Answer:
[tex]\fbox{\begin{minipage}{3em}x = 6\end{minipage}}[/tex]
Step-by-step explanation:
Given:
Equation: [tex]3x - 3 = 27 - 2x[/tex]
Solve for:
[tex]x[/tex]
Solution:
Step 1: Select relevant approach:
Let's move all the components containing x to the left side and other components to the right side (notice the change of sign of each one from + to - or - to +), then calculate [tex]x[/tex]
Step 2: Perform the calculation:
[tex]3x -3 = 27 - 2x[/tex]
Moving components:
<=> [tex]3x + 2x = 27 + 3[/tex]
Adding up components:
<=> [tex]5x = 30[/tex]
Dividing both sides by 5 (coefficient of component containing [tex]x[/tex]:
<=> [tex]\frac{5}{5} x = \frac{30}{5}[/tex]
Simplifying to work out [tex]x[/tex]:
<=>[tex]x = 6[/tex]
Hope this helps!
:)
Answer:
x = 6
Step-by-step explanation:
3x - 3= 27 - 2x
First we put all the x terms to on side, making it 3x + 2x - 3= 27.
Remeber that when we move a term to the other side of the equals sign (=), we change its sign to be the opposite of what it currently is.
Then, we move all the numberics to the other side, so we derieve 3x + 2x = 27 +3. Again, the sign changes when we move it across.
What is left to do is add up the quantities. So 3x + 2x = 5x and 27 +3 = 30.
We are left with 5x = 30. If 5 x's is 30, how much is one? Sinply divide it to get the answer of 30 / 5 which is six!
To make sure the answer is correct substituite 6 in the equation as x and see if its accurate: 3(6) -3 = 7 - 2 (6). And it is!
So x is equal to six.
I’ll mark you brainliest!!!!! Which point is a solution to the inequality represented by this graph?
Answer:
A is a solution because it is in the shaded area.
Step-by-step explanation:
Click on the bubble of the correct
answer.
Chris earned $855 for a temporary
job. She worked 36 hours the first
week and 40 hours the second
week. How much did Chris earn per
hour?
Select one:
Answer:
$11.25 / hr
Step-by-step explanation:
36x+40x=855
76x=855
x=11.25
when rewriting in the form y=a(x-h)+k, by completing the square, the relation y=-x*2+6x+12 becomes:
Answer:
Step-by-step explanation:
you can complete the square or use a calculator online that does it for you.
the equation is in the for y = a(x-h)^2 + k
it should be y = (x + 3)^2 + 3
Answer:
The correct answer is [tex]y = - (x - 3)^{2} +21[/tex].
Step-by-step explanation:
To solve this equation (y = [tex]-x^{2} +6x + 12[/tex]), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve [tex]y = -x^{2} +6x - 9 + 12[/tex].
Then, you want to add the -9 to the other side of the equation to get [tex]y - 9 = -x^{2} + 6x - 9 + 12[/tex].
Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with [tex]y - 9 = -(x^{2} -6x+9) + 12[/tex].
Now, we use an identity in algebra that is difference of two squares identity. This says that [tex]a^{2} -2ab +b^{2} =(a-b)^{2}[/tex].
So, we will then factor the trinomial -[tex]x^{2} -6x+9[/tex] to get [tex]-(x-3)^{2}[/tex]. Our new and updated equation is [tex]y-9 = -(x-3)^{2} +12[/tex].
Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us [tex]y = -(x-3)^{2} +21[/tex].
This is our final equation.
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
Alex, Stephen and Bridget share some sweets in the ratio 4:1:1. Alex gets 36 sweets. How many sweets are there altogether?
Answer:
There are 54 total sweets
Step-by-step explanation:
Alex: Stephen : Bridget : total
4: 1 : 1 : 4+1+1 = 6
Alex gets 36
36/4 = 9
Multiply each number by 9
Alex: Stephen : Bridget : total
4*9: 1*9 : 1*9 : 6*9
36: 9 : 9 : 54
There are 54 total sweets
HELP!!!! Identify the volume of the composite figure rounded to the nearest tenth.
Answer:
4618.1 ft³
Step-by-step explanation:
Volume of the cone:
[tex]V_{cone} = \frac13 \pi r^2 h[/tex]
[tex]V_{cone} = \frac13 \cdot \pi \cdot 49 \cdot 12 = 196\pi[/tex]
Volume of the cilinder:
[tex]V_{cilinder} = \pi r^2 h[/tex]
[tex]V_{cilinder} = \pi \cdot 49 \cdot 22 = 1078\pi[/tex]
Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³
Calculate the measures of variability for the data set. The range is
The probability of getting a number divisible by 3 is 3/10 using a game spinner.
