The solution of the given equation are; X = -2 - 2√3 or x = -2 + 2 √3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given an equation as 3/x-4 = x-5/x
Therefore, 3/x-4 = x-5/x
3 - 4x /x = x² - 5 / x
Cancel out the denominator;
3 - 4x = x² - 5
x² - 5 - 3 + 4x = 0
x² - 8 + 4x = 0
x² + 4x - 8 = 0
For the value of x;
x = 4 + √16 + 32 / 2
x = -2 + 2√3
OR
x = 4 - √16 + 32 / 2
x = -2 - 2√3
Hence, The solution of the given equation are; X = -2 - 2√3 or x = -2 + 2 √3
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heeeyy yall, how do i do this?
Answer:
72 cm²
Identify the given sides:
Length: 6 cmWidth: 3 cmHeight: 2 cmSurface area of rectangular prism:
2 * (Length * Width + Width * Height + Length * Height)2 * (6*3 + 3*2 + 6*2)2 * (18+6+12)2 * (36)72 cm²TSA
2(LB+BH+LH)2(3×6+6×2+3×2)2(18+12+6)2(36)72cm²Anyone understand this ?? Please help, I literally dont understand math at all.
Answer:
A
Step-by-step explanation:
The entire frame is 42 x 23 in, but for each dimension there are two lengths of x inches that are included in the entire dimension but not that of the actual picture. Thus, the correct equation is (42 - 2x)(23 - 2x) = 700 which is choice A.
There are 370 fish in the school pond, and 296 are goldfish. What percent of the fish are goldfish? help pls
Answer:
80% of the fish in the school pond are goldfish.
Step-by-step explanation:
To find the percentage of goldfish in the pond, we need to divide the number of goldfish by the total number of fish and multiply by 100.
percent of goldfish = (number of goldfish / total number of fish) x 100%
So, in this case:
percent of goldfish = (296 / 370) x 100%
percent of goldfish = 0.8 x 100%
percent of goldfish = 80%
given a function f : a → b and subsets w, x ⊆ a, then f (w ∩ x) = f (w)∩ f (x) is false in general. produce a counterexample.
Therefore, f(w ∩ x) = {0} ≠ f(w) ∩ f(x), which shows that the statement f(w ∩ x) = f(w) ∩ f(x) is false in general.
Let's consider the function f: R -> R defined by f(x) = x^2 and the subsets w = {-1, 0} and x = {0, 1} of the domain R.
f(w) = {1, 0} and f(x) = {0, 1}, so f(w) ∩ f(x) = {0}.
On the other hand, w ∩ x = {0}, and f(w ∩ x) = f({0}) = {0}.
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or a population with u = 80 and ao = 10, what is the X value corresponding to z = -2.00?
a) 78
b) 75
c) 70
d) 60*
The X value corresponding to z = -2.00 is 70.
What is the X value when z = -2.00?The X value corresponding to a z-score of -2.00 in a population with a mean (μ) of 80 and a standard deviation (σ) of 10 is 70, which is option (c) in the given choices.
In statistics, the z-score (also known as the standard score) is a measure that quantifies the number of standard deviations a particular observation or raw score is away from the mean of a distribution. It helps in understanding how an individual data point compares to the overall distribution. The formula to convert a z-score to a raw score is given by: X = μ + (z * σ).
In this case, we have a population mean (μ) of 80 and a standard deviation (σ) of 10. Plugging in these values into the formula, we can calculate the X value:
X = 80 + (-2 * 10) = 80 - 20 = 60.
Therefore, the X value corresponding to a z-score of -2.00 is 60. This means that an observation with a raw score of 60 falls two standard deviations below the mean in the population.
It's important to understand the concept of z-scores and their application in statistics. They provide a standardized way to compare data points across different distributions and enable us to make meaningful interpretations about individual observations within a population.
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to estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. a graph of the sample data showed an approximately symmetric distribution with no outliers. the sample mean and standard deviation were $734 and $102, respectively. the journalist will create a 95 percent confidence interval to estimate the population mean. have all conditions for inference been met?
No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.
Based on the information provided, it was reported that a journalist chose a random sample of 15 summer weddings that were hosted in the state in order to determine the average cost of flowers for summer weddings in a particular region.Note that the Z test usually includes more than 30 samples. 15 samples were used in this instance.Because of this, it is not possible to assume the sampling distribution from the sample size.Learn more about sampling on:
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The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree?
Answer:
The proportion that can be used to estimate the height of the tree is option;
A. \(\dfrac{h}{12} = \dfrac{6}{5}\)
Step-by-step explanation:
The given parameters in the question are;
The medium through which the person looks at the top of the tree = A mirror
The angle formed by the person and the tree with the ground = Right angles = 90°
The distance of the person from the mirror, d₁ = 5 ft.
