Answers
Answer:
S.A. = 225 ft²Step-by-step explanation:
We have
the rectangle 12ft × 6ft
two triangles with the base b = 12ft and the height h = 8ft
two triangles with the base b = 6ft and the height h = 9.5ft.
The formula of an area of a rectangle l × w:
[tex]A=lw[/tex]
Substitute:
[tex]A_1=(12)(6)=72\ dt^2[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_2=\dfrac{(12)(8)}{2}=48\ ft^2[/tex]
[tex]A_3=\dfrac{(6)(9.5)}{2}=28.5\ ft^2[/tex]
The Surface Area:
[tex]S.A.=A_1+2A_2+2A_3[/tex]
Substitute:
[tex]S.A.=72+2(48)+2(28.5)=225\ ft^2[/tex]
Answer:
Total surface area of the pyramid = 225 ft²
Step-by-step explanation:
Total surface area of the given pyramid is defined by
(Area of rectangular base) + 2(area of two triangular sides with height 8 ft and base 12 ft) + 2(area of two triangles with height 9.5 ft and base 6 ft)
Total surface area = (12×6) + 2[[tex]\frac{1}{2}\times(h)(b)[/tex]]+2[[tex]\frac{1}{2}\times(h')(b')[/tex]]
= 72 + 2[[tex]\frac{1}{2}\times(8)(12)[/tex]]+2[[tex]\frac{1}{2}\times(9.5)(6)[/tex]]
= 72 + 96 + 57
= 225 ft²
Therefore, total surface area of the pyramid is 225 ft²
Related Questions
-
[tex] - \sqrt{5 } - 3 \sqrt{5} [/tex]
Answers
Step-by-step explanation:
[tex]-\sqrt5-3\sqrt5=-1\sqrt5-3\sqrt5=(-1-3)\sqrt5=-4\sqrt5[/tex]
(06.04 MC) Find the area of the following shape.
Answers
Check the picture below.
well, the purple trapezoid, has a height of 5, and its bases are of 5 units and 8 units, recall the bases are the parallel sides in a trapezoid.
now, the yellow rectangle, is a 6x5, and it has those two green triangles in it, well, if we simply get the area of the rectangle, 30 anyway, and subtract the areas of those green triangles, what's leftover, is the rest of the shape on points DEFA.
keeping in mind that the green triangles have a base of 4 and a height of 3 for the one atop and base of 5 and height of 2 for the bottom one.
[tex]\bf \stackrel{\textit{purple trapezoid}}{\cfrac{\stackrel{h}{5}(\stackrel{a}{5}+\stackrel{b}{8})}{2}}~~+~~\left[ \stackrel{\textit{yellow square}}{(6\cdot 5)}-\stackrel{\textit{two green triangles}}{\cfrac{1}{2}(4)(3)-\cfrac{1}{2}(5)(2)} \right] \\\\\\ \cfrac{5(13)}{2}+[30-6-5]\implies \cfrac{65}{2}+[19]\implies \cfrac{103}{2}\implies 51\frac{1}{2}[/tex]
Do you guys know the answer for number 3
Answers
Answer:
{3,23,39}
Step-by-step explanation:
I think that thing inside the box says 4x-5.
The numbers we are putting in are 2,7, and 11.
So when we put 2 in we get 4(2)-5 which is 8-5=3.
When we put 7 in we get 4(7)-5 which is 28-5=23.
When we put 11 in we get 4(11)-5 which is 44-5=39
So the answer is {3,23,39}.
Erica chops wood in the forest.
The table compares the number of cans of insect repellent Erica uses and the number of mosquito bites she gets each day.
Can the number of mosquito bites be represented as a function of the amount of repellent used?
Answers
Answer:
Yes, the number of mosquito bites can be represented as a function of the amount of repellent used.
Step-by-step explanation:
Let x represents the number of cans of repellent and y represents the number of mosquitos,
If f be the relation from x to y,
Then by the given table,
f(x) = { (0, 11), (1, 8), (5, 2), (4,5), (2, 9), (3, 6)}
∵ If for each input in a relation has exactly one output, the relation is called a function.
Here, for each value of x there is exactly one value of y,
Hence, f(x) is a relation from x to y,
That is, the number of mosquito bites can be represented as a function of the amount of repellent used.
Find my number, if it is a two-digit one, one of its digits is 9, and it has remainder 0 when divided by 6.
Answers
Final answer:
The two-digit number in question is 96, as it has one digit as 9 and is divisible by 6.
