The polynomial f(x)=x^4+3x^2+7 has four roots over the complex numbers according to the fundamental theorem of algebra, counting roots with multiplicity greater than one as distinct. This is consistent with the theorem's stipulation that a polynomial of degree n has exactly n roots.
Explanation:The subject of this question is the fundamental theorem of algebra which belongs to the domain of Mathematics, specifically the study of polynomials. As indicated in the question, we have a function, f(x), which represents a polynomial of degree 4 as shown by the highest exponent. According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicity. This means a function f(x)=x4+3x2+7, which is a fourth degree polynomial, will have four roots over the complex numbers.
This is also true per the theorem when roots with multiplicity greater than one are considered distinct. For example, f(x)=x2 is a polynomial of degree 2; it has two roots, both are zero, hence the two roots are counted as two distinct roots.
While the quadratic formula is used for finding roots of second degree polynomials, it is not directly applicable here since we are dealing with a fourth degree polynomial.
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Please help! Thanks
Answer:
not geometric
Step-by-step explanation:
A geometric series is one where the nth term is multiplied by a common ratio to get the n+1 term.
1 1/2 1/4 1/8 1/16 .....
is a geometric series. the fourth term (1/8) is multiplied by 1/2 to get 1/16.
The series you have been given is not geometric. It reduces to
1/3 1/4 1/5 1/6 which does not give you a common number to multiply the nth term to get to the n+1 term.
Colin and Jezebel are employees at Game Zone. They recorded the number of computer games they sold each week for the past 9 weeks. Colin 15 20 21 9 3 16 9 14 17 Jezebel 10 14 20 11 4 26 5 8 20 (a) All of the games sold of which person had the greatest spread? Explain how you know. (b) The middle 50% of the games sold of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Colin's and Jezebel's sold games?
Answer:
Step-by-step explanation:
1. a) spread is the range which is given as Max(S)- Min(S)
Colin =
[tex]3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\[/tex]
Jezebel=
[tex]=4,5,8,10,11,14,20,20,26\\\\range=26-4=22[/tex]
Jezebel had a greatest spread.It was 22 while for Colin was 18
2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data
Colin=
[tex]=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\[/tex]
⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5
Jezebel
[tex]=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20[/tex]
⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5
Colin had the least spread of 9.5 as compared to Jezebel who had 13.5
c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.
Based on a poll of 100 citizens, a community action group claims that 38% of the population is in favor of the construction of a senior center using tax dollars. A business group claims that the poll is not valid and that 65% of the citizens favor the construction of the senior center using tax dollars.
To determine whether this sample supports the population proportion of 0.38, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.65. The minimum sample proportion from the simulation is 0.42, and the maximum sample proportion from the simulation is 0.72.
The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
Answer:
(0.55, 0.75)
Step-by-step explanation:
The range can be estimated to be 6 standard deviations wide. Therefore, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
The margin of error is ±2σ, so:
ME = ±0.10
Therefore, the interval estimate is:
(0.65 - 0.10, 0.65 + 0.10)
(0.55, 0.75)
The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
B.) Because the margin of error is ±2σ, therefore, we can write,
Margin Of Error = (±0.05)×2 = ±0.10
C.) The interval can be estimated as,
Interval = 0.65±0.10
= 0.65-0.10, 0.65+0.10
= 0.55, 0.75
Hence, the interval estimate of the true population proportion is (0.55, 0.75).
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A park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 \text{ meters}10 meters10, space, m, e, t, e, r, s.
Answer:
What is the area AA of each section of the circle?
Give your answer in terms of pi.
A = 25πm²
Step-by-step explanation:
Given the radius of the circle to be 10
The question is to find area of each sections of the circle .
