Answer:
Two complex roots
Step-by-step explanation:
A discriminant of a quadratic equation ax² + bx +c is:
D= √b²-4acFor the given function f(x)= 6x² - 5x + 3 the discriminant is:
D= √(-5)² - 4*6*3= √25- 72 = √-47= i√47Since it has i element, the roots are complex
Correct option is the first one
Answers:
3x-2y=-12
2x-3y=-12
3x+2y=12
3x+3y=-12
Answer:
3x + 2y = 12.
Step-by-step explanation:
Two conspicuous points on the graph are at (0, 6), and (4, 0).
That means the slope of the line is (6 - 0) / (0 - 4) = 6 / -4 = -3 / 2.
The intercept of the line is at (0, 6).
This means that the equation of the line is y = -3/2x + 6.
y = -3/2x + 6
Add 3/2x to both sides
3/2x + y = 6
Multiply all terms by 2
3x + 2y = 12
Hope this helps!
Assume EFG JKL. If m J = 90 , m K = 26 , and m L = 64 , what is the measure of E?
Answer:
I think its 90
Step-by-step explanation:
Answer:
E=90
Step-by-step explanation:
because EFG=JKL E=J F=K G=L
In a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%. What’s the probability of the student being a male, if you know the student studies Spanish
Answer:
27.8%
Step-by-step explanation:
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
The probability of the student being a male is 27.8%
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that in a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%.
The probability of the student being a male will be calculated as below:-
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
Therefore, the probability of the student being a male is 27.8%
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Find each product
6xy2(x4+3x3y+3xy3)
PLEASE HELP!!! ASAP!!
Answer:
6x^3y^2+18x^4y^3+18x^2y^5
Step-by-step explanation:
Multiply each term:
6x^3y^2+18x^4y^3+18x^2y^5
Plz mark me brainliest!!
Please can someone help me
Answer:
706.86 cm
Step-by-step explanation:
=4pi(r^2)
=12.56(r^2)
=12.56(7.5^2)
=12.56(56.25)
=706.86
HELP ASAP PLEASE
I JUST NEED WORK SHOWN BUT ASAP
Answer:
s = 25.33m
θ = 60.65°
12.37m
A = 160m^2
Step-by-step explanation:
The pyramid has a side base of 35m and a height of 22m.
side base = b = 35m
height of the pyramid = h = 22m
To calculate the slant edge of the pyramid, you first calculate the diagonal of the squared base of the pyramid.
You use the Pythagoras theorem:
[tex]d=\sqrt{(\frac{35}{2})^2+(\frac{35}{2})^2}=24.74[/tex]
With the half of the diagonal and the height, and by using again the Pythagoras theorem you can calculate the slat edge:
[tex]s=\sqrt{(\frac{24.74}{2})^2+(22)^2}=25.23[/tex]
The slant edge of the pyramid is 25.33m
The angle of the base is given by:
[tex]\theta=sin^{-1}(\frac{h}{s})=sin^{-1}(\frac{22}{25.23})=60.65\°[/tex]
The angle of the base is 60.65°
The distance between the corner of the pyramid and its center of its base is half of the diagonal, which is 24.74/2 = 12.37m
The area of one side of the pyramid is given by the following formula:
[tex]A=\frac{(b/2)l}{2}[/tex] (1)
l: height of the side of pyramid
then, you first calculate l by using the information about the side base and the slant.
[tex]l=\sqrt{s^2-(\frac{b}{2}^2)}=\sqrt{(25.33)^2-(\frac{35}{2})^2}\\\\l=18.31m[/tex]
Next, you replace the values of l and b in the equation (1):
[tex]A=\frac{(35/2)(18.31)}{2}=160m^2[/tex]
The area of one aside of the pyramid is 160m^2
Answer? Please make sure you answer it as a simplified fraction.
==================================================
Work Shown:
Let x = 0.363636...
The "36" pattern goes on forever as indicated by the three dots.
Multiply both sides by 100 to get 100x = 36.363636...
Effectively, multiplying by 100 moves the decimal point over 2 spots to the right. The "36" goes on forever here too. The key is to match up the infinite sequences of "36"s and cancel them out through subtraction
36.363636... - 0.363636... = 36
while
100x - x = 99x
So after subtracting the equations, we end up with 99x = 36
From here we solve for x by dividing both sides by 99 and reducing the fraction
99x = 36
x = 36/99
x = (9*4)/(9*11)
x = 4/11
As a check, use your calculator to find that
4/11 = 0.36363636...
so the answer is confirmed
Note: your calculator may display something like 0.3636363636364, that 4 should not be there. It's a result of rounding (due to the next digit being a 6). Keep in mind that rounding error is often a possibility when it comes to approximate calculations. The calculator only has so much memory and display space.
Help please! Thank you
PLZ HELP (BRAINLIEST)
Answer:
C. y = 0.5x + 5
Hope that helps.