The height of the person, h₁ = 6 ft.
The distance of the tree from the mirror, d₂ = 12 ft.
The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂
Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;
TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar
The corresponding legs are;
The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively
The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively
∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR
The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB
Given that θ₁ = θ₂, we have;
tan(θ₁) = tan(θ₂)
∴ tan(∠TMR) = tan(∠AMB)
\(tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}\)
\(tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}\)
\(tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}\)
From tan(∠TMR) = tan(∠AMB), we have;
\(\dfrac{h}{12} = \dfrac{6}{5}\)
\(\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.\)
The height of the tree, h = 14.4 ft.
Therefore, from the proportion \(\dfrac{h}{12} = \dfrac{6}{5}\) the height of the tree can be estimated.
This list gives the lengths of different leaves in centimeters. 7.5, 9.5, 9.0, 8.0, 7.5, 8.5, 7.5, 8.5, 9.5, 8.5, 9.0, 9.5, 8.0, 9.5, 8.0, 9.0, 9.0, 9.0 Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
These are the answers! Let me know if you need the rest of the answers on the assignment.
1.6 radius what is area and circumference
Answer:
See below
Step-by-step explanation:
For a circle:
Area = pi r^2 = 3.14 * 1.6^2 = 8.04 units^2
Circumf = pi * d = pi * 2r = 3.14 * (2 * 1.6) = 10.05 units
The track team won a total of 18 medals. Three of the medals were gold. There were twice as many bronze medals as silver medals. How many bronze medals did the track team win?
Which expression would be easier to simplify if you used the commutative property to change the order of the numbers?
Answer:
B
Step-by-step explanation:
3 to the third power + 42
as a percentage.
Answer:
It is B
Step-by-step explanation:
2. Sarah needs to make at least 60 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 30 thumb drives and 200 key chains.
Let x represent the number of key chains.
Let y represent the number of thumb drives.
Which inequalities are among the constraints for this situation?
The inequalities are among the constraints for this situation include the following;
x + y ≥ 50
x ≥ 5y
y ≤ 30
How to write the required system of inequalities?In order to write a system of inequalities to describe this situation, we would assign variables to the number of key chains and number of thumb drives respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of key chains.Let the variable y represent the number of thumb drives.Based on the information provided, we can logically deduce that there are three (3) inequalities with respect to the constraints for this situation.
Since Sarah needs to make at least (greater than or equal to) 60 gift bags for an event with each gift bag containing at least 1 thumb drive or 1 key chain, we have;
x + y ≥ 50
By using at least 5 times as many key chains as thumb drives, we have;
x ≥ 5y
Lastly, Sarah has 30 thumb drives and 200 key chains;
y ≤ 30
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If two angles are right angles, then they are congruentHypothesis:Conclusion:
A right angle is an angle measuring exactly 90 degrees. A congruent angle is an angle that has the same measure as another angle. Therefore, for two angles to be congruent, they must have the same measure, and if they are right angles, they must each measure exactly 90 degrees.
Since both angles measure exactly 90 degrees, and any two right angles are always equal, the hypothesis that "If two angles are right angles, then they are congruent" is true. A right angle is one of the most common types of angles and is found in a variety of geometric shapes, including squares, rectangles, and triangles.
Because they always measure exactly 90 degrees, they are easy to identify and work with when solving geometry problems. In conclusion, two angles are congruent if they have the same measure, and if they are both right angles, they are also congruent because they both measure exactly 90 degrees.
The hypothesis that "If two angles are right angles, then they are congruent" is true.
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A machine is shut down for repair if a random sample of 100 items selected from the daily output of the machine reveals at least 15% defectives. Assume that daily output is a large number of items. If on one given day the machine is producing only 10% defective items, what is the probability that it will be shut down
Thus, the probability that the machine will be shut down for repair on a day when it is producing only 10% defective items is 3.3%.
The problem statement gives us a threshold of at least 15% defectives for the machine to be shut down for repair. This implies a binomial distribution with n = 100 and p >= 0.15.
Given that the machine is producing only 10% defective items on a given day, we need to find the probability of the sample having at least 15% defectives.
Using the binomial distribution formula, we can calculate the probability of having k or more defectives in a sample of size n with probability of success p:
P(X >= k) = 1 - P(X < k)
where P(X < k) = Σ (n choose i) * p^i * (1-p)^(n-i) for i = 0 to k-1
Plugging in the values, we get:
P(X >= 15) = 1 - P(X < 15)
= 1 - Σ (100 choose i) * 0.1^i * 0.9^(100-i) for i = 0 to 14
Using a calculator or statistical software, we can compute this probability to be approximately 0.033 or 3.3%.
Therefore, the probability that the machine will be shut down for repair on a day when it is producing only 10% defective items is 3.3%.