The formula for calculating the area of a circle is area equals to πr²
A = πr²
Given r = 10m
The next step is to substitute the values into the equations
A = π (10m)²
A = 100πm²
Since the circle is divided into 4 equal sections, we need to find the area of each sections by dividing the complete area of the circle by 4
Therefore,
A = 100πm²/4
A = 25πm²
Answer:
25π[tex]m^{2}[/tex]
Step-by-step explanation:
Help with this question, please! I don't understand!
Answer:
m∠LPM = 60°
Step-by-step explanation:
The measure of the angle facing the marked arcs is the average of the measures of the arcs:
m∠LPM = (1/2)(40° +80°) = 60°
Given: f(x) = 2x + 5 and g(x) = x2 and h(x) = -2x
h(g(f(x))) = ?
Answer:
-2(2x +5)² = -8x² -40x -50
Step-by-step explanation:
Evaluate from the inside out, according to the order of operations.
h(g(f(x))) = h(g(2x +5)) = h((2x +5)²) = -2(2x +5)² = -2(4x² +20x +25)
= -8x² -40x -50
I personally prefer the factored form, but that is not considered "simplified."
Help me with this please don’t understand need answers please !
Answer:
see the attached for the sumsthe magic number (sums of rows, columns, diagonals) is -6Step-by-step explanation:
The directions tell you what to do and give an example. That work is to be repeated 15 more times. The work is tedious, at best. I found it slightly less tedious to enter the 64 numbers into a spreadsheet and let it do the sums. See the attached for the result.
At the bottom of the array are the sums of columns. At the right are the sums of rows. The upper right and lower left numbers are the sums of the corresponding diagonals.
The "pattern" is that the sums are all -6, which is what you expect from a magic square.
Point O is the center of the circle in the diagram. What is m/_BCA
Answer:
< BCA = 70
Step-by-step explanation:
The complete central angle of a circle is 360 degrees. The given portion is 250 degrees.
What is left over? BOA = 360 - 250 = 110
Tangents always meet the radius at 90 degrees. Since there are two tangents <CAO = <BAO = 90 degrees.
So piecing it all together, the equation becomes
<BAO + CAO + BAO + ACB = 360
110 + 90 + 90 + <ACB = 360
290 + <ACB = 360
<ACB + 290 - 290 = 360 - 290
ACB = 70 degrees
Please help me ..... (:
Answer:
162.43
Step-by-step explanation: I hope its helps it's been a couple of years since I have done geometry
Answer:
the total area of the octagon is 8(20.3 in²), or 162.4 in²
Step-by-step explanation:
A regular octagon has 8 pie-shaped sections. Each is triangle of height 7 in and base 5.8 in.
Thus, the area of each such section is, by A = (1/2)(b)(h(),
A = (1/2)(5.8 in)(7 in) = 20.3 in².
There are 8 such sections.
Thus, the total area of the octagon is 8(20.3 in²), or 162.4 in²
Simplify Radicals
What is the difference of 25√7 - 2√63
Answer:
[tex] 19\sqrt{7} [/tex]
Step-by-step explanation:
[tex] 25\sqrt{7} - 2\sqrt{63} = [/tex]
[tex] = 25\sqrt{7} - 2\sqrt{9 \times 7} [/tex]
[tex] = 25\sqrt{7} - 2\sqrt{9} \sqrt{7} [/tex]
[tex] = 25\sqrt{7} - 2\times 3 \sqrt{7} [/tex]
[tex] = 25\sqrt{7} - 6 \sqrt{7} [/tex]
[tex] = 19\sqrt{7} [/tex]
a chemical company makes two brands of antifreeze. the first brand is 40% pure antifreeze, and the second brand is 65% pure antifreeze. in order to obtain 150 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used ?
first brand: ? gallons
second brand: ? gallons
Answer:
first brand 55 gallons
second brand 95 gallons
Step-by-step explanation:
A playing field is rectangular with a length of 100 yards and a width of 53 yards, 1 foot. If a player runs diagonally across this rectangle, how far will he run? [Hint: Use units of feet to perform your calculations.]
How far has the player run?
First convert yards to feet.
