1/3(6x-5)-x = 1/3-2(x+1)
Value of X
Answers
Answer:
x=0
Step-by-step explanation:
do you need work? I did it in my head
Answer:
x=5/24
Step-by-step explanation:
2x-\frac{5}{2}=-2x-\frac{5}{3} Then add 5/2 to both sides 2x-\frac{5}{2}+\frac{5}{2}=-2x-\frac{5}{3}+\frac{5}{2} simplify 2x=-2x+\frac{5}{6} add 2x to both sides 2x+2x=-2x+\frac{5}{6}+2x simplify 4x=\frac{5}{6} divide both sides by 4 \frac{4x}{4}=\frac{\frac{5}{6}}{4} simplify then u get x=5/24
Related Questions
what is the slope and y-intercept of the line given by the equation y=-3+4?
Answers
Answer: Slope: 0
y-intercept: (0,7)
Step-by-step explanation:
PLEASE HELP!!! WILL GIVE BRAINLIEST
Answers
y=-10x-29 and y=-59
substitute the y in the equation for -59:
-59=-10x-29
add 29 on both sides
-30=-10x
divide both sides by -10
3=x
so,
x=3
I put $450 in my
savings account. If the
interest rate is 4.5%, how
much money will be in my
account in 3 years?
Answers
Answer:
60.75
Step-by-step explanation:
It would be I=(450)(0.045)(3).
450x0.045 is 20.25, and 20.25x3 is 60.75.
Hope this helps!
The function f is given by f(x)=(x−2)(x+4) . Without using graphing technology, answer the following questions. 1. What are the x -intercepts of the graph representing f ? Type the answers in the boxes below. ( , ) and ( , ) 2. What are the x - and y -coordinates of the vertex of the graph? Type the answers in the boxes below. x= y= 3. What is the y -intercept? Type the answer in the boxes below. ( , ) 4. Sketch a graph that represents f .
Answers
To find the x-intercepts of the graph, we need to solve for when f(x) = 0.
f(x) = (x - 2)(x + 4) = 0
Setting each factor to zero and solving for x, we get:
x - 2 = 0 or x + 4 = 0 x = 2 or x = -4
Therefore, the x-intercepts of the graph are (2, 0) and (-4, 0).
To find the vertex of the graph, we can use the formula x = -b / (2a) to find the x-coordinate, and then substitute that value into the function to find the corresponding y-coordinate.
f(x) = (x - 2)(x + 4) = x^2 + 2x - 8
a = 1, b = 2
x = -b / (2a) = -2 / (2*1) = -1
f(-1) = (-1)^2 + 2(-1) - 8 = -7
Therefore, the vertex of the graph is (-1, -7).
To find the y-intercept, we can substitute x = 0 into the function and solve for f(x).
f(x) = (x - 2)(x + 4) = x^2 + 2x - 8
f(0) = (0)^2 + 2(0) - 8 = -8
Therefore, the y-intercept of the graph is (0, -8).
Here's a sketch of the graph:
^
|
4 | x
| x
| x
2 | x x
| x x
| x
0--+------------->
|-4 -2 0 2 4
The graph is a parabola that opens upwards and has x-intercepts at (2, 0) and (-4, 0), a y-intercept at (0, -8), and a vertex at (-1, -7).
Which function represents the inverse of function fbelow?
f(x) = 3 x + 5
Answers
Answer:
\(f^{-1}\) (x) = \(\frac{x-5}{3}\)
Step-by-step explanation:
let y = f(x) then rearrange making x the subject , that is
y = 3x + 5 ( subtract 5 from both sides )
y - 5 = 3x ( divide both sides by 3 )
\(\frac{y-5}{3}\) = x
Change y back into terms of x with x = \(f^{-1}\) (x) , then
\(f^{-1}\) (x) = \(\frac{x-5}{3}\)
The roof is leaking in Tim's cabin. He has put small containers (all the same size) and large containers (all the same size) around the cabin to capture the water before it hits the floor Two small containers and one large container together hold 10 cups of water One large container minus one small container leaves 4 cups of water How many cups of water does the large container hold?
Answers
Answer:
The large container holds 6 cups of water
Step-by-step explanation:
If two small containers and one large container equal 10 cups and one large minus one small equals 4 cups then that means that each small container has to equal 2 cups of water.
if i rolled one die 10 times, what is the mode of the values listed that i rolled? 5, 5, 4, 6, 3, 2, 2, 3, 1, 5 responses 2 2 3 3 4 4 5 5 6 6
Answers
mode is 5 and 2 because 2 and 5 occurs more times than other number
Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.
