When solving absolute value inequalities involving the greater than symbol (>) or greater than or equal to symbol (≥), we have to consider two cases absolute value expression greater than the constant and less than the constant.
The absolute value expression is greater than the constant:
|x| > c or |x| ≥ c
In this case, we can split the solution set into two parts: x < -c and x > c. The solution is all real numbers less than -c and all real numbers greater than c.
The absolute value expression is less than the constant:
|x| < c or |x| ≤ c
In this case, we can split the solution set into two parts: -c < x < c. The solution is all real numbers between -c and c, excluding -c and c.
For example, consider the inequality |x| > 2. The solution is x < -2 or x > 2, so the solution set is {x | x < -2 or x > 2}.
--The question is incomplete, answering to the question below--
"When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving >. Explain"
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∆ is an equilateral triangle with a side length of 12 inches. What is the height of ∆? Provide your answer in simplest radical form.
Answer:
Step-by-step explanation:
f f
[Pre-Calculus honors] Find the rotation in revolutions per minute given the angular speed and the radius given the linear speed and the rate of rotation.
37. V= 82.3 m/s, 131 rev/min
38. V= 144.2 ft/min, 10.9 rev/min
39. V= 553 in. /h, 0.09 rev/min
Please do all of them, or at least as many as you can.
Answer: To find the rotation in revolutions per minute (RPM) given the angular speed and the radius, we can use the formula:
RPM = (Angular Speed (rad/s)) / (2 * pi)
To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:
Angular Speed (rad/s) = Linear Speed (m/s) / Radius (m)
Angular Speed = 82.3 m/s / 0.131 m = 630 rad/s
RPM = (630 rad/s) / (2 * pi) = 131 rev/min
To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:
Angular Speed (rad/s) = Linear Speed (ft/min) / (Radius (ft) * 12)
Angular Speed = 144.2 ft/min / (10.9 ft * 12) = 10.9 rad/s
RPM = (10.9 rad/s) / (2 * pi) = 10.9 rev/min
To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:
Angular Speed (rad/s) = Linear Speed (in/h) / (Radius (in) * 3600)
Angular Speed = 553 in/h / (553 in * 3600) = 0.09 rad/s
RPM = (0.09 rad/s) / (2 * pi) = 0.09 rev/min
Step-by-step explanation:
Please help if you can
The exponential function that satisfies the given conditions is given as follows:
[tex]f(t) = 4e^{1.099t}[/tex]
How to model the exponential function?The format of the exponential function for this problem is given as follows:
f(t) = 4e^(kt).
In which k is the exponential growth rate.
After five hours, there was 972 bacteria, meaning that when t = 5, f(t) = 972, hence the growth rate is obtained as follows:
[tex]972 = 4e^{5k}[/tex]
[tex]e^{5k} = 243[/tex]
5k = ln(243)
k = ln(243)/5
k = 1.099.
Meaning that the function is defined as follows:
[tex]f(t) = 4e^{1.099t}[/tex]
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Ryan needs 3 and 1/4 cups of flour for the cookie recipe she is baking. She has already added 2 and 1/2 cups of flour. How much more flour does she need to add? Please help-
The quantity of more flour that she needs to add would be = 3/4
What is a fraction?A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.
The quantity of flour Ryan needs for baking = 3¼
The quantity of flour she has already added = 2½
The remaining amount that she needs to add;
= 3¼-2½
= 3/4
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Please help me asap !
On the graph:
A represents the reactants
B represents the activated complex
C represents the products
D represents the activation energy
What is the information in the energy profile diagram of the reaction shown?The path of energy changes that take place in a reaction, as well as the energy content of the reactants and products, are depicted in the energy profile diagram.
