PLEASE explain this, I'm so lost. 25 points! What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
Answers
a can be found using the sine function. Recall sin = (opp)/(hyp)
Here [tex]sin 60 = \frac{a}{8} [/tex]
[tex] \frac{ \sqrt{3} }{2}= \frac{a}{8} [/tex]
[tex]2a=8 \sqrt{3} [/tex]
[tex]a=4 \sqrt{3} [/tex]
The base can be found using the sin of 30 degrees as this is a 30-60-90 right triangle.
[tex]sin30= \frac{b}{8} [/tex]
[tex]\ \frac{1}{2} = \frac{b}{8} [/tex]
[tex]b=4[/tex]
The area of the triangle in the picture is given by [tex]A=( \frac{1}{2} )bh= (\frac{1}{2})(4)( \frac{ \sqrt{3} }{2} )= \sqrt{3} [/tex].
The base of the pyramid is a hexagon which can be divided into 6 triangles each of which is double the area of the one we just found. So the area of the base = 2(area of the triangle we found)(6) = [tex]12 \sqrt{3} [/tex]
The answer is:
area of base = [tex]12\sqrt{3}[/tex]
Hope it helps!
Related Questions
A cross-country travels 20 kilometers before she realizes that she has to cover at least 75 kilometers in order to qualify for the next race. If the racer travels at a rate of 10 kilometers per hour, how many whole hours will it take her to reach the 75-kilometer mark?
Answers
The surface area of a sphere is found using the formula SA=4πr^2, where r is the radius. If the surface area of a sphere is 64π square feet, what is the radius, in feet? A. 3 B. 18 C. 1 D. 4
Answers
64pi=4pir^2
cancel the pi
64=4r^2
16=r^2
r=4
[tex]64 \pi = 4 \pi r^{2}[/tex]
[tex]16= r^{2}[/tex]
[tex]r^{2}=16[/tex]
[tex]r=4 [/tex] (Answer D)
PLEASE HELP! Two numbers have a sum of one and a product of -6 Use the quadratic equation -n squared plus n plus 6 equals 0 to determine the two numbers
Answers
so let one be x and one be y
you need to find the factors of -6 which is 1 and 6, and 2 and 3
the negative doesn't matter to which one.
only 3 and -2 add up to 1 and have a product of -6
the quadratic equation is ax² + bx + c
-n² + n + 6 = 0
( n + 3 ) ( n - 2 ) = 0
I hope this helps!
Rewrite as a conditional statement.
2. The sprinkler was turned on this morning resulting in the grass getting wet.
Answers
The hours of daylight,y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40) + 12.23. How many hours of daylight, to the nearest tenth,does this model predict for February 14, 2013?
(1) 9.4
(2) 10.4
(3)12.1
(4)12.2
Answers
Answer:
Option (4) 12.2
Step-by-step explanation:
Hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation
y = 3.06 sin ( 0.017x - 1.40 ) + 12.23
We have to calculate the hours of daylight from the given equation for February 14, 2013.
From January 1, 2013 to February 14, 2013 number of days = 31 + 14 = 45 days.
Now we place x = 45 days in the equation
y = 3.06 sin (0.017 × 45 - 1.40) + 12.23
= 3.06 sin ( 0.765 - 1.40 ) + 12.23
= 3.06 sin ( - 0.635 ) + 12.23
= 3.06 ( - 0.0111) + 12.23
= -0.0339 + 12.23 = 12.196 = 12.20
Option (4) 12.2 is the correct answer.
The number of hours of daylight for the model for February 14 , 2013 is 12.2
Given data:
The function is represented as y=3.06sin(0.017x-1.40) + 12.23
To find the number of hours of daylight predicted by the model for February 14, 2013, substitute the corresponding value of x into the equation and evaluate it.
The total number of days , x = 31 days in January + 14 days in February
So, x = 45
Now, substitute x = 45 into the equation:
y = 3.06sin(0.017(45) - 1.40) + 12.23
Calculating the expression inside the sine function:
0.017(45) - 1.40 = -0.635
Substituting this value back into the equation:
y = 3.06sin(-0.635) + 12.23
The sine of -0.635 is approximately -0.593.
y = 3.06(-0.593) + 12.23
y ≈ 10.425
Rounding to the nearest tenth, the predicted number of hours of daylight for February 14, 2013, is 10.4.
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Which expression is a rational number? A) ( 25 + 25 )2 B) ( 25 + 50 )2 C) ( 50 + 75 )2 D) ( 25 + 72 )2
Answers
All expressions given, A, B, C, and D, are rational numbers. This is because they all result in a number that can be expressed as the quotient of two integers when the operations are performed according to the order of operations and squared.