The total outcomes = 7
This is because the cube was rolled 7 times
The value recorded are
2, 1
4, 5
3, 2
2,2
1,3
6,2
5,3
From all the outcomes, the only possible out comes that shows that the sum of two numbers is more than 5 are
4, 5
6, 2,
5,3
Probability = possible outcomes / total outcomes
Possible outcomes = 3
Total outcomes = 7
Probability = 3/7
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A sphere which has a diameter of 6 inches has a volume of:
338 in cubed.
258 in cubed.
113 in cubed.
92 in cubed.
Answers
Hope this helps!
Answer:
V≈113.1in³
so the answer will be 113 in cubed
Step-by-step explanation:
Hope it help you mark as Brainlistan engineer designs an improved light bulb. the previous design had an average lifetime of 1,200 hours. the new bulb had a lifetime of 1,200.2 hours, using a sample of 40,000 bulbs. although the difference is quite small, the effect was statistically significant. the most likely explanation is
Answers
The engineer's improved light bulb likely has a statistically significant longer lifetime than the previous design, with a small but measurable difference of 0.2 hours.
Statistical significance refers to the probability that the observed difference between two groups (in this case, the old light bulbs and the new ones) is not due to chance alone. If the probability is low enough, we can confidently reject the null hypothesis (that there is no difference between the two groups) and conclude that there is a real difference between them.
In this case, a sample size of 40,000 bulbs is quite large, which increases the statistical power of the test and allows for even small differences to be detected as significant. The fact that the new bulb had a slightly longer lifetime of 1,200.2 hours, compared to the old bulb's average lifetime of 1,200 hours, suggests that the engineer's design improvement was successful in making the bulb last longer.
However, it's important to note that while the effect is statistically significant, the practical significance may be less clear. A difference of 0.2 hours may not make a noticeable impact on the bulb's usefulness or longevity in real-world scenarios. Additionally, other factors such as cost or energy efficiency may also need to be considered when evaluating the success of the new design.
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find the slope of (6,1) and (6,-3)
Answers
Answer:
Step-by-step explanation:
Find the equation of the tangent plane to f(x, y) = x^2 − 2xy + 3y^2 having slope 4 in the positive x direction and slope 4 in the positive y direction.
Answers
The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slope 4 in the positive x direction and slope 4 in the positive y direction, is 2x - 2y - 1 = 0.
To find the equation of the tangent plane to the function f(x, y) = x^2 - 2xy + 3y^2, we need to determine the partial derivatives of f with respect to x and y. The partial derivative of f with respect to x, denoted as ∂f/∂x, measures the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y, measures the rate of change of f with respect to y while keeping x constant.
Taking the partial derivatives of f(x, y) = x^2 - 2xy + 3y^2, we get: ∂f/∂x = 2x - 2y ∂f/∂y = -2x + 6y
Next, we need to find the point (a, b) where the tangent plane intersects the surface defined by f(x, y). At this point, the partial derivatives of f must equal the given slopes. So, we have the following equations: 2a - 2b = 4 (slope in the positive x direction) -2a + 6b = 4 (slope in the positive y direction)
Solving these equations simultaneously, we find a = 2 and b = 1.
Finally, using the point-normal form of the equation of a plane, we can write the equation of the tangent plane as: 2x - 2y - f(2, 1) = 0
Substituting the values of a and b into f(x, y), we have: 2x - 2y - (2^2 - 2(2)(1) + 3(1)^2) = 0 2x - 2y - 1 = 0
Therefore, the equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slope 4 in the positive x direction and slope 4 in the positive y direction, is 2x - 2y - 1 = 0.
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A sequence is defined by the rule a= -3(2) n-1 . What is the 5th term of the sequence
Answers
an=-3(2)^n-1
= -3(2^n)(2^-1)
= -0.5(2^n)
= -0.5(2^5)= -48
There are 2 cups of flour in a batch of pancakes Manny is making 3/2 batches. How can Manny tell if he needs more or fewer than 2 cups of flour?
Answers
Answer:
Manny is making 3/2 batches, which is equivalent to 1.5, it's more than one. So, Manny is making more than 1 batch.
According to the problem, 2 cups of flour in a batch, if he's making 1.5 batch, he would need 3 cups of flour, which is more than 2 cups of flour.
Step-by-step explanation:
In ΔLMN, n = 510 cm, l = 820 cm and ∠M=20°. Find ∠L, to the nearest degree
Answers
The angular measure L is : 47°
What are angles?Angles are formed when two lines meet.
Analysis:
Firstly, we calculate for m using cosine rule.
