CPhill

The scale diagram has the length of 7.4cm and the height of 1.8cm and a scale factor of 0.25. What are the dimensions of the actual rectangle

----------------------------------------------------------------------------------------------------------------------------

So the drawing is .25 or 1/4 scale, which means that the actual thing represented by the drawing is four times as large in all respects.

The actual ength would be  7.4 x 4 = 29.6 cm

And the  actual height would be 1.8 x 4 = 7.2 cm.

Nice, Alan !!!

Thumbs UP !!

Two perpendicular chords with lengths 12.2 cm and 8.8 cm have a common endpoint.What is the area of the circle?

----------------------------------------------------------------------------------------------------------------------------

If the chords are perpendicular, they form a right angle, and in a circle, an inscribed angle measures 1/2 of its intercepted arc. So, the arc it intercepts is a half-circle. Thus the remaining side of this right triangle (the hypoteneuse) is a diameter.

So (12.2² + 8.8²)^(1/2)  ≈ 15.04 cm   And half of this is the raius of the circle = 7.52

And the area of the circle is pi*(7.52)²  ≈ 177.66cm²

We need more information to solve this problem, i.e., at least one angle and its position in the triangle.

The cosine only returns values from -1 to 1, inclusive......Since (1.83 / 1.2) > 1, this isn't defined for the cosine function.

Solve by substitution -8x+4y=20 y+6=(x+4)^2

---------------------------------------------------------------------------------------------------------------------------

OK...in the first equation, let's isolate y...we have

4y = 8x + 20   divide by 4 on both sides

y = 2x + 5    so, in the second equation, we have

(2x + 5) + 6 = (x + 4)^2       let's expand the right side and simplify the left

2x + 11 = x^2 + 8x + 16      now subtract the 2x + 11 from both sides

0 = x^2 + 6x +5    And this factors as

0 = (x+1) (x+5)    and setting each factor to 0, we get that x = -1 and x = -5

Using  y = 2x + 5  to find the y values, we have

y = 2(-1) + 5 = 3     and  y = 2(-5) + 5 = -5

So the solutions are (-1, 3)   and  (-5, 5)

BTW......this is the intersection in two points of a parabola (the second equation) and a line (the first equation)

Washington, D.C.

The surface area of a cylinder is given by 2*pi*r*h

Using 3.14 for "pi,'  we have 2*(3.14)*(3m)*(30m) = 565.2 m²

But we only want 1/2 of this........282.6m²

Looks like "a" is your answer.

How do you solve 7-9x-(x+12) < 25?

---------------------------------------------------------------------------------------------------------------------------

Let's start by simplifying the left side - note that the "-" outside the parenthesis makes both the "x" and the "12" inside negative !!    We have

-10x - 5  < 25       add 5 to both sides

-10x < 30        divide by -10 on both sides and reverse the inequality sign (as we always do when multiplying or dividing an inequality by a negative)

x > -3

It's a graph of a linear function with a y-intercept at (0, 7) and an x-intercept at (7, 0) that looks like this: