Answer:
(2x + 1) - (–x² + 3x) is difference .
Step-by-step explanation:
Given : r(x) = –x² + 3x and s(x) = 2x + 1
To find : Find the difference of functions s and r .
Solution : We have given that r(x) = –x² + 3x and s(x) = 2x + 1.
Difference :
(s – r)(x) = s(x) - r(x)
=(2x + 1) - (–x² + 3x)
= 2x +1 + x²-3x
= x²-x +1.
Therefore, (2x + 1) - (–x² + 3x) is difference .
The difference of the function is (2x+1)-(x^2 + 3x)
Difference of functions
Given the following functions
r(x) = –x² + 3x
s(x) = 2x + 1
Taking the difference of the function will give:
(s – r)(x) = 2x - 1 - (-x^2 + 3x)
Expand
(s – r)(x) = 2x - 1 + x^2 - 3x
(s – r)(x) = x^2 - x - 1
Hence the difference of the function is (2x+1)-(x^2 + 3x)
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A square piece of cloth, which is 10 meters on a side, is cut across the diagonal to form two right triangles. What is the length of the diagonal cut?
Answer:
D
Step-by-step
The answer is the square root of 288
The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram
Answer:
Length is 20 meters and width is 16 meters.
Step-by-step explanation:
Given: Perimeter of parallelogram is 72 meters.
Width of the parallelogram is 4 meters less than its length.
To find: Length and width of the parallelogram.
Solution: Let the length of the parallelogram be x meters. So, width of the parallelogram is [tex]x-4[/tex] meters.
As per question,
[tex]x+x+x-4+x-4=72[/tex]
[tex]4x-8=72[/tex]
[tex]4x=72+8[/tex]
[tex]4x=80[/tex]
[tex]x=\frac{80}{4}[/tex]
[tex]x=20[/tex]
Hence, length of the parallelogram is 20 meters, and width of the parallelogram is [tex]20-4=16[/tex] meters.
How much would $400 invested at 9% interest compounded continuously be worth after 3 years? Rounded by the nearest cent
The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation.
Answer:
A
Step-by-step explanation:
Gabrielle's age is three times Mikhail's age. The sum of their ages is 32 . What is Mikhail's age?
g + m = 32
g = 3m
3m + m = 32
4m = 32
m = 32/4
m = 8 (Mikhail's age)
g = 3m
g = 3(8)
g = 24 (Gabrielle's age)
how can you discover a person's age by year?:To find out a person's age, all you need is that person's 12 months of beginning. After this, all you want to do now's subtract the beginning 12 months from the continuing modern year and you will have the age. this can help you to calculate the age from the date of delivery. Age= 2020- 1966 = 54.
How do you calculate age in mm dd yyyy?Your age in the total range of days is calculated as a variety of years, x, with twelve months = 365x plus. a number of years, y, with three hundred and sixty-six days = 366y plus. a number of days in the remaining partial yr.
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Amanda drove 355 miles using 17 gallons of gas. At this rate how many gallons of gas would she need to drive 284 miles?
Mario purchases a prepaid phone plan for $50. Each minute he uses costs $0.13. How many minutes can Mario talk on this plan? Write an inequality that represents this problem and solve the inequality
Final answer:
Mario can talk for up to 384 minutes on his $50 prepaid phone plan. We use the inequality 0.13m ≤ 50 and solve for m to find the maximum number of whole minutes Mario can use.
Explanation:
To solve this problem, we need to set up an inequality that represents the constraints of Mario's prepaid phone plan budget. The inequality will help us determine the maximum number of minutes Mario can talk on this plan.
Let's use m to represent the number of minutes Mario can talk. We know that each minute of talk time costs $0.13, and Mario's prepaid plan is $50. Our inequality should reflect the fact that the total cost of talking m minutes cannot exceed his budget of $50.
