=====================================================
Work Shown:
|3x+12| = 18
3x+12 = 18 or 3x+12 = -18
3x = 18-12 or 3x = -18-12
3x = 6 or 3x = -30
x = 6/3 or x = -30/3
x = 2 or x = -10
The rule used in step 2 is the idea that if |x| = k, for some positive number k, then x = k or x = -k. One equation breaks into two separate ones. From there we solve each equation for x as normal. Follow PEMDAS in reverse, undoing each operation, to isolate x.
If you're curious why the absolute value breaks into two parts, consider something like |x| = 7. This means x is 7 units away from zero on a number line. There are two possible locations where x could be: 7 and -7. This is one example showing why we get two different results. The same applies to our equation as well, just it's a bit more complicated.
What is the slope of the line?
Answer:
See below.
Step-by-step explanation:
(2,1),(7,4)
4-1=3
7-2=5
3/5 is the slope.
-hope it helps
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2,1) and (x₂, y₂ ) = (7, 4) ← 2 points on the line
m = [tex]\frac{4-1}{7-2}[/tex] = [tex]\frac{3}{5}[/tex]
Please can someone help me with this.
y^2 - 2y when y=6
Answer:
See below.
Step-by-step explanation:
y^2-2y
6^2-2(6)
36-12
24
-hope it helps
Which shows the list of numbers in order from least to greatest?
|-4.2|, |-4/5|, |-1|, -2, |3.5|
Answer:
-4.2 (least) < -2 < -1 < -4/5 < 3.5 (greatest)
| | is called absolute value, but you can ignore it as |-4.2| equals to -4.2
Find the area of this parallelogram.
13 cm
15cm
20cm
Answer:
but we need the shape.. to know which is the big and the little basement..
130/240 in its simplest form
Answer:
13/24
Step-by-step explanation:
divide both sides by 10.
pls mark brainliest
Answer:
13/24
Divide the numbers by 10.
[tex]\frac{130/10}{240/10} = \frac{13}{24}[/tex]
With that information, the answer is 13/24.
A car drives 60 mph. Write and solve an eqaution to find the number of hours it takes the car to travel 360 miles.
Answer:
6 hours
Step-by-step explanation:
Let's highlight/bold some important terms.
A car drives 60 mph. Write and solve an eqaution to find the number of hours it takes the car to travel 360 miles.
So we know Speed multiplied by Time is equal to distance, or commonly known as;
S · T = D
So since we know this, we can substitute the values for the variables.
We know the mph is 60. And that's our speed.
The equation is now 60 · T = D
We know that the total distance the car needs to cover is 360.
The equation is now 60 · T = 360
Now we need to find the time it took.
We divide 360/60 to find out the total number of hours it took, and we get 6.
So the answer is that it took 6 hours to travel 360 miles with a speed of 60 mph.
Answer:
6 hours
Step-by-step explanation:
The starting price for a ticket for a high school play is $5. The auditorium capacity is 400 people. The organizer estimates that for every 10 cent increase in the ticket price 5 less people will attend the play. What is the best price and what is the maximum revenue that the school can get?
The best price is $6.50, and the maximum revenue that the school can get is $2,112.50.
Price determinationGiven that the starting price for a ticket for a high school play is $5, and the auditorium capacity is 400 people, and the organizer estimates that for every 10 cent increase in the ticket price 5 fewer people will attend the play, to determine what is the best price and what is the maximum revenue that the school can get, the following calculation must be made:
400 x 5 = 2,000395 x 5.1 = 2,014.5390 x 5.2 = 2028350 x 6 = 2100300 x 7 = 2100325 x 6.5 = 2112.5320 x 6.6 = 2112330 x 6.4 = 2112Therefore, the best price is $6.50, and the maximum revenue that the school can get is $2,112.50.
Learn more about price determination in https://brainly.com/question/13806160
The table shows the monthly profit of a company in the first half of the year 2017.
Months profits
January: 3 950
February: -1 500
March: -720
April: 1 270
May: 3 720
June: -4 800
Calculate the average monthly profit of the company for the first 6 months in 2017
[tex]\huge\underline\mathtt\colorbox{cyan}{320}[/tex]
Step-by-step explanation:
Avg=[tex] \frac{sum of all frequencies(Σfixi) }{number of frequencies(Σfi)} [/tex]Adding all the values gives 1920 So average= [tex] \frac{1920}{6} = 320[/tex]4+4x=2x+8+2x-5
Please help cant figure it out
A company is trying to decide which container of coffee to buy for a staff meeting. Which of the following would be the best deal?
