A swimming pool already contains
a small amount of water when you start filling it at a
constant rate. The pool contains 45 gallons of water after
5 minutes and 120 gallons after 30 minutes. Find the
average rate of change and use it to write a linear model
that relates the amount of water in the pool to the time.

Answer:

The rational roots theorem is a very useful theorem. It tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.

Hope that helps.

Answer:

Finding the Zeros of Polynomial Functions The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function. Given a polynomial functionuse synthetic division to find its zeros.

Step-by-step explanation:

i hope it helpful:)

Answer:

16

Step-by-step explanation:

80% of 20 is 16

Answer:

25

Step-by-step explanation: (My way) If 20 questions equal 80%, then do 20/2 which equals 10. 10 is 40% because 20 was 80%, which was split in half. Now you do 10/2 which is 5. 10 was 40% so 40% got split into 20%. So then you have 5=20%, 10=40%. Now we multiply 10x2 which equals 20. 20=80% so now add 20+5 which is 25. 25 is 100%.

The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.

The correct responses are;

Reasons:

The velocity of the brick as it reaches the ground is given by the formula;

v² = 2·g·h

v = √(2·g·h)

Where;

h = The height of the brick, h = 1.6 m

g = The acceleration due to gravity ≈ 9.81 m/s²

Therefore;

v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s

(a) Momentum = Mass × Velocity

The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s

(b) Impulse = Force × Δt = Mass × Δv

Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s

Therefore, the impulse = 44.8 N·s

(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m

Initial energy in the brick, E = m·g·h

Which gives;

E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J

Energy = Force × Distance

[tex]\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}[/tex]

The average force the carpet exerts, F = 6,278.4 N

(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;

Distance = 6.0 cm = 0.06 m

Therefore;

[tex]\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}[/tex]

The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N

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Given that:

x² + 5x - 6 = 0

Here we see that,

→ Product of coefficient of x² and constant term = 1 × 6 = 6

→Difference of the constant term and the coefficient of x² = 6 - 1 = 5

Now the given equation can be written as,

⇛x² + 6x - 1x - 6 = 0

(Here we simply applied the correc sign and splitted the middle term in two terms)

Now let's take the common terms

⇛x(x + 6) - 1(x + 6) = 0

On grouping we get,

⇛(x - 1)(x + 6) = 0

Here either (x - 1) = 0 or (x + 6) = 0 since the product is zero so anyóne of the terms should be zero.

⇛(x - 1) = 0 or (x + 6) = 0

⇛x - 1 = 0 or x + 6 = 0

⇛x = 1 or x = -6

Here we got two solutions of the equations. This means thet are in correct form.

Answer: The value of X is 1 or -6.

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solve the equation x^2+5x+6=0

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Answer:

Line 3

Step-by-step explanation:

Line three should be

2*3*sqrt(5)-3sqrt(5)

Answer:

Step-by-step explanation:

x=2,−5,5

if any doubt leave a comment

Give BRAINLIEST

Answer:

No

Step-by-step explanation:

Khan told me ;p

Answer:

No

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

Answer:

y = 7

Step-1: Subtract 8 both sides

⇒ [tex]36 = 4y + 8[/tex]

⇒ [tex]36 - 8 = 4y + 8 - 8[/tex]

⇒ [tex]28 = 4y[/tex]

Step-2: Divide 4 both sides

⇒ [tex]28 = 4y[/tex]

⇒ [tex]\frac{28}{4} = \frac{4y}{4}[/tex]

⇒ [tex]7 = y[/tex]

From figure we have , ∠GFH = 80°  and ∠HGF = 60° , ∠GFH = 40° and ∠GFE = x°

Now,

In ∆HGF

Since Sum of the angles of a triangle is 180° :  

∠GFH + ∠HGF + ∠GFH = 180°

80° + 60° + 40° = 180°

14° + 40° = 180°

54° = 180° ………..(1)

∠GFH + ∠GFE = 180° [Linear pair]

80° + x° = 180°

x° = 180°-80°

x° = 100°

Hence the value of ∠x is 100°

Among the given options option (D) 100° is correct.

