3. F(-2) +9
F(x)=-3x-2
Answer:
F(-2) = -3(-2) - 2 = 6 - 2 = 4
F(-2) + 9 = 4 + 9 = 13
Step-by-step explanation:
F(-2) = -3(-2) - 2 = 6 - 2 = 4
F(-2) + 9 = 4 + 9 = 13
Answer attached question, show full working and explain what you are doing in each step
Answer:
the required equation is x² -10x +18 = 0
Step-by-step explanation:
Given side x and diagonal 8 cm of a rectangle with perimeter 20 cm, you want to show that the value of x satisfies an equation of the form ...
x² +ax +b = 0 . . . . . where a and b are integers.
PerimeterThe perimeter is the sum of the side lengths. It can be expressed by the formula ...
P = 2(L +W)
Solving for W gives ...
W = P/2 -L
For the given rectangle, the width is ...
W = 20/2 -x = 10 -x
DiagonalThe length of the diagonal is related to the length and width of the rectangle by the Pythagorean theorem.
c² = a² +b²
8² = x² +(10 -x)² = 2x² -20x +100
32 = x² -10x +50 . . . . . . . . divide by 2
x² -10x +18 = 0 . . . . . . . . . . subtract 32
This shows that x must satisfy a quadratic of the form x² +ax +b = 0, where a=-10, and b=18, both integers.
__
Additional comment
The vertex form of the equation is ...
(x -5)² -7 = 0
This has solutions ...
x = 5 ±√7 ≈ {2.354, 7.646} . . . . centimeters
The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $4 and each adult ticket sells for $9. The auditorium can
hold no more than 110 people. The drama club must make a minimum of $720 from
ticket sales to cover the show's costs. If r represents the number of student tickets
sold and y represents the number of adult tickets sold, write and solve a system of , a
inequalities graphically and determine one possible solution.
Answer: The total number of tickets sold (student and adult) cannot exceed 110, so we can write the first inequality as:
r + y ≤ 110
The minimum amount of money needed from ticket sales is $720, so we can write the second inequality as:
4r + 9y ≥ 720
To graph the system of inequalities, we can start by plotting the two lines corresponding to r + y = 110 and 4r + 9y = 720. The solution to the system of inequalities is the area on the graph that is shared by both of the inequalities (i.e., the area above the line 4r + 9y = 720 and below the line r + y = 110).
One possible solution for the number of student tickets (r) and adult tickets (y) is (30, 80). This means that 30 student tickets and 80 adult tickets can be sold to meet the conditions and raise at least $720.
Step-by-step explanation:
The non-right angles of a right triangle are in the ratio 1: 5, Write an equation that could be used to find the measure of each angle.
Answer: 6x=90
Step-by-step explanation:
We know that one angle in a right triangle is 90 degrees and the sum of all the angles is 180, so we can start by subtracting 90 from 180. We are left with 90 and now we have angle ratios which represent fractional quantities. We know that one of these quantities is 5 and the other is 1. Their sum is 6 and equals 90. So the proportion would be 6x = 90. The larger angle is 75 degrees and the smaller one is 15.
how factors and multiples realted
Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.
what is prime factor ?A prime factor is any semi natural integer that is able to divided only by itself and by 1. Actually, a few of the initial number theory are 2, 3, 5, 7, 11, and so forth. a sum that has multiplied to yield a new sum. For illustrate, if we divide 15 by 3 and 5, we get 3 5 = 15. components: All prime but non-composite components are referred to here as prime factors. 2, 3, and 5 are a some of the major determinants of 30. It is essential to list 2 twice as 2 2 3 (or 22 3) in order to factorise 12 since only 2 and 3 represent prime factors of 12. 2 + 3 can really be added to make 12.
given
As contrast to multiples, which are multiplied by another number to produce particular numbers, factors are the numbers that split the supplied number exactly.
Factors are the objects that numbers can be multiplied by one another to produce another number (e.g., 1, 2, 3, and 6 are factors of 6). When you multiply a number by an integer, you obtain multiples (e.g., 20 is a multiple of 4).
e.g., 1, 2, 3, and 6 are factors of 6
e.g., 20 is a multiple of 4
Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.
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Ryan is taking a survey to find out how many people prefer soda A over soda B. He surveyed 100 people and forty-nine preferred soda A. Seven percent had no preference for soda A or soda B. What percentage of peoples surveyed preferred soda B?