A rational number is a number that can be expressed as the quotient or fraction rac{p}{q} of two integers, a numerator p and a non-zero denominator q. To determine which expression represents a rational number, we look for an outcome that is expressible as such a fraction after carrying out any operations involved in the expression.
Let's evaluate whether the expressions given result in rational numbers when the operations are performed:
A) ( 25 + 25 )2 = [tex](5+5)^2[/tex] = [tex]10^2[/tex] = 100 which is a rational number.B) ( 25 + 50 )2 = [tex](5+10)^2[/tex] = [tex]15^2[/tex] which is a rational number.C) ( 50 + 75 )2 = [tex](2+3)^2[/tex] = [tex]5^2[/tex] which is a rational number.D) ( 25 + 72 )2= [tex](5+14.4)^2[/tex] = [tex]19.4^2[/tex] which is not a perfect square but still a rational number since 19.4 is a rational number and squaring it results in another rational number.Therefore, all given expressions A, B, C, and D result in rational numbers when squared.
Option A, B, C, and D is a rational number.All given expressions result in rational numbers, as each step of their calculations simplifies to integers. Each integer can be expressed as the quotient of two integers, confirming they are rational.
To determine which expression results in a rational number, let's evaluate each option step by step. A rational number is any number that can be expressed as the quotient of two integers.
(25 + 25)2: First, we simplify inside the parentheses: 25 + 25 = 50. Then we square the result: 502 = 2500.(25 + 50)2: Simplify inside the parentheses: 25 + 50 = 75. Then we square the result: 752 = 5625.(50 + 75)2: Simplify inside the parentheses: 50 + 75 = 125. Then we square the result: 1252 = 15625.(25 + 72)2: Simplify inside the parentheses: 25 + 72 = 97. Then we square the result: 972 = 9409.All the results are integers, which are rational numbers because any integer n can be expressed as n/1. Therefore, all given expressions result in rational numbers.
A right triangle has an area of 33 mm 2 2 and a height of 11 mm. How long is the base of the triangle? Enter your answer in the box. mm
Answers
Area: 33/11
Area: 3
The answer is 3 millimeters
The beginning balance in a savings account is $64.98. After a deposit of $73.87, two withdrawals of $51.00 and $23.50, and $1.15 of interest earned, what is the balance? $138.85 $65.50 $64.35 $87.85
Answers
A deposit of $73.87 is made after which the amount in the account is $64.98 + $73.87 = $138.85.
Next come two withdrawals (this is money that is taken out of the account so we need to subtract the amounts given). $138.85 - $51.00 = $87.85 and $87.85 - $23.50 = $64.35.
Interest is added to the account. So we end by adding $1.15 to the amount we just arrived at. That is, $64.35 + $1.15 = $65.50
The balance after these transactions is $65.50
A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square inches.
What is the area of the new photograph?
_____in²
Answers
1^2/5^2 = 1/25
1/25 = 154/x
1x= 154 (25)
1x/1= 3850/1
x= 3850
A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square inches.
Solution:
The photograph is being enlarged by a factor 5.
So, each dimension of the photograph is enlarged by 5
So, area is enlarged by [tex] 5^{2} [/tex]
Or, Area is enlarged by a factor=5*5=25
So, the Area of enlarged photograph=[tex] 5^{2} [/tex] *Area of original photograph
Area of enlarged photograph=25*Area of original photograph
Area of enlarged photograph=25*154
On multiplying 25 by 154 we get 3850
Area of enlarged photograph=3850[tex] inches^{2} [/tex]
Answer:
Area of new photograph=3850[tex] in^{2} [/tex]
Which statement best describes Marcos equation
Answers
Cosine function has period of 2[tex] \pi [/tex] because the function value will be same for variable that 2[tex] \pi [/tex] appart. In the problem, cos [tex]- \pi /2[/tex] and cos [tex] 3 \pi /2 [/tex] difference would be 4[tex] \pi [/tex], which is 2 * [tex] 2 \pi [/tex]. That means they both should have same value.
Convert 302 inches into yards
Answers
302 / 12 = 25.16~
Now, we need to divide that quotient by 3 as there are three feet in a yard.
25.16~ / 3 = 8.38~
302 inches is 8.38~ yards.
I hope this helps!
If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and b contain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse. submit
Answers
The expression for the length of the hypotenuse is c = [tex]\sqrt{a^2 + b^2}[/tex].
The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b.
So, the expression for the length of the hypotenuse c is:
c = [tex]\sqrt{a^2 + b^2}[/tex]
This expression calculates the length of the hypotenuse given the lengths of the shorter sides a and b.
What is the density of a cube with sides of 4 cm and a mass of 512g?
Answers
4 x 4 x 4 cube
To find the density
Density = mass/volume
The volume of this cube is
4*4*4 = 64
Density = mass / volume
density = 512g / 64cm^3
Density = 8 g/cm^3
Hope this helps
The density of the cube whose volume is 64 cm³ and mass is 512 g is given by the equation D = 8 g/cm³
What is the Volume of a Cube?
