We use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
Given,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
We have to Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
We have,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
If we multiply 10 on both sides of the equation, we get
10 (4.2x – 1.5) = 10 (1.7x + 8.3)
10 x 4.2x - 10 x 1.5 = 10 x 1.7x + 10 x 8.3
42x - 15 = 17x + 8.3
We get,
42x - 15 = 17x + 8.3 which is equivalent to equation 2.
This property is called the multiplicative property of equality.
Thus we use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
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James is playing an arcade game with tokens. In the first
game, he hits the jackpot and doubles the number of
tokens that he has. In the second game, James wins 12
more tokens. In his third and final game, he loses 4
tokens. James now has 170 tokens. How many tokens
did he have before he started playing the game?
Answer
81 tokens
Step-by-step explanation:
x+12-4=170
x+8=170
-8 -8
x=162
162/2=81 tokens
The number of tokens he had before he started playing the game is 81 tokens.
Given,
James is playing an arcade game with tokens.
In the first game, he hits the jackpot and doubles the number of tokens that he has.
In the second game, James wins 12 more tokens.
In his third and final game, he loses 4 tokens. James now has 170 tokens.
We need to find how many tokens did he have before he started playing the game.
What does the term mean?Doubles = multiply by 2
x more than M = M + x
Loses x from M = M - x
We have,
Let the number of tokens he had initially be M.
First game:
Doubles the number of tokens
= 2M
Second game:
James wins 12 more tokens.
= 2M + 12
Third game:
Loses 4 tokens.
= 2M + 12 - 4
= 2M + 8
James now has 170 tokens
This means:
2M + 8 = 170
2M = 170 - 8
2M = 162
M = 162 / 2
M = 81
Thus the number of tokens he had before he started playing the game is 81 tokens.
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It takes 15 minutes to preheat your oven to 325 degrees. For an oven preheated to 325 degrees, the recommended cooking time for a turkey is about 16 minutes per pound
(a) Use a formula to express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds.
(b) Use your formula from part (a) to find the approximate time required to prepare a turkey weighing 14 pounds.
(a) The formula for the total time T, in minutes, needed to preheat the oven and bake a turkey weighing p pounds is T = 15 + 16p.
(b) The approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
We have,
(a)
To express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds, we can use the formula:
T = 15 + 16p
The first term, 15, represents the time needed to preheat the oven to 325 degrees (in minutes).
The second term, 16p, represents the recommended cooking time per pound for a turkey weighing p pounds (in minutes).
(b)
Using the formula T = 15 + 16p, we can find the approximate time required to prepare a turkey weighing 14 pounds:
T = 15 + 16 * 14
T = 15 + 224
T = 239
Therefore, the approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
Thus,
(a) The formula for the total time T, in minutes, needed to preheat the oven and bake a turkey weighing p pounds is T = 15 + 16p.
(b) The approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
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Compute 81^3/4
Plz help :)
Answer:
531441/4
Step-by-step explanation:
Answer:
81.75!
Step-by-step explanation:
hope this helps! i worked this one out so if its wrong please tell me! シ︎
Ordering Rational Numbers
Answer:
0.07 < 7/50 < 0.5
Step-by-step explanation:
7/50=0.14
=>0.07<0.14<0.5
what is 2 times 4 equal
Answer:
8
Step-by-step explanation:
Step 1: Convert to math
2 times 4 = 2 x 4
Step 2: Multiply
2 x 4 = 8
This is the same as 2 x 2 x 2 or 2³
Answer:
2 x 4 = 8
Step-by-step explanation:
2(4)=8
2+2+2+2=8
They will build another fence that is 48 feet long. The posts can be a minimum of 5 feet apart and a maximum of 9 feet apart. The posts should be equally separated. Design a fence that uses the fewest posts possible. How far apart should each post be placed?
Hurry
Write 7.63 as a mixed number in simplest form.
[tex]7\frac{63}{100}[/tex]
Step-by-step explanation:
Hey there!
ANSWER: [tex]7\frac{63}{100}[/tex]EXPLANATION:7.63 as a mixed number form
If you want to write 7.63 as a mixed number form, you have to make 7 the whole number because it is in the ones and 63 is the fraction because it comes after the decimal point.
