Answers
Answer:
(i) x = 17 cm
(ii) one end: 360 cm²; both ends: 720 cm²
(iii) 14,400 cm³
(iv) 4000 cm²
Step-by-step explanation:
You want the slant height, base area, volume, and total surface area of a trapezoidal prism with the base isosceles trapezoid having parallel base lengths of 32 and 16, and a height of 15. The distance between bases is 40. All units are cm.
(i) Slant heightIf a center rectangle 16 cm wide and 15 cm high is cut from the base trapezoid, the remaining two triangles have a base of 8 cm and a height of 15 cm. The Pythagorean theorem can be used to find the slant height:
x² = a² +b²
x² = 8² +15² = 64 +225 = 289
x = √289 = 17
The slant height, x, is 17 cm.
(ii) Base areaThe area of the base trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(32 +16)(15) = 360 . . . . square cm
The area of one end surface is 360 cm²; the total area of both end surfaces is 720 cm².
(iii) VolumeThe volume of the prism is the product of the base area and the length of the prism.
V = Bh
V = (360 cm²)(40 cm) = 14,400 cm³
The volume of the trapezoidal prism is 14,400 cm³.
(iv) Total surface areaThe lateral surface area of the prism is the product of the perimeter of the base and the distance between bases.
LA = Ph
LA = (32 +16 +2·17 cm)(40 cm) = 3280 cm²
The total surface area is the sum of the lateral area and the area of the two bases:
SA = LA +2B = (3280 cm²) + 2(360 cm²) = 4000 cm²
The total surface area of the prism is 4000 square centimeters.
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Additional comment
It appears that the top dashed line in the figure is drawn that way in error. It appears to identify a visible edge, so we expect it to be a solid line.
Related Questions
Sean is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 16 inches × 15 1/4 inches. He needs to cut another rectangle that is 10 1/2 inches by 10 1/4 inches. How many total square inches of construction paper does Sean need for his project?
Answers
Answer:
the total square inches of the construction paper is 351.63 square inches
Step-by-step explanation:
The computation of the total square inches of the construction paper is shown below;
= (16 × 15 1 ÷ 4) + (10 1 ÷2 × 10 1 ÷ 4)
= (16 × 61 ÷ 4) + (21 ÷ 2 × 41 ÷ 4)
= (16 × 15.25) + (10.5 × 10.25)
= 244 + 107.625
= 351.63 square inches
Hence, the total square inches of the construction paper is 351.63 square inches
We simply added these two
Help please :(
CROWN ???
Answers
Answer:
7&8 both true
9 is false
Step-by-step explanation:
tghdhfshj
Answer:
True
True
False
Step-by-step explanation:
2(7) -3 = 14 -3 = 11
2(8) -3 = 16 -3 = 13
2(9) - 3 = 15
The answer has to be less than 15
The Jacksons and the Simpsons were competing in the final leg of the Amazing Race, which was 240240240 kilometers long. In their race to the finish, the Jacksons immediately took off traveling at an average speed of vvv kilometers per hour. The Simpsons' start was delayed by an hour. When they eventually took off, they traveled at an average speed that was 404040 kilometers per hour faster than the Jacksons' speed. Sadly for them, that didn't help, and the Jacksons won. Write an inequality in terms of vvv that models the situation.
Answers
Answer:
240/(v+40) + 1 > 240/v
Step-by-step explanation:
Both parties traveled a distance of 240 km.
Simpsons took off at average speed of 40 km/h & 1 hour later: 240/(v+40) + 1
Jacksons took off at average speed of v km/h: 240/v
An inequality in terms of v that models the situation is; [240/(v + 40)] + 1 > 240/v
How to write an inequality?We are told that distance travelled by both Jackson and Simpson is 240 km each.
Jacksons took off at average speed of v km/h. Thus, their time taken is 240/v
The Simpsons took off at an average speed of 40 km/h faster than Jacksons Speed. Since their start was delayed by an hour, then;
Time taken = [240/(v + 40)] + 1
Thus, the inequality that models the situation is; [240/(v + 40)] + 1> 240/v
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Mr. Nguyen opened a savings account with an initial deposit of $480 and will not make any additional deposits or withdrawals. The account earns 2% simple interest. What is the total amount that Mr. Nguyen will have in his account at the end of 3 years?
A $28.80
B $2,880.00
C $508.80
D $768.00
Answers
Answer:
c
Step-by-step explanation:
If a figure can be rotated n times, it has how many lines of rotational symmetry?
