Select all that apply. If x^2+b/ax+c/a=0 ; then: The sum of its roots = -b/a? The difference of its roots =-b/a? The product of its roots = c/a?The division of its roots = c/a? I can select multiple.
Answers
Answer:
The first and the thirdStep-by-step explanation:
[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]
[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]
[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]
Related Questions
The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, calculate the area and perimeternof the shaded region. PLEASE HELP!
Answers
Answer:
Step-by-step explanation:
Given that:
OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm
Using Pythagoras theorem: OB² = OA² + AB²
OB² = 6² + 7²=85
OB = √85 = 9.22 cm
to find ∠O, we use sine rule:
[tex]\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\ \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o[/tex]
AOC is a minor sector with radius 7 cm and angle 40.6
The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²
Area of sector OAC = [tex]\frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2[/tex]
Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²
Perimeter of arc AC = [tex]\frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm[/tex]
CB = OB - OC = 9.22 - 7 = 2.22
Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm
If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?
Answers
Answer:
2/xy
Step-by-step explanation:
you have to do the math but im not very sure on this
HELP ASAP! Will name brainliest!
Answers
Answer:
The answer to your question is given in the attached photo.
Step-by-step explanation:
To determine the answer to the question,
First, we shall determine the value 3A.
This is obtained by multiplying matrix A by 3 as shown in the attached photo.
Next, we shall carry out the operation 3A – B as shown in the attached photo.
find the average speed of car if it travels 18km in 20 minutes.
Answers
Answer:
[tex]\boxed{\sf Average \ Speed = 54\ km/hr}[/tex]
Step-by-step explanation:
Given:
Distance = S = 18 km
Time = t = 20 min = 20/60 = 0.33 hours
Required:
Average Speed = <v> = ?
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
A . S = 18 / 0.33
A.S = 54 km/hr
Answer:
0.9km/minute
or
54km/hour
Step-by-step explanation:
Average speed in km/minutes18km in 20 minutes = 18km/20min
18km/20min = 0.9km/min
Average speed in km/hour1 hour = 60 minutes
20 minutes = 20/60 = 0.3333 hours
18km/20mins = 18km/0.3333hours = 54km/hour
Ama has a rectangular garden measuring 12m and 25m.He wants to divide it into square plots of equal sizes .What is the largest sized square he can use?
Answers
En un colegio, dos séptimos de total de los estudiantes asisten al taller de escultura, un décimo al taller de guitarra y dos quintos al taller de computación. ¿Qué fracción del total de los estudiantes no asiste a estos talleres?
Answers
Answer:
3/14
Step-by-step explanation:
En esta pregunta, nos preocupa calcular la fracción de los estudiantes que no asisten a los talleres.
Para obtener la fracción que no asiste a los talleres, lo que debemos hacer es sumar las fracciones de cada uno de los talleres y restar el total de 1.
Matemáticamente eso sería;
1- (2/7 + 1/10 + 2/5)
Agregando los términos en el paréntesis, tenemos;
(20+ 7 + 28) / 70 = 55/70 = 11/14
Restando esto de 1, tenemos; 1-11 / 14 = 3/14
Please answer question now
Answers
Answer:
469.42 ft²
Step-by-step explanation:
Law of sines;w/sin27 = 38/sin40
w = sin27*38/sin40
w = 26.84 ft
Angle x;∡X = 180 - 27- 40 = 113º
Area;A = 0.5*(26.84)*(38)*sin(113)
A = 469.42 ft²
BRAINLIEST!! GEOMETRY THANKS!!! In rectangle shown B and F are midpoints of AC and AE , respectively. Find the ratio of the area of quadrilateral ABDF to the area of rectangle.
Answers
Answer:
1:2
Step-by-step explanation:
The area of ΔFED must be 1/4th of the entire area and so must the area of ΔBCD because B and F are the midpoints. Therefore, the area of ABDF is 1 - 1/4 - 1/4 = 1/2 of ACDE's are so the ratio is 1:2.
In one month, the median home price in the Northeast rose from $225,400 to $241,500. Find the percent increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:
7.1%
The percentage increase is 7.1%
Step-by-step explanation:
Percentage increase %∆P is the percentage change in the price.
Percentage increase %∆P = ∆P/Pr × 100%
Where;
∆P = change in sales price = $241,500-$225,400
Pr = regular price = $225,400
Substituting the given values;
%∆P = (241,500-225,400)/225,400 × 100%
%∆P = 7.142857142857% = 7.1%
The percentage increase is 7.1%
please help!!! Its not a super hard question i just want to make sure im right
Answers
Answer:
D
Step-by-step explanation:
If you put the equation into a graphing calculator it will give ou a function than is a straight line that is stretched vertically by 3 units
help me pleaseeeeeee,Which of the following choices matches the system? y ≥ 2x + 1 and y ≥ -x + 3 y ≤ 2x + 1 and y ≤ -x + 3 y ≤ 2x + 1 and y ≥ -x + 3 None of these choices are correct.