Find the value of f(g(-2))
Answer:
The correct ans is 3.
g(-2) = 2(-2) + 5
=-4 + 5 = 1
f(g(-2)) = 4 - (1)^2
= 4 - 1
=3
Step-by-step explanation:
what does 30b/6b equal? (30b divided by 6b)
Answer:
5
Step-by-step explanation:
Given
[tex]\frac{30b}{6b}[/tex]
Cancel the b on the numerator/ denominator.
Also the 30 and 6 can both be cancelled by 6 , thus
[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5
Answer:
[tex]\boxed{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{30b}{6b}[/tex]
[tex]\sf Simplify[/tex]
[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]
[tex]5 \times 1[/tex]
[tex]=5[/tex]
True or False: In a uniform probability distribution, any random variable is just as likely as any other random variable to occur, provided the random variables belong to the distribution.'
Answer:
True
Step-by-step explanation:
trust me, i remember this question
Can somebody plz help me [-5+(-7)]^2-(7+3)^2
Answer:
[tex]\boxed{44}[/tex]
Step-by-step explanation:
[tex][-5+(-7)]^2-(7+3)^2[/tex]
Resolving Parenthesis
[tex](-5-7)^2-(10)^2\\(-12)^2-100\\144-100[/tex]
=> 44
Answer:
[tex]\boxed{44}[/tex]
Step-by-step explanation:
[tex][-5+(-7)]^2-(7+3)^2[/tex]
Solve for brackets first.
[tex][-12]^2-(10)^2[/tex]
Solve the exponent or power.
[tex]144-100[/tex]
Subtract the numbers.
[tex]=44[/tex]
ASAP!!! PLEASE help me solve this question!!!! I really need help...
Answer:
304(pi) g
Step-by-step explanation:
First we find the volume of the hollow ball. Then we find the mass using the volume and density.
Let R = exterior radius = 3 cm
Let r = interior radius = 2 cm
volume = exterior volume - interior volume
volume = (4/3)(pi)R^3 - (4/3)(pi)r^3
volume = (4/3)(pi)(R^3 - r^3)
volume = (4/3)(pi)(3^3 - 2^3) cm^3
volume = (4/3)(pi)(27 - 8) cm^3
volume = (76/3)pi cm^3
Now we use the density and the volume to find the mass.
density = mass/volume
mass = density * volume
mass = 12 g/cm^3 * (76/3)pi cm^3
mass = 304(pi) g
Answer: 304(pi) g
Answer:
m=(76π/3 )(12)=304πg
Step-by-step explanation:
volume of sphere=(4πr³)/3
V=4π(2)³/3=32π/3 of the interior
V of exterior=4π(3)³/3=36π
Volume of the whole metal =108π/332π/3=76π/3=25 1/3 π
m=V*D ( volume * density)=
m=(76π/3 )(12)=304πg
Can anyone help me with this please? And QUICK!
Answer:
30.6
Step-by-step explanation:
The following data were obtained from the question:
Angle θ = 23°
Opposite = 13
Adjacent = y
The value of y can be obtained by using the following trig ratio:
Tan θ = Opposite /Adjacent
Tan 23° = 13/y
Cross multiply
y × Tan 23° = 13
Divide both side by Tan 23°
y = 13/Tan 23°
y = 30.6
Therefore, the value of y in the diagram above is 30.6
can you find values of x and y
Answer:
For the second figure
X=10
Y=30
Step-by-step explanation:
3x=(5x-20).... Alternative interior angles
3x=5x-20
20=5x-3x
20=2x
x=10
2y+4y= 180
6y=180
Y=30
PLEASE HELP ASAP ON ALL THE PARTS!!! suppose there is a card game where you are dealt a hand of three cards. you have already learned that the total number of three card hands that can be dealt from a deck of 52 cards is:
Answer:
A. The total number of three-card hands (permutations) that can be made with two aces is 576
B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288
C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130
Step-by-step explanation:
A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:
total number of three-card hands (permutations) that can be made with two aces=4*3*52
total number of three-card hands (permutations) that can be made with two aces=576.
B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:
actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48
4C2=4!/2!2!
C2=6
Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288
C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130
Which of the following describes the graph of 2x + 4y < 16? a:solid line, shaded below b:dashed line, shaded above c:dashed line, shaded below d:solid line, shaded above
Answer: C
Step-by-step explanation:
[tex]2x+4y<16\\=4y<-2x+16\\=y<-\frac{1}{2} x+4[/tex]
Since we are not dividing by a negative at any point during the simplification, the inequality sign won't change.
"<" means that the line will be dashed and shaded below.
Hope this helps!
The description of the inequality is (c) dashed line, shaded below
The inequality is given as:
2x + 4y < 16
The inequality is represented as less than (<)
When the less than sign is used in an inequality, the graph of the inequality would be a dashed line shaded below
Hence, the true statement is (c) dashed line, shaded below
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Write 59/40 as a decimal
Answer:
1.475
Step-by-step explanation:
|x–5|=–5 plzz help me
Answer:
(0-5)=-5
-5-5 = 0
x=0
Step-by-step explanation:
Which of the points listed is the same distance from the y-axis as the point (-4,7.5)?
