Please explain to me how to do this
#43
1+2+3+..+200We may observe. 200+1=201,199+2=201,198+3=201So
200/2=100 pairs of 201
Sum
100(201)=20100#44
1+2+3+..+400400/2=200 pairs of 401
Sum
200+40180200#45
1+2+3+..+800800/2=400 pairs of 801
Sum
400(801)320400#46
1+2+3+..+20002000/2=1000 pairs of 2001
Sum
2001(1000)2001000Answer:
43. 20,100
44. 80,200
45. 320,400
46. 2,001,000
Step-by-step explanation:
Gauss's method
General formula for the sum of the first n integers:
[tex]1+2+3+ \dots +n=\dfrac{1}{2}n(n+1)[/tex]
Question 43
Given sum:
1 + 2 + 3 + ... + 200Therefore, n = 200.
Substitute the value of n into the formula:
[tex]\implies \dfrac{1}{2}(200)(200+1)=100 \cdot 201=20100[/tex]
Question 44
Given sum:
1 + 2 + 3 + ... + 400Therefore, n = 400.
Substitute the value of n into the formula:
[tex]\implies \dfrac{1}{2}(400)(400+1)=200 \cdot 401=80200[/tex]
Question 45
Given sum:
1 + 2 + 3 + ... + 800Therefore, n = 800.
Substitute the value of n into the formula:
[tex]\implies \dfrac{1}{2}(800)(800+1)=400 \cdot 801 =320400[/tex]
Question 46
Given sum:
1 + 2 + 3 + ... + 2000Therefore, n = 2000.
Substitute the value of n into the formula:
[tex]\implies \dfrac{1}{2}(2000)(2000+1)=1000 \cdot 2001=2001000[/tex]
A 7. 12×10−4mol sample of koh is dissolved in water to make up 50. 0ml of solution. what is the ph of the solution at 25. 0∘c? round the answer to three significant figures
The pH of the solution is 12.2.
Molarity (kon) = No. of moles of FoH x 1000
Mckor, 7:12 × 10-4 moles x Looo 50.0 mL.
Volume of solution (m²), McKong = 1.424x102M, [on] =1.424×102M POH = -log [on] pOH =
-log [1.424x102] pon = 1.85.
pH + pOH = 14
PH = 14-pOH = 14-1.85 pH = 12.15.)
12.2.
pH is a measure of the concentration of hydrogen ions in water. Specifically, pH is the negative logarithm of the hydrogen ion (H+) concentration (mol/L) in an aqueous solution. pH = -log10(H+) This term indicates the basicity or acidity of a solution from 0 to 14 where pH 7 is neutral.
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40 points please help
The athlete that has the shortest training ride is athlete A.
The athlete that has the shorter range is Athlete B.
The athlete that has the greater median is Athlete B.
The athlete that has the greater IQR is athlete A.
What are the summary statistics?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.
Range of Athlete A = 36 - 13 = 13
Range of Athlete B = 30 - 19 = 11
Training ride of Athlete A = 16
Training ride of Athlete B = 21
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Median of Athlete A = 20
Median of Athlete B = 25
IQR of Athlete A = 30 - 16 = 14
IQR of Athlete B = 28 - 21 = 7
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Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the pyramid is 34.8 in²
How to find the surface area of the figure?Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.
The area of triangular face
Area of triangular face A' = 1/2bh where
h = height = 4.3 in and b = base = 3 in.So, A' = 1/2 × 4.3 in × 3 in
A' = 1/2 × 12.9 in²
A' = 6.45 in²
The area of square base
Area of square base A" = L² where L = length of base = 3 in
So, A" = (3 in)²
= 9 in²
The Surface area of pyramid.
Surface area of pyramid, A = 4A' + A"
= 4 × 6.45 in² + 9 in²
= 25.8 in² + 9 in²
= 34.8 in²
So, the surface area of the pyramid is 34.8 in²
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The Fruit Juice Company sold 5,909,999,222 cans of juice last year. This
year the company sold 3,999,002,135 cans. Which is the best estimate of
how many more cans were sold last year than this year?
OA) 2,000,000,000
OB) 3,000,000,000
OC) 9,000,000,000
OD) 10,000,000,000
Jason and Britton are driving to St. George. Jason got a 20 mile head start and drove an
average of 65 mph the entire way. Britton drove an average of 75 mph. After how many
hours and miles will Britton catch up to Jason?
Answer:
2 hours, 150 miles
Step-by-step explanation:
The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.
Separation distanceJason got a head start of 20 miles, so that is the initial separation between the two drivers.
Closure speedJason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.