Answers
Answer:
y<=-x+3 and y<=2x+1
Step-by-step explanation:
y=-x+3 is the orange line. The shaded region is below so its y<-x+3
y=2x+1 is the blue line. The shaded region is below so y<2x+1
Please help im stuck
Answers
A woman bought a cup
of beans for 12 and sold it
for ₦15. What was her
percentage profit
Answers
Answer:
25 %Step-by-step explanation:
Given,
Cost price ( CP ) = 12
Selling price ( SP ) = 15
Since, CP < SP , she made a profit
Actual profit = SP - CP
plug the values
[tex] = 15 - 12[/tex]
Subtract the numbers
[tex] = 3[/tex]
Profit = 3
Now,
Profit percent = [tex] \frac{actual \: profit}{cost \: price} \times 100[/tex] %
Plug the values
[tex] = \frac{3}{12} \times 100[/tex] %
Calculate
[tex] = 25[/tex] %
Hope this helps...
Best regards!!
Answer:
25%
Step-by-step explanation:
Cost Price: ₦12
Selling Price: ₦15
Profit: ₦15 - ₦12 = ₦3
Profit Percentage = [tex]\frac{profit}{cost price}[/tex] × [tex]\frac{100}{1}[/tex]
Profit Percentage = [tex]\frac{3}{12}[/tex] × [tex]\frac{100}{1}[/tex]
Profit Percentage = [tex]\frac{1}{4}[/tex] × [tex]\frac{100}{1}[/tex] = 25%
Final Answer = 25%
Factor .
X2-x-56=0
PLEASE HELP!!!
Answers
Answer:
use factoring x (see attachment)
-8 x 7 = -56
-8 + 7 = -1
(x - 8)(x + 7) = 0
x = 8, -7
hope this helps :)
.
Look at the table. Is ƒ(x) an exponential function? If so, identify the base. If not, why not?
No, there is no base common to any two successive terms.
yes, the base is 4
Answers
Answer:
yes, the base is 4
Step-by-step explanation:
If the m1 = 40, what is the m 3
Answers
Explanation:
m1 = 40
m3 = 40 x 3
m3 = 120
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps UGraph the parabola. y=x^2 -4 where do i put the points
Answers
To generate a point, you plug in a number for x to get the corresponding y value.
If x = 0 for instance, then the y value is...
y = x^2 - 4
y = 0^2 - 4 ... x is replaced with 0
y = 0 - 4
y = -4
So x = 0 and y = -4 pair up to get the point (0,-4). This is the y intercept as the parabola crosses the y axis here. It turns out that this is also the vertex point as it is the lowest point on the parabola.
----------------
If x = 1, then,
y = x^2 - 4
y = 1^2 - 4
y = 1 - 4
y = -3
meaning (x,y) = (1,-3) is another point on this line.
----------------
Repeat for x = 2
y = x^2 - 4
y = 2^2 - 4
y = 4-4
y = 0
Since we got a y output of 0, we have found an x intercept located at (2,0). The other x intercept is (-2,0).
-------------------
The idea is to generate as many points as possible. Plot all of the points on the same xy coordinate grid. Then draw a curve through those points the best you can. You should get what you see in the diagram below. I used GeoGebra to make the graph. Desmos is another handy tool I recommend.
Note: the more points you generate, the more accurate the graph will be
The points B(2, 6) and D(0, -2) are two opposite vertices of a square ABCD, find the equation
of the diagonal AC.
Answers
Answer:
y = -x/4 + 9/2
Step-by-step explanation:
The diagonal AC is the perpendicular bisector of BD.
The centre of the square, P, through which both diagonal pass through is at the average of the coordinates of B(2,6) and D(0,-2)
P ((2+0)/2, (6-2)/2) = P(1,2)
The slope of BD,
m = (yd-yb)/(xd-xb) = (-2-6)/(0-2) = -8/-2 =4
Slope of AC
m' = -1 / m = -1/4
Using the point slope form of the line AC, slope m' through P(1,2)
y-yp = m'(x-xp)
y-2 = -(1/4)(x-1)
Simplify and isolate y
y = -x/4 + 1/4 +2 = -x/4 + 9/2
8–2|4–5y|=4 help me as quick as u can plzzz
Answers
Answer: [tex]y=\frac{2}{5}, \frac{6}{5}[/tex]
Step-by-step explanation:
When answering a problem like this, you first isolate the absolute value. TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4. Then divide both sides of the equation to get |4–5y|=2. The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.
