Solve by graphing y= -5/3x + 4 y= -5/3x + 3
This question is about finding the slope of the tangent line to an inverse function. I would love to know if my answer of 1/5 is correct.
g(1) = 2
g^-1(2) = 1
(g^-1(x))' = 1/(g'(g-1(x))
(g^-1(2))' = 1/g'(g-1(2))
(g^-1(2))' = 1/g'(1)
g(x) = x^3 + 2x - 1
g'(x) = 3x^2 + 2
g'(1) = 3+2=5
(g^-1(2))' = 1/5
Daniel is using logarithms to solve the equation 24x = 14. Which of the following equations would be equivalent to his original expression?
2 log 4x = log 14
4x log 2 = log 14
2 log 4 = x log 14
x log 4 = 2 log 14
The resulting expression of the given logarithmic function will be 4xlog2 = log14.
Given the logarithmic expression below:
[tex]2^{4x}=14[/tex]
We are to determine which of the equations would be equivalent to his original expression.
Taking the logarithm of both sides, we will have:
[tex]log2^{4x}=log14\\4xlog2=log14\\[/tex]
From the solution, we can see that the resulting expression will be 4xlog2 = log14.
True or false ???????????????please help
Find one pair of real numbers, $(x,y),$ such that $x + y = 6$ and $x^3 + y^3 = 144.$
[tex]\[\{(3 + \sqrt{5}, 3 - \sqrt{5})}\][/tex] is the one pair of real numbers [tex]\((x, y)\)[/tex] that satisfies the given equations.
Given the system of equations:
[tex]\[x + y = 6\][/tex]
[tex]\[x^3 + y^3 = 144\][/tex]
We can use the identity for the sum of cubes:
[tex]\[x^3 + y^3 = (x + y)(x^2 - xy + y^2)\][/tex]
Substitute [tex]\(x + y = 6\):[/tex]
[tex]\[x^3 + y^3 = 6(x^2 - xy + y^2)\][/tex]
Given [tex]\(x^3 + y^3 = 144\)[/tex], we substitute this into the equation:
[tex]\[144 = 6(x^2 - xy + y^2)\][/tex]
Divide both sides by 6:
[tex]\[24 = x^2 - xy + y^2\][/tex]
Next, we use the square of the sum:
[tex]\[(x + y)^2 = x^2 + 2xy + y^2\][/tex]
Substitute [tex]\(x + y = 6\):[/tex]
[tex]\[6^2 = x^2 + 2xy + y^2\][/tex]
[tex]\[36 = x^2 + 2xy + y^2\][/tex]
We already have [tex]\(x^2 - xy + y^2 = 24\)[/tex]. Let’s denote the first and second equations:
1. [tex]\(x^2 - xy + y^2 = 24\)[/tex]
2. [tex]\(x^2 + 2xy + y^2 = 36\)[/tex]
Subtract the first equation from the second equation:
[tex]\[(x^2 + 2xy + y^2) - (x^2 - xy + y^2) = 36 - 24\][/tex]
[tex]\[3xy = 12\][/tex]
[tex]\[xy = 4\][/tex]
Now, we have two equations:
1. [tex]\(x + y = 6\)[/tex]
2. [tex]\(xy = 4\)[/tex]
We solve these equations using the quadratic formula. Consider the quadratic equation:
[tex]\[t^2 - (x+y)t + xy = 0\][/tex]
[tex]\[t^2 - 6t + 4 = 0\][/tex]
Solve for [tex]\(t\)[/tex] using the quadratic formula [tex]\(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):[/tex]
[tex]\[t = \frac{6 \pm \sqrt{36 - 16}}{2}\][/tex]
[tex]\[t = \frac{6 \pm \sqrt{20}}{2}\][/tex]
[tex]\[t = \frac{6 \pm 2\sqrt{5}}{2}\][/tex]
[tex]\[t = 3 \pm \sqrt{5}\][/tex]
Thus, the solutions for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are:
[tex]\[x = 3 + \sqrt{5}, \quad y = 3 - \sqrt{5}\][/tex]
or
[tex]\[x = 3 - \sqrt{5}, \quad y = 3 + \sqrt{5}\][/tex]
Write an equation of te circle with the center (0,0) and radius square root of 15
Answer:
x² + y² = 15
Explanation:
The formula for the equation of a circle is (x - h)² + (y - k)² = r², where the center of the circle is ordered pair (h, k) and r represents the radius (in units).
Now, we plug the given information into the circle equation and simplify.
radius = √15
center (0, 0), h = 0, k = 0
(x - 0)² + (y - 0)² = (√15)²
(x)² + (y)² = (√15)²
x² + y² = 15
The equation of the circle is x² + y² = 15
The equation of the circle with a center at (0,0) and a radius of the square root of 15 is x² + y² = 15. The standard form of the circle equation, (x - h)² + (y - k)² = r², is used with h and k set to 0 to represent the origin.
