The surface area of the cube is 2,400 square feet.
To find the surface area of a cube, one must use the formula:
[tex]\[ \text{Surface Area} = 6 \times (\text{side length})^2 \][/tex]
Given that the width of the cube is 20 feet, we can assume that all sides of the cube are equal, since a cube has all sides of equal length. Therefore, the side length of the cube is 20 feet.
Now, we can substitute the side length into the formula:
[tex]\[ \text{Surface Area} = 6 \times (20 \text{ ft})^2 \] \[ \text{Surface Area} = 6 \times 400 \text{ ft}^2 \] \[ \text{Surface Area} = 2,400 \text{ ft}^2 \][/tex]
Thus, the surface area of the cube is 2,400 square feet.
if a and b are acute angles such that sinA=4/5 and cosB=12/13, calculate, without using tables: sin(a-b)
Find h(x, y) = g(f(x, y)). g(t) = t + ln(t), f(x, y) = 4 − xy 2 + x2y2 h(x, y) =
The function h(x, y) is given by the composition of the functions g(t) and f(x, y). With the given expressions for f and g, the function h(x, y) = g(f(x, y)) equals to (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).
Explanation:The question asks to find the function h(x, y) from the functions g(t) and f(x, y), where g(t) = t + ln(t), and f(x, y) = 4 − xy^2+ x^2y^2. To begin with, it is necessary to substitute f(x, y) in place of 't' in function g which is g(f(x, y)), since we have h(x, y) = g(f(x, y)).
Performing the substitution, we obtain:
h(x, y) = g(f(x, y)) = (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).
This is your final function h in terms of x and y.
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Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C)
1
2
x + 8 = 10
D)
1
2
(2x - 6) = -6
The answer is C
for X=-3
A classmate believes that a triangle can have both a right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect?
Sum of internal angles in a triangle is 180 degree.
∠A + ∠B + ∠C = 180°
Now we have three cases:
Case 1 : For right anlge triangle.
in this case one angle is 90°. and rest of two angle's sum is 90 degree
it means measure of rest two anles is less than 90 degree.
So, this type trianlge holds one right anlge and two acute angle.
Case 2: If one angle is Obtuse angle(more than 90°)
In this case , rest of two angle's sum is less than 90°
So, this type trianlge holds one obtuse anlge and two acute angle.
Case 3: All angles are acute
In this case all three anles are less than 90°
So, triangle has one obtuse angle, that means rest of two anlges must be less than 90°
The hypotenuse of the right triangle ABC shown below is 17 feet long. The cosine of angle C is 35. How many feet long is the segment AC?
Length of the segment AC is 14 feet
What is Trigonometric function?In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given,
Length of the hypotenuse = 17 feet
Angle of C =35 degrees
We know that,
Cos θ = Adjacent side / Hypotenuse
cos 35 = [tex]\frac{x}{17}[/tex]
x= [tex]17(cos 35)[/tex]
x= 13.9 ≅ 14 feet
Hence, the length of the segment AC is 14 feet
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Titus had 1/2 can of paint. He used 2/3 to paint a tabletop. What fraction of a full can of paint did Titus use?
Titus had half a can of paint and used two-thirds of it, which means he used (1/2) * (2/3) = 2/6, which simplifies to 1/3 of a full can of paint.
Explanation:The student is asking about how to calculate the fraction of a full can of paint Titus used given that he had half a can and used two-thirds of it. To find out what fraction of the full can he used, you need to perform a multiplication of the two fractions.
Here is the step-by-step calculation:
Write down the fractions: 1/2 (half a can of paint Titus had) and 2/3 (the fraction he used).Multiply these two fractions: (1/2) \\times\ (2/3)Simplify the multiplication: The numerators are multiplied together and the denominators are multiplied together: (1 \\times\ 2)/(2 \\times\ 3) = 2/6Reduce the fraction, if possible: 2/6 can be simplified to 1/3 by dividing both numerator and denominator by 2.Therefore, Titus used 1/3 of a full can of paint.
How does one find the equation y=ax²+bx+c when you are only provided with the coordinates of the turning point, (-6,-9)? Note: a is +1 or -1
34+x=46;x=12 is this problem a solution
Final answer:
The solution x=12 is correct for the problem 34+x=46, as substituting x=12 into the original equation results in 46, matching the right side. Verification by substitution is a common practice to confirm the accuracy of solutions, particularly in the case of equations with two solutions.