Explanation:
The student is asking to find a two-digit number where one of the digits is 9, and the number is divisible by 6 without any remainder. To solve this, we need to remember that for a number to be divisible by 6, it must be divisible by both 2 and 3. A two-digit number is divisible by 2 if its last digit is even.
Since one of the digits is 9 (an odd number), the other digit must be even, so our options for the two-digit numbers with a 9 are 90, 92, 94, 96, and 98. To be divisible by 3, the sum of the digits must be divisible by 3. Out of our options, only 96 has a sum of digits (9 + 6) that is divisible by 3. Therefore, the number we are looking for is 96.
31. A driver
can be charged with Driving While Intoxicated (DWI).
A. under 21 years old only
B. over 21 years old only
c. under 18 years old only
D. of any age
Answers
Answer:
D. of any age
Step-by-step explanation:
A driver can be charged with Driving While Intoxicated of any age.
It doesn't matter how old you are because a crime is a crime. If you are younger there will most likely be less of a punishment as adults.
Which set of polar coordinates are plotted in the graph below
Answers
Answer:
C. (-2,2π/3)
Step-by-step explanation:
Given:
In the given plane, each line represents angles and the circles shows the radii. Now as full circle is of 360 degrees or 2π and there are 12 straight lines that means
every angle is π/6 apart (30 degrees).
As the given red point is on circle 2, this means the radii, r=2
and Ф=300 degrees or 5π/3
r=(2,5π/3)
but above is not given in the options.
Polar coordinates can have positive or negative theta and also have positive or negative radii. In case of negative radii the polar coordinate moves in opposite direction of the pole.
if we consider r=-2 then we have to move in opposite direction of pole of Ф=300 degrees or 5π/3 is 120 degrees or 2π/3.
hence r=-2 andФ=2π/3
Correct option is C:(-2,2π/3)!
Use the graph to answer the question.
A line with a slope of negative 5 passing through the origin.
see attached graph
Is the function even, odd, or neither? Why? Select one below
The function is even because it is symmetric about the y-axis.
The function is odd because it is symmetric about the y-axis.
The function is even because it is symmetric about the origin.
The function is neither even nor odd because it is not symmetric about the y-axis or the origin.
The function is odd because it is symmetric about the origin.
Answers
Answer:
The function is odd because it is symmetric about the origin.
Step-by-step explanation:
we know that
A function f(x) is even when
f(x)=f(-x) ----> the function is symmetry about the y-axis
A function is odd when
-f(x)=f(-x) ---> the function is symmetry about the origin
In this problem we have
f(x)=-5x
Verify if the function is even
For x=1 ----> f(1)=-5(1)=-5
For x=-1 ---> f(-1)=-5(-1)=5
so
f(x) is not equal to f(-x)
therefore The function is not even
Verify if the function is odd
we have
f(1)=-5
f(-1)=5
so
-f(1) is equal to f(-1)
-f(x)=f(-x)
therefore
The function is odd because it is symmetric about the origin.
Answer:
The function is odd because it is symmetric about the origin.
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities below?
Answers
Answer:
Graph C is your answer
Step-by-step explanation:
Draw the following graph using the easy coordinates, those are were y axis is zero, and the other were x axis is 0:
[tex]y=-2x+2[/tex]
First point is (1,0) and the other (0,2)
The entire region that belongs to your graph is greater than drawn line.
Draw another graph using the same easy coordinates.
[tex]y=2x-1[/tex]
First point is (0.5,0) and the other (0,-1)
The entire region that belongs to your graph is lesser than the drawn line.
When you merge those graphs into one, you can clearly see that they correspond to the C answer.
Answer:
Graph A.
Step-by-step explanation:
The given inequalities are
[tex]y>-2x+2[/tex]
[tex]y<2x-1[/tex]
The related equation of given inequalities are
[tex]y=-2x+2[/tex]
[tex]y=2x-1[/tex]
The slope of line (1) is -2 and the y-intercept is 2.
The slope of line (2) is 2 and the y-intercept is -1.
Both related lines are dotted line because the points on the line are not included n the solution set.
Check each inequality by (0,0).
[tex]0>-2(0)+2\Rightarrow 0>2[/tex] False statement
[tex]0<2(0)-1\Rightarrow 0<-1[/tex] False statement
So, (0,0) is not included in the shaded area of any of these two inequities.
Therefore, graph A shows the solution to the system of linear inequalities.
