The volume of a rectangular prism is 2x^3 - 6x^2 + 8x , and the volume of a cube is 27x^3. What is the total volume of the prism and the cube?
Answer:
[tex]\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle V_P = 2x^3 - 6x^2 + 8x[/tex]
[tex]\displaystyle V_C = 27x^3[/tex]
Step 2: Find Combined Volume
[Set up] Add: [tex]\displaystyle V_P + V_C = V_{P + C}[/tex]Substitute in variables: [tex]\displaystyle V_{P + C} = 27x^3 + 2x^3 - 6x^2 + 8x[/tex]Combine like terms: [tex]\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x[/tex]The marked price of a tablet is €800. During a sale its sold at €640. This means one saves €160 during the sale
a) Find the percentage discount
Answer:
c. $28.84
Step-by-step explanation:
C 28.84 just multiply 38.45 by .25 then you should get 9.6125 you subtract 38.45 by 9.6125 and get 28.84
When Brianna plays solitaire, she keeps track of how many times she wins and loses. She has won
2
games for every 3 that she has lost. If Brianna has won 18 games, how many games has she played in all?
games
Help tell me the numbers in order
In a snail race, the winning snail traveled 5.85 cm in 3/4 of a minute. How fast was the snail traveling per second?
Answer:
0.13 cm per second
Step-by-step explanation:
Lets convert the minutes to seconds:
3/4 minutes = 3/4(60) = 45 seconds
The snail traveled 5.85 cm in 45 seconds
To find out the speed per second, we set up a proportion:
[tex]\frac{5.85}{45} = \frac{x}{1}[/tex] where 45 and 1 represent the number of seconds, and 5.85 and x represent the distance in that set of time
Let's solve for x, or the distance in 1 second:
[tex]\frac{5.85}{45}=\frac{x}{1}\\\\\\\frac{5.85*1}{45x}\\\\\\x = \frac{5.85}{45}\\\\\\\\\\x = 0.13[/tex]
The snail travels 0.13 cm per second.
-Chetan K
How many meters are in 28% of 15 km?
Explanation Please with proportions.
I will reward the brainiest
Answer:
4200
Step-by-step explanation:
Answer: 4,200 meters
Step-by-step explanation:
[tex]\frac{28}{100} * 15 = 4.2 km = 4200 m[/tex]
A phone company is offering several different prepaid data plans.
Prepaid Single Phone Plan Prepaid Family Plan
$30 for 1 GB $30 for 1 GB
$35 for 6 GB $40 for 6 GB
$45 for 16 GB $50 for 16 GB
$65 for Unlimited Data $70 for Unlimited Data
Which of the following deals has the cheapest price per GB?
A.
Prepaid Single Phone Plan $35 for 6 GB
B.
Prepaid Single Phone Plan $45 for 16 GB
C.
Prepaid Family Plan 1 Person $30 for 1 GB
D.
Prepaid Family Plan 1 Person $50 for 16 GB
The data plan that has the cheapest deal is given by the ratio of the data
plan price to the GB allocated.
The deal that has the cheapest price per GB is B. Prepaid Single Phone Plan $45 for 16 GB.The given phone data plans are;
[tex]\begin{tabular}{|l|cl|}&Prepaid Single Phone Plan&Prepaid Family Plan\\ a&\$30 for 1 GB &\$30 for 1 GB\\b& \$35 for 6 GB & \$40 for 6 GB\\ c&\$45 for 16 GB&\$50 for 16 GB\\d & \$65 for Unlimited Data & \$70 for Unlimited Data\end{array}\right][/tex]
The price per GB are;
Plan a = $30 ÷ 1 = $30 per GB
Plan b = $35 ÷ 6 = $5.8[tex]\overline 3[/tex] per GB and $40÷ 6 = $6.[tex]\overline 6[/tex] per GB for Family Plan
Plan c = 45 ÷ 16 = $2.8125 per GB and $3.125 per GB
Plan d = $65 for Unlimited Data = 65 ÷ ∞ ≈ 0; $70 for Unlimited Data = 0
Therefore, the plan with the cheapest price per GB from the given option is option B. Prepaid Single Phone Plan $45 for 16 GB.
