Given:
A figure of a rectangular prism with length l, width w and height h.
To find:
The surface area of the rectangular prism.
Solution:
The product of twice of the length l and the width w is:
[tex]2\times l\times w=2lw[/tex] ...(i)
The product of twice of the length l and the height is:
[tex]2\times l\times h=2lh[/tex] ...(ii)
The product of twice of the width w and the height h is:
[tex]2\times w\times h=2wh[/tex] ...(iii)
The surface area of the prism is the sum of (i), (ii) and (iii). So, the expression for the surface area is:
[tex]A=2lw+2lh+2wh[/tex]
[tex]A=2(lw+lh+wh)[/tex]
Therefore, the required expression is [tex]2(lw+lh+wh)[/tex].
Find the area of the shaded region in the figure above using two different ways. Do you get the same
answer both ways? Investigate what's going on here.
Answer:
Below
Step-by-step explanation:
First way:
Find the area of the big triangle and subtract the area of the rectangle.
Area of shaded part = 1/2 * 25 * 34 - 10*24 = 185 m^2
Second way:
Add the area of the 3 shaded triangles:
= 1/2 * 15 * 24 + 1/2 * 5 * 10 + 1/2 * 5 * 10
= 180 + 25 + 25 = 230 m^2
The areas are different. The reason must be that given lengths are not possible for this diagram.
Check The length of the hypotenuse of the large triangle by 2 different methods:
The hypotenuse = √(25^2 + 17^2)
= 30.23.
Now let's work out the hypotenuse of the shaded triangles:
Top one = √(15^2 ^ 12^2) = 19.21
Bottom one = √((5^2 + 10^2) = 11.18
Adding these we get 30.39 which is different than previously calculated but it should be the same.
So what we have here is impossible geometry. This accounts for the different areas.
Find the gradient of the line y= -4x + 5
Answer:
m = -4
Step-by-step explanation:
The given y= -4x + 5 exactly matches the format of the slope-intercept equation y = mx + b.
Thus, the gradient (slope) of the given line is -4.
Is -451 in the sequence below?
15,7,-1,-9,,-17..
Answer:
No, the closest to -451 in the sequence is -429
Step-by-step explanation:
Answer:
nope
Step-by-step explanation:
hey again can u help me with this
Answer:
option C
Step-by-step explanation:
We will take 2 coordinates from the graph and Find the equation of the line.
Let the coordinates be : ( 0, 1) and (1, 3)
step 1 : find slope
[tex]slope , m = \frac{y_2 - y_ 1}{x_2 - x_1} = \frac{3-1}{1-0} = 2[/tex]
Step 2 : equation of the line :
[tex]( y - y_1) = m (x- x_1)[/tex]
[tex](y -1) = 2 ( x -0)\\y - 1 = 2x \\y = 2x + 1[/tex]
Therefore, y = 2x + 1 represent the equation of the line.
Answer:
C
Step-by-step explanation:
You need to solve for y = mx + b
You can solve for b right away. It is clear that the line crosses the y axis at (0,1) so you have
y = mx + 1 so far.
Normally you would need two clear points to solve for m, but since you know the y intercept, you need only 1 point.
The clearest point I can see is (-2,-3) which means that
x = -2
y = - 3
Put that into the equation and solve for m.
-3 = m(-2) + 1 Subtract 1 from both sides
-3-1 = m(-2) Combine
-4 = -2 m Divide both sides by - 2
-4/-2 = m
m = 2
Answer
only a and c are real choices. That's because m = 2 in both cases.
The equation we got is y = 2x + 1 which is c
due today pls help me
Answer:
BC = [tex]5\sqrt{5}[/tex]
Step-by-step explanation:
Hope this helps u !!
Please help it's urgent if you do not help you will become Jeffery Epstein son!
Do the side lengths 15,20 and 25 form a right triangle?
