Answer: No real number solutions
The complex number solutions are [tex]x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
where [tex]i = \sqrt{-1}[/tex]
=======================================================
Explanation:
The given equation 3x^2+2x+4 = 0 is in the form ax^2 + bx + c = 0
We have
a = 3b = 2c = 4Let's compute the discriminant.
d = b^2 - 4ac
d = (2)^2-4(3)(4)
d = -44
The result is negative, so there are no real number solutions.
----------------
If you wanted to find the complex valued solutions, then we apply the quadratic formula.
Plug in a = 3, b = 2, c = 4
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(3)(4)}}{2(3)}\\\\x = \frac{-2\pm\sqrt{-44}}{6}\\\\x = \frac{-2\pm\sqrt{-1*4*11}}{6}\\\\x = \frac{-2\pm\sqrt{-1}*\sqrt{4}*\sqrt{11}}{6}\\\\[/tex]
[tex]x = \frac{-2\pm i*2*\sqrt{11}}{6}\\\\x = \frac{-2\pm2i\sqrt{11}}{6}\\\\x = \frac{2(-1\pm i\sqrt{11})}{6}\\\\x = \frac{-1\pm i\sqrt{11}}{3}\\\\x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
Notice in step 3 we have -44 under the square root. The negative value in the square root leads directly to the imaginary number [tex]i = \sqrt{-1}[/tex]
Though the term "imaginary" is a bit unfair and misleading because numbers like -22 are just as imaginary and made up by humans. It just depends on context in which imaginary numbers are useful (eg: with physics or engineering).
Find the value of x.
5x (x+24)
Answer:
5x^2+120x
Step-by-step explanation:
5x(x+24)
Step 1: Use distributive property to expand the expression. Multiply 5x separately with all the terms inside the bracket.
Step 2: 5x(x) = 5x^2
5x(24) = 120x
Answer: 5x^2+120x
Note: If you need to further solve it, you can factor it.
To Factor;
5x^2+120x
Step 1: Factor out the common: 5x
Step 2: 5x times x = x^2
5x times 24 = 120x
Therefore,
Factored answer: 5x(x+24)
Hope this helps.
Answer:x=6
Step-by-step explanation:
5x(x+24)=0
5x = x +24
5x - x = x - x + 24
4x = 24
X = 24/4
X = 6
Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
Answer: The answer is 3211000 :^
Step-by-step explanation: hope this helps
Who ever gets it I will give 20 points and Brainly.
Answer:
104?
Step-by-step explanation:
pretty sure that's it 3x2 =6 10x11=110 but your painting around the window which it 6 ft so take 6 away and boom 104!
Answer:
104 ft²
Step-by-step explanation:
Given :-
Dimensions of wall = 10 x 11Dimensions of window = 2 x 3To Find :-
Area to be PaintedSolving :-
Area (painted) = Area (wall) - Area (window)Area (painted) = 10 x 11 - 2 x 3110 - 6104 ft²can anyone help ?????
Answer:
a), b) and c) are correct.
d) 12g^4h^5
Step-by-step explanation:
Solve the Pythagorean theorem for a, assuming a, b, and c are positive. a^2+b^2=c^2
A. a=c^2+b^2
B. a=c+b
C. a=√c^2-b^2
D. a=c-b
it should be c because the puthagorean theorem is c^2=a^2+b^2 so subtract b^2 to the other side to keep a by itself and then sqare root both sides to get ride of the square on the a
In 2021, Carla was making $15 per hour and worked 20 hours per week for 25
weeks. How many Social Security credits did she earn?
Answer:
Approximately 42 credits
Step-by-step explanation:
First you need to find the amount she makes for one week. Multiply 15 by 20: $375.00
Second find how much she makes for those 25 weeks: 375*25: 65,625
Third according to socialsecurityintelligence.com, in 2021, one credit for each $1,470 of earnings. To a maximum of 4 credit per year.
So for a year she earned 4 credits but not considering the limit, she earned 42.85 credits.
