The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
Determine the compound inequalityA compound inequality is an equation that combines two inequalities with the word "and" or "or".
To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.
For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.
First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4
Next, we will solve 4u+4<28:
4u+4<28 4u<28-4 4u<24 u<6
Now, we will combine the solutions.
Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.
The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).
So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
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Blake collects stamps. He collected a total of 250. If 84% of the stamps he collected were foreign, how many other stamps did he collect?
Solve the following equation exactly. Use an inverse function when appropriate.
√x³ - 100 = 5
Answer:
Starting with the given equation:
√x³ - 100 = 5
Adding 100 to both sides:
√x³ = 105
Squaring both sides:
x³ = 11025
Taking the cube root of both sides:
x = 15
Therefore, the exact solution to the given equation is x = 15.
Note that no inverse functions were needed to solve this equation
Step-by-step explanation:
\( \left[\begin{array}{cc}1 & -1 \\ -2 & 2 \\ 2 & -2\end{array}\right] \)
\( \begin{array}{l}\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right] \\ \frac{1}{\sqrt{2}}\left[\beg
The orthonormal basis for this matrix.
To find the orthonormal basis for the given matrix, you will need to begin by taking the right and left singular vectors of the matrix.
The right singular vector for this matrix is 3(1 -1 1 1).
The left singular vector for this matrix is 2(-2 2 2 -2).
Now, divide each vector by its length to make them unit vectors, and you will get the orthonormal basis for the given matrix.
The orthonormal basis for this matrix is 1/3(1 -1 1 1) 1/2(-2 2 2 -2).
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Which lists all the real zeros of the polynomial p(x)=(2x-7)(x^2-49) ?
The real zeros of the polynomial p(x) are 7/2, -7, and 7. Option D is the correct answer.
What in algebra is the Factor Theorem?According to the algebraic principle known as the Factor Theorem, if a polynomial f(x) has a factor of (x - a), then f(a) = 0. To put it another way, if (x - a) is a factor of f(x), then the polynomial f(x) is equal to zero when x equals a. By finding the components of the polynomial and computing the values of x that make each factor equal to zero, this theorem may be used to locate the roots or zeros of a polynomial. The effective factorization and solution of polynomial problems are made possible by the Factor Theorem, a potent algebraic tool.
The given polynomial can be written as follows:
p(x) = (2x - 7)(x + 7)(x - 7)
The real zeros are the values of x that make the polynomial equal to zero. Therefore, the real zeros are:
x = 7/2, -7, 7
Therefore, the real zeros of the polynomial p(x) are 7/2, -7, and 7.
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4x-25=-125 how do you slove it
Answer: 25
Step-by-step explanation:
4x - 25 = -125
4x = -125 + 25
4x = -100
Divide both sides by 4
x = -25
Find the equation for the line that passes through the point
(3,−2) , and that is perpendicular to the line with the equation
x=2 .
The equation for the line that passes through the point (3,−2) , and that is perpendicular to the line with the equation x=2, is given by y = -2
How do we find the equation?To find the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2, we need to find the slope of the perpendicular line and use the point-slope form of an equation.
The slope of the line x = 2 is undefined, since it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and the slope of a horizontal line is 0.
Using the point-slope form of an equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can plug in the values for the slope and the point:
y - (-2) = 0(x - 3)
Simplifying the equation, we get:
y + 2 = 0
y = -2
So the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2 is y = -2. This is a horizontal line that passes through the y-axis at -2.
Answer: y = -2
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.
What is Graph ?
A graph is a visual representation of data that displays the relationship between variables or sets of data. Graphs are commonly used in various fields such as mathematics, statistics, economics, and science to help people understand and analyze data.
IQR, because it is a measure of variability that is resistant to outliers and is appropriate for both symmetric and skewed distributions. It measures the spread of the middle 50% of the data, which gives a good indication of how consistent the temperatures are around the median.
Therefore, using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.