1 yard = 3 feet.
100 x 3 = 300 feet long.
53 x 3 = 159 + 1 = 160 feet wide.
Now use the Pythagorean theorem to find the diagonal.
x^2 = 300^3 + 160^2
x^2 = 90000 + 25600
x^2 = 115600
x = √115600
x = 340 feet
Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weighs 364 pounds and Kevin weighs 150 pounds. The capacity of the elevator is 2,000 pounds. If six sacks are to be taken at a time, what should be the weight of each sack? Question 6 options: at the most 308 pounds at least 308 pounds exactly 308 pounds at the most 803 pounds
Answer:
at the most 308 pounds
Step-by-step explanation:
Given
Weight of each sack = 364 pounds
Weight of Kevin = w = 150 pounds
Weight that lift can take = 2000 pounds
In order to find the weight of sacks that can be put into the elevator we have to subtract the weight of Kevin from the capacity of the lift.
So, actual weight of sacks that can be taken =[tex]2000-150[/tex]
= 1850 pounds
As 6 sacks have to be taken, to find the weight of one sack
Required weight of one sack = [tex]\frac{1850}{6}[/tex]
= 308.33 pounds
So, each sack has to weigh at the most 308 pounds ..
The correct option is a. at the most 308 pounds. Each sack should weigh at most 308 pounds to ensure that the elevator's weight limit is not exceeded when Kevin is in the elevator with six sacks.
To determine the weight each sack can be so that the elevator capacity is not exceeded, we must consider the total weight limit of the elevator and the weight of Kevin.
The elevator has a capacity of 2,000 pounds. Kevin weighs 150 pounds, and he will be riding the elevator with the sacks. Therefore, the total weight available for the sacks is:
2,000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1,850 pounds.
If six sacks are to be taken at a time, we divide the total available weight by the number of sacks to find the maximum weight each sack can have:
1,850 pounds / 6 sacks = 308.333... pounds.
Since the weight of each sack must be a whole number, we round down to the nearest whole number, which is 308 pounds. This ensures that the elevator's capacity is not exceeded.
Therefore, This allows for a small margin of error in the weight of the sacks, which is safer and more practical than having the sacks weigh exactly 308 pounds each.
This table shows how many sophomores and juniors attended two school events. A student is selected randomly from this group.
Answer: B. 0.45
Step-by-step explanation:
From the given table, the total number of students = 137
The number of students are sophomores =35+42=77
Let A be the event that students are sophomores.
Then probability that students are sophomores is given by :
[tex]\text{P(A)}=\dfrac{77}{137}[/tex]
The number of sophomores who attended the jazz concert = 35
Let B be the event that students attended the jazz concert .
The probability that students attended the jazz concert and are sophomores is given by :
[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]
Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-
[tex]P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45[/tex]
The Jeffer's company has a debt ratio (total debt to total assets) of 0.365. If their total assets are $739,000, what is their total debt?
A) $269,735
B) $469,265
C) $1,008,735
D) $2,024,657
The answer is D 2,024,657
Answer:
A
Step-by-step explanation:
0.365 x 739,000= 269,735
Please help me withe this proof as well.
- D is the midpoint of AB, E is the midpoint of BC
Answer: A. Given
I left off DB||FC because that's not given. But we can construct it.
Construct line through C parallel to AB. Extend DE to intersect and call the meet F.
- DB || FC
By Construction
----
- Angle B congruent to angle FCE
Answer: D. Alternate Interior Angles
We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE
- angle BED congruent to angle CEF
Answer: H. Vertical angles are congruent
When we get lines meeting like this we get the usual congruent and supplementary angles.
- Triangle BED congruent to Triangle CEF
Answer: F. Angle Side Angle
We have BE=CE, DBE=FCE, BED=CEF
- DE congruent to FE and DB congruent to FC
Answer: C. CPTCTF
Corresponding parts ...
