
The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.
Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.
Therefore,
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
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Given f(x)=3x+2f(x)=3x+2, find f(-4)f(−4)
Answer:
16f^2
Step-by-step explanation:
multiply f and f to get f^2
f^2(-4)(-4) multiply -4 and -4 to get 16
f^2 * 16 = 16f^2
HELP!!!
What is the sum of all interior angles of a 35-sided regular polygon?
6,120°
5,940°
180°
170°
Answer:
5,940
Step-by-step explanation:
The sum of the interior angles of a polygon is (n-2)*180 where n is the number of sides. In this case n=35. (35-2)*180 = 33*180 = 5940.
If the sales tax rate in Ohio is 5.5%, how much sales tax does the purchase of a $34
carrying case include?
O $1.87
O $35.88
$17.50
O $5.50
Answer:
The sales tax on a $34 carrying case would be $1.87.
Step-by-step explanation:
The sales tax on a $34 carrying case would be $1.87. To find this, first multiply the price of the carrying case by the sales tax rate to find the amount of tax: $34 * 5.5% = $1.87. The sales tax rate is expressed as a percentage, so you need to convert it to a decimal by dividing by 100: 5.5% / 100 = 0.055. Then multiply the price of the carrying case by this decimal to find the amount of tax: $34 * 0.055 = $1.87.
Find the inverse of the following function. f(x) 8√ x for x > 0
Answer: The inverse of a function is found by switching the positions of the input and output values in the function. For example, if the function is f(x) = 2x, the inverse would be f<sup>-1</sup>(x) = x/2.
In the case of the given function, f(x) = 8√ x, the inverse can be found by switching the positions of the input and output values. This gives us f<sup>-1</sup>(x) = √ x/8. This means that if x is the input value, the output value will be √ x/8. Note that the domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function. In this case, the domain of f<sup>-1</sup>(x) is [0, ∞) and the range is [0, ∞), since these are the range and domain of the original function.
Here is the complete inverse function:
f<sup>-1</sup>(x) = √ x/8 for x > 0.
A groundskeeper needs grass seed
to cover a circular field, 290 feet in diameter.
A store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square feet
of field.
What is the smallest number of bags the groundskeeper must buy to cover the circular field?
Explain or show your reasoning.
The smallest number of bags to cover the circular field is 3.0 pounds.
Area of a circle.
A circle is a shape that has a curved sides referred to as a circumference. Its area can be determined by;
Area of a circle = [tex]\pi r^{2}[/tex]
where r is the radius of the circle
So that,
the radius of the circular field = 290/ 2
= 145 feet
The area of the circular field = [tex]\pi r^{2}[/tex]
= 22/7 x (145)(145)
The area of the circular field = 66078.57 square feet.
Given a bag has a capacity of 50 pounds, and that one pound of grass seed covers about 400 square feet.
Then,
total pounds in a bag = 50 x 400
= 20000 pounds
the number of bags of grass seed needed = 66078.57 / 20000
= 3.304
The number of bags of grass seed needed = 3.30
Thus, the smallest number of bags the groundskeeper must buy to cover the circular field is 3.0 bags.
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Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as
an approximation for x.
• 154 square feet
• 42 square feet
• 419 square feet
•
105 square feet
The Required Area of Shaded Region is 42 sq. ft.
Whhat is Area?
The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
We are given that the length of side of square is 14 ft
so, we can determine thta the radius of the circle is 7 ft
To Calculate the Required Area we need to substract the area of circle from the area of square
Area of Square = Side*Side = 14*14 = 196 sq. ft.
Area of Circle = πr² = 22/7 * 7*7 = 154 sq. ft
Required Area of Shaded Region is 196 - 154 = 42 sq. ft.
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To find the population of a city next year, we multiply its current population by 1.046. By what percent does the population increase per year?
Using percentages we can conclude that by 1.02%, the population increase per year.
What is the Percentage?A relative number called a percentage is used to represent hundredths of any quantity.
Since one percent is denoted by the sign 1%, 100 percent means the full amount, while 200 percent means double the amount.
By multiplying by 100 and adding the "percentage sign"%, a ratio or fraction can be converted to a percentage.
So, we know that to calculate the population of the next year, we multiply by 1.046.
The formula that needs to be used:
% r = x₁-x₂/x₂
Assume that x1 represents the population in year 1. Due to the stated circumstance, a city's population will be x2 next year.
x₂= 1.046 x₁
Now, calculate as follows:
% r = x₁-1.046/1.046
% r = x₁-1.046x₁/1.046x₁
% r = 1.02%
Therefore, using percentages we can conclude that by 1.02%, the population increase per year.
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Solve the inequality, show all of your work: -5x + 2 > 37
Answer:
[tex]x < -7[/tex]
Step-by-step explanation:
First subtract 2 from both sides.
[tex]-5x+2-2 > 37-2[/tex]
[tex]-5x > 35[/tex]
Then divide both sides by -5.
[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]
For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.
What are inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.It is used most often to compare two numbers on the number line by their sizeGiven is the inequality as follows -
- 5x + 2 > 37
The given inequality is -
- 5x + 2 > 37
- 5x + 2 > 37
- 5x + 2 - 2 > 37 - 2
- 5x > 35
x < - 7
Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.
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Please help quickly 15 points and brainlyest if you get the questions right!