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9. An arts and crafts store has a crate that contains glass,
wood, and brass beads. Friends take turns choosing a bead without
looking, recording the bead type, and returning the bead to the
crate. The table shows the results of 300 selections.
a. Write a probability model for choosing a bead.
b. Based on the frequencies in the table, estimate the number of
each type of bead that will be chosen if the friends select a total
of 450 beads from the crate.
Choosing Beads
Glass 60
Wood 96
Brass 144
In regards to question A:
P(G) = 0.2
P(W) = 0.32
P(B) = 0.48
B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.
What is the probability about?a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:
P(G) = [tex]\frac{60}{300}[/tex] = 1 ÷ 5 = 0.2
P(W) = [tex]\frac{96}{300}[/tex] = 8 ÷ 25 = 0.32
P(B) = [tex]\frac{144}{300}[/tex] = 12÷ 25 = 0.48
b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:
E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90
E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144
E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216
Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.
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The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.
Answer:
50
Step-by-step explanation:
good
Use substitution to solve
Answer:
x=4, y=-2
Step-by-step explanation:
[tex]2y=x-8\\2y-x=-8\\2(2x-10)-x=-8\\4x-20-x=-8\\3x-20=-8\\3x=-8+20\\x=12/3\\x=4\\\\\\y=2x-10\\y=2(4)-10\\y=8-10\\y=-2[/tex]
Find the size of angle x. 65° X 35°
The value of 'x' using the Triangle sum theorem is found as: x = 80°.
Explain about the Triangle sum theorem?According to the triangle sum theorem, all of a triangle's inner angles add up to 180 degrees. It is also known as the triangle's angle sum property.The triangle sum principle states that the sum of another three angles of any triangle is 180 degrees. According to their sides and angles, triangles can be classified into various mathematical kinds. These triangles are all three-sided and adhere to the triangle sum concept.Given that the triangle in the image is a triangle and that two of its angles is 65° and 35°.180° = 65°+35°+x
180° = 100°+x
180° - 100° = x
x=80° (value of x)
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The diagram for the question is attached:
i’m literally just trying to know what the answer of this question: “What is the result if you simplify 24/32?” and i can’t find the answer anywhere
Answer:
it is 3/4
Step-by-step explanation:
....................
Evaluate h(x)=−2x+9
when x=−2,0,
and 5
.
h(−2)=
h(0)=
h(5)=
Answer:
h(-2) = 13, h(0) = 9, and h(5) = -1.
Step-by-step explanation:
To evaluate h(x) = -2x + 9 for the given values of x, we can substitute each value of x into the expression and simplify:
h(-2) = -2(-2) + 9 = 13
h(0) = -2(0) + 9 = 9
h(5) = -2(5) + 9 = -1
Therefore, h(-2) = 13, h(0) = 9, and h(5) = -1.
Find the scale factor of a drawing if the scale is 1 inch = 1/8 inch.
Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each function measurement on the design is eight times bigger than its actual-world equivalent.
what is function?Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.
One inch on the illustration equals one eighth of an inch in reality if the scale is 1 inch = 1/8 inch.
We must divide the length of the drawing by the comparable length in reality to determine the scale factor. The scale factor is: because one inch on the design corresponds to 1/8 inch in reality.
1 / (1/8) = 8
Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each measurement on the design is eight times bigger than its actual-world equivalent.
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Michael buys 3 shirts for $25 each. He will also have to pay 7% sales tax.
Find the total amount Michael will pay the cashier.
Answer:$22.84
Step-by-step explanation:
The tax is calculated by 0.075 * 21.25 = 1.59375 or $1.59. So the total bill is the cost of items purchased plus tax, which is $21.25 + $1.59 = $22.84.
Use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
y=?
When x=6, the value of [tex]y=ax^2[/tex] is 11a.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
Assuming that the function [tex]y=ax^2[/tex] is defined for all real numbers x, we can use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
The differences of consecutive y-values for the function y=ax^2 are given by:
[tex]a(2^2 - 1^2), a(3^2 - 2^2), a(4^2 - 3^2), ...[/tex]
Simplifying these expressions, we get:
3a, 5a, 7a, ...