[tex]7.63=7\frac{63}{100} \text{(ANSWER)}[/tex]
Hope this helps!
[tex]\text{-TestedHyperr}[/tex]
The price of an item has been reduced by $8.35. The new sale price is $21.36. What was the original price. answer fast!
Answer:
$29.71
Step-by-step explanation:
just add the reduced price to the amount you took away: 8.35+21.36=29.71
Answer:
$29.71
Step-by-step explanation:
$21.36 + $8.35 = $29.71
hope this helps pls give brainliest
e. Lindsey sold stationery to her family and her mother's friends. She deposited the $125
she earned in a savings account. The account earns 5.18% interest annually. If she does
not deposit or withdraw any money from for 18 months, how much will she have in her
account?
Answer:
$134.71
Step-by-step explanation:
This is a simple interest question
A = P(1 + rt)
A = Amount after t months or years
P = Principal or amount saved
r = interest rate = 5.18% = 0.0518
t = time.in years = 18 months
= 1 year and 6 month
= 1.5 year
A = $125( 1 + 0.0518 × 1.5)
A = $125 ( 1 + 0.0777)
A = $125(1.0777)
A = $134.71
You bought 12 raffle tickets that are good for 4 raffles. If 715 total tickets were sold what is the probability that you will win at least 1 of the raffles?
Answer:
0.06546.
Step-by-step explanation:
Total number of tickets = 715
Good raffle tickets (Prize) = 4
Number of tickets bought = 12
[tex]\text{Probability of winning}=\dfrac{\text{Number of tickets bought}}{\text{Total raffle tickets}}[/tex]
[tex]\text{Probability of winning}=\dfrac{12}{715}[/tex]
[tex]\text{Probability of not winning}=1-\dfrac{12}{715}=\dfrac{703}{715}[/tex]
Let x be event of the number of winning prizes.
Probability that you will win at least 1 of the raffles is
[tex]P(x\geq 1)=1-P(x=0)[/tex]
[tex]P(x\geq 1)=1-^{4}C_0\left(\dfrac{12}{715}\right)^0\left(\dfrac{703}{715}\right)^{4-0}[/tex]
[tex]P(x\geq 1)=1-\left(\dfrac{703}{715}\right)^{4}[/tex]
[tex]P(x\geq 1)=1-0.93454[/tex]
[tex]P(x\geq 1)=0.06546[/tex]
Therefore, the required probability is 0.06546.
Jada is evaluating 8 × 3 × 4. She doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first. Which property is Jada using? associative property distributive property commutative property
Answer:
plz explain correctly please
Answer:
It would be Associative because she is Multiplying in different groups, so for example you said that she didn't know what 24 x 4 was so then she took 3 x 4 so she just regrouped the numbers to get the answer needed.
Find the volume of the parallelepiped with the given vertices:(1,2,1), (2,3,4), (3,4,5), (2,3,2), (3,3,3), (4,4,6), (4,4,4), (5,5,7)
Answer:
0
Step-by-step explanation:
three vectors are
[tex]u=(2,3,4)-(1,2,1)=(1,1,3)[/tex]
[tex]v=(3,4,5)-(1,2,1)=(2,2,4)[/tex]
[tex]w=(2,3,2)-(1,2,1)=(1,1,1)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 2 & 2 & 4 \\ 1 & 1 & 1\end{array}\right|=(-2,2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
2
three vectors are [tex]u=(4,4,6)-(3,3,3)=(1,1,3)[/tex]
[tex]v=(4,4,4)-(3,3,3)=(1,1,1)[/tex]
[tex]w=(5,5,7)-(3,3,3)=(2,2,4)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 1 & 1 & 1 \\ 2 & 2 & 4\end{array}\right|=(2,-2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
Write the sum without sigma notation. Then evaluate the sum.∑2k=1 40k/k+3Choose the correct answer belowA. (40⋅1/1+3)+(40⋅2/2+3) B. 40k/2+3 C. 40⋅2/2+3 D. (40⋅1.1+3)+(40⋅2/2+3)+(40⋅3/3+3)
Answer:
A. (40⋅1/1+3)+(40⋅2/2+3)
Step-by-step explanation:
Given that:
[tex]\sum \limits ^2 _{k=1} \dfrac{40 \ k }{k + 3}[/tex]
which can be expressed as:
=[tex]\dfrac{40\times 1 }{1 + 3} + \dfrac{40\times 2 }{2 + 3}[/tex]
=[tex]\dfrac{40 }{4} + \dfrac{80 }{5}[/tex]
= [tex]10+ 16[/tex]
= 26
∴
[tex]\sum \limits ^2 _{k=1} \dfrac{40 \ k }{k + 3} = 26[/tex]
Express 120 as a percentage of 75
Answer:
62.5%
Step-by-step explanation:
75/120 x 100
= 62.5%
7x2x2x2 is the prime factorization for which of the following
А
72
B
56
С
44
D
28
Last week Asanji ran 17 miles more than Scott. Asanji ran 22 miles. How many miles did Scott run?
