Answer:
The island of Martinique has received $32,000 for hurricane relief efforts. The island’s goal is to fundraise at least y dollars for aid by the end of the month. They receive donations of $4500 each day. Write an inequality that represents this
situation, where x is the number of days.
Step-by-step explanation:
The total amount raised after x days is given by:
Total amount raised = $32,000 + $4,500x
We want this to be at least y by the end of the month. Assuming that there are 30 days in the month, we can write the inequality:
$32,000 + $4,500x ≥ y
Alternatively, if we don't want to assume the number of days in the month, we can use a variable for the number of days:
$32,000 + $4,500x ≥ y
This inequality states that the sum of the initial donation and the donations received each day multiplied by the number of days must be greater than or equal to the fundraising goal y.
Can you guys please help me with this question I think it’s A. but I’m not sure if it’s correct?!PLEASEEE
Answer:
A is correct
Step-by-step explanation:
Whatever value you put in for "y" will keep both of the equations equal
Given that m∠A=(16x)°, m∠C=(8x+20)°, and m∠D=128°, what is m∠B
The value of m∠B is 212 - 24x.
How did we get the value?The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.
As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.
To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.
Thus,
m∠A + m∠B + m∠C + m∠D = 360
Substituting the given values, we get:
(16x)° + m∠B + (8x+20)° + 128° = 360
Simplifying and solving for m∠B, we get:
m∠B = 360 - (16x)° - (8x+20)° - 128°
m∠B = 212 - 24x
Therefore, the value of m∠B is 212 - 24x.
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Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.
To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.
Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:
30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches
The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.
The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.
Now, we can calculate the volume of the box by multiplying its length, width, and height:
Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.
In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.
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Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled 2/5 of the distance from City A to City B and on the second day, she traveled 2/3 of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.A) 1−2/5−2/3B) 1−2/5−2/3(2/5)C) 1−2/5−2/5(1−2/3)D) 1−2/5−2/3(1−2/5)E) 1−2/5−2/3(1−2/5−2/3)
The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).
What is the fraction?The fraction represents a portion or part of a whole.
There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.
The fractional distance traveled on day one = ²/₅
The remaining fractional distance = ³/₅ (1 - ²/₅)
The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)
The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)
Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.
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Can anyone help with this math problem please? Thanks!
New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
How to find reduced area?The area of the tennis court is given by:
A = lw
where l is the length of the court and w is the width of the court.
Substituting the given values, we have:
[tex]$$260.7569 = l \cdot 10.97$$[/tex]
Solving for l, we get:
[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]
To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:
w' = w - 0.25w = 0.75w
Substituting the given values, we have:
[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]
where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:
[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]
Therefore, the new area of the court is reduced by 25%.
To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:
[tex]$w' = 0.75w$$[/tex]
Dividing both sides by w, we get:
[tex]$\frac{w'}{w} = 0.75$$[/tex]
This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
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Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
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a system of equations is shown below. y=2x+1 and y=x+2 what is the solution to the system? A. (0,1) B. (1,2) C. (1,3) D. (2,4)
Answer:
(1,3)
Step-by-step explanation:
Given system of equations is :-
y = 2x + 1y = x + 2We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,
2x + 1 = x + 2
Subtract x on both sides,
2x - x + 1 = 2
Simplify,
x = 2 - 1
x = 1
Substitute this value of x into equation (2) as ,
y = 1 + 2
y = 1 + 2
y = 3
Hence the required answer is (1,3) .
and we are done!
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
If A={1,2,3}, B= {} show that A is not equal to B
In set theory, two sets are considered equal if they have the same elements. In this case, A is a set containing the elements 1, 2, and 3, while B is an empty set (also known as the null set),
A contains three distinct elements, and B contains none, we can conclude that A and B are not equal, i.e., A is not equal to B.