This suggests that the machine is not very likely to be shut down for repair on such a day, but it is still possible. The management may want to keep monitoring the production and take appropriate actions if the defect rate increases in the future.
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If k = 23 and m
-14, what is ✓k + m?
Submit
Answer:
3
Step-by-step explanation:
Evaluate:
Sqrt of k = 32 + m = -14
Sqrt of 32-14 = 9
Sqrt of 9 = 3
Therefore, our answer is 3!
Btw sqrt means: square root
Hope this helps! Have a good day!
calculate the double integral. r 7x x2 y2 da, r = [1, 3] × [0, 1] The value of integral is 7/2 log (5) +21 tan ^- (1/3)- pi/2
The value of the double integral is 140/3.
To calculate the double integral of the function f(x, y) = 7x * x^2 * y^2 over the region R = [1, 3] × [0, 1], we integrate with respect to y first, and then with respect to x.
The integral is given by:
∫∫R 7x * x^2 * y^2 da
First, we integrate with respect to y:
∫[0, 1] 7x * x^2 * y^2 dy
Integrating this with respect to y, we get:
[7x * x^2 * (y^3)/3] evaluated from y = 0 to y = 1
= 7x * x^2 * (1^3)/3 - 7x * x^2 * (0^3)/3
= 7x * x^2/3
Now, we integrate this result with respect to x:
∫[1, 3] 7x * x^2/3 dx
Integrating this with respect to x, we get:
[7/12 * x^4] evaluated from x = 1 to x = 3
= 7/12 * (3^4) - 7/12 * (1^4)
= 7/12 * 81 - 7/12
= 567/12 - 7/12
= 560/12
= 140/3
Therefore, the value of the double integral is 140/3.
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y intercept of graph
Answer:
4
Step-by-step explanation:
Basically the y - intercept is where the graph intercepts with the y axis. The y axis is the vertical line in the middle of the graph. As you can see, the the graph and the y axis intersect at about 4.
Janice ha a collection of 36 hairpin. 1/6 of them are red and the ret are black. How many black hair pin doe Janice have?
The number of black hair pin Janice have is 30.
Given:
Janice ha a collection of 36 hairpin.
1/6 of them are red.
The rest of the pins are black.
we are asked to find the number of black pin Janice have = ?
first calculate the number of red pins:
⇒ 1/6 of 36
⇒ 1/6 × 36
⇒ 6
Janice have 6 red pins, and the remaining as black pins.
⇒ subtract the red pins from the total.
⇒ black pins = 36-6
⇒ black pins = 30
Hence the number of black pins Janice have is 30.
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help please i need it bad
Answer:
-13, -3
15, 2.6
Step-by-step explanation:
x, y are the numbers
x = 5y + 2
x×y = 39
(5y + 2)×y = 39
5y² + 2y - 39 = 0
the solution of a quadratic equation :
y = (-b ± sqrt(b² - 4ac))/2a
a = 5
b = 2
c = -39
y = (-2 ± sqrt(2² - 4×5×-39))/2×5 =
= (-2 ± sqrt(4 + 780))/10 =
= (-2 ± sqrt(784))/10 = (-2 ± 28)/10
y1 = (-2 + 28)/10 = 26/10 = 2.6
y2 = (-2 - 28)/10 = -30/10 = -3
x1 = 5×2.6 + 2 = 13 + 2 = 15
x2 = 5×-3 + 2 = -15 + 2 = -13
Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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Use synthetic division to solve (x3 1) ÷ (x – 1). what is the quotient?
Using synthetic division, the quotient of (x³ + 1) ÷ (x – 1) is x² + x + 1.
How to find quotient using synthetic division?Using sythetic division, the quotient of (x³ + 1) ÷ (x – 1) can be found in the picture below
The remainder is 2 and the quotient is x² + x + 1.
Therefore, it can be represented as follows:
\(x^{2}+x+1 + \frac{2}{x-1}\)
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Given g(x) = x4 + 2x3 - 7x2 - 8x + 12. When g(x) is divided by x - 1, which conclusion about g(x) is true?
1.9(1) = 0
2.9(-1) = 0
3.x + 1 is a factor of g(x).
4. No conclusion can be made regarding g(x).
Answer:
g(1) = 0
There is a remainder of 10 so you can automatically cross out 3 and 4.
