I have already done Number one but I need help with 2. Please help when you find time to!
Answers
Answer:
Step-by-step explanation:
Formulae
Area of a triangle = 1/2 x base x height
Area of a rectangle = width x length
Question 1
Surface area of square based pyramid = area of base + 4 × area of triangle
⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)
= 36 + 168
= 204 yd²
Question 2
Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area
⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)
= 120 + 36 + 60
= 216 mm²
Extra credit question
Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas
base area = 3 × 10 = 30 mm²
triangle area = 1/2 × 3 × 2 = 3 mm²
side area = 10 × 2.5 = 25 mm²
⇒ total SA = 30 + (2 × 3) + (2 × 25)
= 30 + 6 + 50
= 86 mm²
❍ Concept :-
We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,
⠀
[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]
Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.
⠀
✰ Solution :-
⠀
1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,
⠀
[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]
⠀
2. Now, here, we can use the formula of total surface area for cuboid, i.e.
⠀
TSA = 2( lb + bh + hl )
⠀
[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
⠀
Extra Credit Question.
⠀
Here, we can find out the total surface area by finding,
⠀
Base area i.e. length x breadth ( B.A. )
Side area i.e. length x breadth ( S.A. )
triangular area = 1/2 x b x h ( T.A. )
⠀
Now,
⠀
TSA = BA + 2 x S.A. + 2 x T.A.
⠀
[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Related Questions
J^3 = 0.125 (I don’t understand help me please)
Answers
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ J^3=0.125\implies J^3=\cfrac{0125}{1000}\implies J^3=\cfrac{1}{8}\implies J^3=\cfrac{1}{2^3} \\\\\\ J^3=2^{-3}\implies J^3=(2^{-1})^3\implies J=2^{-1}\implies J=\cfrac{1}{2}[/tex]
can someone answer this please
Answers
Answers:
Reason 23: Given
Reason 24: Reflexive Property
Reason 25: AAS
========================================================
Explanation:
Reason 23 is given because we simply restate the initial facts word for word. Whatever is said at the top "given" is copy/pasted into the table below. This explains why the second reason is "given" as well.
Reason 24 is "Reflexive Property" because any segment is congruent to itself. Think "reflexive" as in "mirror reflection".
For reason 25, we will use the AAS (angle angle side) congruence theorem. This is because we have two pairs of congruent angles (statement 1 and statement 2) as well as a pair of congruent sides (statement 3). We don't use ASA because the side FY is not between the angles mentioned. The order is important. Check out the diagram below. Take note of the color coding for the angles.
The area of a circle is 36π cm². What is the circumference, in centimeters? Express your answer in terms of π
Answers
Answer: [tex]12\pi[/tex]
Step-by-step explanation:
The formula for area of a circle is [tex]\pi r^2=A[/tex]
The formula for circumference of a circle is [tex]2r\pi=C[/tex]
Where r is the radius
A is area
C is circumference
Knowing this we can sub our values in and solve for r in the formula for area
Divide both sides by [tex]\pi[/tex] to isolate r
[tex]\pi r^2=A\\\pi r^2=36\pi \\\frac{\pi r^2}{\pi } =\frac{36\pi }{\pi } \\r^2=36[/tex]
Take the square root of both sides
[tex]r^2=36\\\sqrt{r^2} =\sqrt{36} \\r=6[/tex]
Now sub the value of r into the formula for circumference
[tex]2r\pi =C\\2(6)\pi =C\\12\pi[/tex]
Answer:
[tex]12\pi \: c \: m[/tex]
step by step explanation:
[tex]area \: of \: a \: cirle = \pi \: r {}^{2} \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^{2} \\ 36 = r {}^{2} \\ r = 6 \\ for \: circmference \\ 2 \times \pi \: \times 6 = 12\ \: \pi \: cm [/tex]
How do you calculate the diameter of a circle
Answers
Answer: "How do u calculate the diameter of a circle"?
Step-by-step explanation: Calculating diameter is easy you just need the radius, the circumference, or the area. Even if you don't have any of those dimensions, you can still find the diameter if you have a drawing of the circle.
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
8 1/2
Step-by-step explanation:
14 inch - 5 1/2 inches = 8 1/2 inches
Aba's dog grew 8 1/2 inches.
Answer:
8.5 Inches, 2.78 pounds approximately
Step-by-step explanation:
14- n = 5.5. In this case you will have to subtract 5.5 from 14. 14 - 5.5 = 8.5. You get 2.5 pounds because, 1.10 x 2 = 2.20. 2.75 - 2.20= .55. $1.10 is 70 cents. 55/70 = 11/14= is around .78. 2+.78 = 2.78
plss help!
