What is the graph of the function f(x) = the quantity of negative x squared plus 4 x plus 6, all over x plus 4? I am stressing over this question is just confusing for me help me please
Answers
Here is the graph:
Go to WolframAlpha and check by yourself
Answer:
The graph of the function is given below.
We are given the function, [tex]f(x)=\frac{-x^2+4x+6}{x+4}[/tex]
We see that, when x= 0, the value of the function is,
[tex]f(0)=\frac{-0^2+40+6}{x+0}[/tex] i.e. [tex]f(0)=\frac{6}{4}=\frac{3}{2}[/tex].
So, the y-intercept is [tex](0,\frac{3}{2})[/tex].
Also, the zeroes of the function are given by,
[tex]f(x)=\frac{-x^2+4x+6}{x+4}=0[/tex]
i.e.[tex]-x^2+4x+6=0[/tex]
i.e. (x+1.162)(x-5.162)=0
i.e. x= -1.162 and x= 5.162
Thus, the x-intercept are (0,-1.162) and (0,5.162).
The graph of the function is given below.
Related Questions
The sum of two real numbers is 18 and the product is 70. what are the two numbers?
Answers
x+y=18......i
xy=70.........ii
from i
y=18-x.....iii
from ii
y=70/x......iv
substituting iii in iv we get:
70/x=18-x
multiplying through by x;
70=18x-x^2
x^2-18x+70=0
x=12.3 or 5.7
thus:
x=12.3 and y=5.7
The trigonometric form of a complex number is unique - True or false?
Answers
Answer with explanation:
let, Z= a + i b,be a complex number.
Where, a = r cos A
b= r sin A
[tex]a^2 + b^2=(r cos A)^2 +(r sin A)^2\\\\ a^2 + b^2=r^2(cos^2 A+sin^2 A)\\\\ a^2 + b^2=r^2\\\\r=\sqrt{a^2 + b^2}[/tex]
[tex]Z=r cos A + i r sin A\\\\Z=r(cos A + i sin A)\\\\ Z=re^{iA},\text{Where}, e^{i\alpha }=cos \alpha +i sin\alpha[/tex]
Now, if we replace A, by, 2 kπ + A,in the above equation,where k is any positive integer,beginning from ,0.k=0,1,2,3,4,....
[tex]Z=r cos (2k\pi +A) + i r sin(2k\pi + A)\\\\Z=r[cos (2k\pi +A) + i sin(2k\pi + A)]\\\\ Z=re^{i(2k\pi +A)}[/tex]
So, for different value of , k ,there will be Different Complex number.
→So,the Statement: The trigonometric form of a complex number is unique = False
The trigonometric form of a complex number is unique is a false statement. Check the reason why it is false below.
Why is the trigonometric form of a complex number not special?The trigonometric form of a complex number is commonly seen as the polar form of that number.
This is due to the fact that there are lots of infinite choices are often made for θ and as such the trigonometric form of a complex number is said to be not unique in any way.
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A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis?
Answers
VW is the major axis
ST is the minor axis
P is a point on the ellipse
A and B are the foci (or focus)
The length of major axis is given by either VA+AW or AP+BP
One useful fact to know that AP+BP is constant wherever the point P is on the ellipse
We know that the distance of the point 'P' from one focus is 11 units and from the other focus is 7 units, so we know the length of AP and BP.
Hence, the length of major axis is 11+7=18 units
A rectangular flower garden has area 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?
Answers
Area = Length x Width
where length = x ft
width = x - 4 ft
area = 32 ft^2
32 = x (x -4)
32 = x^2 - 4x
Solving for the positive value of x,
x = 8 ft = length
width = x -4 = 8 - 4 = 4 ft
Perimeter = 2(length) + 2(width) = 2(8) + 2(4) = 24 ft
The perimeter of the garden is 24 feet.
What is a Rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
How to solve it?We have, an area is 32 and width is 4,
so, the length will be 32/4 = 8 feet.
The perimeter will be 2(8+4) = 2(12)= 24 feet.
