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VladimirAG [237]

2 years ago

13

A large helium balloon is tethered to the ground by two cables. One cable is 100 feet long and forms an 80 degree angle with the

ground. The second cable forms a 40 degree angle with the ground. How long is the second cable to the nearest foot? Also, how far apart are the tethers, rounded to the nearest foot?

1 answer:

liraira [26]2 years ago

6 0

Hey there :)

Answer attached in image. Check!

~Benjemin360

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Please help! I dont understand! Thank you

Digiron [165]

QUESTION A

The given inequality is

$x-1\:>\:5$

Add 1 to both sides of the inequality to obtain;

$x\:>\:5+1$

$x\:>\:6$

Answer: 2. $x\:>\:6$ , open dot at 6 and shaded to the right.(A)

QUESTION B.

The given inequality is $2x \le 6$ .

Divide both sides by 2;

$x \le \frac{6}{2}$ .

$x \le 3$ .

Answer: 5. $x \le 3$ , closed dot at 3 and shaded to the left(B).

QUESTION C

The given inequality is $x-7\:>\:-4$

Add 7 to both sides to get;

$x\:>\:-4+7$

$\Rightarrow x\:>\:3$

Answer: 7. $x\:>\:3$ , open dot at 3 and shaded to the right.(C)

QUESTION D

We want to solve;

$-2x \:$

Divide through by -2 and reverse the inequality sign;

$x \:>\:\frac{6}{-2}$

$x \:>\:-3$

Answer; 3. $x \:>\:-3$ Open dot at -3 and shaded to the right. (D)

QUESTION E

We have

$4\:$

Divide through by -4 and reverse the sign.

$\frac{4}{-4}\:>\:x$

$-1\:>\:x$

or

$x\:$

Answer: 6. $x\:$ open dot at -1, and shaded to the left(E)

QUESTION F

The given inequality is $-2x+3\:$

Add -3 to both sides to get;

$-2x\:$

$-2x\:$

Divide both sides of the inequality by -2 and reverse the sign;

$x\:>\:5$

Answer:9. $x\:>\:5$ , open dot at 5 and shaded to the right(F)

QUESTION G

The given inequality is

$5x+1\ge11$

$5x\ge11-1$

$5x\ge10$

Divide by 5

$x\ge2$

Answer ; 10. $x\ge2$ , closed dot at 2 and shaded to the right(G)

QUESTION H

We have $3(x+4)\:>\:8x-6$

Expand the bracket to get;

$3x+12\:>\:8x-6$

Group similar terms to get;

$3x-8x\:>\:-6-12$

Simplify

$-5x\:>\:-18$

Divide through by -5 and reverse the sign;

$x\:$

Answer: 1. $x\:$ Open dot at 18/5 and shaded to the left(H)

QUESTION I

We have $-3x+4\:$ .

$-3x+x\:$

$-2x\:$

Divide by -2 and reverse the sign;

$x\:>\:1$

Answer: 8. $x\:>\:1$ , open dot at 1 and shaded to the right(I)

J. The given inequality $-2(x-4)\:>\:5-(x+2)$

Expand the bracket to get;

$-2x+8\:>\:5-x-2$

Group like terms to get;

$-2x+x\:>\:5-2-8$

$-x\:>\:-5$

Divide by -1 and reverse the sign to get;

$x\:$

Answer; 4. $x\:$ , open dot at 5 and shaded to the left.(J)

6 0

3 years ago

In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 25

Anastaziya [24]

Answer:

16 faults

Step-by-step explanation:

<u><em>The correct question is</em></u>

In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 2/5 of all her first serves. If 1/3 of her first serves were returned, how many of the tennis player's first serves were faults?

Let

x -----> the number of all her first servers

y ----> the number of first services returned

z ---> the number of first services faults

we know that

The number of aces plus the number of returned plus the number of faults must be equal to the number of all her first services

so

$x=24+y+z$

step 1

Find out the number of all her first servers

we have that

$24=\frac{2}{5}x$

Solve for x

$x=24(5)/2\\x=60\ first\ services$

step 2

Find out the number of first services returned

$y=\frac{1}{3}x$

substitute the value of x

$y=\frac{1}{3}(60)=20\ returned$

step 3

Find out the number of first services faults

$x=24+y+z$

we have

$x=60\\y=20$

substitute and solve for z

$60=24+20+z$

$60=44+z$

$z=16\ faults$

6 0

3 years ago

Solve the following inequality<br> 9x−2>43

MrRissso [65]

Answer: x > 5

Explanation: First we want to look at our variable and ask ourselves what's happening to it. Since 2 is being subtracted from 9x, we always undo addition and subtraction first so we add 2 to both sides.

That gives us 9x > 45.

Now we need to undo multiplication and division. Since 9 is being multiplied by <em>x</em>, to get <em>x</em> by itself, we need to divide by 9 on the left side of the inequality. If we divide by 9 on the left side, we must also divide by 9 on the right side.

This leaves us with <em>x > 5</em> which is the solution to this inequality.

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Alekssandra [29.7K]

A rectangle is a shape that has 4 sides and 4 90 degree angles, a square however has 4 equal sides, and 4 90 degree angles

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