You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pull the plug, there are 10 gallons left.

Assume that the number of gallons varies linearly with the time since the plug was pulled.


Write the particular equation expressing the number of gallons (g) left in the tub in terms of the number of seconds (s) since you pulled the plug.​

Answer (it has two solutions):

I hope this helps!

Answer:

Step-by-step explanation:

3ab + 7a² + 2b² - (7a² - 4ab + 2b²) = 3ab + 7a² + 2b²  - 7a² + 4ab - 2b²

Now combine like term. Like terms have same variable with same power.

= 3ab + 4ab  + 7a² - 7a²  + 2b² - 2b²

= 7ab

Answer:

a; line BC corresponds to line FG

Step-by-step explanation:

we know that a is correct as after translating BC and FG are on the same side of the rectangle and have the same length

1) (1, -1), (0, -4), (3, 5), and (-2, -10).

2) (5, 2) and (-8, 2)

Answer:

Multiplication

Step-by-step explanation:

[tex]\frac{x}{3} =15[/tex]

To get the 3 out of the denominator, you would have to multiply each side by 3:

[tex]3*\frac{x}{3} =3*15\\x=45[/tex]

Answer:

X=45

Step-by-step explanation:

Multiply 3 on both sides

Answer:

Step-by-step explanation:

to make life easier, i'll give both angles letters

Angle ABC= x

Angle CBD= y

x= y(1/3)

x+y=180

now substitute

y(1/3) +y =180

y(4/3) =180

y(4/3) * (3/4)  = 180  *  (3/4)

y= 135

CBD is 135 degrees

Answer:

[tex]\displaystyle y=\frac{2}{3}(x+5)+2[/tex]

Step-by-step explanation:

We need to find the equation of the line perpendicular to the line 3x+2y=8 and passes through (-5,2).

The given line can be expressed as:

[tex]\displaystyle y=-\frac{3}{2}x+4[/tex]

We can see the slope of this line is m1=-3/2.

The slopes of two perpendicular lines, say m1 and m2, meet the condition:

[tex]m_1.m_2=-1[/tex]

Solving for m2:

[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]

[tex]\displaystyle m_2=-\frac{1}{-\frac{3}{2}}[/tex]

[tex]\displaystyle m_2=\frac{2}{3}[/tex]

Now we know the slope of the new line, we use the slope-point form of the line:

[tex]y=m(x-h)+k[/tex]

Where m is the slope and (h,k) is the point. Using the provided point (-5,2):

[tex]\boxed{\displaystyle y=\frac{2}{3}(x+5)+2}[/tex]

The sample mean of the distribution is an estimate of the population mean

The mean of the sampling distribution of sample means is 51

The given information are:

Population mean, μ = 51

Standard deviation, σ = 9

Sample size, n = 36

The sample mean is an estimate of the population mean.

So, we have:

[tex]\bar x = \mu[/tex]

Substitute known values

[tex]\bar x = 51[/tex]

Hence, the mean of the sampling distribution of sample means is 51

Read more about sampling distributions at:

https://brainly.com/question/15713806

Answer:

166.4

Step-by-step explanation:

Percentage of 12.8% of 1300 = ? 12.8% of 1300 is equivalent to multiplying them: 12.8% × 1300. 12.7% of 1300 = ? 12.9% of 1300 = ? 1% of 1300 = ? Detailed ...

not necessarily. The two sides of equal length could be adjacent sides.

Answer:

a.180-10

[tex]180 - 10 \sqrt{3 } - 60[/tex]

=use your calculator

Answer:

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

the area of a triangle is 1/2hb. so half of the shape's area would be:

(1/2)4x12=24

and 24x2=48

Answer:

56 people

Step-by-step explanation:

49 times 8= 392

392 divided 7= 56

Answer:

Step-by-step explanation:

5 or 4 can be the length. And 5 and 4 can be the width.

length: 5, 4, 2, 10, etc.

width: 5, 4, 2, 10, etc.

the numbers listed above are options. Multiply the numbers.

And

.

there are many more, but these are commonly used. Hope it helps!

Answer:

  4x +3y = -3

Step-by-step explanation:

The standard form equation can be written from ...

  (y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1

  (-13 -3)x -(9 -(-3))y = (-16)(-3) -(12)(3)

  -16x -12y = 12

The standard form has a positive leading coefficient, and all terms mutually prime. We can get that by dividing the equation by -4:

  4x +3y = -3

_____

Additional comment

The form we used above for the equation of the line essentially comes from the fact that the slope of a line is the same everywhere:

  (y2 -y1)/(x2 -x1) = (y -y1)/(x -x1)

Multiplying by the product of denominators and separating variable terms from constant terms gives the form used above.