The formula of volume of the cube is given by:
Volume of Cube = a x a x a
Volume of Cube = a³
where a is the length of its sides or edges
Given data ,
Let the density of the cube be represented as D
Let the volume of the cube be represented as V
Now , the equation will be
The mass of the cube = 512 g
The side length of the cube a = 4 cm
So , Volume of Cube = a³
Substituting the values in the equation , we get
Volume of Cube V = 4 x 4 x 4
Volume of Cube V = 64 cm³
Now ,
The density of the cube D = mass of the cube / Volume of Cube
Substituting the values in the equation , we get
The density of the cube D = 512 / 64
The density of the cube D = 8 g/cm³
Therefore , the value of D is 8 g/cm³
Hence , the density of the cube is 8 g/cm³
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The area of a rectangular room is 120 square feet. The width is 10 feet. What is the length?
Answers
~Deceptiøn
The length of the rectangular room is 12 feet.
To find the length of a rectangular room when the area and width are known, you can use the formula:
Area = Length x Width
Given that the area is 120 square feet and the width is 10 feet,
we can substitute these values into the formula:
120 = Length x 10
Length = 120 / 10
Length = 12
Therefore, the length of the rectangular room is 12 feet.
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PLEASE HELP ASAP!!!!!!!!
Answers
Answer:
A. y = -2x + 4
Step-by-step explanation:
You are given the values of slope (m) and y-intercept (b). The slope-intercept form of the equation for the line is ...
y = mx + b
Putting m=-2 and b=4 into this form, you get ...
y = -2x + 4
What is the solution to the following system?
3x + 10y -12z = 40
x - 5y = 0
x- 4z = 0
--------------------------------------------------------------------
A.) (8, 40, 32)
B.) (10, 2, 3)
C.) (20, 4, 5)
D.) (40, 8, 10)
Answers
Answer: C.) (20, 4, 5)
Step-by-step explanation:
The given system is
[tex]3x + 10y-12z = 40.....................(1)\\x-5y =0..........................(2)\\x- 4z=0............................(3)[/tex]
From (2), we have
[tex]x=5y\\\Rightarrow\ y=\frac{x}{5}[/tex]
From (3)
[tex]x=4z\\\Rightarrow\ z=\frac{x}{4}[/tex]
Substitute the values of y and z in equation (1), we get
[tex]3x+10(\frac{x}{5})-12(\frac{x}{4})=40\\\\\Rightarrow\ 3x+2x-3x=40\\\\\Rightarrow\ 20x=40\\\\\Rightarrow\ x=5[/tex]
Then [tex]y=\frac{20}{5}=4[/tex]
and [tex]z=\frac{20}{4}=5[/tex]
Hence, the solution of the given system is (20,4,5)
x^2-15=0 Find the number of real number solutions for the equation.
Answers
1.1 Factoring: x2-15
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 15 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
2.1 Solve : x2-15 = 0
Add 15 to both sides of the equation :
x2 = 15
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 15
The equation has two real solutions
These solutions are x = ± √15 = ± 3.8730
Final answer:
Explaining the number of real number solutions for the given quadratic equation x²-15=0.
Explanation:
x²-15=0
To find the number of real number solutions for the equation, we start by setting the expression to zero:
x² - 15 = 0
x² = 15
x = ±√15
Therefore, the equation has two real number solutions, which are ±√15.
The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x? Image for option 1 Image for option 2 Image for option 3
Answers
Answer with explanation:
⇒ y=8.1 x
This is a Linear equation depicting linear relationship between y and x which is between the number of hours Alexander works, x, and the dollar amount he earns, y.
To determine a line you need two points.
→Put, x=0,in y=8.1 x, gives y=0 gives a Point (0,0).
→Put,x=1 gives , y=8.1 × 1→y=8.1 gives another point (1,8.1).
→So, Drawn a line passing through (0,0) and (1, 8.1),which is the required image of the equation given.
The value of x is
.
Answers
we know that
The Exterior Angles of a Polygon add up to [tex]360[/tex] degrees
so
in this problem
[tex]130+134+x=360[/tex]
Solve for x
[tex]264+x=360[/tex]
Subtract [tex]264[/tex] from both sides
[tex]264+x-264=360-264[/tex]
[tex]x=96\ degrees[/tex]
therefore
the answer is
the value of x is [tex]96\ degrees[/tex]
Lindesy wants a new bike that costs $230. Her father says that if she saves up 30% of the cost he will pay the rest. How much money does Lindesy need to save?
Answers
Cary is 5 5 years older than dan. in 5 years the sum of their ages will be 81. find the age of each man now.
