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3 years ago

Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven

1 answer:

4 0

Let the three odd integers be x - 2, x and x + 2
x - 2 + x = 3(x + 2) + 7
2x - 2 = 3x + 6 + 7
2x - 2 = 3x + 13
3x - 2x = -2 - 13
x = -15

The three consecutive odd integers are -17, -15 and -13.

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alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS

serious [3.7K]

Answer:

$k=\frac{-11}{2}$ .

Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$ .

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$ .

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$ (-b/a where the quadratic is ax^2+bx+c)

$\alpha \cdot \beta=\frac{2(2k-1)}{1}$ (c/a)

Let's simplify those equations:

$\alpha+\beta=k+6$

$\alpha \cdot \beta=4k-2$

If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$ , then $k+6=\frac{1}{2}$ .

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

Find a common denominator:

$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$ .

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3 years ago

If a number is odd, then it has a remainder of 1 when divided by 2.

kherson [118]

Answer:

The hypothesis of the conditional is "<em>A number is odd</em>".

Step-by-step explanation:

The statement can be represented by the following proposition:

$P \implies Q$ (Eq. 1)

Where:

$P$ is the hypothesis of the proposition.

$Q$ is the conclusion of the proposition.

$\implies$ - Binary connector, which means "If...., then...."

In this case, we present what each propostion represents:

P = A number is odd.

Q = It has a remainder of 1 when divided by 2.

In consequence, the hypothesis of the conditional is "<em>A number is odd</em>".

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alexandr402 [8]

Left or right :]]]]]

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7 lbs is 112 ounces. 112 plus 9 is 121. 121 plus 12 is 133. The total weight of the basket and the watermelon is 133 ounces. I'm not sure how you need the answer so I'll leave it in a couple different forms.

Ounces- 133
Pounds- 8.312 (rounds to the nearest tenth, 8.3)
Pounds and ounces- 8 pounds and 5 ounces

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3 years ago

Terrence is playing a game in which he will randomly select one square tile and one round tile from the tile sets shown below. B

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Answer:

letter c

Step-by-step explanation:

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