Twelve cubes are stacked and if we removed 2 of them how would the surface area change
Answers
If Twelve cubes are stacked its surface area is: 36a² and how would the surface area change if the top two cubes are removed is 6a².
Surface areaa. Surface area
If the length of one side is a the area of one surface is a²
Hence,
Area=a²
a²(6+6+6+6+6+6)
=36a²
b. Change in surface area change if the top two cubes are removed:
a²(6×2+5×2+4×2)
a²(12 + 10 + 8)
=30a²
Hence,
36a²-30a²
=6a²
Therefore If Twelve cubes are stacked its surface area is: 36a² and how would the surface area change if the top two cubes are removed is 6a².
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Related Questions
y varies directly with x .
If x=10 when y=3 , find y when x=4 .
Answers
After direct variation y = 6/5 when x = 4.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = 4.
K constant will be y/x ⇒ 3/10That is y = kx ⇒ y = 4/3 × xWhen x = -3:
y = 3/10 × 4 ⇒ y = 6/5
Therefore, after direct variation y = 6/5 when x = 4.
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Sam chose to buy the BLT bond rather than the stock. Based on Sam's purpose for making the investment, which
sentence provides a valid reason for his investment decision?
O Sam wants an investment that offers capital gains.
Sam wants a steady income from his investment.
O Sam wants an investment that he can quickly sell to raise cash.
Sam wants an investment that offers a higher return than stocks.
Answers
The statement that shows Sam's purpose for making the investment, is; Sam wants an investment that offers a higher return than stocks.
What are bonds?We know that bonds refers to a type of investment that could be held for a while the hope of making returns. Both the bonds and the stocks are common types of investments that are traded in the equities market. They are held by buyers with the sole hope that they could yield returns.
However, the bonds tend to be more secure than the stocks. The stocks are actually an overly volatile kind of investment. The bonds when mature tends to provide a high return on investment for the investor compared to the stocks.
Hence, the statement that shows Sam's purpose for making the investment, is; Sam wants an investment that offers a higher return than stocks.
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Write an equation of the line that passes through (-7,9), (-5,3)
Answers
Answer:
y = - 3x - 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 9 ) and (x₂, y₂ ) = (- 5, 3 )
m = [tex]\frac{3-9}{-5-(-7)}[/tex] = [tex]\frac{-6}{-5+7}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 5, 3 )
3 = 15 + c ⇒ c = - 3 - 15 = - 12
y = - 3x - 12 ← equation of line
Permutation v combination
Answers
The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.
How to explain permutations and combination?Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.
Fir example, if we want to select 2 players from 6. This will be:
= 6! / 2! (6 - 2)!
= 15 ways
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aircraft a has 136 more seats than aircraft b. if their total number of seats is 606, find the number of seats for each aircraft
Answers
Aircraft a has 371 seats and Aircraft b has 235 seats.
What is a linear equation?A linear equation is an algebraic equation that has highest degree of 1.
The total number of seats in both aircraft is 606.
Assuming aircraft b has x number of sheets.
∴ Aircraft a has (x + 136) number of sheets.
From the question itself we can form a numerical expression which is
x + (x + 136) = 606.
2x + 136 = 606.
2x = 606 - 136.
2x = 470.
x = 470/2.
x = 235.
So, Aircraft b has 235 seats and Aircraft a has ( 235 + 136) = 371 seats.
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The equation 9x = 27 has an answer of x = 3.
Write down Pive different equations with an answer of x = 3.
Answers
Answer:
5x = 15
2x = 6
10x = 30
8x = 24
21x = 63
Step-by-step explanation:
The equations that can give you an answer of 3 are the following
[tex]3x=9[/tex]
[tex]6x=18[/tex]
[tex]11x=33[/tex]
[tex]10x=30[/tex]
[tex]7x=21[/tex]
The equations above are one step linear equations
and many many more
A pizza shop charges nine dollars for a large cheese pizza. additional toppings cost $1.25 per topping. heather paid $15.25 for her large pizza. how many toppings that you order
Answers
Solve for x
1.25x = 6.25
x = 5
Heather ordered 5 toppings
Would Diagonal FH be considered perpendicular to side FE?