The letters shown in the diagram represents the following:
A stands for the activation energy, which is the minimal amount of energy required for reactant molecules to produce products.The activated complex, represented by B, is an intermediate state created during the transformation of reactants into products.The reaction's overall enthalpy change is denoted by the letter C.D stands for the products' potential energy, which is contained in their chemical bonds.E stands for the reactants' potential energy, which is the chemical potential energy contained in the bonds that make up the reactant.The reactants are denoted by F.G stands for the goods.Since the energy content of the reactants is higher than that of the products, the reaction is exothermic.Learn more about energy profile diagram at:
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What number goes in the blank to make the number sentence true? 3 x (1 + 6) = (3 x 1) + ( x6)
The required value of x to satisfied the given condition is 1/5.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:We have,
3x (1 + 6) = (3 x 1) + ( 6x)
3x(7) = 3 + 6x
21x = 3 + 6x
15x = 3
x = 1/5
Thus, required value of x is 1/5.
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In order to satisfy the requirement, x must be 1/5 of the desired value.
What is an equation?An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. For instance, the two equations 3x + 5 and 14 are combined to form the equation 3x + 5 = 14, which is denoted by the equal sign.According to what we have3x (1 + 6) = (3 x 1) + ( 6x) ( 6x)3x(7) = 3 + 6x21x = 3 + 6x15x = 3x = 1/5A value of 1/5 for x is therefore necessary.To lean more about Equation refer:
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Please help with question 11!!
“Given the functions f(x) = sqr x^2 - 3 and g(x) = sqr 36-x^2 what is the domain of f- g within the real set of numbers??
PLS HELP!!! THANK YOU!!
The domain of the function f(x) - g(x) is given as follows:
[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
For a square root, the inner term cannot be negative, hence the domain of f(x) is given as follows:
x² - 3 >= 0
|x| >= sqrt(3)
x <= -sqrt(3) or x >= sqrt(3).
For function g(x), the domain is given as follows:
36 - x² >= 0
x² <= 36
|x| <= square root (36)
|x| <= 6.
-6 <= x <= 6.
The domain of the subtraction function is the intersection of the domain of both functions, hence:
[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]
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Pedro buys lunch at school every day. He always gets pizza when it is
available. The cafeteria has pizza about 80% of the time.
Pedro runs a simulation to model this using a random number generator. He
assigns these digits to the possible outcomes for each day of the week:
• Let 0 and 1 = no pizza available
• Let 2, 3, 4, 5, 6, 7, 8, and 9 = pizza available
The table shows the results of the simulation.
95032 47150 71709 38889 94007
35013 57890 72924 19365 47879
What is the estimated probability that Pedro will eat pizza for lunch every way
next week?

The estimated probability that Pedro will eat pizza for lunch every way next week is 1/2
The term called probability in math is known as branch of mathematics that measures the uncertainty of the occurrence of an event using numbers
Here we know that the cafeteria has pizza about 80% of the time.
And here we have also know that Pedro runs a simulation to model this using a random number generator.
The result of the table shows the results of the simulation.
Here we need to estimate the probability that Pedro will eat pizza for lunch every way next week and it can be calculated as,
Here we have know that in each box, here there are 5 digits to represent the 5 days in a week.
And here there’s 10 boxes to represents 10 weeks.
Then in each box there’s a chance out of 5 for Pedro to get pizza.
Then the probability is calculated as,
=> 5/10
=> 1/2
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3. Elizabeth works for Picasso Paint Supplies. Her annual
a. What is Elizabeth's annual Social Security deduction?
b. What is Elirahath's annual Medicare deduction?
c. Elizabeth is paid every other week. What is her biweekly gross pay?
d. Each pay period, Elizabeth's employer deducts 21% for federal withholding tax. What is
the total amount withheld for federal tax from Elizabeth's annual salary?
e: If Elizabeth is taxed at an annual rate of 2. 875% for city tax how much is deducted from
her salary per paycheck to withhold that tax?
f. As of January 1, Elizabeth will receive a 9. 1% raise. What will Elizabeth's annual salary be?