Learn more about ratios here:
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PLEASE HELP ME GUYS!!
this is your answer hope it's helpful for you
The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 50 people.
A. 40 ≤ x ≤ 140
B. 0 ≤ y ≤ 50
C. 40 ≤ y ≤ 140
D. 0 ≤ x ≤ 50
find the value of x and y
answer. X=50
as..
draw a imaginary line between M
let it one side be y and z
y+z=120
now,
y=70(being alternate angle)
y+z =120
so
z=120-70
z=50
as we know,
z is alternate to X
so ,X=50
A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive, and the zoo only has room for a maximum of 20 male birds. Let x represent the number of male birds and y represent the number of female birds. Write the constraints to represent a thriving population of birds at the zoo. X > 0 and y > 0 0 < x ≤ 20 and y > 60 x > 0 and y < 20 0 < x ≤ 20 and 0 < y ≤ 60.
The correct option is D.[tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].
Given, [tex]x[/tex] represent the number of male birds and [tex]y[/tex] represent the number of female birds.
The flock needs to have exactly three times more females than males to thrive.
So, in equation form we have,
[tex]y=3x[/tex]........(1)
Since, The zoo only has room for a maximum of 20 male birds.
So, we can write the inequality for [tex]x[/tex] as,
[tex]0< x\leq 20[/tex]......(2)
Since The maximum number of male birds is 20, so for [tex]x=20[/tex]
y will be,
[tex]y=3\times 20\\[/tex]
[tex]y=60[/tex]
Hence, The maximum number of female birds is 60.
So, we can write the inequality for [tex]y[/tex] as,
[tex]0< y\leq 60[/tex]
Hence the required constraints are [tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].
For more details on Inequality follow the link:
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Answer:d
Step-by-step explanation: did the test
An appropriate tip for a waiter at a restaurant is at least 15%. For a tab of $20, how much money should be left, including tip?
$23, a $20 bill plus $3 tip
The pentagons ABCDE and JKLMN are similar find the length x of JK
Answer:
x = 8
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{JK}{AB}[/tex] = [tex]\frac{KL}{BC}[/tex] , substitute values
[tex]\frac{x}{4}[/tex] = [tex]\frac{6}{3}[/tex] = 2 ( multiply both sides by 4 to clear the fraction )
x = 8
3,415.72 - 1,838.28 = 1577.44
4. Janet earns $6.25 an hour for guarding paintings. If she works 24.3 hours a week for a period of six
weeks, how much does she earn from working six weeks?
PLS HELP ME ASAP
NO LINKS
Answer:a
Step-by-step explanation:
Find the diameter of a circle whose Circumfrence is 66 m
Answer:
21.00845
Step-by-step explanation:
πD = 66m
D = 66x 7/22
D = 21m is your answer brainlist me plz
Please solve this equation: 3 + 4 = 21; 2 + 5 = 14; 7 + 7 = 98; 8 + 6 = ?
Answer:
112
Step-by-step explanation:
It appears that the relation is f(a, b) = a(a+b).
f(3, 4) = 3(3+4) = 21
f(2, 5) = 2(2+5) = 14
f(7, 7) = 7(7+7) = 98
f(8, 6) = 8(8+6) = 112
__
The symbol "+" has apparently been repurposed from its usual meaning in math. It is being used as an infix operator with two arguments. We have shown the relation above as a function f with two arguments (a, b). In our definition ...
f(a, b) = a(a+b)
the symbol "+" has its usual meaning.
_____
Additional comment
This sort of question requires a little bit of "out of the box" thinking. It helps immensely if you're familiar with your addition and multiplication facts. Then you are in a position to recognize how the outputs may be related to the inputs.
