Solve for w.
3w=84
Simplify your answer as much as possible.
w = 1
We can't really use w = 1 in this equation because it would be a false equation.
3w = 84
3(1) = 84
3 ≠ 84
If we were to solve for w then we can divide 3 to both sides.
3w = 84
3w/3 = 84/3
w = 28
______
Best Regards,
Wolfyy :)
Hey there!
3w = 84
DIVIDE 3 to BOTH SIDES
3w/3 = 84/3
CANCEL out: 3/3 because it give you 1
KEEP: 84/3 because it give you the w-value
NEW EQUATION: w = 84/3
SIMPLIFY IT!
w = 28
Therefore, your answer is: w = 28
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A store advertises that customers can take 25% off original price and then take an extra 10% off is this the same as 35% off discount explain
Answer:
Yes
Step-by-step explanation:
the total discount allowed will be 25% of the original price and futher 10% of the original price which will amount to 10%+25% and this equal 35%
What is the equation of a line with a slope of −4 and a point (−2, 5) on the line? Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Answer:
y = - 4x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + b ← is the partial equation
To find b substitute (- 2, 5) into the partial equation
5 = 8 + b ⇒ b = 5 - 8 = - 3
y = - 4x - 3 ← equation of line
Answer:
y= -4x-3
Step-by-step explanation:
to find this, the first step is easy. We know the slope is -4 so we have y= -4x+b. Then we to find the y intersept, so we take the point that we have (-2,5) and make x (the first number) equal to 0. to do this we add two, which means to subtract 8 from give because the slope is -4. This gives the point (0,-3). So the equation is y= -4x-3.
all real numbers y that are less than 4 or greater than 9
Answer:
Y<4 or y>9
Hope this helps you out!
Harper works at an electronics store as a salesperson. Harper earns a 6% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Harper made a total of $2600 in sales and earned $137 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Harper made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
Answer:
The system of equations are
x + y = 2600 …….equation (1)
and, 6x + 5y = 13700 ……equation (2)
Explanation:
Let x = amount of sales of phone;
y = amount of sales of computer
For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.
Similarly for computer,
5% of y = 0.05y
Given the total sales; x + y = 2600
And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700
Therefore the system of equations are
x + y = 2600 …….equation (1)
6 x + 5 y = 13700 ……equation (2)
The camera Melissa wanted for her birthday is on sale at 36% off the usual price. The amount of the discount is $180.00. What was the original price of the camera?
The original price of the camera was $1
Answer:
Original Price = $500
Step-by-step explanation:
The discount is 36%
and the discount amount is $180
Thus,
we can say that 180 is 36% of what number?
We let that number be "x" (original price). So we can say:
180 is 36% of x
In equation that will be:
180=36%*x
180=(36/100)*x
180=0.36x
So,
x = 180/0.36
x = $500
This is the original price.
Can someone help me with this problem? It’s Special Right Triangles: Decimal Answer. Round to the nearest tenth. Thank you ! 10 points
Answer:
h = 1.4
c = 2.8
Step-by-step explanation:
For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.
For the triangle with the variable h:
Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.
In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.
[tex]\frac{1}{\sqrt2} =\frac{h}{2} \\h = 2\frac{1}{\sqrt2} \\h = \frac{2}{\sqrt2} \\h = \frac{2\sqrt2}{2} \\h = \sqrt{2}[/tex]
h = √2
h ≈ 1.4
For the triangle with the variable c:
The is an equilateral triangle cut in half because the angles are 30 and 60.
The side ratio of altitude to hypotenuse is √3 to 2.