Answers
Answer: n + 1
Step-by-step explanation:
Geometry
I just don’t understand this easy math, someone help
Answers
Answer:
Point R: (-2,0)
Point A: (-6,-2)
Point N: (-1,-3)
Step-by-step explanation:
Reflecting a shape across the y-axis means that the y value of the coordinate of the points would reverse its sign, meaning for eg a negative number would turn into a positive one or a positive would turn into a negative.
So in this case, point R would stay the same because it's on the y-axis but the two points A and N would change. Point A is (-6,2) so if we change the y coordinate we would get (-6,-2) and point N is (-1,3) so it would become (-1,-3). Therefore the answer is:
Point R: (-2,0)
Point A: (-6,-2)
Point N: (-1,-3)
i literally don't understand this at all.
Answers
Answer:
its just exaplining how does this exrcise work example 1^1 would be 1x1/
1^3 1x1x1x1/ 3^5 3x3x3x3x3/ 3x3=9 9x3 =27 27x3 =81 81x3=243
Step-by-step explanation:
Can someone help me with this. Will mark brainliest.
Answers
diagonals of a parallelogram bisects each other making an angle of 90°.
so, your answer is True
Answer:
A. True
Step-by-step explanation:
The diagonals of a parallelogram do always bisect each other. However, they only form right angles if the parallelogram is a rhombus or a square.
If w = 6 units, x = 3 units, and y = 5 units, what is the surface area of the figure?
Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
Answers
Answer:
240 units^2
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
178^2 units
Please find where the minimum value occurs. And find the minimum value.
Answers
Answer:
The minimum value would be -4.
What is Find the range of the following data set:
52, 48, 57, 47, 49, 60, 59, 51, 60 plz lmk!!!!!!!!!!!!!!
Answers
Answer:
13
Step-by-step explanation:
60 - 47 = 13
the temperature in Moscow was 2 degrees Celsius then it dropped to 8 degrees Celsius below zero by how many degrees did the temperature drop
Answers
Answer:
11
Step-by-step explanation:
2-8 you need to minus the first number
Find the area of the circle
Answers
Answer:
Q.3 area of circle=pi×r²
area of circle=3.14×(9mm)²
area of circle =254.34mm²
Q.6 area of circle= 3.14×(1.5in)²
area of circle =7.065in²
Answer:
wait what was the question gsdnABNEfglaabgjggse?????
Step-by-step explanation:
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 18
and AC 36, what is the length of AD?
A
D
36
18
B
Answers
Answer:
8 is the length
Step-by-step explanation:
The length of AD is 9 units from the given right triangle ABC.
What is a right triangle?A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.
Given right triangle ABC with altitude BD drawn to hypotenuse AC.
Given that, AB = 18 and AC = 36
Using Pythagoras theorem
AC²=AB²+BC²
⇒ 36²=18²+BC²
⇒ BC²=1296-324
⇒ BC²=972
⇒ BC=31.18 units
We know that, area of a triangle =1/2 × Base × Height
= 1/2 × 31.18 × 18
= 280.62 square units
Now, area of a triangle ABC with base AC and height BD
That is, Area = 1/2 ×36×BD
⇒ 18BD=280.62
⇒ BD=280.62/18
⇒ BD=15.6
Consider ΔBDA
AB²=AD²+BD² (Pythagoras theorem)
18²=x²+15.6²
⇒ x²=18²-15.6²
⇒ x=9 units
Therefore, the length of AD is 9 units from the given right triangle ABC.
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https://brainly.com/question/3770177.
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Meredith went to an aquarium with some of her friends. The tickets cost $12.95 each, and they spent $38 on souvenirs. The total amount spent was $115.70. Which equation can be used to determine how many tickets, t, were purchased?
Answers
Answer:
12.95t+38=115.70
Step-by-step explanation:
could anybody help me pls
Answers
Answer:
all of them are much larger except number 2 which is close to 1
Step-by-step explanation:
PLS HELP
Find (a) the perimeter and (b) the area of the figure. Use 3.14 or 22
for it. Round your answer to the nearest hundredth, if necessary.
-3 ft-
Answers
tep-by-step explanation: Ta
Will give brainlyest to the first correct answer! Easy points
Answers
Answer:
its most likely A
Step-by-step explanation:
Considering it goes at a steady rate with the second variable being reasonably scattered, the level of pure water would obviously go down not up,considering you are adding frogs. than again i havent really reached this degree of mathematics. But through reasoning i beleive it's A
The next model of a sports car will cost 5.6% less than the current model. The current model costs $52,000. How much will the price decrease in dollars? What
will be the price of the next model?