- AD congruent to DB and DB congruent to FC therefore AD congruent to FC
Answer: E. Transitive Property of Congruent
Things congruent to the same thing are congruent
- ADFC is a parallelogram
Answer: G. AD and FC are congruent and parallel
Presumably this is a theorem we have already established.
- DE || AD
Answer: B. Definition of a parallelogram
Reposting because I seriously need help. Please, this is time sensitive!
Which ordered pair is the best estimate for the solution of the system of equations?
{y=4x−19.4 y=0.2x−4.2
(4, −3.4)
(4.9, 0)
(−3.5, 4)
(4.9, −3.5)
The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y = 4x − 19.4 ...1
y = 0.2x−4.2 ...2
From equations 1 and 2, then we have
4x - 19.4 = 0.2x - 4.2
3.8x = 15.2
x = 4
Then the value of the variable 'y' will be calculated as,
y = 4 (4) - 19.4
y = 16 - 19.4
y = - 3.4
The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
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convert y-(51)=15.2(x-(2)) to standard form
I don’t know what the answer is I wish I could help
The answer is y=56.2x-112.4
This rectangular prism is intersected by a plane that contains points D, E, K, and L.
What is the perimeter of the cross section?
Enter your answer in the box. Round only your final answer to the nearest tenth.
m
A rectangular prism with height 5 meters, length 12 meters, and width 4 meters. The vertices are labeled as G, D, H, L, E, F, J, and K.
The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m
Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)
The perimeter of the cross-section is 36.8 m.
Calculations and Parameters:Given that the length of diagonal EK is
[tex]\sqrt{(5^2 + 4^2) }[/tex]
≈ 6.403m
Thus, the perimeter would be
2*(12 + 6.403)
→ 36.8 m.
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The sides of triangle ABC are 3, 4, and 5 inches long. How far is the incenter of the triangle from the circumcenter of the triangle?
Answer:
(√5)/2
Step-by-step explanation:
In the attached figure, we have labeled the circumcenter point D and the incenter point E. The points of tangency of the incircle with sides AB, BC and CA are labeled G, H, and F, respectively.
The distances from any vertex to the two points of tangency from that vertex are the same. So, AG = FA, BG = BH, and CF = CH. If we call the radius of the incircle "r", then we have ...
AG = FA = r, BG = BH = 3-r, CF = CH = 4-r
so the side length BC is ...
BC = BH +CH = (3-r) +(4-r) = 7-2r
We already know that side length BC is 5, so ...
5 = 7 -2r
r = (7 -5)/2 = 1
Of course, the circumcenter of a right triangle is the midpoint of the hypotenuse, so the circumradius "R" is 5/2 = 2.5.
The formula for the distance between the two centers is ...
d = √(R(R -2r)) = √(2.5(2.5 -2)) = √1.25 = (√5)/2
_____
Comment on this answer
We have used a formula for the center-to-center distance found using a web search. The attached diagram shows the coordinates of the two centers, so the distance can be found from those. It is the same.
A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.251.251, point, 25 meters thick.
Answer:
S(t) = 2 - 0.25*t
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.
When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.
S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).
Therefore the equation formed will be linear.
The equation will be of the form y = mx + b
Here S(t) = mt + b
Here m is the slope which is the rate at which ice is melting.
Putting t = 0
S(t) = 2
Putting t = 3,
S(t) = 1.25
Therefore, m*0 + b = 2 or, b = 2
and 3m + b = 1.25
or, 3m = 1.25 - 2 = -0.75
or, t = -0.25
Hence, function's formula = S(t) = -0.25*t + 2
i.e. S(t) = 2 - 0.25*t
Answer:
y = 2 - 0.25x
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.
When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.
S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).
Therefore the equation formed will be linear.
The equation will be of the form y = mx + b
Here S(t) = mt + b
Here m is the slope which is the rate at which ice is melting.
