Answer:
-11.1 and up
Step-by-step explanation:
Verbal
5. How do you graph a piecewise function?
To graph a piecewise function, plot the different parts of the function separately based on the specified conditions or intervals, and ensure continuity at the endpoints.
Here's a step-by-step guide on how to graph a piecewise function:
1. Identify the different conditions or intervals: A piecewise function is defined by different equations or expressions for specific intervals or conditions. Identify these conditions or intervals and the corresponding equations for each interval.
2. Plot the intervals on the x-axis: Identify the range of values for the x-axis based on the given intervals. Mark the intervals on the x-axis accordingly.
3. Graph each part of the function: For each interval, graph the corresponding equation or expression. Treat each part as a separate function within its defined interval.
4. Consider the endpoints of each interval: Pay attention to the endpoints of each interval and determine whether they are included or excluded from the graph. Use open or closed circles to represent the endpoints, depending on whether they are included or excluded.
5. Ensure continuity: Check if the function is continuous across the intervals. Make sure there are no gaps or jumps in the graph where the intervals meet.
6. Label the axes and add any necessary annotations: Label the x-axis and y-axis, and add any necessary annotations such as the function name, equation, or any important points or features.
7. Review and refine: Step back and review the graph to ensure accuracy and clarity. Make any necessary adjustments to the graph to improve its presentation.
Learn more about function here:
https://brainly.com/question/30721594
#SPJ11
At 98°F, a certain insect chirps at a rate of 88 times per minute, and at 107°F, they chirp 151 times per minute. Write an equation in slope-intercept form that represents the situation.
The equation in slope-intercept form that represents the situation is y = 7x - 598
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
The ordered pair are ( 98, 88) and (107, 151)
Equation of line in slope-intercept form is y = mx + c
at x = 98, y =88
so that by substituting we have,
88 = 98m + c -------------------1
at x = 107, y = 151 and by substituting we have
151 = 107m + c -----------------2
subtract equation 1 from 2
63 = 9m
m = 63/9
m = 7
substitute m = 7 in equation 1
88 = 98(7) + c
c = 88 - 686c
c = -598
substitute m and c for their values equation becomes
y = 7x - 598
In conclusion, the equation in slope-intercept form is y = 7x - 598
Learn more about slope: https://brainly.com/question/3493733
#SPJ1
James's Sister is arranging rows of beads. She has 56 yellow beads and 120 blue beads. She wants to arrange them so that all the beads in a row are, are the same color, and so that each row has the same number of beads. What is the least number of rows James's sister can make?
Answer:
22
Step-by-step explanation:
gcf 56, 120 = 8, 56/8=7, 120/8=15, 7+15=22. 22
The larger triangle is a dilation of the smaller triangle with a center of dilation at (1,−1)
What is the scale factor of the dilation? No Links and brainlest
18
14
4
8
Answer:
Scale factor = 4
Step-by-step explanation:
Scale factor = \(\frac{\text{Dimension of the larger (Image) triangle}}{\text{Dimension of the smaller (Preimage) triangle}}\)
From the given triangle,
Length of one side of the larger triangle = 8 units
Length of the corresponding side of the smaller triangle = 2 units
By substituting the values in the formula of scale factor,
Scale factor = \(\frac{8}{2}\)
Scale factor = 4
Hello! I need a little bit of help with this question please. (As of now this is not from an active test, this is a question from a book I am studying in order to take my Army ASVAB later.)
Solution:
Given a triangle;
Where
\(\begin{gathered} RS=RT \\ m\operatorname{\angle}RTS=m\operatorname{\angle}RST\operatorname{\lparen}\text{base angle of an }\imaginaryI\text{sosceles tr}\imaginaryI\text{angle}\operatorname{\rparen} \end{gathered}\)To find the measure of angle S, i.e.
\(\begin{gathered} m\angle RST \\ m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT \end{gathered}\)Where
\(\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST\text{ be represented by x} \\ m\angle SRT=70\degree \end{gathered}\)Then,
\(\begin{gathered} m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT=180\degree\text{ \lparen Sum of angles in a triangle\rparen} \\ x+x+70\degree=180\degree \\ Collect\text{ like terms} \\ 2x=180\degree-70\degree \\ 2x=110\degree \\ x=\frac{110\degree}{2} \\ x=55\degree \end{gathered}\)Recall that;
\(\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST=x=55\degree \\ And; \\ Measure\text{ of angle S}=m\angle RST=55\degree \end{gathered}\)Hence, the measure of angle S is 55°
please answer this for me
Graph the sine function on the interval [0, 2pi] . The lowest point on the graph occurs at (____,-1 ).
