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3 years ago

Solve the inequality. 3(x +1) +11 <-2(x + 13)

Mathematics

1 answer:

TiliK225 [7]3 years ago

7 0

This is the answer for your question.

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Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.

So $7\le k$ ; in set notation,

$\{k\mid 7\le k$

4 0

3 years ago

Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

3 years ago

1.A house worth $250,000 has an coinsurance clause of 90 percent. The owners insure the property for $191,250. They then have a

Arisa [49]

1. Multiply the value of the house by the percent:

250,000 x 0.9 = 225,000

Divide the amount the owner insured by the clause amount:

191,250/225,000 = 0.85

Multiply that by the amount of damage:

0.85 x 80,000 = 68,000

They will receive $68,000

2. Follow the same steps as above:

180,000 x 0.75 = 135,000

101,250 / 135,000 = 0.75

0.75 x 50,000 = 37,500

They will receive $37,500

8 0

3 years ago

Read 2 more answers

PLS HELP ASAP I DONT HAVE TIME FOR THIS, IT ALSO DETECTS IF ITS RIGHT IR WRONG

Airida [17]

Answer:

A, or 50.24 ft.

Step-by-step explanation:

Doing the equation above, we know the radius of the circle, which is 8 ft.

8ft times 2 is 16ft.

16ft times pi gives us (rounded) 50.24 ft.

8 0

3 years ago

A small water bottle holds 75% as much as a large water bottle.

Radda [10]

The answer is 48 units. You do 36 / 75% it is 48. You can also check your answer by doing 48 times 75%, which would equal 36.

8 0

3 years ago