We can see that the differences between consecutive values are all the same, namely 2a. Therefore, we can express any y-value of the function
[tex]y=ax^2[/tex] as:
y = y(1) + (x-1)Δy
where y(1) is the value of y when x=1, and Δy is the common difference between consecutive y-values, which in this case is 2a.
Substituting the values x=6, y(1)=a(1^2)=a, and Δy=2a into this expression, we get:
y = a + (6-1)(2a) = a + 10a = 11a
Therefore, when x=6, the value of [tex]y=ax^2[/tex] is 11a.
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Divide. Check your answer by showing that the product of the divisor and t (16y^(3)+y^(4)+93+61y+49y^(2))/(y+3)
The answer is correct. The division of polynomials is a straight forward process. To divide one polynomial by another, we need to divide each term in the numerator (the top part of the fraction) by the denominator (the bottom part of the fraction). Let's use long division to solve this equation.
Step 1: Divide the leading coefficient (the first number) of the numerator by the leading coefficient of the denominator. [tex]16y3 ÷ (y+3) = 16y2.[/tex]
Step 2: Multiply the result of step 1 by the denominator and subtract it from the numerator. 16y2 (y+3) - 16y3 = -3y2.
Step 3: Bring down the next coefficient from the numerator, y4, and repeat the process.
Step 4: Divide the leading coefficient of the new numerator, -3y2, by the leading coefficient of the denominator, [tex]y+3. -3y2 ÷ (y+3) = -3y.[/tex]
Step 5: Multiply the result of step 4 by the denominator and subtract it from the numerator. -3y (y+3) - (-3y2) = 0.
Step 6: Since the numerator is now 0, the division is complete. The final answer is: [tex]16y2 - 3y + (93 + 61y + 49y2) ÷ (y+3).[/tex]
To check your answer, multiply the divisor (y+3) and the result of the division. If the product is equal to the numerator, then the answer is correct.
Let's check: (y+3)(16y2 - 3y + (93 + 61y + 49y2)) = 16y3 + y4 + 93 + 61y + 49y2, which is the numerator of the original equation.
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Mr Khumalo has a budget of R30000 to fence off the garden
Determine if he will have sufficient funds to fence off the garden if it is further giveb that a gate of 1. 2m width, thats cost R500, will be fitted on one side of the garden
Answer:
No R30000 will be enough as the gate of 1.2m width cost R500
If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To determine if Mr. Khumalo will have sufficient funds to fence off the garden,
We need to calculate the total cost of the fence excluding the cost of the gate.
Let's assume the length of the garden is L meters.
The perimeter of the garden is then 2L + 1.2 meters (due to the gate on one side).
If the cost of fencing per meter is R, then the total cost of the fence will be:
Cost of the fence.
= (2L + 1.2) × R
Since Mr. Khumalo has a budget of R30000, we can set up an inequality to determine if the cost of the fence is within his budget:
(2L + 1.2) × R + 500 ≤ 30000
Simplifying the inequality, we get:
(2L + 1.2) × R ≤ 29500
Therefore,
If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.
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India bought a bag of grapes that weighed 3 pounds, 5 ouncesShe already had a bag at home that weighed pound, 12 ounces. How many pounds/ ounces of grapes does she have altogether?
Answer:
4Pounds 1ounce
Step-by-step explanation:
First bag is 3pound 5ounces
Second bag 12ounces
Add both
3 Pounds and 17ounces
16ounces make 1Pound so 17ounces becomes 1Pound and 1ounces
Add to the 3Pounds
You have 3 Pounds + 1 Pound 1ounce
How much is 80% of water in an apple converted ounces
The weight of the water within an apple is 6.4 ounces if the apple weighs 8 ounces.
The amounts of water in an apple in ounces, given only that it contains 80% water. Yet, it is well known that an average apple contains 84% to 86% water by weight.
We need to know the apple's weight in ounces to translate the water content to 80%.