The lowest point on the graph occurs at point (3π/2, -1)
What is sine function graph?One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.
The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation
The attached graph shows sine function graph plotted with the interval [0, 2pi]
The lowest point is observed to occur at (3π/2, -1)
Learn more about sine function at:
https://brainly.com/question/21902442
#SPJ1
Given that
R
=
9
x
+
8
y
Find
x
when
y
=
3
and
R
=
5
Give your answer as an improper fraction in its simplest form.
Answer:
X = 19/9
Step-by-step explanation:
R = 9x + 8y
R = 5, Y = 3
5 = 9x + 8(3)
9x = 8(3) - 5
9x = 19
x = 19/9
14° plus what equals 90°
How do you solve problems involving sequence? Discuss the mathematics concepts and principles applied when solving problems involving sequence
Step-by-step explanation:
Sequence is defined as arrangement f numbers in a specific or defined pattern. Sequence are categorized into
1) Arithmetic
2) Geometric
Arithmetic sequence are characterized by their common difference while Geometric sequence are characterized by their common ratio.
Given a sequance of numbers say;
T1, T2, T3...
The first term "a" of the sequence is T1
Common difference d = T2-T1 =T3-T2
Common ratio = T2/T1 = T3/T2
The formula for calculating nth term of an Arithmetic sequence is expressed as;
Tn = a+(n-1)d
a is the first term
n is the number of terms
d is the common difference
The nth term of a Geometric sequence is expressed as;
Tn = ar^{n-1}
r is the common ratio
Numbers are arranged in a sequence when they follow a predetermined or established pattern. Sequences can be divided into
1) Mathematics
2) Graphitic
Geometric sequences are characterized by their common ratio, whereas arithmetic sequences are distinguished by their common difference.
Suppose a sequence of numbers is given;
T1, T2, T3...
The sequence's initial term "a" is T1.
common distinction d = T2-T1 =T3-T2
T2/T1 Common Ratio T3/T2
The following is the formula for finding the nth term in an arithmetic sequence:
Tn = a+(n-1)d
The first term is a.
The number of terms is n.
d is the typical discrepancy
The nth term of a Geometric sequence is expressed as;
\(T_{n} =ar^{n-1}\)
r is the common ratio
To learn more about information Sequence :
brainly.com/question/28015562
1) Clare wants to take group fitness classes at a nearby gym, but needs to start by
selecting a membership plan. With the first membership plan, Clare can pay $70 per month,
plus $3 for each group class she attends. Alternately, she can get the second membership
plan and pay $40 per month plus $6 per class. If Clare attends a certain number of classes in
a month, the two membership plans end up costing the same total amount. How many
classes per month is that?
) Write a system of equations, graph them, and type the solution.
Using linear functions, she pays the same for 10 classes, which is represented by the graph at the end of the question.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we consider the flat fee as the intercept and the cost per group class as the slope, hence the functions are given by:
A(x) = 70 + 3x.B(x) = 40 + 6x.She pays the same when:
A(x) = B(x).
70 + 3x = 40 + 6x
3x = 30
x = 10.
Hence when there are 10 classes.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Is -12 = -12 a true or false statement?
Answer: yes it is a true statement
Step-by-step explanation:
-12 is the same as -12
Answer:
True
Step-by-step explanation:
-12 does in fact equal -12, therefore it is a true statement.
What have I divided 220 by to get to 1
Answer:
220 divided by it self (220) will get you 1
Step-by-step explanation:
220/220=1
Answer:
220
Step-by-step explanation:
12 people fit comfortably in a 5 x 5 foot square.use this value to estimate of a crowd that is 10 feet deep on both sides of the street along a 1 mil section of a parade route
Answer:
48 people
Step-by-step explanation:
It states that 12 people fit into a 5 x 5 ft² area.
