Answer:
3/k = x
Step-by-step explanation:
5kx +6 = 7kx
Subtract 5kx from each side
5kx -5kx +6 = 7kx-5kx
6 =2kx
Divide each side by 2k
6 /2k = 2kx/2k
3/k = x
answer this asapp thank u
Answer:
The Expression is : J2-74
URGENT *EASY 10 POINTS* : Show steps to get the expression ln(sqrt(2) +1) - ln(1/sqrt(2)) equal to -ln(1-(1/sqrt2))
Answer:
Step-by-step explanation:
To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:
Step 1: Simplify the expression on the left side:
\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)
Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:
\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)
Step 3: Simplify the expression within the logarithm:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)
Step 4: Simplify the denominator by multiplying by the reciprocal:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
Step 5: Simplify the numerator:
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)
\(\ln\left(2 + \sqrt{2}\right)\)
Now, let's simplify the right side of the equation:
Step 1: Simplify the expression on the right side:
\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)
Step 2: Simplify the expression within the logarithm:
\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)
Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
Step 4: Simplify the expression:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)
\(-\ln\left(2 + \sqrt{2}\right)\)
As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).
What is the slope of the line represented by the equation y = -1/2 X + 1/4
Step-by-step explanation:
y = -1/2 X + 1/4
comparing with y = mx+c
m = -1/2 and m is slop
henve slope = -1/2
Previously: Multiplying
Polynomials
(x - 1)(x² + 3x - 4) = x³ + 2x² − 7x + 4
Solving the provided question, we can say that the quadratic equation is \((x - 1)(x^{2} + 3x - 4)\) = \(x^{3} + 2x^{2} - 7x + 4\) and the roots of the polynomial are x = 1, -1, 4.
A quadratic equation is what?A quadratic polynomial in a single variable is represented by the equation \(ax^{2}+bx+c=0\). a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that it has at least one solution. There are both simple and complex solutions.
A quadratic equation is just that—quadratic. It has at least one word that has to be squared, as shown by this. One of the often used solutions for quadratic equations is "ax2 + bx + c = 0." where X is an undefined variable and a, b, and c are numerical coefficients or constants.
the quadratic equation is
\((x - 1)(x^{2} + 3x - 4)\) = \(x^{3} + 2x^{2} - 7x + 4\)
On multiplying,
⇒ \(x (x^{2} + 3x - 4) - (x^{2} + 3x - 4)\)
⇒ \(x^{3} + 3x^{2} - 4x - x^{2} - 3x + 4\)
⇒ \(x^{3} + 2x^{2} - 7x + 4\)
∴ We can say that LHS = RHS.
From given equation, the roots of the equation will be -
\((x - 1)(x^{2} + 3x - 4)\)
⇒ x - 1 = 0
⇒ x = 1
\(x^{2} + 3x - 4 = 0\)
⇒ \(x^{2} - 4x + x - 4\)
⇒ \(x(x - 4) + 1(x - 4)\)
⇒ (x + 1) (x - 4)
⇒ x = -1, x = 4
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solve algebraic equations with variables on both sides of the equation
6x + 2 = 8
Answer:
x = 1
Step-by-step explanation:
First, you have to eliminate the "2," leaving it as, 6x=6.
Then divide, which will leave the equation to x=1.
hey anyone bother to help
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answer:
x=11, y=1 or (11, 1)
Step-by-step explanation:
I used substitution to solve this. Basically wherever there's an x, I would fill it in as 12-y.
2(12-y)+3y=29
24+2y+3y=29
24+5y=29
subtract 24 from both sides
5y=5
divide by 5
y=1
Now substitute y back in to get x.
x=12-1
x=11
You can also graph this into desmos, and wherever they intercept, that's your answer. I hope this helps!
Help please max points
Answer:
(P,O)(M,N)(M,P)(N,O)
Step-by-step explanation:
brainliest pleeez
PLEASE HELP AS FAST AS YOU CAN ASAP DUE IN 30 MINUTES!!!!
the prism is made up of unit cubes. the side length of the unit cube is 1/4 inch
what us the volume of the prism
A. 3/8
B. 8
C. 24
D. 1/64
please explain as well
Answer:
C
<$&#&#;#;#;#;#
Step-by-step explanation:
1/4= 4x6=24
Answer:
C
Step-by-step explanation:
Can someone please help me with this?
Answer:
I'm gonna say b
Step-by-step explanation:
b should be the answer
Find the missing length of the triangle
Answer:
35/3 yd
Step-by-step explanation:
first convert the hypotenuse into 37/3, then you can write (37/3)^2-(4)^2=a^2. solve to get 35/3
Thank you to who it is that helps me!
Answer:
B
D
D
Step-by-step explanation:
please verify and rate 5 stars and say thank you
Round the number to the place of the underline digit 0.758 the 5 is underline
The weight of an adult standard poodle was found to follow a normal distribution with a mean of 50 pounds and a standard deviation of 15 pounds. If represents the mean weight of a random sample of 7 adult standard poodles, what is (round off to second decimal place)
Using the Central Limit Theorem, it is found that the distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
In this problem, for the population, \(\mu = 50, \sigma = 15\).
