Answer:
a) 4x-8
b) 3y + 27
c) -6 + 2r
Step-by-step explanation:
Here, we want to use the distributive property to evaluate the given expressions
Mathematically, the distributive property is;
(a + b) * c = (a * c) + (b * c)
So we use this on each of our questions;
a) 4(x-2)
= (4 * x) - (4 * 2) = 4x-8
b) 3(y + 9)
= (3 * y) + (3 * 9)
= 3y + 27
c) -2(3-r)
= (-2 * 3) - (-2 * r)
= -6 + 2r
Rewrite the Expressions using Distributive Property
(2+3)6
Answer:
Step-by-step explanation:
If you distribute 6 to the numbers inside the parenthesis, it means that you multiply both number by 6
2 x 6 = 12
3 x 6 = 18
the expression can be rewritten like the following:
12 + 18 = 30
PLEASE HELPPPPPPPPPP
Answer:
20 1/16
Step-by-step explanation:
please give brilliantest pls
Answer:
You have the correct answer [tex]20 \frac{1}{16}[/tex]
Step-by-step explanation:
44 < 5x6 and 5x - 6 ≤ 54
Answer:
5x - 6 ≤ 54
5x-6+6 ≤ 54+6
5x ≤ 60
divide by 5
x ≤ 12
Step-by-step explanation:
It took Jane 3.5 hours to write 1 paper. At this rate, how long would it take Jane to write all 8 of her papers due this semester?
s it true that for any integer n ≤ 2, φ(n) has a primitive root? if so, prove it. if not, give an explicit counterexample
No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root
What is primitive root?In modular arithmetic, a number g is called a primitive root modulo n if every number coprime to n is congruent to a power of modulo . Mathematically, g is a primitive root modulo n if and only if for any integer a such that gcd(a, n)=1 , there exists an integer k such that:
.[tex]g^{k}[/tex]≡ a (mod n)
Now,
Existence of Primitive root modulo n exists if and only if:
n is 1, 2, 4, orn is power of an odd prime number , orn is twice power of an odd prime number .So,
if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.
For example,
As ϕ(11)=10, the order of 2(mod11) must divide 10.
So we check 22≡4(mod11) and 25≡10(mod11).
Since neither of these are 1, and
we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,
ord112=ϕ(11), making 2 a primitive root modulo 11.
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Evaluate the expression when y=−2 and z=−5.
10y2z=
The value of the expression 10y²z is -750.
How to calculate the expression?We are to calculate the expression 10y²z when y=−2 and z=−5.
This will be:
10y²z
= 10 × -5² × -3
= 10 × 25 × -3
= -750
The value of the expression 10y²z is -750.
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Find FH
FH = {Blank}
Answer:
22
Step-by-step explanation:
By the segment addition postulate, FH=8+14=22.
The equation will be,
→ FH = FG + GH
Then the value of FH will be,
→ FH = 8 + 14
→ [ FH = 22 ]
Hence, the value of FH is 22.
A stationery shop orders a batch of pens from a factory. The factory could make the batch of pens in 20 days using 12 machines. Due to a fault, only 9 machines were used for the first 8 days. All 12 machines were used from day 9 onwards. Work out the total number of days taken to make the batch of pens.
The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now, According to the question, the factories used all 12 machines in the last days, Also, for the first 8 days, only 9 machines were in use.
Thus, If the factories used all 12 machines, the batch of pens took 20 days to be manufactured.
Hence, the equation formed from the given information by basic algebra is: 20 + 12 - 9(8) / 12
28 - (72/12)
=28 - 6 = 22
Hence, The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.
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2x-5y=5
x - y table
graphh
Answer: -3/4
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: −3/4
y-intercept: (0,0)
x y
0 0
4 -3
Rhiannon and Sophie both started saving for a new piano this month. Rhiannon will deposit $35.80 per week, but her bank account is currently overdrawn with a -$253.50 balance. Sophie also has a negative bank account balance of -$78.25 and will deposit $23.30 each week. How many weeks (w) will it take for the two bank accounts to have the same balance?
It will take 14.02 weeks for both the accounts to have the same balance
Bank account balance of Rhiannon = -$253.50
Money deposited by Rhiannon in the bank account each week = $35.80
Bank account balance of Sophie = -$78.25
Money deposited by Sophie in the bank account each week = $23.30
Let the number of weeks it takes to have the same account balance be x, therefore formulating the algebric equation we get:
Bank balance of Rhiannon + Money deposited by her each week*No of weeks it will take for the balance to be equal = Bank balance of Sophie + Money deposited by her each week*No of weeks it will take for the balance to be equal
= -253.5 + 35.8(x) = -78.25 + 23.3(x)
= -175.25 = -12.5(x)
x = 14.02 weeks
Therefore, it will take 14.02 weeks for both the accounts to have the same balance
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Given [tex]f(x)=\frac{1}{x+5}[/tex], find the average rate of change of f(x) on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp
The average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
How to find the average rate of change of f(x) on the interval [1,1+h]?The function is given as
f(x) = 1/(x + 5)
The interval is given as
[1, 1 + h]
Calculate f(1) as follows
So, we have
f(1) = 1/(1 + 5)
f(1) = 1/6
Calculate f(1 + h) as follows
So, we have
f(1 + h) = 1/(1 + h + 5)
f(1 + h) = 1/(h + 6)
The average rate of change of f(x) on the interval [1,1+h] is then calculated as
Rate = [f(1 + h) - f(1)]/[1 + h - 1]
This gives
Rate = [1/(h + 6) - 1/6]/h
Hence, the average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
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Write the value of π correct to 5 decimal places.