Elizabeth's annual Social Security deduction is $72580, Medicare deduction is $1053.71 per year, biweekly gross pay is $2796.15, total amount withheld for federal tax is $15336.80, amount deducted is $66.50 and annual salary is $79,307.38
a) Social Security deduction is 6.2% of Elizabeth's annual salary, which is $72,580 x 6.2% = $4,486.76 per year.
b) Medicare deduction is 1.45% of Elizabeth's annual salary, which is $72,580 x 1.45% = $1,053.71 per year.
c) Elizabeth is paid every other week, so her bi-weekly gross pay is $72,580 / 26 = $2,796.15.
d) The total amount withheld for federal tax from Elizabeth's annual salary is $72,580 x 21% = $15,336.80.
e) The amount deducted from Elizabeth's salary per paycheck for city tax is ($72,580 x 2.875%) / 26 = $66.50.
f) As of January 1, Elizabeth will receive a 9.1% raise, so her annual salary will be $72,580 x (1 + 0.091) = $79,307.38.
Correct Question :
Elizabeth works for Picasso Paint Supplies. Her annual salary is $72,580.
a) What is Elizabeth's annual Social Security deduction?
b) What is Elizabeth's annual Medicare deduction?
c) Elizabeth is paid every other week. What is her biweekly gross pay?
d) Each pay period, Elizabeth's employer deducts 21% for federal withholding tax. What is the total amount withheld for federal tax from Elizabeth's annual salary?
e) If Elizabeth is taxed at an annual rate of 2.875% for city tax, how much is deducted from her salary per paycheck to withhold that tax?
f) As of January 1, Elizabeth will receive a 9.1% raise. What will Elizabeth's annual salary be?
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Does someone mind helping me with this problem? Thank you!
Answer: Amber has 50 pennies and 10 dime
Step-by-step explanation:
The number of pennies is represented by x, while the number of dimes is represented by y. This means that the statement, "there are five times as many pennies as dimes" can be written as x = 5.
The sum of the coins is $1.50, which can now be written as
0.01x + 0.1y = 1.50
0.01(5y) + 0.1y = 1.50
0.05y + 0.1y = 1.50
0.15y = 1.50
y = 10
Next up:
x = 5y
x = 5(10)
x = 50
Finally, we can conclude that Amber has 50 pennies and 10 dimes
I hope this helps!
I need the value of x please?????????????
Based on the triangle sum theorem, the value of x is: 45.
What is the Triangle Sum Theorem?The Triangle Sum Theorem states that in any triangle, the sum of the measures of the interior angles is always equal to 180 degrees. This is true for all triangles, regardless of their size or shape.
The theorem can be proven using Euclidean geometry, which states that the sum of the angles in a triangle is always 180 degrees. This theorem is also known as the "angle sum property" of a triangle.
Therefore:
2x + 10 + 30 + 50 = 180 (based on the triangle sum theorem).
Combine like terms:
2x + 90 = 180
2x = 180 - 90
2x = 90
2x/2 = 90/2
x = 45.
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What is the length of the missing side?
Answer:
D: 39
Step-by-step explanation: Using the steps of the Pythagorean theorem.
The manufacturer's price for a Jinko car is $x
Ben was given a 7% discount on the manufacturer's price when he bought a Jinko.
Ben paid $23 622 when he bought his Jinko.
a) Calculate the value of x.
After a year Ben sold his Jinko for $19 880
b) Calculate the percentage loss, to 3 significant figures, on the price Ben paid for his Jinko.
During the year that Ben owned the Jinko, he travelled d km in the car.
The average fuel consumption of the car was 10km per litre. The average cost of the fuel he used was $1.40 per litre.
Other costs for the car in the year came to $938
The cost per km, including the loss in value, of his Jinko to Ben during the year that he owned the car was $0.40
c) Calculate the value of d.
Price paid for car = $23622, The loss value is $3742 and total distance the car was used for is 18000 kilometres.
What is distance?Distance is a measurement of how far apart two objects or points are. It is the length of the actual route taken to get from one place to another. In physics, distance is frequently used to refer to a physical length or an estimation based on other criteria, such as "a few kilometres apart" or "some miles away."