[tex]\frac{\sqrt{3} }{2} =\frac{c}{4} \\\sqrt{3} = \frac{c}{2}\\2\sqrt3 = c[/tex]
c = 2√2
c ≈ 2.8
Brandi jogged 2 1\2 miles in 30 minutes. Sharma jogged 3 1\2 miles in 3\4 hour. who jogged at slower rate
Answer:
The speed of Sharma is slower than the speed of Brandi
I.e ∵ 4.67 miles per hour [tex]<[/tex] 5 miles per hour
∴ [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]
Step-by-step explanation:
Given as :
The distance cover by Brandi = [tex]D_1[/tex] = 2 [tex]\frac{1}{2}[/tex] =[tex]\frac{5}{2}[/tex]
The Time taken by Brandi for jogging = [tex]T_1[/tex] = 30 minutes =[tex]\frac{1}{2}[/tex] hour
Let the speed of Brandi = [tex]S_1[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]
or, [tex]S_1[/tex] = [tex]\dfrac{\textrm [tex]D_1[/tex] }{\textrm [tex]T_1[/tex] }[/tex]
Or. [tex]S_1[/tex] = [tex]\frac{\frac{5}{2}}{\frac{1}{2}}[/tex]
∴ [tex]S_1[/tex] = 5 miles per hour
Again
The distance cover by Sharma = [tex]D_2[/tex] = 3 [tex]\frac{1}{2}[/tex] =[tex]\frac{7}{2}[/tex]
The Time taken by Sharma for jogging = [tex]T_2[/tex] = [tex]\frac{3}{4}[/tex] hour
Let the speed of Sharma = [tex]S_2[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]
or, [tex]S_2[/tex] = [tex]\dfrac{\textrm [tex]D_2[/tex] }{\textrm [tex]T_2[/tex] }[/tex]
Or. [tex]S_2[/tex] = [tex]\frac{\frac{7}{2}}{\frac{3}{4}}[/tex]
∴ [tex]S_2[/tex] = [tex]\frac{14}{3}[/tex] = 4.67 miles per hour
Now, ∵ 4.67 miles per hour [tex]<[/tex] 5 miles per hour
∴ [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]
So, Sharma jogged at slower late
Hence The speed of Sharma is slower than the speed of Brandi Answer
If f(x)=2x^6+x^5+32x+32, is (x+2) a factor of f(x).
Answer:
No
Step-by-step explanation:
By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0
f(- 2)
= 2[tex](-2)^{6}[/tex] + [tex]-2)^{5}[/tex] + 32(- 2) + 32
= 2(64) - 32 - 64 + 32
= 128 - 32 - 64 + 32
= 64 ≠ 0
Hence (x + 2) is not a factor of f(x)
Answer: By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0
f(- 2)
= 2(-2)^{6} + -2)^{5} + 32(- 2) + 32
= 2(64) - 32 - 64 + 32
= 128 - 32 - 64 + 32
= 64 ≠ 0
Hence (x + 2) is not a factor of f(x)
An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t squared plus 120 t describes the height of the debris above the ground, h, in feet, t seconds after the explosion. When will the debris be 56 feet above the ground?
Answer:
The debris will be at a height of 56 ft when time is 0.5 s and 7 s.
Step-by-step explanation:
Given:
Initial speed of debris is, [tex]s=120\ ft/s[/tex]
The height 'h' of the debris above the ground is given as:
[tex]h(t)=-16t^2+120t[/tex]
As per question, [tex]h(t)=56\ ft[/tex]. Therefore,
[tex]56=-16t^2+120t[/tex]
Rewriting the above equation into a standard quadratic equation and solving for 't', we get:
[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]
Using quadratic formula to solve for 't', we get:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]
Therefore, the debris will reach a height of 56 ft twice.
When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.
Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.
Final answer:
To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.
Explanation:
To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:
h = -16t² + 120t
Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:
56 = -16t² + 120t
This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:
-16t² + 120t - 56 = 0
16t² - 120t + 56 = 0
Dividing by 4
4t² - 30t + 14 = 0
Again reducing by dividing by 2
2t² - 15t + 7 = 0
Now, we need two numbers which add to give 15 and multiply to give 14.
The two numbers are 1 and 14.
