graph and label each figure and its image under the translation along the given vector. identify the coordinates of the image.
The transformations are
Transformation 1: The image of the transformation are P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)Transformation 2: The image of the transformation are E'(1, -4), F'(6, 0) and G'(7, -4)How to perform the transformationTransformation 1
Here, we have
The coordinates are given as
P(-5, 4), Q(2, 8), R(6, 1) and S(-1, -3)
The transformation is given as
<2, -4>
This is represented as
(x, y) ⇒ (x + 2, y - 4)
This means that the translation is (x + 2, y - 4)
When this rule is applied on the coordinates, we have
P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
Transformation 2
Here, we have
The coordinates are given as
E(-7, -7), F(-2, -3), G(-1, -6)
The transformation is given as
<8, 3>
This is represented as
(x, y) ⇒ (x + 8, y + 3)
This means that the translation is (x + 8, y + 3)
When this rule is applied on the coordinates, we have
E'(1, -4), F'(6, 0) and G'(7, -4)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
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If f(x)=√x-3, which inequality can be used to find the domain of f(x)?
square root of x - 3 over or equal to zero, x minus three over or equal to zero, square root of x-3 under or equal to zero; x-3 under or equal to 0
The inequality that can be used to find the domain of f(x) is x - 3 ≥ 0.
The correct answer is the second one i.e.x minus three over or equal to zero.
What is the Domain of a Square Root Function?Fundamentally, the square root function has the form f(x) = √x. In other words, f(x) = √x is the parent square root function.A negative number's square root is not a real number. Therefore, negative values cannot be put into the square root function.That is, the set of all real numbers that are not negative constitutes the domain of the square root function, f(x) = √x.Consequently, [0,∞ ) is the square root function domain. It should be noted that the domain also contains 0.Given:
Function f(x) = √x-3
The fact that a negative number cannot be used as the term in the root square, so
x - 3 ≥ 0 which implies that, x ≥ 3.
From the inequality, we can tell that the domain of the function is the interval [3,∞).
Hence the inequality is x - 3 ≥ 0.
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help me
1 Answer:
Evaluate the following expression when q = 13.
q-10
2 Answer:
Evaluate the following expression when x = 4.2.
34.5x
3 Answer:
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
1) When q = 13, the expression q - 10 is; 3
2) When x = 4.2, the expression 34.5x is; 144.9
3) The simple interest you would earn in 2.5 years is; $5.25
How to solve Algebra Word problems?1) We want to evaluate the following expression;
q - 10 when q = 13.
Thu, we will plug in 13 for q to get;
13 - 10 = 3
2) We want to evaluate the following expression;
34.5x when x = 4.2
Plug in 4.2 for x to get;
34.5 * 4.2 = 144.9
3) The formula for simple interest is;
I = PRT/100
Where;
P is principal
R is rate
T is time
We are given;
P = $70
R = 3% = 0.03
Time; T = 2.5 years
Thus;
I = 70 * 0.03 * 2.5
I = $5.25
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devin prepares for a multi day hike by packing his backpack with food,water,bedding, and emergency supplies. the tracks how many pounds of each he's carrying and find the ratio of their respective weights 2:3:1:4 f the total weight of his supplies is 35 pounds how many pounds of water is devin carrying
The amount in pounds of water that's been carried by Devin as described by the ratio given in the task content is; 10.5 pounds.
How many pounds of water is Devin carrying as described in the task content?It follows from the task content that the amount of water Devin is carrying is to be determined.
On this note, since the backpack contains food, water, bedding, and emergency supplies are in the ratio; 2 : 3 : 1 : 4.
It therefore follows from proportion that the ratio representation of total of all supplies is; (2 + 3 + 1 + 4) = 10.
Therefore, since the total weight is; 35 pounds, it follows that the amount of water Devin is carrying can be of help as follows;
w/35 = 3/10.
w = (3 × 35)/10
w = 105/10
w = 10.5 pounds.