Answer:
3.14159
Step-by-step explanation:
The value of π correct to 5 decimal places is 3.14159.
What are Decimal Numbers?Decimal numbers are numbers which includes a whole number part and a fractional part.
The point separating both parts is the decimal point.
Pi, which is written as the Greek symbol π, is defined as the ratio of the circumference of any circle to the diameter of that circle.
We know that,
Circumference of a circle, C = 2 π r, where r is the radius.
2r will be the diameter.
π = C / 2r
The value of pi to 5 decimal places = 3.14159
Normally we use 3.14.
Hence the value of pi is 3.14159 to 5 decimal places.
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Find the least common denominator (LCD) of 5/6 and
8/9
please im begging you help me
Answer: Translation means you move a shape without rotating or flipping it and reflection is a mirror image of the shape. In the current example, the shape is translated right and down a noncalculable amount.
Alyse bought 1/3lb of orange pekoe tea and 1/2lb of
English cinnamon tea. How many pounds of tea did
she buy?
According to the solving Alyse buy 5/6lb pounds fraction of tea.
What in math is a fraction?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator as well as denominator of a complex fraction is a fraction.
How come a fraction is a number?A numerator, which is located above the line, and a denominator make up fractions (which is below the line). You may find out how many equally sized pieces are divided into something by looking at the denominator. How many of these equal components are taken into account is indicated by the numerator.
According to the given fraction:1/3lb of orange pekoe tea.
1/2lb of English cinnamon tea.
find the total pound of tea she buy:
So,
Adding these two fraction we get the total pounds:
= [tex]\frac{1}{3} + \frac{1}{2}[/tex]
= [tex]\frac{2 + 3}{6}[/tex]
= 5/6 lb
According to the solving Alyse buy 5/6lb pounds of tea.
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how many 20mm long wire pieces could be cut from a 1 meter long wire piece
Write the fraction 12/28 in simplest form.
Answer:
3/7
Step-by-step explanation:
12/28=3*4/4*7=3/7
helpppp plssssssssss
Answer:
x=2
Step-by-step explanation:
11-2x=5x-3
the first step, move the 3 over
14-2x=5x
In the second step moves 2x over
14=7x
finally, we just isolate the x from 7 by dividing 7
14/7=7x/7
simplify
2=x or x=2
Answer:
x=2
Step-by-step explanation:
*Shown two ways to solve.
11-2x=5x-3
+2x +2x
11=7x-3
+3 +3
14=7x
Divide by 7.
2=x
11-2x=5x-3
-11 -11
-2x=5x-14
-5x -5x
-7x=-14
Divide by -7.
x=2
Check to see if you're right.
11-2(2)=5(2)-3
11-4=10-3
7=7
Yep, it's correct.
Hope this helps.
CRAFT FAIR Kylie is going to try to sell two of her oil paintings at the local craft fair. She is hoping to earn at least $400.
a. Write the inequality that represents the constraint of the situation, where x is the price of the first oil painting, and y is the price of the second.
b. Graph the inequality that represents the constraint on the sale.
The inequality that represents the constraint of the situation is x+y ≥ 400.
Inequality is defined as the mathematical expression in which both sides are not equal .
In inequalities the two vales are compared by "≤" , "≥" , "≠" .
For Example : 2x+3y≥4 is an example of inequality .
In the given question
Part (a)
Given Kylie sell first oil painting in $x
and second oil painting in $y.
Kylie is trying to earn at least $400.
the term at least means she can earn $400 or greater than $400, so ≥ sign will be used,
According to the question
we get , x+y ≥ 400
So , x+y ≥ 400, is the inequality that represents the constraint of the situation.
Part (b)
The Graph of the inequality x+y ≥ 400 that represents the constraint on the sale is shown below .
Therefore , the inequality that represents the constraint of the situation is x+y ≥ 400.
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Puzzle #4
1: Find the slope:
3: Find the slope:
(2,-6), (-4, -3)
2: Find the slope:
X
Y
-1
-12
1
-8
-4
0
35
5
4: Find the slope:
answer choices
B:
A:
C:
m=-2 m=0 m = 2
D:
m = -4
G:
m=
undefined
E: IF:
m =-
2
m = 4
I
H: -I:
m =
2
m =
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
Does anyone know the code to puzzle 4???? Please
Answer:
1/-2
Step-by-step explanation:
Slope(m) = y2- y1/x2-x1
= -3-(-6)/-4-2
=+3/-6
=1/-2
what is 5,435,778 expressed in scientific notation? a.5.435778 x 10 b.5.435778 x 10 c.5.435778 x 10 d.5.435778 x 10
5,435,778 in scientific notation will be 5.435778×10⁶.