A ≠ B
Set theory is a branch of mathematics that studies collections of objects, called sets, and the relationships between them. A set is defined as a well-defined collection of distinct objects, which can be anything from numbers and letters to more abstract concepts like functions and geometrical shapes. The set theory provides a foundation for other areas of mathematics, including algebra, topology, and logic.
One of the fundamental concepts of set theory is the notion of membership, which states that an object either belongs to a set or does not. Sets can also be combined through operations such as union, intersection, and complementation, and the relationships between sets can be represented using Venn diagrams.
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What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.
Therefore, the measure of ∠D is approximately 60.96 degrees.
What is measure?A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.
by the question.
To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:
[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]
Taking the inverse tangent of both sides, we get:
[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]
Rounding this to the nearest hundredth, we get:
[tex]angleD = 60.95 degrees =60.96 degree.[/tex]
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5. {MCC.6.RP.A.3B} How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes?
*
1 point
Answer:
Step-by-step explanation:
It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.
Answer:
120 minutes / 2 hours
Step-by-step explanation:
time = distance / velocity
[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]
cindy and tom, working together, can rake the yard in 8 hours. working alone, tom takes twice as long as cindy. how many hours does it take cindy to rake the yard alone?
Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours
How do we calculate the time it takes Cindy?To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.
Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.
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50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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Compute the value of the expression without using a calculator
Answer:
Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:
7^(log_7(12)) = 12
Therefore, the value of the expression is 12.
How does the volume of a square pyramid change if the base edge is multiplied by 6?
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]
how can you convert a given number of fluid ounces to find equivalent number of cups explian
Step-by-step explanation:
There are 8 fluid ounces in a cup....
divide the number of ounces by 8 to find the number of cups
# ounces / 8 ounces/cup = cups
successful firms must focus on the quality of the products and services they offer. which of the following factors does not contribute to the quest for quality?
a. Global competition
b. Consumer expectations
c. Technological advances
d. All the answer choices are correct
Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.
Why does a successful firm need to focus on quality?In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.
Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.
How does global competition contribute to the quest for quality?Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.
What are the factors that contribute to the quest for quality?Several factors contribute to the quest for quality. These include:
Consumer expectations: Customers have high expectations when it comes to quality. They expect products and services to be of high quality, and they are willing to pay a premium for quality.Technological advances: Technological advances have made it possible for firms to produce high-quality products and services. Firms can use technology to automate production processes, improve quality control, and reduce defects.Global competition: Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage.Regulations: Regulations require firms to meet certain quality standards. Firms that fail to meet these standards can face legal action and damage to their reputation.Learn more about Global competition here: https://brainly.com/question/29479819
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A function is shown in the box. What is the value of this function for f(-8)?
(Write the answer as an improper fraction in lowest terms.)
Answer:
f(x) = (5/6)x - (1/4)
f(-8) = (5/6)(-8) - (1/4)
f(-8) = (5/3)(-4) - (1/4)
f(-8) = (-20/3) - (1/4)
f(-8) = (-80-3)/12
f(-8) = -83/12
the chance of a blizzard tommorrow is 5%. write the complement of this event
Answer:
the chance of a blizzard tommorrow is 5%. write the complement of this event
Step-by-step explanation:
The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:
100% - 5% = 95%
Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.
the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[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{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
Using the discriminant, how many real solutions does the following quadratic equation have? x^2 +8x+c= 0
The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:
[tex]b^2 - 4ac[/tex]
[tex]= 8^2 - 4(1)(c)[/tex]
[tex]= 64 - 4c[/tex]
Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).
In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.
Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
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Radioactive decay tends to follow an exponential distribution; the half-life of an isotope is the time by which there is a 50% probability that decay has occurred. Cobalt-60 has a half-life of 5.27 years. (a) What is the mean time to decay? (b) What is the standard deviation of the decay time? (c) What is the 99th percentile? (d) You are conducting an experiment which first involves obtaining a single cobalt-60 atom, then observing it over time until it decays. You then obtain a second cobalt-60 atom, and observe it until it decays; and then repeat this a third time. What is the mean and standard deviation of the total time the experiment will last?