Ultimately, the total weight of water Devin is carrying is therefore; 10.5 pounds.
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13. A journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting. He tests a random group of 35 of these components and finds a mean lifespan of 4.05 years. a. What is the mean of the sampling distribution of sample means when 35 random components are tested?
The mean of the sampling distribution of sample means when 35 random components are tested will be 4.05 years.
How to illustrate the information?From the information, it should be noted that the journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.
He then tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.
Therefore from the information, we acne see that the mean lifespan has already been given.
Therefore, the mean lifespan is 4.05 years.
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Florence wishes to retire at age 65 with $1,200,000 in her retirement account. When she turns 22, she decides to begin depositing money into an account with an APR of 7% compounded monthly. What is the monthly deposit that Florence must make in order to reach her goal? Round your answer to the nearest cent, if necessary.
The monthly deposit that Florence must make in order to reach her goal is $366.74.
What should be the monthly deposit?The series of payments that must be made is known as an annuity. An annuity is a series of payment made over a period of time. The amount that is invested monthly would grow at an exponential rate. This is because both the amount invested and the interest that has been accrued grows at each compounding period.
The formula to determine the monthly deposit is:
Monthly deposit = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 7 / 12 = 0.583%n = number of periods = number of years x number of compounding periods(65 - 22) x 12
43 x 12 = 516
1,200,000 ÷ [((1.00583)^516]}- 1 / 0.00583] = $366.74
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At the clothing store where you work, T-shirts are on sale, 3 for $10. A customer at the store says that one T-shirt should cost $7 at this rate. What error did the customer make?
The customer divided 10 by 3 instead of dividing 3 by 10.
The customer divided 3 by 10 instead of dividing 10 by 3.
The customer subtracted 3 from 10 instead of dividing 10 by 3.
The customer added 10 and 3 instead of dividing 3 by 10.
The customer subtracted 3 from 10 instead of dividing 3 by 10.
The error that the customer made was that he subtracted 3 from 10 instead of dividing 3 by 10.
It is given in the question that at the clothing store T-shirts are on sale, 3 for $10. A customer at the store says that one T-shirt should cost $7 at this rate.
We have to find the error made by the customer while calculating the rate of a T- shirt.
To find the rate of a shirt we will divide the number of shirts by the total amount.
Hence, the rate of a shirt will be $ 10/3
But the customer subtracted 3 from 10 to get $ 7 as the rate of a T-shirt.
Hence, the customer subtracted 3 from 10 instead of dividing 3 by 10.
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Equation IQ include many puzzles to advance in the game. 1 puzzle involves a pair of similar triangles. Players must use the clues to find missing side lengths, two triangles are given.
Since the two triangles in the given are similar triangles, we now know that they both have the same angle, but scaled, meaning they have different side lengths.
Base on the given, XA = 15, while XZ = 27
We can now assume that if XA : XZ, BA : YZ
We can rewite this as:
[tex]\frac{XA}{XZ}=\frac{BA}{YZ}[/tex]Now, plugging in the values of XA, XZ, and BA, we can now solve for YZ.
[tex]\frac{XA}{XZ}=\frac{BA}{YZ}[/tex][tex]\frac{15}{27}=\frac{20}{YZ}[/tex][tex]15YZ=20(27)[/tex][tex]YZ=\frac{20(27)}{15}[/tex][tex]YZ=36[/tex]We now see that the length of YZ is 36 inches.
Next, to solve for XY, we will use the same method, but this time we will be using XB instead of BA.
[tex]\frac{XA}{XZ}=\frac{XB}{XY}[/tex][tex]\frac{15}{27}=\frac{10}{XY}[/tex][tex]15XY=10(27)[/tex][tex]XY=\frac{10(27)}{15}[/tex][tex]XY=18[/tex]Therefore, XY is 18 inches long.