\(m^{2}\) = \(510^{2}\) + \(820^{2}\) -2(510)(820) cos 20
\(m^{2}\) = 260100 + 672400 -83600(0.9396)
\(m^{2}\) = 146618.56
m = \(\sqrt{146618.56}\) = 382.9cm
using sine rule to find ∠L
382.9/sin20 = 820/sinL
sinL = 820sin20/382.9
sinL = 820(0.342)/382.9
sinL = 0.732
L = sin inverse of 0.732 = 47°
In conclusion, ∠L is 47°
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Evaluate the limit using L'Hopital's rule \[ \lim _{x \rightarrow \frac{\pi}{2}} 5 \cos (-3 x) \sec (-7 x) \] Answer:
Answers
5cos(−3x)sec(−7x) using L'Hopital's rule is undefined.
To evaluate the limit
lim
�
→
�
2
5
cos
(
−
3
�
)
sec
(
−
7
�
)
lim
x→
2
π
5cos(−3x)sec(−7x) using L'Hopital's rule, we can apply the rule by taking the derivative of both the numerator and the denominator with respect to
�
x.
First, let's find the derivative of the numerator:
�
�
�
(
5
cos
(
−
3
�
)
)
=
−
15
sin
(
−
3
�
)
=
15
sin
(
3
�
)
dx
d
(5cos(−3x))=−15sin(−3x)=15sin(3x)
Next, let's find the derivative of the denominator:
�
�
�
(
sec
(
−
7
�
)
)
=
−
7
sec
(
−
7
�
)
tan
(
−
7
�
)
=
7
sec
(
7
�
)
tan
(
7
�
)
dx
d
(sec(−7x))=−7sec(−7x)tan(−7x)=7sec(7x)tan(7x)
Now, we can rewrite the limit using the derivatives:
lim
�
→
�
2
15
sin
(
3
�
)
7
sec
(
7
�
)
tan
(
7
�
)
lim
x→
2
π
7sec(7x)tan(7x)
15sin(3x)
By applying L'Hopital's rule, we can take the derivative of both the numerator and the denominator one more time.
The second derivative of the numerator:
�
�
�
(
15
sin
(
3
�
)
)
=
45
cos
(
3
�
)
dx
d
(15sin(3x))=45cos(3x)
The second derivative of the denominator:
�
�
�
(
7
sec
(
7
�
)
tan
(
7
�
)
)
=
7
sec
(
7
�
)
tan
(
7
�
)
sec
(
7
�
)
tan
(
7
�
)
+
7
sec
2
(
7
�
)
sec
(
7
�
)
=
7
sec
3
(
7
�
)
tan
2
(
7
�
)
+
7
sec
3
(
7
�
)
dx
d
(7sec(7x)tan(7x))=7sec(7x)tan(7x)sec(7x)tan(7x)+7sec
2
(7x)sec(7x)=7sec
3
(7x)tan
2
(7x)+7sec
3
(7x)
Now, we can rewrite the limit again:
lim
�
→
�
2
45
cos
(
3
�
)
7
sec
3
(
7
�
)
tan
2
(
7
�
)
+
7
sec
3
(
7
�
)
lim
x→
2
π
7sec
3
(7x)tan
2
(7x)+7sec
3
(7x)
45cos(3x)
We can evaluate this limit by substituting
�
=
�
2
x=
2
π
:
45
cos
(
3
⋅
�
2
)
7
sec
3
(
7
⋅
�
2
)
tan
2
(
7
⋅
�
2
)
+
7
sec
3
(
7
⋅
�
2
)
7sec
3
(7⋅
2
π
)tan
2
(7⋅
2
π
)+7sec
3
(7⋅
2
π
)
45cos(3⋅
2
π
)
Simplifying this expression:
45
cos
(
3
�
2
)
7
sec
3
(
7
�
2
)
tan
2
(
7
�
2
)
+
7
sec
3
(
7
�
2
)
7sec
3
(
2
7π
)tan
2
(
2
7π
)+7sec
3
(
2
7π
)
45cos(
2
3π
)
Since
cos
(
3
�
2
)
=
0
cos(
2
3π
)=0 and
tan
(
7
�
2
)
tan(
2
7π
) is undefined, the numerator becomes zero. Additionally, since
sec
(
7
�
2
)
sec(
2
7π
) is undefined, the denominator also becomes undefined.
Therefore, the result of the limit
lim
�
→
�
2
5
cos
(
−
3
�
)
sec
(
−
7
�
)
lim
x→
2
π
5cos(−3x)sec(−7x) using L'Hopital's rule is undefined.
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Solve the following system of equations using Gaussian Elimination. ⎩
⎨
⎧
x+3y−z=4
3x+4y−2z=6
−x+2y+z=−2
Answers
The system of equations is inconsistent, and there is no unique solution.
