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nekit [7.7K]
3 years ago
10

X varies directly with y. if y = -57 when x = 9, find x when y = 27.

Mathematics
1 answer:
kifflom [539]3 years ago
7 0

Answer:

x = -81 / 19

Step-by-step explanation:

y = kx

-57 = 9k

k = -57/9 or -19/3

27 = \frac{-19x}{3}

-19x = 81

x = -81 / 19

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Answer:

12 feet

Step-by-step explanation:

Given: length = 15 feet, width = L x 80%

Unknown: width = ?

 width = L x 80%

        w = (15ft) x 80%     or (15ft) x .80

        w = 12 ft

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Write an equation for the proportional relationship shown in the table.
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Answer:

  y = 38x

Step-by-step explanation:

The constant of proportionality (k) is the value of y when x=1. The table shows that to be 38. Then the equation is ...

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3 0
3 years ago
Directions: Number the distances from the shortest to the longest: 1 being the shortest distance and 5 being the longest. Justif
sleet_krkn [62]

Answer: Number the distances from the shortest to the longest:

1. Hoboken, New Jersey, to New York City is 659,831 cm

2. Cleveland, Ohio, to Akron, Ohio, is 2,521,728 inches

3. Orlando, Florida, to Tampa, Florida, is 446,160 feet

4. Chicago, Illinois, to Milwaukee, Wisconsin, is 161,920 yards

5. Dallas, Texas, to Houston, Texas, is 385 km


Solution:

To compare, all the distances must be in the same unit, for example feet.


a. Dallas, Texas, to Houston, Texas, is 385 km

We must transform from km to feet:

385 km * (1,000 m / 1 km) * (100 cm / 1 m) * ( 1 in / 2.54 cm) * ( 1 feet / 12 in)=

(385*1,000*100*1*1)/(1*1*2.54*12) feet =

38,500,000/30.48 feet =

1,263,123.359 feet =

1,263,123 feet


b. Hoboken, New Jersey, to New York City is 659,831 cm

We must transform cm to feet:

659,831 cm * ( 1 in / 2.54 cm) * ( 1 feet / 12 in)=

(659,831*1*1)/(2.54*12) feet =

659,831/30.48 feet =

21,647.99868 feet =

21,648 feet


c. Orlando, Florida, to Tampa, Florida, is 446,160 feet


d. Cleveland, Ohio, to Akron, Ohio, is 2,521,728 inches

We must transform from inches to feet:

2,521,728 inches * ( 1 feet / 12 inches) =

(2,521,728*1) / 12 feet =

2,521,728/12 feet =

210,144 feet


e. Chicago, Illinois, to Milwaukee, Wisconsin, is 161,920 yards

We must transform from yards to feet:

161,920 yards * (3 feet / 1 yard) =

(161,920*3)/1 feet =

485,763 feet


Ordering the values in feet from the shortest to the longest:

21,648 feet < 210,144 feet < 446,160 feet < 485,763 feet < 1,263,123 feet


With the original units:

659,831 cm < 2,521,728 inches < 446,160 feet < 161,920 yards < 385 km


Then the order is:


1. Hoboken, New Jersey, to New York City is 659,831 cm

2. Cleveland, Ohio, to Akron, Ohio, is 2,521,728 inches

3. Orlando, Florida, to Tampa, Florida, is 446,160 feet

4. Chicago, Illinois, to Milwaukee, Wisconsin, is 161,920 yards

5. Dallas, Texas, to Houston, Texas, is 385 km

6 0
3 years ago
Factor 4n^2 - 5n -6​
Allushta [10]

Answer:

(n-2) • (4n+3)

Step-by-step explanation:

4n2-5n-6  

Final result :

 (n - 2) • (4n + 3)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22n2 -  5n) -  6

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4n2-5n-6  

The first term is,  4n2  its coefficient is  4 .

The middle term is,  -5n  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -6 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

     -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  

                    4n2 - 8n + 3n - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4n • (n-2)

             Add up the last 2 terms, pulling out common factors :

                   3 • (n-2)

Step-5 : Add up the four terms of step 4 :

                   (4n+3)  •  (n-2)

            Which is the desired factorization

Final result :

 (n - 2) • (4n + 3)

3 0
3 years ago
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