Answers
Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.
Why is the triangle congruent?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.We need to check all the statements that are applicable for the diagram.
1) EFGH is a rectangle.
The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.
2). EFGH has 4 congruent sides.
The above statement is also false. EFGH has two opposite sides are congruent.
3). Diagonal FH bisect angles EFG and EHG.
The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.
4). Diagonal FH is perpendicular to side Fe.
The above case is not true in general.
5). Angle FEH is congruent to angle FGH.
Yes, the above statement is the correct one, because both the triangles are congruent to each other.
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The complete question is -
Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent
5−10∣3x+3∣<95
Please give an explanation. I will mark brainliest.
Answers
The value of x in the absolute value inequality is given as5 - 10|3x + 3| < 95 is all set of real numbers
How to determine the values of the absolute inequality?The absolute value inequality is given as
5 - 10|3x + 3| < 95
Subtract 5 from all sides of the absolute value inequality
So, we have
- 10|3x + 3| < 90
Multiply -1/10 to all sides of the absolute value inequality
So, we have
|3x + 3| > -9
This means that the value of x is all set of real numbers
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6(x - 4y) how to I answer this question
Answers
Answer:6x-24y
Step-by-step explanation:You basically distribute the 6 with the x and the you do the same with the 4y. and thats how u get ur answer
Answer:
6x - 24y
Step-by-step explanation:
I'm guessing that they want you to distribute the 6 to each term inside the parentheses...
Solve—a high school athletic dept. I bought 40 soccer uniforms at the cost of $3,000. After the soccer season, they. returned some of the uniforms but only received $40 per uniform. What was? the difference between what they paid for each uniform and what they got for each return?
Answers
Answer: $75 difference per shirt
Step-by-step explanation:
I thought of a number, subtracted
7/18
from it, added 1 5/6 and got 3 2/3.
What was my number?
Answers
Answer:
[tex]\dfrac{20}{9}[/tex]
Step-by-step explanation:
Convert mixed fractions to improper fractions[tex]1\dfrac{5}{6} = \dfrac{1 \cdot6 + 5}{6} = \dfrac{11}{6}\\3\dfrac{2}{3} = \dfrac{3\cdot 3 + 2}{3} = \dfrac{11}{3}[/tex]If the original number was x
then subtracting 7/18 and adding 11/6 to it will be
[tex]x -\dfrac{7}{18} + \dfrac{11}{6}[/tex]and this is = [tex]\dfrac{11}{3}[/tex]so we get the equation
[tex]x -\dfrac{7}{18} + \dfrac{11}{6} = \dfrac{11}{3}[/tex] [tex]\mathrm{Transferring\;\; }-\dfrac{7}{18} + \dfrac{11}{6}[/tex] [tex]\mathrm{to \;the \; right \;side \;gives}[/tex]
[tex]x = +\dfrac{7}{18} - \dfrac{11}{6} + \dfrac{11}{3}[/tex]
(when a term changes sides in an equation the sign of the term changes)To compute the RHS, we need to make the denominators the same
The LCM of 18, 6 and 3 is 18Multiply each term by 18/18
[tex]\dfrac{18}{18}\cdot \dfrac{7}{18} - \dfrac{18}{18}.\dfrac{11}{6} +\dfrac{18}{18}.\dfrac{11}{3}[/tex]
[tex]= \dfrac{7}{18} - \dfrac{33}{18} + \dfrac{66}{18}[/tex]
[tex]= \dfrac{7 - 33 + 66}{18} = \dfrac{40}{18} = \dfrac{20}{9}[/tex]
Answer
[tex]x = \dfrac{20}{9}[/tex]. So the original number = [tex]\dfrac{20}{9}[/tex]
The original number is 20/9.
What is mean by Fraction?
A number expressed as a quotient in which a numerator is divided by denominator is called a fraction.
