Answers
An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]
What is an exponent?In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
Generally speaking, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the law of indices for powers of the same base number, we have the following:
[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]
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Related Questions
help pls show ur work
Answers
The angle of elevation is the angle formed between a horizontal line and a line of sight that is pointing upwards towards an object.
How do we apply angle of elevation and depression?The angle of depression is the angle formed between a horizontal line and a line of sight that is pointing downwards towards an object.
1) Sin 25 = x/15
x = 15 Sin 25
= 6 m
2) Tan 17 = 200/x
x = 200/Tan 17
x = 654 m
3)
Tan 33 = 1500/x
x = 1500/Tan 33
x = 2310 m
4)
x = tan-1(800/1200)
x = 34 degrees
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Which statement about a histogram is true?
• A cluster means the frequency is zero.
© If the graph has a cluster, the data is evenly distributed.
© A mirror image of the left and right side of a histogram means there is a peak in the middle
© A peak is a bar that is higher than the other bars around it.
Answers
Answer:D) A peak is a bar that is higher than the other bars around it is true.Step-by-step explanation:A histogram is an approximate representation of numerical data distribution.When multiple data points on a number line are close to the same value (or a neighbourhood of values), a cluster arises.A peak is a bar that stands taller than the bars around it. A single peak or plateau is formed when two or more adjacent bars are the same height but are taller than the bordering bars. A gap is a class or classes with frequency 0 on one side but non-zero on the other.
Step-by-step explanation:
I need help with this please
Answers
Answer:
d
Step-by-step explanation:
1 kg has 1000 g
Then 2,5 kg has 2,5 × 1000 = 2500 g
You can also make a proportion:
1 kg - 1000 g
2,5 kg - x g
Use the property of the proportion to find x (cross-multiply):
x = 2,5 × 1000 / 1 = 2500 g
Which of the following is part of the set of integers?
negative whole numbers
zero
natural numbers
Answers
Answer:
all of them
Step-by-step explanation:
i hope you find it helpful
Let’s assume that 41% of Californians have been to Disneyland. A random sample of 6 Californians are chosen and asked if they have ever been to Disneyland.
a) Define a random variable X for this situation.
b) Is X binomial or geometric or neither? Explain.
c) Out of the 6 people asked, with is the probability that exactly 3 have been to Disneyland?
d) What is the mean of X?
e) What is the standard deviation of X?
f) What is the probability that the number of Californians in this sample that have been to Disneyland is within one standard deviation of the mean?
Answers
The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland. X is a binomial random variable because each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample. the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%. The mean of X is 2.46. The standard deviation of X is 1.27. The probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.
a) The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland.
b) X is a binomial random variable because the following conditions are met:
Each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.
The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample.
The individuals in the sample are independent of each other.
c) To find the probability that exactly 3 people in the sample have been to Disneyland, we can use the binomial probability formula:
P(X = 3) = (6 choose 3) * (0.41)^3 * (1-0.41)^3 = 0.274
Therefore, the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%.
d) The mean of X is given by the formula:
mean(X) = n * p = 6 * 0.41 = 2.46
Therefore, the mean of X is 2.46.
e) The standard deviation of X is given by the formula:
stddev(X) = sqrt(n * p * (1-p)) = sqrt(6 * 0.41 * (1-0.41)) = 1.27
Therefore, the standard deviation of X is 1.27.
f) To find the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean, we can use the normal approximation to the binomial distribution.
First, we need to find the z-scores corresponding to X = 1 and X = 4:
z1 = (1 - 2.46) / 1.27 = -1.17
z4 = (4 - 2.46) / 1.27 = 1.22
Then, we can use the standard normal distribution table to find the probabilities corresponding to these z-scores:
P(X ≤ 1) = P(Z ≤ -1.17) = 0.121
P(X ≤ 4) = P(Z ≤ 1.22) = 0.888
Finally, we can subtract these probabilities to find the probability that X is within one standard deviation of the mean:
P(1 < X < 4) = P(X ≤ 4) - P(X ≤ 1) = 0.888 - 0.121 = 0.767
Therefore, the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.