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The sum of six consecutive odd numbers is 204. What is the fourth number in the sequence
Answers
6x + 30 = 204
6x = 174
x = 29
six consecutive odd numbers are 29,31,33,35,37,39
answer
the fourth number in the sequence is 35
2n+1 , 2n+3, 2n+5, 2n+7, 2n+9,2n+ 11 and these add up to 204
12n + 36 = 204
12n = 168
n = 14
so fourth number in the sequence is 2(28) + 7 = 63
In which section of the number line is √55?
Answers
________________________________________________________
Explanation:
________________________________________________________
The question asks:
________________________________________________________
"In which section of the number line is √55?"
________________________________________________________
We know that: 7² = 49 ; 8² = 64 .
So, 7 < √55 < 8 ; So, √55 will be in between 7 and 8.
So, √49 < √55 < √64 .
55 - 49 = 6 .
64 - 55 = 9 .
So, there is greater difference between the radicands in
√64 and √55 ; compared to the difference in radicands between
√49 and √55 .
________________________________________________
This tells us that the correct answer is:
________________________________________________
[A] { in the figure shown: "7.0 - 7.5" } ;
________________________________________________
rather than: [B]: { "7.5 - 8.0" } .
________________________________________________
Answer:
A. Section A
Step-by-step explanation:
imagine said it was correct
Do the ratios 1/12 and 8/96 form a proportion? Explain.
Answers
cross multiply
(1)(96) = (8)(12)
96 = 96
yes, this is a true proportion...keep in mind, proportions are nothing but equivalent fractions
1 : 12 = 8 : 96
It's not all that hard, all you need to know is the ''cross-multiplication'' methods for testing this kind of stuff.
1 : 12 = 8 : 96 ?
1 * 96 = 12 * 8 ?
96 = 96 ?
96 = 96 ==> CORRECT
In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl??
Answers
The probability that at least one of them is a girl is about 0.977
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Probability.
Given:
The true probability of a baby being a boy P(B) = 0.534
The true probability that all of six randomly selected births in the country are boys is :
[tex]P(6B) = P(B) \times P(B) \times P(B) \times P(B) \times P(B) \times P(B)[/tex]
[tex]P(6B) = \boxed {(P(B))^6}[/tex]
The true probability that at least one of them is a girl is:
[tex]P(G\geq 1) = 1 - P(6B)[/tex]
[tex]P(G\geq 1) = 1 - (P(B))^6[/tex]
[tex]P(G\geq 1) = 1 - (0.534)^6[/tex]
[tex]P(G\geq 1) \approx \boxed {0.977}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
The probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
What is Probability in Mathematics?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P (Event A) = n(A)/n(S)
where -
n(A) → Number of outcomes favorable to event A.
n(B) → Total number of possible outcomes.
Given is the true probability of a baby being a boy. Its value is -
P(A) = 0.534
Assume that for the next six randomely selected births, the probability that it will be a baby boy is P(B). In one of the six randomely selected births, the probability that it will be a boy is 0.534. Therefore, the probability of being a boy in all the six cases will be -
P(B) = [P(A)]⁶
P(B) = 0.023
Now, for at least one of them to be girl, the probability of the event will be -
P(C) = P(B)' = 1 - 0.023 = 0.98
Therefore, the probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
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Which of the following ordered pairs is a solution to the equation 2x+7y=8
Select one:
a. (3, -2)
b. (2, -3)
c. (-3, 2)
d. (0, 4)
Answers
Conjecture for interior angles of complex polygons
Answers
Final answer:
The conjecture for interior angles of complex polygons involves using the formula (n-2)×180 degrees for regular polygons and more complex considerations for 3D shapes like pentagonal bipyramids or square antiprisms. As the number of sides increases, calculations become more intricate and the interior angles can approach 180 degrees in very large polygons.
Explanation:
The question involves making a conjecture for the interior angles of complex polygons. A commonly used theorem related to this is that the sum of the interior angles of a polygon can be found using the formula (n-2)×180 degrees, where n is the number of sides in the polygon. For instance, to find the sum of the interior angles of a pentagon (a polygon with five sides), we calculate (5-2)×180 degrees = 540 degrees. As the number of sides increases, our calculations can become more complex, especially when dealing with non-regular polygons (where the sides and angles don't all have the same length/measure).
