Identify the vertex and axis of symmetry of 8x $y=-x^(2) +8x-12$

Answers

Answer 1

Answer:

$y=-x^2+8x-12\ny=-(x^2-8x)-12\ny=-[(x^2-8x+16)-16]-12\ny=-[(x-4)^2-16]-12\ny=-(x-4)^2+16-12\ny=-(x-4)^2+4$

Factor the minus or negative off the -x²+8x and don't do anything with -12

Find the number that can complete the square, for x²-8x, it'd be +16.

Just think of debt, you borrow, you have to give back. You borrow +16 then you have to give 16 out so you write -16 out of x²-8x+16 but still inside the bracket.

Distribute the minus/negative inside the bracket as you get -(x-4)²+16-12 because negative multiply negative and you get positive

Then you get y=-(x-4)^2+4

Because a<0, it's inverted parabola as shown below.

therefore, the vertex is at (4,4) or (-(-4), 4) because the vertex is at (-h,k) and h is -4 that means -h = 4

axis of symmetry is -b/2a, our b is 8, -b = -8 and 2a = 2(-1) so -8/-2 = 4 (From the standard form)

therefore, axis of symmetry is 4

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Macy has some ropes, each 2 feet long. Nellie has some ropes, each 3 feet long. Oscar has some ropes, each 5 feet long. What is the length of each line of ropes when they are of the same length?

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A carpenter is cutting down dowels from a piece of wood that is 10 inches long. How many 1/2-inch dowels can the carpenter cut?

Answers

He can cut 5, because 10in divided by 2 is 5.

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What is the perimeter of a trapezoid

Answers

The perimeter is the sum of the lengths
of the trapezoid's four sides.

The perimeter of a figure is the distance around the figure. To find the perimeter of a trapezoid, simply add the lengths of the sides. The sum of all the sides added together will be the perimeter of the trapezoid.

How do u solve 13 5/9 - 8 1/6?

Answers

The difference of the given mixed fractions is $5(7)/(18)$ .

The given fractions are $13(5)/(9)$ and $8(1)/(6)$ .

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Here, $13(5)/(9)$ can be written as $(122)/(9)$ and $8(1)/(6)$ can be written as $(49)/(6)$ .

Now, $(122)/(9)-(49)/(6)$

$=(244)/(18)-(147)/(18)$

$=(244-147)/(18)$

$=(97)/(18)$

$=5(7)/(18)$

Therefore, the difference of the given mixed fractions is $5(7)/(18)$ .

To learn more about the subtraction of fractions visit:

brainly.com/question/5220474.

#SPJ5

An easy way to solve this problem is by finding the same denominators for both of the fractions. You can do this by multiplying 9 times 6 equals 54 and what you do to the bottom you must do to the top. So 5×6=30 and 1×9=9 13 30/54- 8 9/54 = 5 21/54 and then if you can simplify you do.

engineers frequently use triangular trusses in the design of bridges. Examine the illustration below. Determine the length of the beans required for the length of the base of this design

Answers

Okay. So the two sides f the very end right triangle are 10 and 8, 10 is the hypothesis. To find the missing side, you can use the Pythagorean Theorem, which is a² + b² = c². So just fill in the values (c is the hypothesis).

8² + b² = 10² Square the numbers.
64 + b² = 100 Subtract.
b² = 36 Find the square roots.
b = 6

So now you know that the bottom of the right triangle is 6 ft. Now double that to find the base of the whole entire acute triangle, so 12 inches. And you know that the base of the design is made of four triangles, so do 12 x 4. The base of the design is 48 ft.

A porch has the shape of a semicircle with a diameter of 7 ft.What is the approximate area of the porch, rounded to the nearest square foot? Use 3.14 to approximate .

ft2

Answers

A = pi * r^2

R = D / 2

R = 7 / 2

R = 3.5

A = 3.14 * 3.5^2

A = 3.14 * 12.25

A = 38.465

Divide it by 2 since its a semi-circle:

38.465 / 2 = 19.2325

So about 19 square feet.

A = pi * r^2

A = 3.14 * 3.5^2

A = 38.465

38.465/2 = 19.2325 square feet of semicircle

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