Closure timeThe relevant relation is ...
time = distance/speed
Then the time it takes to reduce the separation distance to zero is ...
closure time = separation distance / closure speed = 20 mi / (10 mi/h)
closure time = 2 h
Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.
__
Additional comment
The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.
I need help please with this
Answer:
24
Step-by-step explanation:
thats what i got from the math i did
You have $30 to buy muffins. However, at the shop you can buy 1 muffin for $4. (a) Write an inequality from the above information. (b) Solve this inequality to find the number of muffins you can buy. (c) How much money will you have left over?
Answer:
Let m be the number of muffins.
a) 4m <= 30
b) m <= 7.5, so the maximum number of muffins to buy is 7.
c) $4 × 7 = $28, so $2 will be left over.
Let a_n be the integer obtained by writing all the integers from 1 to n from left to right. For example, a_3 = 123 and a_{11} = 1234567891011. Compute the remainder when a_44 is divided by 45.
Answer:
9
Step-by-step explanation:
The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.
Expanded formThe expanded form of the number can be written as ...
a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...
+10×10^68 +11×10^66 +... +43×10^2 +44×10^0
Powers of 10Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...
10 mod 45 = 10
100 mod 45 = 10
This lets us conclude that any positive power of 10 mod 45 is 10.
Parts of the sumIn short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...
a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45
= (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45
= (((225 mod 45) +(901 mod 45))×10 +44) mod 45
= ((0 +1)×10 +44) mod 45
Final valuea_44 mod 45 = 54 mod 45 = 9
__
Additional comment
The result can be confirmed by a suitable calculator.
__
The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.
Answer: 9
Step-by-step explanation:
we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344
on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.
The graph of the step function g(x) = –⌊x⌋ + 3 is shown.
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, 5) to (negative 1, 5). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, negative 1) to (5, negative 1).
What is the domain of g(x)?
{x| x is a real number}
{x| x is an integer}
{x| –2 ≤ x < 5}
{x| –1 ≤ x ≤ 5
Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
The function described is defined for x between -2 and 5, hence the domain is given by the following interval:
{x| –2 ≤ x <= 5}
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Answer:
{x| –2 ≤ x < 5}
Step-by-step explanation:
The ______ mean is the best estimate of next year's return. multiple choice question. the average of the arithmetic and geometric mean arithmetic geometric
The (B) arithmetic mean is the best estimate of next year's return.
What is the arithmetic mean?The arithmetic mean or arithmetic average, or simply the mean or the average (where the context is obvious), is the sum of a set of numbers divided by the number of numbers in the set. The collection is typically a set of results from an experiment or observational research, or a group of survey results. In some instances in mathematics and statistics, the word "arithmetic mean" is favored since it distinguishes it from other means such as the geometric mean and the harmonic mean. The arithmetic mean is the most accurate predictor of next year's return.Therefore, the (B) arithmetic mean is the best estimate of next year's return.
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The correct question is shown below:
The ______ mean is the best estimate of next year's return. multiple choice question.
(A) the average of the arithmetic and geometric mean
(B) arithmetic
(C) geometric
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: (h - g)(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: h(x) - g(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: - {x}^{2} - x + 3[/tex]
For, (h - g)(2.1), put x = 2.1
[tex]\qquad \sf \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6.51 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 3.51[/tex]
When the points in a scatter plot cluster closely around the regression line, the correlation can be said to be?
The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.
It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.
If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.
When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.
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The equations of two lines are given below.
3 x minus y equals 5
3 y equals x minus 15
Are these lines parallel, perpendicular, or neither?
The lines are neither parallel nor perpendicular
How to determine the relationship between the lines?The equations of the lines are given as
3 x minus y equals 5
3 y equals x minus 15
Rewrite the equations properly
3x - y = 5
3y = x - 15
Make y the subject in both equations
In 3x - y = 5, we have
y = 3x + 5
In 3y = x - 15, we have
y = 1/3x - 5
The slopes of the two lines are
m1 = 3
m2 = 1/3
The above values are not equal, and they are not opposite reciprocal
This means that the lines are neither parallel nor perpendicular
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Find the volume of the following figure. Round your answers to the nearest tenth, if necessary. Use the pi button on your calculator.
The volume of the given figure is 3617.3 km³
Calculating volume of a coneFrom the question, we are to calculate the volume of the given figure
The given figure is a cone.
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume of cone
r is the base-radius of the cone
and h is the height is perpendicular height of the cone
From the given information,
r = 12 km
h = 24 km
Thus,
V = 1/3 × π × 12² × 24
(Take π = 3.14)
V = 1/3 × 3.14 × 12² × 24
V = 1/3 × 3.14 × 144 × 24
V = 1/3 × 10851.84
V = 3617.28 km³
V ≈ 3617.3 km³ (To the nearest tenth)
Hence, the volume of the given figure is 3617.3 km³
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Select the correct answer.