To write an equation of a circle with the center at the origin (0,0) and a radius of the square root of 15, we use the standard form of the circle equation:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the center of the circle and r is the radius. Since the center of the circle in question is at the origin, h = 0 and k = 0. The given radius is the square root of 15, so we have r = √15. Substituting these values into the standard form gives us the equation:
x² + y² = ( √15 )²
Which simplifies to:
x² + y² = 15
This is the equation for the desired circle centered at the origin with radius √15.
Brand x copier has improved its copier so that it produces 10% more copies than its old model. if the old model ran 420 copies per hour, how many copies would the new model run? round your answer to the nearest whole number.
a. 221 copies per hour
c. 462 copies per hour
b. 435 copies per hour
d. 447 copies per hour
Answer:
462
Step-by-step explanation:
A number x, rounded to 1 decimal place is 12.3 write down the error interval for x
The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.
Explanation:If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).
The error interval for x can be written as: 12.25 ≤ x < 12.35.
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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.
To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.
1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.
2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.
So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.
Miriam bought a bushel of apples from the apple orchard to bake apple pies for a bake sale. She started with 126 apples. After the first day of baking, she had 108 apples left. After the second day, she had 90 apples. After the third day, she had 72 apples left.If she continues this pattern, how many apples will she have left after 7 days of baking?
Arithmetic, because the sequence has a common difference. answer on edgenui......
The table below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often?
Options:
20%
31%
43% is wrong
57%
(I already did my other questions, this is the only one I needed help with)
Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?
A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.
Answer:
C. Either 46.27 miles or 17.43 miles
A cruise ship can cover 17 nautical miles in 374 minutes. How many nautical miles will it travel in 330 minutes?
The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.
To find the speed of the ship in very deep water:
Calculate speed = Distance / Time = 17 nmi / 374 min = 0.045 nautical miles per minute.For the ship's speed in shallow water:It depends on the water resistance; usually, in shallow water, the ship's maximum speed decreases due to increased drag and turbulence.!! WILL GIVE BRAINEST TO WHOEVER ANSWERS FIRST !!
Simplify (2√5 + 3√7)² Show ALL your work.
If the pattern below follows the rule "Starting with four, every consecutive line has a number one more than the previous line," how many marbles must be in the seventh line?
The number of balls in 7th line would be 10.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pattern as shown in the image.
An arithmetic sequence is of the form -a, a + d, a + 2d, a + 3d, ......,
{d} is common difference and {a} is first term.We can write the pattern as -
4, 5, 6, 7, .....
This is a arithmetic progression. We can write the nth term as -
a{n} = a + (n - 1)d
a{7} = 4 + (7 - 1) x 1
a{7} = 4 + 6
a{7} = 10
Therefore, the number of balls in 7th line would be 10.
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Jeanine baker makes floral arrangements. she has 18 different cut flowers and plans to use 7 of them. how many different selections of the 7 flowers are possible?
Jeanine can create 43758 different floral arrangements using 7 flowers out of the 18 available. This was calculated using the mathematical concept of combinations.
Explanation:To find the number of different selections of 7 flowers Jeanine can make out of 18, we need to use the mathematical concept of combinations. In this context, the combination formula is used, which is: C(n, k) = n! / [k!(n-k)!]
Where n is the total number, k is the number chosen, and '!' stands for factorial, which is the product of all positive integers less than or equal to the number. Thus, the number of ways Jeanine can choose 7 flowers out of 18 is calculated as follows: C(18, 7) = 18! / [7!(18-7)!] = 43758. Therefore, there are 43758 different ways Jeanine can create floral arrangements using 7 flowers out of the 18 available.
It should be noted that the color of the flowers does not influence the number of combinations if she intends to select any 7 flowers irrespective of their color.
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area of the parrelogram pls 25 points
1.) How is the graph of y equals negative 2 x squared minus 5 different from the graph of y equals negative 2 x squared?
2.)
The transformation on the graph of y = -2x²- 5 is described as 5 units downward.
What is transformation on the graphs?Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
As per the given information:
The graphs are let f(x) = y = -2x²- 5 and g(x) = y = -2x².
As per the definition, the transformation on the graph can be described as,
-5 < 0.
The graph shifts downward.
Therefore, the graph of y = -2x²- 5 is 5 units down than y = -2x².
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a construction company is replacing a window in a house. the window is currently 3 feet wide by 4 feet tall. The homeowner wants to add 4 1/2 inches to each side of the window. What is the new perimeter of the window in feet? Justify your reasoning.
How do science and math relate to each other?
Final answer:
Mathematics and science are foundational to engineering, providing the tools and understanding necessary for the engineering design process. They enable engineers to create models, solve design problems, and innovate, thus influencing education and daily life through engineered products.
Explanation:
Science and mathematics are intimately related, especially in fields such as engineering. Mathematics provides the language and tools for abstract reasoning and quantitative analysis, which are fundamental in engineering. Math is used to create mathematical models that describe physical phenomena and to evaluate the merit of different possible solutions. Science, on the other hand, offers understanding of natural phenomena and constraints that inform engineering solutions. Together, math and science are essential throughout the engineering design process, from conceptualization to detailed design implementation, and in team decision-making.
