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3 years ago

19. Which of the following

Mathematics

1 answer:

Andrew [12]3 years ago

4 0

9514 1404 393

Answer:

b. angle K is acute

Step-by-step explanation:

We're often told not to draw any conclusions from the appearance of a figure in a geometry problem. Here, angle K appears to be somewhat less than 90°, so angle K is acute.

Additional comment

This choice of answer is confirmed by the fact that the other two (visible) choices say the same thing. If one of them is correct, so is the other one. Hence they must both be incorrect. (An obtuse angle is more than 90°.)

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Interception vertical (0,3)

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3 years ago

Divide 16x3 – 12x2 + 20x – 3 by 4x + 5.

nalin [4]

Answer:

$4x^2 - 8x + 15 - \frac{78}{4x+5}$

Step-by-step explanation:

To solve polynomial long division problems like these, it's helpful to build a long division table. Getting used to building these can make problems like this much simpler to solve.

Begin by looking at the first term of the cubic polynomial.

What would we have to multiply $4x + 5$ by to get an expression containing $16x^3$ ? The answer is $4x^2$ , since $(4x + 5) \times 4x^2 = 16x^2 + 20x$ .

This is the first step of our long division, and we write out the start of our long division table like this:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,16x^3 + 20x^2\\$

On the left is the divisor. On top is $4x^2$ . In the middle is the polynomial we are dividing, and on the bottom is the result of multiplying our divisor by

The next step is to subtract the bottom expression from the middle one, like so:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,0x^3 - 32x^2\\$

We are left with $-32x^2$ . The next thing to do is to add the next term of the polynomial we are dividing to the bottom line, like this:

Now we return to the beginning of the instructions, and repeat the process: namely, what would we have to multiply $4x + 5$ by to get an expression containing $-32x^2$ ? The answer is $-8x$ , and we fill out our long division table like so:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2 - \,\,\,\,8x\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 - 40x\\$

Once again, we subtract the bottom expression from the one above it, and include the next term of the divisor, like so:

${ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+ 15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\$

And repeat. What do we multiply $4x + 5$ by to get an expression containing $60x$ ? The answer is 15. Our completed long division table looks like this: ${ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\{ }\qquad{ }\hspace{3cm}\,\,\underline{60x + 75}\\{ }\hspace{4.3cm}\,\,-78$

Now, the expression at the top,

$4x^2 - 8x + 20x + 15$

is our quotient, and the last number, $-78$ , is our remainder.

Hence we arrive at the solution of

$\frac{16x^3-12x^2+20x-3}{4x+5} =4x^2 - 8x + 15 - \frac{78}{4x+5}.$

6 0

3 years ago

Miguel quiere entrenar para la carrera solidaria de verano en uno de los dos parques que tiene cerca de casa. Su plan es correr

kondor19780726 [428]

Answer:

The square park is more convenient.

Explanation:

The translation of the question is:

Miguel wants to train for the summer solidarity race in one of the two parks that he has close to home. His plan is to run about 10 km each day and he wants to do an exact number of laps around the park to always start and end at the entrance. Since he has not quite decided between the square and the rectangular park, he decides to do some calculations to see which one suits him best.

Square park: 423 meters each side

Rectangular park: 673 meters measures the base and 218 meters the height

<h2>Solution</h2>

1. Calculate the perimeter of the square park

The perimeter of a square is the sum of the four side lengths. Since they are equal it is:

Perimeter = 4 × side lenght

Perimeter = 4× 423m = 1,692 m

2. Calculate how many times 1,692m is in 10 km

10 km is 10,000 m. Then, divide 10,000 by 1,692 m:

Number of laps = 10,000m / 1,692m ≈ 5.91 laps

3. Calculate the perimeter of the rectangular park

Perimeter = 2×base + 2×height

Perimeter = 2×673m + 2×218m = 1,782m

4. Calculate how many times 1,782 is in 10km

Number of laps = 10,000m / 1,782m ≈ 5.61 laps

Then, since the number 5.91 is closer to an integer number than 5.61, you conclude that the square park is more conventient, because by running 6 laps around the square park the number of kilometers run will be closer to 10 km than with any number of complete laps in the rectangular park.

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4 years ago

Zara bought 2.4 pounds of grapes and a watermelon what cost $5.28. The total cost of the fruit was 7.32. Which describes a way t

dalvyx [7]

Answer:

The answer is B.

Step-by-step explanation:

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3 years ago

Simplify and write the trigonometric expression in terms of sine and cosine:

asambeis [7]

Answer:

we have the expression as;

1/sin u cos u

Step-by-step explanation:

tan u = sin u/cos u

cot u = cos u/sin u

Thus;

sin u/cos u + cos u/sin u

The lcm is sin u cos u

Thus, we have that;

(sin^2 u + cos^2 u)/sin u cos u

But ; sin^2 u + cos^2 u = 1

so we have ;

1/sin u cos u

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3 years ago