In the diagram the smaller triangle is an image of the larger triangle. a) Name the angle in the image that corresponds to ZT in the preimage. b) List all pairs of corresponding sides.
this is transformations or enlagement of triangle by a certain scale factor.
which simply means it can either be double, or shortened .
solution
a. angle T is the preimange of angle T'
b. line RS and RS'
c. line RT and RT'
line ST and ST'
extra note: this is ∆RST filled over but shortened by x factors to mirror image ∆RST
Can you solve this for me please.
Classify the following
sequence:
1, 4, 9, 16, 25, ...
A. neither
B. geometric
C. arithmetic
FOR ARITHMETIC
[tex]lhs = 9 - 4 \\ lhs = 5 \\ rhs = 4 - 1 \\ rhs= 3 \\ \\ lhs \: not = rhs[/tex]
SINCE THERE IS NO COMMON DIFFERENCE LET US TEST FOR A GEOMETRIC SEQUENCE.
[tex]lhs = \frac{9}{4} \\ \\ rhs = \frac{4}{1} \\ rhs = 4 \\ \\ lhs \: not = rhs[/tex]
THERE IS NO COMMON DIFFERENCE NOR A COMMON RATION THIS MEANS THAT THE SEQUENCE IS NEITHER AN ARITHMETIC NOR A GEOMETRIC SEQUENCE.
THE OPTION IS A.NEITHER.
Can you please explain this to me?
The amplitude is determined as the distance from the midline of the cosine function.
From the graph provided, the depth is shown as 3 units (between 5 units and 2 units) which puts the midline at 3.5 units. The amplitude therefore is 1.5
Simply the expression
3x 3/648x4y8
Answer:
8%3-29xy
Step-by-step explanation:
thats the answer
In the triangle below , XZ=YZ, find the measure of< YZX
ANSWER:
80°
STEP-BY-STEP EXPLANATION:
Since the sides XZ and YZ are equal, the angle We know that the sum of all the angles is equal to 180 °, therefore:
[tex]\begin{gathered} 180=50+50+\text{YZX} \\ \text{YZX}=180-50-50 \\ \text{YZX = }80\text{\degree} \end{gathered}[/tex]if all tree friends worked 20 hours during the week, how much ith each person earn
The amount of money earned by each person will be;
Savannah = $190
Greg = $180
Kevin = $165
How to calculate the amount?From the information, the following can be deduced:
Savannah works $9.50 per hour.
Greg works $9 per hour.
Kevin works $8.25 per hour
Therefore, they all work for 20 hours. The amount for each person will be:
Savannah works $9.50 per hour. = $9.50 × 20 = $190
Greg works $9 per hour. = $9 × 20 = $180
Kevin works $8.25 per hour = $8.25 × 20 = $165
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Savannah works $9.50 per hour.
Greg works $9 per hour.
Kevin works $8.25 per hour
If all tree friends worked 20 hours during the week, how much does each person earn?
Hello I need help for my study guide :(
A rough sketch of the rectangular plot is
The perimeter of the rectangle is given by the formula:
[tex]P=2l+2w[/tex]Where,
and,
i
The perimeter is 320, so we can write:
[tex]\begin{gathered} P=2l+2w \\ 2l+2w=320 \\ 2(l+w)=320 \\ l+w=160 \end{gathered}[/tex]Total fencing cost $3120 and this is 1 length side and 2 width side.
The fencing on length side is $24 per foot and width side is $4 per foot.
e can write an equation:
[tex]\begin{gathered} 24l+2(4w)=3120 \\ 24l+8w=3120 \end{gathered}[/tex]Now, we have to solve the 2 simultaneous equations,
[tex]\begin{gathered} l+w=160 \\ 24l+8w=3120 \end{gathered}[/tex]Let's solve with elimination >>>>
[tex]\begin{gathered} l+w=160 \\ 24l+8w=3120 \\ ----------- \\ -8\times(l+w=160) \\ 24l+8w=3120 \\ ------------ \\ -8l-8w=-1280 \\ 24l+8w=3120 \\ _{\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}} \\ 16l=1840 \\ l=\frac{1840}{16} \\ l=115 \end{gathered}[/tex]We can substitute this value of "l" into the first equation and solve for "w". This is shown below:
[tex]\begin{gathered} l+w=160 \\ 115+w=160 \\ w=160-115 \\ w=45 \end{gathered}[/tex]Thus,
AnswerThe Longer Dimension is 115 feetThe Shorter Dimension is 45 feetMarcel and his 8 friends have a snow shoveling business. Last season, they earned a total of $2,240.64. How much
money did each friend make?
