Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
Answers
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
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Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
Related Questions
Given that a function, g, has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could true for g.
A. g(-4)= -11
B. g(-13)= 20
C. g(0) = 2
D. g(7) = -1
Answers
The statement that could be true for the domain of g is g(-4) = -11.
option A.
Which statement is true for domain of g?
The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.
The given statements that could be true for g is calculated as follows;
Option A: g(-4) = -11
Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.
Therefore, this could be true.
Option B: g(-13) = 20
Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.
Option C: g(0) = 2
We are given that g(0) = -2, so option C is not true.
Option D: g(7) = -1
Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.
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When a retired police officer passes away, he leaves $300,000 to be divided among his three children and six grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
Answers
Answer:
so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand
Step-by-step explanation:
hope this helps !
Which of the following is not a linear transformation?
Select one:
Rotation in geometry
Projection in geometry
None of the options
Reflection in geometry
Answers
The question asks which of these is NOT a linear transformation.
dilations, shears, rotations, reflections and projections are all linear.
Translation is NOT a linear transformation.
can someone help me please
here is the picture is about Row Ops
Answers
The result of engaging in the row multiplication operation in a matrix would be [ 1 /2 0 | 3 / 4 ]
[ -1 5 | 4 ].
How to multiply matrices ?First, you should multiply the first row by the value given of 1 / 4 to be:
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
Then you can replace the values found by the values in the matrix to be :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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11. Higher Order Thinking Gabriela lives.
2 miles from school. On her way home,
she runs of the way and walks the rest.
How far does she walk? Explain.
Answers
Gabriela walks 1 mile distance on her way home from school as she is running part of the way.
What is distance?The distance between two things is measured in distance units like miles, kilometres, or metres. Given that it only possesses magnitude and not direction, distance is a scalar number.
We must ascertain Gabriela's total trip distance before we can respond to this query.
We can get the overall distance by adding the distance she runs to the distance she walks because she runs a portion of the route and walks the other.
Gabriela commutes two miles to school, so
She needs to travel a total of 2 miles.
We need to figure out how far she runs because she is running a portion of the way.
Since running is typically faster than walking, we can infer that she covers the distance in one mile by running half of it.
She will therefore need to walk the additional mile.
Gabriela walks a mile on her way home from school, which is the answer to the question.
This is because she walks the remaining mile and runs the first mile.
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Help with solving This graph
Answers
Answer:
r=4
center: (-2,4)
Step-by-step explanation:
The equation of a circle is:
(x-h)²+(y-k)²=r²
(h,k) would be the center of the circle and r would be length of the radius
To find r, we simply take the square root of 16, which would be 4
And the center is given in the equation
A line passes through the points (8,8) and (5,2). What is its equation in slope-intercept form?
Answers
Step-by-step explanation:
m=y1-y2/x1-x2
m=2-8/5-8
m=-6/-3
m=2
y=m(x-x1)+y1
y=m(x-8)+8
y=2x-16+8
y=2x-22
Answer: Y=mx+c
Step-by-step explanation:
The Slope-Intercept Form can be written in the form: y = mx + c Where “m” is the slope of the line “c” is the y-intercept of the equation of the line
You are told that h is a one to one function with values h(-9)=5 and h(3)= -4 which of the following is true
Answers
If function "h" is one-to-one function which is having values h(-9) = 5, and h(3) = -4, then the inverse statement is (d) h⁻¹(-4) = 3.
We know that the function "h" is a one-to-one function, so, it has an inverse function (h⁻¹). To find the inverse function, we need to exchange roles of "x" and "y" and solve for y. This gives:
x = h(y)
y = h⁻¹(x)
The given values of function "h" are h(-9) = 5 and h(3) = -4, we find the values of h⁻¹(5) and h⁻¹(-4):
h(-9) = 5
So, h⁻¹(5) = -9 (by exchanging roles of x and y)
and h(3) = -4
So, h⁻¹(-4) = 3 (exchanging the roles of x and y)
The function "h⁻¹(-4) = 3" is represented in option (d).
Therefore, the correct option is (d).
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I arrived home to discover that my 50-foot by 40-foot basement has 18 inches of water in it! There are about 7.5 gallons in 1 cubic foot of water. How much water is in the basement?
Calculate using the most appropriate units to describe the amount of water, and state your answer in a meaningful sentence.
Answers
The amount of water in the basement is V = 22,500 gallons
Given data ,
To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.