However, the distance travelled by an object to move from its initial position to its final position will be the same as the distance travelled to move from its final position to its initial position. As a result, distance is independent of a body's motion.
a. Price paid for car = $23622
Discount = 7%
Sale price = $19880
b. The loss value is $3742
c. Let total distance travelled be d
Fuel consumption=10km per litre
Cost of fuel =1.4 per litre
Cost of fuel per kilometre =1.410= 0.14
Other cost = 938
Cost of usage =0.14*d +938
Total cost including loss = 0.14*d +938+3742
The cost per kilometre has been provided as 0.4
Total cost of the vehicle's use = 0.4*d
B=A0.4*d = 0.14*d +938+37420.26*d = 4680d = 18000
Thus, Total distance the car was used for is 18000 kilometres.
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3. Sketch the distance-time graphs for the following scenarios.
a. Stand one meter from the sensor, walk
at a constant (steady) slow pace away
from the sensor.
b. Stand one meter from the sensor, walk
away from the sensor changing your
pace from slow to fast.
The distance-time graphs for the given scenarios have been attached below. The solution has been obtained using distance-time function.
What is distance-time function?
The distance between a person and an object through time is described by distance-time functions. Depending on the kind of movement, a distance-time function may be linear or non-linear, increasing, decreasing, or constant. We need to tell where the object starts, what direction it moves in, how quickly it moves, and whether it is speeding up, slowing down, or travelling at a constant speed in order to explain a distance-time function.
a. The distance-time graph for this scenario is the first graph wherein the line is less steeper than the other graph because the speed is constant.
b. The distance-time graph for this scenario is the second graph wherein the line is steeper than the first one because the speed is changing from slow to fast.
Hence, the distance-time graphs for the given scenarios have been obtained.
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Find the point on the directed segment from (-4, 5) to (12, 13) that divides it into a ratio of 1:5
Answer: x=-4/3, y=19/3
Step-by-step explanation: According to the formula,
x=(mx2+nx1)/(m+n) , y=(my2+ny1)/(m+n)
Here the ratio is 1:5
m=1 , n=5
x1 = -4, x2 = 12
y1 = 5, y2 = 13
Now put in the formula,
[tex]x=\frac{1*12+5(-4)}{1+5}[/tex] , [tex]y=\frac{1*13+5*5}{1+5}[/tex]
x=(12-20)/6 , y= (13+25)/6
x=-8/6 , y=38/6
x=-4/3 , y=19/3
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One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d?
Answer:
By definition, if two angles are complementary, they both will add up to 90 degrees. Knowing this add 18 and (6d-6) together to equal 90.
18+(6d-6)=90
Subtract 18 from both sides, then add 6. This leaves you with 6d equal to 78. Divide by 6 to get 13.
(6d-6)=72
6d=78
d=13 degrees
Make sure of your answer. You know that d is 13, so plug it back into the equation to see if it equals 90 degrees.
18+6(13)-6=90
18+78-6=90
90=90
Simplify the expression
Answer: 5.4h -13 -1.9d
Step-by-step explanation:
combine the like terms together.
How do you proof Triangle BSR is congruent to Triangle DUT
From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given, In the diagram, ABCD is a square, and R, S, T, and U are the midpoints of the sides of ABCD. Also, RT is perpendicular to SU and SV are equals to VU.
Since, R, S, T, and U are midpoints, and since RT is perpendicular to SU
in triangle DUT.
UD = TD
UD is also equal to VT since RT is perpendicular to SU
UD = TD = VT...(1)
And, From the Pythagorean theorem
UT = √(TD² + UD²)
In TRiangle BSR
BR = BS
BS is also equal to RV since RT is perpendicular to SU
BR = BS = RV...(2)
And, From the Pythagorean theorem
SR = √(BR² + BS²)
Since SV is equal to VU.
Thus, RV = VT
From equation 1 and 2
BR = BS = RV = UD = TD = VT
Therefore, From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.
