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What is the measure of ∠HFG?<br> (See attachment)

madam [21]

92 degrees

Triangle= 180 degrees
180-60-28= 92

:)

7 0

2 years ago

Order the racers from first place to fifth place based on the clues.

tester [92]

Answer:

Jennifer - 1st

Susan - 2nd

Emily - 3rd

Janice - 4th

Maria - 5th

Step-by-step explanation:

Susan is 2nd.

Places 1, 3, 4, and 5 are left.

Janice and Jennifer both start with J. None of the other swimmers start with the same first letter. One is 1st and one is 4th.

Since Maria finished immediately after Janice, and Janice must be 1st or 4th, Janice can't be first since 2nd place is already taken. This means that Janice is 4th and Maria is 5th.

Places 1 and 3 are left.

We know Jennifer is 1st or 4th and since 4th is taken, Jennifer is first.

Place 3 is left.

Emily must be 3rd since that is the only spot left.

8 0

2 years ago

Akshat spent 3 hours each day driving to and form work. He opened an office closer to home and now drives 80 minutes to and form

anygoal [31]

3*60 = 180 minutes

80/180 = 0.44

1-0.44 = 0.56

it was a 56% decrease in commute time

4 0

2 years ago

Sylvia and her sister are both reading books. Sylvia reads 2 pages every 5 minutes. Her sister reads 3 pages every 6 minutes. Wh

umka21 [38]

Answer:

6

Step-by-step explanation:

Silvia: 2 pages to 5 minutes

into...

Silvia: 1 page to __ minutes

<u>Find Unit Rate</u> : 5/2= 2.5

Unit Rate for Silvia is 2.5

<u>Written out</u> : 2 pages x 2.5 = 5 minutes

<u>Example</u> : 1 page to 2.5 minutes

<u>What we found</u> : ___ pages to 60 minutes(60 divided by 2.5) is

<h2>24 pages to 60 minutes</h2>

Silvia's sister: 3 pages to 6 minutes

into...

Silvia's sister: 1 pages to ___ minutes

<u>Find Unit Rate</u> : 6/3= 2

Unit Rate for Silvia is 2

<u>Written out</u> : 3 pages x 2 = 6 minutes

<u>Example</u> : 1 page to 2 minute

<u>What we found</u> : ___ pages to 60 minutes(60 divide by 2) is

<h2>30 pages to 60 minutes </h2>

<u>Final Step</u> : 30 - 24 = 6

7 0

2 years ago

Find the general solution of x'1 = 3x1 - x2 + et, x'2 = x1.

Ann [662]

Note that if ${x_2}'=x_1$ , then ${x_2}''={x_1}'$ , and so we can collapse the system of ODEs into a linear ODE:

${x_2}''=3{x_2}'-x_2+e^t$
${x_2}''-3{x_2}'+x_2=e^t$

which is a pretty standard linear ODE with constant coefficients. We have characteristic equation

$r^2-3r+1=\left(r-\dfrac{3+\sqrt5}2\right)\left(r+\dfrac{3+\sqrt5}2\right)=0$

so that the characteristic solution is

${x_2}_C=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}$

Now let's suppose the particular solution is ${x_2}_p=ae^t$ . Then

${x_2}_p={{x_2}_p}'={{x_2}_p}''=ae^t$

and so

$ae^t-3ae^t+ae^t=-ae^t=e^t\implies a=-1$

Thus the general solution for $x_2$ is

$x_2=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}-e^t$

and you can find the solution $x_1$ by simply differentiating $x_2$ .

7 0

2 years ago