Answer: 44%
Step-by-step explanation:
100 - 49 - 7 = 44 people who preferred Soda B
44 of a 100 = 44%
Answer: 44%
Step-by-step explanation:
Since we have 100 people, each person is one percent.
49 people preferred A, so we can subtract 49 from 100.
100 - 49 = 51
7 people didn't have an opinion, so we can subtract 7 from 51.
51 - 7 = 44
That means that 44 people preferred B, which is 44%
How do you describe a calibration curve?
A calibration curve is a graphical representation of the relationship between the output of a measuring instrument and the actual values of the quantity being measured.
What is the calibration curve?
A calibration curve is typically created by measuring a set of known values of the quantity being measured, and plotting the measured values against the actual values. The curve is used to make adjustments to the measurements obtained with the instrument, so that they more accurately reflect the actual values of the quantity being measured.
A calibration curve can be described as a plot of the relationship between the output of a measuring instrument and the actual values of the quantity being measured. The curve is typically linear, and the slope of the curve represents the sensitivity of the instrument. The y-intercept of the curve represents the offset or bias of the instrument, and any deviations from a straight line represent non-linearity in the measurement.
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PLEASE HELP ASAP!!! FIND THE MULTIPLICITY AND ZEROS FOR THE GRAPH.
The zeros and their multiplicity are:
Zero: -1, Multiplicity: 1
Zero: 0, Multiplicity: 1
Zero: 1, Multiplicity: 1
Zero: 2, Multiplicity: 1
Zero: 2.5, Multiplicity: 1
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A graph of a polynomial is given in the diagram.
A polynomial is intercepting the x-axis five times.
That means, there are five zeros.
The zeros and their multiplicity are:
Zero: -1, Multiplicity: 1
Zero: 0, Multiplicity: 1
Zero: 1, Multiplicity: 1
Zero: 2, Multiplicity: 1
Zero: 2.5, Multiplicity: 1
Hence, all the required values are given above.
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A researcher interested in the effectiveness of organized diet groups on weight loss weighed five clients after several weeks on the program. The weight-loss scores (in pounds) were as follows: 13 12 6 9 9 10 Calculate the (a) range, (b) inter-quartile range, and (c) variance and standard deviation for these weight-loss scores.
Range = 7. IQR = 4.5. Variance: 8.67, Std Dev: 2.96 when researcher organized diet groups on weight loss weighed five clients after several weeks on the program.
The range of the weight-loss scores can be calculated by subtracting the smallest value from the largest value. In this case, the range would be
13 - 6 = 7.
The inter-quartile range (IQR) is calculated as the difference between the 75th percentile and the 25th percentile of the data.
IQR: 11.25 - 6.75 = 4.5
To calculate the variance, first find the mean weight-loss score by summing all the scores and dividing by the number of clients: (13 + 12 + 6 + 9 + 9 + 10) / 6 = 9.17. Next, subtract the mean from each score and square the result for each client:
[tex](13 - 9.17)^2 = 3.69\\(12 - 9.17)^2 = 1.69\\(6 - 9.17)^2 = 16.0\\(9 - 9.17)^2 = 0.02\\(9 - 9.17)^2 = 0.02\\(10 - 9.17)^2 = 0.69[/tex]
Next, sum the squared deviations and divide by the number of clients minus one (n-1):
(3.69 + 1.69 + 16.0 + 0.02 + 0.02 + 0.69) / (6-1) = 4.83
The variance is 4.83 and the standard deviation is the square root of the variance: [tex]\sqrt{(4.83)} = 2.19.[/tex]
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19.5 is equal to 4 times some number. What is the number?
Answer:
x=4.875
Step-by-step explanation:
19.5=4x
19.5/4=4.875
x=4.875
Check:
4.875×4=19.5
In triangle FGH, g=8ft, h=13ft, and measure of angle F=72 degree. Find measure of angle G
To find the measure of angle G in triangle FGH, we can use the fact that the sum of angles in a triangle is always 180 degrees.
First, we can find the measure of angle H using the fact that the sum of angles in a triangle is 180 degrees:
H = 180 - F - G
H = 180 - 72 - G
H = 108 - G
Next, we can use the Law of Cosines to find the length of side FG:
FG^2 = GH^2 + FH^2 - 2(GH)(FH)cos(F)
FG^2 = 8^2 + 13^2 - 2(8)(13)cos(72)
FG^2 = 169.21
FG ≈ 13.01 ft
Finally, we can use the Law of Cosines again to find the measure of angle G:
cos(G) = (FG^2 + GH^2 - FH^2) / (2(FG)(GH))
cos(G) = (169.21 + 64 - 169) / (2(8)(13))
cos(G) = 0.7686
G ≈ 40.6 degrees
Therefore, the measure of angle G in triangle FGH is approximately 40.6 degrees.