Given that;
The numbers are 1 5/6 and 3 2/3.
Now, Let us assume original number 'x'.
Change mixed fraction into improper fraction,
1 5/6 = 11/6
3 2/3 = 11/3
Then by the given condition,
Subtracting 7/18 from x and add 11/6, we get;
x - 7/18 + 11/6
And this is equal to = 11/3
So, we get;
x - 7/18 + 11/6 = 11/3
Add 7/18 both side,
x - 7/18 + 11/6 + 7/18 = 11/3 + 7/18
x + 11/6 = 11/3 + 7/18
Subtract 11/6 both side,
x + 11/6 - 11/6 = 11/3 + 7/18 - 11/6
x = 11/3 + 7/18 - 11/6
x = 66/18 + 7/18 - 33/18
x = 40/18
x = 20/9
Thus, The original number is 20/9.
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During spring break, Ian studied 3 hours
on the first day, 6 hours on the second
day, and 4 hours on the third day. How
many hours must he study on the fourth
day if he wants to spend an average
(arithmetic mean) of 5 hours each day
studying?
A. 6
B. 7
C. 8
D. 9
Answers
4 x 5 = 20
20-13 = 7
prove algebraically that the straight line with equation x-=2y+5 is a tangent to the circle with equation x^2+y^2=5
Answers
x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).
This is further explained below.
What is the prove of the tangent line?Generally, the equation for is mathematically given as
Differentiate both sides of the equation of the circle with respect to x, treating y=y(x) as a function of x:
[tex]x^2+y^2=5 \Longrightarrow 2 x+2 y \frac{\mathrm{d} y}{\mathrm{~d} x}=0 \\\\ \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{x}{y}[/tex]
This gives the slope of any line tangent to the circle at the point (x, y). Rewriting the given line in slope-intercept form tells us its slope is
[tex]x=2 y+5 \\\\ y=\frac{1}{2} x-\frac{5}{2} \\\\ slope =\frac{1}{2}[/tex]
In order for this line to be tangent to the circle, it must intersect the circle at the point (x, y) such that
[tex]-\frac{x}{y}=\frac{1}{2} \\ \\\\ y=-2 x[/tex]
In the equation of the circle, we have
[tex]x^2+(-2 x)^2=5 x^2=5 \\\\ x=\pm 1 \\\\ y=\mp 2[/tex]
If x=-1, then
[tex]-1=2 y+5\\\\ y=-3 \neq 2[/tex]
If x=1, then
[tex]1=2 y+5 \\\\ y=-2$[/tex]
In conclusion, as expected. Therefore x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).
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The outside edge of a path around a rectangular swimming pool is 15 m long and 10 m wide. The path is x metres wide.
* Find an expression for the area of the pool in expanded form.
Answers
Answer:
[tex]A = 4x^2 - 50x + 150[/tex]
Step-by-step explanation:
Since we are given that the path is `x` meters wide, e can express both the length and the width of the pool by subtracting `2x` from the length and width of the outside edge of the path.
[tex]w = 15 - 2x\\l = 10 - 2x[/tex]
Therefore, we can express the area of the pool using [tex]x[/tex] by substituting the values of [tex]w[/tex] and [tex]l[/tex] into the formula for the area of a rectangle.
[tex]A = w \times l\\A = (15-2x)(10 - 2x)\\\to A = 15 \times 10 - 15 \times 2x - 2x \times 10 - 2x \times (-2x)\\\to A = 150 - 30x - 20x + 4x^2\\\to A = 4x^2 - 50x + 150[/tex]
4/5-1/4
enter your answer in simplest form
Answers
Answer:
11/20
Step-by-step explanation:
4/5 - 1/4
We need to get a common denominator of 20
4/5 * 4/4 = 16/20
1/4 *5/5 = 5/20
Replacing the fractions with their equivalent fractions
16/20 - 5/20
11/20
Billy is planting a square garden that is 48 ft.² what is the closest side length of each side of the garden
Answers
The closest side length of each side of the garden is 7 feet .
