The solution of the equation is x = -2±2i√2. The solution to the equation is found in the Sridharacharya formula.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
x² + 4x + 12 = 0
The solution to the equation is found as;
x² + 4x + 12 = 0
The solution to the equation is;
[tex]\rm x=-b \pm \frac{\sqrt{b^2-4ac}}{2a} \\\\ \rm x=-4 \pm \frac{\sqrt{4^2-4\times 4 \times 1}}{2\times 4} \\\\[/tex]
x = -2±2i√2
Hence the solution of the equation is x = -2±2i√2.
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please help with this problem
thanks so much
Answer:
5/17
Step-by-step explanation:
If we do the multiplication first, we get:
[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]
If we do the division next, we get:
[tex]\frac{4+1}{13+4} = 5/17[/tex]
Select the correct answer from each drop-down menu.
Consider functions hand k.
h(t) = 5r2 – 1
k(x) = √5x + 1
For > 0, the value of h(k(x)) is
0, functions hand k
For
the value of k(h(r
inverse functions.
Answer:
h(t)= 5r2-1
That the answer for the question
for what value of k will the relation not be a function
R={(k-8.3+2.4k,-5),(3/4k,4)}
Step-by-step explanation:
hope you can understand
Which value is a solution to the inequality x – 4 > 15.5? A) x = 21.4 B) x = 17.3 C) x = 15.5 D) x = 19.3
Answer:
A.) x = 21.4
Step-by-step explanation:
When solving the inequality, you can treat the sign like an equal sign. To isolate the "x" variable, you can add "4" to both sides. This eliminates the -4 from the right side.
You are left with the inequality:
x > 19.5
If "x" must be greater than 19.5, the only answer that satisfies this is A.) x = 21.4. All of the other answers are less than 19.5.
[tex]\bf{x -4 > 15.5}[/tex]
[tex]\bf{Add \ 4 \ to \ both \ sides.}[/tex]
[tex]\bf{x-4+4 > 15.5+4 }[/tex]
[tex]\bf{x > 19.5 === > Answer }[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
What is the solution to the linear equation?
-12 +3b-1-5-b
b=-2
b = -1.5
b = 1.5
b = 2
Answer:
[tex]b = 2[/tex]
Step-by-step explanation:
[tex]( - 12 - 1 - 5) + (3b - b) \\ - 18 + 2b \\ 2b - 18 \\ b = 2[/tex]
Bacteria colonies can increase by 73%
every 2 days. If you start with 55 bacteria
microorganisms, how large would the
colony be after 10 days?
Future Amount = [?] microorganisms
←time
Hint: Future Amount = 1(1+r) periods
↑
initial growth
amount rate
Round to the nearest whole number.
The size of the colony after 10 days is 852.
What is the size of the colony after 10 days?The growth rate of the colony can be represented with an exponential equation with the form:
FV = P(1 + r)^n
Where:
p = present population r = rate of growth n = growth factor = 10 days / 2 days = 555(1.73)^5 = 852
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
In this graph, the number of containers is plotted along the x-axis and the amount of water in the containers is along the y-axis.
The proportionality constant of the graph (y to x) is
The constant of the proportional relationship graphed in this problem is of 10.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the points on the graph are: (0,0), (2,20), (4,40), ..., hence the constant is:
k = 40/4 = 20/2 = 10.
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3. What are the roots of the polynomial y = x³ - 8?
Step-by-step explanation:
x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Cube root of x^3 is x.
Cube root of 8 is 2
So
a=x
b= 2.
[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]
Set these equations equal to zero
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
[tex] {x}^{2} - 2x + 4 = 0[/tex]
If we do the discriminant, we get a negative answer so we would have two imaginary solutions,
Thus the only real root is 2.
If you want imaginary solutions, apply the quadratic formula.
[tex]1 + i \sqrt{ 3 } [/tex]
and
[tex]1 - i \sqrt{3} [/tex]
I really need help on this question. Im stuck any help?
Answer:
170
Step-by-step explanation:
[tex]x+40=210\\x=170[/tex]
If a number, x, is increased by 40 (+40) and is now equal to 210 (=210), then the number, x, is equal to 170.
PLEASE PLEASEEEEEEE HELPPPPPP!! 100 POINTSSSS :)
A Ferris wheel, called the Atlanta Skyview, recently opened in Centennial Olympic Park in the Atlanta, GA area. The diameter of this Atlanta attraction is 200 feet and has 42 gondolas evenly spaced out along the circle. Each sector starts and ends at the point at which the gondola is attached to the Ferris wheel circle.