SOME ONE HELP! I WILL MAKE BRAINLIST!
Note that the proof related to the above parallelogram is given as follows:
ΔSVX ≅ ΔUTX Given
SV || TU Given
SV ≅ TU Corresponding part of congruent triangle
VUTS parallelogram Definition of parallelogram.
What is a Parallelogram?A quadrilateral having two pairs of parallel sides is known as a parallelogram. It is possible to demonstrate that the opposing sides of a parallelogram are congruent.
A parallelogram is any quadrilateral having two pairs of congruent opposing sides. Parallelograms contain two congruent opposing angles, thus a quadrilateral with two congruent opposite angles must be a parallelogram.
A parallelogram's diagonals intersect each other, therefore a quadrilateral with diagonals that bisect each other must be a parallelogram. Finally, if a quadrilateral contains two parallel and congruent sides, it must be a parallelogram.
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write the given argument in words and deter- mine whether each argument is valid. Let p: The for loop is faulty. q: The while loop is faulty.
r: The hardware is unreliable. s: The output is correct. p → (q V r) q → (p V s) p V -q
-s
_________
p V r
All the premises are true and conclusion are also true in all critical rows, then argument is valid. Conclusion (S) is not true in all critical rows, so argument is not valid.
What is for loop?In mathematics, the word "loop" has several different definitions. The simplest definition of a loop is a closed curve whose beginning and terminal points meet in the basepoint, a fixed point. Formally, a loop is a continuous map if is a topological space and.
p: The for loop is faulty.
q: The while loop is faulty.
r: The hardware is unreliable.
s: The output is correct.
p→ (qVr)
q→ (pVs)
pV→q
→s
.............................
∴ pVr
argument in words.
The for loop is faulty then the while loop is faulty or the hardware is unreliable.
The white loop is faulty then the for loop is faculty or the output is correct.
The for loop is faulty or the white loop is not faulty.
The output not correct.
...................................................................................................................
∴ The for loop is faulty or the hardware is unreliable.
next, we determine the argument validity -
Premise S₁: p→ (qvr)
Premise S₂: q→ (pvs)
Premise S₃: pv→q
Premise S₄: →s
.............................
∴ Conclusion S: pvr
When all the premises are true and conclusion are also true in all critical rows, then argument is valid.
Here, conclusion (S) is not true in all critical rows, so argument is not valid.
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Solve with the box method
The expanded expression is [tex]2x^4 + 3x^3 - 10x^2 + 6x - 1.[/tex]
How to calculate the expression?[tex](2x^2 - 3x + 1)(x^2 + 3x - 1)[/tex] can be expanded by multiplying each term in the first equation by each term in the second equation using the distributive property. increase.
= [tex]2x^2(x^2 + 3x - 1) - 3x(x^2 + 3x - 1) + 1(x^2 + 3x - 1)[/tex]
Each term can then be simplified by multiplying by the coefficient and adding the exponent of x.
= [tex]2x^4 + 6x^3 - 2x^2 - 3x^3 - 9x^2 + 3x + x^2 + 3x - 1[/tex]
Then you can combine similar terms.
= [tex]2x^4 + (6x^3 - 3x^3) + (-2x^2 - 9x^2 + x^2) + (6x - 1)[/tex]
= [tex]2x^4 + 3x^3 - 10x^2 + 6x - 1[/tex]
So the expanded expression is [tex]2x^4 + 3x^3 - 10x^2 + 6x - 1.[/tex]
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Explain why the equation 82.5 + 8(0.25x)= 338.5 is equivalent to the equation 82.5 + 2x = 338.5
Step-by-step explanation:
because 0.25 = 1/4.
so, it is actually
82.5 + 8×(1/4)x = 338.5
which is then simplified
82.5 + (8/4)x = 338.5
82.5 + 2x = 338.5
Step-by-step explanation:
[tex]\displaystyle\\8(0.25x)=8(\frac{25}{10}x)=\frac{8*25}{100} x=\frac{200}{100}x=2x[/tex]
Thus, 82.5+8(0.25x)=338.5 ≡ 82.5+2x=338.5
q1 and q2 are 24m apart. if q2 is 49 times q1, where between the two charges would the net electric field be equal to 0
The point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.