Hope it helps <3
A candy store sells mints, taffy, and caramel. If 5/8 of the candy in stock is
mints and 3/16 of the candy in stock is taffy, what part of the candy in stock is
caramel?
Answers
Answer:6/16 or 3/8
Step-by-step explanation:
I did it
Answer: 3/16
Step-by-step explanation:
Which equation is true for the value x = 15? A. 2(x + 3) = 40 B. 2(x − 5) = 30 C. 2(x + 5) = 40 D. x + 2x = 30 E. 3x − x = 45
Answers
I think it is C. Pls comment right or wrong!
The equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
To determine the required equation which is true for the value x = 15
We have to simplify the given equations and solve for x.
A. 2(x + 3) = 40
⇒ 2x + 6 = 40
⇒ 2x = 40 - 6
⇒ 2x = 34
⇒ x = 34/2
⇒ x = 17
B. 2(x − 5) = 30
⇒ 2x - 10 = 30
⇒ 2x = 30 + 10
⇒ 2x = 40
⇒ x = 20
C. 2(x + 5) = 40
⇒ 2x + 10 = 40
⇒ 2x = 40 - 10
⇒ 2x = 30
⇒ x = 15
Hence, the equation 2(x + 5) = 40 is true for the value x = 15 which is the correct answer would be option (C)
Learn more about the equations here:
brainly.com/question/13947055
#SPJ6
if a/b and c/d are rational expressions, then a/b divided by c/d=a•d/b•c
Answers
The expression a/b ÷ c/d = ad/bc is A. true.
To show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc
Rational ExpressionsRational expressions are expressions of the form a/b where a and b are integers and b ≠ 0
If the rational expression a/b is to be divided by c/d, we take the reciprocal of the expression on the right side of the division sign.
So, L.H.S = a/b ÷ c/d
= a/b × 1/(c/d)
= a/b × d/c
= ad/bc
= R.H.S
Since L.H.S = R.H.S.
a/b ÷ c/d = ad/bc
So, the expression a/b ÷ c/d = ad/bc is A. true.
Learn more about rational expressions here:
https://brainly.com/question/12099997
In a survey of 2957 adults, 1455 say hey have started paying bills online in the least year construct a 99% confidence interval for the population proportion
Answers
Answer: 0.49 ± 0.0237
Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:
[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]
[tex]p_{hat}[/tex] is the proportion:
[tex]p_{hat}[/tex] = [tex]\frac{1455}{2957}[/tex]
[tex]p_{hat}[/tex] = 0.49
For a 99% confidence interval, z = 2.576:
0.49 ± 2.576.[tex]\sqrt{\frac{0.49(1-0.49)}{2957} }[/tex]
0.49 ± 2.576.[tex]\sqrt{\frac{0.49*0.51}{2957} }[/tex]
0.49 ± 2.576.(0.0092)
0.49 ± 0.0237
For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237
Sekkrit!!! Find the inverse of f(x) = 3x-5
Answers
Answer:
1/3(x+5)
Step-by-step explanation:
f(x) = 3x-5
y = 3x-5
Exchange x and y
x = 3y-5
Solve for y
Add 5 to each side
x+5 = 3y
Divide each side by 3
1/3 ( x+5) = 3y/3
1/3 ( x+5) = y
The inverse is 1/3(x+5)
Answer:
[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-5[/tex]
[tex]\mathrm{We \: need \: to \: find \: the \: inverse \: of \: the \: function.} \\ \mathrm{The \: inverse \: of \: a \: function \: reverses \: the \: original \: function.}[/tex]
[tex]\mathrm{Plug \: f(x) \: as \: y.}[/tex]
[tex]y=3x-5[/tex]
[tex]\mathrm{Solve \: for \: x.}[/tex]
[tex]\mathrm{Add \: 5 \: to \: both \: sides \: of \: the \: equation.}[/tex]
[tex]y+5=3x[/tex]
[tex]\mathrm{Divide \: both \: sides \: of \: the \: equation \: by \: 3.}[/tex]
[tex]\frac{y+5}{3} =x[/tex]
[tex]\mathrm{Switch \: variables.}[/tex]
[tex]\frac{x+5}{3} =y[/tex]
[tex]\mathrm{Plug \: y \: as \: f^{-1}(x).}[/tex]
[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]
One number is 7 less than 3 times the second number. Their sum is 29. Find the numbers.
Answers
Answer:
The numbers are 20 and 9Step-by-step explanation:
Let the first number be x
Let the second number be y
For the first equation
One number is 7 less than 3 times the second number is written as
x = 3y - 7
For the second equation
The sum of the two numbers is 29
So we have
x + y = 29
Substitute the first equation into the second one
That's
3y - 7 + y = 29
4y = 29 + 7
4y = 36
Divide both sides by 4
y = 9Substitute y = 9 into x = 3y - 7
That's
x = 3(9) - 7
x = 27 - 7
x = 20The numbers are 20 and 9
Hope this helps you
How many triangles does a=6 b=10 A=33° create?