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A professor wants to randomly select 4 students to go to the board. She decides to
randomly select the sixth student who enters the classroom and every seventh student
after that. Determine the students who will be going to the board. Write down the student
numbers.
Using Arithmetic progression, There were 4,13,22,31 pupils chosen out of the applicants.
The professor desires to choose four students at random.
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
The fourth student was chosen at random, followed by every ninth student.
The fourth student is chosen first.
Using the following term formula, which is
=>a + d(n-1) (n-1)
The second student is the one after that.
=>4 + 9(2-1) (2-1)
=>4 + 9(1) (1)
=>4 + 9
=> 13
The third pupil will be
=>4 + 9(3-1) (3-1)
=>4 + 9(2) (2)
=>4 + 18
=> 22
The fourth pupil will be
=>4 + 9(4-1) (4-1)
=>4 + 9(3) (3)
=> 4+ 27
=> 31
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Solve the system of equations.
Answer:
(3,2)
Step-by-step explanation:
2(y = 5x - 13)
-(2y = -5x + 19)
0 = 15x - 45
15x = 45 --> x=3
y = 5(3) - 13
y = 2
if there is a 50% probability that bond a will default next year and 30% probability that bond b will default what is the range of probability that at least one will default
So the range of probability that at least one bond will default next year is between 0% and 80%.
The probability that at least one of two events will occur is the sum of the probability of each event minus the probability that both events will occur. In this case, the probability that at least one bond will default is:
P(A or B) = P(A) + P(B) - P(A and B)
Where P(A) is the probability of bond A defaulting (50%), P(B) is the probability of bond B defaulting (30%), and P(A and B) is the probability that both bonds will default (which we don't know).
So the range of probability that at least one bond will default is:
P(A or B) = 50% + 30% - P(A and B)
The maximum possible probability of both bonds defaulting is (0.5 * 0.3) = 15% and the minimum possible probability of both bonds defaulting is 0%. Therefore, the range of probability that at least one bond will default is:
P(A or B) = 80% - 0% = 80%
So the range of probability that at least one bond will default next year is between 0% and 80%.
It's important to note that the above formula and the range of probability is based on the assumption of independence, i.e the events of Bond A defaulting and Bond B defaulting are independent and don't affect each other.
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what is the total number n of distinct solutions after we impose that x, y and z are all nonnegative integers?
The total number (n) of distinct solutions of the equation (x + y + z = 15) with the assumption that x, y and z are all nonnegative integers is 153.
The generating function for the number of solutions of the equation (x + y + z = n) is given by the binomial coefficient (n+2)C2, where C2 is the number of ways to choose 2 objects from a set of n+2 objects.
The number of solutions for the given equation (x + y + z = 15) is then given by:
(15+2)C2 = (17C2)
We can also use the formula for binomial coefficient: nCr = n! / (r! (n-r)!)
17C2 = (17!) / (2! * 15!) = 153
So the total number of distinct solutions of the equation (x + y + z = 15) with x, y, z non-negative integers is 153.
"
Complete question
what is the total number n of distinct solutions the equation (x + y + z = 15) after we impose that x, y and z are all nonnegative integers?
"
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How many solutions does the following equation have? 6x + 8=2(3x+4)
The equation 6x + 8 = 2(3x + 4) had infinitely many solutions.
How to Find How Many Solution an Equation Has?The equation 6x + 8 = 2(3x + 4) can be solved by isolating x on one side of the equation. To do this, we can first distribute the 2 on the right side of the equation:
6x + 8 = 6x + 8
Then we can subtract 8 from both sides:
6x + 8 - 8 = 6x + 8 - 8
6x = 6x
Divide both sides by 6
6x/6 = 6x/6
x = x
This means x can assume any value which will make the equation true.
Therefore, the equation had infinitely many solutions.
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three computer viruses arrived as an e-mail attachment. virus a damages the system with probability 0.4. independently of it, virus b damages the system with probability 0.5. independently of a and b, virus c damages the system with probability 0.2. what is the probability that the system gets damaged?