2t²- 14t - t + 7 = 0
2t (t - 7) - 1(t - 7) = 0
(t - 7)(2t - 1) = 0
t = 7 or 1/2
Since 1/2 second cannot be an answer, the required answer is 7 seconds
A flock of 20 seagulls merges with a flock of cardinals. The new flock is bigger than either of the original ones, but still, it is no larger than 100 birds. How many birds were in the flock of cardinals?
There are 80 birds in the flock of cardinals.
Solution:Given:- A flock of 20 seagulls or we can say
Number of seagulls in a flock = 20
The new flock is no larger than 100 birds
So, let Total number of birds of new flock = 100
To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.
Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock
Number of birds in cardinal = 100 – 20 =80
Hence there are 80 birds in the flock of cardinals.
The answer explains how to determine the number of birds in the flock of cardinals based on the given conditions.
The number of birds in the flock of cardinals can be calculated as follows:
Let x be the number of birds in the flock of cardinals.
Since the new flock is no larger than 100 birds, the total number of birds after merging is 20 (seagulls) + x (cardinals).
Therefore, the equation to represent this situation is x + 20 ≤ 100, and solving for x, we get x ≤ 80. Thus, there were at most 80 birds in the flock of cardinals.
3) There are 60 total students in two of Mr. Weber's classes. 80% of them say he is
their favorite teacher. How many students think he is their favorite teacher?
Answer:
48 will be the answer.
Step-by-step explanation:
we can simply find the 80 percent of 60.
80 * 60 / 100 = 4800/100 = 48.
so 48 students think he is their favorite teacher.
Which situation has a unit rate of $7?
A
Trevor spent $49 on 2 theater tickets.
B
Sally bought a pack of 5 t-shirts for $35.
C
Brandon bought 7 gallons of gas for $14.
D
Gina bought nail polish for $5 and a pack of gum for $2.
Answer:
C is the answer.
Step-by-step explanation:
Given O below, the arcs wx and 72 must be congruent.
Answer:
B
Step-by-step explanation:
For the arcs WX and YZ to be congruent.
The angles subtended at the centre of the circle must be congruent.
This is not the case here as arc WX subtends 80° and arc YZ subtends 35°
Thus arc WX and arc YZ are not congruent.
The price of a video game was reduced from $60 to $45. by what percentage was the price of the video game reduced what is the answer show the steps
Answer:
Hey.
By what percentage was the price of the video games reduced ?
By 25%.
Step-by-step explanation:
$60 is the 100% price.
Now we have to find what percentage belongs to the reduced price, $45.
45×100/60 = 75.
75% is the percentage of the reduced price.
We can find the difference between them by doing a substraction.
100%-75% = 25%.
Hope I helped you !
The cost function for a company is C(x) = 90x + 1,800, where x is the number of bicycles produced at a cost of $90 each. How many bicycles can be produced for $3,780?
Answer:
22
Step-by-step explanation:
If the total cost of production can be explained with the function [tex]C(X)=1.800+90X[/tex], then when this total cost equals $3.780, we know that [tex]3.780=1.800+90X[/tex].Subtracting 1.800 both sides of the equation yields [tex]1.980=90X[/tex].Finally, dividing both sides by 90 gives us the value of X=22.Then, with $3780 we can produce 22 bicycles.2/3y+1=1/6y+8 equals what
A women bought some large frames for $16 each and some small frames for $9 each at a close out sale. If she bought 16 frames for $165, find how many of each type she bought.
Answer:
3 large, 13 small
Step-by-step explanation:
large: x
small: y
x + y = 16
16x + 9y = 165
Multiply first equation by 9 and subtract the equations.
9x + 9y = 144
-(16x + 9y = 165)
-7x = -21
x = 3
Now substitute this x value into the first equation
x + y = 16
3 + y = 16
y = 13
you begin with $90 in your savings account and your friend begins
with $35 in her savings account. You deposit $10 in savings each
week, and your friend deposits $15 in savings each week.
a. Write and graph a system of linear equations that
represent the amounts in each of your savings
accounts
b. Your friend says that in 10 weeks you will both
have the same amount of money in your savings
accounts. Is your friend correct? Use the graph
from part (a) to explain your answer.