What is the exact value of cos 105°?
A √6-√2
B. √6 + √2
с. V2 - V6
D. -√2+√6
The exact value of cos 105° is equals to √2/4 - √6/4.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In this case, 105 degrees, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression;
cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2.
So, multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2
(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)
The Value of sin (60) is √3/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)
The exact value of sin (45) is √2/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2
Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.
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A clock has a diameter of 16 inches. how far does the hour hand travel during 5 hours? use 3.14 for pi.
Distance hour hand travel in 5 hours is 20.94 inches.
What is a diameter?A diameter of a circle is any straight line segment that passes through the center of the circle and has endpoints on the circle in geometry. It is also known as the circle's longest chord. Both definitions apply to the diameter of a sphere.To find the distance hour hand travel in 5 hours:
Let's say the hour hand completed one full round around the clock. If this was the case, it would have been 2[tex]\pi[/tex]×8 inches around. We know that the hour hand only traveled 5 hours around the clock rather than 12, thus our formula is 2[tex]\pi[/tex]×8×( 5/12 ).Distance hour hand travel is 20.94 inches.Therefore, the distance hour hand travel in 5 hours is 20.94 inches.
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A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years
Answer:
1/64
Step-by-step explanation:
10 = ½
20 = ¼
30 = ⅛
40 = 1/16
50 = 1/32
60 = 1/64
Answer:
0.015625 left.
Step-by-step explanation:
If we start with say 100g of the material, in 10 years there is 100 * 1/2 =
50g left ( = 0.5 left).
In 20 years there is 100*(1/2)^2 = 25 g left.
In n*10 years there is 100(1/2)^2 g
So in 60 years there is 100(1/2)^6 = 1.5625 g left
This is 1.5625 %
= 0.015625 of the origin material left.
An empty box is shaped like a rectangular prism. the box has a base area of square foot and a height of foot. how much packing material is required to fill the box?
3 /10 foot³ packing material is required to fill the box.
What is meant by volume of prism?
The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length. Therefore, The volume of a Prism = Base Area × Length.The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.Volume = base area × height
= 9/10 × 1/3
= 3 /10 foot³
Therefore, 3/10 foot³ packing material is required to fill the box.
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The complete question is-
An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square foot and a height of 1/3 foot. How much packing material is required to fill the box?
Please help me fast
Determine an exact value for the expression and include a complete solution
(sin 225°) ² - cos 330° cos 240°
Answer:
1.187991
Step-by-step explanation:
sin^2(225)−(cos(330))(cos(240))
=(−0.930095)2−(cos(330))(cos(240))
=0.865076−(cos(330))(cos(240))
=0.865076−−0.991199(cos(240))
=0.865076−(−0.991199)(0.325781)
=0.865076−(−0.322914)
=1.187991
olives and pineapple pizza delivered two large pizzas cut into eight slices each. james and his sister both ate 5/8 of the pizza together. how many slices are left?
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
The approximate year at which two revenues were equal is; 7.5 years
How to interpret Revenue Graphs?From the graph attached, we see that in the year 10, the revenue for printed ads was 2 million dollars & 3 million dollars for printed ads and online ads revenue respectively.
Thus, printed ad. Revenue line equation is;
(y - 2) = (3 - 2)(x - 10)/(0 - 10)
y - 2 = (x - 10)/-10
x - 10 = -10(y - 2)
x - 10 = -10y + 20
x - 10 = -10y + 20
x + 10y = 30 -----(1)
At x = 12 years from the graph, we have;
12 + 10y = 30
10y = 18
y = 1.8
Thus, online ad. Revenue line equation is;
(y - 0) = ((3 - 0)/(10 - 0))(x - 0)
y = 3x/10
10y = 3x
10y - 3x = 0 -----(2)
At x = 12, we have;
10y = 3*12
10y = 36
y = 3.6
In year '12' the online ad revenue got doubled as that of printed ad revenue and afterward more than doubled.
B) The approximate year at which two revenues were equal is gotten by solving equation 1 and 2 simultaneously to get;
x = 7.5
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Please help ASAP
A high school principal conducts a survey on whether or not students would be interested in an elective art course. The principal knows that it would be too time-consuming to survey all 482 students in the high school, so he decides to ask the 98 students currently in the cafeteria. One of the students states that this survey cannot be used to make an inference about the entire high school. Which of the following statements best justifies the student's interpretation of the survey?
The survey sample was too small.
B
An art teacher should have conducted the survey.
