Four more than five times a number is -16. What's the number

Which point on the graph shows the amount of water in the bucket after 1 second? Hint: Type your answer in the form (x coordinat

Taya2010 [7]

Answer:

$\displaystyle \left(1,\frac{5}{12}\right)$

Step-by-step explanation:

<u>Graphs</u>

The graph shows the amount of water in gallons as a function of time in seconds.

We are required to find the amount of water in the bucked after 1 second. Since the graph does not show an exact location for t=1, we must find the equation of the line.

Two points are clear on the graph: (0,0) (12,5). This gives us the necessary information to find the equation of the line, which has the form:

$w=mt+b$

Where w is the amount of water in the bucket, t is the time, and m and b are two constants to be determined.

Using the point (0,0):

$0=m(0)+b$

It follows that b=0

The equation now takes the form:

$w=mt$

Using the point (12,5):

$5=m(12)$

We find m:

$\displaystyle m=\frac{5}{12}$

The final equation is:

$\displaystyle w=\frac{5}{12}\cdot t$

Substituting t=1:

$\displaystyle w(1)=\frac{5}{12}\cdot (1)=\frac{5}{12}$

The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:

$\boxed{\displaystyle \left(1,\frac{5}{12}\right)}$

6 0

3 years ago

A box contains balls numbered 3 through 15.

Phantasy [73]

Answer: 6/13

Step-by-step explanation:

A box contains balls numbered 3 through 15. This means that the sample space = {3 , 4 ,5 , 6 ,7, 8, 9, 10, 11, 12, 13, 14, 15,}

The total number of sample space = 13

Therefore : the probability of picking 3, 5, 9, 11, 12, 15 , will be the total number of times they appear in the sample space divided by the number of sample space.

number of times 3 appears = 1

number of times 5 appear = 1

number of times 9 appear = 1

number of times 11 appear = 1

number of times 12 appear = 1

number of times 15 appear = 1

All together , they appeared 6 times

Therefore : the probability of picking one of the numbers = 6/13

8 0

2 years ago

Factorize (x+3)+5(x+3)

Free_Kalibri [48]

6x + 18, that is the answer

8 0

3 years ago

Solve the quadratic equation x2 - x = 30 by completing the square

kap26 [50]

Answer:

A

Step-by-step explanation:

Given

x² - x = 30

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- $\frac{1}{2}$ )x + $\frac{1}{4}$ = 30 + $\frac{1}{4}$

(x - $\frac{1}{2}$ )² = $\frac{121}{4}$

Take the square root of both sides

x - $\frac{1}{2}$ = ± $\sqrt{\frac{121}{4} }$ = ± $\frac{11}{2}$

Add $\frac{1}{2}$ to both sides

x = $\frac{1}{2}$ ± $\frac{11}{2}$ , thus

x = $\frac{1}{2}$ - $\frac{11}{2}$ = - 5

x = $\frac{1}{2}$ + $\frac{11}{2}$ = 6

5 0

3 years ago

Los nutriólogos recomiendan que una persona debe tomar en promedio 2.5 litros de agua en un día, para que esté bien hidratada. ¿

Goshia [24]

the question in English

Nutritionists recommend that a person should drink an average of 2.5 liters of water in a day, to be well hydrated. How many liters of water should a person drink in a month to comply with a good hydration (Consider a month equal to 30 days) Formulate an algebraic expression to determine the total liters of water that a person should drink a given number of days.

Let

x-------> the number of days

y------> the total liters of water

we know that

$y=2.5x$ ------> algebraic expression to determine the total liters of water that a person should drink a given number of days

For x=30 days (1 month)

substitute in the formula

$y=2.5*30=75\ liters$

therefore

<u>the answer is</u>

$75\ liters$

7 0

3 years ago