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3 years ago

A rectangular prism has a volume of 3 m3 , a length of 30 cm , and a width of 40 cm . what is the height of the prism ?

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

6 0

V = lwh
3 = (30)(40)(h)
3 = (1200)(h)
 3 = 1200h
1200 1200
1/400 = h

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Solve each system by substitution. y=-4x-9 y=3x+19

Alekssandra [29.7K]

Answer:

x=-4, y=7

Step-by-step explanation:

According to the first equation, y = -4x - 9, so we can substitute y in the second equation for -4x - 9.

y = 3x + 19

-4x - 9 = 3x + 19

Add 9 to both sides

-4x = 3x + 28

Subtract 3x

-7x = 28

Divide by -7

x = -4

Plugging this into the equation, we have:

y = -4x - 9

y = -4(-4) - 9

y = 16 - 9

y = 7

5 0

2 years ago

Perpendicular to y=4x-7; contains the point (4,3)

san4es73 [151]

Okay, so a general rule for finding perpendicular lines in the form of y = mx + b is y = (-1/m) + b.
First, let's ignore b (-7) because we're going to find that later.
A perpendicular line to y = 4x + b is y = -1/4x + b.
Alright, so now let's plug in the values. They are in the form of (x,y), so let's plug them in accordingly.

3 = -1/4(4) + b
3 = -1 + b
b = 4
y = -1/4x + 4
So a line perpendicular to y = 4x - 7 is y = -1/4x + 4.

5 0

3 years ago

Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

erica [24]

Answer:

(a)

$V=x^3+x^2-9x-9$

(b)

$x=10$

(c)

$x=\frac{7}{2}$

Step-by-step explanation:

we are given

length is x+1

$L=x+1$

width is x+3

$W=x+3$

height is x-3

$H=x-3$

(a)

we can use volume formula

$V=L\times W\times H$

now, we can plug it

$V=(x+1)\times (x+3)\times (x-3)$

now, we can simplify it

$V=x^3+x^2-9x-9$

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

$V=x^3+x^2-9x-9=1001$

now, we can factor it

$\left(x-10\right)\left(x^2+11x+101\right)=0$

$x-10=0$

$x=10$

(b)

we are given volume

so, we can set

$V=14\frac{5}{8}=\frac{14\times 8+5}{8}$

$V=\frac{117}{8}$

and then we can solve for x

$V=x^3+x^2-9x-9=\frac{117}{8}$

now, we can factor it

$8x^3+8x^2-72x-189=0$

$\left(2x-7\right)\left(4x^2+18x+27\right)=0$

$2x-7=0$

$x=\frac{7}{2}$

8 0

3 years ago

Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g

SpyIntel [72]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see $\bf f(x)=\sqrt{x}\qquad 
\begin{array}{llll}
g(x)=&\sqrt{0.5x}\\
&\quad \uparrow \\
&\quad B
\end{array}$

so B went form 1 on f(x), down to 0.5 or 1/2 on g(x)
B = 1/2, thus the graph is stretched by twice as much.

8 0

3 years ago

Read 2 more answers

Please help me it is due tonight

Aneli [31]

Answer: with what

Step-by-step explanation:

8 0

3 years ago