1)correct option is b) true
2)Which of the following expressions always evaluates to true?
correct option is d)(x > 0) && (x == 0)
given that
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.
x = 5 and y = 7
Choose the value of the following expression: (x != 7) && (x <= y)
a. false
b. true
c. 0
d. null
(5! = 7) && (5<=7)
5 ≠ 7
correct option is b) true
Suppose that x is an int variable.
Which of the following expressions always evaluates to true?
a. (x > 0) || ( x <= 0)
b. (x > 0) && ( x <= 0)
c. (x >= 0) 11 (x == 0)
d. (x > 0) && (x == 0)
a) x = 1,2,3.... || x =0,-1,-2,-3......
b)x = 1,2,3.... && x = 0,-1,-2,-3,.....
c) x = 0,1,2,3..... 11 x = 0
d) x = 1,2,3.... && x = 0
correct option is d)(x > 0) && (x == 0)
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Find the derivative of the function. y = arctan √[(1 − x) /(1 + x)]
y' = ?
The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by
y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].
To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is
1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is
-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.
1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]
=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].
When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.
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How much faster is parallel computing?
The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.
What is parallel computing?The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.
Here,
Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.
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How do you find the asymptotes and zeros of a function?
The process to find the asymptote and zeros of the function is explained below.
The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.
Here we need to find the way to identify the asymptotes and zeros of a function.
The process of finding the asymptote is defined as,
If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.
Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.
Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.
The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.
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What type of graph is absolute value?
On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. f has absolute minimum value is 0, and it also has the same relative minimum value (0,0).
What does an absolute value graph look like?On the graph, you are able to see a "open circle" at it when x< 0. (0, 0).
This is due to the fact that, as we've previously demonstrated, the points at y = x approaching (0, 0) as the x-values approach 0.Since x needs strictly be less than zero on only this stretch, the open circle being drawn in its place.When x ≥ 0, a point in (0, 0) is plugged in, thus "plugging" the hole shown by either open circle.Therefore, we get:On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. Function f absolute minimum value is 0, and it also has the same relative minimum value (0,0).F has absolute minimum value is 0, and it also has the same relative minimum value (0, 0). F's highest relative value is zero.There consequently no absolute maximum value of f due to the graph's infinitely high y values.
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N(t) = 8950 times (0.7)^2t
Answer: t = 0
Step-by-step explanation:
Expand 8950×0.7²: 4385.5t
8950(0.7) ²t
8950×0.49t = 4385.5t
N(t) = 4385.5t
N(t) - 4385.5t=0
Factor N(t) - 4385.5t: t (N - 4385.5)
t (N - 4385.5) =0
t=0
4x² - 20x = -21????????
Answer:
x=7/2
x=3/2
Step-by-step explanation:
Answer: ax^2+bx+c=0
(4x^2+20x+20=0)
Step-by-step explanation:
It may not make sense but...
Add -20 to both sides of the equation.
4x-20x=-20
Add -20 to both sides of the equation.
4x^2-20x+20=-20+20
Simplify the expression.
4x^2+20x+20=0
I hope this was what you were looking for. :) If not I'm still glad to help.
What is the opposite inverse of 4?
4 is the additive inverse of -4.
OR
The opposite of 4 is -4, or negative four.
Now, According to the question:
Opposite numbers:-
Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.
If a number is added to its additive inverse, the sum of both the numbers becomes zero.
For any given number, the additive inverse is a number or a value which when added to the original number results in zero.
Mathematically: a + (-a) = 0
So here, 'a' and '-a' are the additive inverses of each other.
Therefore, for 4, the additive inverse is 4 = -4
Thus, 4 is the additive inverse of -4.
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What is a 1 million sided shape called?
A one million sided shape called as Megagon.
We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.
These line segments are known as sides.
A polygon has at least three straight sides and angles.
Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon
We know that a polygon with n sides is called n-gon.
For n = 1000000, i.e., a polygon with one million sides is called as Megagon.
A number of edges and vertices = 1000000
And the internal angle of megagon is about 179.99 degrees.
