You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation $10x+12y=300$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts

The graph of the equation is shown below.

The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.

The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.

Given:

Short-sleeved shirts cost $10 each.  

Long-sleeved shirts cost $12 each.

The total budget is $300.

The given equation is:

where is the number of short-sleeved shirts and is the number of long-sleeved shirts.

To find:

The graph of the given equation and the interpretation for the intercepts.

Explanation:

We have,

Substitute .

So, the y-intercept is at point (0,25).

Substitute .

So, the x-intercept is at point (30,0).

Plot the points (30,0) and (0,25) on a coordinate plane and connect them by a straight line.

The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.

The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.

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a. i) Please see the  included graph of the equation $10·x + $12·y = $300

ii) The intercepts give the maximum number of either short-sleeve (x-intercept) long-sleeved (y-intercept) that can be ordered

Step-by-step explanation:

The given information are;

The cost of each short-sleeved shirt = $10

The cost of each long-sleeved shirt = $12

The amount available in the budget = $300

The equation for the total cost = $10·x + $12·y = $300

Where;

x = The number of short-sleeved shirts

y = The number of long-sleeved shirts

Rewriting the equation given in slope and intercept form, we have;

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Please find attached, the graph of the equation made with Microsoft Excel

The values of the data that can calculated to plot the graph are;

x, y

(0, 25 )

(5, 20.83 )

(10, 16.67)

(15, 12.5 )

(20, 8.33)

(25, 4.17)

(30, 0 )

The x-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget, while the y-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.