The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true
How to determine the true statements?The functions are given as
f(x) = c
Also, we have
f(-x) = c
In the above function definitions, we can see that
The functions f(x) and f(-x) have the same value
i.e. f(x) = f(-x) = c
This means that f(x) =f(-x)
By the symmetric property of an equation, the above can also be rewritten as
f(-x) = f(x)
Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true
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ve the system and find the numbers.
11) One number is four more than a second number. Two times the first number is 4 more than four
times the second number.
A) 7 and 3
C) 6 and 2
D) - 6 and -10
B) 5 and 1
Answer:
6 and 2
Step-by-step explanation:
Let the first and second numbers be x and y respectively.
x = 4 + y..... (1)
2x = 4 + 4y...... (2)
Using the substitution method from Eqn(1) into (2)
Anywhere we see x in Eqn(2) we substitute it with 4 + y
I. E. 2(4 + y) = 4 + 4y
8 + 2y = 4 + 4y
Collect like terms.
8 - 4 = 4y - 2y
4 = 2y
.: y = 2
Put y = 2 in Eqn(1), and we have;
x = 4 + 2
x = 6.
.: the first number is 6 and the second number is 2.
Option C is correct.
By drawing two circles, John got a figure, which consists of three regions(basically a venn diagram). At most how many regions could John get by drawing two squares?
How can you use compatible numbers when you divide decimals
Division is opposite of multiplication. If 3 groups of 4 make 12 in the multiplication, 12 divided into the 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in the each group when sharing fairly.
How to divide the compatible numbers?In divisions involving fractions, numerator is called the dividend while the denominator is called the divisor while the answer is called the quotient.
Now, when Dividing decimal by a whole number, it means the decimal is the numerator while the whole number is the denominator.
The first step is to estimate quotient by approximating the dividend and divisor to the nearest compatible numbers. For example; 6.5/9
The nearest compatible number for numerator is 6 while for the denominator it is 10. Thus, we have;
7/10 = 0.7
Second step is to perform division with original numbers. This gives us;
6.5/9 = 0.722
Third step is to compare the both answers to see if our estimate makes sense.
Using compatible numbers gave us quotient of 0.7 while the normal division gave us a quotient of 0.722
Since both the quotient are very close, then it means our estimated quotient is okay.
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find x if AC=15 , AB=x+14 , and BC= x+13
Given the information, we have the following:
Now, since AC=15, we have the following expression:
[tex]\begin{gathered} AB+BC=AC \\ \Rightarrow(x+14)+(x+13)=15 \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} (x+14)+(x+13)=15 \\ \Rightarrow2x=15-14-13=-12 \\ \Rightarrow2x=-12 \\ \Rightarrow x=\frac{-12}{2}=-6 \\ x=-6 \end{gathered}[/tex]Therefore, x=-6
A kidney stone treatment study found that treatment A had 81 out of 87 successful trials in small stone treatments and 234 out of 270 successful trials in large stone treatments. Treatment B had 234 out of 270 successful trials in small stone treatments and 55 out of 80 trials successful in large stone treatments. Overall which treatment had a better success rate and why? 150 words no copy internet
Using proportions, it is found that due to the higher proportion of successful trials, Treatment A had the better success rate
What is a proportion?A proportion is a fraction of a total amount, and hence it is represented by the sum of the desired amounts divided by the sum of the total amounts.
For Treatment A, we have that:
There was a total of 87 + 270 = 357 trials.Of those, 81 + 234 = 315 trials were successful.Hence the proportion of successful trials for Treatment A is given by:
315/357 = 0.8824.
For Treatment B, we have that:
There was a total of 80 + 270 = 350 trials.Of those, 55 + 234 = 289 trials were successful.Hence the proportion of successful trials for Treatment B is given by:
289/350 = 0.8257.
The proportion for Treatment A is higher, as 0.8824 > 0.8257, hence it had the better success rate.
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Provide the correct reason for the statement in line 4. (please help)
Answer:
d) division property of =
Step-by-step explanation:
by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.
round to 1,600 to the nearest hundred
Answer:1,600
Step-by-step explanation:C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
you already have the answer :)
Which point is part of the solution set of the inequality x < -12?