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Pls help step by step, loves <3 (special right triangles)
Answers
Answer:
x ≈ 30,37
y ≈ 29,00
Step-by-step explanation:
Use trigonometry:
[tex] \sin(38°) = \frac{9}{x} [/tex]
Now, use the property of the proportion to find x:
[tex]x = \frac{9}{ \sin(38°) } ≈30.37[/tex]
Do the same thing to find y:
[tex] \tan(38°) = \frac{9}{y} [/tex]
[tex]y = \frac{9}{ \tan(38°) } ≈29.00[/tex]
Four consecutive odd integers add up to 48. What are the integers?
Answers
Answer:12
Step-by-step explanation: 48/4
Graph the function and describe the domain and range f(x)=(x-2)(x+4)
Answers
The function f(x) = (x-2)(x+4) is a quadratic function that can be written in standard form as f(x) = x^2 + 2x - 8.
To graph this function, we can start by finding the vertex, which is located at x = -b/2a = -2/2 = -1, and then plotting a few additional points to determine the shape of the parabola.
To find the y-coordinate of the vertex, we plug x = -1 into the equation and get f(-1) = (-1)^2 + 2(-1) - 8 = -7. So the vertex is at (-1, -7).
We can also find the x-intercepts by setting f(x) = 0 and solving for x:
(x-2)(x+4) = 0
x-2 = 0 or x+4 = 0
x = 2 or x = -4
So the x-intercepts are at (2, 0) and (-4, 0).
To find the y-intercept, we set x = 0 and get f(0) = (0-2)(0+4) = -8. So the y-intercept is at (0, -8).
Now we can plot these points and sketch the parabola:
```
|
|
|
| *
|
|
------+------------> x
|
|
|
|
|
|
```
The domain of the function is all real numbers, since there are no restrictions on the values that x can take.
To find the range of the function, we can look at the vertex and see that the lowest point on the parabola is at y = -7. Since the parabola opens upward, the range extends from -7 to infinity:
Range: [-7, ∞)
This Took me a long long time
A university is trying to determine what price to charge for tickets to football games. At a price of $27 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number.
Every person at the game spends an average of $3.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?
Answers
Answer:
the university should charge $13.50 per ticket to maximize revenue, and 85,000 people will attend at that price.
Step-by-step explanation:
To find the price per ticket that maximizes revenue, we need to find the price that maximizes the product of the number of tickets sold and the revenue per ticket. Revenue per ticket is equal to the ticket price plus the average concession spending per person, or $27 + $3 = $30.
Let x be the number of $3 decreases in ticket price, so the ticket price can be expressed as $27 - $3x. The number of people attending can be expressed as 40,000 + 10,000x.
Therefore, the revenue can be expressed as:
Revenue = (Ticket price) x (Number of tickets sold) x (Concession spending per person)
Revenue = ($27 - $3x) x (40,000 + 10,000x) x $3.00
Expanding this expression, we get:
Revenue = $81,000,000 + $270,000,000x - $30,000,000x^2
To maximize revenue, we need to find the value of x that maximizes this quadratic function. We can do this by finding the vertex of the parabola, which is located at:
x = -b / 2a
where a = -30,000,000, b = 270,000,000, and c = 81,000,000
x = -270,000,000 / 2(-30,000,000)
x = 4.5
Since x represents the number of $3 decreases in ticket price, we can find the optimal ticket price by subtracting 3 times x from the original price of $27:
Optimal ticket price = $27 - $3(4.5) = $13.50
The optimal number of people attending can be found by substituting x = 4.5 into the expression for the number of people attending:
Number of people attending = 40,000 + 10,000(4.5) = 85,000
Consider the following functions from Z × Z to Z. Which ones are onto? Justify your answer with a proof.
(a) f(x, y) = 2x - 4y
(b) f(x, y) = |x| - |y|
Answers
(a) for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.
(b) f(x, y) = |x| - |y| is not onto.
Which of the function is onto?(a) To show that the function f(x, y) = 2x - 4y is onto, we need to show that for every integer z, there exists integers x and y such that f(x, y) = z.
Let z be an arbitrary integer. Then we need to find integers x and y such that 2x - 4y = z. We can rewrite this equation as x = (z + 4y)/2.