Answer the following questions about this Ferris wheel. Be sure to show and explain all work for each problem.
a. Area of the wheel?
b. measure the central angle in degrees
c. Measure of a central angle in radians
d. Arc length between two gondolas
e. Area of each sector.
The area of the wheel is 31415.9 ft².
The Central angle in degrees is 34.29°
Measure of a central angle in radians is 0.5984 radians
How to calculate the area and central angle of a circle?
A) The image shows an example of this Ferris wheel.
We are given;
Diameter; d = 200 ft
Radius; r = 100 ft
Number of gondolas = 42
Area of the circle wheel = πr²
Area = π * 100²
Area = 31415.9 ft²
B) Now, the sum of angles in a circle is 360°.
Since there are 42 gondola's, then;
Each angle = 360/42 = 60/7°
The central angle will be an angle with its vertex at the center of a circle and with sides that are radii of the circle. From the image, we see that it covers approximately 4 gondola's. Thus;
Central angle = 4 * 60/7° = 34.29°
C) Central Angle in radians will be converted as 0.5984 rad.
D) Arc length between two gondolas is;
S = rθ
S = 100 * 0.5984
S = 59.84 radians
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Figure ABCD is a rhombus. Find the value of x.
58°
x = [ ? ]°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 32°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Diagonals of a Rhombus bisect each other at 90°
[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]
[ Sum of interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]
[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.
Figure ABCD is a rhombus.
Its diagonals intersect at right angle.
Let the another angle be x. Then we have
x + 58° + 90° = 180°
x + 148° = 180°
x = 32°
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A rocket is launched in the air. The graph below shows the height of the rocket hh in meters after tt seconds.
help pls
Answer:
The answers are=
(38, 0)time in seconds(19, 1768.9)Heightin metersThe x-coordinate of the vertex is (38, 0) and the y-coordinate of the vertex is (19, 1768.9).
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The graph of the parabolic path is shown in the picture.
From the graph:
The x-coordinate of the vertex is (38, 0)
The x-coordinate represents time in seconds
The y-coordinate of the vertex is (19, 1768.9)
The y-coordinate represents the height in meters
Thus, the x-coordinate of the vertex is (38, 0) and the y-coordinate of the vertex is (19, 1768.9).
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Considering only the values of β for which (1+cosβ)(1−cosβ)sinβ is defined, which of the following expressions is equivalent to (1+cosβ)(1−cosβ)sinβ?
Select the correct answer below:
sinβ
sin3β
secβ
1
sec2β
The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β
What are Trigonometric Ratios ?In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.
The trigonometric expression given in the question is
(1+cosβ)(1−cosβ)sinβ
(a+b)(a-b) = a² - b²
( 1 - cos²β)sinβ
By the trigonometric Identity
1-cos²β = sin² β
sin² β x sin β
sin³β
Therefore Option B is the correct answer.
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I will give lots of points please help
Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
Part (a)The cake can be modeled as a cylinder with:
diameter = 9 inheight = 4 in[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]
If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.
[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]
Part (c)The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:
[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]
Part (d)Probability is approximately 10.6% (see above for calculation)
Part (e)If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
Tìm số dư trong phép chia 3^{2020} chia cho 13
Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].
Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].
Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,
[tex]3^{12} \equiv 1 \pmod{13}[/tex]
Now, observe that 2020 = 168×12 + 4, so that
[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]
and since 3⁴ = 81 = 6×13 + 3, we end up with
[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
y = x^3 - 4
y = (x - 4)^3
y = (-x - 4)^3
y = (-x)^3 - 4
Please answer the question down below!
Answer:
144°Step-by-step explanation:
regular decagon = all side equal and all angles congruent, so your answer is 144°
Last year over 10,000 students took an entrance exam at a certain state university. Ivanna's score was at the 36th percentile. Aldo's score was at the 19th percentile.
Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Last year, over 10,000 students took an entrance exam at a certain state university.
Let the maximum score be 100.
Ivanna's score was at the 36th percentile, will be
⇒ [(10,000 – 36) / 10,000] x 100
⇒ 99.64
Aldo's score was at the 19th percentile, will be
⇒ [(10,000 – 19) / 10,000] x 100
⇒ 99.81
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Polynomial of lowest degree with zeros of 3/4 (multiplicity 2) and 1/3 (multiplicity 1) and with f(0) = -81
The polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .
What is a Polynomial ?A polynomial is an expression that consists of indeterminate , Coefficients , exponents and mathematical operations.