Sample of 7, hence \(n = 7, s = \frac{15}{\sqrt{7}} = 5.67\)The distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
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Which of the following are solutions to the equation below?
Check all that apply.
(5x- 2)2 = 10
□ A. x = √¹2
B. x= -√2 +2
□ C. x= -√¹2
X=
5
D. x = √√2 + 2
☐ E. x = √10+2
5
OF. x = -√10+2
5
The solution to the equation is given by:
F. x = √10 + 2/5
What is the equation?
It is given by:
(5x-2)²=10
First, we apply the square root to both sides to remove the square, hence:
√(5x-2)²=√10
5x-2=√10
Then, isolating x:
5x = √10+2
x = √10+2/5
Given by option F, which is the solution.
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Which inequality can be used to represent this problem? A company spent $15,000 developing a new graffiti repelling paint. The company makes $10 on the sale of each gallon of paint after subtracting manufacturing costs. How many gallons, x, will they need to sell to have a profit of at least $50,000?
A 10x — 15000 ≥ 50000
B 10x — 15000 > 50000
C 10x + 50000 > 15000
D 10x + 50000 ≥ 15000
Answer:
The correct answer is:
Option A: A 10x — 15000 ≥ 50000
Step-by-step explanation:
Given that the total cost of manufacturing by the company is $15000.
Let x be the number of gallons the company sells.
It is also mentioned that the company earns $10 on each gallon.
So the total profit will be the the difference of the selling cost of gallons and manufacturing cost
Mathematically,
\(10x-15000\)
Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so
\(10x-15000 \geq 50000\)
The number of gallons can be found by solving the obtained inequality.
Hence,
The correct answer is:
Option A: A 10x — 15000 ≥ 50000
Domain or range function or not And explain
An 18-foot ribbon is attached to the top of a pole and is located on the ground 10 feet awayfrom the base of the pole. Suppose Mateo has a second ribbon that will be located anadditional 23 feet away past that point.Find the measure of the angle formed by Mateo's ribbon and the ground. Round the angle tothe nearest tenth of a degree.a10 ft18 ft23 ft8
To begin we need to find the value of a
We apply the Pythagorean theorem
\(\begin{gathered} 18^2=a^2+10^2 \\ a^2=18^2-10^2 \\ a=\sqrt{18^2-10^2} \\ a=4\sqrt{14} \end{gathered}\)Now we find theta
Here we use the tangent that is the oppositive side over the adjacent side
\(\begin{gathered} \tan\theta=\frac{4\sqrt{14}}{33} \\ \\ \theta=\tan^{-1}(\frac{414}{33})=24.39\degree \end{gathered}\)
Which shapes are similar but not congruent to shape 1
There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.
There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.
One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.
A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.
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Krystal placed one
egg in a carton that
holds six eggs. She
wrote 1/6 to show
how many eggs she
has. Jamal has 8
times the number of
eggs Krystal has.
Which fraction
shows how many
eggs Jamal has?
Answer:
Step-by-step explanation:
If Jamal has 8 times the number of eggs then Krystal has \(1\frac{1}{3}\) fraction of eggs.
What is Fraction?A fraction represents a part of a whole.
Given that Krystal placed one egg in a carton that holds six eggs
Krystal has 1 egg out of a carton that holds 6 eggs, so she has 1/6 of a carton.
Jamal has 8 times the number of eggs Krystal has, so he has:
8 x (1/6)
Eight times of one by six
= 8/6
Divide numerator and denominator by two
= 4/3
The given fraction 4/3 is converted to mixed fraction
=\(1\frac{1}{3}\)
The fraction that shows how many eggs Jamal has is \(1\frac{1}{3}\).
Hence, if Jamal has 8 times the number of eggs then Krystal has \(1\frac{1}{3}\) fraction of eggs.
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What is the product of StartFraction 4 Over 9 EndFraction and StartFraction 1 Over 11 EndFraction
Answer:
4/99
Step-by-step explanation:
Periodic grab some phase shifts
Answer:
The sine function is:
\(y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2\)
Step-by-step explanation:
We need to recall that a sine function can write as:
\(y(x)=Asin[B(x+C)]+D\)
Where:
A is the amplitude of the functionB is the periodC is the phase shift leftD is the vertical shiftSo we just need to use the listed attributes
Therefore, the sine function is:
\(y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2\)
I hope it helps you!
A paint manufacturer knows that ultraviolet light can degrade many types of paint. It wants to know which paint composition has the least amount of degradation under ultraviolet light. Three different paint compositions were tested. A wall in a windowed hallway of a paint manufacturing plant was divided into 18 sections, and each of the sections was randomly assigned to one of the three paint compositions. The wall sections were painted and then left to be exposed to sunlight. After 18 months of sunlight exposure, the walls were analyzed to determine the degree of change in pigment of the paint, and the results were compared between paint compositions. What are the individuals in this experiment?