Answer:
Scott ran 5 miles
Step-by-step explanation:
22-17=5
Reasonableness...
5+17=22
Answer: 39 <3 ^_^
Step-by-step explanation: Last week Asanji ran 17 miles more than Scott. Asanji ran 22 miles. How many miles did Scott run? 17+22=
11
Line y is longer than line x. But by how many millimetres? Please show your working out?
(2 points)
x)
y)
CM RULE
0
5 cm
10 cm
Enter your answer
I
Answer:
Step-by-step explanation:
10-5=5
The width of a rectangle is 4 inches less than the length. The perimeter is 60 inches. Find the length and the
width
Answer:
Length=17
width=13
Step-by-step explanation:
W=width
L=length
Perimeter = 2w+2l since it's a rectangle
W=l-4 (given)
Plug into perimeter equation
Perimeter =(2l-8)+2l
=4l-8
60=4l-8
68=4l
17 =l
W=l-4=17-4=13
Find m∠POQ if ∠POQ and ∠QOR form a linear pair, as shown in the figure.
Answer:
155
Step-by-step explanation:
∠QOR= 25
∠POQ = x
here sum of both angles is 180 ( by linear pair)
therefore,
∠QOR + ∠POQ =180
25 + x = 180
x=180-25
x=155
hence, ∠POQ= 155
4x+2x=24 i need the answer
Answer:
x =4Step-by-step explanation:
[tex]4x+2x=24\\\\\mathrm{Add\:similar\:elements:}\:4x+2x=6x\\6x=24\\\\\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{24}{6}\\\\Simplify\\x=4[/tex]
Answer:
x =4
Step-by-step explanation:
[tex]4x+2x=24[/tex]
Simplify
[tex]6x = 24[/tex]
Divide both sides of the equation by 6
[tex]\frac{6x}{6} = \frac{24}{6} \\\\x = 4[/tex]
What is the probability of flipping two coins and both landing tails? Enter your answer in decimal form.
Answer:
If a=100dgree find C pllzzzzzzzzzzzzzzzzs
I can't figure it out
Answer:
Domain: x ≥ 7
Range: y ≥ -1
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Range is the set of y-values that can be outputted from function f(x).
We know that we can't take a square root of a negative and get a real number. The closest we can get is the square root of zero, no less.
What x-value renders the square root 0? x = 7 does, and we can't go less than that or we will get imaginary numbers. Therefore, the domain is x ≥ 7.
To find the range, we simply solve the rest of the function when x = 7, as we cannot go any lower.
y = 0 - 1
y = -1
Therefore, our range has to be y ≥ -1 because that would be the lowest y-value outputted from the lowest x-value.
An education center offers a total of 400 math, physics and
chemistry courses. The ratio of the number of math to physics
to chemistry courses is 3:4:3.
The cost of a math class is $25 per class and the cost of a
physics class is $20 per class. If you took all 400 classes, it
would cost a total of $9,800. What is the price of each
chemistry class?
$
Answer:
$30
Step-by-step explanation:
The price of each chemistry class is $30.
I NEED HELP PLEASE! The approach ramp used by a daredevil motorcyclist for flying over a pit of venomous snakes has a rise of 52 feet for every 80 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent.