Answer:
(4,7.5)
Step-by-step explanation:
Reflect (-4,7.5) at the y-axis
I NEED HELP PLZ Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
19
Step-by-step explanation:
help me please, explanation not necessary but would be appreciated
Answer:
55°
Step-by-step explanation:
The following data were obtained from the diagram given above:
Adjacent = 4
Hypothenus = 7
Angle A =?
The value of angle A can be obtained as follow:
Cos A = Adjacent / Hypothenus
Cos A = 4/7
Take the inverse of Cos.
A = Cos¯¹(4/7)
A = 55.1° ≈ 55°
Therefore, the value of angle A is approximately 55°.
Will give the brains of me brains and my brains and maby ur brain to u how many brains can i give u if u ask this quetion right?
Answer:
$10.5 dollars
Step-by-step explanation:
Keep your brains.
Using the data given:
(18+4+12+8)÷4=
42÷4=
$10.5 dollars
Simplify $(1-3i)(1-i)(1+i)(1+3i)$
[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]
Answer:
[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]
Step-by-step explanation:
[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]
Determine the settlement set of the following trigonometric equations! cos (x - 1/3π) = cos 1/2π, 0 ≤ x ≤ 2π
cos (x - π/3) = cos (π/2)
Then we need x - π/3 = π/2
Solving the equation:
x - π/3 = π/2
x = π/2 + π/3
x = 5π/6
Please Help! Which description best describes the solution to the following system of equations? y = −x + 4 y = 3x + 3 Line y = −x + 4 intersects the line y = 3x + 3. Lines y = −x + 4 and y = 3x + 3 intersect the x-axis. Lines y = −x + 4 and y = 3x + 3 intersect the y-axis. Line y = −x + 4 intersects the origin.
Answer:
Line y = −x + 4 intersects the line y = 3x + 3.
Step-by-step explanation:
Please Help! Which description best describes the solution to the following system of equations?
y = −x + 4
y = 3x + 3
Line y = −x + 4 intersects the line y = 3x + 3.
This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.
Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
Line y = −x + 4 intersects the origin.
What is the solution to the linear equation?
2/3x - 1/2 = 1/3 + 5/6x
X = -5
X = -1/6
X = 1/6
X = 5
Hey there! :)
Answer:
x = -5.
Step-by-step explanation:
Solving for x from the equation:
[tex]\frac{2}{3}x - \frac{1}{2} = \frac{1}{3} +\frac{5}{6}x[/tex]
Begin by creating a common denominator for the terms involving x as well as the constants:
[tex]\frac{4}{6}x - \frac{3}{6} = \frac{2}{6} +\frac{5}{6}x[/tex]
Now that each term has a common denominator, we can begin solving for x by isolating the variable:
Subtract 5/6x from both sides:
[tex]\frac{4}{6}x-\frac{5}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
[tex]-\frac{1}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
Add 3/6 to both sides:
[tex]-\frac{1}{6}x = \frac{5}{6}[/tex]
Divide -1/6 from both sides. (Multiply by the reciprocal, or -6)
[tex]-\frac{1}{6}x(-6) = \frac{5}{6}(-6)[/tex]
x = -5.
You want to buy a new sweater. The regular price was
$48 dollars. The sale price was $34. What was the
percent of discount to the nearest percent?
Answer:
29%
Step-by-step explanation:
48-34 = 14 dollar saving
14/48 = 29.17 % = 29% saving
Answer:
29%
Step-by-step explanation:
48-34= 14 dollar saving
14/48 = 29.17% = 29% saving
Danny drove to Yosemite Park from his home at 60 mph. on his trip home, his rate was 10 mph less and ...?
Answer: 300 mi.
Step-by-step explanation:
Let t be the time taken to drive to the park (at 60 mph)
Let t + 1 be the time taken to drive home from the part (at 50 mph)
Distance to the park = 60t
Distance from the park = 50(t + 1)
Obviously the distances should be the same so equate them.
60t = 50(t + 1)
60t = 50t + 50
10t = 50
t = 50/10
t = 5 hours
Now figure the distance. You can use either equation for the distance to or from the park:
60t = 60(5) = 300 miles
or
50(t+1) = 50(6) = 300 miles
The distance to or from the park will be 300 miles.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let assume t be the time taken to drive to the park (at 60 mph).
Let assume t + 1 be the time taken to drive home from the part (at 50 mph)
The Distance to the park = 60t
The Distance from the park = 50(t + 1)
Obviously the distances should be the same, so equate them;
60t = 50(t + 1)
60t = 50t + 50
10t = 50
t = 50/10
t = 5 hours
Now figure the distance. We can use either equation for the distance to or from the park:
60t = 60(5) = 300 miles
50(t+1) = 50(6) = 300 miles
Therefore, the distance to or from the park will be 300 miles.
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