Here, we are given the length and breath of the side, both 5 ft. And from that, we can estimate the area of the place.
Area of a square is gotten by multiplying both sides together, and thus
5 * 5 = 25 ft²
We are told 12 people fit into 25 ft². In order to get the number of people that fit a 10 x 10, we first need to calculate the area.
We already have the length and breadth to be 10 ft each, so
Area = 10 * 10 = 100 ft²
Now, we calculate.
If
12 people fit into 25 ft²
x people will fit into 100 ft²
If we cross multiply, we have
1200 = 25x
We then divide both sides by 25
x = 1200 / 25
x = 48
Therefore, 48 people will fit into a 10 x 10 ft area
Triangle D E F is shown. Angle D E F is 140 degrees. The length of D E is 11, the length of E F is 9, and the length of D F is e.
In ΔDEF, DE = 11, EF = 9, and angle E = 140°.
Which equation correctly uses the law of cosines to solve for the third side?
e2 = 112 + 92 − 2(11)(9)cos(140°)
112 = e2 + 92 − 2e(9)cos(140°)
92 = e2 + 112 − 2e(11)cos(140°)
e = 11 + 9 − 2(11)(9)cos(140°)
Answer:
e2 = 112 + 92 − 2(11)(9)cos(140°)
Answer:
A
Step-by-step explanation:
2020 Edge
PLEASE HELP!!!!
Given the function ƒ(x )=x^2 - 5, find ƒ(7).
44
2
49
Answer:
(7)^2 - 5 = 49 - 5 = 44
Step-by-step explanation:
Answer:
44
Step-by-step explanation:
\(\displaystyle f(x) = x^2-5\\\\Put \ x = 7\\\\f(7) = (7)^2 - 5\\\\f(7) = 49 - 5 \\\\f(7) = 44\\\\\rule[225]{225}{2}\)
Hope this helped!
~AH1807The sale price of an item is $42 after a 75% discount. What was the original price?
Answer:
73.50
Step-by-step explanation:
42x.75= 31.5
42.0+31.5=73.5
help anyone? i will make you a brainliest.
Answer: can i have the brains? ;)
Step-by-step explanation:
100000000x3,000,000,000,x650000x-200x100-100000000=....?
Answer:
Do you mean this 100000000* 300000000*650000*(-200)*100-100000000 if so the answer is -3.9E26
Step-by-step explanation:
Remove the parentheses from the (-200)
Multiply the numbers 100000000*300000000*650000*200*100
= -3.9E26-100000000
Subtract the numbers -3.9E26-100000000
= -3.9E26
Hope you enjoy this:) If you need me to explain it more I would love too:))
The perimeter of the rectangle below is 16 cm. What is the value of k? 5 cm kcm Not to scale
Answer:
3 cm.
Step-by-step explanation:
Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)
l = k cm (given)
w = 5 cm (given)Substituting these values into the formula, we get:
16 cm = 2(k cm) + 2(5 cm)
Simplifying, we get:
16 cm = 2k cm + 10 cm
Subtracting 10 cm from both sides, we get:6 cm = 2k cm
Dividing both sides by 2, we get:
3 cm = k
Therefore, the value of k is 3 cm.
help
Use Lagrange multipliers to find the dimensions (in meters) of a rectangle with perimeter 120 m whose area is as large as possible. (Enter the dimensions as a comma-separated list.) m
The dimensions of the rectangle with the largest possible area are 30 meters by 20 meters.
We can use Lagrange multipliers to find the dimensions of the rectangle with the largest possible area. The area of the rectangle is given by A = lw, where l is the length and w is the width. The perimeter is given by P = 2l + 2w = 120. We can use Lagrange multipliers to find the critical points of the function A, subject to the constraint P = 120. This gives us the following equations:
λ = 2l / A
λ = 2w / A
Solving these equations, we get the following values for l and w:
l = 30
w = 20
Therefore, the dimensions of the rectangle with the largest possible area are 30 meters by 20 meters.
Here is a diagram that illustrates the solution:
Rectangle with dimensions 30 meters by 20 meters.
As you can see, the rectangle with the largest possible area is a square. This is because a square has the greatest ratio of area to perimeter of any rectangle.
