Answer:
[tex]\sf x=1+i\sqrt{\dfrac{2}{3}} \ \quad and \quad \:x=1-i\sqrt{\dfrac{2}{3}}[/tex]
Explanation:
Given Expression:
3x² - 6x + 5 = 0Use the Quadratic Formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]
insert coefficients
[tex]\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}[/tex]
[tex]\Longrightarrow \sf x =1 \pm i\dfrac{\sqrt{6} }{3}[/tex]
[tex]\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}}, \quad 1-i\sqrt{\dfrac{2}{3}}[/tex]
Use quadratic formula
[tex]\\ \rm\Rrightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm \sqrt{36-60}}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm\sqrt{-24}}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm2\sqrt{6}i}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=1\pm \dfrac{sqrt{2}i}{\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow x=1\pm\sqrt{\dfrac{2}{3}}i[/tex]
The graph of the function f(x)=−4(x−3)2+9 will be a parabola opening in which direction?
Answer:
downwards
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
• if a > 0 then parabola opens upwards
• if a < 0 then parabola opens downwards
for
f(x) = - 4(x - 3)² + 9 with a = - 4 < 0 , then
the parabola opens downwards
Subtract 5x - 4 from the sum of -3x - 4 + y and 4x - y
Answer:
-4x
Step-by-step explanation:
((-3x-4+y) + (4x-y)) - (5x-4)
= (-3x-4+y+4x-y) - 5x+4
= (x-4) -5x+4
=x-4-5x+4
=-4x
Drag and drop a power into each box to match its number.
1,000 --- ( )
10,000 --- ( )
1,000,000 --- ( )
(10^2) (10^3) (10^4) (10^5) (10^6)
The match of the expressions are:
1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6) How to rewrite the numbers as powers?The numbers are products of 10.
This means that the numbers can be represented as exponents, where the base is 10 and the exponent is the number of zeros.
Using the above highlight, we have:
1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6)Read more about powers and exponents at:
https://brainly.com/question/11975096
#SPJ1
Somebody please help me with this question
Answer:
-2
-1
-2
-3
Step-by-step explanation:
For an odd function, f(-x) = -f(x).
f(2) = 2; f(-2) = -2
f(3) = 1; f(-3) = -1
f(4) = 2; f(-4) = -2
f(6) = 3; f(-6) = -3
Mollie wants to measure the capacity of the kitchen sink.
She has a 1 L container and a 10 mL container. Which should she use and why?
A.
10 mL container; the capacity of the sink is close to 10 mL.
B.
10 mL container; the capacity of the sink is less than 1 L so the 1 L container would not give an accurate measurement.
C.
1 L container; the capacity of the sink is at least 1 L.
D.
Either container; or the 10 mL container can measure the capacity as quickly as the 1 L container.
Answer:
1L container as the capacity of the sink is obviously at least 1L and most probably much more than 1L
Step-by-step explanation:
letter C
Use the net to determine the total surface area.
134.4 in
92.8 in
103.2 in
72 in
Use Order of Operations
to solve. PEMDAS
9 + 6(2²+4)
Answer:
57
Step-by-step explanation:
9+6(2^2+4)
Calculate 2 to the power of 2 and get 4.
9+6(4+4)
Add 4 and 4 to get 8.
9+6×8
Multiply 6 and 8 to get 48.
9+48
Add 9 and 48 to get 57.
57
Bill is making a movie and needs to cast some actors. There are 5 actors ( Anne, Lisa, Diana, Maggie, and Susan ) interested in playing the female lead role, and 2 actors ( Jacob and Mark ) interested in playing the male lead role. Anne and Mark are Bill's siblings. What is the probability Bill will cast a family member in the movie?
Answer:
2 out of seven or 2/7 or 28.5%
Step-by-step explanation:
there are two "yeses" out of 7 total choices
What is the answer to this
The Smith family pays a rate of 27 mills in property tax. The assessed value of their home is $98,000. What is their property tax?
Their property tax would be =$ 26,460
Calculation of property taxA mill is one-thousandth of a dollar, and in property tax terms is equal to $1.00 of tax for each.
Therefore 27 mills = $27 for every $1,000 of assessed value, or 2.7%.
To calculate the property tax would
= 27/100× 98,000
= 2646000/100
=$ 26,460
Therefore, Their property tax would be =$ 26,460
Learn more about percentage here:
https://brainly.com/question/24304697
#SPJ1
What is the ratio of 338 and 508
RATIO OF 338 : 508
=> 169 : 254
What is 10 to the power of 3.
