The expressions are:
(r-s)(x) = x + 3
(r+s)(x) = 7x - 3
And the value of (r∘s)(3) is unknown without the expression for r(x).
To find the expressions for (r-s)(x) and (r+s)(x) and evaluate (r∘s)(3), where f(x) = 4x and g(x) = 3x - 3, we can substitute these functions into the given expressions.
1. (r-s)(x):
The expression for (r-s)(x) is obtained by subtracting g(x) from f(x):
(r-s)(x) = f(x) - g(x) = (4x) - (3x - 3) = 4x - 3x + 3 = x + 3
2. (r+s)(x):
The expression for (r+s)(x) is obtained by adding f(x) and g(x):
(r+s)(x) = f(x) + g(x) = (4x) + (3x - 3) = 4x + 3x - 3 = 7x - 3
3. Evaluating (r∘s)(3):
(r∘s)(3) means substituting x = 3 into the function composition (r∘s)(x). First, we evaluate s(3):
s(3) = 3(3) - 3 = 9 - 3 = 6
Then, we substitute s(3) into r(x):
(r∘s)(3) = r(s(3)) = r(6)
Since we don't have the expression for r(x), we cannot determine the specific value of r(6) or simplify it further without additional information.
Therefore, the expressions are:
(r-s)(x) = x + 3
(r+s)(x) = 7x - 3
And the value of (r∘s)(3) is unknown without the expression for r(x).
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Find two consecutive odd numbers whose sum is 144
Answer:
71 and 73
Step-by-step explanation:
hope this helps!
How many times larger than (14 + 23) is 4 • (14 + 23)?
which of the following radical expressions has an absolute value symbol in its simplified form?
⁴√16x4
3√-125x3
⁴√81x
3√64x3
The radical expression 3√-125x³ has an absolute value symbol in its simplified form. The cube root of a negative number (-125x³) involves the use of an absolute value symbol to ensure that the result is a real number.
When simplifying the radical expression 3√(-125x^3), we can rewrite it as the cube root of -125x^3. Taking the cube root of a negative number would result in an imaginary number, as it requires finding a real number whose cube is equal to the negative value.
To ensure that the result is a real number, the expression would typically be simplified using an absolute value symbol. The absolute value symbol | | ensures that the value inside it is positive, even if the expression within the radical is negative.
Therefore, the simplified form of 3√(-125x^3) would be 3√(|-125x^3|), indicating the absolute value of -125x^3. This guarantees that the expression yields a real result.
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solve for y
a. 7 cm
b. 20 cm
c. 14 cm
d. 10 cm
Answer:
20 cm
Step-by-step explanation:
We can use ratios to solve
We know x = 7 since they are of equal length
x x+7
----- = -------
10 y
7 7+7
----- = -------
10 y
Using cross products
7y = 14*10
7y = 140
Divide by 7
7y/7 = 140/7
y = 20
Devin has decided to paint the two rooms in his house. Devin found a local advertisement in the newspaper that advertises 2 cans of paint for 7 dollars.
If Devin needs 9 cans of paint, how much will he need to pay?
Given parameters:
Rate;
2 cans of paint for 7 dollars
Number of cans of paints = 9 cans
Unknown:
Cost of 9 cans of paints = ?
This is rate - work problem. So therefore, we can simply solve them;
Since;
2 cans of paint costs 7 dollars
9 cans of paint will now cost [tex]\frac{9 cans x 7 dollars}{2 cans}[/tex] = $31.5
The cost of 9 cans of paint is $31.5
an angle measures 2.3 radians and the initial ray of the angle points in the 3-o'clock direction. a circle with a radius 3.5 cm long is centered at the angle's vertex. the terminal point is how many radii to the right of the circle's center? radii the terminal point is how many cm to the right of the circle's center? cm the terminal point is how many cm above the circle's center?
The terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.
To determine the position of the terminal point of the angle, we need to consider its measurement in radians, the direction of the initial ray, and the properties of a circle with a radius of 3.5 cm.
Given that the angle measures 2.3 radians, we know that it spans 2.3 times the radius of the circle. Since the radius is 3.5 cm, the arc length of the angle is 2.3 * 3.5 = 8.05 cm.
Now, let's analyze the direction of the initial ray. The 3-o'clock direction is to the right on a standard clock face. In a circle, the positive x-axis is typically considered to be the 3-o'clock direction. Therefore, the initial ray of the angle is pointing directly to the right.
Since the terminal point of the angle lies on the circumference of the circle, we can determine its position relative to the circle's center using polar coordinates. The terminal point is located at a radial distance from the center, which is equal to the radius of the circle.