The denominator of that probability is:
Answer:
B
Step-by-step explanation:
the denominator should be the total amount of outcomes.
The budget for Ohio is 69.1 billion with a population of 11.69 million residents. Round all scientific answers with two decimals with no spaces. Example: 1.23x10^4 or 1.23E4 Write the budget in scientific notation. 1 point Debt: Write the population in scientific notation. 1 point Population: Calculate the Budget Per Capita and write your answer in standard notation. Round to a whole number. 2 points Use the budget per capita in a sentence explaining what this value means. 4 points
Answer:
Step-by-step explanation:
Hello,
This question requires us to convert numbers from standard form to scientific form. This can easily be done using a calculator or just writing the number down then put a decimal point after the first digit and count the rest which would be raised to the power of that number.
Budget = 69.1 billion
Converting this to scientific form = 6.91×10¹⁰
Population = 11.67 million
Converting this to scientific form = 1.167×10⁷
Budget per capita refers to budget allocated to each individual in the population.
Budget per capita is used to compare economic indices or indicators of various countries with different population sizes.
Budget per capita = budget / total population
Budget per capita = 6.91×10¹⁰ / 1.169×⁷
Budget per capita = 5911.03
What this implies is that for each individual living in the state of Ohio, the amount budgeted for that particular period (mostly in a given year) is 5911.03
I really need help with this I don't understand it.
Answer:
(10x + 37) and (15x+7) are vertical angles which are always equal
10x + 37 = 15x +7
5x = 30
x = 6
The angle (15x +7) equals 97 and the other angle (10x + 37) also equals 97 degrees. All 4 of the angles add up to 360 degrees.
Therefore, 360 = 2z + 97 + 97
2z = 166
z = 83
Step-by-step explanation:
What’s the 73rd term of the sequence 18,30,42
Answer:
Let's find the explicit rule for this arithmetic sequence. We have:
aₙ = a₁ + (n - 1) * d
= 18 + 12 * (n - 1)
= 12n + 6.
The 73rd term is 12 (73) + 6 = 882.
What is the angle relationship shown below?
A)Corresponding
B)Same side interior
C)Alternate interior
D)Alternate exterior
E)Vertical
Answer:
The relationship between the angles is alternate exterior angles.
Step-by-step explanation:
Exterior means outside.
Alternate means every other or in this case across form each other.
These angles represent alternate exterior angles because they are on the outside of the transversal and they are alternating each other.
Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
The trip is 45 and 1/2 miles long
Step-by-step explanation:
Is number one congruent? If it is how?
Answer:
Yes, Triangles in (1) are congruent
Step-by-step explanation:
Two conditions must be satisfied before two triangles can be deemed or declared as being congruent.
1.) They must posses similar shape
2.) They must posses similar size ( that is the corresponding sides and angles of both triangles must be the same)
Triangles in (1) meet both criterias by possessing similar shape with the size and length of the corresponding angles also being the same.
Therefore, the two triangles are congruent.
no solution for 6x-3x+4-2x
Answer:
4+x
Step-by-step explanation:
you combine your like terms so you take 6x-3x and you end up with 3x than you take that 3x and subtract the 2x from it so you are left with just x so that would be 4+x
Complete the equation of the line through (–6,5) and (-3, -3).
Use exact numbers.
Answer:
-3, -3
Step-by-step explanation:
What’s the square root of 500
Answer:
22.360679775
Step-by-step explanation:
i used a calulator on the web
Answer:
±10 sqrt(5)
Step-by-step explanation:
sqrt(500)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(100*5)
sqrt(100) sqrt(5)
±10 * sqrt(5)
Write an integer that represents this scenario:
18-point gain
Answer:
+18
Step-by-step explanation:
A gain is a positive number
+18
Answer:
+18
Step-by-step explanation:
Neg = Drop
Pos = Gain
Gain so +
+18
I will mark you brainliest! How much money did Nikki orginally invest?
Answer:D
Step-by-step explanation:
PLZ ANSWER THIS ASAP
Answer:
C. Hollow cone frustum
Step-by-step explanation:
Revolved it in my head, because the line isn't touching the triangle it will be hollow, because the triangle has a slope the shape will taper.
Looking at the histogram, where would the median fall?
Answer:
The median would be found in the middle of the histogram
Step-by-step explanation:
It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.
Hope this helps.
Answer:
70-79
Step-by-step explanation:
I took the test :)
Probability Race game
Read the whole thing. Question 2 will be posted separately to make the question simple.