-2.5y⁰ for y= -1⅔
find the value of the expression
Answers
Clara and her brother, Carl, are at the beach for vacation. They want to rent bikes to ride up and down the boardwalk. One rental shop, Bargain Bikes, advertises rates of $5 plus $1.50 per hour. A second shop, Frugal Wheels, advertises a rate of $6 plus $1.25 an hour. How much does it cost to rent a bike for one hour from each shop? How about 10 hours?
Answers
Answer:
Let's evaluate each rental shop:
Bargain Bikes: $5 plus $1.5 per hour.For one hour, the cost is $5 + $1.5 = $6.5. For ten hours the total cost is: $5 + 10×$1.5 = $20
Frugal Wheels: $6 plus $1.5 an hour.For one hour, the cost is $6 + $1.25 = $7.25. For ten hours the total cost is: $6 + 10×$1.25 = $18.5
If Clara and her brother are thinking about renting a bike for an hour, Bargain Bikes is the best option. On the other hand, if they want to rent it fr several hours Frugal Wheels is the best option.
[2 -6] - [-2 4] please help
Answers
The answer is 20. The explanation is shown in the picture.
Answer:
[tex]\Huge \boxed{20}[/tex]
Step-by-step explanation:
This question is about order of operations. It stands for parenthesis, exponent, multiply, divide, add, and subtract from left to right.
First thing you do is parenthesis.
[tex]\displaystyle [2-6]=-4[/tex]
[tex]\displaystyle -4-[-24][/tex]
Then, add and subtract numbers from left to right to find the answer.
[tex]\displaystyle -4-[-24][/tex]
[tex]\displaystyle -4-[-24]=-4+24=20[/tex]
20, which is our answer.
Hope this helps!
The slope of the line below is - 1. Write a point-slope equation of the line
using the coordinates of the labeled point.
(3, 3)
- 10+
O A. +3 4(x+3)
OB. y-3--|(x-3)
O C. y-3 - 4(x-3)
O D. +3 --{(x+3)
Answers
Answer:
[tex]\large\boxed{y-3=-(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -1 and the point (3, 3).
Substitute:
[tex]y-3=-1(x-3)[/tex]
Factor completely 5xy3 + 15x3y2 − 30x2y2. 5(xy3 + 3x3y2 − 6x2y2) 5x(y3 + 3x2y2 − 6xy2) 5xy2(y + 3x2 − 6x) Prime
Answers
Answer:
5xy^2(y + 3x^2 - 6x).
Step-by-step explanation:
5xy^3 + 15x^3y^2 − 30x^2y^2
The GCF is 5xy^2 so dividing through by this we get the factors:
= 5xy^2(y + 3x^2 - 6x).
Answer:
[tex]5xy^2(y+ 3x^2- 6x)[/tex]
Step-by-step explanation:
[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]
To factor out an expression, factor out GCF
[tex]5xy^3= 5 \cdot x \cdot y \cdot y \cdot y[/tex]
[tex]15x^3y^2= 5 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot y[/tex]
[tex]30x^2y^2= 5 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y[/tex]
GCF is 5 times x times y time y
GCF is 5xy^2. Factor out GCF
[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]
[tex]5xy^2(y+ 3x^2- 6x)[/tex]
A certain type of cell can double itself every hour, because it has a growth factor of 2. A laboratory has 15 of these cells.
Which function best models the amount of cells in the laboratory after x hours?
f(x)=2^x+15
f(x)=15⋅2^x
f(x)=2⋅15^x
f(x)=15^x+2
Answers
Answer:
Second one
Step-by-step explanation:
Second choice.
Second one is growing by a factor of 2 because the exponent on 2 tells me that 2 is is being repeated as a factor.
If x=0 then 15*2^0=15(1)=15 which is what we have initially.
Final answer:
The correct option is f(x)=15⋅2^x. The function that best models the cell growth after x hours is f(x) = 15⋅ 2^x, illustrating the exponential nature of cell division starting with 15 cells.
Explanation:
The amount of cells in the laboratory after x hours, when the number of cells doubles every hour, is best represented by the function f(x) = 15⋅ 2^x. This is because the cell population increases exponentially, starting with 15 cells and doubling each hour. The formula represents exponential growth where the original amount of cells (15) is multiplied by two raised to the power of the number of hours elapsed (x).
what is 81-86÷2+(9×2)-50=pmdas
Answers
Answer:
6
Step-by-step explanation:
=81−43+(9)(2)−50
=38+(9)(2)−50
=38+18−50
=56−50
=6
Answer:
6.
Step-by-step explanation:
81-86÷2+(9×2)-50
work out the parentheses first;
= 81 - 86 / 2 + 18 - 50
Now the division:
= 81 - 43 + 18 - 50
= 38 + 18 - 50
= 56 - 50
= 6.
