Answer:
x = -1/3 or 0
Step-by-step explanation:
Given equation:
[tex]36x^{2} + 12x = 0[/tex]We can factor 12x on the L.H.S since 12x is divisible by 36x² and 12x.
[tex]\implies 36x^{2} + 12x = 0[/tex]
[tex]\implies 12x(3x + 1) = 0[/tex]
This can lead to two solutions. I have listed them below!
Solution 1:Divide 12x on both sides to open the parentheses.
[tex]\implies 12x(3x + 1) = 0[/tex]
[tex]\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}[/tex]
Note: zero divided by any non-zero number is 0.
[tex]\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}[/tex]
[tex]\implies 3x + 1 = 0[/tex]
Isolate 3x on one side of the equation.
[tex]\implies 3x + 1 = 0[/tex]
[tex]\implies 3x = 0 - 1[/tex]
[tex]\implies 3x = -1[/tex]
Divide 3 both sides to determine the value of x.
[tex]\implies 3x = -1[/tex]
[tex]\implies \dfrac{3x}{3} = \dfrac{-1}{3}[/tex]
[tex]\implies \boxed{x = \dfrac{-1}{3}}[/tex]
Solution 2:Divide (3x + 1) on both sides to isolate 12x.
[tex]\implies 12x(3x + 1) = 0[/tex]
[tex]\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}[/tex]
Note: zero divided by any non-zero number is 0.
[tex]\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}[/tex]
[tex]\implies 12x = 0[/tex]
Divide 12 both sides to determine the value of x.
[tex]\implies 12x = 0[/tex]
[tex]\implies \dfrac{12x}{12} = \dfrac{0}{12}[/tex]
[tex]\implies \boxed{x = 0}[/tex]
Therefore, the solutions for x are -1/3 or 0.
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Answer:
x = 0 or x = -1/3
Step-by-step explanation:
In the equation 36x²+12x=0 we have :
36x² = 6x × (6x)
12x = 2 × (6x)
This means that 6x is a common factor,so let’s factor :
36x²+12x=0
⇔ 6x × (6x) + 2 × (6x) = 0
⇔ 6x × (6x + 2) = 0
⇔ 6x = 0 or 6x + 2 = 0
⇔ x = 0 or x = -2/6
The inverse of the function f(x) = 1/2x+10?
Answer:
f'(x) = 2x - 20
Step-by-step explanation:
f(x) = 1/2 x + 10
Switch x and y.
y = 1/2 x + 10
Solve for y by itself.
x = 1/2 y + 10
x - 10 = 1/2 y
y = 2 * (x - 10)
f'(x) = 2x - 20
Kieran enters four events in an athletics
competition. The probability of him winning each
of the events is shown below.
Order the probabilities from least likely to most
likely.
100 m
Long jump
Discus
Hurdles
2
0.46
²3
23%
3
10
5
Answer:
Discus, Hurdles, Long jump, and 100m
Step-by-step explanation:
need help with this math
Answer:
h = 5 :)
Step-by-step explanation:
Nick has planted 20 flowers and can plant 7 flowers an hour, Rachel planted 5 flowers and can plant 10 flowers an hour.
f = 7h + 20
f = 10h + 5
f = 7(1) + 20 = 27
f = 10(1) + 5 = 15
(Not this one)
f = 7(2) + 20 = 34
f = 10(2) + 5 = 25
(nope..)
f = 7(3) + 20 = 41
f = 10(3) + 5 = 35
(nope!)
f = 7(4) + 20 = 48
f = 10(4) + 5 = 45
(close, but no)
f = 7(5) + 20 = 55
f = 10(5) + 5 = 55
(Yes!)
Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend Their goal is to earn $1,500 from ticket sales. Write a system of equations to model the ticket sales, assuming the student councll> meets their goal. Use the model to determine the number of adult tickets and student tickets they expect to sell. Show work.
Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Number of adults that attend.Variable s: Number of students that attend.They expect that twice as many students as adults will attend, hence:
s = 2a.
Their goal is to earn $1,500 from ticket sales, hence:
10a + 5s = 1500.
10a + 5(2a) = 1500.
20a = 1500.
a = 1500/20.
a = 175.
s = 2a = 2 x 175 = 350.
They expect to sell 175 adult tickets and 350 student tickets.
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Please answer asap! show work!
11. What is (f.g)(x)?
f(x) = x3 +3
g(x) = 2x2 + x - 1
Answer:
2x⁵ + x⁴ - x³ + 6x² + 3x - 3
Step-by-step explanation:
Given :
f(x) = x³ + 3g(x) = 2x² + x - 1Finding (f × g)(x) :
f(x) × g(x)(x³ + 3)(2x² + x - 1)2x⁵ + 6x² + x⁴ + 3x - x³ - 32x⁵ + x⁴ - x³ + 6x² + 3x - 3Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
O It has infinitely many solutions.
O It has two solutions.
O It has one solution.
It has no solution.
