The two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19
What are the two equations to set up to solve the equation?The equation is given as
|3x - 2| = 19
The above equation is an absolute value equation.
When it is split, the constant would be represented as positive and negative
So, the equivalent equations are
3x - 2 = 19 and 3x - 2 = -19
Hence, the two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19
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Part A
A video streaming company offers two monthly plans.
Plan A: $3 per video viewed, plus a flat rate of $8 per month
Plan B: $5 per video viewed and no additional flat rate
A. Write an inequality to determine when the cost of viewing n videos using Plan A is less than the cost of viewing n videos using Plan B.
Choose...
Choose...
Choose...
Part B
Plan A is less expensive when
Choose...
.
Greetings from Brasil...
Let Ca be the function for Plan A and Cb the function for Plan B.
According to the problem statement, we can conclude that:
Ca(n) = 3n + 8Cb(n) = 5nwhere C is the cost and n is the number of videos
Cost that the user will pay for having watched n videos
Ca = cost of Plan A
Cb = cost of Plan B
Is there any point (n) that Ca will be equal to Cb??? Let's equate the functions to check if there is a common point and if there is, what would it be.
Ca = Cb
3n + 8 = 5n
2n = 8
n = 4
In n = 4 we have a condition for the cost that does not matter Ca or Cb.
I will present 2 ways to solve:
1 - building the graph of the functions and observing the points where the Y axis (cost axis) its smaller
2 - assigning 2 points - below n = 4 and above n = 4 - to observe the cost behavior
1 - see attachment
2 - let's choose the points n = 1 and n = 10 (as already said, n=4 does not matter Ca or Cb - meeting point / intersection point)
n = 1
Ca(1) = 3.1 + 8 = 11
Cb(1) = 5.1 = 5
Ca > Cb, then Cb better to the user
n = 10
Ca(10) = 3.10 + 8 = 38
Cb(10) = 5.10 = 50
Ca < Cb, then Ca better to the user
We can come to the following conclusion:
0 < n < 4 → better use Plan B (in this interval the cost to the user will be lower with Plan B)
n = 4 → It doesn't matter to use Plan A or Plan B.
n > 4 → better use Plan A (for n above 4 the cost to the user will be lower with Plan A)
use the drop downs to determine which symbols would complete the inequality for the domain. −4 (a) x (b) 4 (a) (b) ✔ less than
The gathering of x-values determines domain the symbols so one can entire the inequality for the desired area.
All x-values for which the characteristic f(x) exists or is described are in the area of an inequality.The complete inequality may be summarised as follows:-4 ≤ x ≤ 4, (this feature consists of each -four and four within the set of x values)-four < x < 4, (this selection excludes -4 and 4 in the set of x values)-4 ≤ x < 4, (this selection consists of -4 and excludes four inside the set of x values)-four < x ≤ 4, (this selection excludes -4 and consists of four within the set of x values)As a result, the gathering of x-values determines the image that will entire the inequality for the specified domain.To learn more about domain, visit :
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The temperature outside was 22˚F. The wind chill made it feel like -8˚F. Find the difference between the real temperature and the apparent temperature.
please help
The difference between the real temperature and the apparent temperature is - 30˚F.
What is Subtraction?
Subtraction is an operation which is used to find the difference between two numbers.
Given that;
The temperature outside (real temperature) = 22˚F
The wind chill made it feel like -8˚F.
That is, The apparent temperature = -8˚F
Now,
The difference between the real temperature and the apparent temperature = - 8˚F - 22˚F
= - 30˚F
Hence, The difference between the real temperature and the apparent temperature is - 30˚F.
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how many license plates consist of letters followed by digits, if one of the digits must be odd and the other must be even?
There are six slots; first three for letters and the next three for numerals. Each of the slots for letters can be filled in 26 ways; and, each of the slots for numerals can be filled in 9 ways.
Therefore, possible number of license plates = (26 * 26 * 26 * 9 * 9 * 9) = (26^3) * (9^3) = 17576 * 729 = 12812904.
In order to calculate the probability of a compound event A, we use a technique we refer to as "The Slot Method," in which we first calculate the total number of outcomes, n(S), and the total number of successful outcomes, n(A), and then use slots for each of the independent or dependent events that make up the compound event.