When considering the interior angles of complex geometries like a pentagonal bipyramid or a square antiprism, it's essential to recognize that their interior angles may involve multiple planes and hence cannot be calculated using the simple 2D polygon interior angle sum formula. These shapes involve three-dimensional calculations and often require advanced geometry or trigonometry to dissect into understandable components.
Considering large numbers of sides and complex figures, the interior angle measures can approach different limits. For example, as the number of sides I becomes very large, the interior angle measures can become very close to 180 degrees, which is suggested by the idea that for a polygon with infinitely many sides (approaching a circle), each interior angle would be 180 degrees.
Shawn wants to buy a cd player that costs $48.00. If he has already saved $30.00, what percent of the price of the cd player has he saved?
Answers
the answer is 62.5%
100%/x%=48/30
Multiply both sides by x.
(100/x)x=(48/30)x
100=1.6x
Divide both sides by 1.6.
100/1.6=x
62.5=x
30 is 62.5% of 48
A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) represents any point on the directrix.
What are the steps required to find the equation of the parabola?
Answers
We have the focus [tex](a,b) = (2, -0.5)[/tex]
The point [tex]P(x,y)[/tex]
The directrix, c at [tex]y=-1.5[/tex]
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; [tex](2, -0.5)[/tex] and [tex](x,y)[/tex].
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
[tex] \sqrt{ (x-a)^{2}+ (y-b)^{2} } [/tex]
Step 2
Find the distance between the point P to the directrix [tex]c[/tex]. It is a vertical distance between y and c, expressed as [tex]y-c[/tex]
Step 3
The equation of parabola is then given as
[tex] \sqrt{ (x-a)^{2}+ (y-b)^{2} } [/tex]=[tex]y-c[/tex]
[tex] (x-a)^{2}+ (y-b)^{2}= (y-c)^{2} [/tex] ⇒ substituting a, b and c
[tex] (x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2} [/tex]
[tex] (x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2} [/tex]⇒Rearranging and making [tex]y[/tex] the subject gives
[tex]y= \frac{ x^{2} }{2} -2x+1[/tex]
Candida bought 334 yards of fabric. If she uses 23 of the fabric to make a dress, how much fabric will she have left?
Answers
just minus 23 from 334
23 yards are 828 inches
She has 11,196 inches or 311 yards left
Use the given graph to determine the limit, if it exists.
limf(x)
x-->2
Answers
Answer:
Step-by-step explanation:
4
The limit as x tends to 2 is -1
How to find the limit
The limit is sought by investigating the graph. More attention is directed to when the domain or the x-value is at 2.
It can be observed that at this point we have 2 open dots and one closed dot.
The closed dot implies there is a value for x = 2, hence we trace the y coordinate at this point.
Tracing the y coordinate shows that the value is -1
What is something that multipys to 72 and adds -27?
Answers
What is the factored form of the expression
Answers
In other words, D) (3g²-2)(5g+6)
What is the shape of the graph of any geometric sequence?
Answers
Final answer:
The graph of a geometric sequence forms either an exponential decay or growth curve, depending on the common ratio, with the sequence appearing as a straight line on a semi-logarithmic scale.
Explanation:
The graph of any geometric sequence takes on a distinctive shape. If the common ratio of the geometric sequence is between -1 and 1 (excluding 0), the points of the graph will form a curve that approaches the x-axis as the number of terms increases, which is known as an exponential decay if the common ratio is positive, and an oscillating decay if it is negative. Similarly, if the common ratio is greater than 1 or less than -1, the sequence will exhibit exponential growth with each subsequent term becoming larger, and the points will diverge away from the x-axis forming an upward curve if the common ratio is positive or oscillating upward if it is negative. The graph may have a y-intercept, where it crosses the y-axis, and when graphed on a semi-logarithmic scale, the sequence with a positive common ratio will appear as a straight line.
Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data reflect a mean price of $3.42 with a standard deviation of 0.07. Van’s data reflect a mean price of $3.78 with a standard deviation of 0.23. Which statement is true about their gas-price data? Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78. Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78. Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42. Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.
