Mary Stevens earns $6 an hour at her job and is entitled to time-and-a-half for overtime and double time on holidays. Last week she worked 40 hours of regular time, 61/2 hours of overtime, and 8 hours of holiday time. How much did she earn?
f(x)=-x^2+8x-20 find the min/max value
The maximum value of the quadratic function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4. This value can be found by using the vertex formula for parabolas.
The function in question is f(x)=-[tex]x^2[/tex]+8x-20. This is a quadratic function, and since the coefficient of [tex]x^2[/tex] is negative, the graph of the function will be a downward-opening parabola. To find the maximum value of this function, we need to determine the vertex of the parabola.
The vertex of a parabola in the form of f(x)=[tex]ax^2[/tex]+bx+c is given by the formula h=-b/(2a). Plugging in our coefficients a=-1 and b=8, we find the x-coordinate of the vertex to be h=-8/(2(-1))=4. To find the corresponding y-coordinate, which is the maximum value, we substitute x=4 into the original function [tex]ax^2[/tex]+bx+c:
f(4)=[tex]-4^2+8\times4-20[/tex]
f(4)=-16+32-20
f(4)=-4
Therefore, the maximum value of the function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4.
5x-2y=8 solve for y
[tex]5x-2y=8\ \ \ \ |-5x\\\\-2y=8-5x\ \ \ |:(-2)\\\\y=-4+2.5x\\\\\boxed{y=2.5x-4}[/tex]
Jay Downs only worked 15 of his scheduled hours last week. If he worked 75% of his scheduled hours, how many hours was he scheduled to work?
divide 15 hours by 75%
15 / 0.75 = 20
he was scheduled for 20 hours
What is lineAF? 11 units 15 units 43 units 51 units
Answer:
d.51
Step-by-step explanation:
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PLOT THE X- AND Y- INTERCEPTS TO GRAPH THE EQUATION
Y = 1/3 x - 1
Simplify (4/7) divided by (3/-8)
it would be -32/21 because if you multiple 4/7 -8/3 it would be -32/21
Solve for s.
2/3s+5/6s=21
Enter the answer, as a whole number or as a fraction in simplest form, in the box.
s =
To solve the equation 2/3s + 5/6s = 21, you first combine the fraction terms into 1.5s = 21, then solve for s by dividing both sides of the equation by 1.5, giving you s = 14.
Explanation:To solve for s, you need to first combine like terms on the left-hand side of the equation 2/3s + 5/6s = 21.
To add these fractions, you first need to find a common denominator, which is 6 in this case. So, the equation becomes 4/6s + 5/6s = 21, which simplifies to 9/6s = 21 or 1.5s = 21.
Now you can solve for s by dividing both sides of the equation by 1.5, resulting in s = 21 / 1.5.
So, the solution for s is 14, which can be entered as a whole number.
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Which word sentence represents the equation?
6(x + 3) = 42
A. The sum of 3 and six times some number is 42.
B. Three plus 3 times some number is 42.
C. Six times some number plus 3 is 42.
D. Six times the sum of a number and 3 is 42.
The word sentence that represents the equation 6(x + 3) = 42 is option A: The sum of 3 and six times some number is 42.
Explanation:The word sentence that represents the equation 6(x + 3) = 42 is option A. The sum of 3 and six times some number is 42.
To understand why, let's break down the equation step-by-step:
We have the expression (x + 3) in parentheses, which means that whatever number the student chooses to replace x with should be added to 3.Next, we multiply the entire expression (x + 3) by 6.The result of that multiplication should equal 42.So, option A correctly expresses the equation by stating that the sum of 3 and six times some number is 42.
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Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
15% tip on a bill of $46.62
The amount of the tip is approximately...?
which letters have rotational symmetry ? answers : W , K, Y , O , P , Z
How do I solve 26/5+8.8?
What would x equal? Please help
23*2 = 46
5x-4 =46
5x = 50
x = 50/5 = 10
x = 10
A farmer had 1,000 horses and cows. After selling some of them, he had 550 horses and 350 cows left. How many horses and cows did he sell altogether?
Answer:
he sold 450 horses and 650 cows
Step-by-step explanation:
number of horses he sell =total horses - sold horses
number of cows he sell = total cows- sold cows
need help with this if someone could help me please and thank you
Can someone help me solve X please?
Find the GCF of 44j5k4 and 121j2k6.
Answer:
The GCF is [tex]11j^{2} k^{4}[/tex]
Step-by-step explanation: I did the assignment on edge.
Please don't answer if you don't know.
Find the x-intercept of the line:
-4x - 2y = 16
Question 6 options:
a) (-4,0)
b) (4,0)
c) (0,8)
d) (0.-8)
A scuba diver is 3.8 meters below the surface of the water. He is descending at a rate of 0.5 meters per minute.
Part 1:
Write an algebraic expression to describe the depth of the scuba diver after any number of minutes.
Part 2:
Describe what the variable represents in this situation.
Answer:
[tex]-3.8-0.5x[/tex]
Step-by-step explanation:
A scuba diver is 3.8 meters below the surface of the water.
So, Depth of scuba driver is - 3.8 m
He is descending at a rate of 0.5 meters per minute.
So, Rate = -0.5 m . min
So,Distance traveled in x minutes = -0.05 x
So, The depth after x minutes = -3.8-0.5x
So, an algebraic expression to describe the depth of the scuba diver after any number of minutes is -3.8-0.5x
The variable x represents the no. of minutes .