In every game you play at a casino, the odds are stacked against you. The chances of winning the top prize when using the maximum coin play range from one in 5,000 to one in approximately 34 million, making slot machine odds some of the worst.
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Jake eat 1 1/2 cups of almonds over a 6-days period. How many cups did he eat per day? Find the solution and what it means in the context of the problem.
Answer: 1/3
Step-by-step explanation:
It is
Write an equation for a line that is perpendicular to the line given by x=9 and passes through the point (-6,-3)
Answer:
y = -3
Step-by-step explanation:
We are given an equation of the line, x=9.
And we want to write another equation of the line that is perpendicular to x=9 and passes through (-6, -3).
There are 3 ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept. Standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be 0, while a also cannot be negative.Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Any one of these forms would work, but let's use slope-intercept form, as it is the most common way to write the equation of the line.
Perpendicular lines have slopes that multiply to get -1. They are also considered negative and reciprocal. For example, 5 and -1/5 would be the slopes of perpendicular lines.
So, let's find the slope of x=9.
If a line is written like x=9, it means that when it is graphed, it will be a vertical line, and a vertical line has an undefined slope.
As you may know, [tex]\frac{1}{0}[/tex] is also considered to be undefined. This means that the slope of this vertical line can be written as [tex]\frac{1}{0}[/tex].
Now, let's get the reciprocal of this slope (put the value of the numerator on the denominator and vice versa), then add a minus sign after it.
[tex]\frac{1}{0}[/tex] => [tex]-\frac{0}{1}[/tex] => 0
The slope of the line we're writing is 0.
We can replace m in y=mx+b with 0.
y = 0x + b
Now we need to find b.
As the equation passes through the point (-6,-3), we can use its values to help solve for b.
Substitute -6 as x and -3 as y in the equation.
-3 = 0(-6) + b
Multiply.
-3 = b
Replace b with -3 in the equation.
y = 0x - 3
This can also be written as:
y = -3
suppose you need of grade 70 tow chain, which has a diameter of and weighs , to tow a car. how would you calculate the mass of this much chain? set the math up. but don't do any of it. just leave your answer as a math expression. also, be sure your answer includes all the correct unit symbols.
The mass of 7m chain = 7 x 2.16 kg = 15.12 kg
It says that 7m of grade 70 tow chain which has a diameter of 3/8'' is required to tow a car.
So length of the chain = 7m
Now given that the weight of the chain = 2.16kg/m
That is weight of 1m of chain = 2.16 kg = mass of 1m of chain
Here, weight corresponds to the mass itself, since both has the same unit 'kilograms(kg)'.
So to find the mass of 7m chain, we need to multiply mass of 1m chain to the length of the chain.
Thus, the mass of 7m chain = 7 x 2.16 kg = 15.12 kg
The question is incomplete. Find the complete question here:
Suppose you need 7m of grade 70 tow chain, which has a diameter of 3/8'' and weighs 2.16kg/m, to tow a car. How would you calculate the mass of this much chain? set the math up. but don't do any of it. just leave your answer as a math expression. also, be sure your answer includes all the correct unit symbols.
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PLEASE HELP FAST!!!!!!!
Answer:
A; x= 8
B; x= -5
C; x= -12
Step-by-step explanation:
a => (7x-1)+(15x+5) = 180
22x +4 = 180
22x = 176
x= 8
b=> (x+135)= 130
x= -5
c=> x+60=48
x= -12
nth term of the sequence 9 6 3 0 -3 -6
Answer:
-3n+12
Step-by-step explanation:
Term to term rule:
9-6=3
6-3=3
3-0=3
term to term rule is -3
-3 x n + 9 - (-3)
-3n + 12
I need these answers for a bell ringer, and I think im worrying too much, but until i get my grade out of the bad zone, I'm grounded from gaming!
The relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.
How to Determine a Relation that is not a Function?A relation is not a function if there are more than one y-value (range element) that is assigned to one x-value (domain element).
In the first relation, the x-value 1, has three different y-values, 10, 20 , and 30.
However, In the second, third, and fourth relations, each of the x-values has exactly one y-value that corresponds to it. These are all relations that represent functions except the relation in A.