Help me :) Please and Thanks
Answer:
0.65
Step-by-step explanation:
the number is greater than 0.5 and less than 7, that would usually be 0.6 but since it has two decimal places, it can be 0.61 to 0.68 since 0.69 would be the largest
What type of angles are these?
Answer:
7. Consecutive Interior Angles that are Supplementary
8. Alternate Exterior Angles that are Congruent
9. Alternate Exterior Angles that are Congruent
10. Alternate Exterior Angles that are Congruent
11. Same Side Exterior Angles that are Supplementary
12. Consecutive Interior Angles that are Supplementary
Step-by-step explanation:
Not sure if I even got them in the correct order, my apologies. The picture provided was a bit hard to read.
Correct me if I am incorrect.
Triangle HAM is reflected over the y-axis using the rule (x, y) → (−x, y) to create triangle H′A′M′. If a line segment is drawn from point A to point A′, which statement would best describe the line segment drawn in relation to the y-axis?
They create concentric circles.
They are parallel to each other.
The y-axis is a bisector of the segment drawn.
The segment drawn and the y-axis are congruent to each other.
The statement that best describes the line segment drawn in relation to the y-axis is (c) the y-axis is a bisector of the segment drawn.
The transformation rule is given as:
[tex](x,y) \to (-x,y)[/tex]
When the triangle is reflected to form triangle H'A'M', the vertices of triangle H'A'M' would be:
[tex]H'A'M' = (-x,y)[/tex]
So, the distance from point A to the y-axis is equidistant to the distance from point A' to the y-axis.
This, in other words means that the y-axis bisects the line segment AA'.
Hence, the relation between the segment and the y-axis is (c)
Read more about reflection at:
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Answer:
C. The y-axis is a bisector of the segment drawn.
Step-by-step explanation:
Question 10
The graph below shows a rational function.
10-
5
-
1
2
3
4
5
6
-3
-6
-5
-4
-2
-5
10-
15+
Select the function that represents the graph.
32+5
A y =
2+1
O
0
B
y =
32+5
2+2
22
с
y =
D
y=2-1
According to it's asymptotes, the function represented by the graph is:
[tex]y = \frac{3x + 5}{x + 1}[/tex]
The vertical asympotes of a function f(x) is the points which are outside the function domain.
In a fraction, they are given by the zeroes of the denominator.In this problem, there is a vertical asymptote at x = -1, which is a zero of the denominator, hence the denominator is x + 1.
The horizontal asymptotes are the values of the function as x goes to infinity.
In this problem, they are given by:
[tex]\lim_{x \rightarrow -\infty} f(x) = -3[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]
Hence, the option that satisfies it is:
[tex]y = \frac{3x + 5}{x + 1}[/tex]
To learn more about asymptotes, you can take a look at https://brainly.com/question/16948935.
Not drawn
to scale
(x - 2)cm
D
The diagram shows two joined rectangles.
The total area of the compound shape
ABCDEF is 36 cm
2x cm
c
By considering the areas of the two rectangles,
show that 2x2 - 5x - 18 = 0 and hence find B
the value of length AB.
x cm
A
+
(x - 4)cm
Note: Please make sure your final line only shows your final answer written as AB = ...
First find the areas of the two separate rectangles where:
Area of rectangle = length x width
Area of the small rectangle = x(x–4)
Area of small rectangle = [tex]x^{2} -4x[/tex]
Area of big rectangle = (x–2)(2x+x)
Area of big rectangle = (x–2)(3x)
Area of big rectangle = [tex]3x^{2} -6x[/tex]
The total area of the compound shape is 36, therefore:
[tex]3x^{2} -6x +x^{2} -4x=36[/tex]
[tex]4x^{2} -10x-36=0[/tex] (collecting like-terms and by bringing the +36 to the other side)
By dividing this by 2, you get:
[tex]2(2x^{2} -5x-18)=0[/tex]
[tex]2x^{2} -5x-18=0[/tex]
To find the length of AB (x), solve the quadratic by either factorising, completing the square or by using the quadratic formula, etc to solve for x.