Me podrian ayudar con ese ejercisio por favor?? Me salvarian 4. Dadas las sucesiones de término general an = n + 3 y bn = 5n − 1 , realiza las siguientes operaciones: a) an – bn b) an + 3bn 5. Escribe los ocho primeros términos de la sucesión ( an ) dada por: a1 = 1, a2 = 1, an = an−1 + an−2
Explicación paso a paso:
Dado
an = n + 3
bn = 5n-1
a) an-bn = n + 3- (5n-1)
= n + 3-5n + 1
= n-5n + 3 + 1
= -4n + 4
an-bn = 4-4n
b) an + 3bn = (n + 3) +3 (5n-1)
= n + 3 + 3 (5n) +3 (-1)
= n + 3 + 15n-3
= n + 15n + 3-3
= 16n + 0
= 16n
an + 3bn = 16n
3) Dado a1 = 1, a2 = 1
an = an-1 + an-2
Debemos escribir los primeros ocho términos de la secuencia.
a3 = a3-1 + a3-2
a3 = a2 + a1
a3 = 1 + 1
a3 = 2
a4 = a3 + a2
a4 = 2 + 1
a4 = 3
a5 = a4 + a3
a5 = 3 + 2
a5 = 5
a6 = a5 + a4
a6 = 5 + 3
a6 = 8
a7 = a6-a5
a7 = 8 + 5
a7 = 13
a8 = a7 + a6
a8 = 13 + 8
a8 = 21
Por tanto, los primeros ocho términos de la secuencia son 1, 1, 2, 3, 5, 8, 13 y 21
The measures of the angles of a triangle are shown in the figure below . Solve for x
Answer:
180=90+63+4x+3
6=x
Step-by-step explanation:
the GCF of 44 and 20
Find the area of the shape. Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal. PLSS HELP!
[tex] \alpha = \frac{3\pi}{4} r {}^{2}[/tex]
[tex] \alpha = \frac{3 \times 3.14}{4} \times (2) {}^{2} [/tex]
[tex] \alpha = 9.42[/tex]
Normally the area would be given by a=πr², but since we have three quarters of a circle, we can just say a=3π/4 (r)²Area=3π if you want it in radians :)
HEY CAN ANYONE PLS ANSWER MY MATH QUESTION!!!!1
Answer:
The blue and yellow macaw is 33 inches long.
Step-by-step explanation:
If the toucan is 22 inches long and it's two thirds the length of the macaw you can divide by two to find what one third is.
22 ÷ 2 = 11
So then you have to multiply by 3 to find what the full length is.
3 x 11 = 33 inches
Hope that helps and have a great day!
Answer:
33 inStep-by-step explanation:
Let the length of the macaw be xThe length of the toucan is 22 inThen we have equation
x*2/3 = 22x = 22 ÷ 2/3x = 22*3/2x = 33 inBlue-and-yellow macaw is 33 in long
11. Tom works at an aquarium, he is asked to clean the coral reef tank. The function
graphed below represents the amount of water in gallons, y, of a the tank after x, hours.
y
225
Word Bank.
200
175
Slope, linear, quadratic,
exponential, y = mx +b, y =
ax²+bx+c, y-intercept, x-
intercept.
150
Water (gallons)
125
100
75
50
25
o
0 1 2 3 4 5 6 7 8
Time (hours)
The graph represents a
function. In which the equation is
The
feature of the graph shows the point at which
the tank ends its draining. The
shows the initial amount of water in
the tank before cleaning which is
The
is negative which shows
the amount of water being drained over the number of hours.
The graph represents a linear function. The y intercept shows the initial amount of water in the tank before cleaning which is 175 gallons. The slope is negative which shows the amount of water being drained over the number of hours.
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the amount of water in gallon after x hours.
The y intercept is (0, 175), hence b = 175.
The line passes through (0, 175) and (7, 0), hence::
Slope = (0 - 175) / (7 - 0) = -25
The equation is y = -25x + 175
The graph represents a linear function in which the equation is linear. The linear feature of the graph shows the point at which the tank ends its draining. The y intercept shows the initial amount of water in the tank before cleaning which is 175 gallons. The slope is negative which shows the amount of water being drained over the number of hours.
