A right triangular prism is shown. Find (A) the total surface area and (B) the volume. You must show formulas and your work.
10m height
8m width
10.77m
Answers
We are going to use the rectangular prism of the image as a guide:
First of all, the AC segment is calculated using the Pythagoras' theorem:
[tex]AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m[/tex]
(A) The surface area of a prism is the sum of the surface areas of each face.
For the 2 triangles ABC and DEF
[tex]A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m[/tex]
For the ABEF Rectangle
[tex]A=w*l=10,77m*10m=107,7m^{2}[/tex]
For the ACDE Rectangle
[tex]A=w*l=10,77m*12,81m=137,96 m^{2}[/tex]
For the BCDF Rectangle
[tex]A=w*l=10,77m*8m=86,16 m^{2}[/tex]
To finish you need to sum up the areas of each face:
[tex]SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2} [/tex]
(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows
[tex]V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3} [/tex]
Related Questions
((5x−16)^3−4)^3=216,000
Answers
Final answer:
To solve the equation ((5x−16)^3−4)^3=216,000, one must apply the rules of exponents and algebraic manipulation step by step, isolating x and using mathematical operations to simplify the expression.
Explanation:
Solving an Equation with Powers
The problem ((5x−16)^3−4)^3=216,000 involves understanding the rules of exponents and algebraic manipulation. When you're dealing with expressions raised to a power, it's important to remember that the power affects everything inside the parentheses, including the number. This is evident in expressions like (5³)* which is equivalent to 5⅜⅓ and results in 5 multiplied by itself 12 times, giving 5⁼.
When approaching the given equation, you would first look to isolate the base of the cube on one side, leading to the cube root to undo the cube power. You would continue simplifying step by step until you isolate x, the variable in question. The key here is to perform operations that counteract the powers and other mathematical operations presented.
In some cases, you might encounter a polynomial long division such as dividing S=9x⁵ +4x⁴ - 5x³ +6x² + 2x - 3 by another polynomial. This requires knowledge of the long division algorithm adapted for polynomials. Each term is divided individually to find the quotient.
48 students are going to the zoo. one-fourth brought umbrellas. how many people did not bring umbrellas
?
Answers
48-12=36
Answer is 36.
That would be 12 because 48/4 = 12,
Now, if you read the question, you realize that 12 is the number of people who brought an umbrella.
Soo you subtract 48 - 12, which equals 36.
36 people didnt bring umbrellas.
A tennis star was hired at a convention. She was paid $3000 plus 2% of all admission fees collected at the door. The total amount she received for the day was $3440. Find the total amount collected at the door.
Answers
440=2%
2% x 50 = 100%
440 x 50 = 22000
3440-3000=440
440 represents 2% of the admission fees
this means that 220 represents 1%
the total of admission fees is 220*100=22,000 dollars
Please help and show work
Answers
.. = 5.76*10^7 cans/(48 h)
Selection G is appropriate.