Answer:
all the number to the left of -12 on a number line. -12 is not a solution. If we were graphing this, we would have an open circle above -12 on a number line and the dark ray points to the left of -12
Step-by-step explanation:
Solve all
1. (25+5) x3-13
2. 19+12x2-4
3. 42+32+4
4. 12+34x2÷2
5. (4+3) x (2+5)
6. 2+14x5-5
7. 22+4x5-13
8. 13-42+7+2
9. 15+2-14÷7
10. (18-7)x2
Minh paints 12 rooms to paint 3 he needs 2 cans of paint . He wants to know how many cans he needs in all. Which tools would be appropriate for Minh to use to solve the problem? Choose all that apply
Minh can use unitary method to determine how many cans he will need in all to paint the 12 rooms, which will give a total of 8 cans as requirement. The tools he'll need for the same are : counters, pencil and paper.
In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.
How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units.
This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.
Given, He requires 2 paint cans to paint 3 rooms.
Once more, he will require 2/3 of a can of paint to paint 1 room.
He will thus require cans of paint to paint 12 rooms, which equals (2/3)*23 = 8.
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what is the method used to complete the table?
Answer:
see attached
Step-by-step explanation:
You want to finish filling the given 2-way table.
TotalsAny single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.
It is basically a series of subtraction problems.
For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.
Which of the following parent functions has a domain of all real values of x
and a range of 0?
Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles?
The pairs of angles that are alternate interior angles will be angle 6 and angle 8.
What are alternate interior angles?When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
Angles that are exterior to the lines, have different vertices, and sit on different sides of the transversal are referred to as alternate exterior angles. In other words, eight angles are created when a transversal intersects two parallel lines.
These van be illustrated in angle 6 and 8
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Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles? ∠1 and ∠4 ∠2 and ∠3 ∠6 and ∠8
Given the relation R {(4,2), (3,6), (x,8), (1,4)} Which value of x would make this relation a function?
(1) 4
(2) 3
(3) 1
(4) 0
Answer:
SOLUTION
TO CHOOSE THE CORRECT
OPTION
Given the relation R = {(6,4), (8,-1), (x,7), (-3,-6)}. Which of the following values for x will make relation R a function
(a) 8
(b) 6
(c) -3
(d) 1
CONCEPT TO BE IMPLEMENTED
FUNCTION
Let A and B are two non empty sets. A Mapping (function ) f from A to B is a rule that assigns to each element x of A a definite element y in B
EVALUATION
Here the given relation
R = {(6,4), (8,-1), (x,7), (-3,-6)}
Take A = {6,8,x,-3}
B={-6, -1, 4,7}
In order to satisfy all requirement for R to be mapping is R will have to assign to each element x of A a definite element y in B
Since R has mapped 6, 8, -3 already
So R can not map 6, 8, - 3 again
So R can not be any of 6, 8, - 3
.'. X = = 1
FINAL ANSWER
The correct option is (d) 1
1. . A relation R in the set of real numbers R defined as R = {(a,b): √a = b} is a
function or not. Justify
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2. Let R be a relation on a collection of sets defined as follows,
R={(A,B)|ACB}
Then pick out the correct statement(s).
Find the slope of a line containing
P1(3, 7)
and
P2(6, 9).
The slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.
Slope, also called as gradient of a line is a value or number that describes both of the directions x and y. It basically tells the steepness of the line.
To find the slope of line, formula given below is used
[tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex] = slope
Here, y2 = 9
y1 = 7
x2 = 6
x1 = 3
Thus, 9 - 7/6 - 3
= 2/3
Therefore, we can conclude that the slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.
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Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)
we have the expression
[tex]\frac{4}{3x^2-23x+40}[/tex]Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)
In this problem
3x^2-23x+40=3(x-5)(3x-8)
so
[tex]\frac{4}{3x^2-23x+40}=\frac{4}{3\mleft(x-5\mright)\mleft(3x-8\mright)}[/tex]Multiply by (x-3)/(x-3)
[tex]\frac{4}{3(x-5)(3x-8)}\cdot\frac{(x-3)}{(x-3)}=\frac{4(x-3)}{3(x-5)(3x-8)(x-3)}[/tex]Part 2
we have the expression
[tex]\frac{9x}{3x^2-17x+24}[/tex]we have that
3x^2-17x+24=3(3x-8)(x-3)
so
[tex]\frac{9x}{3x^2-17x+24}=\frac{9x}{3\mleft(3x-8\mright)\mleft(x-3\mright)}=\frac{3x}{(3x-8)(x-3)}[/tex]Multiply the expression by (x-5)/(x-5)
[tex]\frac{3x}{(3x-8)(x-3)}\cdot\frac{(x-5)}{(x-5)}=\frac{3x(x-5)}{(3x-8)(x-3)(x-5)}[/tex]calculate the complement of a 26° angle.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
angle = 26 degress
complement angle = ?