Assume for the moment that the apple weighs 8 ounces. 80% is listed as the water content percentage. We may use the following formula to determine how much water is in an apple:
Weight of water = (water content percentage / 100) x weight of the apple
By entering the specified values, we obtain:
Weight of water = (80 / 100) x 8 ounces = 6.4 ounces.
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Given the cost formula Y= $15,000 + $5X, what is the total cost at an activity level of 8,000 units? (2 marks) $23,000. $40,000 $15,000 $55,000
The total cost at an activity level of 8,000 units is $55,000.
The total cost at an activity level of 8,000 units can be found by plugging in the value of X into the cost formula Y= $15,000 + $5X.
Step 1: Plug in the value of X into the cost formula:
Y= $15,000 + $5(8,000)
Step 2: Simplify the equation by multiplying $5 and 8,000:
Y= $15,000 + $40,000
Step 3: Add $15,000 and $40,000 to get the total cost:
Y= $55,000
Therefore, the total cost at an activity level of 8,000 units is $55,000. The correct answer is $55,000.
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Suppose that y varies directly as the cube root of x, and that y=100 when x=6859. What is y when x=1331? Round your answer to two decimal places if necessary.
The value of y = 57.86 when x = 1331.
We are given that y varies directly as the cube root of x. This means that the equation relating y and x is of the form:
y = k * cube_root(x)
Where k is the constant of proportionality. We are also given that y = 100 when x = 6859. We can use this information to find the value of k:
100 = k * cube_root(6859)
k = 100 / cube_root(6859)
k = 100 / 19
k = 5.26
Now we can use the value of k to find y when x = 1331:
y = 5.26 * cube_root(1331)
y = 5.26 * 11
y = 57.86
Therefore, y is approximately 57.86 when x is 1331. We can round this answer to two decimal places to get:
y = 57.86
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At a restaurant, 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant?
Answer: The correct answer would be Graph H.
Step-by-step explanation:
Answer:
top right
Step-by-step explanation:
600 per 10 hours is a rate of 60/hour.
You need a graph that has a slope of 60 and includes the point (1, 60).
Answer: top right
Choose the answer to complete each statement.
The slope of the line is ___.
The y-intercept is at ___.
The graph represents the function ___.
Answer:
Step-by-step explanation:
slope of line = 7/3
y-intercept is = 7
Given the following functions, evaluate each of the following: f(x) = x2 + 4x – 5 x x- 9(2) = x - 1 (f+g)(9) = (f -9)(9) = (fog)(9) = (1) (9) = g
The given functions f(x) = x² + 4x – 5 and g(x) = x - 1 are to be evaluated.
(f+g)(9). The addition of two functions is denoted by (f+g)(x) = f(x) + g(x). Now, we need to find the value of (f+g)(9). Substituting the values in the formula, we get:
(f+g)(x) = f(x) + g(x)f(x) = x² + 4x – 5g(x) = x - 1
(f+g)(9) = f(9) + g(9) = (9)² + 4(9) – 5 + (9) - 1= 81 + 36 – 5 + 9 - 1= 120
Therefore, (f+g)(9) = 120.
The subtraction of two functions is denoted by (f-g)(x) = f(x) - g(x). Now, we need to find the value of (f-9)(9). Substituting the values in the formula, we get:(f-g)(x) = f(x) - g(x)f(x) = x² + 4x – 5g(x) = x - 1(f-9)(9) = f(9) - g(9) = (9)² + 4(9) – 5 - (9) + 1= 81 + 36 – 5 - 9 + 1= 104
Therefore, (f-9)(9) = 104.3. (fog)(9)The composition of two functions is denoted by (fog)(x) = f(g(x)). Now, we need to find the value of (fog)(9).
Substituting the values in the formula, we get:
(fog)(x) = f(g(x))
f(x) = x² + 4x – 5
g(x) = x - 1
(fog)(9) = f(g(9)) = f(9 - 1) = f(8)= 8² + 4(8) – 5= 64 + 32 – 5= 91
Therefore, (fog)(9) = 91.4. g(x) = x - 1
Now, we need to evaluate g(9). Substituting x = 9 in the formula, we get:
g(x) = x - 1
g(9) = 9 - 1= 8
Therefore, g(9) = 8.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please help!