Describe charge?Charge is a fundamental property of matter that describes its electrical state. It is a scalar quantity that can be either positive, negative, or neutral, and is measured in Coulombs (C). The concept of charge is used to explain many of the phenomena that occur in electricity and magnetism, such as electric fields, currents, and voltages. Positive and negative charges are thought to be due to the presence or absence of electrons, which are the smallest negatively charged particles in matter. Neutral objects have an equal number of positive and negative charges, resulting in a net charge of zero. The interaction of charges with each other results in many of the electrical and magnetic phenomena observed in the world around us.
The net electric field at a point is equal to zero if the electric field due to one charge is exactly canceled by the electric field due to the other charge.
Since q2 is 49 times greater than q1, the electric field due to q2 will be 49 times greater than the electric field due to q1 at any given point. In order to cancel the electric field due to q1, we need to place q2 at a point that is 49 times closer to q1 than the original separation of 24m.
Let's call the new separation between the charges x. Then, x = 24m / 49, which is approximately equal to 0.48936m.
So, the point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.
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What is 4x^3+4x^m+8x^5+4 written in polynomial standard form?
The polynomial in standard form is 8x^5 + 4x^4 + 4x^3 + 4
How to determine the standard form of the polynomialFrom the question, we have the following parameters that can be used in our computation:
4x^3+4x^m+8x^5+4
Express properly
So, we have the following representation
4x^3 + 4x^4 + 8x^5 + 4
Order the powers in decreasing order
This gives
8x^5 + 4x^4 + 4x^3 + 4
Hence, the standard form is 8x^5 + 4x^4 + 4x^3 + 4
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Have been completely stuck can I get some help on this?
Answer:
1/2x + 6
4
-2x + 5
Step-by-step explanation:
Find the slope (rise over run) and the y intercept for each function.
What is the Mode, Median, Mean and range for the following $32, $87, $67, $32, $32, $87, $77 and $25
Answer:
Mean = $54.875 ($54.88 to nearest cent because $54.875 is impossible)
Median = $32
Mode = $32
Step-by-step explanation:
Mean = all numbers added together / amount of numbers in dataset
$32 + $87 + $67 + $32 + $32 + $87 + $77 + $25 = $439
$439/8= $54.875 = $54.88 to the nearest cent.
Median =
1. Order the numbers. Here's how it's ordered: $25,$32,$32,$32,$67,$77,$87
2. Calculate the middle position with the formula [tex](n+1)/2[/tex] where n is the amount of numbers in dataset (for odd datasets) or find the two middle values (for even datasets.) In this case, it is an odd dataset, so we use the formula.
(7+1)/2 = 4
In the 4th position, the number is $32, so the median is $32.
Mode = The numbers that comes up most often.
In this case, $32 comes up 4 times, which is the most, so the mode is $32.
Brainliest please!
what quantity of 63% chlorine solution must be mixed with a 12% chlorine solution to produce 3876 ml of 15% solution
6^5 is the same thing as what number squared.
Answer:
Below
Step-by-step explanation:
6^5 = x^2
7776 = x^2 sqrt both sides
x = ± 88.18
That ratio of the risk premium to the standard deviation of the excess returns is known as the reward-to-volatility or the _ ratio.
Answer:
Sharpe Ratio?
if you looking for a name for your definition, thats it
good luck!
Approximate the area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2]
by calculating the sum of the areas of 4 rectangles with…….
The approximate area between the x-axis and the function, f(x) = x² + 3, obtained by finding the sum of the of the four rectangles is Area ≈ 9.75
What is the area between the x-axis and the graph of a function?The area between the x-axis and the graph under a function can be referred to as the area under a curve of the function, which can be found using definite integrals.
The area between the x-axis and the function f(x) = x² + 3 over the interval [0, 2], can be found by finding the area of the rectangular bars, A, in the figure as follows;
The values at the endpoints of the rectangles are; 0.5, 1, 1.5, and 2
Therefore;
f(0.5) = 0.5² + 3 = 3.25
f(1) = 1² + 3 = 4
f(1.5) = 1.5² + 3 = 5.25
f(2) = 2² + 3 = 7
Therefore; A = 0.5 × f(0.5) + 0.5 × f(1) + 0.5 × f(1.5) + 0.5 × f(2)
Plugging in the values of the function, we get;
Area ≈ 0.5 × 3.25 + 0.5 × 4 + 0.5 × 5.25 + 0.5 × 7 = 9.75
The approximate area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2] is about 9.75 square units
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Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
The expression that is not equivalent is 23 + (-27) + 16 + 32. Option C
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the arithmetic operations in the other of their usage in calculation.