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
2x-2x-7=-7
We need to solve it first as follows:
[tex]2x-2x-7=-7[/tex]
[tex]2x-2x=-7+7[/tex]
[tex]0=0[/tex]
Since L.H.S. = R.H.S.
So, it satisfies the equation for all x.
So, there will be infinitely many solutions.
Hence, Option 'a' is correct.
there are light-bulbs at the factory
nice. are they filament lightbulbs or fluorecent lightbulbs
How to simplify question below ?
Answer:
[tex]3x^2y[/tex]
Step-by-step explanation:
The cube root of 27 is 3.
With indices, cube rooting them is the equivalent of multiplying by 1/3 so:
[tex]x^2y[/tex].
Put these 2 things together and you get:
[tex]3x^2y[/tex]
convert 32 table spoons to cup
Answer:
2 cups
Step-by-step explanation:
Formula: divide the volume value by 16
so its 32 divided by 16
Why can’t you Factor x^2+9
Answer:
You can't answer this because there isn't a regular x value, there is only a x squared
Step-by-step explanation:
[tex]~~~~~~x^2 +9 = 0\\\\\implies x^2 = -9\\\\\implies x = \pm\sqrt{-9}\\\\\implies x=\pm 3i\\\\\text{Which is not real, so the given expression can't be factored for} ~x \in \mathbb{R}.[/tex]
Solve Algebraically
y=x2−4x+3
y=x−5
Answer:
then
x2-4x+3=x-5
or,x2-4x-x= -5-3
or,x2-5x+8=0
A dance CD has 10 songs on it - 8 are slow, and 2 are fast. When the DJ at a dance plays a song it is not played again. All songs from the CD are played at random.
What is the probability that the first two songs played are slow songs?
The probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.
To calculate the probability that the first two songs played are slow songs, we need to consider the total number of ways the first two songs can be selected and the number of ways to choose two slow songs out of the eight available.
Given:
Total number of songs = 10
Number of slow songs = 8
Step 1: Calculate the total number of ways to choose two songs out of ten (without replacement), which is represented by "10C2" (combinations of 10 things taken 2 at a time):
10C2 = (10 * 9) / (2 * 1) = 45
Step 2: Calculate the number of ways to choose two slow songs out of eight:
8C2 = (8 * 7) / (2 * 1) = 28
Step 3: Find the probability that the first two songs played are slow songs by dividing the number of favorable outcomes (choosing two slow songs) by the total number of possible outcomes (choosing any two songs from the CD):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 28 / 45 ≈ 0.622
So, the probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.
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What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(0,0) (4,-2)
Answer:
y = -2x
Step-by-step explanation:
From the figure, the given line passes through the points (0, 0) and (-4, 8).
Recall that the equation of a straight line is given by
Thus, the equation of the given figure is given by
-4y = 8x
Therefore, the answer is y = -2x.
Simplify the expression below as much as possible.
(7-i) + (5 + 3i) - (-3 + 2i)
A. 15
OB. 9
O C. 15-4i
OD. 9-4i
answer: 15
steps:
i means √-1
but in this problem treat
i like x
(7-i) + (5 + 3i) - (-3 + 2i) =
(7-i) + (5 + 3i) +3 - 2i
7-i + 5 + 3i +3 - 2i =
7-i + 5 + 3i +3 - 2i
7+5+3-i+3i-2i
7+5+3+2i-2i
7+5+3 =
15
Pls, look at the picture for the question.
Answer:
B
Step-by-step explanation:
surface area = area of base + area of lateral faces
Area of base:
A = lw
A = 4(4)
A = 16
Area of Lateral faces:
A = 1/2 bh
A = 1/2(5)(4)
A = 1/2(20)
A = 10
There are for lateral faces.
s = 16 + 10 + 10 + 10 + 10
Kenny plotted the following pairs of points and said they made a symmetric figure about a line with the rule: y is always 4
PLEASE HELP MEE ANSWER THIS
Volume of a Rectangular Prism = length x width x height
Length = 4
Width = 2
Height = a
Volume = 7.2
7.2 = 4 x 2 x a
7.2 = 8 x a
a = 0.9
Answer: a = 0.9
Hope this helps!
Answer:
a = 0.9 cm
Step-by-step explanation:
Volume of a rectangular prism: L*W*H
L = 4 cmW = 2 cmH = a cmV = 7.2 cm³Substitute the values above into the formula:
V = L*W*H
7.2 = 4*2*a
7.2 = 8a
/8 /8
0.9 = a
Therefore, the value of a is 0.9 cm.
Hope this helps!
ANSWER THIS CORRECTLY FOR BRAINLIEST!!!!
This is 8th grade
algebra btw
Answer:
V = 2143.57
Step-by-step explanation:
To find the volume of a sphere you need to use this formula:
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
r = radius
Solve:
You need the radius from the diameter. Divide 16/2 which is
8.