Question 1:
Why should you not play this game with Roland? Use probability to prove that
the game is unfair and Roland is likely to win. SHOW ALL YOUR WORK!
Answer:
see below
Step-by-step explanation:
There are 36 possible outcomes when rolling 2 die
P( number) = number of times the sum appears / total outcomes
p(1) =0/36
P(2) = 1/36
p(3) = 2/36
p(4) = 3/36
p(5) = 4/36
p(6) = 5/36
p(7) = 6/36
p(8) = 5/36
p(9) = 4/36
p(10) = 3/36
p(11) = 2/36
p(12) = 1/36
Since he picked first he has the greatest odds so he is most likely to win
The equation a=180(n-2)/n represent the angle measures,a in a regular n-sided polygon. When the equation is Solved for n,n is equal to a fraction with a denominator of a-180. What is the numerator of the fraction.
Answer:
The
numerator is 360
Step-by-step explanation:
What we need to do here is make n the subject of the formula;
a = 180(n-2)/n
an = 180n-360
180n - an = 360
n(180-a) = 360
n = 360/(180-a)
Fatima has 72 oranges. Four oranges are needed to make a glass of freshly squeezed orange juice. How many glasses of orange juice can she make?
Answer:
Step-by-step explanation:
18
Which datum is most unlikely to occur? A. a 7 foot tall person if the mean is 6 feet and the standard deviation is 3 inches B. a 13 foot tall moose if the mean is 12 feet and the standard deviation is 4 inches C. a 17 foot tall filbert tree if if the mean is 20 feet and the standard deviation is 6 inches D. a 20 foot tall giraffe if the mean is 23 feet and the
Answer: idk man
Step-by-step explanation: rg
Answer:iidk
Step-by-step explanation:
what does the symbol mean on the image?
Answer:
Step-by-step explanation:
a) U -----> union
Union of two sets is the set of all distinct elements that are in A or B
A U B = {8 , 14 , 17 , 16, 9 , 15}
∩ ----------> intersection
Intersection of two sets is the set of all distinct elements that are in both A and B
A ∩ B = {14,17}
b) A' = {9 , 15 , 16 , 10 , 11 , 12 , 13}
P(A') = 7/10
what is the answer to 18−(2x+1) = ???
Answer & Step-by-step explanation:
18 - (2x + 1)
Distribute the negative sign (-) to 2x + 1.
18 - 2x - 1
Put -2x in the beginning of the expression and combine like terms.
-2x + 17
So, the answer to 18 - (2x + 1) is -2x + 17.
En una granja se observa que por 12 patos hay 5 gallinas, por tres gallinas hay 8 pavos ;por 10 pavos hay 9 cerdos. ¿A cuantos patos equivalen 7 cerdos?
Answer:
7 ducks equals 7 pigs.
Step-by-step explanation:
English Translation
On a farm it is observed that for 12 ducks there are 5 chickens, for three chickens there are 8 turkeys, for 10 turkeys there are 9 pigs. How many ducks equals 7 pigs?
Solution
For 12 ducks, there are 5 chickens
12 ducks = 5 chickens
For 3 chickens, there are 8 turkeys
3 chickens = 8 turkeys
For 10 turkeys, there are 9 pigs
10 turkeys = 9 pigs
We first need to create a direct relationship between ducks and pigs to know how many ducks are equivalent to 7 pigs.
9 pigs = 10 turkeys
8 turkeys = 3 chickens
10 turkeys = (10×3/8) chickens = 3.75 chickens
Hence, 9 pigs = 10 turkeys = 3.75 chickens
9 pigs = 3.75 chickens.
12 ducks = 5 chickens
5 chickens = 12 ducks
3.75 chickens = (3.75×12/5) ducks = 9 ducks.
9 pigs = 3.75 chickens = 9 ducks
9 pigs = 9 ducks.
Hence, 7 pigs = 7 ducks too.
Hope this Helps!!!
21. A quantity of food would last a
family of 5 for 21 days. How long
would the same quantity last a
family of 7 if thev all eat at the same
rate?
Answer:
15 days
Step-by-step explanation:
5 x 21 = 105
105/7 = 15
Answer:
15 days
Step-by-step explanation:
As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.
Let the number of days taken by a family of 7 to finish a quantity of food be x.
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{1}{\frac{7}{5} }[/tex]
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{5}{7}[/tex]
⇒ x = [tex]\frac{21 * 5}{7}[/tex]
x = 15
∴ It would take a family of 7 15 days to finish a quantity of food.
Hope this helps!!!
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!
Answer:
-2 = not in domain
0= in domain
3= in domain