[tex]2x^{2} -5x-18=0[/tex]
[tex](2x-9)(x+2)=0[/tex]
[tex]x=\frac{9}{2}[/tex]
[tex]x=-2[/tex]
However, a length cannot be negative, so x must be [tex]\frac{9}{2}[/tex] or 4.5cm, so length AB = 4.5cm.
Hope this helps :)
Hugo is mixing blue paint with red paint to create purple paint.
The ratio of blue to red is 3 to 2.
How many pints of blue paint will he use to create 40 pints of purple paint?
Answer:
24 pints of blue paint. I don't know of this is a solid way to get the answer, but I added 3+2=5. then 40/5=8. Then multiplied 8*3=24 and 2*8=16
Step-by-step explanation:
what's the Answer ?
[tex] \tiny\sf{6 + 6 \div 3}[/tex]
Answer: 8
Step-by-step explanation:
PEMDAS
division first
6 + 2
8
Answer:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Step-by-step explanation:
6/3 = 2
6+2 = 8
HAVE A NICE DAY
The angle of elevation to a nearby tree from a point on the ground is measured to be
73°. How tall is the tree if the point on the ground is 28 feet from the tree? Round
your answer to the nearest tenth of a foot if necessary.
Answer:91.6
Step-by-step explanation:
The height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.
The angle of elevation is given 73°. The distance between the point on the ground and the tree is 28 feet.
What is a trigonometric function?In mathematics, the trigonometric function is a function that deals with the sides of the right-angled triangle and angles.
sin, cos, tan, cosec, sec, and cot are the basic function of trigonometric.
We know that tan Ф = perpendicular / Base
tan 73° = h / 28
tan 73° × 28 = h
3.27 × 28 =h
h = 91.5 ft
Therefore, the height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.
Learn more about a trigonometric function;
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Solve |6x + 3| = 27.
A. x = 4 and x = -5
B. x = -4 and x = -5
C. x = -4 and x = 5
D. x = 4 and x = -4.
Answer:
it's d
.
hope I helped! I need to write more words so I can send this
Answer:
The answer is A
Step-by-step explanation:
|6x + 3| = 27
Use the definition of absolute value6x + 3 = 27
6x + 3 = -27
Subtract three from both sides of the equation.6x = 24
6x = -30
Divide both sides by 6.x = 4
x = -5
So:
x = 4, -5
Allison has 10 coins in dimes and nickels in her purse. The value of the coins is $0.70. Which pair of equations can be used to find the number of dimes, d, and nickels, n, Allison has in her purse?
Answer:
A lot
Step-by-step explanation:
Does this girl not have a credit card
The pair of equations is d + n = 10 and d + 5 n = 7 that can be used to find the number of dimes and nickels.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Number of dimes = d
And number of nickels = n.
Total number of coins = 10.
Also, the value of coins = $0.70.
According to given conditions,
Since, Total number of coins is 10,
The equation can be written as,
d + n = 10
Total value of coins are = 0.70
0.1d + 0.05n = 0.70
1/10 d / 5n / 100 = 0.70
10 d + 50 n = 70
d + 5 n = 7
The required pair of equations are d + n = 10 and d + 5 n = 7.
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c. What variable will be eliminated when the equations are combined after
the multiplication? (1 point)
Answer: The variable that will be eliminated when the equations are combined after the multiplication is y.
Step-by-step explanation: Happy to help :D
Shelly has a plan to save $500 for a trip that is 8 weeks away. She already has $50 in her
account. How much will she need to save weekly to meet her goal?
Answer:
She will still need about 450$
Step-by-step explanation:
So from what I have learned, she will need to work in order to get the money, but even when she is working, she may have expenses to pay and she may not make it, but she will because she can do loans and when she earns the money from loans, then she can pay, then she may have left over money she can use while on trip.
A map is drawn using a scale of 1 centimeter to 25 kilometers.
What actual distance is represented by a map length of 3.2 centimeters?