The inequality will look like this:
0.13m ≤ 50
To solve for m, we divide both sides of the inequality by 0.13:
m ≤ 50 / 0.13
When we calculate 50 divided by 0.13, we get approximately 384.6154. Since Mario cannot talk for a partial minute on his prepaid plan, we round this number down to the nearest whole minute, which is 384 minutes.
Therefore, Mario can talk for up to 384 minutes on his prepaid phone plan.
To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality: 0.13x <= 50. Solving this inequality, we find that Mario can talk for a maximum of 384 minutes.
Explanation:To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality based on the cost. Let x represent the number of minutes. The cost of the phone plan is $50, and each minute costs $0.13. So, the inequality is: 0.13x <= 50. To solve this inequality, we divide both sides by 0.13 to isolate x and find: x <= 50 / 0.13. Using long division or a calculator, we can find that x is approximately 384.61, but since we can't have a fraction of a minute, the maximum number of minutes Mario can talk on this plan is 384 minutes.
Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?
Is 5.78778778 a rational or irrational number? Explain
The number 5.78778778 is a rational number because it has a repeating decimal pattern that can be expressed as the fraction 573/99.
The number 5.78778778 is a rational number. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers.
In this case, the number 5.78778778 has a repeating decimal pattern, which is a hallmark of rational numbers.
We can convert this repeating decimal into a fraction by setting it equal to a variable, say x, subtracting a shifted version of x to isolate the repeating part, and then solving for x to find its fractional equivalent.
If we perform this process, we can turn 5.78778778... into a fraction. For example:
→ Let x = 5.78778778...
→ Multiply both sides of the equation by 100 to shift the decimal two places: 100x = 578.78778778...
→ Subtract the original x from this new equation: (100x - x) = (578.78778778... - 5.78778778...)
→ This simplifies to 99x = 573
→ Divide both sides by 99 to solve for x: x = 573/99
→ This fraction represents the decimal number 5.78778778..., confirming it is rational.
What is the vertex of the graph of the function below? y = x2 - 4x + 3
The vertex of the function y = x2 - 4x + 3 is at (2,-1). You can find this by using the formula -b/2a for the x-coordinate of the vertex and then substituting this x-value into the original equation to find the y-coordinate.
Explanation:The function you are asking about, y = x2 - 4x + 3, is a quadratic function, and the graph of a quadratic function is a parabola.
The vertex of this parabola can be found using the formula -b/2a for the x-coordinate and then substituting this value into the original equation to find the y-coordinate. For this function, the coefficients a and b (from the general form ax2 + bx + c) are 1 and -4 respectively. Using the formula, the x-coordinate of the vertex is -(-4)/2*1 = 2. We then substitute x = 2 into the original equation to find y = (2)2 - 4*(2) + 3 = -1. Thus, the vertex of the function y = x2 - 4x + 3 is at (2,-1).
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He sum of three consecutive integers is −369−369. find the three integers.
What is the domain of the inverse of a relation?
The length of a rectangle is 3 inches less than 4 times the width. If the perimeter is 55 inches, what is the width of the rectangle?
The width of the rectangle is 6.1 in.
What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.
Perimeter of the rectangle = 2(L + W) unit
WE have been given that length of a rectangle is 3 inches less than 4 times the width.
Length = 4x-3
width = x
If the perimeter is 55 inches, then
Perimeter of the rectangle = 2(L + W) unit
55= 2(4x-3 +x)
55 = 2(5x-3)
27.5 = 5x-3
27.5+3 = 5x
30.5/5 = x
6.1=x
Thus, Width is 6.1 in
The length (4 x 6.1 -3) = 21.4
Hence, the width of the rectangle is 6.1 in.
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4. One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?
x = the age of Heather
One half of Heather's age two years from now plus one-third of her age three years ago is twenty years
(x + 2)/2 + (x - 3)/3 = 20
by solving the equation we find
x = 24 years
Can the following question be considered a statistical question and why or why not? Do students at Bryan Middle School exercise?