Answer:
F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.
F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.
When you graph the equations, plugging in different values for t, you can see that the graphs intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200. They will not have the same amount of money in 10 weeks.
Answer:
a. [tex]y=10x+90[/tex][tex]y=15x+35[/tex]
b. Your friend is wrong.Step-by-step explanation:
If you begin with $90 and add $10 each week, then we express it as
[tex]y=10x+90[/tex]
Where [tex]x[/tex] refers to weeks and [tex]y[/tex] refers to the total amount of money in you savings account.
On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is
[tex]y=15x+35[/tex]
Therefore, the sytem of linear equation that models this situation is
[tex]y=10x+90[/tex]
[tex]y=15x+35[/tex]
The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.
Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.
ALOT OF POINTS IF YOU HELP ME PLEASE EXPLAIN
Answer:
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Step-by-step explanation:
Misha's group was asked to write an expression equivalent to
7y²z + 3yz² - 3
When Mr. Chen checked their answers, he found only one to be correct.
And she was Helena.
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Because, (7y²z + 6yz²- 5 - 3yz² + 2)
= 7y²z + (6yz² - 3yz²) - (5 - 2)
= 7y²z + 3yz² - 3 (Answer)
the ratio of cats to dogs at an animal shelter is 5:2. currently there is 63 cats and dogs are up for adoption. how many cats are up for adoption
Answer:
45 cats 18 dogs
Step-by-step explanation:
63/7 = 9
9*5=45
9*2=18
45+18=63
The number of cats up for adoption is 45.
Given that, the ratio of cats to dogs=5:2.
The total number of cats and dogs up for adoption is 63.
What are ratios?In mathematics, a ratio indicates how many times one number contains another.
Now, 5+2=7
Number of cats=5/7×63=45
Therefore, the number of cats up for adoption is 45.
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EXPERT ANSWER,WILL GIVE BRAINLEST
Answer:
yes you can look below for details
Step-by-step explanation:
one reason is because opposite sides are congruent, which means that it is a parallelogram.
another way is to see if the two triangles created by an diagonal is congruent:
construct AC to get two triangles ABC and ADC
AC =CA because of reflection
BA=DC because its given
BC=DA because its also Given
so
triangle ABC= triangle CDA because of SSS(side side side)
Question 1) Refer to the equation 2x-6y=12. A) Create a table of values for at least 4 points. Show your work. B) Use the table of values to graph the line. ( Question 2) I posted a picture of question 2. Will Mark Brainliest. Has to be turned in tonight
Answer:
Question 1)
Rearrange 2x-6y=12 to slope-intercept form by isolating y
y = (1/3)x - 2
Sub each x value to get the y value
x y
-3 -3
0 -2
3 1
6 0
y = (1/3)x - 2
y = (1/3)(-3) - 2
y = -3
Point (-3, -3)
y = (1/3)x - 2
y = (1/3)(0) - 2
y = -2
Point (0, -2)
y = (1/3)x - 2
y = (1/3)(3) - 2
y = 1
Point (3, 1)
y = (1/3)x - 2
y = (1/3)(6) - 2
y = 0
Point (6, 0)
See graph below
Question 2)
a) No, each support does not have the same starting coordinates. For example, the first support from the left starts at (0,0) and the second support from the left starts at (2,1).
b) No, each support does not have the same ending coordinates. For example, the first support from the left ends at (2,1) and the second support from the left ends at (6,3).
c) No, each support does not have the same change in x-values from the start to end.
The first support starts at the x-value 0 and ends at the x-value 2. It increased by 2.
The second support starts at the x-value 2 and ends at the x-value 6. It increased by 4.
d) No, each support does not have the same change in y-values from the start to end.
The first support starts at the y-value 0 and ends at the x-value 1. It increased by 1.