This question uses the experimental study concept.
Doing this, we have that the walls analyzed are the individuals.
First, the concept of experimental study is presented:
Experimental study: In an experimental study, there is an intervention in the individuals, and it's effect is studied.In this question:
There is an intervention in the walls, they are painted, using three different paint compositions, and then they are exposed to sunlight, and after that the walls were analyzed, to study the degree of change in pigment of the paint, being compared between different paint compositions.
Thus, since the intervention was in the walls, they are the individuals in this experiment.
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4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
Answer:
x is -7.5 or -14/2 or -7½
Step-by-step explanation:
- Supposing y varies directly with x
\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)
[k is a constant of proportionality (k ≠ 0)]
- When y is 6, x is -2
\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)
- Therefore, the equation is;
\({ \boxed{ \tt{y = - 2x}}}\)
- What is x when y is 15
\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)
The value of x is -5
The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:
k = y/x
k = 6/-2
k = -3
Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation
15 = -3x
Then solve x,
x = \(\frac{-15}{3}\)
x = -5
Therefore, when y = 15, x = -5.
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Select the correct answer.
Solve the following equation for x.
x2 - 36 = 0
A.
x = 1; x = -36
B.
x = -1; x = 36
C.
x = -6; x = 6
D.
x = -18; x = 18
Answer: D
Step-by-step explanation:
2x-36=0
+36 +36
___________
2x=36
x=18
Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.
The following are the ages (years) of 5 people in a room: 12, 20, 22, 22, 23 A person enters the room. The mean age of the 6 people is now 23. What is the age of the person who entered the room?
Answer:
39
Step-by-step explanation:
12+20+22+22+23=99
new mean=23
23*6=138
138-99=39
An international company has 17.900 employees in one country. If this represents 28.7% of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.
Answer:
513,730
Step-by-step explanation:
You times 17,900 by 28.7 to get 513,730.
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Answer:
Step-by-step explanation:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. X = the number of unbroken eggs in a randomly chosen standard egg carton Y = 5 the number of students on a class list for a partic- ular course who are absent on the first day of classes U = 5 the number of times a duffer has to swing at a golf ball before hitting it X = 5 the length of a randomly selected rattlesnake Z = 5 the sales tax percentage for a randomly selected amazon.com purchase Y = 5 the pH of a randomly chosen soil sample X = 5 the tension (psi) at which a randomly selected tennis racket has been strung X = 5 the total number of times three tennis players must spin their rackets to obtain something other than UUU or DDD (to determine which two play next)
In the order provided in the question, X is a discrete random variable, Y is not a random variable, U is a discrete random variable, X is a continuous random variable, Z is a continuous random variable, Y is a continuous random variable, X is a continuous random variable, and X is a discrete random variable.
• X = the number of unbroken eggs in a randomly chosen standard egg carton The possible values for X are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, as an egg carton can have anywhere between 0 and 12 unbroken eggs. X is a discrete random variable since it takes on a finite number of possible values.
• Y = 5 the number of students on a class list for a particular course who are absent on the first day of classes The only possible value for Y is 5, so it is not a random variable.
• U = 5 the number of times a duffer has to swing at a golf ball before hitting it The possible values for U are all positive integers starting from 5. U is a discrete random variable since it takes on a countable number of possible values.
• X = 5 the length of a randomly selected rattlesnake. The possible values for X are all positive real numbers. X is a continuous random variable since it can take on any value within a range of values.
• Z = 5 the sales tax percentage for a randomly selected amazon.com purchase The possible values for Z are all percentages between 0% and 100%, including decimal values. Z is a continuous random variable since it can take on any value within a range of values.
• Y = 5 the pH of a randomly chosen soil sample. The possible values for Y are all positive real numbers. Y is a continuous random variable since it can take on any value within a range of values.
• X = 5 the tension (psi) at which a randomly selected tennis racket has been strung. The possible values for X are all positive real numbers. X is a continuous random variable since it can take on any value within a range of values.
• X = 5 the total number of times three tennis players must spin their rackets to obtain something other than UUU or DDD (to determine which two play next) The possible values for X are 1, 2, 3, and so on, since the players can keep spinning the rackets indefinitely. X is a discrete random variable since it takes on a countable number of possible values.
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They can buy 120 vans, 60 small trucks, and 80 large trucks.
How to find the number of van, small trucks and large truck needed?The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck
Therefore,
let
s = number of small truck
number of van = v
let
l = number of large truck
v + s + l = 260
25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000
v + 2s + 2l = 400
Hence,
v = 2s
So,
2s + 2s + 2l = 400
4s + 2l = 400
2s + s + l = 260
3s + l = 260
2s + l = 200
s = 60
l = 200 - 2(60)
l = 200 - 120
l = 80
v = 2(600 = 120
Therefore, they can buy the following:
number of small truck = 60
number of van = 120
number of large truck = 80
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Find the value of x.
x = ___