Answer:
1: B
2: A
3: D
4: A
5: A, B
Step-by-step explanation:
1: 6/5 is 1.2 2/10 is 1/5
2: 6/14= 3/7 or 6/14
3: 3/12 is 1/4 or 3/12
4: 28/13 is 2 2/13
5: 35/6 which is also 2 3/16
#/# means divide so 35/6 is 35 divided by 6
catelyn invested 7000 in an account that earns 5.6% interest compounded annaully
the furomula for compound interest is A(t)=p(1+i)t
Answer: 392
Step-by-step explanation:
7000 x 5.6%
Determine the intercepts of the line.
Do not round your answers.
y=6x+13y=6x+13
Answer: X= -2.1667 Y= 13
the amount of money you spend on coffees every month can be calculated as a function of the number of drinks you order every month. what are the independent and dependent variables in this function?
The independent and dependent variables in this function are order p Variable
Mathematically, discrete random variables are stated to be impartial if: P(X=x, Y=y) = P(X=x) P(Y=y), for all x,y. Intuitively, for impartial random variables understanding the price of one in every of them, does now no longer extrade the chances of the opposite. The impartial variable is the cause. Its price is impartial of different variables for your study.
The structured variable is the effect. Its price relies upon on adjustments withinside the impartial variable.An impartial variable is precisely what it sounds like. It is a variable that stands on my own and isn't always modified with the aid of using the opposite variables you are attempting to measure. For example, a persons age is probably an impartial variable.
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What is the slope intercept form of the linear equation 4x - 5y = 20
The solution is y = ( 4/5 )x - 4
The slope intercept form of the equation is y = ( 4/5 )x - 4 where the slope of the line is 4/5 and the y intercept is -4
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is given as
4x - 5y = 20 be equation (1)
On simplifying the equation , we get
Adding 5y on both sides of the equation , we get
5y + 20 = 4x
Subtracting 20 on both sides of the equation , we get
5y = 4x - 20
Divide by 5 on both sides of the equation , we get
y = ( 4/5 ) x - 4
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Therefore , the value of A is y = ( 4/5 ) x - 4
Hence , The slope intercept form of the equation is y = ( 4/5 )x - 4
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At the neighborhood grocery, 44 pounds of steak cost \$45.80$45.80. How much would it cost to buy 2.62.6 pounds of steak?
The value of the 2.6 pounds of steak cost $27.06 in the neighborhood grocery.
Explain the ratio of the numbers?An item set of numbers both a b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls .For the given question;
44 pounds of steak cost $45.80.
Let 'x' be the amount for the 2.6 pounds of steak.
Then, ratio of the quantity becomes,
44/45.80 = 26/x
On simplification,
x = (26 x 45.80)/44
x = $27.06
Thus, the value of the 2.6 pounds of steak cost $27.06 in the neighborhood grocery.
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The correct question is-
At the neighborhood grocery, 44 pounds of steak cost $45.80. How much would it cost to buy 2.6 pounds of steak?
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter. How much money did Trevor's family spend, in total, on shower water in the past month?
The money Trevor's family spend, in total, on shower water in the past month is $14.4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms.
In the past month, each person showered for an average of 480 minutes
an average 72 liters of shower water (over the entire month)
The cost of water per litre is 0.20 dollars.
We need to find the money Trevor's family spend, in total, on shower water in the past month
Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter
= 72 / 480 × 0.20
= 0.15 × 0.20
= $0.03.
Now 0.03×480=14.4.
Hence, 14.4 is the money Trevor's family spend, in total, on shower water in the past month.
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In 2008, Yolanda paid $3,875 in Social Security tax. If the Social Security tax rate was 6.2% to the maximum income of $94,200 that year, what was Yolanda's taxable income
The Yolanda's taxable income is $62,500.
What is income tax?
An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.
Given:
In 2008, Yolanda paid $3,875 in Social Security tax.
The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.
Lets assume Yolanda´s income be `x`.
Now, calculating the taxable income of Yolanda
6.2% x (x) = 3875
[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]
Hence, the Yolanda's taxable income is $62,500.
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rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?
a. 2w^2+5W,where w is the width
b. 2w^2+5,where w is the width
c. 2w^2,where w is the width
d. 10w^2,where w is the width
The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width. The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width
How to calculate Area of rectangle?The area of the rectangle is the floor space the rectangle can occupy at a given time.
The given parameters are
L= 2w+5
The width = w
Then area is given by the formula
A=L*W
A=2w*w+5
Simplify the expression you have
A=2w²+5 where w is the width
Therefore the area is b. 2w²+5, where w is the width
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C. Investigate the patterns of the coordinates of image and preimage when points are rotated 270°
Counterclockwise
Our point A(x, y) becomes Something' when a point is rotated 270 degrees counterclockwise around the origin (y,-x). This implies that we reverse x and y and turn x negative.
What do math coordinates mean?A pair of numbers that provide the position of a point on such a coordinate plane using the horizontal as well as separations first from two reference axes. usually represented by a pair of x-values and y-values (x,y).
How do you solve difficulties using coordinates?To find a point's coordinates in some kind of a co - ordinate system, you perform the opposite. Starting at the point, travel vertically up or down until your reach the x-axis. There seems to be your x-coordinate shown. Continue the previous procedure while staying on a horizontal line to obtain the y-coordinate.
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Which statement can you conclude is true from
the given information?
Given: AB is the perpendicular bisector of IK.
( please help me , answers my questions )
As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?
A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?
A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G) i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f) i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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