The Volume of the cube is [tex]$$\left(64 x^6+144 x^4+108 x^2+27\right)\\[/tex].
[tex]we \ know \that \ The \ volume \ of \ a \ cube \ is \ equal \ to \ $$V=s^3$$[/tex]
[tex]$$ where$s$ is the length side of the cubeIn this problem we have$$s=\left(4 x^2+3\right)$$Substitute$$V=\left(4 x^2+3\right)^3$$Remember that$$\begin{aligned}&\left(4 x^2+3\right)^3=\left(4 x^2+3\right)^2\left(4 x^2+3\right) \\&\left(4 x^2+3\right)^2\left(4 x^2+3\right)=\left[16 x^4+24 x^2+9\right]\left(4 x^2+3\right) \\&=64 x^6+48 x^4+96 x^4+72 x^2+36 x^2+27\end{aligned}$$Combine like terms$$=64 x^6+144 x^4+108 x^2+27$$[/tex]
What is cube ?In geometry, a cube is a three-dimensional solid object bounded by six square faces, faces or sides, three of which meet at each vertex.
The cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices.
A cube is also a square parallelepiped, an equilateral cube and a right rhombohedron 3-ribbed. It is a regular square prism in three directions and a triangular trapezoid in four directions.
A cube is a double point with an octahedron. It has cubic or octahedral symmetry.
A cube is the only convex polyhedron that has all its faces square.
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how do you know when to add or subtract when doing the distributive property for (2-6s)(-5)
Here, we want to use the distributive property
To use this, the operator at the middle of the two initial terms will tell us the sign to use
Looking at the first expression, we can see a negative sign between 2 and -6s
Thus, in this case, when using the distributive property, we proceed as follows;
[tex]\begin{gathered} (2-6s)(-5)\text{ = (2}\times(-5))\text{ - (6s}\times(-5)) \\ =\text{ -10 - (-30s)} \\ =\text{ -10 +30s = 30s-10} \end{gathered}[/tex]Write an equation for the line that passes through (2, 5) and (6, 7). You may use graphing paper as needed for this question.
Enter in the equation below:
The equation of the line that passes through the point (2, 5) and (6, 7) is
y = (1/2)x + 4.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
We have,
The equation of a line passes through points (2, 5) and (6, 7).
The equation of a line can be written as:
y = mx + c ______(1)
Points (2, 5) and (6, 7) must satisfy line (1).
5 = 2m + c _____(A)
7 = 6m + c ______(B)
From (A),
c = 5 - 2m
Putting in (B).
7 = 6m + 5 - 2m
7 = 4m + 5
2 = 4m
m = 1/2
Putting in (A) we get,
5 = 2 x 1/2 + c
5 = 1 + c
c = 4
Now,
The equation of the line is:
y = (1/2)x + 4.
Thus,
The equation of the line that passes through the point (2, 5) and (6, 7) is
y = (1/2)x + 4.
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I need help to understand why there is a 12 in the formulaThe repayment parameters of the $10,000 loan Trey qualifies for are given as follows; = $185.48 × 5 × 12 = $11,128.8While the total repayment amount for the 10 year loan term, '' is given as follows; = $102.63 × 10 × 12 = $12,315.6The difference between the total repayment for the 10-year term and the 5-year term loan, - , is given as follows; - = $12,315.6 - $11,128.8 = $1,186.80Therefore, the 5-year term is lower than the 10-year term by $1,186.80
Given the monthly payments for each one of the two terms, we can calculate the total repayment of the 5-year and 10- years term.
As for the 5-year plan,
[tex]\begin{gathered} 5\cdot12=60\to\text{months in 5 years} \\ 60\cdot185.48=11128.8 \end{gathered}[/tex]Similarly, for the 10-year plan,
[tex]\begin{gathered} 10\cdot12=120\to\text{months in 10 years} \\ 120\cdot102.63=12315.6 \end{gathered}[/tex]Finally, the difference between these two quantities is
[tex]12315.6-11128.8=1186.8[/tex]The answer is 'The 5-year term would be 1186.80 lower', option B
How many times will you use the digit 0 if you write all the natural numbers from 1 to
100?
Answer:
From 1 to100 11 times 0 will be used
Answer:
11
Step-by-step explanation:
this is the answer to your question
Can someone please help me with these asap and show a step by step?
The width of prism is 9yards.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.
Given Data
Rectangular prism:
Volume = 990 yd³
Length = 10 yards
Height = 11 yards
Volume of rectangular prism = Length× Height× Width
990 = 10 ×11× width
Width = [tex]\frac{990}{10(11)}[/tex]
Width = 9
The width of prism is 9yards.