In high school and college, a strong foundation in math and science courses is crucial for success in engineering education. For instance, courses like thermodynamics, circuits, and fluids—commonly referred to as engineering science courses—are grounded in these basic disciplines. The role of science and mathematics in engineering extends beyond educational prerequisites; they are operational tools that engineers use in their work every day to innovate and create products that improve our lives, such as the pocket radio, cell phones, and computers.
The connections between math, science, and engineering are dynamic and multidimensional. They enable engineers to navigate through the iterative steps of the engineering design process, which include analyzing problems, developing solutions, and optimizing products, often moving nonlinearly as real-world complexities dictate adjustments and refinements.
When Mr. Peters drives from Boston to Worcester it takes him 30 minutes travelling at a speed of 60 miles per hour. Mrs. Peters drives from Boston to Worcester and leaves 5 minutes after Mr. Peters but travels at a speed of 90 miles per hour. Who will arrive first? By how many minutes?
Mrs. Peter arrives 5 minutes before Mr. Peter
To find who arrives first we first need to find the speed and time they require to arrive.
Given : From Boston to Worcester
Mr. Peter takes [tex]\rm time=30 \; minutes \; and \;speed= 60 miles /hr[/tex]
Mrs. Peter takes [tex]\rm speed=90 miles/hr[/tex]
We will now calculate Mr. Peters speed,
[tex]\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}[/tex]
How to find distance from Boston to Worecester?To find the distance, we will use distance formula
[tex]\rm Distance=speed\times time[/tex]
Here,given that the Mr Peters speed is [tex]\rm 60 miles /hr[/tex] and time is [tex]\rm 30 minutes[/tex]so by distance formula we will find distance of Mr. Peter
[tex]\rm Distance=\dfrac{mile}{min} \times 30 minutes[/tex]
[tex]\rm Distance= 30 miles[/tex]
Similarly, we will now calculate Mrs. Peters speed,
[tex]\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}[/tex]
by the given informations we know both covers the same distance
[tex]\rm ie. \;30 miles[/tex]
we will now find distance of Mrs. Peter
[tex]\rm Distance=speed\times time\\ 30miles=1.5\dfrac{miles}{min} \times time\\ time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\ time=20 minutes[/tex]
Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.
[tex]\rm time=20 minutes+ 5 minutes\\ time=25 minutes[/tex]
Therefore, it is clear that Mrs.Peter arrive before Mr Peter by 5minutes.
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What is the total surface area of the rectangular pyramid below?
(please see attached picture)
404 square feet
596 square feet
788 square feet
1,000 square feet
Answer:
596 square feet
Answer:
b I did the
Step-by-step explanation:
Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches. A) 338 in2 B) 422 in2 C) 520 in2 D) 1364 in2
If you can, please explain. Thank you vv much! :D
Answer:
422 in.2
Step-by-step explanation:
Substitute the measurements of the rectangular prism into the formula SA = 2(lw) + 2 (lw) + 2(lh): 2(13)(7) + 2(6)(7) + 2(13)(6) = 422 in2.
If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest
On two examinations, you have grades of 83 and 89. there is an optional final examination, which counts as one grade. you decide to take the final in order to get a course grade of a, meaning a final average of at least 90
PLS ANSWER! THE WORLD HATES ME!!
0.29999999999 As a fraction
Here is your answer:
All you need to do is keep the 29 and then add a hundred because of how many 9's there are.
Also, you could see that:
[tex] .29999999999 \neq \frac{29999999999}{100000000000} [/tex]
Which would also mean that:
[tex] \frac{29999999999}{100000000000} \neq \frac{29}{100} [/tex]
Therefore the answer is "29/100."
Hope this helps!
Answer:
13/46
Step-by-step explanation:
Suppose the diameter of a circle is \color{green}{10}10 start color green, 10, end color green. what is its radius
Simplify the expression -2x^2(4x − 3).
-8x3 − 6x2
-8x3 + 6x2
8x3 − 6x2
8x3 + 6x2
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ruth was hauling a wide load out of portland. at 7:00 am she headed north from exit 102 at an average speed of 35 pmh. michael headed north from the same exit at 9:00 am in his pontiac. by 3:00 pm the same day michael was 20 miles ahead of ruth. what was michael's average speed
Answer:
Ruth was out of Portland at 35mph at 7:00 am
so at 9 am, she was 70 miles ahead of Michael
but Michael was 20 miles ahead by 3 pm.
so in 6 hours, he went past Ruth by 90 miles which is 90/6 = 15mph
Michael speed = ruth speed + 15. = 35 + 15 = 50mph
Write the equation of a line going through the point (-3,5) that is parallel to the line 2x+y=-8
A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght
Answer:
The answer should be C.