write a piece-wise function for the following graph. Hint: find linear equations for each "piece" of the function with its associated domain restriction.
Answers
Answer
At values of x less than -2, (x < -2)
y = 1
At velues of x between -2 and 0, (-2 ≤ x < 0)
y = -1.5x - 2
At values of x between 0 and 3, (0 ≤ x < 3)
y = -2
At values of x between 3 and 5, (3 ≤ x < 5)
y = x - 5
At values of x greater than 5, (x > 5)
y = 3x - 15
Explanation
To answer this, we will just break the domains into the x-value regions as obtainable from the graph. Starting from the left hand side
At values of x less than -2, (x < -2)
y = 1
At velues of x between -2 and 0, (-2 ≤ x < 0)
To write the equation of the line at this point, we need to note that
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For this question,
b = y-intercept = -2
We need to calculate the slope.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
\(Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}\)For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 1) and (0, -2)
\(\text{Slope = }\frac{-2-1}{0-(-2)}=\frac{-3}{0+2}=\frac{-3}{2}=-1.5\)So, for this region,
y = mx + b
y = -1.5x - 2
At values of x between 0 and 3, (0 ≤ x < 3)
y = -2
At values of x between 3 and 5, (3 ≤ x < 5)
We need to find the equation of the line at this point.
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
Point = (x₁, y₁) = (3, -2)
x₁ = 3
y₁ = -2
So, we need to solve for the slope
(x₁, y₁) and (x₂, y₂) are (3, -2) and (5, 0)
\(\text{Slope = }\frac{0-(-2)}{5-3}=\frac{0+2}{2}=\frac{2}{2}=1\)y - y₁ = m (x - x₁)
m = 1
x₁ = 3, y₁ = -2
y - y₁ = m (x - x₁)
y - (-2) = 1 (x - 3)
y + 2 = x - 3
y = x - 3 - 2
y = x - 5
At values of x greater than 5, (x > 5)
For these parts, we just do it similarly to the region before this
Point = (x₁, y₁) = (5, 0)
x₁ = 5
y₁ = 0
(x₁, y₁) and (x₂, y₂) are (5, 0) and (6, 3)
\(\text{Slope = }\frac{3-0}{6-5}=\frac{3}{1}=3\)y - y₁ = m (x - x₁)
m = 3
x₁ = 5, y₁ = 0
y - y₁ = m (x - x₁)
y - 0 = 3 (x - 5)
y = 3x - 15
Hope this Helps!!!
Related Questions
help. use the figure shown to the right to find the value of x
Answers
Answer:
\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)
Step-by-step explanation:
We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:
\(a^2 + b^2 = c^2\)
↓ plugging in the given values
\(a^2 + 2^2 = 14^2\)
↓ subtracting 2² from both sides
\(a^2 = 14^2 - 2^2\)
\(a^2 = 196 - 4\)
\(a^2 = 192\)
↓ taking the square root of both sides
\(a = \sqrt{192\)
↓ simplifying the square root
\(a = \sqrt{2^6 \cdot 3\)
\(a = 2^{\, 6 / 2} \cdot \sqrt3\)
\(a = 2^3\sqrt3\)
\(a = 8\sqrt3\)
Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.
\(a = \dfrac{1}{2}x\)
↓ plugging in the a-value we solved for
\(8\sqrt3 = \dfrac{1}2x\)
↓ multiplying both sides by 2
\(\boxed{x = 16\sqrt3}\)
4x – 2y = 10
у=-2x-1
Answers
Answer:
I love algebra
The ans is in the picture
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x - 2(-2x - 1) = 10
4x + 4x + 2 = 10
8x + 2 = 10
8x = 8
x= 1
y = -2(1) - 1
y = -2 - 1
y = -3
(1, -3)
Starting salaries of 130 college graduates who have taken a statistics course have a mean of $44,783. The population standard deviation is known to be $10,272. Using 99% confidence, find both of the following:
A.The margin of error:
B. Confidence interval:
Answers
A. The margin of error for a 99% confidence interval is $$2,320.75.
B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75
How to find both of the margin of error and confidence interval?PART A.
The margin of error (ME) is determined using the formula:
ME= z ∗ σ/√n
where:
z is the z-score for the desired confidence level
σ is the population standard deviation
n is the sample size
For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.
Substituting these values into the formula, we have:
ME = 2.576 ∗ 10272/√130
ME = $2,320.75
PART B
The confidence interval (CI) is determined using the formula:
CI = \(\bar{x}\) ± ME
where:
\(\bar{x}\) is the sample mean
ME is the margin of error
The sample mean is $44,783, and the margin of error is $2,320.75.
