Given:
A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.
To find:
The total surface area of the prism.
Solution:
We have,
Height of prism = 7½ = 7.5
Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because
[tex]5^2+12^2=13^2[/tex]
[tex]25+144=169[/tex]
[tex]169=169[/tex]
So, the base of the prism is a right triangle.
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times base \times height[/tex]
[tex]A_1=\dfrac{1}{2}\times 5\times 12[/tex]
[tex]A_1=30[/tex]
The area of the base is equal to the area of the top, i.e., [tex]A_2=30[/tex] sq units.
Perimeter of the base is
[tex]P=5+12+13[/tex]
[tex]P=30[/tex]
The curved surface area of the prism is
[tex]CSA=\text{Perimeter of the base}\times \text{Height of the prism}[/tex]
[tex]CSA=30\times 7.5[/tex]
[tex]CSA=225[/tex]
Now, the total area of the prism is
[tex]A=A_1+A_2+CSA[/tex]
[tex]A=30+30+225[/tex]
[tex]A=285[/tex]
Therefore, the total surface area of the triangular prism is 285 square units.
Show work A circular pond has a circumference of about C feet. The diameter of the pond is 7 feet. Which expression best represents the value of pi?
Answer: 7
Step-by-step explanation:
7x1x1=7/1=7
A large chocolate bunny costs $2.07. Chris only has $1.12. How much more money does Chris need in order to buy the bunny?
Answer
0.95 more cents
Step-by-step explanation:
2.07-1.12=0.95
find the coordinates of the point p that divides the directed line segment from A(-1,-4) to B (6,10) in ratio of 2 to 5
Answer:
bo0by
Step-by-step explanation:
Which equation represents a slope of 4 and (5,-2)?
y-2=4(x-5)
y-5=4(x-2)
y+2=4(x+5)
y+2=4(x-5)
Answer:
Step-by-step explanation:
the formula is named the point slope formula for a reason. and you have show both of them in the question , the slope and the point are given
y - y1 = m(x-x1)
so for your answer
y-(-2) = 4(x-5)
y+2 = 4(x-5) is the right answer
4x^2 - 5x when x = 3
^ is squared
Answer:
-5
Step-by-step explanation:
Write two numbers that multiply to the value on top and add to the value on bottom.
a triangle can be drawn with angle measure of 60 degrees, 60 degrees, and 70 degrees
true or false?
Answer:
False. All triangles must have a total of 180°. 60° + 60° + 70° = 190°.
Find the slope of the line above.
m =?
It is dinos birthday today. She is 9 years older than tyger. Altogether, their ages add up to 23 years. How old is dino?
Answer:
7
Step-by-step explanation:
Tyger = x
Dinos = x + 9
Total = 23
x + x+9 = 23
2x + 9 = 23
2x = 23 - 9
2x = 14
x = 14/2 = 7
I hope im right!!
How to round 8.6023 in the nearest tenth?
Answer:
8.6
Step-by-step explanation:
https://www.you.tube.com/watch?v=32gDF10ZXOA
( it might be wrong pls dont report me just let me kno y its wrong )
Answer:
8.6
Step-by-step explanation:
First of all consider the thousands in the decimal which is 2. Since 2 is not greater than 5 we have to remove the number 2 and 3 from the 8.6023.
We're left with 8.60. Now we see that there's a 0 in the hundredths so since it's not greater than 5 we remove it.
Now we're left with 8.6 which is to the nearest tenth.
Si los conjuntos:
K = {a; x + y}
L = {a + 1; x – y}
Son iguales, halla el valor de ( x - a) a la 2Y
The vertex of this parabola is at (3, 5) . When the y-value is 6, the x-value is - 1 What is the coefficient of the squared term in the parabola's equation? (3, 5) A. -4 B. 4 C. 2 D.2
Answer:
The correct approach is Option A (-4).
Step-by-step explanation:
The given values are:
Vertex of the parabola,
(h, k) = (3, 5)
Passing through,
(x, y) = (-1, 6)
As we know,
The equation of parabola is:
⇒ [tex]x=a(y-k)^2+h[/tex]
On substituting the given values in the above equation, we get
⇒ [tex]-1=a(6-5)^2+3[/tex]
⇒ [tex]-1=a+3[/tex]
On substracting "3" from both sides, we get
⇒ [tex]-1-3=a+3-3[/tex]
⇒ [tex]a=-4[/tex] (coefficient of squared term)
Thus the above is the right choice.
An artist is creating tiles to use in a project. Each tile is to be in the shape of a right triangle. One of the legs of the tile is to be 3 Inches long. The hypotenuse is to be z Inches long.
Write an expression in terms of 3 that models the other leg of a tile.
Answer:
???
Step-by-step explanation:
Joshua drove his car a distance of 321.7 miles, and it required 13.6 gallons of gasoline (petrol). How many liters of fuel will it take to go 100 kilometers?