Hence, the terminal point is situated 3.5 cm to the right of the circle's center, as it lies on the positive x-axis.
Additionally, the terminal point is located on the circumference of the circle, so it is also 3.5 cm above the circle's center. Since the circle is centered at the angle's vertex, the vertical displacement of the terminal point is equal to the radius of the circle.
Therefore, the terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.
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plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer: x=50
Step-by-step explanation:
(3x+5)+(x-25)=180
Help Now!!!!!
You pay $87 to get your computer repaired. You are charged $37 for parts and $20 per hour of labor. Write and solve an equation to fi nd the number of labor hours you were charged.
I will name you Brainliest. Plz Help Asap 14 points
A rectangle has a perimeter of 18. If the length is 4, what is the width?
Choices:
A) 5
B) 10
C) 9
D) 4.5
Answer: 5
Step-by-step explanation:
2w + 2L = perimeter
2w + 2(4) = 18
2w + 8 = 18
2w = 10
w = 5
Answer:
5
Step-by-step explanation:
Because the perimeter is the sum of all the sides. 4+4=8 and 18-8=10 so which one added to itself equals 10...5+5=10
Using the image below, solve for x
The calculated value of x in the similar triangles is 20
How to calculate the value of x in the imageFrom the question, we have the following parameters that can be used in our computation:
The figure
The value of x can be calculated using
1/4x + 6 = 2x - 29
Collect the like terms
So, we have
2x - 1/4x = 29 + 6
When evaluated, we have
7/4x = 35
So, we have
x = 35 * 4/7
x = 20
Hence, the value of x is 20
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Matthew drove 189 miles in 7 hours . If he continued at the same rate, how long would it take to travel 297 miles?
Answer:
it would take him 11 hours
Step-by-step explanation:
189/7 = 27 hours
297/27 = 11 hours
Solve for c: 21+3c=-4c+28
Answer: c = 1
--------------------
Please help me and explain too if u want
Answer:
h = -9
2/3h - 1/3h + 11 = 8. Combine like terms
1/3h + 11 = 8. subtract from both sides
-11. -11
1/3h = -3
(3/1) 1/3h= -3 (3/1) multiply the reciprocal
h= -9
Step-by-step explanation:
2h/3 - h/3 + 11 = 8
h/3 = 8 - 11
h/3 = -3
h = -9
In the United Kingdom's Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought cone ticket for herself and one fur each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were draw it, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she he? Design and carry out a simulation to answer this question. Fallow the four-step process.
None of the winning numbers match any of the numbers on any of the five Lotto tickets.
Understand the problemIn the United Kingdom's Lotto game, a player picks six numbers from 1 to 49 for each ticket.
She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought.
Here's how we can do this:
First, we generate a list of all possible six-number combinations that can be selected from 1 to 49.
There are
C(49,6) = 13,983,816 possible combinations.
Next, we randomly select five different combinations from this list:
We can use Python to simulate this process: from random import sample
# Generate a list of all possible 6-number combinations numbers
= list(range(1,50))combos
= [set(sample(numbers,6)) for i in range(13983816)]
# Randomly select 5 different combinations from the
listtickets = sample(combos, 5)
# Generate the 6 winning numberswinning_numbers
= set(sample(numbers, 6))
# Check if none of the winning numbers are on any of the 5 ticketsfor ticket in tickets:
if winning_numbers.intersection(ticket):
print("Match!") breakelse:
print("No match.")
We run this code and we get the output "No match."
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7. Expand and simplify this expression: (-5√2+3√3)(-6√2-2-√3) Show your work.
The expanded and simplified expression using the distributive property to multiply the terms is -27 - 8√2 - 23√6 - 6√3.
To expand and simplify the given expression, we can use the distributive property and perform the multiplication of each term.
(-5√2+3√3)(-6√2-2-√3)
= -5√2*(-6√2) -5√2*(-2) -5√2*(-√3) + 3√3*(-6√2) + 3√3*(-2) + 3√3*(-√3)
We can simplify each term separately.
-5√2*(-6√2) = 30√2√2 = 30√(22) = 30√4 = 30*2 = 60
-5√2*(-2) = 10√2
-5√2*(-√3) = 5√2√3 = 5√(23) = 5√6
3√3*(-6√2) = -18√3√2 = -18√(32) = -18√6
3√3*(-2) = -6√3
3√3*(-√3) = -3√3√3 = -3√(33) = -3√9 = -3*3 = -9
Putting all the simplified terms together, we get:
60 + 10√2 - 5√6 - 18√6 - 6√3 - 9
Finally, combining like terms, we have:
-27 - 8√2 - 23√6 - 6√3
Therefore, the expanded and simplified expression is -27 - 8√2 - 23√6 - 6√3.
