Answers
[tex]\bf \begin{array}{llll} y=&{{ a}}x^2&{{ +b}}x&{{ +c}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \\\\\\ discriminant\implies b^2-4ac= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]
31)
a simple case for that would just be, using an equation with an imaginary value, let's do so
[tex]\bf \sqrt{-5}=x\implies \sqrt{-1\cdot 5}=x\implies \sqrt{-1}\sqrt{5}=x\implies i\sqrt{5}=x\\\\ -------------------------------\\\\ \textit{so, we'll use that imaginary value then}\\\\ \sqrt{-5}=x\implies -5=x^2\implies 0=x^2+5\implies \boxed{y=x^2+5}[/tex]
when you get a "solution" or zero with an "i" or an imaginary value, is just a way to say, there's really no solution, the function never touches the x-axis
Related Questions
Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the round trip was one hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.
A.
0.47 miles
B.
212 miles
C.
239 miles
D.
3,600 miles
Answers
d r t
there d 450 t
back d 400 1-t
Let me explain this table to you. The distance is d, we don't know what it is, that's what we are actually looking for. We only know that if we go somewhere from point A to point B, then back again to point A, the distance there is the same as the distance back. Hence, the d in both spaces. There he flew 450 mph, back he flew 400 mph. If the total distance was 1 hour, he flew an unknown time there and one hour minus that unknown time back. For example, if he flew for 20 minutes there, one hour minus 20 minutes means that he flew 60 minutes - 20 minutes = 40 minutes back. See? Now, because the distance there = the distance back, we can set the rt in both equal to each other. If d = rt there and d = rt back and the d's are the same, then we can set the rt's equal to each other. 450t = 400(1-t) and
450t = 400 - 400t and 850t = 400. Solve for t to get t = .47058. Now, t is time, not the distance and we are looking for distance. So multiply that t value by the rate (cuz d = r*t) to get that the distance one way is
d = 450(.470580 and d = 211. 76 or, rounded like you need, 212.
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.
Answers
check the picture below.
Answer:
x^2/25 + y^2/81 =1
Step-by-step explanation:
solved it
The equation =+y3115
is solved in several steps below.
For each step, choose the reason that best justifies it.
Answers
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16
Answers
It's false, because if [tex]x^2=16[/tex], then [tex]x=4 \vee x=-4[/tex]
Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N
Answers
We know that shape RIAN is a parallelogram with RN || IA and RI || NA
RG is a part of the line RN, so RG is also parallel to IA
-----------------------------------------------------------------------------------------------------------------
m∠TRG = m∠I : Corresponding angle on a transversal
Line TI is a transversal to the parallel lines RN and IA.
m∠TRG and m∠I are corresponding to each other
----------------------------------------------------------------------------------------------------------------
m∠TGR = m∠NGA: Opposite angles on a transversal
Line TA is a transversal on line RN and IA
----------------------------------------------------------------------------------------------------------------
ΔTGR = ΔNGA: Opposite angles property in a parallelogram
Opposite angles on a parallelogram are equal
---------------------------------------------------------------------------------------------------------------
∠T = ∠N: Angle sum of triangle
∠T = 180° - (∠R + ∠G)
∠N = 180° - (∠G + ∠N)
What are radians, how do I solve for the measurement of radians in the angle of BAC
Answers
So BAC = 45 degrees, which is 45 / 360 * 2pi = pi/4
A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent
Answers
Hope this helps! :)
If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?
Answers
Answer: The required ratio of the volumes of two spheres is 125 : 512.
Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.
We are to find the ratio of the volumes of the two spheres.
Let, 'r' and 'R' represents the radii of the two spheres, so
r : R = 5 : 8.
The volume of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Let, V and V' be the volumes of the spheres with radius r and R units respectively.
Then, the ratio of the volumes of the two spheres will be
[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]
Thus, the required ratio of the volumes of two spheres is 125 : 512.