First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:
50 feet x 40 feet x 1.5 feet = 3,000 cubic feet
There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:
3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons
Hence , there are 22,500 gallons of water in the basement
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PLEASE HELP I NEED TO PASS THIS Using the probability distribution represented by the graph
below, find the probability that the random variable, X, falls
in the shaded region.
Answers
Answer: C: 5/8
Step-by-step explanation:
Simply 5/8 of the bar is filled in
Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.
Here, we have,
Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.
Positive Outcomes/Total Results = x/n = Probability(Event)
Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.
Here in the question,
Total region = 8.
Shaded region = 5
So, probability of falling in the shaded region = 5/8
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ACTIVITY 2: Solve the following problems completely.
Answers
1) The amount is php 340,060
2) The rate is 13%
3) The amount is php 137,622
What is the compound interest?Compound interest is commonly used in many types of financial products, such as savings accounts, CDs, and loans.
1)
[tex]A = P(1 + r/n)^nt\\A = 80000( 1 + 0.16)^9.75\\A = php 340,060[/tex]
2)
[tex]12300 = 9750(1 + r)^2\\12300/9750 = (1 + r)^21.26 = (1 + r)^2\\ln 1.26 = 2 ln1 + r\\ln 1.26/2 = ln1 + r\\0.12 = ln1 + r\\e^{0.12} = 1 + r\\r = e^{0.12} - 1\\r = 0.13\\r = 13%[/tex]
3)
[tex]A = 50000(1 + 0.15/2)^2 * 7\\A = php 137,622[/tex]
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Solve for x. Round to the nearest tenth, if necessary
Answers
Answer:
Set your calculator to degree mode.
cos(37°) = 52/x
x cos(37°) = 52
x = 52/cos(37°) = 65.1
Suppose that $2000 is invested at a rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 6 years
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer:
$2,631.55
Step-by-step explanation:
To find the total amount in the account after 6 years, we can use the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $2,000r = 4.6% = 0.046n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]
[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]
[tex]\implies \sf A=2631.54794...[/tex]
Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.
please help me understand
Answers
when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
What is Graph ?A chart can be defined as a pictorial representation or diagram that presents data or values in an organized manner. Points on a graph often represent a relationship between two or more things.
We can use a linear equation of the form to describe a function that relates the number of pages read to the time elapsed since the start of reading:
L = mT + b
where L is the number of pages remaining, T is the elapsed time in hours, m is the page read rate in pages per hour, and b is the original number of pages remaining when T = 0.
In this case, we know that Ray is reading at a constant rate of 25 pages per hour, so m = -25 (since we are counting the remaining pages). We also know that when T = 0 (start of reading), 150 pages remain unread, so b = 150. Combining everything we get:
L = -25T + 150
This formula describes a function that combines the number of pages being read with the time elapsed since the start of reading. Note that when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
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Use the estimated angle to find the distance of the life-raft from the lighthouse.
Answers
The correct angle of elevation for the lighthouse's top is roughly 1.91°.
How to find the distance of the lift-raft from the lighthouse?Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.
The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".
a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.
[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]
putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.
[tex]tan3 = \frac{20}{d}[/tex]
[tex]d = \frac{20}{tan3}[/tex]
d = 354.14 (rounded to 2 decimal points
The life raft is therefore roughly 354.14 meters away from the lighthouse.
b)
Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.
[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]
solving for [tex]\alpha[/tex] we get,
[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]
Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.
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The complete question in the form of the image below:
Construct a 90 % confidence interval of the population proportion using the given information.
x = 105 n =150
Answers
The 90% confidence interval based on the data provided will be (0.6152, 0.7848)
How to calculate the confidence intervalIt should be noted that standard error = ✓[(p * q) / n]
p = population proportion
q = 1 - p
n = sample size
sample proportion = x / n = 105 / 150 = 0.7
standard error = ✓(p * q) / n] = sqrt[(0.7 * 0.3) / 150] = 0.0516
margin of error = 1.645 * 0.0516 = 0.0848
Confidence interval = sample proportion ± margin of error
= 0.7 ± 0.0848
= (0.6152, 0.7848)
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which value represents a percentage between 11% and 17%
Answers
Answer:
Step-by-step explanation:
a
Please help me this is so hard and i really dont get this. if you help me with both parts ill give you 60 points
Answers
h(t) = -5t^2 + 40t
h(t) = -5(t^2 - 8t)
h(t) = -5(t^2 - 8t + 16) + 80 (adding and subtracting 16 inside the parentheses to complete the square)
h(t) = -5(t - 4)^2 + 80 (factoring and simplifying)
So, the function in vertex form is h(t) = -5(t - 4)^2 + 80.