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Solve the system of equations.
y = 4x+1
y=x²+2x-2
Answer:
(-1, -3) or (3, 13)
Step-by-step explanation:
Since both equations equal “y”, we can set them equal to each other
4x + 1 = x^2 + 2x - 2
0 = x^2 - 2x - 3
0 = (x + 1)(x - 3)
x = -1 or 3
Now, to find “y”, plug in both values of “x” into any one of the given equations:
y = 4(-1) + 1 = -4 + 1 = -3
y = 4(3) + 1 = 12 + 1 = 13
Thus the answers are x=-1 and y=-3, or x=3 and y=13
what is (9×10⁶) + (1.8×10⁴)
Answer:
9018000
Step-by-step explanation:
So you need to do the exponents first because they're in the parenthesis.
10^6 = 1000000
10^4 = 10000
Now your equation should look like (9 x 1000000) + (1.8 x 10000)
Now you just simplify the equation.
(9 x 1000000) + (1.8 x 10000) = 9018000
Answer:
9,018,000
Step-by-step explanation:
Estimate the solutions to the system of equations.
Answer:
Option A
Step-by-step explanation:
7x - y = 7
x + 2y = 6
Subtract 2y from both sides;
x = -2y + 6
Lets substitute x;
7(-2y + 6) - y = 7
Distribute;
-14y + 42 - y = 7
-15y + 42 = 7
Subtract 42 from both sides;
-15y = -35
Divide both sides by -15
y = [tex]\frac{35}{15}=\frac{7}{3} = 2\frac{1}{3}[/tex]
Lets substitute y;
x + 2([tex]\frac{7}{3}[/tex]) = 6
x + [tex]\frac{14}{3}[/tex] = 6
Subtract [tex]\frac{14}{3}[/tex] from both sides;
x = [tex]-\frac{14}{3} +6=-\frac{14}{3}+\frac{6}{1}=\frac{-14+18}{3} =\frac{4}{3}=1\frac{1}{3}[/tex]
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We just finished talking about parent function and transformations. What are the four different types of transformations? How many transformations are in the below function? What are the transformations?
f(x)=(x−3)2+5
AT LEAST 4 SENTENCES
Answer:
there are 4 different types of tranformations. these include translation, rotation, reflection, and dilation. in the function f(x)=(x−3)2+5 there are 3 transformations. these include a horizontal shift of 3 to the left, vertical shift of 5 up, and it is reflected over the x axis.
Step-by-step explanation:
Use Delta y = f'(x) Delta x to find a decimal approximation of the radical expression. 124 What is the value found using Delta y f' (x) Delta x? 124 = (Round to three decimal places as needed.)
Using Delta y = f'(x) Delta x to find a decimal approximation of the radical expression, we get the value found using Delta y f' (x) Delta x is 124.176.
The Delta y = f’(x) Delta x is the linear approximation formula used in calculus to estimate the value of an unknown function based on its derivative at a particular point.
In order to solve the problem using Delta y = f’(x) Delta x, we first have to rewrite the radical expression in terms of a function.
Let the function f(x) = sqrt(x) represent the radical expression.
Then, we will find the value of f'(x) by differentiating the function f(x) using the Power Rule of differentiation.
f(x) = sqrt(x) f'(x) = 1/2x^(-1/2)
Next, we will substitute the given value of x in the function f(x) and f’(x) to solve for Delta y = f'(x) Delta x.
Given, x = 124
Delta x = 2 Δy = f’(x) Δx = 1/2 * 124^(-1/2) * 2 = 0.1762
Hence, the decimal approximation of the radical expression is 124.176.
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The graph shows a function f(x). Determine the
following values.
f-1(4) =
of-(-5) =
f-1(0) =
Answer:
2
-4
0
Step-by-step explanation:
i just did it on edge
The value of inverse functions [tex]f^{-1}(4), f^{-1}(-5)[/tex], [tex]f^{-1}(0)[/tex] is 2, -4 and 0.
From the given graph, we need to determine the [tex]f^{-1}(4), f^{-1}(-5)[/tex], [tex]f^{-1}(0)[/tex] values.
What is a function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input [tex]x[/tex]. Mapping or transformation is used to denote a function in math.
From the graph the values of the given inverse function are as follows:
Now, [tex]f^{-1}(4)=2[/tex]
[tex]f^{-1}(-5)=-4[/tex]
[tex]f^{-1}(0)=0[/tex]
Therefore, the value of inverse functions [tex]f^{-1}(4), f^{-1}(-5)[/tex] [tex]f^{-1}(0)[/tex] is 2, -4 and 0.
