Given:
The bases of triangular prism are right triangles with a base of 12 inches and height of 9 inches.
The height of the prism is 11 inches.
To find:
The surface area of the triangular prism.
Solution:
Using the Pythagoras theorem, the hypotenuse of the bases of the triangular prism is:
[tex]Hypotenuse^2=Base^2+Height^2[/tex]
[tex]Hypotenuse^2=12^2+9^2[/tex]
[tex]Hypotenuse^2=144+81[/tex]
[tex]Hypotenuse^2=225[/tex]
Taking square root on both sides.
[tex]Hypotenuse=15[/tex]
The surface after of the triangular prism contains 3 rectangles of dimensions 12 inches by 11 inches, 9 inches by 11 inches, 15 inches by 11 inches and two triangles with base 12 inches and height 9 inches.
Area of the rectangle:
[tex]Area=Length \times Width[/tex]
So, the area of three rectangles are:
[tex]A_1=12 \times 11[/tex]
[tex]A_1=132[/tex]
[tex]A_2=9 \times 11[/tex]
[tex]A_2=99[/tex]
[tex]A_3=15 \times 11[/tex]
[tex]A_3=165[/tex]
Area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base \times height[/tex]
So, the area of the triangles is:
[tex]A_4=\dfrac{1}{2}\times 12 \times 9[/tex]
[tex]A_4=6 \times 9[/tex]
[tex]A_4=54[/tex]
And, the triangles have same dimensions so their areas are equal.
[tex]A_4=A_5=54[/tex]
Now,
[tex]Area=A_1+A_2+A_3+A_4+A_5[/tex]
[tex]Area=132+99+165+54+54[/tex]
[tex]Area=504[/tex]
Therefore, the surface area of the triangular prism is 504 sq. inches.
HELPPP i need some help solving this out please explain
Answer:
Step-by-step explanation:
The triangle sum therom states that the interior angles of a triangle add up to 180 degrees. So all you have to do is make an equation 2x+2x+x=180 and solve from there.
Delaney is saving money in an account that offers 9% simple interest. She deposits 2000 from her grandmother into the account and makes no additional deposits or withdraws. How many years will it take to grow to 4,700
Answer:
15years
Step-by-step explanation:
Given data
Rate= 9%
Principal= $2000
Final amount= $4700
The simple interest formula is given as
A= P(1+rt)
Substitute
4700=2000(1+0.09*t)
4700= 2000+ 180t
4700-2000= 180t
2700=180t
t= 2700/180
t= 15 years
Hence the time is 15years
if I cupcake have 240 calories for 3 servings how many calories would it have for 5 servings
Answer:
400 calories
Step-by-step explanation:
One cupcake has 80 calories. 80 x 5 = 400
Answer:
400 Calories
Step-by-step explanation:
If there are 240 calories in 3 servings, In one serving there must be 80 because
240/3 = 80
And since there are 80 calories in one serving, in 5 servings there will be 5 times the amount of calories there is in one serving so
5 * 80 = 400
factor the polynomial completely f(x)=x^4-6x^3-8x+48;x-6
Answer:
Factor x^3+8x^2+6x+48. x3+8x2+6x+48 x 3 + 8 x 2 + 6 x + 48. Factor out the greatest common factor from each group.
Which set of angle measurements CANNOT be angle measures of a triangle?
Answer:
180
Step-by-step explanation:
Explanation: In a triangle, there can only be one obtuse angle. Additionally, all the angle measures must add up to 180.
Triangle ABC is reflected over the x-axis. У C(5, - 1) | A(0, - 2) -3 -4 B(2, - 4) 5 -6 What are the vertices of AA'B'C '?
Answer:
The vertices of the triangle A'B'C' are [tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex] and [tex]C'(x,y) = (-5,1)[/tex], respectively.
Step-by-step explanation:
Vectorially speaking, the reflection of a point over the x-axis is defined by the following expression:
[tex]P'(x,y) = P(x,y) -2\cdot P(x,y)[/tex]
[tex]P'(x,y) = -P(x,y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Reflected point.
If we know that [tex]A(x,y) = (0,-2)[/tex], [tex]B(x,y) = (2,-4)[/tex] and [tex]C(x,y) = (5,-1)[/tex], then the vertices of the triangle A'B'C':
[tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex], [tex]C'(x,y) = (-5,1)[/tex]
The vertices of the triangle A'B'C' are [tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex] and [tex]C'(x,y) = (-5,1)[/tex], respectively.
Here are five cards. 1 5 7 9 11 One of the cards is removed. The mean of the numbers on the remaining four cards is 6 Which card was removed
Answer:
Number 9 was removed
PS: Please give me brainly if im correct!
Plz help me out and hurry plz
Answer:
a
Step-by-step explanation:
Determine whether the polygons are similar.
