Subtracting from both sides leaves you with . Since subtraction can be written as addition (adding the opposite), the addition property of equality. If two expressions are equal to each other and you add the same value to both sides of the equation, the equation will remain equal.
The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. ... Performing the same operation on both sides of an equation does not change the validity of the equation, or the value of the variable that satisfies it.
Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Logan made a profit of $210. 00 as a mobile groomer. He charged $75. 00 per appointment and received $35. 00 in tips, but also had to pay a rental fee for the truck at $10. 00 per appointment. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
A) It is stated that Maci once earned $170 by grooming dogs.
For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;
170 = 60x + 50
the number of appointments is x.
B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;
210 = 75x + 35 - 10x
the number of appointments is x.
C) The quantity of tips they will receive even without an appointment varies between the formulae.
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For problems 1 - 6, determine whether the relationships represented are A. Exponential., B. Linear., or C. Neither.
Step-by-step explanation:
a linear function is following
y = ax + b
that means the ratio of the y and x differences between the data points is constant (a).
an exponential function is in the form y = a^x. or some constant variations of it.
the base is constant (a), and the exponent of the constant is the variable (x).
1.
clearly exponential.
this is the typical graph of an exponential function.
it looks like y = 2^x, as e.g. f(4) = 2⁴ = 16, and the graph seems to be at least very close to this.
2.
exponential.
y = 3^(x - 0.5)
3¹ = 3
3² = 9
3³ = 27
3⁵ = 243
this is just y = 3^x shifted to the right by 0.5 units.
3.
linear.
the difference ratio between the data points is constant :
x is the row number (1, 2, 3, 4, 5, ...).
y is the number of seats per row (14, 16, 18, 20, 22, ...).
so,
(16-14)/(2-1) = 2/1 = 2
(18-16)/(3-2) = 2/1 = 2
...
(22-14)/(5-1) = 8/4 = 2
always constant (2).
4.
neither.
it is y = x²
when you compare 4. and 1. you see the clear difference between the 2 graphs.
5.
exponential.
remember, y = a^x.
well, here, a = 1/2. but that is still constant and doesnot change the principle.
the factor 10 stretches the graph a bit up (in fact, this 10 is the starting number of an exponential growth). but the function in its core is still exponential.
6.
linear.
when written that way, it just means that x = n, and for every increase of n by 1, y (f(n)) increases by +4.
so, the difference ratio stays constant (4/1 = 4).
If the total daily wages of 7 women or 5 men is $525.What will be the daily wage of 13 and 7 women and men respectively?
Answer:
Daily wages of 13 woman = $975
Daily wages of 7 man = $735
Step-by-step explanation:
Given:
Daily wages of 7 women or 5 men = $525
Find:
Daily wage of 13 women and 7 men
Computation:
Daily wages of 1 woman = 525 / 7
Daily wages of 1 woman = $75
Daily wages of 1 man = 525 / 5
Daily wages of 1 man = $105
Daily wages of 13 woman = 13 x Daily wages of 1 woman
Daily wages of 13 woman = 13 x 75
Daily wages of 13 woman = $975
Daily wages of 7 man = 7 x Daily wages of 1 man
Daily wages of 7 man = 7 x 105
Daily wages of 7 man = $735
A cookery course is divided into two groups. In group X, the average score in the test was 76. In group Y, the average score in the test was 70. If the average score of all 30 trainees in the course was 74, how many trainees are in group X
On solving the provided question, we can say that by equation 8 trainees are in group X
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let a be the number of trainees in group X
76*a + 70 (30 - a) = 30*74
76a + 2,100 - 70a = 2,220
6a = 120
a = 20
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What is equal to 7 x 98
Answer:
[tex] \huge \colorbox{red}{Question}[/tex]
What is equal to 7 x 98️️️️
️️
️️️️
[tex] \huge \colorbox{green}{✍ Answer}[/tex]
7 × 98
7 × 98 = 686
Is 4/10 less than 4/6?
Answer:
No. 4/10 >4/6
Step-by-step explanation:
I hope this helps you :)
I don’t know this question
Help me
Answer: Probably negative 69
find the measure of y
Answer:
y+73=180
y=180-73
y=107°
Greta's bill for brunch was at a restaurant was $35. She left a 20% tip. What was the amount of the tip
Answer:
$7.00
Step-by-step explanation:
20% = 0.2
35(0.2) = 7
No solutions which one? This is well worth your time please assist.