Answers
Answer:
49,088
Step-by-step explanation:
First you need to find 5.6% of 52,000. Simply multiply 52,000 by 0.056 (change the percent to a decimal) then you get 2,912.
Second, you need to subtract 2,912 from 52,000 which is 49,088
Add fractions with unlike denominators
Answers
Answer:
1 5/12 i think im sorry if i get it wrong.
Step-by-step explanation:
Q. Identify the slope-intercept equation
Answers
Please give me Brainliest
Pls help meeeee and thank you so so so much
Answers
Answer: 1/3 x + -1
Step-by-step explanation:
Answer:
y = 2x -1
Step-by-step explanation:
Use slope intercept. The line is rising by 2 points and the y-intercept lies at -1.
pls help
3(x+2)=3x < 2x+18
Answers
Answer:
Step-by-step explanation:
3x + 6 - 3x < 2x + 18
6 < 2x + 18
-12 < 2x
-6 < x
Solution Set = {-5,-4,-3,-2,-1,0......}
Please mark as brainliest for further answers :)
50 points!!! Will mark brainliest if correct!! Pls help me!!
Answers
Answer:
3rd option is correct, give me brainiest
convert 0.00001 to a power of 10
Answers
Answer:
1 × 10⁻⁵
Step-by-step explanation:
A camping store is having a summer sale. Stoves are being sold at 40% off. If the sale price is $57 what was the original price of the stove before the sale
Answers
Answer:
The original price was $142.5.
Step-by-step explanation:
40 ÷ 100 = 0.4
$57 ÷ 0.4 = $142.5
Therefore, $142.5 is our answer.
Answer:
142.5
Step-by-step explanation:
Let's say the original price of the store before the sale is x
so 40% x X = $57
40/100 (X ) =57
0.4 (X) = 57 ====> X = 57 / 0.4 = 142.5
The original price of the stove before the sale is $ 142.5
Use the information in the picture.
Is it a parallelogram? YES
NO
If yes, give the theorem:
Answers
write an equation of the line that passes through 3,1 and 0,10
Answers
Answer:y = -3x + 10
Step-by-step explanation:
To find an equation of a line that passes through two points, we have to first find the slope between the two equation. We can do this by using the slope formula:
where (x₁, y₁) and (x₂, y₂) are the two points that we are finding the slope between.
Lets make (x₁, y₁) equal to (0, 10) and (x₂, y₂) equal to (3, 1). Now we plug them into the slope formula:
So the slope between the two points is -3.
From here, I would normally take one of the points given to us and plug in the point and slope into the point-slope form of a line and then simplify until we get it in slope-intercept form. But if you look carefully, the y-intercept is given to us as the point (0, 10). So we now know that the y-intercept of the line is 10. We can now take the y-intercept and the slope and plug it into the slope-intercept form of a line to get out equation:
y = mx + b
plug in -3 for m (the slope) and 10 for b (the y-intercept)
y = -3x + 10
So now we have our equation.
I hope you find my answer and explanation helpful. Happy studying. :)
Find the length of a diagonal of a square with a perimeter of 16.
Answers
Answer:
4√2
Step-by-step explanation:
If a square has a perimeter of 16, then its side lengths are 4.
Use the pythagorean theorem to find the diagonal.
4^2+4^2=c^216+16=c^232=c^2c=√32√32 can be simplified to 4√2.
The length of the diagonal of the square whose perimeter is 16 is 4√2
What is diagonal of the square?
The length of a diagonal is equal to the length of a side multiplied by the square root of 2
Given data ,
Let d be the diagonal of a square
Perimeter of square = 16
Perimeter of square = 4 x A
16 = 4 x A
A = 4
Therefore , diagonal of square is = 4√2
Hence ,The length of the diagonal of the square whose perimeter is 16 is 4√2
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SOMEONE PLS HELP ASAP I RLLY NEED HELP PLS DONT BE A BOT PLS AND TY
Answers
Answer:
x = 4
Step-by-step explanation:
Given a tangent and a secant from an external point, then
square of the hypotenuse is equal to the product of the external part and the entire secant, that is
DB × CB = AB² , that is
9x = 36 ( divide both sides by 9 )
x = 4