It is given that
The zero of the function is at 3/4 with multiplicity of 2 = (x - 3/4)²
The zero of the function is at 1/3 with multiplicity of 1 = (x - 1/3)
The polynomial can be written as
f(x) = a (4x − 3)² (3x - 1)
-81 = a (0 − 3)² (0 -1)
a = 9
f(x) = 9(4x − 3)² (3x - 1)
Therefore the polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .
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What data collection
used in face-to-face
or written questionnaires?
method is
interview
O A. survey
O B. observation
O C. experiment
O D. publication
Answer:
survey (A)
A questionnaire (or someone asking questions) is considered to be a survey. It is "surveying" someone's opinion on data.
hope this helps!!
Giving a test to a group of students, the grades and gender are summarized below
Grades vs. Gender
A B C
Male 17 18 5
Female 12 3 14
If one student was chosen at random,
find the probability that the student was female.
Probability = (Round to 4 decimal places)
Out of 310 racers who started the marathon, 289 completed the race, 18 gave up, and 3 were disqualified. What percentage did not complet
Answer:
7.1%
Step-by-step explanation:
Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%
Determine the equation of the tangent line in both cases
1. x^2/x+2 at (2,1)
2. x^3+2y^2=10y at (2,1)
Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.
1.
[tex]y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}[/tex]
When x = 2, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34[/tex]
Then the equation of the tangent line at (2, 1) is
[tex]y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}[/tex]
2.
[tex]x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}[/tex]
When x = 2 and y = 1, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2[/tex]
Then the tangent at (2, 1) has equation
[tex]y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}[/tex]
1. The function j(x) is shown on the graph below.
Answer:
1) k = -3
2) B. The curve would be narrower, but the vertex would be in the same position.
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Question 1
When a graph is shifted up or down we add or subtract the number of units it has shifted from the function.
From inspection of the graph, the vertex of function j(x) is (0, 2)
From inspection of the graph, the vertex of function j(x) + k is (0, -1)
Therefore, function j(x) has been translated 3 units down.
Therefore, the value of k is -3, since the function of the graph is j(x) -3
Question 2
When discussing the stretching of curves, it is usual to always refer to it as a "stretch" rather than a stretch or compression.
If the scale factor a is 0 < a < 1 then the graph gets wider.
If the scale factor a is a > 1 then the graph gets narrower (i.e. "compressed").
h(x) to h(2x) means that the function h(x) has been stretched horizontally by a factor of 1/2. The other way to say this is that is have been compressed horizontally by a factor of 2. In any case, as a > 1 the graph gets narrower.
Therefore, the vertex would stay in the same place but the curve would be narrower.
If you currently makes 425 What is the gross they will earn If they work every week If the year
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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i need to Match each equation that represents each situation.
Step-by-step explanation:
this is quite easy, when you use just common sense and identify the right numbers and variable names.
they is nothing special needed, you don't even need to create the equations yourself.
$4.99 per pound. buys b pounds and pays $14.95.
14.95 = 4.99 × b
$4.99 per pound. buys b pounds and pays c.
this is exactly the same as before, just that this time the total amount is not given as a constant but as a variable.
c = 4.99 × b
d dollars per pound. buys b pounds and pays t.
the same as the 2 cases before, just now everything is a variable. no more constants, but otherwise the completely same structure and method.
t = d × b
earned $275, which is $45 more than Noah ("n").
$275 = n + $45
earned m dollars, which is $45 more than Noah ("n").
m = n + $45
earned m dollars, which is y dollars more than Noah (we are asked that Noah's earnings are now called "v").
here your teacher made a mistake.
sure, the only remaining answer is
v = m + y
but it is not correct. given the names of the prime and associated variables the correct answer would be
m = v + y or v = m - y
What to do when forget the pasword to the account?
Answer:
usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"
NEED HELP ASAP PLEASEE
Answer:
2nd one is the correct
Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Answer:
The mid-point is (9,-9/2)
Step-by-step explanation:
You would use the mid-point formula for this
[tex](\frac{x_{2} +x_{1} }{2} , \frac{y_{2}+y_{1} }{2} )[/tex]
if you plug that in it is ([tex]\frac{13-2}{2}, \frac{-7+5}{2}[/tex])
resulting in (11/2,-2/2) = (11/2,-1)
Which of the following slopes of a line pass through points (1, -3) and (0, 2)?
m=5
m = -5
m = undefined
None of these choices are correct.
The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.
What is the Slope of a Line?Slope (m) = rise / run = change in y / change in x.
Given the points, (1, -3) and (0, 2):
Slope (m) = (-3 - 2)/(1 - 0)
Slope (m) = -5/1
Slope (m) = -5
Therefore, the slope of the line is: B. m = -5.
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