Answer:
Option BStep-by-step explanation:
A linear system has no solution if both lines are parallel.It is when the lines have same slope but different y-intercepts.Review the options1. Option A.
If you double the first equation, then it will be exact copy of the second one. It means the lines overlap, and there are infinitely many solutions.
No2. Option B
Both the x and y have same coefficients, it means the slopes are same. The y-intercepts are different, so the lines are parallel and no solution.
Yes3. Option C
Multiply one of the equations by -1 to get exact same of the other equation. Same as option A, infinitely many solutions.
No4. Option D
Multiply the send equation by 6 and we'll have different slopes and y-intercepts. It means the lines intersect at one point so there is one solution.
NoWhats the value of x?
A. 12.73
B. 9
C. 25.46
D. 31.18
Answer:
if u feel like u find the value that is correct but if u didn't find it it can be 1 the power of x can be 1
Answer:
B.9
all done hope it help
Which region had the greatest growth in percentage of households with a computer between 2008 and 2018
The Africa region saw the largest increase in the proportion of households with computers between 2008 and 2018.
Which US has the lowest number of net customers?The least connected US in the arena is dictator-ruled Eritrea, located in the Horn of Africa, where it is most effective. Her 91% of citizens have internet access.In rural areas, almost a quarter of the population (14.5 million people) do not have access to this service. Nearly one-third of the population is inaccessible in tribal areas. Even in areas where broadband is available, about 100 million Americans are still unsubscribed.North Korea tops the list with near-zero internet penetration as citizens remain blocked from the internet.Interestingly, a small but growing percentage of offline households (4% in 2021) is reporting no internet access in the area, outnumbering households reporting their computers are not working. (Which was a big barrier 10 years ago). It was used but seems to have decreased significantly over time.To learn more about least net customers refers to:
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HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
☆ Emily has $16 more
Step-by-step explanation:
FOR JAXON:
You want to calculate the interest on $600 at 2.5% interest per year after 3 year(s).
The formula we'll use for this is the simple interest formula, or:
Where:
P is the principal amount, $600.00.
r is the interest rate, 2.5% per year, or in decimal form, 2.5/100=0.025.
t is the time involved, 3....year(s) time periods.
So, t is 3....year time periods.
To find the simple interest, we multiply 600 × 0.025 × 3 to get that:
The interest is: $45.00
Usually now, the interest is added onto the principal to figure some new amount after 3 year(s),
or 600.00 + 45.00 = 645.00.
Jaxon will have $645 after he closes his account.
FOR EMILY
You want to calculate the interest on $600 at 5.1% interest per year after 2 year(s).
The formula we'll use for this is the simple interest formula, or:
Where:
P is the principal amount, $600.00.
r is the interest rate, 5.1% per year, or in decimal form, 5.1/100=0.051.
t is the time involved, 2....year(s) time periods.
So, t is 2....year time periods.
To find the simple interest, we multiply 600 × 0.051 × 2 to get that:
The interest is: $61.20
Usually now, the interest is added onto the principal to figure some new amount after 2 year(s),
or 600.00 + 61.20 = 661.20.
Emily will have $661 when she closes her account.
☆ Therefore, Emily will have $16 more than Jaxon.
I would really appreciate if you would mark me brainliest!!
I hope you have a good day!!! ☆ :D
Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, use the drop-down menu below to write an inequality representing ss, the number of sets of glasses Julia should buy.
The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:
286 + 6s ≥ 316
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PLEASE SOMEONE ANSWER THIS ASAP I NEED YOUR HELP:
PQR is a non-right-angled triangle. QR is 5.1cm, RP is 7.8cm and PQ is 6.2cm. Find the area of PQR
Using Heron's formula the area of the triangle is 15.78cm²
What is Heron's FormulaHeron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:
Area = √s(s-a)(s-b)(s-c)
Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:
s = (a + b + c)/2
Let's define the variables as;
a = 5.1b = 7.8c = 6.2s = (5.1 + 7.8 + 6.2) / 2
s = 9.55cm
The area can be calculated as;
A = √s(s - a)(s - b)(s - c)
A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)
A = 15.78cm²
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Find X and Y.
I really need help on this. It’s confusing.
Step-by-step explanation:
7x-2 ) + (١١x -34)
so u will get the answer
after getting it u can easy get y
i neeeed helpppppppppppppp
Answer:
y = -3x + 5/2
Step-by-step explanation:
y = -3x + 5/2
In the figure shown, what is the value of x?