To solve the system of equations using Gaussian Elimination, we'll perform row operations to transform the system into an upper triangular form.
The given system of equations is:
x + 3y - z = 4
3x + 4y - 2z = 6
-x + 2y + z = -2
Let's start by eliminating the x-coefficient below the first equation. We'll multiply the first equation by 3 and subtract it from the second equation:
3 * (x + 3y - z) = 3 * 4
3x + 9y - 3z = 12
3x + 4y - 2z - (3x + 9y - 3z) = 6 - 12
-5y = -6
Simplifying, we get:
-5y = -6
Now, we can solve for y:
y = 6/5
Next, we substitute the value of y back into the first equation and solve for x:
x + 3(6/5) - z = 4
x + 18/5 - z = 4
x - z = 4 - 18/5
x - z = 20/5 - 18/5
x - z = 2/5
Now, we substitute the values of x and y into the third equation and solve for z:
-x + 2(6/5) + z = -2
-z + 12/5 + z = -2
12/5 = -2
This equation has no solution. Hence, the system of equations is inconsistent, and there is no unique solution.
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Julius is buying beverages for brunch. He needs to buy a total of 5
gallons of beverages. He decides to buy two containers of each
beverage. How many gallons of beverages did he buy?
the beverages:
2 pints of milk, 2 quarts of orange juice, 16 cups of chocolate milk, and 32 ounces of lemonade.
PLSSSSS HELLLPPP LIKE ASAP
Answers
There are 8 pints in a gallon (8 x 2)
There are 4 quarts in a gallon (4 x 2)
There are 16 cups in a gallon (16 x 2)
There are 128 ounces in a gallon (128 x 2)
With that being said, we can add these to find the total amount of gallons of beverages Julius bought. 16 + 8 + 8 + 32 + 256 = 320.
Hopefully this helps!
(b) Find the mean value of the following: 5, 11, 14, 10, 8, 6
Answers
Explanation: All you have to do is add app your numbers then divide by how many numbers there are.
Example: 5+11+14+10+8+6=54 then divide that by 6 which gives you 9
Sorry I didn’t see this earlier.
The mean value of the following: 5, 11, 14, 10, 8, 6 is equal to 9.
The mean of given observation is the sum total of all observations divided by the total number of observations . The mean is also called as average or central tendency of the data. It is one of the tools to summarize the data.
\(mean = \frac{total \ of \ all \ observations }{number \ of \ observations}\)
Given,
data: 5, 11, 14, 10, 8, 6
sum of observations = 5+11+14+10+8+6 = 54
number of observations = 6
\(mean = \frac{total \ of \ all \ observations }{number \ of \ observations}\\\\mean = \frac{54}{6} = 9\)
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Becky and Barbara are shopping for clothes. Becky bought dresses that cost $14.50 and $20 and a pair of flip-flops for $8.25. Barbara bought a blouse for $8.25, a skirt for $20 and a pair of jeans for $14.50. How much did the two women spend together?
Answers
Answer:
$85.50 dollars
Step-by-step explanation:
Becky bought a $14.50 and $20 dress, and a $8.25 pair of flipflops. That is $42.75 . Barbara bought differernt things but still spent the same amount of $42.75 . So if you add those up, it would be $85.50 that they have spent together. Hope this helps :)
31. Suppose that y varies inversely with x and that y = 4 when x = 6. What is an equation for the
inverse variation?
(1 po
6
Oy=
4x
24
y= —
2
24
Answers
Answer:
y = \(\frac{24}{x}\)
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = \(\frac{k}{x}\) ← k is the constant of variation
To find k use the condition y = 4 when x = 6 , then
4 = \(\frac{k}{6}\) ( multiply both sides by 6 )
24 = k
y = \(\frac{24}{x}\) ← equation of variation
Christian is conducting a survey to find out what technology device is the most popular. He wants to make sure his question is relevant to his topic. What question should Christian ask on his survey? (2 points) How many hours do you spend on technology every day? What do you use your technology devices for? Do you have a technology device? What technology devices do you use every day?
Answers
Answer:
What technology devices do you use everyday?
Step-by-step explanation:
Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.
Answer:
What technology devices do you use everyday?
Step-by-step explanation:
Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.
You buy a car for $22,000 and every year your car depreciates by 14% (in other words, you car decreases in value by 14% every year). What is your car worth in 4 years?
(Create an exponential function to solve this problem.)
Question options:
$18,920
$37,157
$12,034
$25,080
Answers
$12034 is the worth of the car after 4 years.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that we purchased a car for $22,000
Every year your car depreciates by 14%
We have to find the worth of the car after 4 years.