The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.
It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.
(a) The mean time to decay for Cobalt-60 is 5.27 years.
(b) The standard deviation of the decay time is 2.6355 years.
(c) The 99th percentile is 13.6825 years.
(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.
Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.
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HHHHEEEEELLLPPPPPP
Solve for x. using the tangent lines.
50 deg
X
x =[?]^
from the given circle having tangents, the value of x is 130°.
What does a tangent line mean?A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).
In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.
In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.
From the given figure,
We know that
50 + AB = 180
AB = 180 - 50
AB = 130
The value of x or arc AB is 130°.
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Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
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To make a fruit smoothie, Olivia uses 4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango. What is the ratio of blueberries to banana?
Thus, the ratio for the number of blueberries to banana is 4:1.
Define about the ratios of the numbers?A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.
A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.
The given data for preparing fruit smoothie:
4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango.
Then,
ratio of blueberries to banana:
blueberries/banana = 4/1
Thus, the ratio for the number of blueberries to banana is 4:1.
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f.
The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x)) is 1
Calculating the inverse of g(x)Given that
f(x) = 3 - 2x
Rewrite as
g(x) = -x² + x + 1
Express as vertex form
g(x) = -(x - 0.5)² + 1.25
Express as equation and swap x & y
x = -(y - 0.5)² + 1.25
Make y the subject
y = 0.5 + √(1.25 - x)
So, the inverse is
g⁻¹(x) = 0.5 + √(1.25 - x)
Calculating the value of xHere, we have
f(g(x)) = g(f(x))
This means that
f(g(x)) = 3 - 2(-x² + x + 1)
g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1
Using a graphing tool, we have
f(g(x)) = g(f(x)) when x = 1
Hence, the value of x is 1
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Complete question
f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers
Find the inverse of G and the value for x for which f(g(x)) = g(f(x)).
What are the zeros of g(x) = x3 + 6x2 − 9x − 54?
Answer:
Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.
What is the value of this expression when x = -6 and y=-1/2
The resultant value of the given expression 4(x²+3)-2y is 157 respectively.
What are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.
Here, we refer to these letters as variables.
An expression is a group of words with operators between them.
The equation is the union of two expressions joined by the symbol "equal to" (=).
For instance, 3x-8. Ex: 3x-8 = 16.
So, the value would be:
4(x²+3)-2y
Insert values as follows:
=4((-6)²+3)-2(-1/2)
=4(36+3)+1=157
Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.
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Complete question:
What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y
Which of these planes is NOT in the {100} family for a tetragonal crystal? (A tetragonal unit cell drawn to proportion is included below for reference.)(A) (010)(B) (001)(C) (110)(D) Both B & C(E) All of these planes are in the {100} family.
The answer is (001). This is because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family.
The question is asking which of the planes (A), (B), (C), and (D) is not part of the {100} family for a tetragonal crystal.A tetragonal crystal is a three-dimensional structure made up of four faces that intersect at right angles, forming a unit cell. Each face of the unit cell is defined by a Miller index. A Miller index is a set of three integers written in the form {hkl}, which describes the orientation of the face relative to the crystal lattice. In a tetragonal crystal, the {100} family is the set of faces described by {hkl} such that h = k = 0 and l ≠ 0.
Therefore, A (010), C (110), and E (all of these planes are in the {100} family) are all part of the {100} family for a tetragonal crystal, while B (001) is not. because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family. In conclusion, the correct answer to the question is B (001).
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Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.
The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.
We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:
x_1 = y
x_2 = y'
x_3 = y''
with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.
The resulting system of equations is:
x_1' = x_2
x_2' = x_3
x_3' = (2t^2 - t)x_2 - 4x_3 + 2t
This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.
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