Therefore, the relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.
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If BE−→ bisects ∠ABD and m∠ABD = 62°, find m∠ABE.
Answer:
31°
Step-by-step explanation:
A bisector splits an angle into two congruent parts.
I need to find the values of X
Answer:
[tex](f + g)( \times ) = { \times }^{4} [/tex]
Solve the inequality.
x+1>3
0 −4 < x < 2
Ox<-4 orx > 2
O-2
O x < -2 or x > 4
Answer:
answer of the first one
x+1>3 equal to x>2 by subtracting 1 from each side
so x>2 equal ]2,infinity[
answer of the second
-4<x<2 so the quantity of x is all the numbers from -4 to 2 but when it be greater than or smaller than without saying or equal we put the brackets opened so the result is ]-4,2[
but i can,t understand 3 and 4
per gallon, the cost of all the ingredients in your stew is $2.76. you consistently sell 57 gallons of stew per week for $435.98 in total sales. what is your food cost percentage?
The cost percentage is 3.61 %.
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting.
A percentage is calculated by dividing a value or a number by its sum, then multiplying the result by 100. The percentage calculation formula is ( value / total value) × 100%.
The cost of all ingredients mixed in the stew is $2.76.
The total sales is $435.98.
57 gallons of stew are sold per week.
Therefore, the total sales per week is
= $2.76 × 57 = $157.32
Hence, the cost percentage of food is:
= ( 2.76 × 57 ) / 435.98
= 157.32 / 435.98
= 0.361
= 3.61 %
The cost percentage of the food is 3.61 %.
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A cylinder has a surface area of about 221.1 square meters and a height of
7.8 meters. What is the approximate radius of the cylinder?
OA. 3.2 meters
OB. 4.5 meters
OC. 2.1 meters
OD. 6.4 meters
The approximate radius of the cylinder is 4.5m
Surface area of cylinderThe formula for calculating the surface area of cylinder is expressed as:
SA = 2πr(r+h)
where
r is the radius
h is the height
Given the following parameters
SA = 221.1 square meters
height = 7.8m
Substitute
221.1= 2(3.14)r(r+7.8)
221.1 = 6.28r^2 + 15.6r
Factorize to have
6.28r^2 + 15.6r - 221.6 = 0
On factoring, the value of the radius is 4.5 meters
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Answer:
the answer is A
Step-by-step explanation:
I hope it helps you
find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.) 27???? 4
The exact trigonometric ratios for the angle x is second quadrant.
Given Radian equals to θ = 27π / 4, we need to find all the Trigonometric ratios for the same -
Lets calculate the value of θ first.
We know π equals 180 degree angle and 2π equals 360 degree, hence with each 2π the radian moves back to zero degree. Which means
θ = 27π / 4 can be reduced to θ = 3π / 4
Hence θ = 135 degree which can be represented as below -
As This lies in second quadrant, hence on x-axis (Value of base , needs to be taken as -1)
sin θ = 1/√2 cosec θ = √2
cos θ = -1/√2 sec θ = - √2
tan θ = -1 cot θ = - 1
What is trigonometric ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
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segment pqis tangent to the circle at point q. which equation describes the relationship between the tangent and secant line segments? a. (pq)2
The equation describes the relationship between the tangent and secant line segments will be PR · PB = PQ². Then the correct option is B.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The combination of the measurements of the secant section and its outside secant segment is approximately the square of the length of the tangent segment if a tangent section and a secant section are drawn to a circular from an exterior endpoint.
The segment PQ is tangent to the circle at point Q.
The equation describes the relationship between the tangent and secant line segments will be PR · PB = PQ². Then the correct option is B.
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one of your friends missed the class on scientific notation. describe how you would explain to your friend what it means for a number to be in scientific notation and how to convert a number from standard form to scientific notation.
We write 5.14*10^5 to convert from 5.14*10^5.
What is scientific notation?
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.Scientific notation consists of a coefficient multiplied by 10 raised to an exponent . To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 × 10 × 10 × 10 × 10 × 10 = 514000(here are only 4 zeros because you cancel one zero to remove decimal) so we write 5.14*10^5 to convert from 5.14*10^5.
