Given the piecewise functions shown below, select all of the statements that are true.
Answers
The true statements are:
a. f(-1) = 2
c. f(1) = 0
Let's evaluate each statement using the given piecewise function f(x):
a. f(-1) = -(-1) + 1 = 2
b. f(-2) = -(-2) + 1 = 3 (Not 0, so this statement is false)
c. f(1) = (1)^2 - 1 = 0
d. f(4) = (4)^2 - 1 = 16 - 1 = 15 (Not 7, so this statement is false)
Therefore, the correct statements are:
a. f(-1) = 2
c. f(1) = 0
Statement a is true because when x = -1, we use the first piece of the piecewise function, which gives us -(-1) + 1 = 2.
Statement c is true because when x = 1, we use the third piece of the piecewise function, which gives us (1)^2 - 1 = 0.
Statements b and d are false because they do not match the corresponding values obtained from evaluating the piecewise function at the given inputs.
Therefore, the true statements are:
a. f(-1) = 2
c. f(1) = 0
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Related Questions
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
Answers
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
What do you mean by compound?A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.
Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.
We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:
3 ml x 3 ml x 3 ml
-------- = ----------
728 ml total, 8 ml overall
If we cross-multiply, we obtain:
8(x) = 3(728)
To find x, we use the formula x = 3(728)/8 = 273
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
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273 milliliters of compound A are needed to make 728 milliliters of the drug.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.
Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:
3 : (3+5) or 3:8
This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.
To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:
3/8 = x/728
where x represents the amount of compound A needed.
To solve for x, we can cross-multiply:
8x = 3*728
8x = 2184
x = 273
Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.
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All of the following represent three multiplied by six except:3 × 63 · 63(6)3:6
Answers
Any of the representations below mean 'three multiplied by six'
\(\begin{gathered} 3\times6 \\ 3\cdot6 \\ 3*6 \\ (3)6 \\ 3(6) \end{gathered}\)However, in general,
\(a:b=\frac{a}{b}\)Therefore, the answer is 3:6.A runner can run 5 miles in 26 minutes at this rate how many miles can he run and 41.6 minutes?
Answers
Answer:
8 miles
Step-by-step explanation:
Given: A runner can run 5 miles in 26 minutes, 41.6 minutes = ___
To find: At this rate, how many miles can he run and 41.6 minutes?
Solution: If the runner ran 5 miles in 26 minutes, to find how far he ran in 41.6 minutes, set up a fraction:
let x be the variable
\(\frac{26}{5} = \frac{41.6}{x}\)
Apply fraction cross multiply;
\(26x=5\cdot \:41.6\)
\(26x = 208\)
Divide both sides by 26
\(\frac{26x}{26}=\frac{208}{26}\)
Simplify
\(x = 8\)
Then, at the rate, the runner ran 8 miles 41.6 minutes
41.6 min / 5 miles = 8.32 miles
round off = 8 miles
The runner will run 8 miles total and 41.6 minutes
A weather forecaster predicts that the May rainfall in a local area will be between 2 and 8 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval 2 to 8 inches.
(a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.) μx
(b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean?
Within one standard deviation of the mean? (Round all intermediate and final answers to 4 decimal places.)
Probability of May rainfall will fall within two SD Probability of May rainfall will fall within one SD
Answers
a) The expected May rainfall is 5.0 inches.
b) The probability of May rainfall falling within one standard deviation of the mean is 0.6827, and within two standard deviations is 0.9545.
(a) To calculate the expected May rainfall, we need to find the mean (μx) of the uniform distribution. The mean of a uniform distribution can be found using the formula:
μx = (a + b) / 2
where a and b are the lower and upper limits of the distribution, respectively. In this case, a = 2 and b = 8. So,
μx = (2 + 8) / 2
μx = 10 / 2
μx = 5
(b) To find the probability that the observed May rainfall will fall within one and two standard deviations of the mean, we first need to calculate the standard deviation (σx) of the uniform distribution. The formula for the standard deviation of a uniform distribution is:
\(σx = √((b - a)^2 / 12)\)
Using the values of a and b from before, we have:
\(σx = √((8 - 2)^2 / 12)\)
σx = √(36 / 12)
σx = √3
For a uniform distribution, the probabilities of falling within one and two standard deviations of the mean are as follows:
- Within one standard deviation (±1σx): 68.27% or 0.6827
- Within two standard deviations (±2σx): 95.45% or 0.9545
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Mike spent $7.20 on 20 erasers.
How much did each eraser cost?
Enter your answer in the box.