Not Similar
Similar
Pls help and hurry i will report if you answer any unnecessary answers.
Answer:
847.8 sq meters
Step-by-step explanation:
Formula:
A= 2πrh + 2πr^2
A= 2(3.14)(9)(6) + 2(3.14)9^2
A= 339.12 + 508.68
A= 847.8
Plz help me I’m not good at math
Answer:
second one
Step-by-step explanation:
am pretty sure
Answer:
8x - 4y = 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2 and c = - [tex]\frac{3}{4}[/tex] , then
y = 2x - [tex]\frac{3}{4}[/tex] ← in slope- intercept form
Multiply through by 4 to clear the fraction
4y = 8x - 3 ( subtract 4y from both sides )
0 = 8x - 4y - 3 ( add 3 to both sides )
3 = 8x - 4y , or
8x - 4y = 3 ← in standard form
which expression is equivalent to 2 3/5 divided by 7/9
Answer:
I don't know look it up lol
Step-by-step explanation:
that's what I did go to answers. com that's where I get all my answers that brainly doesn't provide that or ask a tutor
How do I express the letters in bracket as the subject of the formula ?
especially the 1/2 power is new and unfamiliar to me.
Answer:
[tex]n = 144m^2 - 1[/tex]
Step-by-step explanation:
__________________________________________________________
FACTS TO KNOW BEFORE SOLVING :-
Let x be a number. ⇒ [tex]x^{\frac{1}{2}}[/tex] can also be written as [tex]\sqrt{x}[/tex].To make any variable the subject of any formula , we need to isolate it.__________________________________________________________
According to the question ,
[tex]3m = \frac{(n + 1)^{\frac{1}{2} }}{4}[/tex]
Lets multiply both the sides by 4.
[tex]=> \frac{(n + 1)^{\frac{1}{2} }}{4} \times 4 = 3m \times 4[/tex]
[tex]=> (n + 1)^{\frac{1}{2} } = 12m[/tex]
It can be also written as :-
[tex]=> \sqrt{(n + 1)} = 12m[/tex]
Lets square both the sides.
[tex]=> [\sqrt{(n + 1)} ]^{2} = (12m)^{2}[/tex]
[tex]=> n + 1 =144m^2[/tex]
[tex]=> n = 144m^2 - 1[/tex]
Find length of BA don’t answer if you’re a fake bot
Answer:
BA = 22.57
Step-by-step explanation:
perimeter = 60
2BZ + 2ZA = 60
BZ + ZA = 30, BZ = 30 - ZA
tan 25° = 0.4663
0.4663 = ZA/BZ = ZA/(30 - ZA)
multiply both sides by (30 - ZA):
0.4663(30 - ZA) = ZA
simplify:
13.99 -0.4663ZA = ZA
add 0.4663ZA to each side:
13.99 = 1.4663ZA
divide both sides by 1.4663:
ZA = 9.54
BZ = 30 - 9.54 = 20.46
BA² = 9.54² + 20.46²
BA² = 509.62
BA = 22.57
Yensen is biking in a race that is 80 miles long. He has completed 35% of the race. How many miles has Yensen biked?
Answer:
28 miles
Step-by-step explanation:
here's your solution
=> total distance of race = 80 miles
=> percentage of race that is completed
= 30%
=> now we have to find out 35% of 80
=>. distance covered = 35/100*80
=>. 28 miles
hope it helps
Someone please help me find x.
what is the value of x in the equation x^3=.027
A.0.03
B.0.5
C. 3
D. .09
Answer:
D.
Step-by-step explanation:
Find the value of x
Answer:
x= 3.5
Step-by-step explanation:
To solve the equation below, you would?
X – 70 = 135
A) add 70 to each side
B) subtract 70 from each side
C) multiply each side by 70
D) add 135 to each side
Step-by-step explanation:
step 1. x - 70 = 135
step 2. x = 205. add 70 to each side
For volunteers picked up letter from the park Dominic you collect and 15 for your pieces a litter than Sarah Sarah collect the 12 more pieces in piper piper collected 1/4 as many pieces of litter as Vaughn Vaughn has collected nine more pieces of wood or than everyone else combine the X represent the number of pieces of litter Vaughn Collection
So many confusing details. So, I rephrase the question as:
Four volunteers picked up litters from the park.