Answer:
Step-by-step explanation:
So first you have to divide the monkey by the + sign then when you did that you take the exponent and turn it into a ratio. When you are done doing that you have to multiply and divide and then you have your answer.
Ramu bought 12 metre long ribbon. He cut it into 2and 3 by 4 m and 1 and 1 by 2 meter long. Find the length of remaining ribbon
Ramu bought 12 metre long ribbon, and he cut it into different pieces then the length of remaining ribbon is equals to the 10 metre.
Ramu bought a long ribbon with lengths in meters. We have to calculate the length of remaining ribbon.
Total length of ribbon, L = 12 meters
After that he cut it into 2 and 3 by 4 m and 1 and 1 by 2 meter long. Two pieces of ribbon has length of 3/4 metre in each piece. So, total length of two pieces
= 2×3/4 = 3/2 meters
Also, he cut one piece of ribbon
length of this piece = 1/2 meter
Thus, total length of cutting pieces of ribbon = 3/2 metre + 1/2 metre
= 4/2 = 2 metre
The length of remaining ribbon = total length of ribbon - cutting pieces length
= 12 metre - 2 metre
= 10 metre
Hence, the required length is 10 metre.
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Solve for w. -(7)/((w+1)(w-7))=4+(3)/(w-7) If there is more than one solution, separate the
The two possible solutions for w are 6 and -3/4.
To solve for w, we need to use algebraic manipulation to isolate w on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by (w+1)(w-7) to clear the fractions: -(7) = 4(w+1)(w-7) + 3(w+1)
2. Distribute the 4 and 3 on the right side of the equation: -(7) = 4w^2 - 24w - 28 + 3w + 3
3. Combine like terms on the right side of the equation: -(7) = 4w^2 - 21w - 25
4. Move all terms to one side of the equation: 4w^2 - 21w - 18 = 0
5. Use the quadratic formula to solve for w: w = (-(-21) ± √((-21)^2 - 4(4)(-18)))/(2(4))
6. Simplify the equation: w = (21 ± √(441 + 288))/(8)
7. Simplify the equation further: w = (21 ± √729)/(8)
8. Solve for the two possible values of w: w = (21 + 27)/(8) or w = (21 - 27)/(8)
9. Simplify the two possible values of w: w = 48/8 or w = -6/8
10. Simplify the two possible values of w further: w = 6 or w = -3/4
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Molly is verifying if the two functions are inverses of each other? Her answer is as follows:
f(g(x))=x+5 g(f(x))=x+5
She stated that they are not inverses of each other. Is she correct and why? Explain.
Answer:
Molly is correct in stating that the two functions are not inverses of each other.
To be inverses of each other, two functions must satisfy the property that when they are composed in either order, they result in the identity function, which is represented by f(x) = x.
In this case, we have:
f(g(x)) = (x + 5) + 5 = x + 10
g(f(x)) = (x + 5) + 5 = x + 10
Since both compositions of the functions result in x + 10, which is not equal to x, the two functions are not inverses of each other.
Step-by-step explanation:
Answer:
Molly is correct. The fact that $f(g(x)) = g(f(x)) = x+5$ indicates that the two functions, $f$ and $g$, are symmetric about the line $y=x$, which means that they are not inverses of each other.
To determine whether two functions are inverses of each other, we need to show that their composition results in the identity function. That is, if $f(x)$ and $g(x)$ are two functions, then $f(g(x)) = g(f(x)) = x$ for all $x$ in the domain of $f$ and $g$.
In this case, we see that $f(g(x)) = g(f(x)) = x+5$, which is not the identity function. Therefore, the two functions are not inverses of each other.
if three times a number is increased by 4 the result is -8
Answer:
-4
Step-by-step explanation:
3x + 4 = -8
3x = -8 -4
3x = -12 /3
x = -4