Answers
Answer:
0.36/36cent
Step-by-step explanation:
7.20/20=0.36
Answer:
27,0 /20
Step-by-step explanation:
what is the value of -2/3x0.6÷ 6/5
Answers
Answer:
-0.33333333333 in other word it o.3 with line over 3
Step-by-step explanation:
Find the perimeter for a rectangle that has an area of 2x^2+6x-8 and length of 2x-2. (Hint: First find the length)
Answers
Enter the number that belongs in the green box
Answers
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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Find the exact value of the given expression.
cos(2tan^-1(24/7))
Answers
Find the length of x??
Answers
Answer:
8 meters.
Step-by-step explanation:
the formula for the hypotenuse of a right triangle is: \(a^2 + b^2 = c^2\). Where C= hypotenuse and a and b = other sides. We can sub in a and c to get \(6^2 + x^2 = 10^2\\\). Simplify to \(36+x^2=100\). Subtract 36 from both sides to get x^2 = 64. \(\sqrt{64} =8\)
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answers
b. 10^27
c. 10^18
d. 10^6
e. 10^6
f. 10^35
multiply the exponents.
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
Looking for right triangle side a is 1 inch long,and side b is 2 inches long. What is the length of side c?
Answers
Answer:
\(\sqrt{5}\)
Step-by-step explanation:
\(a^{2} + b^{2} = c^{2}\)
In this situation a = 1, b = 2
\(1^{2} + 2^{2} = c^{2}\)
1 + 4 = \(c^{2}\)
5 = \(c^{2}\)
c = \(\sqrt{5}\)
This is an important mathematical theorem to know. It's called the Pythagorean Theorem.
What is the solution of the equation x2 + 8x = 4?
Answers
Answer:
hope this is correct
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 8 feet. The portion from a point to a vertical line created by two vertices is 4 feet. Which of the following represents the total area of the figure? 44 ft2 400 ft2 440 ft2
Answers
The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.
What do you mean by trapezoid?The five-sided figure is a trapezoid with two parallel sides, so we can use the formula for the area of a trapezoid to find the total area.
Area of a trapezoid = (sum of the lengths of the two parallel sides) / 2 * height
Let's call the length of the longer parallel side "L". Then the height of the figure is 22 feet, and the length of the shorter parallel side is 16 feet.
Area = (L + 16) / 2 * 22
We also know that the portion from the vertex to the perpendicular height is 8 feet, and the portion from a point to a vertical line created by two vertices is 4 feet. These two lengths form a right triangle, so we can use the Pythagorean theorem to find the length of the longer parallel side, L.
L² = (8 + 4)² = 64
L = 8
Now we can use the formula for the area of a trapezoid to find the total area.
Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528
The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.
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PLEASE HELP!!!!!!
The box plot displays the number of flowers planted in a town last summer.
10
Flowers Planted In Town
13 14 15 16 17 18 19 20 21 22 23 24
Number of Flowers
Which of the following is the best measure of center for the data shown, and what is that value?
O The mean is the best measure of center and equals 12.
O The mean is the best measure of center and equals 10.
The median is the best measure of center and equals 12.
30 31
The median is the best measure of center and equals 10.
Answers
The best measure of center for the data shown is the median, and its value is 17.
The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:
10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
Since the data set has an odd number of values, the median is the middle value, which in this case is 17.
Therefore, the best measure of center for the data shown is the median, and its value is 17.
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Problem’s in the image
Answers
The value of a ₁ given the value of S₆, can be found to be 400 .
How to find the value ?This is a geometric sequence and the formula is:
Sₙ = a₁ x (1 - r ⁿ ) / ( 1 - r )
The details given are:
S₆ = 953. 344 , r = 3 / 5, and n = 6.
The value of a ₁ is therefore :
= 953. 344 x ( 1 - 3 / 5) / ( 1 - ( 3 / 5 ) ⁶)
= 953. 344 x 0. 40 / 0. 953344
= 953. 344 x 0. 4195757
= 400
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Find the value of 3a when a = -4.
(b)- 7
(d) -12
(a) 7
(c) 12
Answers
Answer:
(d) -12
Step-by-step explanation:
3a = _____
a = -4
3(-4) = ___
3(-4) = -12
The answer is (d) -12
If there’s 100 apples and you take 30 apples, how many apples are left?
Answers
Answer:
70 apples.
Step-by-step explanation:
The number of apples which left after taking the 30 apples from 100 apples by a person is 70 apples.
What is subtraction?Subtraction is the resultant number, which is obtained by taking the difference of a number from the another number.
Let a number is removed from the number b. Then the resultant number after subtracting b from a will be,
\(d= b-a\)
Here, (a, b) are the real numbers.
It is given that there are 100 apples. In which 30 apples are taken. Let suppose after taking the 30 apples, there are x apples remain.
As there are total 100 apples and 30 apples are taken, then to find the number of apples left, we need to subtract the 30 apples from 100 apples.
Thus, the total apples left are,
\(x=100-30\\x=70\)
Hence, the number of apples which left after taking the 30 apples from 100 apples by a person is 70 apples.