The probability that the system gets damaged is 0.685.
Virus A damages the system with probability 0.4.
Independently of it, virus B damages the system with probability 0.5.
Independently of A and B virus C damages the system with probability 0.2.
We have to find the probability that the system gets damaged.
P(system will not be damaged by virus 1) = 1 - 0.1 = 0.9
P(system will not be damaged by virus 2) = 1 - 0.5 = 0.5
P(system will not be damaged by virus 3) = 1 - 0.3 = 0.7
P(the system will be damaged) = 1 - P(system will not be damaged)
P(the system will be damaged) = 1 - P(system will not be damaged by virus 1) x P(system will not be damaged by virus 2) x P(system will not be damaged by virus 3)
P(the system will be damaged) = 1 - 0.9x0.5x0.7
P(the system will be damaged) = 0.685
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3.
3a
Which is cheaper: 115 plums for $276.00 at Shop ZYX or 198 plums for $633.60 at Shop PWR?
What is the cost of a single plum at Shop ZYX?
= Enter your next step here
dollars
Shop ZYX represents the cheaper plan, with a cost of $2.4 per plum.
How to obtain the cheaper plan?To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.
The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.
Hence the cost per plum in each shop is given as follows:
Shop ZYX: 276/115 = $2.4.Shop PWR: 633.6/198 = $3.2.(division of the total cost by the number of plums).
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Can someone check my answer for the first one and help me with the rest? Thank you!
Step-by-step explanation:
First one is good, all you have to do is combine like terms
-28x and +4x are like terms because they both have X
Combining those is -28x+4x=+24x
Making #1 7+24x
Answer:
(Their all down there)
Step-by-step explanation:
Okie dokie so! Your answer for 17 is technically correct but you need to imply it further so it would be [tex]7-24x[/tex]
18. [tex]-2(-6+5k)-1[/tex]
do distributive property
[tex]12-10k-1[/tex] combine like terms (12 and -1)
[tex]-10k+11[/tex]
19. [tex]6(v-5)+1\\[/tex]
do distributive property
[tex]6v-30+1[/tex] combine like terms (-30 and 1)
[tex]6v-29\\[/tex]
20. [tex]10(n+5)-5n[/tex]
do distributive property
[tex]10n+50-5n[/tex] combine like terms (10n and -5n)
[tex]5n+50[/tex]
21. [tex]-7(8+8x)-6x[/tex]
do distributive property
-[tex]56-56x-6x[/tex] combine like terms (-56x and -6x)
[tex]-56-62x[/tex]
22. [tex]6(x-9)+5[/tex]
do distributive property
[tex]6x-54+5[/tex] combine like terms (-54 and 5)
[tex]6x-49[/tex]
what is 193 divide by 5 =
Answer:38.6
Step-by-step explanation:
1. If mA = 3x° and
m
what is the value
of x?
Answer: here
Step-by-step explanation:
Divide each term in ma=3xma=3x by aa and simplify.m=3xa
Given f (x)=-4x-5 find f(5)
Answer: -25
Step-by-step explanation:
For f(x) functions, all you do is plug in whatever value that is given in the parenthesis into x.
f(5) = -4(5) - 5
= -20 -5
= -25
The teachers have $25 to buy supplies. Write and evaluate a numerical expression to show how much more money they will need to buy the cups and napkins.
Cups : $3.50 - 12 per package
Napkins : $4.25 - 10 per package
Please explain ty!!
The amount of money that will be needed more to buy the amount of cups and napkins by the teacher would be = $57.5
How to calculate the extra amount of money needed?The amount of cups needed = 12 packages
The price per package of cup = $3.50
The total money needed for cup = 12× $3.50 = $42
The amount of napkins needed = 10 package
The price per package of napkins = $4.25
The total money needed for napkins = 10×4.25 = $42.5
The total amount needed = 42+42.5 = $82.5
The difference between the amount available and the total amount = the extra money needed ;
= 82.5-25 = $57.5
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