Now, if z is even, then we can choose any even number for y and solve for x using the above equation. Conversely, if z is odd, we can choose any odd number for y and solve for x.
Therefore, for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.
(b) To show that the function f(x, y) = |x| - |y| is not onto, we need to find an integer z such that there does not exist integers x and y such that f(x, y) = z.
Let z = -1. Then we need to find integers x and y such that |x| - |y| = -1. However, the absolute value of any integer is non-negative, so |x| and |y| are both non-negative.
Therefore, |x| - |y| is non-negative, and it is impossible for f(x, y) to equal -1.
Hence, there does not exist integers x and y such that f(x, y) = -1, and thus f(x, y) is not onto.
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Select all edges where this rectangle could be added in order to complete the net. Anyone help?
Answers
The edges where this rectangle could be added in order to complete the net are edges A, H, E and D.
What is a net shape?The net shape of a rectangular pyramid is a two-dimensional representation of the three-dimensional shape that can be cut out and folded to create the actual pyramid. It consists of a rectangular base and four triangular faces that meet at a single point or vertex.
To create the net shape of a rectangular pyramid, start with a rectangular base and draw four lines from each of the four corners of the base to a single point above the center of the rectangle. These lines should be equal in length and form four congruent triangles.
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its supossed to be a puzzle of some kind?
Answers
61,23,46,821,652,215
Jami is an accountant at a mid-sized firm and has been hired by an investor to make recommendations about fi
local small businesses. These businesses are all in debt, but the investor sees potential in each idea. The investor wom
to know when each company is projected to break even and would prefer companies that will turn a profit with
the next 24 months. The investor secured the expense and revenue reports of each of the businesses to review.
Jami has created linear models to project the Cost and Revenue of each business and now must use the results
finalize her findings. In each equation x represents months. What should her recommendation be? How do
businesses rank?
Cost
Revenue
Blysis
of the evidence
Evidence
Appster
Enrich
(Technology Start-up) (Education Program)
y-13124.3190x y-6941915384x
y-3586x
y-21954x
¡.
Green Team
(Alternate Energy)
y 178420 64421x
y-68419x
Southwest Fusion
(Restaurant)
y-4289115387x
y-13174x
ons and show work.
Zoo to You
(Children's Parties)
y54209539
y-10381x
Conclusion
or Recommendation
e Clark Creative Ex
Answers
Answer:
To determine when each company is projected to break even, Jami needs to find the point where the Cost and Revenue equations intersect. This point will represent the month when the business is projected to break even, as the Cost and Revenue will be equal.
Using the given equations, we can set the Cost equation equal to the Revenue equation for each business:
Blysis: -13124.3190x + 3586 = -6941915384x + 21954
Solving for x, we get x = 0.00057 months.
Since this value is extremely small, we can assume that Blysis is already profitable.
Appster: -13124.3190x + 3586 = -6941915384x + 21954
Solving for x, we get x = 0.00057 months.
Since this value is extremely small, we can assume that Appster is already profitable.
Enrich: -3586x - 21954 = -6941915384x + 13174
Solving for x, we get x = 0.0035 months.
Since this value is also very small, we can assume that Enrich is already profitable.
Green Team: 178420.64421x - 68419 = -4289115387x + 13174
Solving for x, we get x = 0.0009 months.
Since this value is extremely small, we can assume that Green Team is already profitable.
Southwest Fusion: -13124.3190x + 4289115387x = 13174
Solving for x, we get x = 35.23 months.
This value indicates that Southwest Fusion is projected to break even in approximately 35 months.
Zoo to You: -13124.3190x + 54209539 = -10381x
Solving for x, we get x = 4.05 months.
This value indicates that Zoo to You is projected to break even in approximately 4 months.
Based on these projections, Jami should recommend Blysis, Appster, Enrich, and Green Team to the investor, as they are already profitable or expected to break even within the next 24 months. Southwest Fusion and Zoo to You may not be as attractive for investment, as they are projected to take longer to become profitable.
Step-by-step explanation:
What is the measure of the angle marked "C"? 38- A 40%
Answers
The measure of the angle marked "C" based on the information will be 42.8°.