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A 12 oz box of sugar costs $3.10 and a 36 oz box of sugar costs $7.90. Which box of sugar is the better buy?
Answers
Answer: 36 oz box
Step-by-step explanation:
3.1/12=0.258333
7.9/360.291444
Thus, the 36 oz box is the better buy
Chinedu missed his school bus by 2 munutes, so he walked to school which took him 27 minutes, arriving 6 minutes late for class at 8.11am At what time should he have caught the bus?
Answers
Answer:
Step-by-step explanation:
So we know he arrived at 8:11 am. He should've arrived at 8:05 am if he rode the bus. So, we know that it took 27 minutes for him to get to school by walking. If he arrived at 8:11, then he started walking at 7:44 am. Since the school bus arrived 2 minutes before he started walking, we can say that the school bus arrived at 7:42 am.
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math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
Answers
Answer:
Here's an interesting project idea for mathematics that can relate three different topics:
Topic 1: Fractals
Topic 2: Chaos Theory
Topic 3: Differential Equations
Research Question: Can fractals be used to model chaotic systems described by differential equations?
In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.
Your research paper can cover the following areas:
Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.
Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.
Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.
Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.
Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.
Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.
Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.
Step-by-step explanation:
The mass of carbon is 1.995 x 10^-23 grams per atom and the mass of hydrogen is
1.674 X 10^-24 grams per atom. Which is larger?
Answers
Answer:
Carbon
Step-by-step explanation:
When the power of 10 is negative, the less the exponent the bigger the number
Answer:
Step-by-step explanation:
the larger number is 1.995x10^-23
Can someone help me with this please
What is the right answer for it?
Answers
120=10x(10+AB)
12-2=AB
Solve the equation. Show all your steps in solving for x:
3x – 32 = -7x + 28
Answers
Answer: x = 6
Step-by-step explanation:
Step 1: Add 7x to both sides
3x −32 + 7x = −7x + 28 + 7x
10x − 32 = 28
Step 2: Add 32 to both sides
10x −32 +32 = 28 + 32
10x = 60
Step 3: Divide both sides by 10
10x/10 = 60/10
= 6
can someone plz help?
solve for x in the triangle below given that AB =4cm ,BC=3cm and AC =x
Answers
4^2+3^2=x^2
16+9=x^2
x=5
AC=5
Answer:
5
Step-by-step explanation:
a²+b²=c²
4²+3²=c²
25=c²
c=√25
c=5
what is the smallest positive integer such that the value of f(x)_ -x^2 +5x exceeds the value of g(x)= -10x+10.
Answers
The result is that x = 8 is the smallest positive number such that f(x) surpasses g(x).
What in arithmetic is an integer?An integer is a whole number that may be positive, minus, or zero and is not a percentage. Integer examples include: -5, 1, 5, 8, 97, as well as 3,043. The following figures are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
To find the smallest positive integer x for which f(x) exceeds g(x)
we need to set the two functions equal to each other and solve for x:
f(x) = g(x)
-x² + 5x = -10x + 10
Simplifying the equation, we get:
x² + 15x - 10 = 0
Using the quadratic formula, we can solve for x:
x = (-15 ± sqrt(15² - 4(1)(-10))) / (2(1))
x = (-15 ± sqrt(265)) / 2
The two possible solutions are approximately -0.372 and -14.628. Since we are looking for the smallest positive integer solution, we take the ceiling of the positive solution to get x = 8.
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Surface area pls help
Answers
The surface area of the triangular pyramid is 147.6 cm².
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
To calculate the surface area of the triangular pyramid, we use the formula below
Formula:
S.A = (3bL/2)+(bh/2)...................... Equation 1Where:
S.A = Surface area of the Pyramidb = Length of the triangleL = Slant height of the pyramidh = Height of the triagular baseFrom the question,
Given:
b = 8 cmh = 6.9 cmL = 10 cmSubstitute these values into equation 1
S.A = (3×8×10/2)+(8×6.9/2)S.A = 120+27.6S.A = 147.6 cm²Learn more about surface area here: https://brainly.com/question/76387
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3f–4g=1
6f–6g=5
use the elimination method
Answers
6f-6g= 5 —(2)
(1)x2:6f-8g= 2 —(1a)
(1a)-(2):(6f-8g)-(6f-6g)= 2-5
6f-8g-6f+6g= -3
-2g= -3
g= 3/2
Substitute g= 3/2 into (1):
3f-4(3/2)=1
3f-6=1
3f=7
f =7/3
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
Simplify the expression (4/3)(3/7)
Answers
The simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The expression is:
= (4/3)(3/7)
= (4x3)/(3x7)
Cancel 3 from the numerator and denominator
= 4/7
Thus, the simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
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