(ax + 5)(x-b)+4x=(2x × 2x)+ cx-10
Equating coefficients in identities
Answers
4 x + (x - b) (a x + 5) = -10 + c x + 4 x^2
Expand and collect in terms of x:
-5 b + x (9 - a b) + a x^2 = -10 + c x + 4 x^2
Subtract -10 + c x + 4 x^2 from both sides:
10 - 5 b + x (9 - a b) - c x - 4 x^2 + a x^2 = 0
Expand and collect in terms of x:
10 - 5 b + x (9 - a b - c) + x^2 (a - 4) = 0
Divide both sides by a - 4:
(10 - 5 b)/(a - 4) + (x (9 - a b - c))/(a - 4) + x^2 = 0
Subtract (10 - 5 b)/(a - 4) from both sides:
(x (9 - a b - c))/(a - 4) + x^2 = -(10 - 5 b)/(a - 4)
Add (9 - a b - c)^2/(4 (a - 4)^2) to both sides:
(9 - a b - c)^2/(4 (a - 4)^2) + (x (9 - a b - c))/(a - 4) + x^2 = (9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)
Write the left hand side as a square:
((9 - a b - c)/(2 (a - 4)) + x)^2 = (9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)
Take the square root of both sides:
(9 - a b - c)/(2 (a - 4)) + x = sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) or (9 - a b - c)/(2 (a - 4)) + x = -sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4))
Subtract (9 - a b - c)/(2 (a - 4)) from both sides:
x = sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4)) or (9 - a b - c)/(2 (a - 4)) + x = -sqrt((9 - a b - c)^2/(4 (a - 4)^2) - (10 - 5 b)/(a - 4))
Subtract (9 - a b - c)/(2 (a - 4)) from both sides:
Answer: x = sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4)) or x = -sqrt(((9 - a b - c)^2)/(4 (a - 4)^2) - (10 - 5 b)/(a - 4)) - (9 - a b - c)/(2 (a - 4))
Can someone please help! \
Please
Answers
Given: p: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q? If x – 5 ≠ 10, then 4x + 1 ≠ 61. If 4x + 1 ≠ 61, then x – 5 ≠ 10. If x – 5 = 10, then 4x + 1 = 61. If 4x + 1 = 61, then x – 5 = 10.
Answers
Justification:
1) The inverse of a conditional is negating both the hipothesis and the conclusion of the conditional, keeping the same sense of the implication.
2) This is the scheme (the symbol ~ is used to negate)
conditional: p → q
hypothesis: p
conclusion: q
negated hypothesis: ~p
negated conclusion: ~ q
inverse conditional: ~p → ~q
3) So, for the hypotheis p: x – 5 =10 and the conclusion q: 4x + 1 = 61, the conditional p→ q is:
if x - 5 = 10 then 4x + 1 = 61.
And the inverse is negating both the x - 5 = 10 and 4x + 1 = 61, leading to:
If x – 5 ≠ 10, then 4x + 1 ≠ 61, which is the answer.
Answer:If
x – 5 ≠ 10, then 4x + 1 ≠ 61.
Step-by-step explanation:
I just completed the test
Mr.holms used 4/5 of a carton of orange juice.he used equal amounts of leftover juice for two servings what fraction of the whole carton of juice did he use for each serving
Answers
Mr. Holms used 4/5 of the carton already, right? So that means he has 1/5 of the carton remaining.
He used half of that 1/5 to make 2 servings. 1/5 divided by 2 is just 1/5 times 1/2 which is 1/10.
Mr. Holms used 1/10 of the carton for each serving.
Check Your Answer: 4/5 + 1/10 + 1/10 = 8/10 + 1/10 + 1/10 = 10/10 = 1 whole carton. BOMB! Right on the money.
What is the median value of the data set shown on the line plot? Enter your answer in the box. A line plot with twenty-two data values. Labels are at zero, three, six, nine, and twelve. Tick marks are every one unit. Values appear as x marks above the line. Plot data values are one x mark above one, one x mark above two, two x marks above three, two x marks above four, three x marks above five, four x marks above six, three x marks above seven, three x marks above eight, two x marks above nine, and one x mark above eleven.
Answers
Then, we start by crossing off one value on each side of the data to work our way towards the middle. Once we come to the middle, we see that there are two values in the middle: 6 and 6.
To find the median when we have two values in the middle, we must add them, then divide by two.
6 + 6 = 12
12 ÷ 2 = 6
So, the median for this data set is 6.
The median is 6.
This median is easy to find-- you place all your numbers in numerical order and choose the number(s) in the middle-- for this question the median is 6.
I believe your line plot looks like this [Screenshot was taken on K12]:
Please forgive me if this is wrong, and please tell me the correct answer if this incorrect.
Which equation can be used to find the unknown length, a, in this triangle?
Answers
The unknown length, a, in this triangle can be found using the formula in the first option, a² + 15² = 17².
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given is a right angled triangle.
We know the Pythagoras Theorem which states that,
Hypotenuse² = Base² + Altitude²
Hypotenuse is the side opposite to the right angle.