Answer:
1005.68 litres
Step-by-step explanation:
Steps to answering this question
Convert miles to kilometers and gallons to litresThen divide the converted miles by the converted gallons Multiply the value gotten from the above step by 100 km1 gallon = 3.78541 litres
13.6 gallons x 3.78541 = 51.48 litres
1 mile = 1.60934 km
321.7 miles x 1.60934 = 517.72 km
Litre needed per kilometer = 517.72 km / 51.48 = 10.06
Litres needed for 100 km = 100km x 10.06 = 1005.68 litres
Mia bought 2 adult tickets and 4 kid's tickets. Each adult ticket cost $13.50 and each kid ticket cost $10.25. How much did Mia spend on tickets
Answer:
Mia spent 68 dollars.
Step-by-step explanation:
The equation would be 2(13.50) + 4(10.25) = x
Solving for the first part, you get 27 for adult tickets and 41 for the children tickets. When you add the two values, you get 68.
Which of these is equivalent to x + 1 + x + 2 + x + 3 + x + 4?
Answer:
what are the options?
Answer:
x + 1 + x + 2+ x + 3 + x + 4
4x + 10
2( 2x + 5)
hope it helps
The middle person in a row is the 18th, how many persons are in the row?
Answer:
35
Step-by-step explanation:
You have 17 either side to make 18 the middle e.g if 2 was the middle then you have 1 either side.
Answer:
36
Step-by-step explanation:
if 18 is the middle there are 17 on each side of that person so 17+17+1=36
f – 5.2 1.6
answer pls
Answer: what u mean
Step-by-step explanation:
Answer:
huh what do you mean picture?
Sydney ran 4 miles in 1 hour and 20 minutes. What was Sydney's average speed in miles per minute?
Determine the domain of the following graph:
Answer:
[0,11)
Step-by-step explanation:
the function is defined over {0,11) because it includes x=0, but has an open dot at x=11.
Need help ASAP!! What is the value of x?
Answer:
98
Step-by-step explanation:
the exterior angle is equal to the sum of the opposite interior angles
-Sumin <3
Answer:
98
Step-by-step explanation:
53+45+x = 180
53+45=98
180-98=82
82 (interior)
82+98=180
x = 98
if i got shorts for 30 dollars and the original price was 40 what was the discount
Answer:
25%
Step-by-step explanation:
30/40 = 0.75 = 75% paid
100-75 = 25% discount
Answer:
[tex]25\%[/tex]
Step-by-step explanation:
To find the discount of an object, one must set up the equation, the difference between the original and the paid price, over the original price, equals percent over 100. In essence;
[tex]\frac{(original-paid)}{original}=\frac{percent}{100}[/tex]
Substitute in the given values;
[tex]\frac{(40)-(30)}{40}=\frac{percnet}{100}[/tex]
Solve;
[tex]\frac{10}{40}=\frac{percent}{100}[/tex]
Simplify,
[tex]\frac{1}{4}=\frac{percent}{100}[/tex]
Cross products,
[tex]100 = 4(percent)[/tex]
Inverse operations,
[tex]100=4(percent)\\/4\\\\25 = percent[/tex]
Which of the values in the set {3,4,5,6} is a solution to the equation 4x + 2 = 22?
A) 3
B)4
C)5
D)6
Which pairs of expressions are equivalent
More the 1 answer
Answer:
The first 3 pairs of expressions are equivalent.
Step-by-step explanation:
someone please help me please
Answer:
D
Step-by-step explanation:
I tried all the other equations by plugging in numbers and disproving their accuracy. D was the only one that worked.
help me please i appreciate it.
Answer:
c
Step-by-step explanation:
because all the three laws are applicable for polygons
A rectangular prism is filled with 356 cubes with an edge length of 1/4 what is the volume of this prism
Answer: volume = 5.5625 cubic units.
Step-by-step explanation:
A rectangular prism is filled with 356 cubes, then the volume of the prism will be equal to 356 times the volume of a single cube.
We know that for a cube with side length L, the volume is:
V = L^3
And we know that these small cubes have an edge length of 1/4 units.
Then the volume of each small cube is:
V = (1/4)^3 cubic units
V = (1/64) cubic units
And the volume of the prism will be 356 times that, then the volume of the prism is:
volume = 356*(1/64) cubic units
volume = 5.5625 cubic units.
how do u find surface area for this
Answer:
416.23
Step-by-step explanation:
A=a2+2aa2
4+h2=102+2·10·102
4+152≈416.22777
Answer:
find the areas of the individual triangles then add those ares
together.
Step-by-step explanation:
During a basketball game, one of the players scores 8 points for her team. If the points she scored represent 20% of the team's total points, as shown below, how many points did the team score during the game?
Answer:
40points
Step-by-step explanation:
Given data
Let the total points the team scored be x
so that
20% of x= 8 points
let us solve for x
20/100*x= 8
0.2*x= 8
0.2x= 8
Divide both sides by 0.2
x= 8/0.2
x= 40 points
Hence the time scored 40points
3. Jessie is looking for the volume of the cone
below, and she is using the formula V = (1/3)Bh.
Which of the following is the value of “B”?
Answer:
A
Step-by-step explanation:
The base is the circle.
To find the area of the circle, use pi*r^2
pi = 3.14
r = 6
Area = 3.14 * 6^2Area = 3.14 * 36Area = 113.04Answer:
C. 414.48
Step-by-step explanation:
1/3 x 3.14 x 6² x 11 = 4.14.48