Find out more on linear equation at: https://brainly.com/question/14323743
whats 3x+27=39 will mark brainliest
Answer:
x=4
Step-by-step explanation:
Answer:
Step-by-step explanation:
5x+39=3x+27 i think your welcome :)
i need help on this i don't understand
Answer: Approximately 8.5 units
Step-by-step explanation:
Substitute M(2, -2) and N(8, 4) for the coordinates in the distance formula and solve for d
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
[tex]d = \sqrt {\left( {8-2 } \right)^2 + \left( {4-(-2)} \right)^2 }[/tex]
[tex]d = \sqrt {\left( {6 } \right)^2 + \left( {6} \right)^2 }[/tex]
[tex]d = \sqrt {\left( {36 } \right) + \left( {36} \right) }[/tex]
[tex]d = \sqrt {72}[/tex]
[tex]d \approx 8.5\hspace2 units[/tex]
Therefore the length of [tex]\overline{MN}[/tex] is approximately 8.5 units
Choose two numbers which absolute value of 5 1/2
Answer:
11/2,5.5
Step-by-step explanation:
I WILL GIVE BRAINLEST.Raquel has 4 brownies. She wants to give an equal share to each of her friends. How would Raquel share these brownies equally among herself and 5 friends? Use words, pictures, and an equation to explain your thinking.
Answer:
4/5 brownies for each person.
Step-by-step explanation:
4 brownies between 5 people equals 4/5, or 4 divided by 5.
Is there any trinomial antonyms.
Can anyone answer this?
To say that two or more angles are equal, we draw a little arc. If there are two arcs then it means that the angle with also two arcs marked is equal in measure, and so on
--> so:
∠A ≅ ∠Y
∠B ≅ ∠Z
∠C ≅ ∠X
To say that two more sides are equal, we draw a little tic mark. If there are two tics then it means that the sides with also two tics marked are equal in length, and so on.
--> so:
AB ≅ YZ
AC ≅ YX
BC ≅ ZX
And thus ΔACB ≅ ΔYXZ <-- we got this by matching corresponding angles of equal length
Hope it helps!
What is the value of x?
o x=2
o x=3
o x=4
o x=6
Answer: x=3
Step-by-step explanation:
Let f(x) = -2x +49 and g(x) = -4x + 3. Find
(fºg)(-5).
Answer:
3 i think
Step-by-step explanation:
so we substitute -5 to g(x)
g(x) = -4(-5) + 3
= 20 + 3
= 23
now we substitute it to f(x)
f(x) = -2x + 49
= -2(23) + 49
= -46 + 49
= 3
Answer:
3
Step-by-step explanation:
f(x) = -2x + 49
g(x) = -4x + 3
(fºg)(x) = f(g(x)) = -2(-4x + 3) + 49
(fºg)(x) = 8x - 6 + 49
(fºg)(x) = 8x + 43
(fºg)(-5) = 8(-5) + 43
(fºg)(-5) = 3
.
Are the ratios 1:2 and 9:18 equivalent?
Answer:
Yes! Because they are in proportion: 1x9 = 9, 2x9 = 18 therefore, 1:2 and 9:18 are equivalent. Similar to equivalent fractions - you need to multiply both numbers by the same number. Hope this helped!
Step-by-step explanation:
If you need further help, let me know!
- profparis
A golf ball was hit and modeled by
-16x2 + 11x + 6 = 0
When will the golf ball hit the ground?
Round to the nearest hundreths
By using the quadratic formula, we can conclude that the golf ball will hit the ground at x = 0.5 seconds.
What is the quadratic formula?
The quadratic formula is a formula that gives the solutions of a quadratic equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants and x is the variable. The formula is:
x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a
This formula can be used to find the values of x that satisfy the quadratic equation.
To find when the golf ball will hit the ground, we need to find the value of x when the height of the golf ball is equal to zero. We can do this by solving the quadratic equation [tex]-16x^2 + 11x + 6 = 0[/tex] using the quadratic formula:
x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a
where a = -16, b = 11, and c = 6. Substituting these values, we get:
x = (-11 ± [tex]\sqrt{11^2 - 4(-16)(6)}[/tex] ) / 2(-16)
x = (-11 ± [tex]\sqrt{361}[/tex])/ (-32)
Simplifying this expression, we get:
x = (-11 ± 19) / (-32)
So the two possible values of x are:
x = 8/16 = 0.5 and x = 30/16 = 1.88
Since the height of the golf ball is equal to zero when it hits the ground, we can conclude that the golf ball will hit the ground at x = 0.5 seconds (rounded to the nearest hundredth).
To know more about quadratic formulas visit:
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Lenny has a job that pays $8 per hour plus tips (t). Lenny worked for 4 hours Monday and made $65 in all. Which equation could be used to find t, the amount Lenny made in tips?
Answer:
t= 33
Step-by-step explanation:
4(8) +t = 65
32+t=65
t=33
Hope this helps!