PLEASEEEE HELPPPP!!! asap
===================================================
Work Shown:
a^2+b^2 = c^2
15^2+20^2 = 25^2
225+400 = 625
625 = 625
Since the last equation is true, this makes the first equation true for those a,b,c values. Therefore, by the pythagorean theorem converse, this is a right triangle.
Side note: c is always the longest side.
assssssssssssssssssssssssssssssssss
Answer:
15, 9, 3n
Step-by-step explanation:
Just multiply the number of red balls by 3 to get total number, and divide the total number by three to get the number of red balls
Answer:
What math game is this?
Oh and this guy is correct.
Step-by-step explanation:
please help i dont understand this
Answer:
yeah me too
Step-by-step explanation:
please help me i have 5 minutes left: )! ill give Brainliest thanks<3
The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?
0.27 goldfish per cubic foot
3.75 goldfish per cubic foot
33 goldfish per cubic foot
57 goldfish per cubic foot
Answer:
0.27 goldfish per cubic foot
Step-by-step explanation:
Find the density of the tank by dividing the number of goldfish by the volume of the tank:
12/45
= 0.27
So, the density of the tank is 0.27 goldfish per cubic foot
Answer:
0.27 is the answer
Step-by-step explanation:
I took the test :)
Which phrase describes the variable expression 11 • X?
O A. 11 decreased by x
OB. 11 increased by x
C. The produqt of 11 and x
odust
O D. The quotient of 11 and x
SUBA
Answer:
B or C
Step-by-step explanation:
if its refering to the answer of 11 × X then the answer is C, but if its not the answer might be B.
Use an algebraic approach to solve the problem.
Judy bought a coat at a 10% discount sale for $63. What was the original price of the coat?
Answer:
$70
Step-by-step explanation:
essentially, Judy paid 90% of the original price
therefore you can write this equation where 'x' equals the original price:
.9x = 63
x = 63/.9
x = 70
What is the area of the sector that is not shaded?
0 12 tt units
O 24 tt units?
0 120rt units
O 144rt units?
The area of the sector that is not shaded is 120π units²
Option C is the correct answer
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is pir^2.
We have,
The circle has 360°.
This can be written as,
Area = πr² x 360/360
Now,
The area of the not-shaded part has (360 - 60)°
So,
Area = πr² x 300/360
Now,
r = 12 units
Area = π x 12 x 12 x 300/360
Area = 120π units²
Thus,
The area of the sector that is not shaded is 120π units²
Learn more about circle here:
https://brainly.com/question/11833983
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What is the factorization of the trinomial below?
2x2 + 11x + 12
O A. (2x + 1)(x+12)
O B. (2x+3)(x + 4)
O C. (2x + 4)(x+3)
O D. (2x+6)(x + 2)
Answer:
O B. (2x+3)(x + 4)
Step-by-step explanation:
[tex]2x^{2} +11x+12[/tex]
[tex]2x^{2} +8x+3x+12[/tex]
[tex]2x(x+4)+3(x+4)[/tex]
[tex](2x+3)(x+4)[/tex]
Someone please help me ASAP!!
Answer:
B' = (-6,6)
Step-by-step explanation:
The coordinates of B are (-2,2)
If the figure is to become 3 times as large, B' would be 3(-2,2) = (-6,6)
Solve the inequality.
pls pls help
Answer:
first u will find de L.C.M which is 6
so u will multiply de whole equation by 6 hence
6(x/3)- 6(x-1/ 2) greater or equal to 6(1)
u will then cancel getting de equation to be
2(x)-3(x-1) greater or equal to 6 (1)
now, u will expand de equation
2x-3x+3 greater or equal to 6
now u group like terms
2x-3x greater or equal to 6-3
hint: greater or equal to must be done with it's symbol
so now for de answer, u will get -x greater or equal to 3
wen u get this, u change de operation to be opposite of de current sign
now de final answer becomes
-x less or equal to 3They are selling lollipops for $0.50 and candy bars for $1.50
Lydia buys 6 lollipops and some candy bars.
