The box's dimensions are 3 × 6 × 6.
What are dimensions?The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics.
So, let 'a represent the box's height and 'b' represent one of the box's base sides.
Then,
Volume = ab² = 108
a = 180/b² ...(1)
The box's surface area is now:
SA = b² + 4ab ...(2)
We get from equations (1) and (2):
SA = b² + 4 × (180/b²) × b
SA = b² + 432/b ...(3)
Using equation (3) to differentiate for the smallest surface area possible, we obtain:
d(SA)/db = 2b - 432/b² ....(4)
Now solve for zero in equation (4) to get:
2b - 432/b² = 0
b³ = 216
b = 6m
When we now enter the value of b into equation (1), we obtain:
a = 3 m
the box's dimensions are 3 × 6 × 6.
Therefore, the box's dimensions are 3 × 6 × 6.
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what does it mean for two shapes to be proportional.
Answer:
It means that the quantities have the same relative size. In other words they have the same ratio.
Step-by-step explanation:
For example look at the attached files
If triangle xyz is translated using the rule (x, y) → (x − 3, y − 2) and then reflected across the y-axis to create triangle x″y″z″, what is the location of z″? (−7, 1) (−3, −1) (−1, −3) (3, 3)
The location of the y-axis to create a triangle is a(0,2).
So if the point X is (-3, -2) is translated using the rule
x,y ---> (x+3),(y+4)
then you simply plug-in the values of x and y which are x = -3 and y = -2
x,y ---> ((-3) +3), ((-2) + 4) which is (0, 2)
This is the new coordinate for X
so the answer is a(0,2).
What is a triangle?
A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as triangle ABC.
In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high-dimensional Euclidean space.
Therefore, the location of the y-axis to create triangle is a(0,2).
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helpppppp maeeeeeeee
Answer:
x= -7
Step-by-step explanation:
The sum of the angles in a triangle is 180°. This can be abbreviated to ∠ sum of ∆.
Adding the angles in the triangle,
84° +(x +59)° +(x +51)°= 180° (∠ sum of ∆)
2x= 180 -84 -59 -51
2x= -14
Divide both sides by 2:
x= -14 ÷2
x= -7
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PLEASE ILL DO ANYTHING I ALREADY OFFERED AS MUCH POINTS AS POSSIBLE
Answer:
A, B, D, E
Step-by-step explanation:
Given expression:
(0.06) · (0.154)When multiplying decimals, multiply as if there are no decimal points:
[tex]\implies 6 \times 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.06 → 2 digits0.154 → 3 digitsTherefore, there is a total of 5 digits.
Put the same number of total digits after the decimal point in the product:
[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]
-----------------------------------------------------------------------------------------------
Answer option A
[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]
When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.
Therefore:
6 ÷ 100 = 0.06154 ÷ 1000 = 0.154[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]
Therefore, this is a valid answer option.
Answer option B
[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]
Multiply the numbers 6 and 154:
[tex]\implies 6 \times 154 = 924[/tex]
Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).
[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option C
[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]
Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:
[tex]\implies 6 \cdot 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.1 → 1 digit0.01 → 2 digitsTherefore, there is a total of 3 digits.
Put the same number of digits after the decimal point in the product:
[tex]\implies 0.924[/tex]
Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.
Answer option D
[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]
Again, employing the technique of multiplying decimals.
As there are a total of 5 digits after the decimals:
[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option E
[tex]\boxed{0.00924}[/tex]
As we have already calculated, (0.06) · (0.154) = 0.00924.
Therefore, this is a valid answer option.
What is the formula for simple interest
Answer: The formula for simple interest is P*R*T/100
Step-by-step explanation: Where P stands for Principal and R for Rate T for Time
Each week, Tasha saves 60% of the money she earns babysitting and spends the rest. This week she
earned $60.00
How much more money did she save than spend this week?
ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
intuitive distortion
The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and XY ≅ FE .
What is ASA and AAS?The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.
The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.
From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.
Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:
∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .
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Activity class has 20 women and 13 men. A committee of five is chosen at random. Find (a) p(the committee consists of all women). (b) p(the committee consists of all men) (c) p(the committee consists of all of the same sex) Activity Suppose that a die is loaded (biased) such that 3 appears twice as often as each other number but that the other 5 numbers are equally likely. What is the probability that an odd number appears when we roll this die?
the probability of the committee consisting of all women is 6.53%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
number of women = 20
number of men = 13
Total number of persons = 20+ 13 = 33
A committee of 5 people is chosen at random. Total number of ways in which the committee of 5 can be chosen N
N = C(33 5) = 33! / 5!*28!
N = 237336
p(the committee consists of all women) = C (20 3)*C(13 0)/N
p = 15504 / 237336
p = 0.0653
Hence, the probability of the committee consisting of all women is 6.53%
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Tracy is saving to buy a new guitar that costs $253. 77 (including tax). Tracy has saved $136. 27, and she can save $23. 50 each week. How many more weeks will it take her to save enough money?.
Tracy need 5 weeks to save enough money to buy a new guitar.
Given that,
Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).
Tracy has already saved $136. 27.
Now she needs = 253. 77- 136. 27
= $117.50
she can save each week = $23. 50
Tracy will take weeks to save enough money
= [tex]\frac{117.50}{23.50}[/tex]
= 5 weeks.
Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.
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Use the zero-product property to solve the equation.
(x + 3)^2 = 0
Helppppp, I don’t know what to do, I just really need the answer
The completed statement on the exponential model that fits the data in the question is presented as follows;
The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.
What is a correlation coefficient?The correlation coefficient is an indication of the level at which the variables are interdependent.
The table of values in the question can be entered into a spreadsheet application as follows;
In the spreadsheet application, enter Year since 1960 values in a column, and the Plastic Production in an adjacent columnSelect the all the data entered into the spreadsheet document such as MS Excel, then select the Insert tabIn the charts section select scatter plot to create a scatter plot of the dataIn the Design tab, that appears when the chart is selected, select the Add Chart Element button access the Trendline functionSelect the Exponential trendline from the menu for trendlinesThe exponential trendline is then created by the spreadsheet applicationThe equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)
The growth rate from the above exponential function is 7·88% per year
The production 15 years after 1960 is therefore;
f(15) = 9.2179·e^(0.0788 × 15) ≈30.06
The number of plastic produced 15 years after 1960 is about 30 million metric tons
The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model
The prediction is correct based on the strong correlation between the year and the number of plastic produced.
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please help im suffering right now
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
May I please have brainliest for this? Thank you very much!
What is 5% of 60 use a double number line diagram to show your work
Using the proportion , the 5% of 60 would be 3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the number of 5% of 60.
5% of 60
= 0.05 x 60
= 3
Therefore, the 5% of 60 would be 3.
Using the proportion , the 5% of 60 would be 3.
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Simplify the expression. negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
Using mathematical operators, the expression [15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100] is simplified as [5(20x + 409)] / 4500x - 407
ExpressionAn expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
In this problem, we have to first of all write out the words and expression in mathematical form. To do this, we have to apply mathematical operators like addition, subtraction, multiplication and division.
This can be rewritten as:-
[15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100]
Simplifying this, we have;
[5(20x + 409)] / 4500x - 407
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Help me please, I don’t understand this question.
The average rate of change of the function:
f(x) = x^2 + 7x + 9
On the interval [-9, 0] is -2.
How to find the average rate of change?
For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is:
f(x) = x^2 + 7x + 9
And the interval is -9 ≤ x ≤ 0, it can also be written as [-9, 0]
Evaluating the function in the extremes of the interval we get:
f(0) = 0^2 + 7*0 + 9 = 9
f(-9) = (-9)^2 + 7*(-9) + 9 = 27
Then the average rate of change is:
r = ( f(0) - f(9))/( 0 - (-9)) = (9 - 27)/(9) = -18/9 = -2
The average rate of change is -2.