I would like to thank everyone that asked and answered questions I was stuck on. I graduated last week and couldnt have done it without Brainly.
Answer:
1000
Step-by-step explanation:
Hello!
10³ can be expanded to 10 x 10 x 10
Multiplying it out, we get 1000.
When multiplying by 10 you basically add a zero to the end, so we add 3 zeroes in total, which gives us 1000.
ExponentsWarning! [tex]x^y[/tex] is not [tex]x*y[/tex]. A very common error.
Instead, picture it as we are multiplying "x" by itself for "y" number of times.
I appreciate your kind comments!
PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Circumference: 25.12m
Area: 50.24 [tex]m^{2}[/tex]
Step-by-step explanation:
Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius
C=3.14*2*4=3.14*8=25.12
Formula for area of a circle: A=[tex]\pi r^{2}[/tex]
A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24
The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?
The time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?The time will be calculated as:-
First, we will calculate the speed to cover the distance of Brother's house:-
Speed = Distance / Time
Speed = 481 / 13 = 37 miles per hour.
Now the time to cover a distance of 814 miles will be calculated as:-
Time = Distance / Speed
Time = 814 / 37
Time = 22 hours
Therefore the time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
To know more about Speed follow
https://brainly.com/question/6504879
#SPJ1
7x^2+3y^2+12x+2y-6=0 Help me find the value of a,b,c and the discriminant number
Answer:
b o a h d
Step-by-step explanation:
1*5 3%9 46% &45 that is the answer
Which of the following functions best fits the data shown in the scatterplot below? y=100x+2y is equal to 100 x plus 2 y=20x2+10y is equal to 20 x squared plus 10 y=4x+8y is equal to 4 to the x th power plus 8 y=2x+5y is equal to 2 to the x th power plus 5
The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{102 - 2}{1 - 0}[/tex]
m = 100
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 100(x -0) + 2
Evaluate
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
Read more about scatter plot at:
https://brainly.com/question/6592115
#SPJ1
Pls Help I’m so confused how do you do this
Answer: A
Step-by-step explanation:
[tex]$$Given $m \angle A=9 x-7, \quad m \angle B=7 x-9, m \angle C=28-2 x$ \\For the triangle $m \angle A+m \angle B+m \angle c=180$$$\begin{aligned}&\Rightarrow(9 x-7)+(7 x-9)+(28-2 x)=180 \\&\Rightarrow 9 x+7 x-2 x-7-9+28=180 \\&\Rightarrow 14 x=180-28+16 \\&\Rightarrow 14 x=168 \\&\Rightarrow \quad x=12\end{aligned}[/tex]
[tex]$$Therefore,\\&m \angle A=9 x-7=9 \times 12-7=101^{\circ}\\&m \angle B=7 x-9=7 \times 12-9=75^{\circ} \\&m \angle C=28-2 x=28-2 \times 12=28-24=4^{\circ}\\[/tex]
[tex]$$Since $m \angle A=101^{\circ}$ so $B C$ is the longest side of a triangle $\triangle A B C$ \\\\Since $m \angle C=4^{\circ} S 0$ SB is the shortest side of a triangle $\triangle A B C$\\\\So listing the sides in $\triangle A B C$ from shortest to longest is: (a) $\overline{A B}, \overline{A C}, \overline{B C}$[/tex]
32 of the 49 8th Graders said that they
prefer dogs over cats.
22 of the 38 9th Graders said that they
prefer dogs.
Did a higher percentage of 8th Graders or
9th Graders prefer dogs?
8th Graders
9th Graders
Answer:
8th graders i think is the answer
Step-by-step explanation:
Answer:
The 9th grades had given a higher percentage because even without converting to a percent, you can tell just by seeing that there is a 1 number difference if you would try to add.
hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
What is the radius of the circle with center at (-6, -4) that goes through the point (1, -7) rounded to the nearest tenth?
Answer:
dhususbdgdg
Step-by-step explanation:
hdhakuxtsjwkbevdvsiw in e
I donot understand what so ever but brainly has def been helping
Answer:
what happened to you brooooooooo
what is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval
The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π
How to solve trigonometric inequality?We are given the trigonometric Inequality;
2 sin(x) + 3 > sin²(x)
Rearranging gives us;
sin²(x) - 2 sin(x) - 3 < 0
Factorizing this gives us;
(sin(x) - 3)(sin(x) + 1) < 0
Thus;
sin(x) - 3 = 0 or sin(x) + 1 = 0
sin(x) = 3 or sin(x) = -1
sin(x) = 3 is not possible because sin(x) ≤ 1.