True or False? The first distribution shown below has a smaller mean tha
does the second distribution.
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112
Answers
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
1st mean: 65
2nd mean: 106.5
evaluate the expression 3x + 21 for x=3
Answers
Answer:
30
Step-by-step explanation:
Problem = 3x + 21 for x=3
3(3) +21 --- subsitute the three for the x
9 + 21 ---- multiply the 3s together
30 ----- add
if the point (-4,5) and (0,2) are used to find the slope of the line the slope is -3/4 what is the slope if the points (0,2) and (4,-1) are used
Answers
To find slope you just place the change in y over the change in x.
2- -1=3
0-4= -4
The slope is -3/4 which is the same as before
What is LCM of 30 and 62 using Division Method
Answers
Answer:
930
Step-by-step explanation:
To use the division method
Write the given numbers in a horizontal row separated by commas.
Divide them by a suitable prime number
Place the quotient under the numbers in the next row. If a number is not divided exactly then bring it down to the next row.
Repeat the process until only co prime numbers are left in the last row.
Multiply all the prime numbers used as divisors.
The product is the LCM
Given 30 and 62, then
2 | 30, 62
3 | 15, 31
5 | 5, 31
31 | 1, 31
| 1, 1 ← co primes left
Hence LCM = 2 × 3 × 5 × 31 = 930
What is the general form of the equation of a circle with its center at (-2,1) and passing through (-4,1)
Answers
Answer:
(x + 2)^2 + (y - 1)^2 = 2^2
Step-by-step explanation:
The equation of this circle is
(x + 2)^2 + (y - 1)^2 = r^2, and we are to determine the values of r^2 and r by substituting -4 for x and 1 for y:
(-4 + 2)^2 + (1 - 1)^2 = r^2, or:
(-2)^2 = r^2, or
4 = r^2
Then r = 2.
The desired equation is:
(x + 2)^2 + (y - 1)^2 = 2^2
Find the value for the following determinant.
Answers
Answer:
5
Step-by-step explanation:
The matrix is in the form
a b
c d
The determinant is
ad -bc
2 *4 - 1 *3
8 - 3
5
What are the coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) that portions the segment into ratio of 3 to 2
Answers
Answer:
4) (1,-1)
Step-by-step explanation:
Let the points be
[tex](x_1,y_1) = K(-5,-4)\\(x_2,y_2) = L(5,1)\\[/tex]
The formula for finding the coordinates of point that divides the line in a:b is:
[tex]x = \frac{bx_1+ax_2}{a+b} \\y = \frac{by_1+ay_2}{a+b}[/tex]
Here x and y are the coordinates of the point that will partition the line into given ratios
Our ratio is 3 to 2,
So,
a=3
b=2
Putting the values in the formula
[tex]x = \frac{(2)(-5)+(3)(5)}{3+2}\\x = \frac{-10+15}{5}\\x =\frac{5}{5}\\ x =1\\y = \frac{(2)(-4)+(3)(1)}{3+2}\\y = \frac{-8+3}{5}\\y = \frac{-5}{5}\\ y = -1[/tex]
Hence, the correct answer is:
4) (1,-1) ..
The coordinate of the point on the directed line segment is (1, -1). Then the correct option is D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
The coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) portions the segment into a ratio of 3: 2.
Let the coordinate of the point be (x,y).
We know that the section formula
[tex]\rm (x,y) = (\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2})[/tex]
We have
m₁: m₂ = 3: 2
(x₁, y₁) = (-5, -4)
(x₂, y₂) = (5, 1)
Then we have
[tex]\rm (x, y) = (\dfrac{3*5 + 2*(-5)}{3+2} , \dfrac{3*1 + 2*(-4)}{3+2})\\\\\\(x, y) = (\dfrac{5}{5}, \dfrac{-5}{5})\\\\\\(x, y) = (1,-1)[/tex]
More about the coordinate geometry link is given below.
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Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 5x + 15
Answers
Answer:
(3x^2+5)(x+3)
Step-by-step explanation:
The given expression is:
3x3 + 9x2 + 5x + 15
First of all group the first two terms and last two terms:
(3x3 + 9x2) + (5x + 15)
Now factor out the greatest common factor from each group:
3x^2(x+3)+5(x+3)
(3x^2+5)(x+3)
Thus the factors of 3x3 + 9x2 + 5x + 15 are:
(3x^2+5)(x+3) ....
Answer:(3x^2 + 5)(x + 3)
Step-by-step explanation:
B.