Area is the space covered by an object. It is the realm occupied by all forms. When measuring the area of a square, we only consider the length of the sides. Since all sides of a square are equal, its area is equal to the square of the sides which is given by [tex]Area=a^2[/tex] ....(1) where "a" is the side of the square.It is given that Billy is planting a square garden that is 48 ft.²
Putting A = 48 ft.² in equation (1) , we get
[tex]48=a^2\\a=\sqrt{48} \\a=6.92[/tex]
which is approximately equal to 7
Hence , closest side will be 7 ft.
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1. The table shows the estimated profits y (in dollars) for a concert
when the charge is x dollars per ticket. Write and evaluate a
function to determine the maximum profit.
Ticket price, x
Profit, y
0
-1000
3
4100
6
7400
9
8900
12
8600
15
6500
Please help, dont troll me
Answers
The profit function for the concert is presented as follows;
y = -100•x² + 2,000•x - 1,000
The maximum profit is $9,000
What is a profit function?A profit function is one that gives the profit of a business which is the difference between the business's revenue and the costs of the business.
Profit = Revenue - Cost
Revenue = Quantity × Ticket price
Cost = Quantity × unit cost
Which gives;
y = Q•x - Q•c = Q•(x - c)
Given that the quantity, Q, varies, and Q•(x - c) is the product of two variables, a quadratic function is used as follows;
y = a•x² + b•x + c
When x = 0, y = -1000
Which gives;
y = a×0² + b×0 + c = -1000
c = -1000
When x = 3, y = 4,100
Which gives;
4,100 = a•3² + b•3 - 1000 = 9•a + 3•b - 1000
4,100 = 9•a + 3•b - 1000
5,100 = 9•a + 3•b
When x = 6, y = 7,400
Which gives;
7,400 = a•6² + b•6 - 1000 = 36•a + 6•b - 1000
7,400 = 36•a + 6•b - 1000
8,400 = 36•a + 6•b
Solving gives;
a = -100, b = 2,000
Which gives;
y = -100•x² + 2,000•x - 1,000
The profit function is therefore;
y = -100•x² + 2,000•x - 1,000The maximum profit is therefore at point, x = -2000/(2×(-100)) = 10
Which gives;
Max profit = -100×10² + 2,000×10 - 1,000 = 9,000
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A figure has two pairs of parallel sides and four right angles. The figure is translated 4 units down. How many parallel sides does the image have?
Answers
Answer:
4
Step-by-step explanation:
because if it has two Pairs that's 2 on each side of the side of the shape
so, when you have a figure of 2 parallel sides id would be a parallelogram
Find the inverse of each function. Is the inverse a function?
y=3 x+2
Answers
The inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.
What exactly is the inverse variation?Inverse variation refers to a relationship between two variables in which the value of one increases while the value of the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
All we have to do to find the inverse of an equation is switch the variables x and y.
x = 3y + 2Now, solve for y as follows:
3y = x - 2y = x/3 - 2/3Therefore, the inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.
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What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Answers
The equation of the line y = mx + b can be used to calculate the slope of a line m = ( y₂ - y₁ ) / ( x₂ - x₁ ) that passes through two points.
A line is defined as a curve showing the shortest distance between 2 points.
Here,
The slope of the line passing through two points ( x₁, y₁ ) and ( x₂, y₂ ) is given as :
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The line that connects two locations has the equation y = mx + b, where m is the slope of the line and b is a constant.
We can find b, using the x, y, and m values in the equation of a line to obtain the y-intercept.
Therefore, the Slope of the line can be given as m = ( y₂ - y₁ ) / ( x₂ - x₁ ) and equation of line y = mx +b.
Hence, option A is correct.
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Answer:
A or Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Step-by-step explanation:
A number c decreased by 12 is 4 as an equation
Answers
Answer:
c - 12 = 4
Step-by-step explanation:
Hello!
Decreasing a number by something is subtracting that number with something.
c decreased by 12 can be represented as c - 12.
When something is something, we set it equal to each other. We can set that equal to 4 to find our equation.