Putting t = 0
S(t) = 2
Putting t = 3,
S(t) = 1.25
Therefore, m*0 + b = 2 or, b = 2
and 3m + b = 1.25
or, 3m = 1.25 - 2 = -0.75
or, t = -0.25
Hence, function's formula = S(t) = -0.25*t + 2
i.e. S(t) = 2 - 0.25*t
ANSWER INCLUDED: What is the solution of log3x + 4 4096 = 4?
x=-1
x=0
x=4/3
x=3
We solve for x by simplifying both sides of the equation, then isolate the variable.
ANSWER:
C (x=4/3)
Answer:
C [tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
The given logarithmic equation is:
[tex]\log_{3x+4}(4096)=4[/tex]
We rewrite in exponential form; to get;
[tex]4096=(3x+4)^4[/tex]
We rewrite the LHS as a certain natural number exponent 4.
[tex]8^4=(3x+4)^4[/tex]
The exponents are the same, hence the bases must also be the same.
[tex]\implies 3x+4=8[/tex]
[tex]\implies 3x=8-4[/tex]
[tex]\implies 3x=4[/tex]
Divide both sides by 3;
[tex]\implie x=\frac{4}{3}[/tex]
The correct answer is C
please help 80 points for 2 questions please answer all parts and show your work! due today!!!!
Part A
The scatterplot is shown the attachment.
Part B
Using a linear regression equation that models Patrick's referrals has a positive slope.
This means that, there is a positive relation between time(number of days),x and the number of personal recommendations, y.
In other words, as the number of days increases, the number of personal recommendations also increases.
Question 2.
The given functions are:
[tex]y=x^2+3x-5[/tex]
[tex]y=4x+1[/tex]
To find the point where the graphs of these functions intersect,we solve the two equations simultaneously.
We equate the two equations to get:
[tex]x^2+3x-5=4x+1[/tex]
[tex]x^2+3x-4x-5-1=0[/tex]
[tex]x^2-x-6=0[/tex]
Factor to obtain:
[tex](x-3)(x+2)=0[/tex]
x=3 and x=-2
We put x=-2, into [tex]y=4x+1[/tex] to get;
[tex]y=4(-2)+1=-7[/tex]
when x=3 [tex]y=4(3)+1=13[/tex]
Therefore the graphs intersect at (-2,-7) and(3,13).
Yes, solution is correct.
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
x =
Answer:
67.1
Step-by-step explanation:
we need to use trig to work this out
(Soh Cah Toa)
The answer will be 67.11461952384143
to nearest tenth its
67.1
Answer:
x = 67.1°
Step-by-step explanation:
Cos(x) = Adj./Hypo.
Cos(x) = 28/72
Cos(x) = 0.3889
x = 67.1°
Which graph shows a car traveling at 50 miles per hour?
Answer: The answer to your question would be the third graph to your left
Step-by-step explanation: because when you calculate the rate of change from these points:
(50,1)
(100,2)
(150,3)
(200,4)
The rate of change would be 50 miles/ km per hour
Finding the slope formula: [tex]m= y2-y1/ x2-x1[/tex]
And when you take any two points from the graph, for example: (50,1) and (200,4), it would look like this:
[tex]\frac{200-150}{4-1}= 50/1= 50 miles/km per hour[/tex]
The correct graph is 3rd.
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Considering the 3rd graph, the coordinates are :-
(50,1)
(100,2)
(150,3)
(200,4)
Finding the slope = (y₂-y₁) / (x₂-x₁)
considering the points (50,1) and (200,4), slope =
slope = 4-1 / 200-50 = 1/50
Since the slope shows the rate, and the rate of change would be 50 miles/ km per hour
Hence, the correct graph is 3rd one.
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What do a rectangle and a rhombus have in common? Select all that apply. The opposite sides are parallel. They have four right angles. Their angle measures add to 360°. They have four congruent sides. you can pick more than one so plz pick more than one be positive
Final answer:
A rectangle and a rhombus both have opposite sides that are parallel and their interior angles add up to 360 degrees. They differ in that a rectangle has four right angles and a rhombus has four congruent sides, which are not necessarily attributes they share unless they are both squares.