Step 02:
26 + x = 90
x = 90 - 26
x = 64
The answer is:
The complement angle is 64 degrees
Ration of adults to children is 16to 10 40 adults
A relationship between two quantities that is typically stated as the product of their respective quotients.
The ratio of red to blue marbles, or 6:4, is, for instance, 6:4 if a box contains six red and four blue marbles. Decimal or percentage expressions of ratios are also possible. This implies that there would be 10 children for every 16 adults.
The number of children there would be for 40 adults can be calculated by dividing 40 by 16, then multiplying the result by 10.
40/16=2.5
2.5×10=25
25 kids.
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Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
Since we see that P is a point on the perpendicular bisector, l, of MN, we have proven the required PM = PN by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
How to Interpret the Perpendicular Bisector?We are given :
P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove the assertion that PM = PN
A Reflection is defined as a transformation in which a given figure is the mirror image of the other. This means that every point on the new image is a mirror reflection of itself .
From the question, we can say that by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
The perpendicular bisector, l is acting as a Line of symmetry which is also called axis of reflection.
Now, due to the fact that reflections preserve lengths in transformation, it means that we have; PM = PN.
Therefore, we see that point N is the image of M .
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Answer:
Point M
Step-by-step explanation:
there are 248 students in a large-lecture history course. on the first exam, 12% got an A, 28% a B, 41% a C, 11% a D, and the rest failed. Based on these results, whats the probability that a randomly selected student will (a) Get better than a C on the second test? (b) Fail the second test? (c) Not get an A on the second test
Assuming that the scores on the first exam are a representation for the ones in the second exam, we will see that the probabilities are:
a) P = 40%b) P = 8%c) P = 88%How to get the probabilities?First we want to get the probability that a randomly selected student gets better than a C on the second test.
We assume the percentages for the first test can be applied for the second, so, the ones that got better than a C on the first exam are:
A: 12%
B: 28%
Then the probability is:
P( more than a C) = 12% + 28% = 40% (or 0.40 in actual probability notation)
b) Now we want to find the probability of fail.
The percentage that failed the first test is:
100% - 12% - 28% - 41% - 11% = 8%
So 8% of the students failed the first exam, this means that the probability that a randomly selected student fails the second exam is:
P = 8% or 0.8 in decimal notation.
C) 12% of the students tgot an A, so the probability that a randomly selected student does not get an A is:
P = 100% - 12% =88%
or 0.88 in decimal notation.
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Help find X-coordinate
The value of x coordinate be 0 or -2.
Given,
Vertex of the graph, f(x) = x² + 2x + 2
We have to find the x coordinate.
Here,
f(x) = x² + 2x + 2 is in the form of quadratic equation.
So, we can find x coordinate by using quadratic formula.
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 1, b = 2 and c = 2
So,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-2(+-)\sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]
= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]
= (-2±(-√4)) ÷ 2
= (-2±(-2)) ÷ 2
Solve for.
-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2
Solve for,
-2 - (-2) / 2 = -2 + 2 / 2 = 0
That is,
The value of x coordinate be 0 or -2.
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a skydiver is falling at about 176 ft per second. how many feet per second is he falling?
Now multiply 176 by 60 and that is the answer, Khalil :=)
what is the z-score of the value 9 rounded to the nearest tenth?
Please, let me know if you have any question anytimeGiven:
mean = μ = 8
standard deviation = σ = 0.7
random value = x = 9
Then, the formula to calculate the z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values:
[tex]z=\frac{9-8}{0.7}=\frac{1}{0.7}=1.428\approx1.4[/tex]Answer: 1.4
I need help with my math
The definition of the slope can be interpreted by the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]selcect two points from the graph
(0,-2)
(0,-4)
replace the points into the formula
[tex]\begin{gathered} m=\frac{(-4)-(-2)}{0-0} \\ m=\frac{-4+2}{0} \\ m=\frac{-2}{0} \\ m=\text{IND} \end{gathered}[/tex]Since any number divided by 0 is indetermined, the slope of the line is undefined.
8. [-/1 Points]
SPRECALC7 1.7.071.
A pilot flew a jet from City A to City B, a distance of 1600 ml. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 8 h 20 min. What was the speed from
City A to City B?
mi/h
DETAILS
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
The speed from City A to City B is 352 miles/hour.
What is the relationship between speed, distance, and time?By dividing the distance traveled by the time required to travel it, speed is calculated.Speed is inversely correlated with time and directly correlated with distance. Thus, distance equals speed times time.Distance divided by speed equals time; as speed rises, time goes down, and vice versa.Given:
Distance for trip = 1600 miles
Distance for return trip = 1600 miles
The round-trip took 8 h 20 min.