The second support starts at the y-value 1 and ends at the x-value 3. It increased by 2.
e) Yes, each support has the same change in the ratio of y-values over x-values. For the first support, the change is y-values is 1 and the change in x-values is 2. (1/2)
For the second support, the change in y-values is 2 and the change in x-values is 4. (2/4 = 1/2)
They both have the ratio of change in y-values over x-values 1/2.
A taxi charges a base fee plus $0.75/km.
A 10-km trip costs $8.70.
a) What is the rate of change in this situation?
b) Write an equation for the cost of hiring a taxi in terms of length of the trip.
c) What does initial value represent in this situation.
a) The rate of change in this situation is 0.75 dollars/km
b) The equation for the cost of hiring a taxi in terms of length of the
trip is y = 0.75 x + b
c) The initial value represents in this situation is $1.2
Step-by-step explanation:
The given is:
A taxi charges a base fee plus $0.75/km.A 10-km trip costs $8.70∵ A rate of change is a rate that describes how one quantity
changes in relation to another quantity
∵ The unit cost of a taxi is 0.75 dollars for each 1 kilometer
∴ The rate of change = 0.75 dollars/km
a) The rate of change in this situation is 0.75 dollars/km
Assume that the cost of hiring a taxi is $y for length of a trip x km
and a base fee of $b
∵ The length of the trip = x km
∵ The cost per km = $0.75
∵ The base fee = $b
∵ The cost of hiring a taxi = $y
- Write an equation for the the cost of hiring a taxi
∴ y = 0.75 x + b
b) The equation for the cost of hiring a taxi in terms of length
of the trip is y = 0.75 x + b
∵ The length of the trip is 10 km
∴ x = 10
∵ The cost of the hiring a taxi is $8.70
∴ y = 8.70
- Substitute these values in the equation of part (b)
∵ y = 0.75 x + b
∴ 8.70 = 0.75(10) + b
∴ 8.70 = 7.5 + b
- Subtract 7.5 from both sides
∴ 1.2 = b
∵ b is the base fee
∴ b is the initial value
∴ The initial value = $1.2
c) The initial value represents in this situation is $1.2
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Answer:
a) $0.75/Km
b) [tex]F(x)=1.2+0.75x[/tex]
c) The fixed base charge
Step-by-step explanation:
We know the taxi charges $0.75 per km and we are told a 10-Km trip costs $8.70. We can clearly see there is a base charge and a variable charge
a) The rate of change tells us the variation of the charges with the distance of the trip. In this case, the rate of change is $0.75/Km
b) If x is the length of the trip in Km, the equation of the total fare F(x) is
[tex]F(x)=A+0.75x[/tex]
We know a 10-Km trip costs $8.70. Replacing those values would give us the value of A
8.70=A+0.75(10)
8.70=A+7.5
[tex]=> A=8.70-7.5= 1.2[/tex]
Using the value of A we have
[tex]\boxed{F(x)=1.2+0.75x}[/tex]
c) The initial value represents the charge a customer has to pay even if they don't travel any distance, i.e. the fixed base charge
rewrite 1/2(x+3)(x+5) in standard form
ANSWER:
1/2 (x+3)(x+5)
= 1/2(x^2+8x+15)_This is the right answer
= x^2/2 + 8x/2 + 15/2
= x^2/2 + 4x + 15/2
Mark me as brainst answer
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Image point B'(4,-8) was transformed using the translation (x - 2, y + 3). What were the coordinates of B?
Answer:
B(6, - 11 )
Step-by-step explanation:
Since the translation rule is (x - 2, y + 3 )
Then to go back the way do the opposite, that is
(x + 2, y - 3 ), thus
B(4 + 2, - 8 - 3 ) → B(6, - 11 )
Answer:(6, -11)
Step-by-step explanation:
Which question should you expect to be answered with variable data?
A-How far is it from Chicago to New York City?
B-How many books have each of my classmates read this year?
C-How many people attended the high school football game last Friday?
D-What is the age of my English teacher?