They are;
ParenthesesExponentDivisionMultiplicationAdditionSubtractionFrom the information given, we have that;
23 + ( − 27 ) − 16 − ( − 32 )
expand the parentheses, we get;
23 - 27 - 16 + 32
Add the values
23 - 27 - 16
Now, subtract the values
-20
Hence, the value is -20
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The complete question
Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
23 - 27 - 16 + 3223 - 27 - 16- (-32)23 + (-27) + 16 + 3223 + (-27) + (-16)- (-32)Type your response in the box. Here is a function that describes a sequence called the Lucas numbers, which is similar to the Fibonacci sequence: f(n) = f(n – 1) + f(n – 2); f(1) = 2; f(2) = 1. Describe in words the relationship between the terms created by this algebraic rule. List the first six terms of the sequence. Find the 12th term.
The first six terms of the sequence are 2, 1, 3, 4, 7, and 11.
The 12th term is 199.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(1) = 2
f(2) = 1
f(n) = f(n - 1) + f(n - 2)
Now,
For n = 3,
f(3) = f(3 - 1) + f(3 - 2) = f(2) + f(1) = 1 + 2 = 3
f(4) = f(4 - 1) + f(4 - 2) = f(3) + f(2) = 3 + 1 = 4
f(5) = f(5 - 1) + f(5 - 2) = f(4) + f(3) = 4 + 3 = 7
We see that,
The next sequence is the addition of the previous two sequences.
So,
The sequence is:
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199
i.e
12th term = 199.
Thus,
First six terms of the sequence = 2, 1, 3, 4, 7, 11
12th term = 199.
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Answer: The first term of the sequence is 2, and the second is 1. The function adds the previous two terms to get the next term.
To get the first six terms of the sequence, start by finding the third term by substituting the values of the first two terms in the function:
f(3) = f(2) + f(1) = 1 + 2 = 3.
In the same way, find the remaining three terms and get the sequence as (2, 1, 3, 4, 7, 11, . . .).
To find the 12th term of the sequence, continue using the rule to find all terms until the 12th. So, the sequence is (2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, . . .).
The 12th term is 199.
Step-by-step explanation:
Edmentum Answer
HELP PLEASEEEEEEEEEEEEEEEEEE
AROC formula
(f(b)-f(a))/b-a
f(11)-f(3) / 11 - 3
-623 -(-47) / 8
= -72
Hope this helps,
- Jeron :- )
Eric works for a salary of $3,500 per month.
What is Eric’s gross pay for one year?
Eric’s gross pay for one year if he earns a salary of $3,500 per month is $42,000.
What is Eric’s gross pay for one year?The total amount of money an employee receives before taxes is referred to as gross pay.
Given that;
Eric's salary per month = $3,500 Eric’s gross pay for one year = ?Eric’s gross pay for one year = Eric's salary per month × 12 months
Eric’s gross pay for one year = $3,500 × 12
Eric’s gross pay for one year = $42,000
Therefore, the gross pay is $42,000.
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A train leaves San Diego at 4:00 PM. A second train leaves the same city in the same direction at 6:00 PM. The second train travels 42mph faster than the first. If the second train overtakes the first at 8:00 PM, what is the speed of each of the two trains?
what is the weight of a 3-pound human brain in ounces
Answer:
The average weight of a 3-pound human brain in ounces is approximately 48 ounces.
Tallulah wants to buy a car for \$18,500$18,500, but can only get a loan from the bank for \$15,725$15,725. What percentage does Tallulah have to put down in order to pay for the car?
The percentage Tallulah have to put down in order to pay for the car is given by the equation A = 15 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage Tallulah have to put down in order to pay be A
Now , the equation will be
The price of the car = $ 18,500
The amount of money Tallulah can get from the bank = $ 15,725
So , the remaining amount = price of the car - amount of money Tallulah can get from the bank
Substituting the values in the equation , we get
The remaining amount = 18,500 - 15,725
The remaining amount = $ 2,775
Now , $ 2,775 = A % of price of the car
So , 2,775 = ( A/100 ) x 18,500
On simplifying the equation , we get
Divide by 18,500 on both sides of the equation , we get
A/100 = 0.15
Multiply by 100 on both sides of the equation , we get
A = 15 %
Hence , the percentage is 15 %
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