Here length of hypotenuse = 17 m
Length of base = 15 m
Length of altitude = a
Using the theorem,
17² = 15² + a²
Or,
a² + 15² = 17²
Hence the correct formula is a² + 15² = 17².
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A study was done to investigate the relationship between outdoor temperature and the amount of fluids an outdoor athlete drinks per day. The correlating linear model is shown below, where x represents the number of degrees over 80°F, and y represents the amount of fluids drank (in liters). Interpret the y-intercept. y = 3.85 + 0.55x A. An athlete drinks 7 L per day when the temperature is 80°F. B. An athlete drinks 4.4 L per day when the temperature is 80°F. C. An athlete drinks 3.85 L per day when the temperature is 80°F. D. An athlete drinks 0.55 L per day when the temperature is 80°F.
Answers
Hope this helps!
Answer:
C. An athlete drinks 3.85 L per day when the temperature is 80°F
Step-by-step explanation:
Y-intercept of a linear model, equation or a straight line refers the point at which a line crosses the y-axis of a graph. It generally indicates a point on the graph where x equals 0.
For the equation y = 3.85 + 0.55x
At y-intercept, x = 0. Substitute x into the equation, we have:
y = 3.85 + 0.55 (0)
y = 3.85 + 0
y = 3.85
This implies that the value of fluid drank by an athlete at the starting temperature of 80°F (at x=0) is 3.85 L per day
A triangle contains the angles 75" and 45". What is the missing angle in the triangle
Answers
West Side Middle School and Jefferson Middle School recycled newspaper and kept track of how many pounds of paper each student collected.
Looking at the data as a whole, which school appears to have brought in more newspapers on a daily basis?
A) Jefferson Middle School
B) West Side Middle School
C) They brought in equal amounts on a daily basis.
D) This information cannot be determined.
Answers
Answer:
The correct answer is answer B
Step-by-step explanation:
The picture I added
Can you help me pleas now?
Answers
-2 & 6 -> this makes a total of 4
-1 & 5 -> this makes a total of 4
So now we have our three pairs with the same total.
To arrange the six numbers into three pairs so that the sum of each pair is equal, you could create the pairings of 4 and -2, -1 and 5, and 6 and 8. Each of these pairs has a sum of 2, 4, and 14 respectively.
Explanation:The six number cards provided are 4, -2, -1, 5, 6 and 8. The task is to arrange these into three pairs, such that the sum of each pair is equal. Based on these conditions, our possible pairs are:
4 and -2-1 and 56 and 8These pairs are obtained by adding the numbers together. For example, the pair 4 and -2 results in a sum of 2 (4 + -2 = 2). Similarly, -1 and 5 also results in a sum of 4 (-1 + 5 = 4), and 6 and 8 results in a sum of 14 (6 + 8 = 14). Two pairs have the same sum of 4 while one pair has the sum of 14.
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Therefore, the complete question is
Here are six number cards
-4, -2, -1, 5, 6, 8
Arrange the cards into three pairs with the same total.
• Please write each pair on separate lines and use the word 'and' between the numbers (eg. 7 and -3)
Can someone figure out the area ?
Answers
area of full circle = 3.14 x 1.3^2 = 5.3066 = 5.31
area of the shaded area = 80/360 x 5.31 = 1.18 square cm
In triangle FGH, mF is 94°, mG is 49°, and mH is 37°. The exterior angles of triangle FGH are J, K, and L, and they are adjacent to F, G, and H, respectively.
What is mK?
A. 86°
B. 49°
C. 143°
D. 131°
Answers
The exterior angles theorem tells us that the measure of an exterior angle of a triangle is equal to the sum of the other two angles of the triangle. Since m∠G=94°, m∠K=180-94=131°.
Using the property of exterior angles, mK is found by adding the measures of the non-adjacent interior angles mF and mH, resulting in mK being equal to 131°.