Step-by-step explanation:
T = hourly pay (8$)
Y = hours worked
T • Y = 32
65-32 = 33$ in tips
WILL GIVE BRAINLIEST!!!
(06.02 MC)
A scatter plot with a line is shown:
Which statement is most likely correct about the line? (5 points)
It can be a line of best fit because it passes through all the data points
It can be a line of best fit because it is close to most data points
it cannot be a line of best fit because it does not pass through all the points.
it cannot be a line of best fit because it does not pass through the first and last points
Answer: The answer is B:)))
Step-by-step explanation:
It can be the line of best fit because it is close to most data points.
What is the equation of the following line written in slope-intercept form? x-intercept of 2
1.y = 2
2.x=2
3.x = -2
Answer:
The correct answer is x=2
Step-by-step explanation:
The equation of the given line written in slope-intercept form is y=x-2.
From the given figure, x-intercept of 2.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Here, slope is 0
Substitute (x, y)=(2, 0) and m=1 in y=mx+c, we get
0=1(2)+c
c=-2
Put m=1 and c=-2 in y=mx+c, we get
y=x(1)-2
⇒y=x-2
Therefore, the equation of the given line written in slope-intercept form is y=x-2.
To learn more about the slope intercept form visit:
brainly.com/question/9682526.
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10 pts. for whoever solves this!
Answer:
x = 4
Step-by-step explanation:
the segment inside the triangle is an angle bisector and divide the opposite side into segments that are proportional to the other two sides, that is
[tex]\frac{x}{x+4}[/tex] = [tex]\frac{x+6}{2x+12}[/tex] = [tex]\frac{x+6}{2(x+6)}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = x + 4 ( subtract x from both sides )
x = 4
HEEEEELLLLPP
What is the measure of <6
5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12
Step-by-step explanation:
sper ca team ajutat
Answer:
∠ 6 = 45°
Step-by-step explanation:
∠ 6 and 45° are vertically opposite angles and are congruent , so
∠ 6 = 45°
The first term of a sequence is 2, the third term is 18, and the fifth term is 162. What is
the second term of the sequence?
Answer:
[tex]a_2=6[/tex]
Step-by-step explanation:
Geometric sequence general formula: [tex]a_n=ar^{n-1}[/tex]
Given:
[tex]a_1=2[/tex][tex]a_3=18[/tex][tex]a_5=162[/tex]Therefore,
[tex]a_1=2 \implies a=2[/tex]
[tex]a_3=2 \cdot r^2=18[/tex]
[tex]a_5=2 \cdot r^4=162[/tex]
To find common ratio r, divide 5th and 3rd terms:
[tex]\dfrac{a_5}{a_3}=\dfrac{2 \cdot r^4}{2 \cdot r^2}=\dfrac{162}{18}[/tex]
[tex]\implies r^2=9[/tex]
[tex]\implies r=\sqrt{9}=3[/tex]
Therefore, geometric sequence formula: [tex]a_n=2 \cdot 9^{n-1}[/tex]
So second term of sequence:
[tex]\implies a_2=2 \cdot 3^{2-1}=6[/tex]
Price is $79.99 sales tax is 5.5% what is the total cost
Answer:
$84.38
Step-by-step explanation:
i did 5.5% of 79.99=4.39
79.99+4.39=84.38
Use distributive property to factor method 1. Use distributive property to expand method 2.
Step-by-step explanation:
I guess method 1 means to deal with whole factors.
x + 5 = (x - 2)(x + 5)
for (x + 5) <> 0 we can divide both sides by this factor :
1 = x - 2
x = 3
for the second solution we deal with
x + 5 = 0
x = -5
so, for x = -5 and x = 3 both functions deliver the same output, and these are the intersection points.
method 2 : we multiply the expression out and solve it then
x + 5 = (x - 2)(x + 5)
x + 5 = x² + 5x - 2x - 10 = x² + 3x - 10
0 = x² + 2x - 15
the general solution to such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -15
x = (-2 ± sqrt(2² - 4×1×-15))/(2×1) =
= (-2 ± sqrt(4 + 60))/2 = (-2 ± sqrt(64))/2 = (-2 ± 8)/2 =
= -1 ± 4
x1 = -1 + 4 = 3
x2 = -1 - 4 = -5
and you get the 2 solutions again. as expected, they are the same as with method 1, of course.