How to calculate the angleIt should be noted that to find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,
sinA / a = sinB / b = sinC / c
where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.
Given ∠A = 61°, c = 35, a = 45
∴( sinA)/a = (sinC)/c
(sin 61° )/ 45 = (sin C) / 35
sin c = ((sin 61°) / 45) × 35
sin c = 0.68
c ≈ 42.8°
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The average width of a movie theater seat is 23 inches. Thirty years ago, the typical movie theater seat was approximately 19 inches wide. Current movie theater seats are what percent of a theater seat from 30 years ago?
Answers
Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.
Explain about the percentage increase:The change between a final value and even an initial value, presented as a percentage of the starting value, is the percent increase over two values. Subtract the starting value from the ending value to get the percent increase.
Next, divide the difference by the starting amount. In order to convert this value to a percentage, multiply it by 100%. The difference in percentage between the two numbers will be shown in the final result.
Given data:
width of current movie theatre seat = 23 inches.
width of 30 years ago movie theatre seat = 19 inches.
Let x be the percentage increase:
19 + x%19 = 23
1 + x% = 23/19
x/100 = 23/19 - 1
x/100 = 4/19
x = 400/19
x = 21.05 %
Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.
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A line in the coordinate plane has the equation 5a + b = 7,
where a represents the independent variable, and b
represents the dependent variable. Which of the following is
the equation of a line that is perpendicular to 5a+b=7?
A. b=5a+3
B. b=-5a-5
C. b= (1/5)a-2
D. b=(-1/5)a + 1
Answers
Explanation:
I'll use x in place of 'a'
I'll also use y in place of b.
The equation 5a+b = 7 turns into 5x+y = 7
Solve for y to get
5x+y = 7
y = -5x+7
This is in slope-intercept form y = mx+b
m = -5 = slopeb = 7 = y interceptThe negative reciprocal of the slope is 1/5. Flip the fraction and flip the sign. So if -5 is the original slope, then 1/5 is the perpendicular slope.
Of the answer choices, only choice C has a slope of 1/5. Think of b = (1/5)a-2 as y = (1/5)x - 2
Therefore, choice C is the answer.
The equation of a line that is perpendicular to '5a+b = 7' is 'b = (1/5)a + c'. Therefore, the correct option among given choices is 'b = (1/5)a - 2' (option C).
Explanation:To start with, the given line's equation, 5a + b = 7, can be converted to slope-intercept form (b = mx + c), where m represents the slope of line, and 'c' is the y-intercept.
Converting the equation, 5a + b = 7, we get b = -5a + 7. This tells us the slope of our original line is -5.
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. So, the line perpendicular to the one with a slope of -5 would have a slope of 1/5. Therefore, the equation of a line perpendicular to '5a+b = 7' would be in the form 'b = (1/5)a + c'.
Thus, the correct answer is option C : b = (1/5)a - 2.
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I need help with this please
Answers
Answer:
i think it would be 24 times 6 althought since this is a college question its probably a lot more complex but ill just give it a shot and say its 168.
Step-by-step explanation:
i think its 168 because it woud be 6 more layers of that 24 cube layer so thatd be 6 times 24 which is 144 and then plus the other 24 thats already there it would be 168.
Answer:
144
Step-by-step explanation:
Area= L*W*H
(4*6)*6
24*6=144
It the photo at the bottom
Answers
Hence the sum of rational expressions is [tex]\frac{9x^2-5x+2}{7x^2-14x}[/tex] option D is correct.
You must be familiar with rational numbers, which are written as p/q. On the other hand, rational expressions are the ratio of two polynomials.
Polynomial expressions must be set equal to zero in order to find the root or zero. But, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.
The lowest terms are those in which neither the numerator nor the denominator has any common factors. It is not in the lowest form, like in the case of a fraction, like 2/8. Taking 2 into consideration as a common element will further minimize it. The lowest form is therefore 1/4.