Answers
- Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
Answer:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
Step-by-step explanation:
We know that a standard deviation is a measure that is used to find the amount of dispersion or variation of the data set.If standard deviation is low this means that the data points tends close to the mean of the data set.while a higher standard deviation means that the data values are spread to a greater range.Hence, form the given information we may imply that:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
( Since, the standard deviation of Raquel's data is low which is 0.07 as compared to Van's data ( which is 0.23).
Hence, the Raquel's data will tend close to the mean which is $ 3.42. )
Substituting x-4=y and -5y+8x=29
Answers
-5x+20+8x=29
3x+20=29
3x=9
X=3
In the diagram below, an and bc are tangent to o. What is the measure of adc
Answers
40° = ½ (ADC -140°)
40° = ½ ADC -70°
110° = ½ ADC
ADC = 220°
Answer:
mADC = 220°
Step-by-step explanation:
In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.
By theorem of tangents and arcs.
m∠ABC = [tex]\frac{1}{2}[/tex] [m ADC- m AC ]
Since it is given in the question
∠ABC = 40 & AC = 140°
Therefore, 40 = [tex]\frac{1}{2}[/tex] [ m ADC - 140 ]
40 × 2 = m ADC - 140
80 + 140 = m ADC
mADC = 220°
Are 60 meters equal to, greater than, or less than 6 km?
Answers
Final answer:
60 meters is significantly less than 6 kilometers, as 6 kilometers is equal to 6,000 meters.
Explanation:
To answer this, we need to compare the two measurements in the same unit. We know that 1 kilometer is equivalent to 1,000 meters, so to convert 6 kilometers to meters, we multiply by 1,000:
6 km imes 1,000 = 6,000 m
Now we can compare the two measurements:
60 m
6,000 m
Since 60 is less than 6,000, we can conclude that 60 meters is less than 6 kilometers.
What is the average of three checks, one for $16.00, one for $40.00 and one for $130?
Answers
add them then divide by 3
16.00 + 40.00 + 130 = 186.00
186.00/3 = 62.00
the average is 62.00
1. In how many different ways can 5 people be seated at a round table?
2. Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
3. How many different "words" can be made from the given word by re-arranging the letters?
a) VECTOR
B) TRUST
Answers
Assume the people A, B, C, D and E are sitting in a row.
since there are 5 positions, they can sit in 5*4*3*2*1=120 ways.
consider 1 certain sitting position, for example ABCDE, that is B has A to his right, C to his left. D has C to his right and E to his left. And so on.
the positions
ABCDE
BCDEA
CDEAB
DEABC
EABCD
while in a row are different positions, in a round table they are the same thing.
(read the letters starting from A, and when the letters finish, continue reading from the beginning of the row. They all read "ABCDE")
This means that any arrangement in a round table, is converted to 5 arrangements in a row.
So there are in total [tex] \frac{5!}{5}=4*3*2*1=24 [/tex] arrangements of 5 people around a table.
2. check picture.
Consider the case where A is at (2, 2) and B is at (5, 6)
A can move to B through 3 horizontal units to the right, we call them E (for East) and 4 vertical units up, which we call N (for north).
the total path is 7 units.
it can be done in several ways, for example:
ENNNENE (the red path shown in the figure)
NNEEENN (the black path shown in the figure)
In total there are
[tex] \frac{7!}{3!*4!}= \frac{7*6*5*4!}{3!*4!}= \frac{7*6*5}{3!}= 35 [/tex] paths.
Remark: 7! is the number of arrangements if the letters were different. We divide by 3! because of the 3 E's and 4! because of the 4 N's.
Another possibility could be A'(3, -5), B'(8,-3).
From A' to B' we go by a total of 5 E and 2 N, so there are
[tex] \frac{7!}{2!*5!}= \frac{7*6*5!}{2!*5!}= \frac{7*6}{2}= 42 [/tex] paths in total.
there is one more possibility
[tex] \frac{7!}{1!(6!)}=7 [/tex]
C.
a) consider the letters {V,E,C,T,O,R}
we can form 6*5*4*3*2*1=720 words, as the first digit can be any of the 6 letters, combined with 5 for the second letter and so on.
b) the difference with a is that we have 5 letters and we have 2 T.
we have in total 5*4*3*2*1=120 arrangements of these letters, if the 2 T's were considered as separate.
consider the arrangements:
[tex]T_1RUST_2[/tex] and [tex]T_2RUST_1[/tex].
