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2 years ago

Which of the following expressions is equivalent to?

Mathematics

1 answer:

gayaneshka [121]2 years ago

7 0

Answer:

It's the last choice: 2x^2 - 5x - 8 - 37/(x - 5).

Step-by-step explanation:

Long division:

2x^2 - 5x -8 <---------------Quotient

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

x - 5 ) 2x^3 - 15x^2 + 17x + 3

2x^3 - 10x^2

- 5x^2 + 17x

- 5x^2 + 25x

- 8x + 3

- 8x + 40

-37 <------ Remainder.

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Andre45 [30]

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2 years ago

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Find the area of the figure

Pavlova-9 [17]

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2 years ago

The sum of the first three terms in a GP is 38.Their product is 1728.Find the values of the three terms.

dusya [7]

Answer:

The value of the three terms is 8 and 18

Step-by-step explanation:

Let "a" be the first term and "r" be the common ratio.

Then from the condition, we have these two equations

a + ar + ar^2 = 38, (1)

a*(ar*)*(ar^2) = 1728. (2)

From equation (2), a^3*r^3 = 1728, or (ar)^3 = 1728, which implies

ar = root%283%2C1728%29 = 12; (3)

hence,

r = 12%2Fa. (4)

Now, in equation (1) replace the term ar by 12, based on (3). You will get

a + 12 + ar^2 = 38, which implies

a + ar^2 = 26. (5)

Next, substitute r = 12%2Fa into equation (5), replacing "r" there. You will get

a + a%2A%28144%2Fa%5E2%29 = 26, or

a + 144%2Fa = 26.

Multiply by "a" both sides and simplify

a^2 - 26a + 144 = 0,

%28a-13%29%5E2 - 169 + 144 = 0

%28a-13%29%5E2 = 25

a - 13 = +/- sqrt%2825%29 = +/- 5.

Thus two solutions for "a" are a = 13 + 5 = 18 or a = 13 - 5 = 8.

If a = 8, then from (4) r = 12%2F8 = 3%2F2.

If a = 18, then from (4) r = 12%2F18 = 2%2F3.

In the first case, if a = 8, then the three terms are 8, 8%2A%283%2F2%29 = 12 and 8%2A%283%2F2%29%5E2 = 18.

In this case, the sum of terms is 8 + 12 + 18 = 38, so this solution does work.

In the second case, if a = 18, then the three terms are 18, 18%2A%282%2F3%29 = 12 and 18%2A%282%2F3%29%5E2 = 8.

In this case, the sum of terms is 18 + 12 + 8 = 38, so this solution does work, too.

ANSWER. The problem has two solution:

a) first term is 18; the common difference is 2%2F3 and the progression is 18, 12, 8.

b) first term is 8; the common difference is 3%2F2 and the progression is 8, 12, 18.

4 0

2 years ago

QR is the radius of R and PQ is the tangent to R. Find the value of x.

steposvetlana [31]

Answer:

x = 39

Step-by-step explanation:

We know that PRQ is a right triangle, so we use the pythagorean theorem to solve the problem. The theorem states that a^2 + b^2 = c^2. Let's assume that the length of RP is c, the length of PQ is a and x is b. We plug the lengths into the equation and solve it:

80^2 + x^2 = 89^2

6400 +x^2 = 7921

x^2 = 1521

x = $\sqrt{1521}$

x = 39

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2 years ago

Please help me with math, it’s easy!! explanation needed!

Olenka [21]

Answer:

Step-by-step explanation:

This equation is in "vertex form," meaning that you can identify the vertex and other features of the graph from the equation.

y = a(x -h)² +k . . . . . the vertex is (h, k); the vertical scale factor is "a"

Comparing to your equation, you see ...

a = -1/2, h = 3, k = -1

The vertex is (h, k) = (3, -1). The vertical scale factor is negative.

This tells you the graph opens downward (the scale factor is negative), and the vertex (maximum point) is below the x-axis. (It has a negative y-coordinate.)

Because it start below the x-axis and goes down from there, the graph does not intersect the x-axis. There are zero (0) x-intercepts.

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2 years ago