The rational expression is
[tex]\frac{2x-1}{7x}+\frac{x}{x-2}[/tex]
to add expression first take LCM
and cross multiply
[tex]=\frac{(2x-1)(x-2)+7x^2}{7x(x-2)}\\\\=\frac{2x^2-4x-x+2+7x^2}{7x^2-14x}\\\\=\frac{9x^2-5x+2}{7x^2-14x}[/tex]
Hence the sum of a rational expression is [tex]\frac{9x^2-5x+2}{7x^2-14x}[/tex] option D is correct.
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It is estimated that 1.4% of the population has an allergy to peanuts. If the population of the United States is 328.2 million, how many Americans could we expect to have a peanut allergy?
Answers
Answer:4.592million
Step-by-step explanation:
328.2million----------------100%
x-----------------1.4%
x=328million*1.4/100=4.592million
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{1.4\% of 328,200,000}}{\left( \cfrac{1.4}{100} \right)328,200,000}\implies \text{\LARGE 4,594,800}[/tex]
Which choices are equivalent to the quotient below? Check all that apply.
sqrt 75/ sqrt 15
A. sqrt 3
b. 5
c sqrt 15 / sqrt 3
d.sqrt 25 / sqrt 5
e. 15/3
f. sqrt 5
will give brainly to correct answer
Answers
The equivalent choices are (A) sqrt 3 and (F) sqrt 5. We can simplify the given quotient by rationalizing the denominator.
To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt 15. This gives us:
sqrt 75 / sqrt 15 = (sqrt 75 / sqrt 15) * (sqrt 15 / sqrt 15) = sqrt (75 * 15) / 15 = sqrt 1125 / 15
Now we can simplify the numerator by factoring out perfect squares. We have:
sqrt 1125 = sqrt (225 * 5) = sqrt 225 * sqrt 5 = 15 * sqrt 5
Substituting this back into our expression, we get:
sqrt 75 / sqrt 15 = (15 * sqrt 5) / 15 = sqrt 5
Therefore, the equivalent choices are (A) sqrt 3 and (F) sqrt 5. Choice (B) 5 is not equivalent because it does not have a square root, while (C) sqrt 15 / sqrt 3 and (D) sqrt 25 / sqrt 5 are not equivalent because they are not in simplest form. Choice (E) 15/3 is equivalent to 5 but not to the given expression sqrt 75 / sqrt 15.
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For each expression, select all equivalent expressions from the list.
(a) 11x-4x+5x
12x
12+x
7x-5x
7x+5x
(b) 7(1+8y)
7+8y
7+56y
7•1-+7•8y
7+1•7+8y
Selective answer choice
Answers
Answer: a
Step-by-step explanation:
7(x -5)
12 + x
The table represents the number of
elective classes offered at different
middle schools. Find the mean.
# OF CLASSES 7 8
q
2 3 2
FREQUENCY
COLUMN #2
10
1
Answers
The mean number of elective classes offered at different middle schools is given as follows:
8.25 elective classes per school.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The data-set in this problem is given as follows:
2 schools offer 7 classes.3 schools offer 8 classes.2 schools offer 9 classes.1 school offers 10 classes.Hence the sum of the observations is given as follows:
2 x 7 + 3 x 8 + 2 x 9 + 1 x 10 = 66.
The number of observations is given as follows:
2 + 3 + 2 + 1 = 8 schools.
Hence the mean number is given as follows:
66/8 = 8.25 elective classes per school.
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how to calculate with pie squared?
Answers
Answer:
I assume you mean pi (π) squared, which is π^2. Calculating with π^2 is similar to calculating with any other number, except that you use π^2 instead of a regular number. Here are a few examples:
Example 1: Find the circumference of a circle with radius 5π.
The formula for the circumference of a circle is C = 2πr, where r is the radius. Substituting 5π for r, we get:
C = 2π(5π) = 10π^2
Therefore, the circumference of the circle is 10π^2.
Example 2: Find the area of a circle with diameter 3π.
The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter is 3 times the radius, we have:
r = (1/2)(3π) = (3/2)π
Substituting this into the formula, we get:
A = π((3/2)π)^2 = (9/4)π^3
Therefore, the area of the circle is (9/4)π^3.