Answer:

c = -1

b = 9

a = 8

Step-by-step explanation:

16 = a × 1² + b × 1 + c

-2 = a × (-1)² + b × (-1) + c

-1 = a × 0² + b × 0 + c .........-> -1 = c

16 = a + b + c

-2 = a - b + c

16 = a + b - 1

-2 = a - b - 1

a + b = 17

a - b = -1 .......-> a = b - 1 ........ a = 9 - 1 = 8

(b - 1) + b = 17

2b - 1 = 17

2b = 18 .......-> b = 18/2 = 9

Answer:

  y = 8x² +9x -1

Step-by-step explanation:

The coefficients of the quadratic function can be found from three points by substituting the point values into the equation and solving for the coefficients.

The equation we want to find coefficients for is ...

  y = ax² +bx +c

For point (1, 16), the equation is 16 = a(1²) +b(1) +c

For point (-1, -2), the equation is -2 = a(-1)² +b(-1) +c

For point (0, -1), the equation is -1 = a(0) +b(0) +c

__

The last of these equations gives a value for c (c=-1). Substituting that into the other two gives the equations in a and b as ...

  a + b = 17

  a - b = -1

Adding the two equations gives ...

  2a = 16   ⇒   a = 8

Subtracting the second from the first gives ...

  2b = 18   ⇒   b = 9

Then the desired quadratic equation is ...

  y = 8x² +9x -1

Answer:

A

Because you have to Multiply  

189 by 36

Answer:

27 feet

Step-by-step explanation:

We can set up a proportion comparing the height of each object to the length of the shadow.

h/s

h/15=18/10

Cross multiply.

10*h=18*15

10h=270

Use the multiplicative Inverse

10/10=270/10

h=27

Answer:

Line EF is a secant. I hope this helps!

Answer:line ef

Step-by-step explanation:

Answer:

x=20

Step-by-step explanation:

The range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = x² + 3x - 4

The domain of the f(x) is all real numbers

The range of the g(x) is [-6.25, ∞)

g(x) is shown in the table:

x      –6     –3     –1       4

g(x)    13      4     –2    –17

The linear function g(x) is:

[tex]\rm g(x) = \ -13=\dfrac{\left(4-13\right)}{-3+6}\left(x+6\right)[/tex]

g(x) = -3x - 5

(f + g)(x) = f(x) + g(x)

= x² + 3x - 4 - 3x - 5

(f + g)(x) = x² - 9

The domain of the function is all real numbers.

The range of the function (-9, ∞)

Thus, the range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

Answer: Social science or sociology is considered as science but it is a pseudoscience.

Step-by-step explanation:

The sociology is considered as science as the study of social class, ethnicity, and religion abide by people of the society. Like, other factual sciences like chemistry, biology, and physics the facts cannot be rectified or verified by experimental trials. Instead, it is based on assumption and day to day experience with surrounding social environment. Thus, we can say that sociology is a science is a lie.

Answer:

The blank should say 'protractor'.

Step-by-step explanation:

I do not have one sorry,

[tex]i = \sqrt{ - 1}[/tex]

[tex]i {}^{2} = - 1[/tex]

[tex]i {}^{ 3} = - 1 \sqrt{ - 1} [/tex]

[tex]i {}^{4} = 1[/tex]

[tex]i {}^{8} = i {}^{4} \times i {}^{4} = 1 \times 1 = 1[/tex]

Answer:

Cindy has $45 and Emily has $60

Step-by-step explanation:

let x be the amount of money , then

[tex]\frac{1}{2}[/tex] x + [tex]\frac{2}{3}[/tex] x = 105

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

3x + 4x = 630 , that is

7x = 630 ( divide both sides by 7 )

x = 90

Cindy has [tex]\frac{1}{2}[/tex] × 90 = $45

Emily has [tex]\frac{2}{3}[/tex] × 90 = $60

Answer:

should be 8 unless the first term is 56? or the question asks for 5th term which is 16

Step-by-step explanation:

Difference between 1st term and 2nd:

48-40  =8

Difference between 2nd term and 3rd:

40-32  =8

Clearly the jump between 1 point and the next is subtracting 8 or adding -8:

so 5th term will

24-8  =16

6th term:

16-8  =8

Answer:

16

Step-by-step explanation:

d=8

a=T1-d

48-8=4

T6=T5-d=8

Answer:

EX: 1.5436666=1.5437

1.12455555=1.1246

1.29244827=1.2924