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of my handwriting is bad then sorry.
3x + 8y = 14 find the x and y intercepts of each function
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Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,
or in matrix form,
If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be
and this is what we wanted to prove. QED
This figure is what we would call a composite figure. A composite figure is a shape that is made up of multiple other shapes. when looking at the pond and the border that surrounds it, we can see that this heart shape is made up of two semi circles and a square. To find the area of the border, we will use the area formulas for semi circles and for squares:
Semi Circle Area Formula:
÷ 2
Square Area Formula: length x width
Pi = 3.14
Radius = Half of the diameter, in this case 6
After finding the area of each shape, we can subtract the 2 ft width to find the area of the flower bed border.
Semi Circle Area Formula:
Square Area Formula: length x width
Pi = 3.14
Radius = Half of the diameter, in this case 6
After finding the area of each shape, we can subtract the 2 ft width to find the area of the flower bed border.
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Use a proportion to find how many seconds are needed to fold 5 shirts.
We are given that he takes 28 seconds to fold 2 shirts:
28 sec : 2 shirts
We are not given the amount of time needed for 5 shirts, which we need to solve:
x seconds : 5 shirts
Express in a fraction:
Cross multiply and simplify:
Therefore, he needs 70 seconds to fold 5 shirts.