In general, whenever you see π^2 in a formula, you can just substitute it for the regular number. Keep in mind that π is an irrational number (it goes on forever without repeating), so you may need to use an approximation like 3.14 or 22/7 depending on the level of accuracy required in your calculations.
Step-by-step explanation:
explanation included above with examples.
type in symbols to make 3,7,12,2 equal 15
Answers
12 + 7 - 3 - 2
There are many ways to use mathematical symbols to make 3, 7, 12, and 2 equal 15. Here are a few examples:
3 + 7 + 2 + 3 = 15
(Add the first three numbers together, then add one of the 3's to get 15)
12 - 7 - 3 + 13 = 15
(Subtract 7 and 3 from 12 to get 2, then add 13)
2(7 + 3) - 12 = 15
(Add 7 and 3 together, multiply by 2, then subtract 12)
7(2) + 3 + 3 - 4 = 15
(Multiply 7 by 2, add 3 and the other 3, then subtract 4)
These are just a few examples - there are many other ways to use mathematical symbols to make these numbers equal 15!
(pls pls help!!) Calculate each value for ⊙P.
=
Area of shaded factor = (fraction) ft
Area of unshaded factor = (fraction) ft
Answers
The area of the shaded sector is 575π/9 square units.
The area of the unshaded sector is 325π/9 square units
What is the area of the sectors?
The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.
To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (230/360) x π(10)²
= (23/36) x 100π
= 575π/9 square units
To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (130/360) x π(10)^2
= (13/36) x 100π
= 325π/9 square units
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-2x+y=4
-5x+2y=1
I need the ordered pairs for these two
Answers
Answer:
(7,18)
Step-by-step explanation:
I think that you are asking for a solution to both equations
-2x + y = 4 → x -2 → 4x -2y = -8
-5x + 2y = 1 → (+) -5x + 2y = 1
-x = -7
x = 7
Substitute 7 for x in either of the two equations and solve for y.
-2(7) + y = 4
-14 + y = 4 Add 14 to both sides
y = 18
The solution is (7,18).
Check:
-2x + y = 4
-2(7) + 18 = 4
-14 + 18 = 4
4=4 Checks.
-5x + 2y = 1
-5(7) + 2(18) = 1
-35 + 36 = 1
1 = 1 checks
Helping in the name of Jesus.
Rasheed signed a 2 year lease. He pays $565 a month. If he wants to move out 6 months early, how much money will he owe when he moves out?
Answers
Answer
3390
Step-by-step explanation:
rasheed still owes six months of rent because thats the lease that they signed so 565 times six is 3390. hope this helps.
CALC PLEASE HELP!!
Let f(x)= x³ - 27x.
(i) Find the domain of f(x).
(ii) Compute f'(x) and f"(x).
(iii) Give the coordinates of the critical points.
(iv) Find the intervals where f(x) is increasing / decreasing.
(v) Give the coordinates of the relative extrema. Classify each extrema as a relative maximum
or a relative minimum.
ALSO
(vi) Find the intervals where f(x) is concave up/ concave down.
(vii) Give the coordinates of any points of inflection.
(viii) Sketch the graph of f(x).
Answers
Answer:
Step-by-step explanation:
y = x³ - 27x
(i). Domain: x ∈ ( - ∞ , ∞ )
(ii). f'(x) = 3x² - 27 ; f''(x) = 6x
(iii). 3x² - 27 = 0 ⇔ x² - 9 = 0 ⇒ [tex]x_{12}[/tex] = ± 3
If [tex]x_{1}[/tex] = - 3 , then [tex]y_{1}[/tex] = 54
If [tex]x_{2}[/tex] = 3 , then [tex]y_{1}[/tex] = - 54
Points are ( - 3 , 54 ) and ( 3 , - 54 )
(iv). ( - ∞ , - 3 ) ∪ ( - 3 , 3 ) ∪ ( 3 , ∞ )
increasing ----> decreasing -----> increasing
(v). x = - 3 is the maxima, the local maximum value is 54, f(-3) = 54
x = 3 is the minima, the local minimum value is ( - 54 ), f(3) = - 54
(vi). Concave up if f''(x) > 0 ; The interval is ( - ∞ , 0 )
Concave down if f''(x) < 0 ; The interval is ( 0 , ∞ )
(vii). Point of inflection is ( 0 , 0 )
f''(x) = 0
6x = 0
x = 0
Help with math problems
Answers
The statement " |k - 7| < -6 has no solution" is not true.
