10 The table shows the cost of blueberries at a local farmer's
1 answer:
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Answer:
y+3=2(x-1)
Step-by-step explanation:
Point-slope form is . In order to write a linear equation using this form, the
,
and
must be substituted by real numbers.
The represents the slope of the equation. We know that the answer has to be parallel to the line y=2x-1. y=2x-1 is already in slope-intercept form, or
, in which
represents the slope. We can see that the
is in place of that
, therefore 2 is the slope of y=2x-1. Lines that are parallel have the same slope, so we know that the slope of the new equation must be 2 as well.
The and
represent the x and y values of one point that the line passes through. We know that the new equation must pass through the point (1, -3), so we'll substitute 1 in place of the
and -3 in place of the
.
Substituting for those three values will give you an equation like this, therefore it is the answer:
Answer:
x = 2√2
y = 2√6
Step-by-step explanation:
Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)
These will be equal since the triangles are similar
shorter leg : longer leg
(blue triangle = red triangle)
⇒ x : 4 = 2 : x
⇒ x/4 = 2/x
⇒ x² = 8
⇒ x = √8
⇒ x = 2√2
Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.
Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)
⇒ 4² + (2√2)² = y²
⇒ y² = 24
⇒ y = √24
⇒ y = 2√6