How do you find the max or min of a function?
Answers
Answer:
If parabolas open down, then their vertices are at a maximum point, whereas if parabolas open up, their vertices are at a minimum point.
I hope this was the answer you were looking for, and as always, I am joyous to assist anyone at any time.
To find the max/min of a function, find where the function's first derivative is zero. Check those points with the second derivative: a positive value indicates a minimum and a negative value indicates a maximum.
Explanation:To find the maximum or minimum of a function, you should first understand that these points occur where the derivative of the function is zero, which corresponds to the points with a flat tangent line (no slope). To derive this, differentiate the function and mark all the points where the derivative equals zero. These are potential maximum or minimum points, also known as extrema.
However, it's also important to note that a zero derivative does not always mean a maximum or minimum is present. To confirm this, you need to perform the second-derivative test. If after differentiating the first derivative you get a positive value, the original function has a minimum at that point. If it's negative, the function has a maximum.
For example, let's take the function f(x) = x². The derivative f'(x) = 2x, and setting this to zero gives us x = 0 as the only point whose derivative equals zero. Further, the second derivative, f''(x), equals 2, which is positive, indicating a minimum occurs at x = 0.
Learn more about Max/Min of a Function here:https://brainly.com/question/17800323
#SPJ12
Solve the equation for x.
the square root of the quantity x plus 5 end quantity minus 3 equals 4
x = 2
x = 12
x = 44
x = 53
Answers
Answer:
x = 44
Step-by-step explanation:
sqrt(x+5) -3 =4
Add 3 to each side
sqrt(x+5) -3+3 =4+3
sqrt(x+5) =7
Square each side
(sqrt(x+5))^2 =7^2
x+5 = 49
Subtract 5 from each side
x+5-5 = 49-5
x=44
Answer:
x is 44
Step-by-step explanation:
What is the value of f(6) in the function below?
f(x) = 2x
Answers
Answer:
see below
Step-by-step explanation:
f(x) = 2x
Let x = 6
f(6) = 2*6 = 12
If you meant f(x) = 2^x
Let x = 6
f(6) = 2^6 = 64
1800 doubles in value every 7 years
Answers
Answer: 25200
Step-by-step explanation:
I hope that this is helpful, I'm bad at explaining answers so i wont. XD
Which number line shows the solution to the inequality x + 3 \< 1?
\< = less than or equal to
Answers
Answer:
For every real number x, C expresses the solution to the inequality
Final answer:
To find the solution to the inequality x + 3 < 1, subtract 3 from both sides to get x < -2. The number line would have an open circle at -2 and be shaded to the left, indicating all numbers less than -2.
Explanation:
To solve the inequality x + 3 < 1, we need to find the value of x that makes the inequality true. We start by subtracting 3 from both sides of the inequality:
x + 3 - 3 < 1 - 3x < -2The number line for this inequality would have an open circle at -2 (since -2 is not included in the solution) and shade to the left of -2 to show that all numbers less than -2 are included. The reason we shade to the left is because those are the numbers that are less than -2, thus satisfying the inequality.
A company is replacing cables with fiber optic lines in rectangular casing BCDE. If line segment DE = 3 cm and line segment BE = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth.
3.54 cm
3.91 cm
4.24 cm
4.95 cm
Answers
Answer:
The correct option is C.
Step-by-step explanation:
Given information: BCDE is a rectangular casing, DE = 3 cm and BE = 3 cm.
We need to find the smallest diameter of pipe that will fit the fiber optic line. It means we have to find the measure of DB.
The measure of all interior angles of a rectangle or square is 90°.
[tex]\angle DEB=90^{\circ}[/tex]
It means the DEB is right angled triangle.
According to the Pythagoras theorem:
[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]
In triangle DEB,
[tex](DB)^2=(DE)^2+(BE)^2[/tex]
[tex](DB)^2=(3)^2+(3)^2[/tex]
[tex](DB)^2=9+9[/tex]
[tex](DB)^2=18[/tex]
Taking square root both sides.
[tex]DB=\sqrt{18}[/tex]
[tex]DB=4.24264068712[/tex]
[tex]DB\approx 4.24[/tex]
Therefore the correct option is C.
Based on the information given, the smallest diameter will be C. 4.24 cm.
Based on the information given, it can be noted that triangle DEB us a right angle triangle. Therefore, the Pythagoras theorem can be used.DB² = 3² + 3²
DB² = 9 + 9
DB² = 18
DB = ✓18
DB = 4.24
Therefore, the correct option is 4.24.
Learn more about diameter on:
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