[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]
V = 2143.57
find the volume of the shape
Answer:
hmmm the mass are the numbers of the up and volume of the bottom
Step-by-step explanation:
Find the value marked b?
Based on the alternate interior angles theorem, the value marked b is calculated as: 190°
What is the Alternate Interior Angles Theorem?The theorem states that two alternate interior angles are always congruent to each other.
The measure of angle b based on the alternate interior angles theorem would be:
m∠b = 50 + (320 - 180)
m∠b = 190°
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A midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 120. 132. 160.
The midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 132.
How to calculate the midpoint?The value of f(1/2) will be:
= 2(1/2)(1/2 - 4)(1/2 - 8)
= 105/4
The value of f(3/2) will be:
= 2(3/2)(3/2 - 4)(3/2 - 8)
= 195/4
The value of f(5/2) will be:
= 2(5/2)(5/2 - 4)(5/2 - 8)
= 165/4
The value of f(7/2) will be:
= 2(7/2)(7/2 - 4(7/2 - 8)
= 63/4
Therefore, the midpoint approximation will be:
= 1/4(105 + 195 + 165 + 63)
= 132
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x^2+4x-4=0
Solve by factoring.
Answer:
1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2
S(x) = ( ) + ( ) =3
P(x) = ( ) * ( ) =2
S(x) = ( 2 ) + ( 1 ) =3
P(x) = ( 2 ) * ( 1 ) =2
These numbers in bold will be coeficients of x.
Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2
So x²+3x+2 =x²+2x+1x+2
x² +2x+x+2 Put the x in evidence
x(x+2)+1(x+2) Find the Maximum Common Divider
(x+1)(x+2)
2) x²+x-6=0
Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?
S(x) = ( 3 ) + ( -2 ) =1
P(x) = ( 3 ) * ( -2 ) =-6
Rewrite
x²+x-6
x²+3x-2x-6 Group them
x(x+3)-2(x+3) Common Term
(x+3)(x-2)
3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0
Firstly multiply a*c, in this case -2 * 30 = -60
Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.
P(x)= ( 10 ) * ( - 6 ) = -60
S(x) = ( 10 ) + ( -6 ) = 4
Rewriting
-2x²+10x-6x+30 Group them
2x(x+5) -6(x+5)
(2x-6)(x+5) Inserting the -1 to finally adjust
-1(2x-6)(x+5)
4) Explanation is the same principle as a≠1
3x²+4x-4=0
P(x) = ( 6 ) * (-2 ) = -12
S(x) = ( 6 ) + ( -2 ) = 4
3x²+4x-4 = 3x²+6x-2x-4
3x²+6x -2x+4
3x(x+2)-2(x-2)
(3x-2)(x+2)
The other ones are just applications of these, above.
Step-by-step explanation:
If x=−4 is a solution to the equation x2+11x+K=0 , then K= ?
Answer:
x^2 + 11x + k = 0
(-4) ^2 + 11 (-4) + k = 0
16 - 44 + k = 0
-28 + k = 0
K = 28
Hope Helpful ~
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -3/2x + 8
Step-by-step explanation:
Slope: y2 - y1 / x2 - x1
= 5-2 / 2-4
= -2/3
Y intercept is 8
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, what is the volume of the water that was displaced (in cubic inches)?
The volume of the water that was displaced will be 0.06 cubic feet.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
mass = density × volume
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water.
Then the volume of the water that was displaced will be
We know that the density of the water is 62.4 pounds per cubic foot.
Then we have
3.7 = 62.4 × volume
Volume = 0.059
Volume ≅ 0.06 cubic-foot
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[tex] \sqrt[3]{800} [/tex]
between 2 and 3
between 4 and 5
between 9 and 10
Determine the measure of LUXW in the diagram.
Y
66°
U
W
X
The measure of LUXW is
57°
Z
Answer:
33°
Step-by-step explanation:
Where a transversal crosses parallel lines at right angles, all of the angles at their points of intersection are right angles.
__
Angles at U are right angles, congruent to ∠UXZ. So, acute angle UXW in right triangle UXW is the complement of acute angle UWX:
∠UXW = 90° -57° = 33°
Help and show explanation please
Answer:
This app is very good,it help us do our homework.and we make a good passed.
he average of 7 consecutive even integers is 10. What is the largest
of the 7 integers?
Answer:
only two brother ok bye
due to inflatation, the cost of harys hot wings grows by 4% every year. this year a dozen hot wings cost 5.99
part a. how much will a dozen hot wings cost next year
part b. how much will a dozen hot wings cost in 2 years
Answer:
Part A : $6.23
Part B : $6.48
Step-by-step explanation:
Let's apply the Simple Interest Formula, which is :
Simple Interest = Principal Amount x Interest rate x Time Period
In one year :
I = 5.99 x 4% x 1I = $0.24Cost = $5.99 + $0.24Cost = $6.23In 2 years :
I = $6.23 x 4% x 1I = $0.25Cost = $6.23 + $0.25Cost = $6.48