Thus, we will work with;
sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.
Then, x = sin⁻¹(-1)
x = 3π/2.
Now, if we split up the solution domain into two intervals, we have;
from 0 ≤ x < 3π/2, at x = 0. Then;
sin²(0) - 2 sin(0) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 0 ≤ x < 3π/2 is true.
From 3π/2 < x ≤ 2π, take x = 2π. Then;
sin²(2π) - 2 sin(2π) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 3π/2 < x ≤ 2π is also true.
Read more about trigonometric inequality at; https://brainly.com/question/27862380
#SPJ1
If 30% of a number is 78 and 65% of the same number is 169, find 95% of that
number.
Answer:
let say the number is x, then 30x÷100=78, x=260...from this we can calculate 95 percent of 260 which is equal to 247
The 95 percentage of the number is A = 247
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the number be represented as n
Now , We can set up two equations based on the given information
30 percentage of the number is 78 ,
So , 0.3 ( n ) = 78
0.65 ( n ) = 169
Solving for n in the first equation, we get:
n = 260
Substituting n = 260 into the second equation, we can check that it is true:
0.65(260) = 169
Now, we can find 95% of the number by multiplying it by 0.95
0.95 x 260 = 247
Hence , 95% of the number is 247
To learn more about percentage click :
https://brainly.com/question/12861068
#SPJ2
I need help with question 24
Answer:
D
Step-by-step explanation:
angle ABC=angle ADC
angle BAC=angle DCA
AC=CA
help pleaseeeeeeeeee
Please explain as well!
Answer:
The height of the other book is 2 3/4 inches.Step-by-step explanation:
From the information,we get:
Two stacks of books together are = 7 1/2 inches tall.
One stack is given,that is = 4 3/4 inches.
To Find:
The height of the other.Solution:
Let us assume that the other height of the book be x.
Then the equation will be:
[tex] 4\cfrac{3}{4} + x = 7\cfrac{1}{2} [/tex]
Solve for x to get the other book's height.Convert the mixed fractions to fractions:
[tex] \implies \: \cfrac{19}{4 } + x = \cfrac{15}{2} [/tex]
Subtract 19/4 from both sides:
[tex] \implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4} [/tex]
[tex] \implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}[/tex]
Hence, we can conclude that:
The height of the other book is 2 3/4 inches.
Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
The probability that the second ball drawn is black is 4/10 = 2/5
How to find the probability?
There are two cases. The case where the first ball is red is the first one.
The probability of drawing a red ball is equal to the quotient between the number of red balls and the total number of balls.
p = 3/5
Then, the probability of drawing a black ball in the second attempt is computed in the same way, but because we already drew a ball, now the total number of balls is 4, so we have:
q = 2/4 = 1/2.
So the joint probability is:
P = (3/5)*(1/2) = 3/10.
Then we have the case where both balls are black, the probabilities now are:
p = 2/5
q = 1/4
So the joint probability is:
P = (2/5)*(1/4) = 1/10
The total probability is the sum of the two above:
probability = 3/10 + 1/10 = 4/10.
The probability that the second ball drawn is black is 4/10 = 2/5
If you want to learn more about probability:
https://brainly.com/question/251701
#SPJ1
Which graph represents exponential decay?
ty
80
60
40
20
80
60
40
20
2
1 2
3
80
60
40
20
ty
O
2 3
x
80
60
40
20
ty
1
2
3
Using exponential function concepts, it is found that the first graph to the similar problem represents an exponential decay.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.As x goes to positive infinity, a exponential function approaches a constant, hence a graph similar to the first one of the similar problem linked below represents exponential decay.
More can be learned about exponential functions at https://brainly.com/question/17747948
#SPJ1
which function below has the smallest slope?
f(x)
f(x) = 2x - 3
Answer:
f(x)
Step-by-step explanation:
f(x) is a little represented number after solving for x but
f(x)=2x-3 is more bigger
PLEASE HELP!!!!!! WHAT IS THE ANSWER
Answer:
B
Step-by-step explanation:
Divide y by x for each ordered pair:
2/4 = 1/2
3/6 = 1/2
5/10 = 1/2
7/14 = 1/2
All ratios are equal, so it is proportional.
Answer: B
Answer:
b
Step-by-step explanation:
mark brainliest