Answer: 125:512
Step-by-step explanation:
a p e x
Hey rectangular pan has a link that is for third the with the total area of the pan is 432 in.² what is the width of the cake pan
Answers
Find the value of 'y' in the equation 3/y-3 =8
A.) y= -2 3/8
B.) y= -1 5/8
C.) y= 1 5/8
D.) y= 2 3/8
Answers
3 = 8(y - 2)
3 = 8y - 16
3 + 16 = 8y
19 = 8y
19/8 = y
2 3/8 = y <==
Help!!!!ASAP PLEASE
Answers
If you add 10 in, plus 10 in below it, then the 6 in, and the 8 in, and 3 in and the other 3 in, you should get 40 in.
The length of the rectangle is 4 times the height. the area of the triangle is 63 cm2. Find the width. Round to the nearest tenth of an inch
Answers
area = l x h
l=4h
area = 4h x h = 4h^2
4h^2 =63
63/4 = 15.75
h^2 = 15.75
sqrt(15.75)=h
h = 3.968cm
rounded to nearest tenth would be 4.0cm
check L=4(4) = 16 x 4 = 64 ( since it was round 64 is pretty close to 63)
A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.
Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?
Answers
Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1.
Answers
(x-h)²/a² + (y-k)²/b², where h, k are the coordinates of the center, a & b represent half of the major & minor axis respectively.
The given equation is:
x²/100 + y²/36 = 1.( a =10 and b = 6)
CENTER: Since h and k = 0, then the center of this ellipse is the origin (0,0)
VERTICES: a² = 100, → a = +10 and a = -10, then the right vertex is (10,0) and the left vertex is (-10,0)
FOCI: The distance "c" from the center to the focus is given by the following:
c² = a² - b²
c² = 100 - 36 = 64 and c = +8 and - 8
The coordinate of the right focus F₁(8,0) and F₂(-8,0) for the left focus
Which table represents the second piece of the function f(x)
Answers
8-2(1)=6
8-2(2)=4
8-2(3)=2
So it is the third table.
Answer:
Third table represents the second piece of the function f(x)
Step-by-step explanation:
The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
[tex]f(1)=8-2(1)\\f(1)=6[/tex]
For x = 2
[tex]f(2)=8-2(2)\\f(2)=4[/tex]
For x = 3
[tex]f(3)=8-2(3)\\f(3)=6[/tex]
Among the given tables, third tables contains these values.
Third table represents the second piece of the function f(x)
ANSWER PLEASE
In the figure, sin ∠MQP =
a. cos N and sin R
b. sin R and sin N
c. cos N and sin M
d. cos R and sin N
Answers
sin ∠MQP = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠R = sin(34) = 0.559
sin ∠N = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠M = sin(90) = 1
cos ∠R = cos(34) = 0.828
Based on these findings, it is obvious that sin ∠MQP is equal to cos ∠R and sin ∠N.
Thus, the correct choice is "d".
A man paid the bank $4,080 at the end of three years. This was the amount borrowed plus 12% interest for three years. How much money had he borrowed?
Answers
(rounded to the nearest tenth)
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
Answers
The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4
What is the simplification of an algebraic expression?The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.
From the given algebraic expression, we have:
0.3(4x – 8) – 0.5(–2.4x + 4)
Open brackets1.2x - 2.4 + 1.2x - 2
Collect like terms1.2x + 1.2x = 2.4 + 2
2.4x = 4.4
2.4x - 4.4
Learn more about algebraic expression here:
https://brainly.com/question/2164351
Answer:
simply d
Step-by-step explanation:
An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?
A) 0.125 hours
B) 5 hours
C) 8 hours
D) 9 hours
Answers
Which equation would best help solve the following problem? Rennie kicks a field goal with an initial vertical velocity of 31 m/s. How long will it take the football to hit the ground?