Dominic collect 15 pieces less than Sarah. Sarah collects 12 more pieces than Piper. Piper collected 1/4 as many pieces of letter as Vaughn. Vaughn has collected nine more pieces of letter than everyone else combined. Let x represent the number of pieces of litter in Vaughn's Collection. Find x
Answer:
[tex]x = 72[/tex]
Step-by-step explanation:
Let:
[tex]D = Dominic;\ \ S = Sarah;\ \ P = Piper;\ \ V = Vaughn[/tex]
From the [rephrased] question, we have:
[tex]D = S - 15[/tex]
[tex]S = 12 + P[/tex]
[tex]P = \frac{1}{4}V[/tex]
[tex]V = 9 + D + S + P[/tex]
Substitute [tex]S = 12 + P[/tex] in [tex]D = S - 15[/tex]
[tex]D = 12 + P - 15[/tex]
[tex]D = P+12 - 15[/tex]
[tex]D = P-3[/tex]
Make V the subject in [tex]P = \frac{1}{4}V[/tex]
[tex]V = 4P[/tex]
Substitute: [tex]V = 4P[/tex], [tex]D = P-3[/tex] and [tex]S = 12 + P[/tex] in [tex]V = 9 + D + S + P[/tex]
[tex]4P= 9 + P - 3 + 12 + P +P[/tex]
Collect like terms
[tex]4P - P -P-P= 9 - 3 + 12[/tex]
[tex]P= 18[/tex]
Substitute [tex]P= 18[/tex] in [tex]S = 12 + P[/tex]
[tex]S = 12 +18[/tex]
[tex]S = 30[/tex]
Substitute [tex]S = 30[/tex] in [tex]D = S - 15[/tex]
[tex]D = 30 - 15[/tex]
[tex]D =15[/tex]
Substitute [tex]D =15[/tex], [tex]S = 30[/tex] and [tex]P= 18[/tex] in [tex]V = 9 + D + S + P[/tex]
[tex]V = 9 + 15 + 30 + 18[/tex]
[tex]V = 72[/tex]
x represents the number collected by Vaughan.
So:
[tex]x = 72[/tex]
Which statements describe the functions? Check all that apply.
Answer: wheres the picture??????
Step-by-step explanation:
Answer: a,d,e
Step-by-step explanation:
did it on edge
The cost c in dollars of manufacturing x bicycles at a production plant is given by th function shown below C(x)=5x^2-1000x+63,500. How many bicycles must be manufactured to minimize the cost
Answer:
100 bicycle
Step-by-step explanation:
Given the cost c in dollars of manufacturing x bicycles at a production plant expressed as C(x)=5x^2-1000x+63,500.
x is the number of bikes
To minimize the cost, dC/dx = 0
dC/dx = 10x - 1000
Since dC/dx = 0
0 = 10x - 1000
-10x = -1000
x = 1000/10
x = 100
Hence the number of bicycles that must be manufactured to minimize the cost is 100 bicycle
sally’s huge dog weighed 175 pounds in 2018 and then weighed 145 pounds in 2020 what is the rate of change and weight?
Answer:17.14%
Step-by-step explanation:
145 x
_____=_____
175 100
145(100)=175(x)
14500=175x
__________
175 175
x=82.86
100-82.86=17.14%
The radius of a circle is 8 miles. What is the diameter?
Answer:
16 miles
Step-by-step explanation:
8*2=16
Brainlest pls?
Andy bought one candy bar. He ate
7/12
of his candy bar on Monday and
1/6
of his candy bar on Tuesday. How much of Andy's candy bar was still there after Tuesday?
-4 and 3x + 5y = 0
Solve the system of equations 5x +9y
by combining the equations.
Answer:
Sorry this question does not make any sense. Delete it and re-type the equations correctly.
Step-by-step explanation:
marty has 1 1/3 jugs of apple juice. he uses 3/4 of the juice to make freeze pops. what fraction amount of a jus doe marty have?
Answer:
He has 1/3 of a jug left.
Step-by-step explanation:
He starts with 1 1/3 jugs.
He uses 3/4 of 1 1/3 jugs.
A full amount is 1 or 4/4. If he uses 3/4, he has 1/4 left since
1 - 3/4 = 4/4 - 3/4 = 1/4
That means he has 1/4 of 1 1/3 jugs left.
We need to multiply 1/4 by 1 1/3.
1/4 * 1 1/3 =
= 1/4 * 4/3
= 4/12
= 1/3
Answer: He has 1/3 of a jug left.
The table below shows the number of people attending a charity event, x, and the total cost of hosting the event, y. Number of People (x) 2 3 4 5 6 7 Total Cost (y) $2,630 $2,695 $2,760 $2,825 $2,890 $2,955
Which linear function models this situation?
A. y = 2,630x + 65
B. y = 65x + 2,630
C. y = 2,500x + 65
D. y = 65x + 2,500
please help me , i will give a lot of points
Answer:
no pic
STEP-BY-STEP-EXPLANATION
About how much glass is needed to cover a circular window with a diameter of
4.8ft?
A) 4.5ft2
B) 7.5ft2
C) 15ft2
D) 18ft2
Answer:
it is A) 4.5ft2 is your answer