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Naddika [18.5K]

3 years ago

5

Alyn drives 20.4 miles in 17 minutes.

1 answer:

Galina-37 [17]3 years ago

5 0

Answer:

12 mph

Step-by-step explanation:

<em>Speed = distance/time</em>

Distance = 20.4 miles
Time = 17 minutes = 17*1/60 hours = 17/60 hours

<u>Speed is:</u>

20.4 : 17/60 =
20.4*60/17 =
72 mph

<u>Alyn exceeded the limit by:</u>

72 - 60 = 12 mph

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Can anyone help me with this geometry question?

Serhud [2]

Answer:

49-31 gets you da answer

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Step-by-step explanation:

6 0

4 years ago

Determine whether the following series converges. Summation from k equals 2 to infinity (negative 1 )Superscript k Baseline Star

Ket [755]

Answer:

$a_k=\left|\dfrac{k^2-3}{k^2+4}\right|;\text{ is nondecreasing for $k>2$}$

$\lim\limits_{k \to \infty} a_k =1$

The series does not converge

Step-by-step explanation:

<u>Given</u> ...

$S=\displaystyle\sum\limits_{k=2}^{\infty}{x_k}\\\\x_k=(-1)^k\cdot\dfrac{k^2-3}{k^2+4}\\\\a_k=|x_k|$

<u>Find</u>

whether S converges.

<u>Solution</u>

The (-1)^k factor has a magnitude of 1, so the magnitude of term k can be written as ...

$\boxed{a_k=1-\dfrac{7}{k^2+4}}$

This is non-decreasing for k>1 (all k-values of interest)

As k gets large, the fraction tends toward zero, so we have ...

$\boxed{\lim\limits_{k\to\infty}{a_k}=1}$

Terms of the sum alternate sign, approaching a difference of 1. The series does not converge.

7 0

3 years ago

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

4 years ago

Solve this system:<br><br> 2x+5y+z=3<br> x-3y+2z=2<br> -x+2y-3z=-7

12345 [234]

Answer:

x= -3

y= 1

z= 4

Step-by-step explanation:

Please see the attached pictures for the full solution.

*I evaluated the determinants using Sarrus' rule (see last picture):

∆= aei +bfg +cdh -gec -hfa -idb

*The symbol '∆' (delta) is usually used to denote a determinant.

4 0

4 years ago

write the equation of the line in slope intercept form with the given conditions (slope = 3 and passes through (1,-3))

cupoosta [38]

Answer:

Because we have a point and slope, we can use at the beginning the point-slope form: y-y1=m(x-x1)

Step-by-step explanation:

m=3 , x1=1 , y=-3

y-(-3)=3(x-1)

y+3=3x-3 subtract 3 from both sides

y=3x-6 the answer in the slope-intercept form y=mx+b

3 0

4 years ago