If she spends $15.00 in total, how many candy bars, b, did Lydia buy?
need help ASAP thank you :)
Expand the following: a)2(x - 1) b) 3(2x + 3) c) 7(x + 5 d) 5(2x - y) o Tyne here to search
Step-by-step explanation:
a )2x-2
b)6x+9
c)7x+35d
for these type of questions you basically just times the out side number of the brackets by the inside one.
hope this helps u understand:)
Please help!!!!!! I’ll give the brainliest !!!!!!!
For f(x) = 3x + 1 and g(x) = x ^ 2 - 6 find (8/f)(x)
Answer:
9x² + 6x - 5
Step-by-step explanation:
If you mean g(f(x))
g(x) = x² - 6
f(x) = 3x + 1
Then, g(f(x)) = g(3x + 1)
but g(x) = x² - 6
g(3x + 1) = (3x + 1)² - 6 = 9x² + 6x + 1 - 6
= 9x² + 6x - 5
The perimeter of a rectangle is twice the sum of its length and its width. The perimeter is 22 meters and its length is 2 meters more than twice its width. 0
Answer:
Length = 6.5 meters
Width = 4.5 meters
Step-by-step explanation:
Given,
Perimeter of a rectangle is twice the sum of it's length and width.
Length is 2 meters more than twice its width, let the length be x meters so the width becomes (x-2) meters
perimeter of the rectangle,
2{x+(x-2)} meters which is 22 meters (given)
so,
2{x+(x-2)}=22
or, 2(x+x-2)=22
or, 2(2x-2)=22
or, 2x-2=11
or, 2x=13
or, x=6.5
so the length is 6.5 meters and the width is 6.5-2 = 4.5 meters.
Answered by GAUTHMATH
Work out m and c for the line:
y=x-8
never mind i got it
Answer:
m = 1 c = -8
Step-by-step explanation:
Can someone help me? It's urgent and thank you!
Answer:
-6 and -1
Step-by-step explanation:
The excluded values are the values of x that satisfy [tex]2x^{2} + 14x + 12 = 0[/tex]
Let us solve the equation [tex]2x^{2} + 14x + 12 = 0[/tex]
It's a quadratic equation
Thus, let us calculate the discriminant Δ
Δ [tex]= 14^{2} - 4 .2.12 = 100[/tex]
the discriminant is greater than 0, so the equation has two solutions
[tex]x = \frac{-14 - 10}{4} = \frac{-24}{4} = -6[/tex] or [tex]x = \frac{-14+10}{4} = \frac{-4}{4} = -1[/tex]
the excluded values are -6 and -1
WILL MARK BRAINLIEST!!!!!find the length of AC
Answer:
20
Step-by-step explanation:
a²+b²=c²
25²-15²=b²
625-225=b²
400=b²
√400=√b²
20=b
Select the correct answer.
A triangle with vertices at A(0, 0), BIO, 4), and C16, 0) is dilated to yield a triangle with vertices at Ato, O), BIO, 10), and C[15, 0). The origin is the center of dilation. What is the
scale factor of the dilation?
OA 1.5
OB.
2
OC. 2.5
OD. 3
Answer:
c. 2.5
Step-by-step explanation:
4×2.5 => 10
6×2.5 => 15
so scale factor = 2.5
Which table shows a proportional relationship between x and y?
In the graph above, what's the distance between (0, 2) and (5, 2)? Question 16 options: A) 2 units B) 5 units C) –5 units D) 4 units
Answer:
B) 5 units
Step-by-step explanation:
The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The two pints are given below.
(0, 2) and (5, 2)
Then the distance between these points (0, 2) and (5, 2) will be given as,
D² = (5 - 0)² + (2 - 2)²
D² = 5²
D = 5 units
The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.
Learn more about the distance between two points here:
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i’ll give you what eva you like
Answer:
Number of additional inches= x
Number of additional topping= y
Total cost= 8+1.5(x)+0.75(y)
cost of pizza= 8+1.5x+0.75y-----------------------
hope it helps...
have a great day!!
Semi easy-which boxplot represent the 5 number summary