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What is the probability a rolling a 1, 2 or 3 on a number cube on your first roll, then a 5 or 6 the second roll?
% (answer as a percent round to the nearest whole percent)
The probability of rolling dice twice
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Total no. of outcomes = 6
The probability of getting a 1,2 or 3 from the first rolling is 3/6.
The probability of getting a 5 or 6 from second rolling is 2/6
As the two rollings are independent,
you can just multiply two probability values to come up with a final answer.
Which is,
= (3/6) x (2/6)
= (1/2) x (1/3)
= (1/6)
The probability a rolling a 1, 2 or 3 on a number cube on your first roll, then a 5 or 6 the second roll is 1/6 or 0.16
Probability in % will be
0.16 x 100/100
= 16%
Hence, The probability a rolling a 1, 2 or 3 on a number cube on your first roll, then a 5 or 6 the second roll is 16%
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david and daniel were given the same number of dollars by their father. david earned money doing chores until he had twice as much as he started with. daniel didn't earn any more, but he reciaved $12 for his birthday. if the boys still have the same amount of money, how much did their father give each one?
David and Daniel were given $12 each in the beginning as the given condition.
What are conditions?
A condition that must be met in order for the given statement or theorem to hold. also known as a problem.A necessary condition is one that must exist in order for the given statement to be true (if satisfied it maybe true as there maybe more than one necessary conditions). On the other hand, a sufficient condition is one that, even if it is satisfied, does not automatically imply that the proposition is true.Let david and daniel were given = $x each as per statement.
at the end david had = 2x
and daniel had= x+12
Condition is given that : in the end, the boys still have the same amount of money.
Therefore, equating both what David and Daniel had
2x=x+12
x=12
David and Daniel were given $12 each in the beginning as the given condition.
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Calculate the simple interest on $8,500 at an 8% interest rate for 6 months.
The simple interest formula is
[tex]I=P\cdot r\cdot t[/tex]Where P is the principal, r is the interest rate and t is time in years.
Replacing the given information, we have
[tex]I=8,500\cdot0.08\cdot\frac{6}{12}=340[/tex]Therefore, the simple interest would be $340.Find JKL and LKM if JKM = 140.
The measure of angles JKL and LKM are 100° and 40° respectively.
What is a supplementary angle?A supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles JKL, LKM and JKM are not supplementary angles:
m∠JKL + m∠LKM = m∠JKM
Substituting the given parameters into the formula, we have;
4x° + (2x − 10)° = 140°
6x° − 10 = 140°
6x° = 140° + 10°
6x° = 150°
x° = 150/6
x = 25°
For angle JKL, we have:
m∠JKL = 4x
m∠JKL = 4(25)
m∠JKL = 100°.
For angle LKM, we have:
m∠LKM = 2x − 10
m∠LKM = 2(25) − 10
m∠LKM = 50 − 10
m∠LKM = 40°
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HELP?
Line segment AB has a length of 5 units. It is translated 3 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime? (5 points)
Group of answer choices
5 units
2 units
4 units
3 units
The length of A'B' = 5 units
The line segment AB is of 5 units. AB is then transformed through translation of 3 units to the right.
The translation only means change through a straight line. This transformation does not change the length of a line segment.
So the length of A'B' will also be 5 units.
But the position of A'B' will be different from that of AB on the co-ordinate plane. To be exactly, A'B' would be 3 units right to the position of AB on the co-ordinate plane.
Also the co-ordinates of A'B' will be different. Still their lengths will be same.
Thus the length of A'B' = 5 units
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if G(x)=−3x+5, find: G(x-4)
Answer:G(x-4)=-3x+17
Step-by-step explanation:
First, replace everywhere in the equation that there is x to (x-4)
then you simplify it
=-3(x-4)+5
=-3x+12+5
=-3x+17
138×14÷28+209
A)278
B)288
C)298
D)388
Answer: A
Step-by-step explanation:
First you multiply 138 x 14 =1932 then divide 28 then you have 69 then add 209 then you have 278.
sorry if its wrong.
Answer:
A) 278
Step-by-step explanation:
Use PEMDAS for order of operations:
Start with anything in parentheses, and then operations are performed on any exponents (also called powers). Next, perform operations on multiplication or division from left to right. Finally, operations on addition or subtraction are performed from left to right.
What will be the answers to these questions?
(a). 4,5,6,7,...... , ......
The term-to-term rule is Aₙ = Aₙ₋₁ + 1The next numbers in the sequence is 8 , 9The position-to-term rule is Aₙ = 1 + (n - 1)*1Consecutive rule is works for the first three terms.(b) . 10,11,12,13,......,......
