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masya89 [10]
3 years ago
5

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)
<u>    </u><u>3  </u><u>  </u><u /> = <u>1200h</u>
 1200      1200
1/400 = h
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Solve each system by substitution.<br> 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}&#10;\\ \quad \\\\&#10;% left side templates&#10;\begin{array}{llll}&#10;f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}&#10;\end{array}\\\\&#10;--------------------\\\\

\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\&#10;\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\&#10;\left. \qquad   \right.  \textit{reflection over the x-axis}&#10;\\\\&#10;\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\&#10;\left. \qquad   \right.  \textit{reflection over the y-axis}

\bf \bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\&#10;\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\&#10;\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\&#10;\bullet \textit{ vertical shift by }{{  D}}\\&#10;\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\&#10;\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\&#10;\bullet \textit{ period of }\frac{2\pi }{{{  B}}}

with that template in mind, let's see    \bf f(x)=\sqrt{x}\qquad &#10;\begin{array}{llll}&#10;g(x)=&\sqrt{0.5x}\\&#10;&\quad \uparrow \\&#10;&\quad  B&#10;\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
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