Simplify.
12.13 - 3.2 × 2.3 + 0.5^2
a jigsaw puzzle has edge pieces and inside pieces. the ratio 3:22. there are 924 inside pieces. calculate the total number of pieces in the puzzle
The jigsaw puzzle has a total of 1050 pieces, with 126 edge pieces and 924 inside pieces, based on the ratio 3:22 provided in the question.
To calculate the total number of pieces in the jigsaw puzzle, we need to use the given ratio of edge pieces to inside pieces, which is 3:22. If there are 924 inside pieces, and the ratio of edge pieces to inside pieces must remain constant, we can set up a proportion where the number of edge pieces is represented by x and the number of inside pieces by 924.
3:22 = x:924
To find the value of x, we can cross-multiply:
3 * 924 = 22 * x
This gives us :
2772 = 22x
Now, we can solve for x by dividing both sides of the equation by 22:
x = 2772 / 22
x = 126
This means there are 126 edge pieces. To find the total number of pieces in the jigsaw puzzle, we add the edge pieces to the inside pieces:
Total pieces = edge pieces + inside pieces = 126 + 924 = 1050
Relationship A has a greater rate than Relationship B. This table represents Relationship B.
Hours worked 2 4 5 8
Amount paid ($) 25 50 62.50 100
Which equation could represent Relationship A? Hours worked is represented by x and Amount paid is represented by y. Select each correct answer
a] y = 12.25xb] y = 13x
c] y = 12.75xd] y = 11.5x
Answer:
12.75 and 13x
Step-by-step explanation:
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Carson was building a greenhouse. He has a board that is 6 1/3 ft long. He’s needs the board to measure 5 1/6 fr. how much will he need to cut off of the board?
Apply the definition of subtraction and properties of operations to find the result. (3/2 + 2/3) - 3/8
explain the. different ways that u can use multiplication to estimate. and solve. division problems
Answer:
Instead of divide the dividend by the divisor to get a quotient, you can estimate an approximate quotient and then multiply it by the dividend. If the result is greater than the divisor, then your estimated quotient was greater than the actual quotient, in the case that the result is lower than the divisor, then your estimated quotient was lower than the actual quotient. After that you proceed to estimate again the quotient. For example:
First approximation:
192/12 ≈ 14
12*14 = 168 < 192
Second approximation:
192/12 ≈ 20
12*20 = 240
So, the answer is between 14 and 20
Third approximation:
192/12 ≈ 16
12*16 = 192
Then, 16 is the correct answer
What is 6×2 49÷7 +5=
sanjay can travel 342 miles in 6 hours. at this rate, how far can he travel in 5 hours?
When your graphing inequality how do you know which side to shade in
Describe why it might not be a good idea to use a key where each symbol stands for 1 in a picture graph
Final answer:
It is inefficient to use a key where each symbol represents the value 1 in a picture graph because it can make the graph cluttered and hard to interpret, especially with large data sets. Picture graphs should simplify visualization of data, yet remain clear and easily comprehensible.
Explanation:
Using a key where each symbol stands for 1 in a picture graph might not be a good idea because picture graphs are meant to represent larger sets of data visually and efficiently. If each symbol represents only 1, the graph could quickly become cluttered and hard to read, especially if the data set is large. This defeats the purpose of a picture graph, which is to provide a clear and simplified visual representation of the data. Moreover, the choice of symbols in a mathematical context is arbitrary; they are placeholders that have no intrinsic significance, and what matters is the concept they represent.
For instance, when dealing with large quantities, using symbols that represent 10, 100, or any other convenient large number makes the graph much more readable and helps to emphasize important relationships and comparisons between different data sets. Similarly, when using equations, symbols are used as stand-ins for numbers, and changing a symbol does not affect the underlying relationship they represent. Introducing more effective representations pictures the concept that equations capture. Likewise, the practicality of picture graphs can be compared to other types of graphs, like pie graphs, bar graphs, and line graphs, each of which serves a different purpose and has its own best use scenario.
Using a key where each symbol stands for 1 in a picture graph can make it cluttered and confusing, especially for large data sets. It is advisable to use symbols to represent larger values or to choose different types of graphs for readability and clear communication of the data's relationships.
Explanation:Using a key where each symbol stands for 1 in a picture graph could be inadvisable in some situations. For large quantities, having one symbol represent a single unit could make the graph cluttered and difficult to read. It is more effective to have symbols represent larger, rounded values so the graph remains clear and interpretable. The use of symbols in mathematics and graphs is generally arbitrary, and they can be chosen to best represent the data being visualized. For example, in equations or graphs illustrating one-dimensional kinematics, symbols are chosen to present information on position, velocity, and acceleration over time in a way that makes relationships between these physical quantities easily understandable.
When considering how to best display data, it's crucial to think about readability and the ease of extracting useful information from the graph. If a picture graph with one symbol representing 1 becomes too complex, it might be better to opt for other types of graphs like bar graphs or line graphs, depending on the data's characteristics. Furthermore, the real purpose of graphs is to capture and represent relationships or trends, which is often better achieved with symbols that represent more suitable quantities, especially when dealing with large numbers.
The glossary of key symbols and notation in mathematics reaffirms the concept that the symbols themselves are not inherently meaningful, but are placeholders to facilitate understanding of the relationships and quantities they represent. Therefore, when creating picture graphs, the key chosen should enhance the viewer's ability to quickly grasp the depicted information.