Answer:
D) 45 ounces for $4.50
Step-by-step explanation:
You have to find the price of one unit (ounce) for each. You can do this by dividing the price by quantity. The one with the lowest price is the best deal.
A) 32 ounces for $4.00
$0.13 for 1 ounce
B) 60 ounces for $6.75
$0.11 for 1 ounce
C) 48 ounces for $5.00
$0.11 for 1 ounce
D) 45 ounces for $4.50
$0.10 for 1 ounce
The best choice will be option D. That is 45 ounces for $4.50.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
You have to find the price of one unit (ounce) for each. You can do this by dividing the price by quantity. The one with the lowest price is the best deal.
A) 32 ounces for $4.00
$0.13 for 1 ounce
B) 60 ounces for $6.75
$0.11 for 1 ounce
C) 48 ounces for $5.00
$0.11 for 1 ounce
D) 45 ounces for $4.50
$0.10 for 1 ounce
The complete question is given below.
A company is trying to decide which container of coffee to buy for a staff meeting. Which of the following would be the best deal? Hint: find the best unit cost
Group of answer choices
32 ounces for $4.00
60 ounces for $6.75
48 ounces for $5.00
45 ounces for $4.50
To know more about an expression follow
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#SPJ2
I need help!! Can an awesome genius please help me out?
Answer:
D
Step-by-step explanation:
Find a whole number $a$ such that the numbers $\frac{2}{a}$ , $\frac{a}{8}$ , and $63\%$ are in order from least to greatest
If 2/a, a/8, and 63% = 63/100 are in numerical order, then
2/a < a/8 < 63/100
Multiply each "side" of the inequality by 8a :
16 < a² < 126a/25
a has to be a whole number, and since 4² = 16, we must have at least a ≥ 5.
Divide through by a :
16/a < a < 126/25 = 5 + 1/25
Then at most, a ≤ 5.
So, both a ≥ 5 and a ≤ 5, which means a = 5.
Just to check that the list is in order, we have
2/a = 2/5 = 0.4
a/8 = 5/8 = 0.625
and 0.4 < 0.625 < 0.63.
Eli measures the length of a painted stripe on one wall of his room. The stripe is 1012 feet long. He wants to mark sections on the stripe that are each 78 feet long.
How many sections will be marked on the stripe?
(It says high school but it’s middle)
Answer:
im pretty sure its 12
Step-by-step explanation:
you have to do 1012 divided by 78 and you get 12.97, but since he wants them to all be 78 feet long, it cant be 13.
At the beginning of a snowstorm, Brianna had 2 inches of snow on her lawn . The snow began to fall at a constant rate of 2.5 inches per hour. Assuming no snow was melting, how much snow would Brianna have on her lawn 2 hours after the snow began to fall ? How much would Brianna have on her lawn after t hours of snow falling ?
Snow on lawn after 2 hours ?
Snow on her lawn after t hours ?
Answer:
2.11 inches long and 2.11 inches wide
State if the two triangles are congruent. If they are, state how you know.
Explanation:
AAS = angle angle side
The arc markings show us which pairs of angles are congruent. The pair of congruent sides are the shared overlapping sides. Notice that the sides are not between the red angles, so we go for AAS instead of ASA. The order is important.
We cannot use SAS because we only know info about one pair of congruent sides (not two).
