Answer:
Step-by-step explanation:19 and 31
Answer:
Herman needs to buy 3 sticker packs to have a total of 100 stickers.
Explanation:
33 x 3 = 99
99 + 1 = 100
Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = 1 + 7 = 8 ⇒ (- 1, 8 )
Answer:
its volume would be the shape of a rectangle
Step-by-step explanation:
This is geometry through and through. Plus a little trig thrown in for fun. If you inscribe an equilateral triangle inside a circle and the triangle has side lengths of 12, you have part of what you need to use Pythagorean's Theorem to find the hypotenuse of the triangle which is also the radius of the circle. First, use the formula 360/3 to find that the central angle measure of each angle INSIDE a triangle is 120. So you have 3 triangles within the large one, each with a top angle of 120 and a base of 12. If you extract that one triangle and then split it in half, you have a right triangle with a base of 6. This is a 30-60-90 triangle and this is important so you can check your work. Now use the apothem formula for a right triangle as it relates to a side in an equilateral triangle, which is a = sqrt3/6 * s. Our values are a = sqrt3/6(12) which simplifies to 2sqrt3. That's our apothem. If you're familiar with a 30-60-0 triangle, you could check this to see it's correct. Now you have the base leg of 6 and the height of 2sqrt3, now use Pythagorean's Theorem to find the hypotenuse, which is also the radius of the circle. This was really a difficult one to explain.