2) To find when the ball hits the ground, we need to find when h(t) = 0, since h(t) represents the height of the ball above the ground.
0 = -5(t - 4)^2 + 80 (substituting h(t) = 0)
5(t - 4)^2 = 80
(t - 4)^2 = 16
t - 4 = ±4
t = 4 ± 4
So, the ball hits the ground at t = 0 or t = 8 seconds after launch. However, we can discard the t = 0 solution because that represents the time when the ball is launched, and we are looking for when it hits the ground. Therefore, the ball hits the ground at t = 8 seconds after launch.
please help, will give brainiest!
Answers
Answer:
See explanation.
Step-by-step explanation:
Let's analyze each solution to determine if it's viable or non-viable based on the given constraints: Johnnie and Amy have $38.50, and they cannot buy more than 7 lunches.
1. 8 slices of pizza and 0 hamburgers
This solution is non-viable because they are not allowed to buy more than 7 lunches. In this case, they would be buying 8 lunches.
2. 5 slices of pizza and 2 hamburgers
Cost: 5×4.75+2×5.55=23.75+11.10=34.85
This solution is viable because the total cost is within their budget, and they are buying 7 lunches.
3. 4 slices of pizza and 3 hamburgers
Cost: 4×4.75+3×5.55=19.00+16.65=35.65
This solution is viable because the total cost is within their budget, and they are buying 7 lunches.
4. 3 slices of pizza and 2 hamburgers
Cost: 3×4.75+2×5.55=14.25+11.10=25.35
This solution is non-viable because they are only buying 5 lunches, which is less than the maximum allowed. But if it is acceptable to only buy below 7 lunches, then this solution can be viable.
5. 2 slices of pizza and 6 hamburgers
Cost: 2×4.75+6×5.55=9.50+33.30=42.80
This solution is non-viable because the total cost exceeds their budget.
6. 0 slices of pizza and 7 hamburgers
Cost: 7×5.55=38.85
This solution is non-viable because the total cost exceeds their budget.
In conclusion, the viable solutions are:
5 slices of pizza and 2 hamburgers
4 slices of pizza and 3 hamburgers
Possible in being viable:
3 slices of pizza and 2 hamburgers
I really need hel with this please
Answers
The resulting matrix after row 1 is multiplied by 2 is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
The first row is given as follows:
7, -4 and 8.
Multiplying the first row by two, we have that:
7 x 2 = 14.-4 x 8 = -8.8 x 2 = 16.(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
(the second row was kept constant, while the first row was multiplied by 2).
Missing InformationThe matrix is:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
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The perimeter of a rectangle is 18 feet, and the area of the rectangle is 14 square feet. What is the length of the rectangle?
Answers
The length of the rectangle with the above information is calculated as: 7 feet.
How to Determine the Length of the Rectangle?Let the length of the rectangle be l and the width be w. Then, we know that:
Perimeter = 2(l + w) = 18 feet
Area = lw = 14 square feet
We can use the first equation to solve for one of the variables in terms of the other:
l + w = 9
l = 9 - w
Substituting l = 9 - w into the equation for the area, we get:
(9 - w)w = 14
w² - 9w + 14 = 0
Factorize
(w - 2)(w - 7) = 0
Therefore, w = 2 or w = 7. Since the length of the rectangle must be larger than its width, we choose w = 2 and l = 9 - w = 7.
Thus, the length of the rectangle is 7 feet.
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exponent property of nth roots
Answers
The exponent property of nth roots states that for any real number a and any positive integer n, the nth root of a raised to the nth power equals a.
What is the use of this property ?The property of nth roots, concerning exponents states that if 'a' is a real number and 'n' is a positive integer, then the nth root of 'a' when raised to the nth power will always be equal to 'a':
√ ( a ⁿ ) = a
This can greatly simplify expressions involving nth roots by multiplying the exponent by 'n', taking the nth root of the base:
( √ a ) ⁿ = √ ( a ⁿ )
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What is the discriminant of the quadratic equation − � 2 − 9 � − 8 = 0 −x 2 −9x−8=0?
Answers
we know that
discriminant of quadratic is [tex]b^{2}[/tex]-4ac
putting values we get
81-32
= 49
hence the discriminant is 49
Solve. Show the system of equations used and your work in solving the system.