Therefore, a shape with 1 million sides is known as a Megagon
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1/4 - 7/1 (pls i nee answer)
Answer:3/4 is the answer
Step-by-step explanation:
Answer:(s)
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed number: - 6 3/4
Step-by-step explanation:
1/4 - 7/1 = - 27/4 or - 6.75 or - 6 3/4
LCM: 4, 1 = 4
Adjust Fraction Based On LCM:
1/4 - 28/4
Apply The Fraction Rule:
a/c - b/c = a - b/c
1 - 28/4
Subtract the numbers:
1 - 28 = - 27
= -27/4
Apply Fraction Rule:
- a/b = - a/b
Thus:
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed Number Form - 6 3/4
I hope that helps you!!!
Pls help me with solving systems of linear equations by elimination
Answer:
Step-by-step explanation:
A. 2x = -6
x = -3
3 + y = 5
y = 2
(-3, 2)
-9 - 2 = -11
-11 = -11
3 + 2 = 5
5 = 5
B. 4x + 2y = 1
6x + 4y = 1
-8x - 4y = -2
6x + 4y = 1
-2x = -1
x = 1/2
4(1/2) + 2y = 1
2 + 2y = 1
2y = -1
y = -1/2
-2(-1/2) + 3 = 4(1/2) + 2
1 + 3 = 2 + 2
4 = 4
6(1/2) + 4(-1/2) = 1
3 - 2 = 1
1 = 1
C.
-x + 32y = -25
4x + 8y = 100
-4x + 128y = -100
136y = 0
y = 0
-x = -25
x = 25
(25, 0)
32(0) - 25= -25
-25= -25
5(25) = 100 + 25 - 8(0)
125 = 125
D.
3x + 2y = 6
4x + 5y = -20
-12x - 8y = -24
12x + 15y = -60
7y = -84
y = -12
2(-12) + 3x = 6
-24 + 3x = 6
3x = 30
x = 10
(10, -12)
2(-12) + 3(10) = 6
-24 + 30 = 6
6 = 6
4(10) + 5(-12) + 20 = 0
40 - 60 + 20 = 0
-20 + 20 = 0
0 = 0
At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 1/2 cups of flour 2 eggs, 3 tablespoons butter, 3/4 cups sugar 1 package of chocolate drops They will make only full recipes, no partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25%. How many recipes of cookies should they make for their smaller party? (Some eggs and some cookies may be left over. )
(A) 1.
(B) 2.
(C) 5.
(D) 7.
(E) 15
The correct option is option (E) 15
To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.
=108 students * 0.75 = 81 students.
To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.
Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.
Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.
As 11 is not a given option, we consider the option which is greater than 11, which is 15.
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Simplify (4s^5t^-7/-2s^-2t^4). Write your answer using only positive exponents. Evaluate any numerical powers.
I'LL NAME YOU BRAINLIEST
please help!!
In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.
What is polynomial?A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here,
=4s⁵*t⁻⁷/-2s⁻²*-2t⁴
=s⁷/t¹¹
The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.
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Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 8 + 27) + 52 and 8 + (27 + 52)
Which one is correct
yes, it uses the Commutative Property
yes, it uses the Identity Property
yes, it uses the Associative Property
no they are not equivalent
Answer:
yes, it uses the Associative Property
Step-by-step explanation:
The two expressions (8 + 27) + 52 and 8 + (27 + 52) are equivalent because they both equal 87. This is an example of the Associative Property of Addition which states that the order of the terms within an expression can be changed without changing the result.
Mike is saving money for a new bike that costs $180.00
If represents the amount of money he has saved so far, which expression represents the amount of money,in dollars, he still needs to save?
A
180+m180+m180+m
B
180−m180-m180−m
C
180×m180\times m180×m
D
180÷m180\div m180÷m
Answer: B
Step-by-step explanation:
B) 180−m180-m180−m
please help it's for a test Which is an x-intercept of the graph of the function y=tan(x-5 pie/6)?
Answer:
5pie/6,0
Step-by-step explanation:
i graphed it
Zachary is a waiter at a restaurant. Each day he works, Zachary will make a guaranteed wage of $40, however the additional amount that Zachary earns from tips depends on the number of tables he waits on that day. From past experience, Zachary noticed that he will get about $7 in tips for each table he waits on. How much would Zachary expect to earn in a day on which he waits on 11 tables? How much would Zachary expect to make in a day when waiting on tt tables?
Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables
If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.
When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.