Scientific notation is the way to represents huge numbers in simple form. This ease understanding and calculation of the numbers. When written in a scientific notation, the number is called coefficient, the number to which power is raised is called base and raised power is called exponent. For instance, in the given answer, 5.435778 is coefficient, 10 is base and 6 is exponent.
While converting the numbers into scientific notation, we need to remember following points -
If the number is greater than 1 or is a multiple of 10, the decimal will be placed on the Left Hand Side. Like in the number in question, decimal moved to left and we got positive exponent. If the number is less than 1, then decimal will be placed at Right Hand Side. In this case, the exponent will be negative. For instance, we will represent 0.005 as 5*10-³.Learn more about scientific notation -
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The complete question is -
what is 5,435,778 expressed in scientific notation? a.5.435778 x 10⁷ b.5.435778 x 10³ c.5.435778 x 10⁶ d.5.435778 x 10⁵
3/ax - 4 = 20 What is x?
x =
Answer:
[tex] \sf \large \: x=8a[/tex]
Step-by-step explanation:
Let's solve for x.
3/ax−4=20
Step 1: Multiply both sides by a.
−4a+3x=20a
Step 2: Add 4a to both sides.
−4a+3x+4a=20a+4a
3x=24a
Step 3: Divide both sides by 3.
3x/3 = 24a/3
x=8a
Given that
3x8 7:2
Calculate the value of x.
Give your answer in its simplest form.
X =
The value of x in the equation is x = -8/30
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?The equation is given as
3x + 8 = 7.2
Subtract 8 from both sides of the equation
3x = -0.8
Divide both sides by 3
x = -0.8/3
Rewrite as
x = -8/30
Hence, the value of x in the equation is x = -8/30
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how many different letter arrangements can be obtained from the letters of the word statistically, using all the letters?
Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800
Given,
Total number of arrangements obtained = 6,48,64,800
Given words = STATISTICALLY
Total word count = 13
Here we have repeated alphabets as -
"S"s = 2
"T"s = 3
"A"s = 2
"I"s = 2
"L" = 2
Total permutations we have here = 13! / 2!2!2!2!3!
= 6,22,70,20,800 / 96
= 6,48,64,800
What is Permutation?A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
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What is the difference between -21 and -8?
Answer:
-13
Step-by-step explanation:
(-21) - (-8) = -13
-21 - -8 = -13
Because of the two subtract signs next to each other before the number 8, they change to an addition sign.
From -21, move right 8 places along the number line because it is add 8.
-21 -20 -19 -18 -17 -16 -15 -14 -13
And you get to -13
Therefore, -21 + 8 = -13
Multiply. 6/7 ⋅ 4/15
A. 8/35
B. 14/45
C. 5/11
D. I don't know
Answer:
A
Step-by-step explanation:
Multply = 24/105
Divide by 3
8/35
HELPP DUE TODAY
Geometry bisectors
Answer:
Step-by-step explanation:
Bisects means that ∠RED will be divided in two parts by segment EB. This means that ∠REB = ∠BED. So,
5x-3 + 5x-3 = 8x+16
10x-6 = 8x+16
2x = 22
x = 11
Keep in mind that 11 is NOT the angle of ∠BED. You will plug it back into ∠REB to get
5(11)-3 = 52
Therefore, ∠BED = 52°
I am willing to give a brainliest to anybody, just please help !!!
During which game is she more effective serving?
How did you find this answer and please show your work?
Answer: The First game with 16/19 serves
Step-by-step explanation: Fraction also means division. So once you divide both fractions, you'll see that 16/19 > 13/16. That shows that she was more effective in the first game.
Simplify
x2 - 7x + 12
x2 -2x - 8
Answer:
5x+12
-8
Step-by-step explanation:
i think you have the problem wrong
The inventor of a new game believes that the variable cost for producing the game is $0.50 per unit and the fixed costs are $4,300. the inventor sells each game for $1.89. let x be the number of games produced. (a) the total cost for a business is the sum of the variable cost and the fixed costs. write the total cost c (in dollars) as a function of the number of games produced. c = (b) write the average cost (in dollars) per unit c = c x as a function of x. c =
The total cost is represented as C = $0.50x + $4300 and the average cost as avgC = $0.50 + $4300/x
We have been given that,
The variable cost for producing the game = $0.50 per unit
The fixed cost for producing the game = $4300
Let the total cost be denoted by C.
And let x be the number of games produced.
a) Total cost = variable cost + fixed cost
C = $0.50x + $4300
b) Average cost = total cost/number of games produced
= C/x
= ($0.50x + $4300)/x
= $0.50 + $4300/x
Hence the total cost is C = $0.50x + $4300 and the average cost is $0.50 + $4300/x
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