A phone store sells Android phones for $400 and iOS phones for $650 each. This
week they sold a total of 110 phones and earned $54,000. How many Android and
how many iOS phones did they sell?
Answers
Let's assume that the number of Android phones sold is x and the number of iOS phones sold is y. Then we can write two equations based on the given information:
x + y = 110 (equation 1)
400x + 650y = 54000 (equation 2)
To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method:
From equation 1, we can solve for x in terms of y: x = 110 - y
Substitute x = 110 - y into equation 2 and solve for y:
400(110 - y) + 650y = 54000
44000 - 400y + 650y = 54000
250y = 10000
y = 40
Substitute y = 40 into equation 1 and solve for x:
x + 40 = 110
x = 70
Therefore, the phone store sold 70 Android phones and 40 iOS phones.
The line plot shows a student's quiz scores. Which measures of center and variability should be used to describe the data?
Quiz Scores
0=1
1,2,3,4=0
5=2
6=4
7=2
8=2
9=1
10=0
Answers
The measures of center for this data set are the mean and median. The mean is 5.1 and median is 6.
The measure of variability is the range. The range is 10.
How to explain the informationThe measures of center describe the typical or central value of the data. For this data set, we can use the mean or the median as measures of center. The mean is the average of all the quiz scores, while the median is the middle value when the scores are arranged in order.
Mean = (0x1 + 1x0 + 2x0 + 3x0 + 4x0 + 5x2 + 6x4 + 7x2 + 8x2 + 9x1 + 10x0) / (1+0+0+0+0+2+4+2+2+1+0) = 5.1
Median = 6 (the middle score)
The measures of variability describe the spread or dispersion of the data. For this data set, we can use the range. The range will be:
= Highest score - Lowest score
= 10 - 0
= 10
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The line plot shows a student's quiz scores.
Quiz Scores
0 = 1
1,2,3,4 = 0
5 = 2
6 = 4
7 = 2
8 = 2
9 = 1
10 = 0
Which measures of center and variability should be used to describe the data?
I understand the lower and upper class limits but there are only one number but I don't know what to do
Answers
The class mark of the modal class is: 25
How to solveFrom the given histogram, the following Frequency Distribution is obtained:
Class Interval Mid point Frequency
625-675 650 3
676-726 701 5
727 - 777 752 7
778 - 828 803 8
829 - 879 854 6
880 - 930 905 2
931 - 981 956 0
982 - 1032 1007 1
b. To find the lower class limit of the first class:
First class: 625
c. The upper limit of the first class is:
First class: 676
The class mark of the modal class is:
The modal class is: 803
The class mark is upper limit + lower limit/2
Thus, 828-778/2
=> 50/2
The class mark of the modal class is: 25
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HELP ASAP PLEASE 20 POINTS!!!!!
Answers
Answer:
5.6 mi
Step-by-step explanation:
1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that
how do you do comparison for percents
Answers
In order to do a comparison for percents, you must convert them to decimal form and then juxtapose the decimal values side by side to see which is greater or less.
What are percents?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent sign is commonly used, however the acronyms pct., pct, and sometimes pc are also used. A % is a number with no dimensions; it has no unit of measurement.
To calculate the percentage, divide the amount by the total value and multiply the result by 100.
Divide a percentage by 100 to get a decimal. So 25% is equal to 25/100, or 0.25. Multiply a decimal by 100 (simply shift the decimal point two places to the right) to convert it to a percentage. For example, 0.065 equals 6.5% and 3.75 equals 375%.
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Select the incorrect phrases in the paragraph.
Given:
is a right angle
is a right angle
Prove:
Four lines M A, M B, M C, and M D that starts from point M are drawn such that angle A M C equals 90 degrees, and angle B M D equals 90 degrees.
1. Angle A M C is a right angle. It leads to angle A M B and angle B M C are complementary 2. Angle B M D is a right angle. It leads to angle B M C and angle C M D are complementary. 1 and 2 lead to Angle A M B which approximately equals angle C M D.
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
is a right angleis given.
is a right angleis also given.Since
is a right angle,
and
are complementary.Since
is a right angle,
and
are complementary.By the Congruent Complements Theorem,
.
Answers
Note that in the proof stated above, there is no incorrect statement.
How is this so?The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.
The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.
The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.
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ACTIVITY 4: Solve the following inequalities.
Answers
The solutions of the inequalities are shown below
x [tex]\geq[/tex] 5
x< 13
x[tex]\geq[/tex]1
x> 1
How do you solve inequalities?Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.
[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]
[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]
[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]
[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]
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