When \(g(x) = x^4 + 2x^3-7x^2-8x+12\) is divided by x - 1, the only true conclusion is g(1) = 0
The given equation is:
\(g(x) = x^4 + 2x^3-7x^2-8x+12\)
x- 1 is a factor of \(g(x) = x^4 + 2x^3-7x^2-8x+12\) only if g(1) = 0
Let us find g(1) by substituting x = 1 into \(g(x) = x^4 + 2x^3-7x^2-8x+12\)
\(g(x) = x^4 + 2x^3-7x^2-8x+12\)
\(g(1) = 1^4+2(1^3)-7(1^2)-8(1)+12\\\\g(1) = 1 + 2 - 7 - 8 + 12\\\\g(1) = -12 + 12\\\\g(1) = 0\)
Therefore, when \(g(x) = x^4 + 2x^3-7x^2-8x+12\) is divided by x - 1, the only true conclusion is g(1) = 0
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Carl jumped 11512 feet in the long jump. Ben jumped 978 feet. How much farther did Carl jump than Ben? A. 1 5/12feet B. 1 13/24feet C. 2 11/24feet D. 2 1/2feet
Answer:
carl and ben aint human chief
Step-by-step explanation:
Answer:
1 11/12
because they ain't human chief ant answer
Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.
Jeremiah: The y-intercept is at (15, 0).
Lindsay: The x-intercepts are at (–3, 0) and (5, 0).
Stephen: The vertex is at (–4, –1).
Alexis: The midpoint between the x-intercepts is at (4, 0).
the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
Which claims are true?
Here we have the quadratic equation:
f(x) = (x + 3)*(x + 5)
The first claim is: "The y-intercept is at (15, 0)."
This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.
The second claim is:
"The x-intercepts are at (–3, 0) and (5, 0)"
This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.
Third claim:
"The vertex is at (-4, -1)"
The middle value between the zeros is:
(-3 + (-5))/2 = -4
Evaluating the function in x = -4 we get the y-value of the vertex:
f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1
So the vertex is at (-4, -1), this claim is true.
The fourth claim is:
"The midpoint between the x-intercepts is at (4, 0)."
Which is false, we already saw that the midpoint between the x-intercepts is at x = -4
Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
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The smallest composite number that can be written as a product of 4 different prime number are
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
the smallest composite number that can be written as a product of four different prime numbers is 6
A lawn mowing company is trying to grow it's buisness. It had 30 clans when it started its buisness and wants to increase by 6 new clients each week. Use ab arithmetic sequence to write a function to represent the real world situation and determine the range of the function for the first four weeks of data.
Answer:
The situation per week is 30 + 6n
where n is the number of weeks
Range of the function is 18 for the first four weeks of data
Step-by-step explanation:
Here, we are to use an arithmetic sequence for a representation.
The first term here is a which is 30 clients while the common difference of d is 6 new clients per week
So we can write the nth term of the sequence as;
Tn = a + (n-1)d
Tn = 30 + (n-1)6
Tn = 30+ 6n -6
Tn = 24 + 6n
where n is the number of weeks
Now for the second week we shall have a total of a+ d clients = 30 + 6 = 36
For the third we have 24 + 6(3) = 24 + 18 = 42
For the fourth, we have 24 + 6(4) = 24 + 24 = 48
Thus the range mathematically means the difference between the highest and lowest for that four weeks = 48-30 = 18
Answer:
A lawn-mowing company is trying to grow its business. It had 18 clients when they started its business and wants to increase by 4 new clients each week.
Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
f(x) = 4x + 18; 0 ≤ y ≤ 4
You are walking directly away from your house. You are 5 miles away from your house when you start walking, so you can determine your distance from your house by adding 5 to the number of miles you have walked. In the equation below, x represents the number of miles you have walked, and y represents your distance from home in miles.
The relationship between these two variables can be expressed by the following equation:
y=x+5
Identify the dependent and independent variables.
Answer:
y is the dependent variable and x is the independent variable
Step-by-step explanation
The number on the right of the equal sign is always the independent variable and the number on the left is always the dependent variable.
independent variable = dependent variable +5
I need help!! I have a bunch of other math questions too-
Answer:
56
Step-by-step explanation:
2x2x2=8 so 7x8=56
The function C = 2x + 3y is minimized at the vertex point of the feasible region at (4, 0). What is the minimum value?
The required minimum value of the function C = 2x + 3y is 8.
Given that,
The function C = 2x + 3y is minimized at the vertex point of the feasible region at (4, 0). What is the minimum value is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
C = 2x + 3y
At the vertex point of the feasible region at (4, 0).
C = 2*4 + 3*0
C = 8
Thus, the required minimum value of the function C = 2x + 3y is 8.
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What is a horizontal integration simple definition?
Using the business strategy of horizontal integration, a firm will buy out or combine with another business in its sector at the same stage of development.
Obtaining access to new goods, technology, or distribution routes, enables the acquiring firm to boost its market share and competitiveness.
Simply put, horizontal integration refers to the purchase or merger of rival businesses operating in the same sector. The objective is to lessen competition and boost economies of scale, which can result in greater effectiveness and financial success.
In sectors like retail, where huge chains may buy smaller rivals to broaden their geographic reach or product offers, horizontal integration is frequent.
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