Answer:
B-How many books have each of my classmates read this year?
Step-by-step explanation:
Every year the number of books each classmate read would be different
Answer:
b
Step-by-step explanation:
Plz help i can't figure this out for the life of me and it's due tmr
Answer:
D
Step-by-step explanation:
The diagram shows the rectangle with vertices at A(3,4), B(3,7), C(4,7) and D(4,4).
1. Rotate rectangle ABCD by 180° about the point (3,4) (vertex A). This rotation has the rule:
[tex](x,y)\rightarrow (6-x,8-y)[/tex]
So, the image points have the coordinates A'(3,4), B'(3,1), C'(2,1) and D'(2,4)
2. Dilate by a scale factor of 2 with the center of dilation at origin. This dilation has the rule:
[tex](x,y)\rightarrow (2x,2y)[/tex]
So, the image points have the coordinates A''(6,8), B''(6,2), C''(4,2) and D''(4,8)
3. Reflect it over the y-axis. This reflection has the rule:
[tex](x,y)\rightarrow (-x,y)[/tex]
So, the image points have the coordinates A'''(-6,8), B'''(-6,2), C'''(-4,2) and D'''(-4,8) that are exactly the coordinates of the second rectangle shown.
Thus, correct option is option D.
Simplify the expression |ab| if a<0 and b>0
Write the expression without the absolute value sign:
|2b|, where b<0
Write the expression without the absolute value sign:
|c|, where c<0
In simple terms, absolute value makes a negative number positive. So, |ab| simplifies to -ab when a<0 and b>0, |2b| simplifies to -2b when b<0, and |c| simplifies to -c when c<0.
Explanation:The expression |ab| simply represents the absolute value of the product of a and b. Absolute value is a mathematical function that determines the distance of a number from zero. In this case, as a is less than 0 (negative) and b is greater than 0 (positive), the product ab would be negative. But absolute value always returns a positive output or zero, so, |ab| would be -ab because absolute value would remove the negative sign.
The expression |2b|, where b is less than 0, would simplify to -2b, as b is negative so absolute value removes the negative sign.
Lastly, the expression |c|, when c is negative, simplifies to -c as the absolute value would remove the negative sign from c.
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Final answer:
To simplify expressions with absolute value signs, one must take into account the sign of the variables involved. If the result inside the absolute value sign is negative, then removing the absolute value signs will result in its positive counterpart.
Explanation:
When simplifying the expression |ab| given that a<0 and b>0, we consider that since a is negative and b is positive, their product ab will be negative. However, the absolute value signs indicate the positive magnitude of the result, thus |ab| = -ab.
For the expression |2b| where b<0, since b is negative, 2b will also be negative. Removing the absolute value sign should result in a positive number; thus |2b| = -2b.
Lastly, with |c| where c<0, the absolute value of a negative number c is the positive version of the number. Therefore, |c| = -c.
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets-2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
Answer:
Number of Adult's tickets sold on Saturday = 3,356
Number of Children's tickets sold on Saturday = 2, 928
Total number of tickets sold over these two days is 8,938.
Step-by-step explanation:
Here, the number of tickets sold on FRIDAY:
Adult Ticket sold = 1,678
Children's Tickets sold = 976
So, the total number of tickets sold on Friday
= Sum of ( Adult + Children's ) tickets = 1,678 + 976 = 2,654 .... (1)
The number of tickets sold on SATURDAY:
Adult Ticket sold = 2 times the number of adult tickets sold on Friday
= 1,678 x 2 = 3,356
Children's Tickets sold = 3 times the number of children's tickets sold on Friday.
= 976 x 3 = 2, 928
So, the total number of tickets sold on Saturday
= Sum of ( Adult + Children's ) tickets = 3,356 + 2,928 = 6, 284 .... (2)
Now, the total number of tickets booked in these two days :
Sum of tickets booked on (Friday + Saturday)
= 2,654 + 6, 284 = 8,938
Hence, total number of tickets sold over these two days is 8,938.