C
The survey method was flawed since the sample was not random.
D
An observational study, rather than a sample survey, should have been used.
The survey method was flawed since the sample was not random.
What is a survey?A survey is an investigation that is carried out on a sample of a population. However, for the sample to be representative of the population, care must be taken to pick the participants in the survey at random. The principal ought to have carefully crafted a method in which the sample can be selected in a randomized manner.
For instance, the principal could have decided to take the fifth student in every row in all the classes in the school. In that way, the sample would be adequately randomized hence the result of the survey would be adjudged as representative of the situation in the entire population and thus it will be reliable as a tool that can be used to make scientific inferences.
Thus, the survey method was flawed since the sample was not random.
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Answer: C
Step-by-step explanation:
The survey method was flawed since the sample was not random.
Translate the triangle by
(-2
-4)
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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What is the factored form of 5x − 625x4
Options:
A. 5x(1 + 5x)(1 - 5x + 25x2)
B. 5x(1 - 5x)(1 + 5x + 25x2)
C. (1 - 5x)(1 + 5x + 25x2)
D. (1 + 5x)(1 - 5x + 25x2)
Answer:
B
Step-by-step explanation:
5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term
= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
1 - 125x³
= 1³ - (5x)³
= (1 - 5x) (1² + 5x(1) + (5x)² )
= (1 - 5x) (1 + 5x + 25x²)
Then
5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)
How can you make iot clear that a measured value of 980 inches actually has 3 significant figures?
The figure 980 inches can be written as 980.0 inches. It contains two non-zero digits and a zero trailing before the decimal point. Hence, it has three significant figures.
Rules to Determine Number of Significant Figures:
There are three fundamental rules that one can use to determine the significant figures in any given number or value. These rules go as follows:
Digits that are not zero are always counted among significant figures.Any zeros in the range of two significant digits are to be counted.The zeroes at the end of any number are significant unless they have been used after a decimal point.For the portion followed by a decimal point, zeroes at the end are not counted, but zero between two non-zero digits and zero in the initial portion of the floating point are counted while taking note of the significant figures in a decimal value.
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Please Help!
A dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.
The dog can wander an area of ___ square feet
(exact answer, using the pi symbol)
The area that the dog can wander based on the information provided will be 931π.
How to calculate the area?From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.
In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.
The area that the dog can wander will be:
= 3/4(π35²) + 1/4(π(35 - 28)²)
= 3/4π(35)² + 1/4π(7)²
= (3/4 × 1225)π + (1/4 × 49)π
= 918.75π + 12.25π
= 931π
Therefore, the area that the dog can wander based on the information provided will be 931π.
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The population of a bacteria culture after t hours is given by P = 400 - 8t2. What is the rate of change at 6 hours?
1. 0
2. -56
3. -96
4. -48
The rate of change at 6 hours is -96
How to determine the rate of change?The function is given as:
P = 400 - 8t^2
Differentiate the function
P' = -16t
Set t = 6
P' = -16 * 6
Evaluate
P' = -96
Hence, the rate of change at 6 hours is -96
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The diameter of a sphere measures 10.4 inches. what is the surface area of the sphere?
Area of the sphere ≅ 339.62 in².
What is Sphere?A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.
Area of sphere = 4[tex]\pi r^{2}[/tex]
diameter d = 2r
Given that,
diameter d = 10.4 , r =5.2 in
then, Area of sphere = 4[tex]\pi r^{2}[/tex]
= 4×3.14×5.2×5.2
≅ 339.62 in²
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Answer:
108.16 to the second power
Step-by-step explanation:
Which inequality written in vertex form represents the graphed region?
Answer:
C
Step-by-step explanation:
The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.
Option C is the correct answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
Inequalities where we need to find the coordinates and see which inequalities represent the graph.
y < 4 (x- 1)² - 11 ____(1)
y < -4 (x-1)² - 11 _____(2)
y < 4 (x-1)² - 16 ______(3)
From (1),
y = 4 (x- 1)² - 11
x = 0, y = 4 x 1 - 11 = 4 - 11 = -7
From (2),
y = -4 (x-1)² - 11
y = -4 x 1 - 11 = -4 - 11 = -15
From (3),
y = 4 (x-1)² - 16
x = 0, y = 4 x 1 - 16 = 4 - 16 = -12
We see that,
y < 4 (x-1)² - 16 gives us the coordinates (0, -12) on the graph.
Similarly,
x = 1, y = 4 x 0 - 16 = 0 -16 = -16
x = 1, y = 4 x 1 - 16 = 4 - 16 = -12
(1, -16) and (2, -12) coordinates are on the graph.
Thus,
The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.
Option C is the correct answer.
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