Question: Find a,b and c
Answers
Answer:
See below, please
Step-by-step explanation:
The right：
[tex] {(y + c)}^{2} - b \times (x + a) \\ = ( {y}^{2} + 2yc + {c}^{2} ) - bx - ba = [/tex]
[tex] = {y}^{2} - bx + 2cy + {c}^{2} - ab[/tex]
The left:
[tex] = {y}^{2} - 7x - 18y + 109[/tex]
So, after comparing the right side and the left side of this equation, we know
1)
[tex]b = 7[/tex]
2)
[tex]2c = - 18 \\ so \\ c = - 9[/tex]
3)
[tex] {c}^{2} - ab = 109[/tex]
So,
[tex]a = \frac{ {c}^{2} - 109}{b} = \frac{ { (- 9)}^{2} - 109}{7} = \frac{ - 28}{7} = - 4[/tex]
Which expression is equivalent to 3
5v ?
Answers
Answer:
x ^5/3 y ^1/3 (the second option listed)
Step-by-step explanation:
So without even solving the expression, you can find the correct option. If you're finding the cube root (or really any square root), you know it will be less than your original number (unless you are working with imaginary numbers, but you aren't).
So, if you are finding the cube root of an expression, you're finding the cube root of each number separately.
You wouldn't be cubing y, you would be finding the cube root. You wouldn't be leaving y the same, you are finding the cube root.
This means that without even solving (which I will explain),
the correct option is the second one on the screen.
Here's how to actually solve the equation:
So, if we are finding the cube root of a variable with an exponent, we can divide that exponent by 3 (because it is a cube root).
When we have a square root, you know that we are breaking down each number/variable into an even exponent to solve the expression. When taking the square root of an even exponent, such as 4, you would divide by 2.
This same strategy applies to cube roots. You are dividing the exponent of both variables by 3.
[remember: the exponent of a variable without an exponent is essentially an invisible exponent of 1.]
Solve the equation:
3/4x - 12 = 12
Answers
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
What is the surface area of this right triangular prism? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
where is the prism???
i can't answer without seeing the question
Determine which of the following is true for expression x^3+x^2-2x
A. The equation is prime
B. x can be factored from each term of the trinomial to obtain x(x^2+x-2),which is completely factored.
C. x can be factored from each term of the trinomial to obtain x(x^2+x-1), and the resulting trinomial can be factored to obtain x(x+2)(x+1), which is completely factored
D. The trinomial is equivalent to (x+2)(x-1)
Answers
Answer:
D. The trinomial is equivalent to (x+2)(x-1)
Step-by-step explanation:
1. Factor out the common term x:
= x(x^2+x-2)
2. Factor the equation:
= x(x - 1)(x + 2)
From this, we can see that because the equation was factorable, it is not prime. Option B is not completely factored, so it is incorrect. The final ordered pair shown in Option C is has (x + 1), when it should be (x - 1), so it is also incorrect. Option D is the true statement.
Help me, please guyyyyyyusssssss.
Answers
Answer:
Step-by-step explanation:
7) Volume of the shape = Volume of triangular prism - volume of cylinder
Triangular prism:
[tex]\boxed{ \text{Volume of triangular prism = base area * h }}[/tex]
b = 6 ft & height of the triangle = 5 ft
[tex]\sf Base \ area = \dfrac{1}{2}* 6* 5[/tex]
= 3*5
= 15 ft²
Volume of prism = 15 * 4
= 60 ft³
Cylinder:
r = 2÷2 = 1 ft & h = 4 ft
Volume of cylinder = 3.14 * 1 * 1 * 4
= 12.56 ft³
Volume of the shape = 60 - 12.56
= 47.44 ft³
8) Volume = Volume of Pyramid - Volume of cone
[tex]\boxed{\text{Volume of the Pyramid = base area * h} }[/tex]
[tex]\text {base area = length * width}\\\\\\[/tex]
= 9 * 9
= 81 m²
Volume of Pyramid = 81 * 8
= 648 m³
[tex]\boxed{ \text{Volume of cone = \dfrac{1}{3} \pi r^{2}h}}[/tex][tex]\boxed{ \text{Volume of cone = $\dfrac{1}{3} \pi r^{2}h$}}[/tex]
r = diameter ÷ 2 = 6÷2
r = 3 m & h = 8 m
[tex]\text{ Volume of cone =$\dfrac{1}{3}*3.14* 3*3*8$}[/tex]
= 3.14 * 3 * 8
= 75.36 m³
Volume of the shape = 648 - 75.36
= 572.64 m³
9) Volume of the shape = volume of cylinder + volume of cone
Cylinder:
h = 7 in ; r = 3
[tex]\boxed{\text{Volume of cylinder =$ \pi r^{2}h$}}[/tex]
[tex]=\dfrac{22}{7}*3*3*7[/tex]
= 22 *3 * 3
= 198 in³
Cone:
r = 3 in & h = 4 in
[tex]\text{Volume of cone = $ \dfrac{1}{3}*3.14*3*3*4$}[/tex]
= 3.14 * 3 * 4
= 37.68 in³
Volume of the shape = 198 + 37.68
= 235.68 in³
10) Volume of the shape = Volume of outer cyliner - volume of inner cylinder
Volume of outer cylinder:
R = 9 m & h = 3 m
Volume of outer cylinder = 3.14 * 9 * 9 * 3
= 763.02 m³
Volume of inner cylinder:
r = 5 m & h = 3 m
Volume of inner cylinder = 3.14 * 5 * 5 * 3
= 235.5 m³
Volume of the shape = 763.02 - 235.5
= 527.52 m³
(NEED ANSWER TODAY!) The dimensions of this figure are changed so that the new surface area is exactly 1/3 what it was originally.What is the new surface area?Enter your answer as a decimal in the box.