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HELP MEEEEEEEE I WILL GIVE BRAINLIST 2 AND EXTRA POINTS
why do 3 wholes 1/2- 4 wholes 7/8 = 3/8
PLEASE HELPPPPPPPPPP
3 1/2 subtracted from 4 7/8 is equal to 3/8.
What is the value of the subtraction?A fraction is a quantity that is not a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/2.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
Subtraction is the mathematical operation that is used to determine the difference of two or more numbers. The sign used to represent subtraction is -.
[tex]3\frac{1}{2} - 4\frac{7}{8}[/tex]
[tex]-1\frac{4 - 7}{8}[/tex]
[tex]-1\frac{-3}{8}[/tex] = 3/8.
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On a snow day, Jada created two snowmen in her yard. Snowman A was built to a height of 51 inches and Snowman B was built to a height of 36 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decreased by 6 inches per hour and Snowman B's height decreased by 3 inches per hour. Let AA represent the height of Snowman A tt hours after sunrise and let BB represent the height of Snowman B tt hours after sunrise. Graph each function to determine the number of hours after sunrise when both snowmen have an equal height.
From the graph of the linear functions, we have that both snowman's will have the same height of 21 inches after 5 hours.
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 have that:
The initial height is the intercept.The melting rate, as a negative, is the slope.Hence the functions are given as follows:
A(t) = 51 - 6t.B(t) = 36 - 3t.The functions are graphed at the end of the answer, with A(t) in red and B(t) in blue, and they intersect at (5,21), meaning that both snowman's will have the same height of 21 inches after 5 hours.
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Is it fine if I cancel out the minus sign from both the numerator and the denominator and change the plus-minus sign into a plus sign? If not, pls tell me why :D (Be as detailed as u can :D)
Answer:
unfortunately no
Step-by-step explanation:
with ± (plus-minus) sign, you have to work out the two cases.Therefore there're two solutions for this question i.e
[tex]x = \dfrac{ \pm4i}{-2} \implies x _{1} = \dfrac{4i}{-2} \: \: \text{and} \: \: x _{2} = \dfrac{ - 4i}{-2}[/tex]
and this simplifies to [tex]x_1=-2i,x_2=2i[/tex]
HELPP PLEASE IVE STAYED UP ALL NIGHT TRYING TO FIGURE THIS OUT!!!!
In the diagram, points A, B, C, and D are collinear, points C, X, Y, and Z
are collinear, AB = BC = CX = YZ, AD = 54, XY = 22, and XZ = 33. Find
the indicated length.
Based on the segment addition postulate, we have:
19. AB = 11
20. BD = 43
21. CY = 33
22. CD = 32
23. XC = 11
24. CZ = 44
25. ST = 24
26. AC = 20
How to Apply the Segment Addition Postulate?Given the following:
AB = BC = CX = YZ
AD = 54
XY = 22
XZ = 33
Applying the segment addition postulate, we would have the following:
19. AB = YZ
YZ = XZ - XY
Substitute
YZ = 33 - 22
YZ = 11
AB = YZ = 11
AB = 11
20. BD = AD - AB
Substitute
BD = 54 - 11
BD = 43
21. CY = XY + CX
CX = AB = 11
Substitute
CY = 22 + 11
CY = 33
22. CD = AD - 2(AB)
CD = 54 - 2(11)
CD = 32
23. XC = AB = 11
XC = 11
24. CZ = CX + XY + YZ
CZ = 11 + 22 + 11
CZ = 44
25. 4x + 12x = 32 [segment addition postulate]
16x = 32
x = 2
ST = 12x = 12(2)
ST = 24
26. 14 + 3x - 4 = 4x + 4 [segment addition postulate]
10 + 3x = 4x + 4
10 - 4 = 4x - 3x
6 = x
x = 6
AC = 4x + 4 = 4(6) - 4
AC = 20
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In a home run derby competition, there were 32 home runs out of 124 hits. approximately what percent of hits were home run?