Answer:
Step-by-step explanation:
SHOW HIGH CLARITY IMAGE, BUT USE CONGRUENCE OF TRINALGES AND FIND X BY EQUATING THE GIVEN SIDE I GUESS
IF YES MARK ME BRAINLIEST
2/3
21 and 23 can best be described as
4
Answer:
A) Vertical angles
----------------------
1 and 3 and 2 and 4 are vertically opposite angles or vertical angles, so option A is correct.
-----------------------
hope it helps...
have a great day!!
I need help with this as well ty lol
Answer:
about 21.4
following Pythagorean theorem
JK and KL are the legs
Rule 1: Multiply by 2, then add 1/3 starting from 1. Rule 2: Add 1/2, then multiply by 4 starting from 0. What is the fourth ordered pair using the two sequences
Answer:
(10 1/3, 42)
Step-by-step explanation:
a1 = 1
a2 = a1×2 + 1/3 = 2 1/3
a3 = a2×2 + 1/3 = (a1×2 + 1/3)×2 + 1/3 = a1×4 + 2/3 + 1/3 =
= 4 + 3/3 = 5
a4 = a3×2 + 1/3 = ... = 10 1/3
b1 = 0
b2 = (b1 + 1/2)×4 = (0 + 1/2)×4 = 1/2 × 4 = 2
b3 = (b2 + 1/2)×4 = ((b1 + 1/2)×4 +1/2)×4 = 16×b1 + 16/2 + 4/2=
= 16/2 + 4/2 = 8 + 2 = 10
or (to check we made no mistake)
= (2 + 1/2)×4 = 8 + 2 = 10. => all ok, no mistake
b4 = (b3 + 1/2)×4 = ... = (10 + 1/2)×4 = 40 + 2 = 42
so, the fourth ordered pair (= the fourth elements of each sequence) is therefore (10 1/3, 42)
How many divisors of 4! x 3! x 2! x 1! are perfect squares?
There are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.
What is Number system?A number system is defined as a system of writing to express numbers.
The factorial 4! is 24
Factorial value of 3!=6
Factorial value 2!=2
Factorial value 1!=1
4! x 3! x 2! x 1! =24×6×2×1=288
288 can be written as a product 2 and 144 which are perfect squares.
So 2 and 144 are the divisors of 4! x 3! x 2! x 1!
Hence, there are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.
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Which expression is equivalent to 2.5(x - 1) + 4.5(-x - 2)?
Angle A and Angle B are complementary angles. The measure of Angle A is twice the measure of Angle B.
Write and equation to represent the complementary angle relationship between Angle A and Angle B. Use the equation to find
the measure of Angle A and B. Show all of your work.
Answer:
Acc.to question,
A+B=90° (since,they are complementary angles)
or,A+ A/2=90°(since,A is. twice the measure of B)
or,3A/2=90°
or,A=(90°×2)/3
:.A=60°
Also,
B=A/2=60/2=30°
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the greatest common factor of 12x-18
Answer:
6
Step-by-step explanation:
The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.
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The temperature in knowlton is 2.5 C colder than the terminal elmwood. Which equation shows the temperature, in C, in knowlton? 9 - 2.5 = 6.5 or 9 + 2.5 = 11.5 or -9 - 2.5 = - 11.5 or -9 + 2.5 = -6.5
The equation representing the asked situation is (9 - 2.5) = 6.5
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The temperature in Knowlton is 2.5 C colder than the terminal Elmwood.
We know, that, if temperature is colder in any area A than another area B then, A will have less temperature than B.
Therefore, temperature in Knowlton is less than that of in Elmwood.
Therefore, if the temperature in Elmwood is 9 the temperature in Knowlton will be 9-2.5 = 6.5
Hence, the required equation is 9-2.5 = 6.5
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Find the volume of the cone. Round your answer to the nearest tenth.
Answer:
The volume of the cone is 16.8 in cubed.
Step-by-step explanation:
The formula for a cone is πr^2 multiplied by h/3. The r is radius and h is height. So throwing in the values for the variables we get 16.8 in cubed.
1
Which line is pointing to the cell body?
A. 1
B. 2
C. 4
D. 5
2
3
4
5
Image by Dhp 1080
The line 2 is pointing towards the body of the cell, in the given image of a neuron.
What is cell body?The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.
When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.
The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.
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