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2 years ago

Find the surface area of the prism

Mathematics

1 answer:

scoray [572]2 years ago

3 0

Surface area of one face = 9x9 = 81
total no. of faces = 6
total surface area of prism = 81 x 6 = 486in.

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Explain how to find the vertex of 2x^2+12x+16

Elina [12.6K]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

Use $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2$

<h3>Answer: (-3, -2).</h3>

Other method:

$f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+16=2(9)-36+16=18-36+16=-2$

<h3>Answer: (-3, -2).</h3>

5 0

3 years ago

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vladimir1956 [14]

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3 years ago

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Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does

sveta [45]

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3 years ago

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What is the value of the numerical expression 5/8-5/12(3-1/4)+2/3

vlabodo [156]

Make bottom numbers same
find least common multipules of 8,12,4 and 3
8=2 times 2 times 2
12=2 times 2 times 3
4=2 times 2
3=3
lcm=2 times 2 times 2 times 3=24

5/8 times 3/3=15/24
5/12 times 2/2=10/24
3/1 times 24/24=72/24
1/4 times 6/6=6/24
2/3 times 8/8=16/24
we now have
15/24-10/24(72/24-6/24)+16/24
pemdas
simplify parenthasees first
72/24-6/24=66/24

now we have
15/24-10/24(66/24)+16/24
multiply
15/24-660/576+16/24
make same bottom number
15/24 times 24/24=360/576
16/24 times 24/24=384/576
360/576-660/576+384/576
84/576
7/48

answer is 7/48

3 0

3 years ago

Find the total surface area of the rectangular prism in square millimeters. 2cm 6 cm 9cm

Ket [755]

<h3>Answer: 168 square cm</h3>

==============================================

Work Shown:

L = 2 = length
W = 6 = width
H = 9 = height

The order of length, width and height doesn't matter

SA = surface area of rectangular prism

SA = 2*(LW + LH + WH)

SA = 2*(2*6 + 2*9 + 6*9)

SA = 2*(12 + 18 + 54)

SA = 2*(30+54)

SA = 2*(84)

SA = 168 square cm

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3 years ago