lmc of x^2-4 and x^2-5x-14
Answer:
[tex]\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x^2-4,\:x^2-5x-14[/tex]
[tex]\mathrm{The\:LCM\:of\:}a,\:b\:\mathrm{is\:the\:smallest\:multiplier\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b[/tex]
[tex]x^2-4[/tex]
[tex]\mathrm{Rewrite\:}4\mathrm{\:as\:}2^2[/tex]
[tex]=x^2-2^2[/tex]
[tex]x^2-2^2=\left(x+2\right)\left(x-2\right)[/tex]
[tex]=\left(x+2\right)\left(x-2\right)[/tex]
[tex]x^2-5x-14[/tex]
[tex]=\left(x^2+2x\right)+\left(-7x-14\right)[/tex]
[tex]=x\left(x+2\right)-7\left(x+2\right)[/tex]
[tex]=\left(x+2\right)\left(x-7\right)[/tex]
[tex]\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power:}[/tex]
[tex]\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)[/tex]
Jimmy is in charge of seating students at a essembly one table can seat 6 students 78 students are going to the assembly how many tables will jimmy need
Answer:
13 tables
Step-by-step explanation:
Just do 78÷6 to get your answer
A train is traveling at a speed of 80 km/h when the conductor applies the brakes. The train slows with a constant acceleration of magnitude .5 m/s^2. We want to find the distance the train travels from the time the brakes are applied until the train comes to a complete stop. Which kinematic formula would be most useful to solve for the target unknown?
Answer:
The train will travel 493.817 meters until it stops completely.
Step-by-step explanation:
In this case, we know that train applies the brakes and decelerates at constant rate until rest is reached after travelling an unknown distance. Travelled distance ([tex]\Delta s[/tex]), measured in meters, can be found by using this kinematic formula:
[tex]v^{2} = v_{o}^{2}+2\cdot a \cdot \Delta s[/tex] (Eq. 1)
Where:
[tex]v_{o}[/tex] - Initial speed, measured in meters per second.
[tex]v[/tex] - Final speed, measured in meters per second.
[tex]a[/tex] - Acceleration, measured in meters per square second.
Now travelled distance is cleared within the formula:
[tex]\Delta s = \frac{v^{2}-v_{o}^{2}}{2\cdot a}[/tex]
If we know that [tex]v_{o} = 22.222\,\frac{m}{s}[/tex], [tex]v = 0\,\frac{m}{s}[/tex] and [tex]a = -0.5\,\frac{m}{s^{2}}[/tex], then the distance travelled by the train is:
[tex]\Delta s = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(22.222\,\frac{m}{s} \right)^{2}}{2\cdot \left(-0.5\,\frac{m}{s^{2}}\right) }[/tex]
[tex]\Delta s = 493.817\,m[/tex]
The train will travel 493.817 meters until it stops completely.
Answer:
v² = v²0 + 2aΔx
Step-by-step explanation:
At Tamu's Rental Center, customers can rent a moon bounce for a $50 rental fee plus $12 for each
hour they use the equipment.
Part A
Identify the initial value and the rate of change for the function that represents the situation.
The initial value is
The rate of change is
Part B
Write an equation in slope-intercept form that represents the situation. Use c to represent the total
cost.
What is .5 written as a fraction?
Answer:
1/2
Step-by-step explanation:
can someone help me it’s very urgent due soon!
Answer:
c
Step-by-step explanation:
Answer: I think A but im not 100% sure
Step-by-step explanation:
sorry if i let you down...
I dont understand this, please give an explanation
Answer:
[tex]\bold\blue{x {}^{2} + 5x + 4} [/tex]
Here ,
we just need to substitute " x = - 5 " in the equation above.
[tex]\bold{x {}^{2} + 5x + 4} \\\bold{ ( - 5) {}^{2} + 5( - 5) + 4} \\ \bold{ \cancel{25} - \cancel{25} + 4} \\ \fbox\pink{⇢ 4}[/tex]
hope helpful ~
[tex] \huge \qquad \boxed{ \sf Aᥒsᥕᥱr ☂}[/tex]
let's plug in the value of x as -5, in the given expression ~
[tex] \qquad\rightarrowtail \sf {x}^{2} + 5x - 4[/tex]
[tex] \qquad\rightarrowtail \sf { (- 5)}^{2} + 5( - 5) - 4[/tex]
[tex] \qquad\rightarrowtail \sf 25 - 25 + 4[/tex]
[tex] \qquad\rightarrowtail \sf 4[/tex]
Therefore, we got the required value 4
Basic Properties of Angles
Measure the angle in degrees.
120-
130
07
140-
Og
OZ
1504
160-
OT
70-
180
The angle measure is
Prove or disprove each of these statements about the floor and ceiling functions. a) ⌊⌈x⌉⌋ = ⌈x⌉ for all real numbers x. b) ⌊x+y⌋=⌊x⌋+⌊y⌋for all real numbers x and y. c) ⌈⌈x∕2⌉ ∕2⌉ = ⌈x∕4⌉ for all real numbers x. d)⌊√⌈x⌉⌋ = ⌊√x ⌋ for all positive real numbers x. e) ⌊x⌋+⌊y⌋+⌊x+y⌋≤⌊2x⌋+⌊2y⌋forall real numbers x and y.