Answer:
this is a multiple choice question with 4 answers
Yes, it specifies the population
No, it does not specify the population
Yes, it anticipates enough variability in responses
No, it does not anticipate enough variability in responses
I think the answer is.......... (Drum roll please)........... D.
Step-by-step explanation:
There is not any variability in this question it is just a yes or no question. If the question was "How long does an average person exercise for "
The function L = 0.8T2 models the relationship between L, the length in feet of a pendulum, and T, the period in seconds of the pendulum. Which value is closest to the period in seconds for a pendulum that is 30 ft long?
A) 5.4 s
B) 4.9 s
C) 6.8 s
D) 6.1 s
Please help A.S.A.P
Final answer:
Using the formula L = 0.8T², we find that a pendulum 30 ft long has a period of approximately 6.1 seconds, which corresponds to Option D.
Explanation:
The question is about finding the period, T, in seconds for a pendulum that is 30 ft long, using the formula L = 0.8T2. First, to solve for T given that L = 30, we rearrange the equation to T = √(L/0.8). Plugging in L = 30, we have T = √(30/0.8), which simplifies to T = √(37.5).
Calculating further, we find T ≈ 6.12 seconds. Therefore, the answer closest to the period in seconds for a pendulum that is 30 ft long is 6.1 seconds (Option D).
How do you solve -2(6x+3)=-27–5x ?
Show all work please!!!!!!
1. PB (there is a line on top) is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
2. The midpoint of CD (there is a line on top) is E(-1, 0). One endpoint is C(5,2). What are the coordinates of the other endpoint?
3. Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7, -7).
For a percentage increase of 36%, state the multiplier
3x - 24= -6 solve for x
Is the number x positive? (1) on the number line, 0 is closer to x – 1 than to x. (2) on the number line, 0 is closer to x than to x + 1?
I hope that helps!
For each handmade greeting card jacqui sells, she makes a profit of $0.35. In one week , she made a profit of $42 .she sells the cards for $0.75 each.
Part A: About how much did she earn before paying expenses?
Answer:
$ 90
Step-by-step explanation:
Given,
The profit in each card = $ 0.35,
If she sold x cards,
Then the total profit she earned = profit in each card × number of cards
= 0.35x dollars,
According to the question,
0.35x = 42
[tex]\implies x = \frac{42}{0.35}=120[/tex]
Thus, she sold 120 cards,
Now, if the selling price of each card = $ 0.75,
Hence, total earning before paying expenses
= selling price of each card × total cards
= 0.75 × 120 = $ 90
What is 8.63 repeating as a fraction?
Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). Pease show how!
Liam uses checks and a debit card, but does it not always right all the transactions and his checkbook register. He has lost track of his checkbook balance. Liam looks up the "available balance" using online banking, and write it on the next line as his new checkbook balance available to spend. What is wrong with Liam's method
Answer:
All of the above is the answer
Step-by-step explanation:
What's the answer to 3/2(16n+3)=24n
Plz help! Convert 6/9 into fractions with a denominater of 27 A. 6/7 B.21/27 C. 9/27 D.18/27
I need the answer Algebra question
Answer: $32
Step-by-step explanation:
add 7+9+12+4 =32
1. Find a counterexample.
If two angles are complementary, then they are not congruent.
Complementary angles are angles that add up to 90 degrees but may not have the same measure. A counterexample to the statement would be two angles that are complementary but not congruent.
Explanation:Complementary angles are angles that add up to 90 degrees. Congruent angles are angles that have the same measure.
A counterexample is a situation where the statement is false. In this case, a counterexample would be two angles that are complementary but not congruent.
For example, let's consider a 45-degree angle and a 45-degree angle. These angles are complementary because their sum is 90 degrees. However, they are not congruent because they have different measures.
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What is −20÷45 ?−25−16−116−125
Its -25 i just did the test