Explanation:The student is asking to find the measure of exterior angle mK in triangle FGH. To find mK, which is the exterior angle adjacent to G, we need to use the property of exterior angles in a triangle. This property states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
To find mK we add the measures of angles mF and mH:
mK = mF + mH
mK = 94° + 37°
mK = 131°
Therefore, the measure of the exterior angle K is 131°, which corresponds to answer choice D.
Complete the work to determine the value of a. Use the law of sines: . Substitute: . Cross multiply: 8sin(45°) = asin(77°). Solve for a and round to the nearest hundredth: a ≈ .
Answers
The value of a is 5.81 to the nearest hundredth.
What is the Law of Sines?The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides or the opposing angles.
Using the law of sines, we have:
sin(45°)/a = sin(77°)/8
To solve for a, we can cross-multiply and simplify:
8sin(45°) = asin(77°)
a = (8sin(45°))/sin(77°)
Using a calculator, we get:
a ≈ 5.81 (rounded to the nearest hundredth)
Therefore, a ≈ 5.81.
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A rectangular prism has a length of 312 inches, a width of 312 inches, and a height of 7 inches. Danny has a storage container for the prism that has a volume of 90 cubic inches.
What is the difference in volume between the prism and the storage container?
Enter your answer in the box as a simplified mixed number or a decimal.
Answers
Answer:
The answer would be 4 1/4
Step-by-step explanation:
The difference in volume between the prism and the storage container is 68,580 cubic inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of the rectangular prism is:
V = l × w × h
= 312 in × 312 in × 7 in
= 68,670 in³
The volume of the storage container is given as 90 cubic inches.
The difference in volume between the prism and the storage container is:
68,670 in³ - 90 in³ = 68,580 in³
Therefore, the difference in volume between the prism and the storage container is 68,580 cubic inches.
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what is the place value of 7 in 3.567
Answers
there you go bud
write in simplest form 12:3
Answers
12÷3= 4
3÷3=1
So 4:1 is the simplest form of 12:3.
Tell me if this helps!!
Here is your answer:
The proper answer to your question is "4/1 or 4".
Here is how:
12÷3=4
3÷3=1
=4/1 or 4!
Your answer is 4/1 or 4!
If you need anymore help feel free to ask me!
Hope this helps!
In Mr.Martinez's sixth period class, there are 8 boys and 12 girls. what is the probability of randomly selecting a girl?
Answers
the nth term to a sequence n+7 first 3 terms
Answers
Hey !!
Check the attachment.
Hope it helps you :)
The first three terms of sequence whose nth term is n+7 are 8, 9 and 10.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that the nth term of a sequence is n+7.
We need to find the first three terms of the sequence.
Tₙ=n+7
To find the first 3 terms, replace value of n with 1,2 and 3.
When n=1
T₁=1+7=8
When n=2,
T₂=2+7=9
When n=3
T₃=3+7=10
Hence, the first three terms of sequence whose nth term is n+7 are 8, 9 and 10.
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Multiply and simplify. 6xy^3z⋅3x^2yx^2
a) 18(xyz)^10
b) 9x^5y^4z
c) 18x^5y^4z
d) 18x^4y^3z
Answers
Multiplying and simplifying 6xy³z · 3x²yx² gives;
C: 18x⁵y⁴z
Solving ExponentsWe want to multiply and simplify;
6xy³z · 3x²yx²
Let us first group the like terms to get;
(6 * 3) * (x · x² · x²) * (y³ · y) * z
According to laws of exponents;
a³ × a² = a⁽³ ⁺ ²⁾ = a⁵
Thus;
(6 * 3) * (x · x² · x²) * (y³ · y) * z = 18x⁵y⁴z
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In one hour 3/4 pint of a chemical can be filtered how long in HOURS will it take to filter 2 1/2 pints of chemical
Answers
↓
2 1/2 multiply by 4/3
2 1/2 same as 2*2+1/2 which is 5/2
5/2*3/4= 15/8= 1 7/8
in 1 7/8 hours it will be filled
What is the measure of each base angle on an isosceles triangle it it's vertex angle measures 28 degrees and it's 2 congruent sides measure 12 units
Answers
Final answer:
The measure of each base angle in an isosceles triangle with a 28-degree vertex angle is 76 degrees, which is the result of subtracting the vertex angle from 180 and dividing by 2.