Explanation:
Both a rectangle and a rhombus share some properties as they are both quadrilaterals. Firstly, the opposite sides are parallel in both shapes. Secondly, the angle measures add to 360° which is a property of all quadrilaterals. However, they differ in other aspects; a rectangle has four right angles, whereas a rhombus generally does not unless it's a square. A rhombus has four congruent sides, and a rectangle does not unless it's a square. Therefore, the correct selections based on their commonalities are that the opposite sides are parallel and their angle measures add up to 360°.
Which of the following illustrates the truth value of the given conditional statement? If 3 + 2 = 5, then 5 + 5 = 10. T F → F T T → T F T → T F F → F
Answer:
T T → T
Step-by-step explanation:
A conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 3 + 2 = 5 which is true and 5 + 5 = 10 which is also true.
how do you find the vertex of 2x+y^2=0
[tex]\bf \textit{vertex of a horizonal parabola, using f(y) for "x"} \\\\ x=\stackrel{\stackrel{a}{\downarrow }}{a}y^2\stackrel{\stackrel{b}{\downarrow }}{+b}y\stackrel{\stackrel{c}{\downarrow }}{+c} \qquad \left(f\left(-\cfrac{ b}{2 a}\right)~~~~ ,~~~~ -\cfrac{ b}{2 a} \right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 2x+y^2=0\implies 2x=-y^2\implies x=\cfrac{-y^2}{2}\implies x=\stackrel{\stackrel{a}{\downarrow }}{-\cfrac{1}{2}}y^2\stackrel{\stackrel{b}{\downarrow }}{+0}y\stackrel{\stackrel{c}{\downarrow }}{+0} \\\\\\ -\cfrac{b}{2a}\implies -\cfrac{0}{2\left(-\frac{1}{2} \right)}\implies 0\qquad therefore\qquad (f(0)~~,~~0)\implies \stackrel{vertex}{(0,0)}[/tex]
you can see it this way, x = -(1/2)y² is just a horizontal parabola opening to the left-hand-side, the -1/2 is just a stretch transformation of the parent function x = y², but as much as it stretches, their vertex is the same, at the origin.
What is the x-coordinate of the solution of the following system of equations?
3x + y = 6
x - y = 6
Answer:
x = 3
Step-by-step explanation:
By rearranging the equations,
y = 6 - 3x
y = x - 6
x - 6 = 6 - 3x
4x - 6 = 6
4x = 12
x = 3
Answer:
x = 3
Step-by-step explanation:
Follow the elimination method like so:
3x + y = 6 The Ys cross each other out.
x - y = 6 Add to get:
4x = 12
4x = 12 Divide to get:
4 4
x = 3
Hope this helps! :)
30 points!!!!
Given the hexagon below, find the measures of angles 1 through 7.
1: 107
2: 73
3; 123
4: 62
5: 116
6: 16
7: 92
The missing angle measures in the hexagon are:
∠5 = 116°
∠4 = 62°
∠3 = 123°
∠2 = 73°
∠6 = 16°
∠7 = 92°
∠1 = 107°
What is a Hexagon?A hexagon is a six-sided polygon, whose sum of interior angles equals 720°.
∠5 = 180 - 54 = 116° (supplementary angles)
∠4 = 180 - 118 = 62° (supplementary angles)
∠3 = 180 - 57 = 123° (supplementary angles)
∠6 = 180 - 164 = 16° (supplementary angles)
∠7 = 180 - 88 = 92° (supplementary angles)
∠1 = 720 - 116 - 118 - 123 - 164 - 92 = 107° (sum of interior angles in a hexagon )
∠2 = 180 - 107 = 73° (supplementary angles)
Learn more about hexagon on:
https://brainly.com/question/1615720
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