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Alex17521 [72]
3 years ago
13

Open-Ended Question*Picture*

Mathematics
1 answer:
My name is Ann [436]3 years ago
8 0
We have to calculate the volume of the right rectangular prism.
lenght=4 1/2 in=(4+1/2) in=9/2 in
width=5 in
height=3 3/4 in=(3+3/4) in=15/4 in

Volume (right rectangular prism = lenght x width x height.
volume=9/2 in * 5 in * 15/4 in=675/8 in³

we calculate the volume of this little cube.
volume=side³
volume=(1/4 in )³=1/64 in³

Now, we calculate the number of small cubes are needed to fit the right rectangular pris by the rule of three.

1 small cube----------------1/64 in³
x---------------------------------675/8 in³

x=(1 small cube * 675/8 in³) / 1/64 in³=5400 small cubes.

Answer: we need 5400 small cubes to fit the right rectangular prism.
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7 0
3 years ago
Which system of equations could be graphed to solve the equation below? log Subscript 0. 5 Baseline x = log Subscript 3 Baseline
Vanyuwa [196]

You can use the fact that two expressions in equality can be considered to be equal to a third variable(not used in given context).

The system of equations that could be graphed to solve the equation given is

  • y = \log_{0.5}(x)\\\\
  • y = \log_3(2+x)

<h3>How can we form a system of equations from an equation?</h3>

Suppose the equation be a = b\\

Let there is a symbol c such that we have a = b = c

It is because a and b are same measure (that is exactly what a = b means)

and we gave another name c to that measure.

Thus, we have

a = c\\b = c

in addition to  a = b\\

<h3>Using the above method to find the system of equations needed</h3>

Since the given equation is log_{0.5}(x) = log_2(2+x)

The 2d graphs are usually expressed as y = f(x) on X-Y plane.

Taking the equation's expressions equal to y, we get

log_{0.5}(x) = log_2(2+x) = y

or, we get system of equations as

y = log_{0.5}(x)\\\\y = log_3{(2 + x)}

Their graph is plotted below. The intersection point of both curves is the solution to the given equation as it satisfies both the equations of the system of equations formed from the given equation.

Thus,

The system of equations that could be graphed to solve the equation given is

  • y = \log_{0.5}(x)\\\\
  • y = \log_3(2+x)

Learn more about solutions to system of equations here:

brainly.com/question/14550337

4 0
2 years ago
Indicate the equation of the line, in standard form, that is the perpendicular bisector of the segment with endpoints (4, 1) and
jenyasd209 [6]

Equation of a line is x+3y =-3.

<h3>What is a perpendicular bisector of the line segment?</h3>

A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

Given that,

Endpoints of the line segment are (x_{1},y_{1}) = (4, 1) and (x_{2},y_{2}) = (2, -5).

First find the midpoints of the given line segment.

M = \left(\frac{x_{1}+x_{2}  }{2},\frac{y_{1}+y_{2}  }{2}\Right)

    =  \left(\frac{4+2  }{2},\frac{1-5  }{2}\Right)

M   =  (3,-2)

Now, Find the slope of the line :

It is perpendicular to the line with (4,1) and (2,-5)

Slope between (x_{1},y_{1}) and (x_{2},y_{2}) = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

so,

the slope between (4,1) and (2,-5)  =  \frac{-5-1  }{2-4 }

                                                         = 3

perpendicular lines have slopes the multiply to get -1

3 times m=-1

m= \frac{-1}{3}

The equation of a line that has a slope of m and passes through the midpoints M(3,-2)  is

y-y_{1} =m(x-x_{1} )

y-(-2) =\frac{-1}{3} (x-3 )

(y+2) =\frac{-1}{3} (x-3 )

if we want slope intercept form

(y+2) =\frac{-1}{3} x+1

y= \frac{-1}{3} x-1

If we want standard form

\frac{1}{3} x+y = -1

x+3y =-3

Hence, Equation of a line is x+3y =-3.

To learn more about perpendicular bisector of the line segment from the given link:

brainly.com/question/4428422

#SPJ4

   

7 0
1 year ago
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