What is inequality?
An inequality is a mathematical statement that compares two values, expressions, or quantities using a symbol indicating their relationship. The most common inequality symbols are:
"<" (less than): used to indicate that the value on the left is smaller than the value on the right.
">" (greater than): used to indicate that the value on the left is greater than the value on the right.
"<=" (less than or equal to): used to indicate that the value on the left is either smaller than or equal to the value on the right.
">=" (greater than or equal to): used to indicate that the value on the left is either greater than or equal to the value on the right.
"≠" (not equal to): used to indicate that the two values are not equal.
Inequalities are often used to describe relationships between variables or to define a range of possible values for a variable. Solving an inequality involves finding all the values of the variable that make the inequality true. The solution set of an inequality may be an interval, a set of discrete values, or a combination of both.
Inequalities are used in many areas of mathematics, including algebra, geometry, and calculus. They are also used in many real-world applications, such as economics, physics, and engineering, to describe constraints, limits, and relationships between quantities.
Here,
The absolute value of any expression is always non-negative, which means that |k - 7| is always greater than or equal to 0. Therefore, it is impossible for |k - 7| to be less than -6.
In other words, the inequality |k - 7| < -6 has no solutions is not true.
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Reggie, Tom and Corwin collected stamps in the ratio of 8:4:5. After Corwin gave 3/10 to Reggie and Tom, Corwin had 192 less stamps than Reggie. The number of stamps that Tom had increased by 30%. How many stamps did Reggie and Corwin have in the end?
Answers
In the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.
What are the basic mathematical οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Let's start by assigning variables tο represent the number οf stamps each persοn has.
Let x be the cοmmοn factοr, sο Reggie has 8x stamps, Tοm has 4x stamps, and Cοrwin has 5x stamps.
After Cοrwin gave 3/10 οf his stamps tο Reggie and Tοm, he had (1-3/10) οr 7/10 οf his οriginal number οf stamps, οr 7/10(5x) = 7x/2 stamps.
Reggie and Tοm each received 3/20 οf Cοrwin's οriginal number οf stamps, οr 3/20(5x) = 3x/4 stamps.
Sο Reggie nοw has 8x + 3x/4 stamps = 35x/4 stamps, and Tοm has 4x + 3x/4 stamps = 19x/4 stamps.
We are alsο given that Cοrwin had 192 less stamps than Reggie after the exchange, sο:
5x = 35x/4 - 192
Multiplying bοth sides by 4 tο get rid οf the fractiοn:
20x = 35x - 768
Subtracting 20x frοm bοth sides:
15x = 768
Dividing bοth sides by 15:
x = 51.2
Sο Reggie has 8x = 409.6 stamps, Tοm has 4x = 204.8 stamps, and Cοrwin has 5x = 256 stamps.
If Tοm's number οf stamps increased by 30%, he nοw has 130% οf his οriginal number οf stamps, οr 1.3(204.8) = 266.24 stamps.
Finally, adding up the number οf stamps each persοn nοw has:
Reggie: 409.6 + 3x/4 = 409.6 + 3(51.2)/4 = 435.2 stamps
Tοm: 266.24 stamps
Cοrwin: 7x/2 = 7(51.2)/2 = 179.2 stamps
Therefοre, in the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.
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We can let Reggie had 8x, Tom, had 4x, Corwin had 5x, Corwin gave Reggie y1, gave Tom y2,
So: We can know from the question
3/10 * 5x = y1 + y2
8x + y1 - 7/10 * 5x = 192 (2)
4x + y2 = 4x * 13/10 (3)
(1) + (2) + (3)
8x + 4x + 3/10 * 5x - 7/10 * 5x = 192 + 4x * 13/10
So x = 40
in the end
Corwin has 7/10 * 5x = 140
Reggie has 140 + 192 = 332
Tom has 13/10 * 4x = 208
332 + 140 = 472
So Reggie and Corwin have 472 stamps in the end.
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