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jeka57 [31]
2 years ago
7

joyce traveled at an average speed of 60 miles per hour for 4.5 hours and then traveled at an average speed of 35 miles per hour

for 1.5 hours. What was the total distance in miles that joyce traveled during this time ?
Mathematics
1 answer:
SVEN [57.7K]2 years ago
8 0

Answer:

322 1/2 miles

Step-by-step explanation:

Recall how s = d/t ; speed = distance/time.

To effectively solve for distance traveled, rearrange the formula so that distance is on the left-hand side by multiplying speed, and time.

speed × time = distance/time × time

speed × time = distance

distance = speed × time ; d = st.

Now to find the total distance traveled, individually multiply the rate of speed with the time. Time will cancel, and we will get the total mileage.

Given an average speed of 60 mph at a certain time for 4.5 hours, and another average speed of 35 mph at another time of 1.5. Calculate the distance individually, and then add both distances together. Distance 1 = 60 mph × 4.5 h = 60 miles / h × 4.5h = 60 miles × 4.5 = 270 miles.

Distance 2 = 35mph × 1.5h = 35 miles / h × 1.5h = 35 miles × 1.5 = 52 1/2 miles.

Distance 1 + Distance 2 = Total distance.

270 miles + 52 1/2 miles = 322 1/2 miles.

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Alona [7]

Answer:

We have the equation

c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]

Then, the augmented matrix of the system is

\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]

We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:

\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]

This matrix is in echelon form. Then, now we apply backward substitution:

1.

8c_4=0\\c_4=0

2.

4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0

3.

3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0

4.

c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0

Then the system has unique solution that is (c_1,c_2c_3,c_4)=(0,0,0,0) and this imply that the vectors v_1,v_2,v_3,v_4 are linear independent.

4 0
3 years ago
A rectangular prism has a width of 51 ft and a volume of 144 ft3. Find the volume of a similar prism with a width of 17 ft. Roun
meriva

Answer:

5.3\ ft^3

Step-by-step explanation:

Similar shapes with scale factor k have proportional volumes with coefficient k^3 i.e.

\dfrac{V_{large}}{V_{small}}=k^3,

where

k=\dfrac{\text{width of large prism}}{\text{width of small prism}}.

Since

\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,

then

k=\dfrac{51}{17}=3.

Hence,

\dfrac{144}{V_{small}}=3^3\Rightarrow V_{small}=\dfrac{144}{27}=\dfrac{16}{3}=5\dfrac{1}{3}\approx 5.3\ ft^3.

7 0
3 years ago
HELP ILL AWARD BRAINLIEST
inna [77]

Answer:

Think about it

Step-by-step explanation:

If you made $20 in 2 hrs you made $10 per hour

To find out how much you make per certain number of hrs multiply $10 by the number of hours

The equation is y = 10x + 0 <-- this is also answer to number 4

10x is the constant of proportionality I think.

5 0
3 years ago
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Two parallel lines are crossed by a transversal. If measure of angle 6 is 123.5 then measure of angle 1 is.....
GalinKa [24]
The picture in the attached figure

we know that
m ∠ 6=123.5°

m ∠6+m∠2=180°-------> by supplementary angles
so
m∠2=180-m∠6-----> 180-123.5------> m∠2=56.5°

m∠1=m∠2--------> by corresponding angles
so
m∠1=56.5°

the answer is
m∠1 is 56.5°

7 0
3 years ago
A plane of symmetry divides a solid into __________. A) two congruent solids B) three congruent solids C) unequal parts D) diffe
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The best and most correct answer among the choices provided by your question is the first choice or letter A.

<span>A plane of symmetry divides a solid into two congruent solids.</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
8 0
2 years ago
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