Substituting the values into the formula, we get:
CI= 44783 ± 2320.75
CI = $42,462.25 to $47,103.75
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Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)
\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)
Please answer this I will give brainliest
Answers
lol i donyt k n o w thts just dum
Compare using <, >, or =. 72 ___ 26
Answers
Answer:
72 > 26
Step-by-step explanation:
72 is bigger than 26
Which expression is equivalent to (3x² + 4x-7)(x-2)?
OA. (3x2 + 4x-7)(x) + (3x² + 4x-7)(-2)
OB. 2x(3x² + 4x-7)
OC. x(3x² + 4x-7) - 2
OD. x(3x² + 4x-7)+2(3x² + 4x-7)
Answers
Answer: A
Step-by-step explanation:
The expressions are equivalent by the distributive property.
PLS HELP FAST
rotations on the coordinate plane
........
why does nobody talk to circles?
Answers
Step-by-step explanation:
Becuase all circles are similar.
Noboday talks about the circle due to all circle are similar.
We have find the rotation of coordinate plane also we have talk about the coordinate plane in circle.
What is the rotations on the coordinate plane?
Rotations coordinate plane may be clockwise or counterclockwise.
When we are working in the coordinate plane assume the center of rotation to be the origin unless told otherwise.
Nobody talk to circles because there is no point, all circle are similar.
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2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
Answers
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
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I've tried everything I could think of someone help
Answers
Answer:
2.5
Step-by-step explanation:
\( \frac{7.5}{3} = 2.5\)
2.5 + 2.5 + 2.5 = 7.5
Answer:
2.5
Step-by-step explanation:
Multiplying is a shorter form of adding. For example 3*5 = 5+5+5 = 3+3+3+3+3 = 15.
We have three spaces. This means that we have to divide by three in order to get the result.
7.5/3=2.5
what is Twenty-nine million, one hundred three thousand, and nine tenths in numbers
Answers
Answer:
29,103,000.9
Step-by-step explanation:
Answer:
20,103.9
:))))))))))))))))))
what number represents the same amount as 2 hundreds + 12 tens + 6 ones ?
Answers
Answer:
326
Step-by-step explanation:
The value of the given expression is 326.
Given:
The given expression 2 hundreds + 12 tens + 6 ones.
To find:
The value of the given expression.
Explanation:
The numeric form of given expression is:
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
Therefore, the value of the given expression is 326.
QUICK HELP PLS!! Tell all steps :) 100 POINTS!!
The two triangles above are similar.
Find x using the ratio of the sides 12 cm and 16 cm:
x
20
=
12
16
. Show your work.
Find x using the ratio of the sides 6 cm and 8 cm. Show your work.
Explain why the answers to (a) and (b) should be the same.
Answers
a. Using the ratio of the sides 12 cm and 16 cm
x/20 = 12/16
x = (12(20)) / 16 = 15
b. Using the ratio of the sides 6 cm and 8 cm
x/20 = 6/8
x = (6(20)) / 8 = 15
c. The answer is the same since the ratio 12/16 and 6/8 is both equal to ¾.
Hope this answer will be a good help for you.
What is the value of |-25|?
Answers
Answer:
25
Step-by-step explanation:
|-25| means the absolute value of -25
The absolute value means how far a number is away from zero without consideration of whether or not the number is positive or negative, so the answer would be 25.
Evie's beginning balance in her checkbook was $623.65. She made depositsof $225, wrote checks for $168.75, and had to pay a bank charge of$3.50. What was her ending balance for the month?a. $550.25b. $887.75c. $880.75d. $676.40
Answers
You know that her beginning balance was $623.65. Then, if she deposited $225, that money must be added to the beginning balance. After that deposit, she had:
\(623.65+225=848.65\)After that, she wrote checks for $168.75 and she also paid $3.50 for the bank charge. Therefore, you need to subtract these amounts of money from the sum found before, in order to calculate Evie's ending balance (in dollars) for the month.
Then, you get that this is:
\(\begin{gathered} EndingBalance=848.65-168.75-3.50 \\ EndingBalance=676.40 \end{gathered}\)The answer is: Option d.
Determine the validity of the converse and give a counterexample if the converse is not valid.
If it is sunny, then it is 80° Fahrenheit. The converse is valid.
If it is 80° Fahrenheit, then it is sunny. The converse is valid.
If it is not sunny, then it is not 80° Fahrenheit. The converse is invalid; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is invalid; a counterexample is a day that is 80° and cloudy.
Answers
Your analysis is correct. Here's a summary:
If it is sunny, then it is 80° Fahrenheit. (Original statement)
Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)
If it is not sunny, then it is not 80° Fahrenheit. (Original statement)
Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)
Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)
Counterexample: A day that is 80° Fahrenheit and cloudy.
In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").
Find the measure of
Answers
Answer:
y = 15, so m∡B = 56°
m∡A = 60°
m∡BCA = 180-116, or 64°
Step-by-step explanation:
Out of 1,400 students, 60% have a dog. How many students have a dog?