$280.08
B$17,925.12
$248.96
D) $20,165.76
int(s)
HIDE HINT
1/1
| How many people were there all together?
There are 18 boys and 46 girls in class. 87.5% of the students in the class take the
bus to school. How many students do not take the bus to school?
Reason:
87.5% of the students take the bus to school
100% - 87.5% = 12.5% of the students do not take the bus to school
The info about the "18 boys and 46 girls" is put there as a distraction since it's never used.
Using point P, which point would form a line parallel to line AB?
(-6,4)
(3,2)
(1,1)
(-2,3)
Answer:
(3,2)
Step-by-step explanation:
The equation of the line graphed is
y = 2/3x + 2
Parallel lines have the same slope.
y = mx + b
y = 2/3x + 0 P tells me that the y-intercept is 0
y = 2/3 x Which point would make this true?
Point (3,2) We plug in 3 for x and 2 for y
2 = 2/3(3)
2 = 2 This is a true statement, so the point (3,2) is on the line.
PLEASE HELP ME 1. A different pool had an area that is of the form
▢ × 102 + ▢ × 101 + 6
and that can be written in the form x3 ,
where x is a whole number.
A) Decide what your number could be.
B) What is the perfect square number that is closest to the number you chose? What would the side length of a square pool with that area be?
C) Estimate the side length of a square pool with the area you chose in part a).
The solutions to the questions are
The number we are using is 5The perfect square number closest to the area is 1024The estimated side length is 32What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
The number to useThe area expression is given as
Area = ▢ × 102 + ▢ × 101 + 6
From the question, we can use any number
However, this number must be positive
Assume the number is 5
So, we have
Area = 5 × 102 + 5 × 101 + 6
The perfect square number closest to the resultIn (a), we have:
Area = 5 × 102 + 5 × 101 + 6
Evaluate
Area = 1021
The perfect square number closest to this is
Closest = 1024
The estimated side lengthIn (b), we have
Closest = 1024
Rewrite as
Area = 1024
Take the square roots
Length = 32
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Which of the m-values satisfy the following inequality? 5m + 1 <_ 4Choose all answers that apply: A.) m = 0B.) m = 1C.) m = 2
We want to know which values of m satisfy ≤
5m + 1 4
Substracting 1 both sides:
-1 - 1
+03
5m ≤ 3
Dividing by 5 both sides
/5/5
m ≤ 3/5
m ≤ 0.6
Since 1 and 2 are higher than 0.6 and 0 ≤ 0.6
Then if m=0 it is satisfied
Answer: AHelp please thank you
If $44,900 is invested at an interest rate of 7% per year,investment at the end of 5 years is
1)Annual =61712.27
2)Semiannual=62066.34
3)monthly= 62375.51
4)daily = 62287.59
What is compound interest ?Over a specific time period, compound interest builds up on both the principal and interest. A principal is also included when accounting for interest that has accrued on it over time. The cumulative principal value is used to calculate interest for the upcoming period as well.
Given that : If $44,900 is invested at an interest rate of 7% per year .
p =44,000
R = 7%
t =5
(2)Semiannual means compounding is in a year done means two times hence, n = 2
We know
A(t) =p[tex][1 +\frac{r}{n} ]^{nt}[/tex]
A(5) = 44000[tex][1+\frac{0.07}{2} ]^{2(5)}[/tex]
A(5)=62066.34
(1) Annual means. compounding is done 1 time for a year
So, n = 1
A (5) = 44000[tex][1 + 0.07]^{(5)}\\[/tex]
A(5)= 61712.27
(3)Monthly means compounding is done 12 times in a year.