Answers
ANSWER: 202.46 if you need all the question answers just ask :D
the bill for three bags of peanuts on two medium drinks at the movies with 11.15 dollars is a bag of peanuts cost to $35 how much was 1 drink
Answers
Answer:
5.575
Step-by-step explanation:
divide it by 2 its easy
ILL GIVE BRAINLIEST. ANSWER ASAP
Answers
Answer:
283 m^2
Step-by-step explanation:
To find the area of a circle, you need to times pi, in this case 3.14, by the radius,9.5 here, squared.
A= π (r^2)
In the figure below, triangle ABC undergoes a reflection and a translation to become triangle PQR. In triangle ABC, m
The angle measures of triangle PQR are: m
Answers
Answer:
Step-by-step explanation:
A corresponds to angle P, so angle P measues 70 degrees.
Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.
Freida tossed a coin 3 times and it always landed on head. Fine the probability of tossing a head.
Answers
Answer: 1/2
Step-by-step explanation: This is a coin. Having heads three times in a row will never change that a coin is two sided and random, meaning it will never affect the coin to always be heads. They were most likely just lucky to get heads all the time. It will always be 1/2 since the coin is inanimate and is not like selecting classmates from a team, it cannot know it's probabilities and affect it. Thus it is 1/2 probability.
This can be simplified in the equation: P(H) = 1/2, P(T) = 1/2, P(H | T) = 1/2
In a rhombus, the difference of the measures of the two angles between a side and the diagonals is 32°. What are the measures of the angles of the rhombus?
Answers
Answer:
122 and 58
Step-by-step explanation:
The size of the rat population of a wharf area grows at a rate of 5% monthly. If there are
200 rats in June, find how many rats should be expected by next June.
Answers
Answer:
200+10×12=320
Step-by-step explanation:
Determine whether each relation is a function. Explain. {(2,0), (2, 2), (2, 4), (2, 6)}
Answers
This example is not a function, as the independent variable (2) appears more than once.
The rule is that the independent variable(x) cannot appear more than once as the same value and the dependant variable(y) can appear more than once as the same value.
Hope this helps!
10 A grocery store bought 1,600 cans of
vegetables in different sizes. Of the cans,
25% contained less than 400 grams of
vegetables, 15% contained between 400
and 500 grams of vegetables, and the
rest contained more than 500 grams of
vegetables.
How many cans contained more than 500
grams of vegetables?
F 1,120
H 640
G 800
J 960
Answers
Answer:
1020 cans
Step-by-step explanation:
100-25
=75%
0.75x1600
1200cans
100-15
=85%
0.85x1200
=1020 cans
Find the total amount
$16.000 at 14% compounded
semiannually for 2 years
Answers
Answer:
The answer would be 20.97273616 or (rounded to the nearest cent) would be $20.97
Step-by-step explanation:
The reason for this is that the formula for compounded interest is [tex]A=P(1+\frac{r}{n})^\frac{t}{n}[/tex] where A is the total amount, P is the initial amount, r is the growth factor or the percent, n is the number of compounding periods, and t is the time. You would substitute P for 16, r for 0.14 (14%), n for 2 as it compounded semiannually so it for every 6 months instead of 1 year (annual) so is compounded 2 times per year, and t for 2. And just solve the equation and you get that A is equal to 20.97273616 but since we are talking about money( only round if asked) then it would be 20.97.
Hope this helps!!!!