We read bth as just TRUST, but the permutation formula 5*4*3*2*1 considers these as 2 different.
this is why we need to divide 120 by 2, to get the actual number of words that can be formed. So the number is 60.
Answers:
1) 24
2) 7, 35 or 42. it depends on the positions of A and B, check the solution
3) a-720, b-160
Solve m=10x−x for x
help
Answers
m = 10x - x, solve for x.
First, we need to combine like-terms.
10x - x = 9x.
We now have:
m = 9x
Divide both sides by 9 to solve for x.
x = [tex] \frac{m}{9} [/tex]
I hope this helps!
Solving for x in terms of m will give [tex]\frac{m}{9}[/tex]
The given expression:
m = 10x - x
To find:
x in terms of mTo find x in terms of m, we use the following simple approach;
[tex]m = 10x - x \ \ \ (you \ can \ subtract \ 'x" \ from \ "10x" \ since \ they \ are \ similar)\\\\m = 9x\\\\divide \ both \ side s\ by \ 9\\\\\frac{m}{9} = \frac{9x}{9} \\\\\frac{m}{9} = x[/tex]
Thus, solving for x in terms of m will give [tex]\frac{m}{9}[/tex]
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The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)
Answers
There are already derived equations for this so it is already convenient. However, your given equation for range is incomplete. The correct equation is:
R = v₀²sin2θ/g
where
R = 140 ft
v₀ = 120 ft/s
g = 32.2 m/s²
Substituting the values,
sin 2θ = Rg/v₀²
sin 2θ = (140)(32.2)/(120²)
sin 2θ = 0.313
2θ = sin ⁻¹ (0.313)
2θ = 18.24°
θ =18.24°/2
θ = 9.12°
Where do the following graphs intersect? Show how you can find the intersection point algebraically.
1) y-2x=3
2) y-3= x^2
Answers
y-2x = 3
y-2x+2x = 3+2x
y = 2x+3
Plug that into equation (2)
y - 3 = x^2
2x+3 - 3 = x^2
2x = x^2
Get everything to one side
2x = x^2
2x-2x = x^2-2x
0 = x^2-2x
x^2-2x = 0
Now factor and use the zero product property to find the solutions for x
x^2-2x = 0
x(x-2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2
If x = 0, then y is...
y = 2x+3
y = 2(0)+3
y = 3
So (x,y) = (0,3) is one solution of the system. This is one point where the graphs intersect.
If x = 2, then y is...
y = 2x+3
y = 2(2)+3
y = 4+3
y = 7
So (x,y) = (2,7) is another solution to the system. This is another point where the graphs intersect.
See the attached image for a visual. The two curves cross at point A and point B
A = (0,3)
B = (2,7)
if the average (arithmetic mean) of two, seven, and X is 12, what is the value of X?
Answers
(2+7+x)/3=12
Multiply both sides by 3
2+7+x=36
Combine like terms
9+x=36
Subtract 9 from both sides
x=27
Final answer: x=27
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of π
Answers
C=2(18)π
C=36π in.
C = 2*pi*18
C = 36pi
What is the square root of pi?
Answers
Hope this helps! :)
Find the equation of the line perpendicular to -9x+4y=8 that contains the point (9,7)
Answers
Answer:
[tex]\[y=-\frac{4}{9}x+11\][/tex]
Step-by-step explanation:
Equation of the given line is [tex]\[-9x+4y=8\][/tex]
Slope of the line = [tex]\[\frac{9}{4}\][/tex]
Slope of the perpendicular line = [tex]\[-\frac{4}{9}\][/tex]
Equation of the line perpendicular to the given line is [tex]\[y=mx+c\][/tex]
[tex]\[y=-\frac{4}{9}x+c\][/tex]
But this line passes through (9,7)
Substituting the values in the equation:
[tex]\[7=-4+c\][/tex]
=> [tex]\[c=7+4=11\][/tex]
So the overall equation of the parallel line is given by [tex]\[y=-\frac{4}{9}x+11\][/tex]