So, n = 12
= 44000[tex][1 + \frac{0.07}{12} ]^{60}\\[/tex]
= 62375.51
(4)For daily put n = 365
A(5) = 44000[tex][1 + \frac{0.07}{5} ]^{5(5)}\\[/tex]
= 44000[tex][1 + \frac{0.07}{5} ]^{25}\\[/tex]
=62287.59
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Hi hi job hi thank everyone for
We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:
We can use the function tangent since this is defined as:
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex]Now, we plug in the values:
[tex]\tan\theta=\frac{3000}{x}[/tex]Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:
[tex]\tan\theta=\frac{3000}{2000}[/tex]Now, we take the inverse function of the tangent:
[tex]\theta=\tan^{-1}(\frac{3000}{2000})[/tex]Solving the operations we get:
[tex]\theta=56.31°[/tex]Therefore, the angle is 56.31 degrees or 0.983 radians.
We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:
[tex]\frac{dx}{dt}=-200\frac{ft}{s}[/tex]Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:
[tex]\frac{d}{dt}(\tan\theta)=\frac{d}{dt}(\frac{3000}{x})[/tex]For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:
[tex]\sec^2(\theta)\frac{d\theta}{dt}=\frac{d}{dt}(\frac{3000}{x})[/tex]Now, we determine the derivative on the right side using the following formula:
[tex]\frac{d}{dx}(\frac{a}{x})=-\frac{a}{x^2}[/tex]Applying the rule we get:
[tex]\sec^2\theta\frac{d\theta}{dt}=-\frac{3000}{x^2}\frac{dx}{dt}[/tex]Now, we solve for the derivative of the angle with respect to time:
[tex]\frac{d\theta}{dt}=-\frac{1}{\sec^2\theta}(\frac{3000}{x^2})\frac{dx}{dt}[/tex]Now, we substitute the values:
[tex]\frac{d\theta}{dt}=-\frac{1}{\sec^2(0.983)}(\frac{3000ft}{(2000ft)^2})(-200\frac{ft}{s})[/tex]Solving the operations:
[tex]\frac{d\theta}{dt}=0.047\frac{rad}{s}[/tex]Therefore, the variation of the angle with respect to time is 0.047 rad/s.
This means that the dish is rotating at a speed of 0.047 rad/s.
Answer: We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:We can use the function tangent since this is defined as:Now, we plug in the values:Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:Now, we take the inverse function of the tangent:Solving the operations we get:Therefore, the angle is 56.31 degrees or 0.983 radians. We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:Now, we determine the derivative on the right side using the following formula:Applying the rule we get:Now, we solve for the derivative of the angle with respect to time:Now, we substitute the values:Solving the operations:Therefore, the variation of the angle with respect to time is 0.047 rad/s.This means that the dish is rotating at a speed of 0.047 rad/s.
Step-by-step explanation:
Tell whether each number is a real number, a rational number, an irrational number, an integer or a whole number. Then order the numbers from these to greatest
26. -11.5, -11, -10, 12.5, 12
The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
What are whole number?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold math Z.
What are real numbers?The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.
Given numbers are -11.5, -11, -10, 12.5, 12
The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
Real numbers: -11.5, -11, -10, 12, 12.5.
Rational numbers: -115/10, 125/10
Integer numbers: -11.5, -11, -10, 12, 12.5.
Whole numbers: 12, 12.5, 26
Therefore, the order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
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A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total
possible outcomes are there when choosing a marble from the bag?
Answer: 14
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What is the simplified base of the function f(x) = (108)*?