A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 4500 seats. The students left 3105 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answers
[tex]\bull[/tex]Total number of seats in theatre = 4500
[tex]\bull[/tex]Total number of seats left vacant = 3105
Solution:-[tex]\longrightarrow[/tex]Number of seats occupied = Total number of seats in theatre - Total number of seats left vacant
[tex]\longrightarrow[/tex]Number of seats occupied
[tex]\quad[/tex]= 4500 - 3105
[tex]\longrightarrow[/tex] 1395
[tex]\\[/tex]
Now,
[tex]\begin{gathered}\bull \sf Percentage \:of \:seats \:filled = \frac{Seats \: filled \: by \:6th \:grader }{Total \:number \:of \:seats} \times 100 \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\bull \sf Percentage \: of \:seats \: filled = \frac{1395}{45\cancel{00}} \times \cancel{100} \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf \frac{1395}{45} \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 31 \% \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Thus , 31 % of seats in the theater were filled by the 6th graders on the trip
40 points please help
Answers
IJKL is a rectangle, so opposite sides have the same length:
• IJ = KL ⇒ 6y - 6 = 2x + 20
• JK = IL ⇒ 3x + 21 = 6y
Substitute the second equation into the first and solve for x :
6y - 6 = 2x + 20
(3x + 21) - 6 = 2x + 20
3x + 15 = 2x + 20
x = 5
Solve for y :
3x + 21 = 6y
15 + 21 = 6y
36 = 6y
y = 6
If the m<4 = 15, find the measure of <2
Answers
Answer: 75 Degrees
Step-by-step explanation: 1. Due to the law of opposite adjacent angles, we can determine angle 1 is congruent to angle 4 and therefore is 15 degrees 2. Angle 3 is shown to be a right angle (90 degrees) 3. Since angles 1,2, and 3 are on a flat line, the sum of all 3 is 180 4. 15+90 is 105 5. 180-105 is 75 which is the measure of angle 2
The area of this rectangle is 132 square units.
h = 11
What is the base of the re
angle?
Please help begging u ..
Answers
Answer=12
Step-by-step explanation:
The area of a rectangle is h×b.
h=11
11×b=132
b=132/11=12 units
Would a compound event involving a standard number cube and a spinner be dependent or independent?
Answers
Since the result of the number cube and the result of the spinner do not effect each other, the events are independent.
What are dependent and independent events?When one trial affects the next trial, the events are called dependent. One example is taken a card without replacement from a standard deck, as in each trial, the number of cards remaining decreases, hence the probabilities are affected.When there is no effect of one trial on another, the events are called independent.In this problem, the result of the number cube does not affect the result of the spinner, as they are rolled separately, hence the events are independent.
More can be learned about independent events at https://brainly.com/question/14478923
Find all solutions of the equation below.
7^5-3=7^5x-19
Answers
Answer:
7⁵-3=7⁵x- 19
Step-by-step explanation:
16807 - 3 = 7⁵x - 19
16804 = 7⁵x - 19
16804 = 16807x - 1
adding 19 on both sides
16804 + 19 = 16807x - 19 + 19
16823 = 16807x
x = 16823 / 16807
16823 upon 16807 is the x
pls help ill give 15 brainliest and 5 starts question is down below
Answers
Answer:
1 is 9 sq units
2 is 12
3 is 24cm^2
Step-by-step explanation:
2 1/3 + 3 1/8 + 1 1/24
Answers
Answer:
the answer is 6 1/2
Step-by-step explanation:
I solved using calculator
Answer:
6 1/2
Step-by-step explanation:
At a movie theater, the manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365-day year, what position in line gives you the best chance of being the first duplicate birthday?
please explain how you got this answer. Thank you!
Answers
The best chance is an illustration of probability
The 21st position in line gives you the best chance of being the first duplicate birthday
How to determine the best position?
Assume you are in the nth position, the probability of getting a free ticket is:
P(n) = P'(first n - 1 people share a birthday) * P(birthday with first n -1 people)
Mathematically, the above can be represented as:
P(n) = [365/365 * 364/365 * 363/365 * ... * (365 - (n -2))/365] * [(n -1)/365]
Such that: n [tex]\le[/tex] 365
When simplified, the equation becomes
p(n)/p(n+1) = 365/(366 - n) * (n - 1)/n
Where
p(n)/p(n+1) > 1
So, we have:
365/(366 - n) * (n - 1)/n > 1
Evaluate the product
(365n -365)/(366n - n²) > 1
Cross multiply
365n -365 > 366n - n²
Collect like terms
n² + 365n - 366n - 365 > 0
Evaluate the difference
n² - n - 365 > 0
Solve for n using a graphing calculator;
n > - 18.6 or n >19.6
n cannot be negative.
So, we have:
n > 19.6
Approximate to nearest integer
n > 20
The least integer value of n is:
n = 21
Hence, the 21st position in line gives you the best chance of being the first duplicate birthday
Read more about probability at:
https://brainly.com/question/25870256