To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:
Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)
So if tt represents the number of tables Zachary waits on, then he can expect to earn:
Earnings = $40 + $7 x tt
For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.
Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.
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Lorraine prepared a 1.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars
can Lorraine fill?
A.) 03 jars
B.)O4 jars
C.)05 jars
D.)O8 jars
If 1 gallon equals 4 quarts, Lorraine fill can 4 jars. Hence option B is the correct option.
What is the unit of an object?
The user can describe locations and dimensions in a wide range of various coordinate systems using unit objects. Every drawing is done in relation to a viewport, and the units determine the coordinate system to use there. "npc" is one example of a unit (coordinate system).
Given Lorraine filled a pot with tomatoes and the volume of the pot is 1.5 gallons.
She wants to fill the tomatoes in jars. The volume of the jar is 1.5 quarts.
1 gallon is equal to 4 quarts.
1.5 gallons is equal to 1.5 × 4 quarts = 6 quarts.
The number of jars that are filled with tomatoes is 6 quarts/ 1.5 quarts = 4.
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A) A sequence is defined using this term-to-term rule.
Un+1 = 2un+ 20
If uy = 8, find u2
b) Another sequence is defined using this term-to-term rule,
unty = ku,+r
where k and rare constants.
Given that u, = 37, uz = 188 and ug = 943, find the value of k and
the value of r.
The Value of the two constants K and R are 5 and 3 respectively.
a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:
u2 = 2u1 + 20 = 2(8) + 20 = 36
So u2 = 36.
b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:
u2 = ku1 + ru3 = ku2 + rSubstituting in the given values:
u2 = 188 = k(37) + ru3 = 943 = k(188) + rSolving for r and k, we get:
k = 5 and r = 3.
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1
5.
grilato 6.
7.
PS).
se
8.
9.
10.
11.
-2619 12.
t-
13.
to
7-
14.
otal deposit for Problems 5 through 19.
Currency
Tens Fives Ones Half Dollars Quarters Dimes Nickels Pennies Checks Total
$96.23 $
6.51
63 874.56
85
123.65
347.98
134.97
0
43.44
5
168.14
31
777.50
154 123.19
12 11
32
9
40
54
75
32
8
7
11
13
10
12
1
16
67
3
133 19
8
15
23
74
0
9
6
7
4
27
11
9
40
15
13
7
0
3
13
34
or
Coins
18
32
56
13
9
5
7
12
11
62
21
86
11
6
8
17
3
319
45
70
27
13
2
13
7
99
0
37
15. Jess Norton stopped at an ATM location to deposit 2 one hundred-dollar
bills and checks for $474.85 and $321.15. He received $50.00 in cash.
16. Olive Baker, Spirit club treasurer, deposits the club's receipts. She has 4
checks for $10.00 each, 12 for $7.50, and cash consisting of six 20-dollar
bills, five 10-dollar bills, and 18 one-dollar bills.
17. Cyndi Winer deposits three checks for $425.22, $883.99, and $57.05. She
also deposits cash of 45 one-dollar bills, 15 five-dollar bills, and 12 ten-
dollar bills. The change deposited includes 28 quarters, 16 dimes, 19
nickels, and 65 pennies. She would like to receive $60.00 in cash.
18. Elias Rubio deposits three checks for $598.20, $2,274.26, and $3,248.79.
His cash consists of 75 one-dollar bills, 78 five-dollar bills, 33 ten-dollar
bills, 80 quarters, 32 dimes, 95 nickels, and 5 pennies. He would like to
receive $40.00 in cash.
The total cost of Jess Norton is $995.85 and the total cost of Olive Baker is $678 .
What is total cost ?
The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula.
In economics, total cost is the total of all expenses a company incurs to produce a particular level of output.
The average cost, or the typical sum of money required to create a unit, can be determined using the cost function. The average cost function is A(x)=C(x)x, where x > 0 and C is the constant. Calculating the average cost per unit requires dividing the total cost by the quantity of units produced.