Explanation:
The problem provided is 34+x=46; you have also provided that x=12 is the solution. To verify if x=12 is the correct solution, we substitute x=12 into the original equation: 34+12=46. Upon calculating, 34+12 equals 46, which is indeed the right side of the equation, confirming that the solution x=12 is correct.
Moreover, in general mathematical practice, checking solutions by substituting them back into the original equation is a reliable method for verification. If a problem has two solutions, as some quadratic equations do, both solutions should be checked in this way to ensure that each solution satisfies the original equation, indicating that both are correct. For example, if we have a quadratic equation like 2x²-8=0, solving it would give us two possible values for x that can be substituted back into the equation to verify if the identity holds true for both solutions.
Final answer:
The given solution x=12 for the equation 34+x=46 is correct because when substituted back into the original equation, it results in an identity, confirming the solution's validity.
Explanation:
In mathematics, particularly in algebra, when we have an equation such as 34 + x = 46, and we are given a solution, in this case x=12, we can verify its correctness by substituting the value back into the original equation. If the equation simplifies to an identity, which is an equation that always holds true like 6 = 6, then the given solution is correct. To check if x=12 is a solution for the original problem, we perform the substitution:
34 + 12 = 46
After the substitution, the equation simplifies to:
46 = 46
This results in an identity, confirming that the given solution x=12 is indeed correct.
This process is similar to checking solutions for other types of equations, such as linear, quadratic, or higher-degree polynomials. Whether a problem has a single solution like in this case, or multiple solutions such as x=3, x=-7, each potential solution must be verified individually by substituting them back into the original equation to ensure they lead to an identity.
You want to buy a jet ski 5 years from now, and you plan to save $600 per year, beginning today. you will deposit your savings in an account that pays 8% interest. how much will you have 5 years from now?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The Balance after the fifth year from now is 3801.56.
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The balance in the accounts can be calculated as,
Balance after the first year,
A = 600×(1.08) = 648
Balance after the second year,
A = (600+648)(1.08) = 1248(1.08) = 1347.84
Balance after the third year,
A = (1347.84+600)(1.08) = 1947.84 (1.08) = 2103.67
Balance after the fourth year,
A = (2103.67+600)(1.08) = 2703.67 (1.08) = 2919.96
Balance after the fifth year,
A = (2919.96+600)(1.08) = 3519.96 (1.08) = 3801.56
Hence, the Balance after the fifth year from now is 3801.56.
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Find the orbital period (in years) of an asteroid whose average distance from the sun is 5 au.
Final answer:
To find the orbital period of an asteroid at 5 AU, apply Kepler's Third Law, resulting in approximately 11.18 years.
Explanation:
The question asks to find the orbital period of an asteroid with an average distance of 5 astronomical units (AU) from the Sun. We can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (T, in years) is proportional to the cube of the average distance from the Sun (a, in astronomical units) for any object orbiting the Sun, expressed as-
[tex]T^2 = a^3[/tex]
Applying the formula for the asteroid in question:
Identify the average distance from the Sun, which is given as 5 AU.Calculate the cube of this distance: 53 = 125.Find the square root to determine the orbital period: √125 ≈ 11.18 years.Therefore, the orbital period of the asteroid is approximately 11.18 years.
2 (x-4)=22
[tex]2(x - 4) = 22[/tex]
Answer:
x=15
Step-by-step explanation:
To get the answer I thought, what times 2 equals 22 and i got 11. 15-4=11. so i figured x=15.
This is the graph of f(x). What is the value of f(3)?
A. 5
B. 6
C. 8
D. 3
Will ran four miles on his first day of training. The next day he ran one-third that distance. How far did he ran the second day?
0.75 degrees centigrade is this a positive or negative temperature?
0.75 degrees centigrade is a positive temperature.
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
Temperature= 0.75 Centigrade
Now, As, the temperature 0.75 lies between whole number 0 and 1.
also, 0.75 is greater than 0.
Any number greater than is a positive number.
Hence, 0.75 is Integer integer.
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A carpenter is assigned the job of expanding a rectangular deck where the length is four times the width. The width of the deck is to be expanded by 3 feet and the length is to be expanded by the new width. If the area of the new rectangular deck is 124 ft larger than the area of the original deck,find the dimensions of the original deck
Find the perimeter of a square measuring 5.35cm on a side
The perimeter of a square measuring 5.35 cm on a side is 21.4 cm
Further explanationTo solve the above questions, we need to recall some of the formulas as follows:
Area of Square = (Length of Side)²
Perimeter of Square = 4 × (Length of Side)
Area of Rectangle = Length × Width
Perimeter of Rectangle = 2 × ( Length + Width )
Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Rhombus = 4 × ( Length of Side )
Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )
Let us now tackle the problem !