The term-to-term rule is Aₙ = Aₙ₋₁ + 1The next numbers in the sequence is 14 , 15The position-to-term rule is Aₙ = 1 + (n - 1)*1Consecutive rule is works for the first three terms.(c) . 24,25,26,27,.....,....
The term-to-term rule is Aₙ = Aₙ₋₁ + 1The next numbers in the sequence is 28 , 29The position-to-term rule is Aₙ = 1 + (n - 1)*1Consecutive rule is works for the first three terms.(d) . 1,3,5,7,......,.....
The term-to-term rule is Aₙ = Aₙ₋₁ + 2The next numbers in the sequence is 9 , 11The position-to-term rule is Aₙ = 2 + (n - 1)*2Consecutive rule is works for the first three terms.Here we have the sequence:
(a) . 4,5,6,7,...,.....
To check this, let's find the difference between the consecutive terms:
5 - 4 = 1
6 - 5 = 1
7 - 6 = 1
(i) . The term-to-term rule is the rule that defines the [tex]n^{th}[/tex] term based on the previous terms.
Here we already know that each term in this sequence is the previous one plus six, so we can write this as:
Aₙ = Aₙ₋₁ + 1
(ii) . Then the next number in the sequence will be equal to the previous number plus 1, this is:
7 + 1 = 8
8 + 1 = 9
The next numbers in the sequence is 8 , 9
(iii) . The position-to-term rule is the general one.
Here we need to know that, the first term, A₁ = 1
Then, the [tex]n^{th}[/tex] term will be A₁ plus (n - 1) times 1.
Then the rule is:
Aₙ = A₁ + (n - 1)*1
Replacing A₁ by its value, the rule becomes:
Aₙ = 1 + (n - 1)*1
(iv) . We can assume that this is an arithmetic sequence, this is, the difference between any two consecutive terms is always the same, D.
5 - 4 = 1
6 - 5 = 1
7 - 6 = 1
So we can conclude that this is an arithmetic sequence, and the difference between any two consecutive terms is always 1.
Hence, Consecutive rule is works for the first three terms.
(b) . 10,11,12,13,.......,......
To check this, let's find the difference between the consecutive terms:
11 - 10 = 1
12 - 11 = 1
13 - 12 = 1
So, b is same to a.
(c) . 24,25,26,27,......,.....
To check this, let's find the difference between the consecutive terms:
25 - 24 = 1
26 - 25 = 1
27 - 26 = 1
(i) . The term-to-term rule is the rule that defines the [tex]n^{th}[/tex] term based on the previous terms.
Here we already know that each term in this sequence is the previous one plus six, so we can write this as:
Aₙ = Aₙ₋₁ + 1
(ii) . Then the next number in the sequence will be equal to the previous number plus 1, this is:
27 + 1 = 28
28 + 1 = 29
The next numbers in the sequence is 28 , 29
(iii) . The position-to-term rule is the general one.
Here we need to know that, the first term, A₁ = 1
Then, the [tex]n^{th}[/tex] term will be A₁ plus (n - 1) times 1.
Then the rule is:
Aₙ = A₁ + (n - 1)*1
Replacing A₁ by its value, the rule becomes:
Aₙ = 1 + (n - 1)*1
(iv) . We can assume that this is an arithmetic sequence, this is, the difference between any two consecutive terms is always the same, D.
25 - 24 = 1
26 - 25 = 1
27 - 26 = 1
So we can conclude that this is an arithmetic sequence, and the difference between any two consecutive terms is always 1.
Hence, Consecutive rule is works for the first three terms.
(d) . 1,3,5,7,......,......
To check this, let's find the difference between the consecutive terms:
3 - 1 = 2
5 - 3 = 2
7 - 5 = 2
(i) . The term-to-term rule is the rule that defines the [tex]n^{th}[/tex] term based on the previous terms.
Here we already know that each term in this sequence is the previous one plus six, so we can write this as:
Aₙ = Aₙ₋₁ + 2
(ii) . Then the next number in the sequence will be equal to the previous number plus 1, this is:
7 + 2 = 9
9 + 2 = 11
The next numbers in the sequence is 9 , 11
(iii) . The position-to-term rule is the general one.
Here we need to know that, the first term, A₁ = 2
Then, the [tex]n^{th}[/tex] term will be A₁ plus (n - 1) times 1.