For Jees Norton,2 one hundred dollar bills = 2 x $100
= $200
Total deposits = 2 one hundred dollar bills + Checks
= $200 + $474.85 + $321
= $995.85
For Olive Baker,
Checks amount = $100 x 4
= $400
12 for $7.5
= 12 x $7.5
= $90
Six 20-dollar bills = 6 x $20
= $120
Five 10-dollar bills = 5 x $10
= $50
Eighteen 1-dollar bills = 18 x $1
= $18
Total deposits = $400 + $90 + $120 + $50 + $18
= $678
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18
The table shows information about the numbers of points scored by 28 students in a quiz.
Number of points
0
1
2
3
4
5
(a) Find the modal number of points.
(b) Work out the total number of points scored.
Frequency
5
4
5
5
6
3
(1)
Consequently, this student's quiz results have a median, or "middle," value of 16.
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.
Exam results:
9, 13, 20, 15, 18, 17
Number the rows and columns.
9, 13, 15, 17, 18, 20
Calculate the "middle" value:
9, 13, 15, 17, 18, 20
If there are two middle values, put them together and divide by two.
15 + 17 = 32
32/2 = 16
Consequently, this student's quiz results have a median, or "middle," value of 16.
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Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.
The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.
To compute this, first convert 5 to binary and base-4:
5 in binary: 101
5 in base-4: 11
Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.
To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:
11 in binary: 1011
11 in base-4: 111
Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.
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Which planets have surface features (e.g., mountains, canyons, volcanoes, etc.)?
Answer:
The answer is Terrestrial planets
Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?
A) the terminal point of vector cu lies in quadrant II
B) the terminal point of vector cu lies in quadrant III
C) the terminal point of vector cu lies in quadrant I
D) the terminal point of vector cu lies in quadrant IV
The terminal point of vector cu lies in quadrant III.
Option B is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
p = (0, 0) and Q = (9, 12)
u = PQ = (9 - 0, 12 - 0) = (9 , 12)
Now,
cu = (9c, 12c)
where c < 0
If c = -1
cu = (-9, -12)
The coordinates (-x, -y) lie in quadrant III.
(-9, -12) is in quadrant III.
Thus,
Vector cu lies in quadrant III.
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A box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. Assume the plain donuts are identical, and the chocolate donuts are identical. How many visually distinct arrangements of the donuts are there?
If a box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. The number of visually distinct arrangements of the donuts that are there is: 60.
How to find the number of visually distinct arrangements?Using this formula to find the number of visually distinct arrangements of the donut that are there.
Number visually distinct arrangements = Box of donuts!/ Plain donuts! × Chocolate donuts! × Blueberry donut!
Let plug in the formula
Number visually distinct arrangements = 6!/ 3! × 2! × 1!
Number visually distinct arrangements = 720/ 6 ×2 × 1
Number visually distinct arrangements = 720 /12
Number visually distinct arrangements = 60
Therefore the number of Number visually distinct arrangements is 12.
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What are the three types of algorithms?
The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.
What is Brute Force algorithm?As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.
In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.
A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.
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In a circle, an angle measuring 5. 5 radians intercepts an arc of length 8. 4. Find the
radius of the circle to the nearest 10th.
The circle's radius is equal to 3.659 or 3.7.
What is Radius?A circle's or a sphere's radius is the length of the line between the center and the edge.
From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.
Its diameter is halved by its length.
A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I
t is a crucial component of spheres and circles and is frequently abbreviated as "r."
When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.
Hence, The circle's radius is equal to 3.659 or 3.7.
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Which of these is the absolute value parent function?
A. f(x) = x
OB. f(x) = 2ˣ
OC. f(x) = x²
OD. f(x) = Ixl
Option D) f(x) = |x|, is Correct.
What is parent function?
A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.
The absolute value parent function is represented by the following function:
D. f(x) = |x|
The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.
A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function
B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function
C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function
D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.
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Michael's pumpkin farm sold 75 pumpkins on October 24 that day they made $600. What did Michael charge for each pumpkin?
Answer:
$8.
Step-by-step explanation:
right!!
L) simplify
cos²x - sin²x
Answer:
cos(2x)
Step-by-step explanation:
To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).
This identity can be derived by using the double angle formula for cosine:
cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x
Therefore, the expression cos²x - sin²x can be simplified to cos(2x).
(NEED HELP ASAP!!)
What are the coordinates of the focus of the parabola?
A: (8, 6)
B: (-8, 6)
C: (-8, 2)
D: (8, 2)
Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]