–4.9t2 + 31t = 0
–4.9t2 – 31t = 0
16t2 + 31t = 0
–16t2+ 31t = 0
Answers
v=⌠a
v=gt+vi
h=⌠v
h=gt^2/2+vit+hi
So height as a function of time is:
h(t)=gt^2/2+vit+hi
g=-9.8m/s^2, vi=31m/s, hi=0 so
h(t)=-4.9t^2+31t
And it will hit the ground when h(t)=0 so
-4.9t^2+31t=0
Given a polynomial f(x), if (x + 7) is a factor, what else must be true? Help plzzz im running out of time
f(0) = 7
f(0) = −7
f(−7) = 0
f(7) = 0
Answers
For the factored form of f(x), if x = -7, then one of the factors will be equal to 0, since (-7 + 7) = 0. This will cause the entire y-value to be 0, because anything multiplied by 0 = 0.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x)= 3x^2+9x+12
Answers
f(x) = 3(x^2 + 3x) + 12 = 3(x+1.5)^2 +5.25
So you can see the vertex is at (0,5.25) when x = -1.5
The axis of symmetry then lies in x = -1.5
Answer with explanation:
Equation of the Parabola is
[tex]f(x)= y=3x^2+9x+12\\\\y=3[x^2+3 x+4]\\\\y=3[(x+\frac{3}{2})^2+4-(\frac{3}{2})^2]\\\\y=3[(x+\frac{3}{2})^2+(\frac{\sqrt 7}{2})^2]\\\\y-\frac{21}{4}=3[(x+\frac{3}{2})^2][/tex]
Vertex of the parabola can be obtained by
[tex]x+\frac{3}{2}=0\\\\ x=\frac{-3}{2}\\\\ y-\frac{21}{4}=0\\\\y=\frac{21}{4}\\\\ Vertex(\frac{-3}{2},\frac{21}{4})[/tex]
Axis is that line of parabola which divides the parabola into two equal halves.
[tex]x+\frac{3}{2}=0\\\\x=-\frac{3}{2}[/tex]
Can someone help me with this math question?
Answers
42-23=19
Let me know if you need any further help.
Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 A. (–10, 3) B. (–3, 10) C. (0,0) D. Infinitely many solutions
Answers
Step 1: Solve for x or y in either of the two equations. I will choose to solve for y in the equation 8x + 9y = -5
8x + 9y = -5
- 8x + 8x
-------------------------
9y = 8x - 5
----- ----- -----
9 9 9
y = 8/9x - 5/9
Step 2: Plug in the value you got for x or y into the equation that you have not worked with yet.
8x - 9(8/9x - 5/9) = 5
8x - 8x + 5 = 5
0x + 5 = 5
5 = 5
This turns out to be a true statement, so the answer to your system will be infinitely many solutions.
If y varies inversely as the square of x and y=4 when x=5, find y when x is 2
Answers
need to kind K
Y=k x 1/x^2 = k/x^2
Find K when y=4 & x=5
Y=k/x^2 =
4=k/5^2=
4=k/25
K=4*25 =100
When x = 2
Y=100/2^2
Y=100/4
Y=25
how do you solve this system of linear equation by substitution
x-3y=-12
y=2x+9
Answers
If y=2x+9, substitute y into the equation x-3y=-12.
You will get: x-3(2x+9)=-12
Now, distribute: x-6x-27=-12
Add like terms: -5x-27=-12
Add 27 to both sides: -5x=15
Divide both sides by -5: x=-3
Now, substitute this value of x into the equation to find y: y=2(-3)+9
Multiply: y=-6+9
Add: y=3
Here is the solution: (x,y)=(-3,3)
Hope this explanation helped!
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period and why?
A) Mean, because there are no outliers that affect the center.
B) Median, because there is 1 outlier that affects the center.
C) Interquartile range, because there is 1 outlier that affects the center.
D) Standard deviation, because there are no outliers that affect the center
Answers
I believe the answer is D.
Answer:
B) Median, because there is one outlier that affects the center
I need some assistance in figuring this out
Answers
Question 1(Multiple Choice Worth 5 points) (07.05 HC)
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
Answers
Step 2: 5x − 7 = 14 + 2x wrong. Must be 6x - 12 = 14 + 2x
Eight people enter a race. If there are no ties, in how many ways can the first two places come out
Answers
The number of ways the first two places can come out is 56.
Permutation and CombinationPermutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given to us,Eight people enter a race, n = 8,
There are no ties, r = 2,
As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.
Permutation[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]
Hence, the number of ways the first two places can come out is 56.
Learn more about Permutation and Combination:
https://brainly.com/question/11732255