Given:
Length of Side = 5.35 cm
Unknown:
Perimeter = ?
Solution:
Perimeter of Square = 4 × ( Length of Side )
Perimeter of Square = 4 × ( 5.35 )
Perimeter of Square = 21.4 cmLearn moreThe perimeter of a polygon : https://brainly.com/question/6361596The perimeter of a rectangle : https://brainly.com/question/7619923The perimeter of a triangle : https://brainly.com/question/2299951Answer detailsGrade: College
Subject: Mathematics
Chapter: Two Dimensional Figures
Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width
North Carolina has 12 less electoral votes than Florida right and solve a subtraction equation to find the number of electoral votes for Florida
Number of Electoral votes for Florida is 29.
The question: North Carolina has 12 less electoral votes than Florida. To find the number of electoral votes for Florida, we can set up a subtraction equation.
Let x be the number of electoral votes for Florida.
Since North Carolina has 12 less electoral votes, the equation would be x = x + 12.
Solving for x, Florida has 29 electoral votes.
Find an equation for the nth term of the arithmetic sequence.
-17, -12, -7, -2, ...
Answer Choices
A: an = -17 + 5(n + 2)
B: an = -17 + 5(n + 1)
C: an = -17 + 5(n - 1)
D: an = -17 x 5(n - 1)
The equation for the nth term of the given arithmetic sequence is an = -17 + 5(n - 1), which matches answer choice C.
The given sequence is an arithmetic sequence, where each term increases by a common difference. To find the equation for the nth term (an), you start with the first term (a1 = -17) and add the common difference (d = 5) multiplied by (n - 1), since the first term is already in place.
A correct formula for an arithmetic sequence is an = a1 + (n - 1)d. Applying this to the given sequence, we have an = -17 + (n - 1)5. Simplifying this expression gives us an = -17 + 5n - 5, which further simplifies to an = 5n - 22. Thus, the correct answer is an = -17 + 5(n - 1), which corresponds to answer choice C.
Consider the function f(x)=8-3x^2. Find the value of f(x) when x=3 and select the correct answer below.
A.-19
B.-10
C.26
D.35
In a game, the two players scored a total of 121 points. One player had 13 more points than the other player. How many points did the player with the fewer points score?
The equation below shows the total volume (V), in cubic units, of 2 identical boxes with each side equal to s units:
V = 2s^3
If s = 3.5 units, what is the value of V?
the equation of a line that goes through the points (0,0) and (300000,365)
A rectangular park is 5/6 miles wide and 1 5/7 miles long. What is the area of the park?
Please help. Answer this ASAP!!!!
Thank You!!!!
Answer:1 3/7
Step-by-step explanation: A mathematical equation
Let x and y be independent each uniformly distributed on {1,2,...,n} find p(x < y )
How many different four-digit numbers can be made using the digits 1, 2, 3, 4, 5, 6 if no digit can be used more than once?
solve.
[tex] \sqrt{3 x - 11} - \sqrt{x} + 5 = 6[/tex]
suling bought 3meters of ribbons she used 5/6meter to make a bow find the length of the ribbon left
Choose the correct simplification of the expression (5xy5)2(y3)4. 25x2y22 10x2y22 25x3y14 10x3y14
Answer:
A) [tex]25x^2y^{22}[/tex]
Step-by-step explanation:
The given expression is [tex](5xy^{5})^2 . (y^3)^4[/tex]
Here we have to use exponent rules and simplify the expression.
Power rule : [tex](a^m)^n = a^{mn}[/tex]
Using the above rule, we can write
[tex](5xy^{5} )^2 = 5^2.x^2.y^{5*2}[/tex]
= [tex]25.x^2.y^10[/tex]
Again using the power rule
[tex](y^{3} )^4 = y^12[/tex]
Now we have to put together this expression, we get
= [tex]25.x^2.y^{10} .y^{12}[/tex]
Now we have to use product rule.
Product rule: [tex]a^m . a^n = a^{m + n}[/tex]
Using this rule, we can simplify further
= [tex]25..x^2.y^{10 +12}[/tex]
= [tex]25x^2y^{22}[/tex]
Answer:
Option A) 25x^2y^22
Step-by-step explanation:
Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. How can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? What does a positive correlation tell you about the dependent and independent variables?