\(A=P(1-r)^{t}\)
P is the principal amount=$12000
r is rate of interest =14%=0.14
t is time =4 years
A=22000(1-0.14)⁴
A=22000(0.86)⁴
A=22000×0.547
A=$12034
Hence, $12034 is the worth of the car after 4 years.
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You are buying carpet to cover a room that measures 42 ft by 48 ft. The carpet cost $ 22 per square yard. How much will the carpet cost?
The carpet costs
Answers
Susie ran a race. she ran 5 miles an hour and the race took her t hours to complete.
how long was the race ?
write your answer as an expression
Answers
Answer:
5 x 2
Step-by-step explanation:
5 x 2 is the answer because it says she ran 5 miles and took 2 hours to complete!
1. Given the equation 3x – 4y = 24.
a) Find two solutions to the equation. Show your work. See pages 82 – 85 in your reference guide. Write your answer as coordinates.
b) Using your answers from part a, what is the slope of the given equation. Show your work. See pages 88 – 90 in your reference guide.
c) Convert the given equation into slope-intercept form. Show your work. See page 91 - 93 in your reference guide.
Answers
Answer:
Step-by-step explanation:
Given the equation 3x-4y = 24
The solution occurs at when x = 0 and y = 0
when x = 0:
3(0)-4y = 24
0-4y = 24
-4y = 24
y = 24/-4
y = -6
when y = 0
3x-4(0) = 24
3x = 24
x = 24/3
x = 8
Hence the solution (x, y) is expressed as (8, -6)
b) Slope of the given equation will be expressed as
m = y/x
From the coordinate, y = -6 x = 8
m = -6/8
m = -3/4
c) The equation of a line in slope-intercept form is expressed as y = mx+c
Rewrite the given equation in this form as shown
Given 3x – 4y = 24.
-4y = -3x+24
Divide through by -4
-4y/-4 = -3x/-4 + 24/-4
y = 3/4 x - 6
Hence the equation in slope intercept form is y = 3/4 x - 6
point e is the midpoint of segment DF.if de is 8 what is the length of df
Answers
If e is the midpoint than that means it is in the middle so if there is 8 on one side than there is 8 on the other side as well.
Therefore 8 (DE) + 8 (EF) = 16 (DF)
If 7 carpenters need to share 23 gallons of paint equally how many gallons of point will each carpenter use? between what two whole numbers does your answer lie?
Answers
Each carpenter will use 3.28 gallons of paint, which lies between the whole numbers 3 and 4.
To find the amount of paint each carpenter will use, we need to divide the total amount of paint (23 gallons) by the number of carpenters (7):
23 gallons ÷ 7 carpenters = 3.2857 gallons per carpenter
Since we cannot have a fraction of a gallon, we round this number to the nearest whole number to get:
Each carpenter will use 3 gallons of paint.
However, since 3.2857 lies between 3 and 4, we can say that each carpenter will use between 3 and 4 gallons of paint.
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What is derivative of arcsin x?
Answers
Derivative of arcsin x is 1/√1-x²
What is derivative of arcsin x?The derivative of arcsin x is denoted by d/dx(arcsin x) (or) d/dx(sin-1x) (or) (arcsin x)' (or) (sin-1x)'. Its value is 1/√1 - x². We will prove it in two methods in the upcoming sections. The two methods are:
Using the chain rule
Using the first principles
Derivative of arcsin x Formula
The derivative of the arcsin function is,
d/dx(arcsin x) = 1/√1 - x² (OR)
d/dx(sin^-1x) = 1/√1 - x²
Derivative of Arcsin
d/dx(arcsinx) (or) d/dx(sin^-1x)
=1/√1-x²
arcsinx=1/√1-x²
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hello today is my birthday please help !!
Answers
Answer:
the last one(y=2(2/3)^x) is the correct answer
Step-by-step explanation:
I identify two coordinate on the graph (0,2) and (1,3) and I noticed only the last one gives you a appropriate output if you plug the correspond input value
Which expression is NOT a polynomial?
Answers
Answer:
The last expression.
Step-by-step explanation:
The last expression is not a polynomial because x is in the denominator of the second term.
Answer:
\(4x^2+\frac{5}{x} -6\)
Step-by-step explanation:
A rule for polynomials, is that if they have variables, the powers should be positive whole numbers. Basically, this means you cannot divide by a variable, but in option 4, second term, you are dividing 5 by x, which is the same as\(5*x^{-1}\). This means you are not raising the variable to a positive power, which means the whole 4th option is not a polynomial.