Learn more about rectangle here: brainly.com/question/15019502
#SPJ11
The dimensions of the rectangle with the largest possible area are 30 meters by 20 meters.
We can use Lagrange multipliers to find the dimensions of the rectangle with the largest possible area. The area of the rectangle is given by A = lw, where l is the length and w is the width. The perimeter is given by P = 2l + 2w = 120. We can use Lagrange multipliers to find the critical points of the function A, subject to the constraint P = 120. This gives us the following equations: λ = 2l / A
λ = 2w / A
Solving these equations, we get the following values for l and w:
l = 30, w = 20. Therefore, the dimensions of the rectangle with the largest possible area are 30 meters by 20 meters. Here is a diagram that illustrates the solution: Rectangle with dimensions 30 meters by 20 meters. As you can see, the rectangle with the largest possible area is a square. This is because a square has the greatest ratio of area to perimeter of any rectangle.
Learn more about rectangle here: brainly.com/question/15019502
#SPJ11
Which equation represents a line passing through the points (0, 1) and (2, -3)?
The equation of the line passing through the points (0, 1) and (2, -3) is y = -2x + 1.
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (0, 1) and (2, -3).
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (-3 - 1) / (2 - 0)
m = -4 / 2
m = -2
Using the point-slope form, plug in one of the given points and slope m = -2 to find the equation of the line.
Let's use the point (0, 1):
y - y₁ = m(x - x₁)
y - 1 = -2(x - 0)
y - 1 = -2x
y = -2x + 1
Therefore, the equation of the line is y = -2x + 1.
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
The functions
=
shown in the graph.
f(2)= - x + 2 and
g(x) = (1)* + 1 are
- x + 2 = (*)* + 1
Ex+2
;
-3 -2 -1
1 2 3
What are the solutions to
3
=
-1
-2
Select each correct answer.
0-1
ОО
1
02
3
Answer:
0 and 1
Step-by-step explanation:
f(x) = g(x) at the point the touch each other.
Here they touch each other when x = 0 (touching the y axis) and x = 1
Rewrite 2/5 book 1/2 hour as a unit rate
Answer:
4/5 book per hour
Step-by-step explanation:
In this question, we are to rewrite (2/5)/(1/2) as unit rate.
To write this as a unit rate, what we need to do
is to divide 2/5 by 1/2.
That means 2/5 divided by 1/2
Removing the division and replacing with multiplication will give 2/5 * 2/1 = 4/5 books/hour
Step-by-step explanation:
4/5 books/hour
A painter charges $15.33 per hour, plus an additional amount for the supplies. If he made $188.18 on a job where he worked 7 hours, how much did the supplies cost?
There are green grapes and black grapes in the ratio 3:4 if there are 24 green grapes how many black grapes are there?
I need help 4k - 13 = 6k + 5
Answer:
k = -9
Step-by-step explanation:
4k - 13 = 6k + 5
4k - 6k = 5 + 13
-2k = 18
k = 18 / -2
k = -9
What is the equation of this line in slope-intercept form?
y = 3x + 1
y = -3x - 1
y = -1/3x - 1
y = 3x - 1
Answer:
y = -3x - 1
Step-by-step explanation:
-1 is the slope intercept, as you can see where the line goes through the y-axis.
The line is also negative, as it's going down, and the slope is three down (negative) and one over. Since slope is written as y over x (y/x), 3 is y. One, the x, doesn't need to be written because 3 is already a whole number.
Expand and simplify:
3(2p - 5) + 2(p + 3)
Answer:
8p - 9
Step-by-step explanation:
→ Expand brackets
6p - 15 + 2p + 6
→ Collect like terms
8p - 9
If A is symmetric matrix, then A^3 is a _______ matrix.
If A is a symmetric matrix, then A³ is also a symmetric matrix.
To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.
Now, let's look at A³:
A³ = A * A * A
We can replace each A with A^T, since they are equal:
A³ = A^T * A^T * A^T
Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:
A³ = (A^T * A^T * A^T)^T
A³ = (A^T)^T * (A^T)^T * (A^T)^T
Since the transpose of a transpose is the original matrix, we can simplify:
A³ = A * A * A
Therefore, A³ is also a symmetric matrix.
More information about the symmetric matrix here:
https://brainly.com/question/16374195
#SPJ11