Answers
Answer:
840
Step-by-step explanation:
Answer:
840 students have a dog
Step-by-step explanation:
0.60 * 1400=
840 have a dog
extra answer: 560 do not have a dog
Bobby is having a summer barbecue. He is inviting 7 of his friends. He wants to have enough food for everyone to have two hot dogs. How many hot dogs will bobby need to cook for himself and his friends?
Answers
Answer:
16
Step-by-step explanation:
7 friends = 14 hotdogs + bobby (2 hotdogs) = 16 hotdogs
Answer:
16 hot dogs
Step-by-step explanation:
since he has 7 friends + himself, we're going to have a total of 8 persons
and since it's expected for each person to have two hot dogs,
total hotdogs Bobby need to cook= 8×2= 16 hot dogs
If $12,000 is invested at 7% for 9 years, find the future value if the interest is compounded daily.
Answers
The future value is 6,495,554.308.
What has compounded annually?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.
Compound interest can be calculated in math in a variety of ways depending on the circumstances. To make the calculations simpler, we can use the compound interest formula. We need to know the amount and the principal in order to calculate compound interest. The distinction is between the amount and the principal.
Given that $12,000 is invested in a project at 7% for 9 years.
The formula of compound interest is
A = P(1+r/n)^nt
A = amount
P = principal
r = rate of interest
t = time
n = number of compound interest per annum
For the given problem:
P =12,000, r = 7%, t = 9, n = 365:
The amount after 9 years will be:
A = 12,000(1+0.07/365)^(365×9)
A = 6,495,554.308
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MATH
Systems of Linear Equations
1. Determine if each system of equations below is linear or nonlinear.
A. -9x+8y = 9x 7y+8=8x
Linear or nonlinear?
D. 6y+x=12 y-x=1-x
B.
2.3y+1.2x = 0
1.1x+0.1y 1.2
C.
2 7-3y=- 2x+9= 3y
Linear or nonlinear?
Linear or nonlinear?
E. 45x + y = 12 y+x² = 1-x²
Linear or nonlinear?
G
0.2x+9.1y9.1√x
7x+1=8√y
Linear or nonlinear?
F. x+8y = 81 x-7y = 32
Linear or nonlinear?
H.
98317y= 1010 + 2965x
-71389y=5692x - 1001
3 xx y-5= 1 zy+3x=-21
Linear or nonlinear?
Linear or nonlinear?
Linear or nonlinear?
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
Answers
The system of equations -9x+8y = 9x and 7y+8=8x is linear.
A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.
In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).
Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).
Therefore, the system of equations is linear.
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Plsss help me
what is 1 1/2 divided by 2/5? Show your work.
Answers
Answer:
3.75 or 3 3/4
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
1.5/.4=3.75
Answer:
\(3 \frac{3}{4}\)
Step-by-step explanation:
\(1 \frac{1}{2} / \frac{2}{5} = \frac{3}{2} / \frac{2}{5}\)
\(\frac{3}{2}\) × \(\frac{5}{2}\)
\(\frac{3 times 5 }{2 times 2}\)
\(\frac{15}{4} = 3 \frac{3}{4}\)
I don't need help but I am giving the answer to everyone :) hope it helps
Answers
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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hi I'm looking for the answers for my work I already did this agistment but failed it and need help getting my grade up
Answers
Answer:
amswer
Step-by-step explanation:
ALGEBRA please put a very small explanation to the awnser
Answers
Certainly! The problem can be solved using the Pythagorean theorem,
which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.
The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.
By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.
Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.
We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.
Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.
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Vivek graphs the equations and to solve the equation His graph is shown below.
What are the solutions of
–4 and 2
–4 and 1
0 and 4
1 and 4
Answers
The solutions of the equation of the graph is -4 and 2.
What is solution of equation?An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.
We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.
In the given graph the point of intersection of the two equations are at x = -4 and x = 2.
Hence, the solutions of the equation of the graph is -4 and 2.
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The complete question is:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
Find the missing side. 31° Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21
![Find the missing side. 31 Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9Wo53l4VJj28ga8aoyl87alnvnYAbri4.jpeg)
Answers
A²+B²= C²
31²+ 21²= z²
961+441 = z²
1402= z²
z= 37.443290454
For the function f(x) = 2 - 3x, find f(-4).
-10
-5
12
14
Answers
Answer: 12
Step-by-step explanation: f(-4)= 2-3(-4) which =2+12=14
5) What is the solution to this equation?
x+ 20 + 10x=20+ 9x
A. x= 10
B.x=0
C. X = 20
D. x=2
Answers
Answer:
x=0
Step-by-step explanation:
11x-9x=20-20
2x=0
x=0