In the home run derby competition the percent of hits that were home run is: 25.8%
Information about the problem:
home runs = 32hits = 124hits were home (%) = ?To solve this exercise we have to apply the percentage formula:
hits were home (%) = (home runs/ hits) * 100
hits were home (%) = (32/ 124) * 100
hits were home (%) = 0.2580 * 100
hits were home (%) = 25.8%
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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Answer number 6 pleaseeeee
Answer:
Step-by-step explanation: The answer is B
solve the inequality 8 + 3x < 2 + x and 2x + 23 ≤ 11
Answer:
8 + 3x < 2 + x the answer would be x<-3
2x + 23 ≤ 11 the answer would be [tex]x\leq -6[/tex]
1) 8 + 3x < 2
To solve this, you first want to subtract 8 from both sides to isolate 3x on one side.
This gives you 3x < 2 - 8, which can be simplified to 3x < -6.
After you have this, you want to get x on its own. To do this, divide both sides of the inequality by 3 to get x < -6
2) 2x + 23 [tex]\leq[/tex] 11
For this one, we use the same steps. First, subtract 23 from both sides to isolate 2x, giving us 2x [tex]\leq[/tex] 11 - 23, which we simplify down to 2x [tex]\leq[/tex] -12.
From here, we divide both sides of the inequality by 2 to get x on its own. This gives us x [tex]\leq[/tex] -6
PLEASE HELP RIGHT NOW I HAVE IT DUE IN 20 MINUTES!!
The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.
What did Maya do wrong in the simplification of a mathematic expression?
A procedure of solution is shown and we must check if Maya did all the right steps to get a correct result. We proceed to present our procedure to be compared with that of Maya to find the mistake, that is, the step in which all divergences start.
(a³ - b³) / 5, a = 2, b = - 3 Given
[2³ - (- 3)³] / 5 Substitution
[8 - (- 27)] / 5 Definition of power / Power with negative base
(8 + 27) / 5 Additive inverse of an additive inverse
35 / 5 Definition of addition
7 Definition of division / Result
The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.
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Which equation is correctly rewritten to solve for x? -fx -g = h
To solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.
Which equation is correctly rewritten to solve for x?An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.
Given the equation in the question;
-fx - g = h
Solve for x.
To solve for x simply means to make x the subject of the formula or equation.
-fx - g = h
Add g to both side
-fx - g + g = h + g
Negative g and positive g cancels out.
-fx = h + g
Now, divide each term in the equation by the coefficient of x
-fx/-f = h/-f + g/-f
x = -h/f + (-g/f)
x = -h/f - g/f
Therefore, to solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.
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Please help due in 20mins
Using the common factors, the expression can be rewritten as follows:
1 / 4 xy (x² + 3y)How to rewrite an expression using common factors?The expression can be represented as follow using common factor.
1 / 4 x³y + 3 / 4 xy²
Using the common factors,
The common factors of 1 / 4 x³y and 3 / 4 xy² is 1 / 4 xy.
Therefore,
1 / 4 x³y + 3 / 4 xy² = 1 / 4 xy (x² + 3y)
Therefore, rewriting 1 / 4 x³y + 3 / 4 xy² using the common factors is 1 / 4 xy (x² + 3y).
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W ALL STEPS!
2(x-8) + 4x = 6(x-2)-4
All numbers to the equation 2(x-8) + 4x = 6(x-2)-4 are solutions.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
2(x-8) + 4x = 6(x-2)-4
On further solving
2x- 16 + 4x = 6x - 12 -4
2x + 4x -6x = -12 -4 +16
6x -6x = 0
6x = 6x
As, both sides are equivalent, all numbers are solutions.
Hence, All numbers are solutions.
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what is a possible absolute value inequality to represent -1≤x≤5?
My possible absolute value is -3 ≤ lx - 2l ≤ 3
What is Absolute Value?
The absolute value (or modulus) l x l of a real number x is the non - negative value of x without regard to its sign. For example, the absolute value of 5 is 5 , and the absolute value of -5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
Now, the question is:
what is a possible absolute value inequality to represent -1≤x≤5
The representation of inequality -1≤x≤5 of absolute value will be :
-3 ≤ lx - 2l ≤ 3
Now, add 2 to each segment of the system of inequalities to solve for x while keeping the equation balanced:
-3 + 2 ≤ x -2 + 2 ≤ 3+2
-1 ≤ x ≤ 5
Hence, my possible absolute value is -3 ≤ lx - 2l ≤ 3
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