Then the rule is:
Aₙ = A₁ + (n - 1)*1
Replacing A₁ by its value, the rule becomes:
Aₙ = 2 + (n - 1)*2
(iv) . We can assume that this is an arithmetic sequence, this is, the difference between any two consecutive terms is always the same, D.
3 - 1 = 2
5 - 3 = 2
7 - 5 = 2
So we can conclude that this is an arithmetic sequence, and the difference between any two consecutive terms is always 2.
Hence, Consecutive rule is works for the first three terms.
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7. You have $170. You start a part-time job that pays $8.50 per hour.
a. Does the situation represent a function? If so, identify the independent and
dependent variables.
b. You work no more than 4 hours. Find the domain and range.
The situation represent the relation as I = 170+8.50t, where I= income is the dependent variable and t is working hour, is the independent variable.
What is dependent variable and independent variable?
The dependent variable is the variable in a function or experiment whose value depends on the independent variable. The independent variable is the known variable that is manipulated in order to determine its effect (if any) on the dependent variable.
The situation describes the function of income from working hours.
I = 170+8.50t.
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Write an algebraic expression to model this word phrase: The quotient of the sum of 6 and a number, x, and 4
Answer:
(6+x)/4
Step-by-step explanation:
7. K Corporation sells 4 times as many GE dishwashers as Wallace Company. The difference
between their sales is 180 dishwashers. How many GE dishwashers did each sell?
Number of GE dishwashers sell by K corporation and Wallace company is equal to 240 and 60 respectively.
As given in the question,
Let x be the number of dishwasher sell by K Corporation
And y be the number of dishwasher sell by Wallace Company
K Corporation sells 4 times GE dishwashers as compare to Wallace Company.
x = 4y ___(1)
Difference between sells of K Corporation and Wallace Company
x - y = 180 __(2)
Substitute the value of (1) in (2)
4y - y =180
⇒ 3y = 180
⇒ y = 60
Hence, x = 4 ×60
= 240
Therefore, number of GE dishwashers sell by K corporation and Wallace company is equal to 240 and 60 respectively.
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
The publisher should produce and sell 2356 books so that the production costs will equal the money from sales.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book.
Assume the number of books to be printed be [x].
Then, we can write -
24149 + 11.50x = 21.75x
21.75x - 11.5x = 24149
10.25x = 24149
x = 2356 books
Therefore, the publisher should produce and sell 2356 books so that the production costs will equal the money from sales.
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which number would go outside the circles?
Answer:
D. 7/9
Step-by-step explanation:
Whole numbers are all natural numbers, or positive numbers that are not fractions (including 0). A and C are whole numbers because they are positive and not fractions.
Integers are all whole numbers, but negative numbers are included as well. B is an integer because it is the negative version of a whole number.
D is a fraction, therefore being neither.
V : 33= 7 : 11 what is the answer to this please
The value of V illustrated in the ratio V : 33= 7 : 11 is 21.
What is a ratio?It should be noted that a ratio is simply used to show the relationship between the variables and illustrate the comparison.
In this case, the value of V can be illustrated as:.
V/33 = 7/11
Cross multiply
11V = 33 × 7
V = (33 × 7) / 11
V = 21
Therefore, V is 21.
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what is the answer to1 /2 ÷ –4 /7
Answer:1/2-1/4
(1/2x2)-1/4
2/4-1/4
2-1
1
1/4
Step-by-step explanation: i did this good luck
Write the equation in slope intercept form. -5y + 10x = 20 help meeee
Kimi and Jordan are both working during the summer to earn money and they are saving all their money. Kimi earns $9 an hour at her job, and has $6 saved up initially. Jordan earns $7.50 an hour, and has $18 saved up initially.
Using linear functions, it is found that they will have the same amount after 8 hours.
What is a linear function?A linear function, in slope-intercept format, is given by:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).In the context of this problem, for their earning functions, we have that:
The slope is represented by the hourly earnings.The intercept is represented by the initial amount saved.Hence the functions are given as follows:
Kimi: K(x) = 6 + 9x.Jordan: J(x) = 18 + 7.5x.The number of hours after which they will have the same amount is found solving the following equation for x.
K(x) = J(x)
6 + 9x = 18 + 7.5x.
1.5x = 12
x = 12/1.5
x = 8 hours.
What is the missing information?This problem is incomplete, hence we suppose that it asks after how many hours they will have the same amount.
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C1 Determine the Greatest Common Factor of polynomials
To find the greatest common factor of a polynomial, find a number that all of its coefficients are divisible by, for example, the GCF of an 8x 2 + 4x + 2 is 2 because all of the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x2 + 2x + 1).
What is the Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.