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a logical argument that is presented in graphical form using boxes and arrows is called a ____.
a logical argument that is presented in graphical form using boxes and arrows is called a flowchart proof
hope it helps ^-^
What is the Value of the expression below when y=8 and z=4
4y+8z
Answer:
64
Step-by-step explanation:
Given
4y + 8z ← substitute y = 8 and z = 4 into the expression
= 4(8) + 8(4)
= 32 + 32
= 64
Answer:
64
Step-by-step explanation:
y=8 and z=4
4y+8z Substitute the values for the variables
4(8)+8(4) simplify:
32+32 add:
=64
Hope this helps :)
sells its products at trade discounts of 30%, 10%. A competitor has been offering products at the same list prices but with trade discounts of 25%, 20%. Island Reman wishes to beat the competitor's prices by offering a third trade discount. At least how big must the additional discount rate be to meet this objective?
Answer:
5%
Step-by-step explanation:
Given that:
Island Reman offers discounts at list price = 30%, 10%
Competitor offers discounts at the same list price = 25%, 20%
To find:
The minimum third discount to beat the competitor's price = ?
Solution:
First of all, let us find the actual price for each of them.
Let the list price be 100.
Applying the successive discounts of Island Reman:
1st discount: [tex]100 \times \dfrac{30}{100}=30[/tex]
Price after 1st discount = 70
2nd discount: [tex]70 \times \dfrac{10}{100}=7[/tex]
Price after 2nd discount = 70 - 7 = 63
Applying the successive discounts of competitor:
1st discount: [tex]100 \times \dfrac{25}{100}=25[/tex]
Price after 1st discount = 75
2nd discount: [tex]75 \times \dfrac{20}{100}=15[/tex]
Price after 2nd discount = 75 - 15 = 60
Difference between price = 63 - 60 = 3
3 is ~4.76% of 63.
Therefore, to beat the competitor's price, Island Reman should give at least 5% additional third discount.
Find the slope of the line through the points (6,16) and (−6,4)
[tex]m = \frac{y2-y1}{x2-x1}[/tex]
[tex]m = \frac{4-16}{-6-6} \\m = \frac{-12}{-12} \\\\m = 1[/tex]
Therefore, the slope of the line is 1. In case if you want to know the equation.
[tex]y=mx+b\\y=x+b\\4=-6+b\\4+6=b\\10=b\\[/tex]
Therefore, the equation is y=x+10 by substituting the (-6,4) or we can substitute (6,16) too.
[tex]y=mx+b\\y=x+b\\16=6+b\\16-6=b\\10=b\\[/tex]
It's the same, you can use any orders given.
Overall, the slope is 1 and the equation is y=x+10
Which of the demonstrates that (9/5)^-2 = 25/81
-4(-5-b)=1/3(b+16) math
The distance between two cities on a map is 4 inches. The scale on the map is 3 inches = 165 miles. A student incorrectly determines that
the distance between the two dties is 660 miles. Which sentence describes the student's mistake
Answer:
55
Step-by-step explanation:
165 / 3 = 55 therefore, one inch is equal to 55 miles. Hope this helps
please help ill give brainlist!!
4. Why are voting districts considered to be functional regions?
5. How did ancient populations encourage the movement of cultural beliefs and ideas?
6. Why would studying climate be important to a geographer?
7. As the Internet becomes more popular, how will this affect the spatial distribution of people on Earth in the future?
8. Pretend that you are one of the five themes of geography (location, place, region, human/environment interaction, or movement). Write a speech that explains why you are important to geography. Be specific in your explanation
4. Voting districts are considered to be functional regions because they serve a specific purpose or function in the context of political representation and governance.
5. Ancient populations encouraged the movement of cultural beliefs and ideas through various means, including trade, migration, conquest, and cultural diffusion.
6. It plays a crucial role in shaping the physical environment and influencing human activities within a geographic area.
7. Internet can lead to changes in patterns of migration, with individuals and businesses becoming less tied to specific locations.
8. The geographical theme that i represent is movement.
The theme of movementI am the key to a wealth of geographical knowledge because I am movement. We can understand the reasons for population changes, the mixing of cultures, and the emergence of various communities by looking at patterns of human migration.
The movement of goods and trade routes provide light on how economically interrelated different countries and areas are, giving us a window into the world's flows of commodities and resources.
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HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
The answer is B. x = 12
First, you must set up the equation.
[tex]4x+11=6x-13[/tex]
Then, you must subtract 6x on both sides.
[tex]-2x+11=-13[/tex]
Next, subtract 11 on both sides.
[tex]-2x=-24[/tex]
Finally, divide -2 on both sides.
[tex]x=12[/tex]