3
33/4
633
27
Answer:33/4
Step-by-step explanation: its hard to explain but thats the correct answer 33/4 decimal form is 8.25 and mixed number is 8 1/4
Graph the function h(x) =-3x-1
we have the function
h(x)=-3x-1
this is the equation of a line
To graph a line we need at least two points
so
Find out the intercepts
step 1
Find out the x-intercept (value of x when the value of y=0)
For h(x)=0
substitute
0=-3x-1
3x=-1
x=-1/3
the x-intercept is (-1/3,0)
as the value is a fraction, take another point
For x=2
h(x)=-3(2)-1
h(x)=-7
we have the point (2,-7)
step 2
Find out the y-intercept (value of h(x) when the value of x=0)
For x=0
h(x)=-3(0)-1
h(x)=-1
the y-intercept is (0,-1)
step 3
we have the points
(2,-7)
(0,-1)
To graph, the line, plot the given points and join them
using a graphing tool
In ΔLMN, \overline{LN} LN is extended through point N to point O, \text{m}\angle MNO (5x+2)^{\circ}m∠MNO(5x+2)∘,\text{m}\angle NLM = (x+10)^{\circ}m∠NLM=(x+10) ∘,and \text{m}\angle LMN = (x+16)^{\circ}m∠LMN=(x+16)∘. What is the value of x?x?
Using the exterior angle theorem, the value of x in the triangle is: x = 8.
What is the Exterior Angle Theorem?The exterior angle theorem states that the measure of the angle formed outside a triangle when a side is extended through one of the points of the triangle is equal to the sum of the remote interior angles of the triangle.
Triangle LMN is shown in the diagram attached below, where:
The measure of angle MNO = (5x + 2)°
The measure of angle NLM = (x + 10)°
The measure of angle LMN = (x + 16)°
Therefore:
Measure of angle MNO = measure of angle NLM + measure of angle LMN [based on the exterior angle theorem]
Substitute
(5x + 2)° = (x + 10)° + (x + 16)°
Solve for x
5x + 2 = x + 10 + x + 16
Combine like terms
5x + 2 = 2x + 26
5x + 2 - 2x = 2x - 2x + 26 [subtraction property of equality]
3x + 2 = 26
3x + 2 - 2 = 26 - 2 [subtraction property of equality]
3x = 24
3x/3 = 24/3 [division property of equality]
x = 8
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Two distinct lines, & and m, are each perpendicular to the same line n.
a. What is the measure of the angle where line / meets line n?
b. What is the measure of the angle where line m meets line n?
A. The measure of the angle where line | meets line n is ___ degrees
B. The measure of the angle where line meets line n is ____ degrees
The two distinct lines, line l and line m, have the following relationship with line n
A. The measure of the angle where line | meets line n is 90 degrees
B. The measure of the angle where line meets line n is 90 degrees
What are perpendicular lines?This is a term used to refer to lines that intersect at angle 90 degrees. perpendicular lines are also found in right angle triangle. Hence it is right to say that two sides of a right angled triangle are perpendicular to each other.
The features of perpendicularity also helps in defining a squire and rectangles. This is true because the sides meet at angle 90 degrees
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1) Which of the following is the additive inverse of a - b ?
The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in mathematics. The opposite (number),[1] sign change,[2] and negation are other names for this number. [3] The additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive, when applied to a real number. The additive inverse of zero is zero.
Associated with subtractionSubtraction, which can be seen as adding the opposite, is closely related to additive inverse:
a − b = a + (−b).
On the other hand, additive inverse can be compared as subtracting from zero:
−a = 0 − a.
As a result, the unary minus sign can be used to represent subtraction without using the "0" symbol, even though there shouldn't be a space after the unary "-" in proper typography.
Other featuresNegation has the following algebraic characteristics in addition to the identities mentioned above:
It is an Involution operation when (a) = a.
−(a + b) = (−a) + (−b)
−(a − b) = b − a
a − (−b) = a + b \s(−a) × b = a × (−b) = −(a × b)
(−a) × (−b) = a × b
Particularly, (a)2 = a2.
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