To find the greatest common factor of a polynomial, find a number that all the coefficients of the polynomial are divisible by i.e. the GCF of a 8x^2 + 4x + 2 is 2 because all the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x^2 + 2x + 1).
The GCF can be smaller than the smallest coefficient, for example 20x^2 + 15x + 10 (GCF is 5, smallest coefficient is 10) and 5 < 10. However it cannot be larger than the smallest coefficient.
Therefore the smallest coefficient should be larger than or equal to the GCF in order to be divisible.
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Kylie buys a two-quart bottle of juice for $9.60. What is the unit rate of the
cost of the juice per fluid ounce?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
Before you try that problem, answer the question
below.
How many fluid ounces of juice did Kylie buy?
Answer:
Answer 1:$0.15(15 cents) is the unit rate.
Answer 2:Kylie bought 64 fluid ounces.
Step-by-step explanation:
Step 1
2 quarts=4 pints
4 pints=8 cups
8 cups=64 fluid ounces
Step 2
$9.60÷64=0.15$
Sarah's wrote the equation y = 2 + 3x. Why is Sarah's equation incorrect? What is the correct equation?
Question NEEDS ANSWERING
Evaluate. (−13+0.6(−12)+1)2 What is the value of the expression? Enter your answer as a simplified fraction in the box.
The numeric value of the given expression is as follows:
121/900.
Numeric value of expressionThe expression is defined as follows:
[tex]\left(-\frac{1}{3} + 0.6\left(-\frac{1}{2}\right) + 1\right)^2[/tex]
The parenthesis take precedence. If there are more than one parenthesis, the inside one takes precedence.
The fraction equivalent of 0.6 is of 3/5, hence:
[tex]\left(-\frac{1}{3} + \frac{3}{5}\left(-\frac{1}{2}\right) + 1\right)^2[/tex]
Solving the internal parenthesis, the expression is:
[tex]\left(-\frac{1}{3} - \frac{3}{10} + 1\right)^2[/tex]
The least common multiple of 3, 10 and 1 is of 30, hence:
[tex]\left(-\frac{1}{3} - \frac{3}{10} + 1\right)^2 = \left(\frac{-10 - 9 + 30}{30}\right)^2 = \left(\frac{11}{30}\right)^2[/tex]
To find the square of the fraction, we find the square of the numerator and the denominator, hence the numeric value of the expression is:
121/900.
Missing informationThe expression is:
[tex]\left(-\frac{1}{3} + 0.6\left(-\frac{1}{2}\right) + 1\right)^2[/tex]
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5. Find the selling Price of an item that originally cost a store $70 was marked up20% and then after no selling for 6 months was discounted 10%?
Answer:
$75.6
Explanation:
If the original cost was $70 and it was marked up 20%, the price after this is calculated as:
$70 + $70(0.2) = $70 + $14 = $84
Where $70(0.2) = $14 is the amount added to the original when it is marked up 20%.
Then, it was discounted 10%, we get that the selling price is
$84 - $84(0.1) = $84 - $8.4 = $75.6
Where $84(0.1) = $8.4 is the discount made on the initial price.
Therefore, the answer is $75.6
Solve for x.
5r — 29 >_34
OR 2x +31 < 29
The value of the variable 'x' by using simplification method is: x > -1
What is simplification?
In mathematics, the simplification method is used to simplify the complicated or inequality expression. Basically, it convert the complicated expression to simpler one to make the easy calculation.
According to the question, the given inequality equations are as follows:
5r — 29 >_34 and 2x +31 < 29
For the variable 'x', the given equation can be simplified by using simplification method, we get:
2x +31 < 29 ⇒ 2x < 29 - 31 ⇒ 2x < -2 ⇒ x > -1
Hence, the value of the variable 'x' by using simplification method is: x > -1
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I need help on A, E on these questions thank you in advance!!
Answer: (-10, 20) and (6.5, 14)
Step-by-step explanation:
When x is -3 the equation would look as so:
y=6(-3)+8
y=-18+8
Then you would simplify: -18+8=-10
So: y=-10 when x is -3
Next, when x is 2 the equation would look as so:
y=6(2)+8
y=12+8
Simplify: 12+8=20
So: y is 20 when x is 2
For the equation y=1.5x+11 and x is -3 the equation will look like:
y=1.5(-3)+11
y=-4.5+11
Simplify: -4.5+11= 6.5
So y is 6.5 when x is -3
Next when x is 2 the equation would look like:
y=1.5(2)+11
y=3+11
Simplify: 3+11=14
So y is 14 when x is 2
1/2 (9+8) please answer
Step-by-step explanation:
8.5 I believe is the answer