Total time taken for both trips = 8 hours 20 minutes = 8 + (1/3) hours = 25/3 hours
It is mentioned that on the return trip, the average speed was 20% faster than the outbound speed.
Let's assume x is the speed for an outbound trip.
So, x + 20% of x is the average speed of the return trip
x + 20% of x = x + 0.2x = 1.2x
Speed for the return trip = 1.2x
Total time = (distance/speed of outbound trip) + (distance/speed of return trip)
⇒ [tex]\frac{25}{3} =\frac{1600}{x} +\frac{1600}{1.2x}[/tex]
⇒ [tex]\frac{25x}{3} =\frac{1600*1.2 +1600}{1.2}[/tex]
⇒ [tex]10x = 3520[/tex]
⇒ [tex]x = 352[/tex]
Therefore, the speed from City A to City B is 352 miles/hour.
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Home Depot wants to buy a new line of fertilizers. Manufacturer A offers a 22/14 chain discount. Manufacturer B offers a 25/8 chain
discount. Both manufacturers have the same list price.
a. What is the percentage of discount for both manufacturers?
Note: Do not round intermediate calculations. Round your final answers to the nearest hundredth percent.
Manufacturer A
Manufacturer B
Percentage of
Discount
%
%
b. What manufacturer should Home Depot buy from?
Manufacturer B
Manufacturer A
(a) The percentage of discounts for manufacturers A and B is 32.92% and 31%, respectively.
(b) The Home Depot should buy from manufacturer A.
Home Depot wants to buy a new line of fertilizers.The manufacturer A offers a chain discount of 22/14.The manufacturer B offers a chain discount of 25/8.The list price of the manufacturers is the same.Let the list price be "x".For manufacturer A:The price after the first discount is x*(1-22%).The price after first and second discount is x*(1-22%)(1-14%).The price is 0.6708x.The total discount is 1-0.6708.The total discount percentage is 32.92%.For manufacturer B:The price after the first discount is x*(1-25%).The price after first and second discount is x*(1-25%)(1-8%).The price is 0.69x.The total discount is 1-0.69.The total discount percentage is 31%.Home Depot should buy from manufacturer A due to the greater discount.To learn more about percentage, visit :
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Solve I =prt for p when I =5,480,r =.04, and t=7. Round your answers to two decimal pla
We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:
We use the simple interest formula:
I = P r t
in our case: I = (5480) (0.04) (7) = 1534.4
So the interest is: 1534.40
We answer using two decimal places because this is refering to cents of a dollar.
If $2,000 is invested at 11% annual interest compounded quarterly, what is the account balance after 10 years, assuming no additional deposits or withdrawals are made?
Answer:
$5,919.75
Step-by-step explanation:
What is Annual Compound Interest?
Annual compound interest is represented by this formula:
[tex]A = P ( 1 + \frac{r}{n}) ^{(n)(t)}[/tex]
A= Final value (including interest)P = principal/original amount: $2000r = rate as a decimal: 0.11n= number of times compounded yearly: quarterly: 4t= numbers of years borrowed for: 10You have been giving all the information needed to solve this equation, so plug in what you have. and solve for A.
[tex]A = (2000)( 1 + \frac{0.11}{4} )^{(4)(10)}[/tex]
[tex]A = (2000) (1.0275)^{40}[/tex]
[tex]A = (2000) (2.9598739872)\\[/tex]
[tex]A = 5919.74797[/tex]
Round your answer to the nearest hundred, and the account balance after 10 years should be $5,919. 75
show work help plsss
The required quotient is 6.5625 when -5 2/8 is divided by (-4)/5.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
The quotient is given in the question:
-5 2/8 ÷ (-4)/5
-(42/8) / (-4)/5
Reciprocal the term in the denominator
-(42/8) × -(5)/4
210/32
6.5625
Therefore, the required quotient is -5 2/8 ÷ (-4)/5 = 6.5625.
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Katie earns $549 each week working her full time job. Her employer has a 14.3% tax deduction on all monies earned each week. Calculate the tax deduction Katie paid for that week.
The tax deduction Katie paid for that week will be $78.5.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Katie earns $549 each week working her full-time job. Her employer has a 14.3% tax deduction on all monies earned each week.
The deduction will be calculated as follows:-
Deduction = ( 549 x 14.3 ) / 100
Deduction = 7850.7 / 100
Deduction = $78.50
Therefore, the tax deduction Katie paid for that week will be $78.5.
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