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Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
The value of car after 6 years is £498.53
Define Modeling Exponential Decay
A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.A(1 - r)^tA = Present value , r = rate, t = timeGiven that,
Dan buys a car = £700
Depreciates at a rate of = 5.5% per year
The value after 6 years = 700 (1 - 5.5 / 100) ^6
= 498.527 or 498.53
Therefore, the value of car after 6 years is £498.53
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Evaluate the expression when b=9
4b+10-b
Group of answer choices
37
47
27
17
Answer:
37
Step-by-step explanation:
4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37
Which expression is equivalent to log2-log6
Answer: log2-log6=-log3
Step-by-step explanation:
[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]
select all that are equal to 6^4(6^-5)
The options that are equal to 6⁴/(6⁻⁵) using laws of exponents are;
b. 1/6
c. 6^-1
d. 1/6^1
How to use laws of exponents?The laws of exponents are;
Product of powers rule.Quotient of powers rule.Power of a power rule.Power of a product rule.Power of a quotient rule.Zero power rule.Negative exponent rule.The exponent we are supposed to solve is;
6⁴/(6⁻⁵)
According to laws of exponents, we know that;
x³/x² = x^(3 - 2)
Thus;
6⁴(6⁻⁵) = 6^(4 + (-5)) = 6^(-1) = 1/6
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Complete question is;
Select all the are equal to 6^4(6^-5)
a. 1\6^-1
b. 1/6
c. 6^-1
d. 1/6^1
e. 1/-6
the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Julian sells 4 pieces of artwork for $72, and each piece is sold at the same rate.
How much does one piece of Julian's artwork cost?
Enter your answer as a number, like this: 42
Answer: 18
Step-by-step explanation: 72 divided by 4= 18
What is 3x+6 I don’t know what this is
Answer:
it is a function.
Step-by-step explanation:
The answer is just 3x+6
Answer:
3x+6 can be be the result of 3(x+2) and then you distribute to get 3x+6
If you are asking how to solve you need an equal sign in the equation for example: 3x+6=27 you would have to solve to figure out wht x is. x is any unknown number we use x or any letter in the alphabet to fill in. You have to olve for the variable now.
A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.
Use addition or subtraction to isolate the variable term on one side of the equation.
Use multiplication or division to solve for the variable.
Step-by-step explanation:
A drawing ha a cale of 1:30. An a drawing, a kitchen i a rectangle meauring 12cm by 27cm. A bedroom ha an actual area of 300000cm
which ha the bigger actual area, the kitchen or the bedroom?
you mut how your working
Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.
As per the given question,
Given drawing scale is:
1 : 30
Shape of the kitchen is rectangle with measurements = 12cm by 27cm
Using scale :
Length = 12cm
Actual length = 12 × 30
= 360cm
Width = 27cm
Actual width = 27 × 30
= 810 cm
Actual area of kitchen = 360 × 810
= 291,600 cm²
Actual area of bedroom = 300,000cm²
300,000 > 291,600
Actual area of bedroom > Actual area of kitchen
Therefore, actual area of bedroom is bigger than the actual area pf kitchen.
The complete question is:
A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
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Can walk 4 miles in one hour and can run 8 miles in one hour what percent of average running speed is her average walking speed 
Answer: 50% of her average running speed is her average walking speed
Step-by-step explanation:
60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.
Given that z=x + i y, find the values of real numbers x and y such that z - 4iz' + 3 = 0, when z' is the conjugate of z.
THANKS IN ADVANCE!!!
The value of z = 0 + 0i
What is complex numbers ?
A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.
( x + iy ) - 4i ( x - iy ) = 0
x + iy - 4ix + 4i²y = 0
x + i (-4x + y ) + 4y = 0
x + 4y + ( - 4x + y )i = 0
Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation
x + 4y = 0 ⇒(1)
-4x + y = 0 ⇒ (2)
Multiplying equation (1) with 4
4x + 16y = 0
Solving the equations
4x + 16 y = 0
-4x + y = 0
17 y = 0
y = 0
Putting the value of y in (1)
x + 4(0) = 0
x = 0
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a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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