Equation: c - 12 = 4
Solve each equation. If necessary, round to the nearest ten-thousandth. 4 log₃2-2 log₃x=1
Answers
The value of x for the equation 4 log₃2-2 log₃x=1 is 2.30946
What is logarithmic function?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to obtain a specific number x, is represented by the logarithm of that number.
Given,
4 log₃2-2 log₃x=1
log₃ 2⁴ - log₃ x² = 1
using logₐ(m - n) = logₐ(m/n)
log₃(2⁴ / x²) = 1
2⁴ / x² = 3¹
x = 4/√3
x = 2.30946
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5. yo-yos the largest yo-yo in the world is 37.8 feet in circumference. the formula for the
circumference of a circle is c = 2tr, where c represents circumference and r represents
radius.
a. solve the formula for r.
b. find the radius of the yo-yo?
Answers
The formula for r will be C/2π.
The radius of the yo-yo will be 6.02 feet.
What is circumference?It should be noted that circumference simply means the distance round the circle.
In this case, the circumference is given as 37.8 feet.
The formula is illustrated as:
C = 2πr
r = C/2π
The radius will be:
r = C / 2π
r = 37.8 / (2 × 3.14)
r = 37.8 / 6.28
r = 6.02
Therefore, the radius of the yo-yo will be 6.02 feet.
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Solve each equation. Check your answers. 3 ln x+ ln 5=7
Answers
The solution 'x' of the expressed logarithmic expression is 17.65.
What exactly is the logarithmic expression?A logarithmic equation one in which the variable x contains a logarithm.
The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿExponent Rule = e∧lnx = xNow, as per the stated log expression;
3 ln x + ln 5 = 7
Apply the Power Rule on the first term of the given equation;
ln x³ + ln 5 = 7
Now, by the Product Rule, we can re-write the equation in the form;
ln (x³×5) = 7
ln (5x³) = 7
Using the exponent form of the log on both side.
e∧ln (5x³) = e⁷
As, we have the same base for the obtained expression. Use the exponent rule;
(5x³) = e⁷
x³ = e⁷/5
Substitute the value of exponent e = 2.72
x³ = (2.72)⁷/5
x³ = 5507.5
Take cube root on both side;
x = 17.65
Thus, solution for the value of 'x' for expressed logarithmic expression is 17.65.
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Simplify each expression.
log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)
Answers
Simplification of given expression is , -1
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a . b = log a + log b log a/b = log a - log blog a^x = x log alog a^a = 1According to question,
log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)
applying formula of log a - log b , equation can be written as
[tex]= log_3(\frac{x+1}{3x^{2} -3x-6} ) + log_3(x-2)\\\\=log_3(\frac{x+1}{3{(x+1)(x-2)} } ) + log_3(x-2)\\\\= log_3(\frac{1}{3 {(x-2)} } ) + log_3(x-2)[/tex]
now, applying formula of log a+ log b
[tex]=log_3(\frac{1}{3{(x-2)} } (x-2)) \\\\=log_3(\frac{1}{3} )\\[/tex]
apply, [tex]log_a(\frac{1}{x}) = -log_a x[/tex]
[tex]= - log_33[/tex]
= -1
Thus, Simplification of given expression is , -1
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer: A, C and F
Step-by-step explanation:
Write a quadratic polynomial in standard form with a zero at 8i and has a leading coefficient of 5.
Answers
Answer:
4
Step-by-step explanation:
Well, 2*2 = 4, so the answer is 4
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=3/√x
Answers
Answer to this question is:
Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(0,∞)
Set-Builder Notation:{x|x>0}
The set of all valid y values constitutes the range.Graph may be used to find the values.
Interval Notation:(0,∞)
Set-Builder Notation:{y|y>0}
For calculation of inverse:
Interchange the variables x=3/√ySolve for yy=9/x²Replace y with f^-1(x)f^-1(x)=9/x²∴Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
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Find the gcf of 18a and 20ab
Answers
Answer:
the gfc is 1 because of the unknowns which are a and b