Answer:
A) equality function will hold
B) equality function doesn't hold
C) equality function holds )
D) equality function doesn't hold
E) equality function holds
Step-by-step explanation:
a) ⌊⌈x⌉⌋ = ⌈x⌉ for all real numbers x.
The ceiling function will yield an integer, that is greater ≥ x.
Also the floor function when applied to an integer will yield the same integer value. hence the two sides will become the same Therefore the equality function will hold
b) ⌊x+y⌋=⌊x⌋+⌊y⌋ for all real numbers x and y
The floor function of this statement yields a value that is ≤ inserted value and this makes the right hand side of the statement to be 1 less than the sum produced from the left hand side of the statement, therefore the equality function doesn't hold
c) ⌈⌈x∕2⌉ ∕2⌉ = ⌈x∕4⌉ for all real numbers x.
The ceiling function produces an integer that is ≥ value inserted and the integer gotten is divided by 2 and this serves a s an input to the ceiling function( which means X has been divide by 4 ) making the two sides of the equation the same ( equality function holds )
d)⌊√⌈x⌉⌋ = ⌊√x ⌋ for all positive real numbers x
The ceiling function is applied to the value inserted in x(on the left hand side ), and the result will not be equal to that in the right hand side.
Therefore the equality function doesn't hold
e) ⌊x⌋+⌊y⌋+⌊x+y⌋≤⌊2x⌋+⌊2y⌋forall real numbers x and y.
If the value of the fractional part of x or y is > 0.5, then the right hand side will be greater than the left hand side by 1.
Otherwise, both left and right hand sides yield equal answers. therefore equality function holds
(18,15),(16,-6) what the answer to this problem
Answer:
whats the question? not enough info
richard built a model of a ferris wheel the model has a height of 18 cm the actual ferris wheel has a height of 72m what scale factor did richard use for the model
Answer:
1:400
Step-by-step explanation:
1 m = 100 cm
72 m = 7200 cm
Ratio of model size to real size
18 cm : 7200 cm
Divide both numbers by 18.
1 cm : 400 cm
Divide both sides by cm.
1:400
Pam and her brother both open savings accounts. Each begins with a balance of zero dollars. For every two dollars that Pam saves in her account, her brother saves five dollars in his account. 1. Determine a ratio to describe the money in Pam’s account to the money in her brother’s account.
Answer:
b
Step-by-step explanation:
please
work out
∛15.76 - 4.6³ ÷2.5/3
Answer:
-10.47413972 or -10.47
Step-by-step explanation:
Calculator
Answer:
-10.47 is the answer
Step-by-step explanation:
Calculator
which is the greatest value A.two and hundredhs B.two and five thousandths C.two and five tenths
Answer:
Two and hundredths
Step-by-step explanation: I'm in college so I think I am capable of answering a middle school question thank you very much, and make sure to mar me brainliest.
The class scores of a history test have a normal distribution with a mean Mu = 79 and a standard deviation Sigma = 7. If Opal’s test score was 72, which expression would she write to find the z-score of her test score?.
Using the normal distribution, we got that expression for the z-score of her test score is
[tex]z= \frac{72-29}{7} \\\\z=-7/7\\\\z=-1[/tex]
What is Normal Probability Distribution?it's a type of probability distribution which is symmetric about the mean, it gives data near the mean are more frequent than data far from the mean.
Given that mean =[tex]\mu=79[/tex]
and standard deviation =[tex]\sigma = 7[/tex]
X=73
we know that formula of z-score is
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Hence Z-score can be calculated as
[tex]z= \frac{72-29}{7} \\\\z=-7/7\\\\z=-1[/tex]
Using the normal distribution, we got that expression for the z-score of her test score is
[tex]z= \frac{72-29}{7} \\\\z=-7/7\\\\z=-1[/tex]
To learn more about the normal distribution visit : brainly.com/question/24663213
Answer:
72-29/7
Step-by-step explanation: i just took the test it's A