Explanation:
To find the measure of each base angle of an isosceles triangle when the vertex angle is given, you can use the fact that the sum of all angles in a triangle is 180 degrees. Since in an isosceles triangle the two base angles are congruent (equal in measure), you can subtract the vertex angle from 180 degrees and then divide the result by 2 to find the measure of each base angle.
For the given triangle with a vertex angle of 28 degrees:
Subtract the vertex angle from 180 degrees: 180 - 28 = 152 degrees.Divide the result by 2 to find each base angle: 152 / 2 = 76 degrees.Thus, the measure of each base angle in the given isosceles triangle is 76 degrees.
Kate has 12 1/2 pounds of chocolate. She gives each of her 5 friends x pounds each and has 3 1/3 pounds left over. How much did she give each of her friends?
Answers
12 1/2 = 5x + 3 1/3
rewrite the mixed fractions as improper fractions and with denominator 6
75/6 = 5x + 20/6
subtract 20/6 from both sides
55/6 = 5x
divide both sides by 5 to isolate x
11/6 = x
That is 1 and 5/6 pounds per each of the friends
To check:
12 1/2 =?= 5(1 5/6) + 3 1/3
12 1/2 =?= 55/6 + 3 1/3
12 1/2 =?= 25/2
12 1/2 = 12 1/2
Hope this helps
In health class, students record the weights of the sandwiches they have for lunch. The weights are shown in the line plot below. What is the average weight of one sandwich?
Answers
The mean of the value of a data is the sum of the data divided by the sample size. The average weight of one sandwich is 3/10
How to calculate the mean of data?The mean of the value of a data is the sum of the data divided by the sample size.
Mean = sum/sample size
Find the mean
Sum = 1/8 + 1/8 + 4(1/4) + 2(3/8) + 2(1/2)
Sum = 1/4 + 1+ 3/4 + 1
Sum = 3
Sample size = 10
Mean = 3/10
Hence the average weight of one sandwich is 3/10
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A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15 and the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the remaining yard?
A.) 2x^2 (75-8 [tex] \pi [/tex])
B.) 150x^2-4 [tex] \pi [/tex] x^2
C.) 134 [tex] \pi [/tex] x^2
D.) 134x^2
Answers
A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15x and the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the remaining yard?
Step 1
find the area of rectangular yard (A1)
A1=(10*x)*15*x=150*x² units²
Step 2
find the area of the circular fountain (A2)
A2=pi*r²---------> pi*(4x)²=16*pi*x²
Step 3
find the area of the remaining yard (A3)
A3=A1-A2----------> 150*x²-16*pi*x²----> x²*[150-16*pi]----> 2*x²*[75-8*pi]
the answer is the option A)
2x² (75-8pi )
What is a net? WIll mark brainliest!!!
Answers
It is Jamie’s birthday and her mom just bought her an Xbox. She’s trying to find the surface area of the box so she can determine how much wrapping paper to use. The box is 24 inches long 12 inches wide and 10 launch is high what is the surface area of Jamie’s new Xbox?
Answers
The dimensions of the box are given 24 inches long, 12 inches wide, and 10 inches high. The box is in the shape of a rectangular prism.
We know the formula of surface area of rectangular prism is given by :-
[tex] Surface\;\; area = 2*(lw+wh+hl) [/tex]
where l is length, w is width, and h is height of the rectangular prism.
We can plug the given values l = 24, w = 12, and h = 10 into the formula and solve it for answer.
Surface area = 2 x (24x12 + 12x10 + 10x24)
Surface area = 2 x (288 + 120 + 240)
Surface area = 2 x 648
Surface area = 1296 squared inches.
So she needs 1296 squared inches of wrapping paper.
Hence, the final answer is 1296 squared inches.