Answer:
65%
Step-by-step explanation:
The formula for the grade of the ramp = Rise of the ramp/ horizontal distance of the ramp
Rise of the ramp = 52 feet
Horizontal distance = 80 feet
Grade of the ramp = 52 feet/80 feet
= 0.65
The grade of the ramp is 0.65
Rounding up to the nearest whole percent
Grade of the ramp = 0.65 × 100
= 65%
Therefore, the grade of the ramp to the nearest whole percent = 65%
An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there altogether?
Answer:
1050
Step-by-step explanation:
I'm pretty positive it would be 1050 by multiplying 50 and 20 and adding 50
The total number of seats in the auditorium are 2225.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats.
We can write the sequence as -
20, 21, 22, 23, 24, .......,
It is a arithmetic sequence. We can write the total number of seats in the auditorium as the sum of the terms of the sequence. We can write -
S{n} = (50/2)(2 x 20 + 49 x 1)
S{n} = 25(40 + 49)
S{n} = 25 x 89
S{n} = 2225
Therefore, the total number of seats in the auditorium are 2225.
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during the week of the country fair, fifteen thousand, six hundred nine entry tickets were sold. Is it correct to write the number as 15,069 explain.
Answer:
No. It's 15,609
Step-by-step explanation:
The fifteen thousand represents the 15,000
The six hundred is 600
The nine is 9.
So it is 15,609
9
Dusty found out that each grain of sand weighs 40000 or .000025 of a pound. He decides to write this
number in scientific notation.
2.5 x 10
What value should Dusty record in the box?
Record your answer and fill in the bubbles on your answer
document. Be sure to use the correct place value.
Answer:
[tex]n = -5[/tex]
Step-by-step explanation:
Given
[tex]Digit = 0.000025[/tex]
Required
Rewrite using scientific notation, then find n
[tex]Digit = 0.000025[/tex]
Express as fraction
[tex]Digit =\frac{25}{1000000}[/tex]
This can be splitted to
[tex]Digit = 25 * 10^{-6}[/tex]
The first number must be between 1 and 10; hence, 25 can be expressed as 2..5 * 10
[tex]Digit = 2.5 * 10* 10^{-6}[/tex]
Apply law of indices
[tex]Digit = 2.5 * 10^{1-6}[/tex]
[tex]Digit = 2.5 * 10^{-5}[/tex]
Comparing n, the given options
[tex]n = -5[/tex]
Write the rule for the table, use x for the input.
Input Output
-1,0,1,2,3,4 1,9,17,25,33,41
Step-by-step explanation:
so you take the numbers and put them in order from least to greatest. so it would be negative -1, 0, 1, 1, 2, 3, 4, 9, 17, 25, 33, 41 .
Vanessa runs a dog kennel. There are 45 dogs at the kennel today, and she needs to collect the correct size bowls for feeding time. 1/5 of the dogs need a small size bowl 20 of the dogs need a medium size bowl the rest need a large size bowl How many dogs need a large size bowl?
Answer:
20
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
One fifth of 45 = 45/5=9
This means 9 dogs require small bowls.
If 9 require small, 20 require medium and the rest require large, then 45-9-20=16
16 dogs need large size bowl.
Hope this helped!
Diego arranges the students in his math class from shortest to tallest and measures the height in inches of each student in the class. Use the shape of the distribution to compare the mean and median. Are the mean and median equal? If not, which is greater? Explain your reasoning.
Answer:
Explained below.
Step-by-step explanation:
A graph is formed using the height of students in Diego's math class.
It is provided that he arranges the students from shortest to tallest and measures the height in inches of each student in the class.
A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution and the graph has a longer tail towards the right.
For a positively skewed data: Mean > Median
A distribution is said to be skewed to the left, or negatively skewed, if maximum of the data are collected on the right of the distribution and the graph has a longer tail towards the left.
For a negatively skewed data: Mean < Median
A distribution is said to be symmetric, if maximum of the data are collected in the middle of the distribution and the graph has equal proportion of tails on both sides.
For a symmetric data: Mean = Median