Answers
Answer:
2 triangles are possible.
Step-by-step explanation:
Given
a=6
b=10
[tex]\angle[/tex]A=33°
To find:
Number of triangles possible ?
Solution:
First of all, let us use the sine rule:
As per Sine Rule:
[tex]\dfrac{a}{sinA}=\dfrac{b}{sinB}[/tex]
And let us find the angle B.
[tex]\dfrac{6}{sin33}=\dfrac{10}{sinB}\\sinB = \dfrac{10}{6}\times sin33\\B =sin^{-1}(1.67 \times 0.545)\\B =sin^{-1}(0.9095) =65.44^\circ[/tex]
This value is in the 1st quadrant i.e. acute angle.
One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 = [tex]114.56^\circ[/tex]
For the value of [tex]\angle B = 65.44^\circ[/tex], let us find [tex]\angle C[/tex]:
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+65.44+\angle C = 180\\\Rightarrow \angle C = 180-98.44 = 81.56^\circ[/tex]
Let us find side c using sine rule again:
[tex]\dfrac{6}{sin33}=\dfrac{c}{sin81.56^\circ}\\\Rightarrow c = 11.02 \times sin81.56^\circ = 10.89[/tex]
So, one possible triangle is:
a = 6, b = 10, c = 10.89
[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=65.44°, [tex]\angle[/tex]C=81.56°
For the value of [tex]\angle B =[/tex][tex]114.56^\circ[/tex], let us find [tex]\angle C[/tex]:
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+114.56+\angle C = 180\\\Rightarrow \angle C = 180-147.56 = 32.44^\circ[/tex]
Let us find side c using sine rule again:
[tex]\dfrac{6}{sin33}=\dfrac{c}{sin32.44^\circ}\\\Rightarrow c = 11.02 \times sin32.44^\circ = 5.91[/tex]
So, second possible triangle is:
a = 6, b = 10, c = 5.91
[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=114.56°, [tex]\angle[/tex]C=32.44°
So, answer is : 2 triangles are possible.
11.1/0.01= what is the answer
Answers
11.1/.01=1,110
Answer:
1,110
Step-by-step explanation:
calculator
Probability people where you at? 《brainlist if correct》
90% of households in a certain region have answering machines. 50% of the
households have both an answering machine and call-waiting. A household chosen at random was found to have the answering machine.
What is the probability that it also has call-waiting?
Answers
As an approximate decimal, this is 0.5556 which converts to 55.56%
======================================================
Explanation:
Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.
We then select a house at random. Someone tells us (or we have some kind of prior knowledge) that whichever house is selected, they have an answering machine. We can ignore the 10 households that don't have an answering machine. Out of those 90 households, 50 have both features. So 50/90 = 5/9 is the probability of getting a household with both features.
The answer would be 1/2 or 50% if we didn't have the prior knowledge of the household having an answering machine. But with this prior knowledge, the conditions change and so does the probability.
----------------
You could also compute 0.50/0.90 to get the same answer.
Which of the following graphs is the graph of
Answers
Answer:
Graph A is the one that represents the given piecewise function.
Step-by-step explanation:
Notice that the Domain of the given function has been partitioned in three sections:
[tex]-2\leq x<0\,\,; \,\,\,x = 0\,\,;\,\,\,0<x\leq 2[/tex]
in the first section we have that the function responds to [tex]f(x)=x-1[/tex], which is a line of positive slope (ascending line) equal to "1", and y-intercept at y= -1.
This line should therefore start at the point (-2, -3) (when x = -2) and end at y almost equal to -1, when x approaches the value zero; and an empty dot should be seen in the position (0, -1)
For x = 0 we should see a solid dot located at the position (0, 1) on the plane.
And finally for the third section we should see a horizontal segment (that represents a constant value of 3, starting with an empty dot at the point (0, 3), and ending on a solid dot located at (2, 3).
This is what we see represented by the graph labeled A in the list of answer options.
Answer:
B
Step-by-step explanation:
what are the lengths for x and y
Answers
Answer:
They are both equal to 7.07
Step-by-step explanation:
Using SohCahToa to find x you use the opposite and the hypotenuse if you use the 45 degree angle.
Now you use sin(45)=x/10
x=7.07
Now using SohCahToa to find y you use hypotenuse and adjacent, if using the 45 degree angle.
Now you use cos(45)=y/10
y=7.07
Answer: side y=7.1
side x= 7.1
Step-by-step explanation:
[tex]sin(45)=\frac{x}{10}[/tex]
[tex]x=7.07...[/tex]
[tex]cos(45)=\frac{y}{10}[/tex]
[tex]y=7.07...[/tex]