Answers
C - 55 = D
(C + 5) + (D + 5) = 81
C = D + 55
(D + 55 + 5) + (D + 5) = 81
(D + 60) + (D + 5) = 81
2D = 16
D = 8
C = 8 + 55 = 63
Cary is 63 years old, and Dan is 8 years old
y = x - 55
x + 5 + y + 5 = 81
Then,
x + 5 + x - 55 + 5 = 81
2x - 45 = 81
2x = 81 + 45
2x = 126
x = 126/2 = 63
Now, let's find y.
y = 63 - 55 = 8.
Therefore Cary is 63 years old and Dan is 8 years old.
Hope this helps !
Photon
PLEASE HELP
Andre must pay a co-pay of $15 for an office visit. his insurance company will then pay 80% of the cost of the visit. how much will andre pay for an office visit that costs $310
$62
$65
$77
$80
Answers
Answer:
C. $77
Step-by-step explanation:
1000p for an answer pleaseeeeee
Answers
but the 3 has a line above. which means repeated
Math help? One question?
Answers
_____
The law of cosines is usually used for this.
EF^2 = DE^2 +DF^2 -2*DE*DF*cos(D)
.. = 6^2 +11^2 -2*6*11*cos(40°)
.. ≈ 55.88
EF ≈ √55.88 ≈ 7.5 . . . ft
Describe a situation in which there would be a positive association between two variables.
Answers
.. number of miles driven
.. number of gallons of gas used
Solve for x. 35x+5=45 Enter your answer in the box. x =
Answers
35x=45-5
35x=40
x=40/35 simplify
x=8/7
Jennifer is calculating her gpa. if she uses "=(a1+a2+a3+a4)/4", this is an example of which type of entry?
Answers
(GPA) = Grade Point Average.
Effectively in a program like excel she can use:
GPA = (a1 + a2 + a3 + a4) / 4
Where,
ai = represents each of the notes (i: 1,2,3,4)
However, this is also an example of the following type of entry:
GPA = AVERAGE (a1: a4)
Answer:
Entry:
Formulas: are references of cells, names of cells or ranges, functions or operators that result in a value from other existing values.
Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
Which could be the measures of angle POS and angle POQ?
Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees
Answers
The correct answer is:
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Explanation:
OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.
This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.
If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.
PLEASE HELP
8.02
1. Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1.
A) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-8, 0), (8, 0)
B) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -8), (0, 8)
C) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-6, 0), (6, 0)
D) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -6), (0, 6)
2. Find the center, vertices, and foci of the ellipse with equation 2x2 + 6y2 = 12.
A) Center: (0, 0); Vertices: point negative square root of six comma zero and point square root of six comma zero ; Foci: (-2, 0), (2, 0)
B) Center: (0, 0); Vertices: (0, -6), (0, 6); Foci: Ordered pair zero comma negative four square root two and ordered pair zero comma four square root two ;
C) Center: (0, 0); Vertices: point zero comma negative square root of six and point zero comma square root of six ; Foci: (0, -2), (0, 2)
D) Center: (0, 0); Vertices: (-6, 0), (6, 0); Foci: Ordered pair negative four square root two comma zero and ordered pair four square root two comma zero
3. Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
A) A vertical ellipse is shown on the coordinate plane centered at, five, two, with vertices at, five, seven, and five, negative three and minor axis endpoints at three, two, and seven, two.
B) A horizontal ellipse is shown on the coordinate plane centered at five, two, with vertices at zero, two, and ten, two and minor axis endpoints at five, four and five, zero.
C) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at zero, five and zero, negative five and minor axis endpoints at, negative two, zero and two, zero.
D) A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at, negative five, zero and, five, zero and minor axis endpoints at, zero, two and zero, negative two.
4. Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.
A) x squared divided by two plus y squared divided by three = 1
B) x squared divided by nine plus y squared divided by four = 1
C) x squared divided by three plus y squared divided by two = 1
D) x squared divided by four plus y squared divided by nine = 1
5. An elliptical riding path is to be built on a rectangular piece of property, as shown below.
A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.
The rectangular piece of property measures 8 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.
Answers
Please, see the detailed solution in the attached files.
Thanks.
Marge wants to build a sidewalk of uniform width around a rectangular swimming pool that is 80 feet long and 50 feet wide.she has 2000 square feet of concrete to create the sidewalk.what should be the width of the sidewalk
Answers
We have then:
(80 + 2W) (50 + 2W) - 80 (50) = 2,000
Rewriting we have:
4000 + 160W + 100W + 4W ^ 2 - 4000 = 2000
4W ^ 2 + 260W - 2000 = 0
W1 = 6.949334595148748
W2 = -71.94933459514874 (ignore)
round:
W = 6.95
Answer:
the width of the sidewalk should be:
W = 6.95 feet