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this answers is 8 am I right

Answer:

  p(c) = 3c +5

Step-by-step explanation:

Effectively, you want to solve for p.

  6c = 2p -10

  6c +10 = 2p

  3c +5 = p

  p(c) = 3c +5 . . . . function notation (p is a function of c)

Answer:

1. 5/3 is not equal to 3/5.

2. 7-(4+3) is equal to (4+3)-7

3. (x + y) + 1 is equal to x + (y + 1)

Step-by-step explanation:

1. 5/3 and 3/5 are completely different fractions and when you switch the denominator and the numerator you get a different fraction: 5/3 = 1 2/3, 3/5

2. If you solve both of them, they are equal because 7-7 = 7-7

3. This is equal due to the associative addition property, which means that when the addition of three or more numbers, the total/sum will be the same, even when the grouping of addends are changed.

Plz mark brainliest thx

#1

[tex]\boxed{\dfrac{a}{b}=\dfrac{b}{a},a=b}[/tex]

Here 5[tex]\neq 3[/tex]

Hence inequality holds

#2

[tex]\\ \sf\longmapsto 7-(4+3)=(4+3)-7[/tex]

[tex]\\ \sf\longmapsto 7-7=7-7[/tex]

[tex]\\ \sf\longmapsto 0=0[/tex]

Equality holds

#3

[tex]\\ \sf\longmapsto (x+y)+1=x+(y+1)[/tex]

Equality holds

Done

Answer:

27 π

Step-by-step explanation:

Notice that the shape is 3/4 of a circle with radius 6. So we need to find 3/4 of the area of a circle with radius 6. The area of a circle with radius 6 is [tex]\pi r^2 = \pi \cdot 6^2 = 36\pi[/tex].

3/4 of this is [tex]\frac{3}{4} \cdot 36\pi = \boxed{27\pi.}[/tex]

Answer:

-2/9

Step-by-step explanation:

if the line is parallel it has the same slope.

The equation can be written as y = -2/9x - 35/9

so the slope is -2/9

Answer:

30 feet

Step-by-step explanation:

The height of the tree is 24 feet casting a shadow of 40 feet long.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Assuming the height of the tree to be x feet.

15 : 25 : : x : 40.

15/25 = x/40.

25x = 600.

x = 24

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Answer:

b)  ±2

Step-by-step explanation:

3x² = 12

divide each side by 3 to get:

x² = 4

x = ±2

The value of the equation 3x² = 12 is x = ±2.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 6 is an equation.

We have,

3x² = 12

Divide 3 on both sides.

x² = 4

x = ±√4

x = ±2

Thus,

The value of x is  ±2.

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#SPJ2

Answer:

x=9

Step-by-step explanation:

-3 + 5x = 42

add 3 to both sides

5x=45

divide both sides by 5

x=9

Answer:

x=9

Step-by-step explanation:

Answer:

10 cents per apple

Step-by-step explanation:

1 divided by 10 which is 1. And move the decimal one place to the left, leaving you with .1 or 0.1 or 0.10

she got a 110 score

explanation: sorry ignore just had to do 20 characters

Answer:

13/15

Step-by-step explanation:

15 is the least common denominator,

so 1/5 = 3/15

2/3 = 10/15

3/15 + 10/15 = 13/15

It can't be reduced.

Answer:

Step-by-step explanation:

The lowest common multiple of these 2 denominators is 3 * 5 since 3 and 5 are prime to each other. (They share no common factor.)

1/5 * 3/3 = 3/15

2/3 * 5/5 = 10/15

3/15 + 10/15 = 13 / 15

Answer:12m

Step-by-step explanation:

Because you are given that this is a right angled triangle, you can apply the pythagoras theorem where a^2 = b^2 + c^2

15^2 = 9^2 + x^2

225-81 = x^2

144 = x^2

x = 12m

Answer:

y=2

x=3

Step-by-step explanation:

make x - y = 1 into x= y + 1

put that wherever x is in the other equation

so y + 1 + 2y =7. then combine like terms into 3y =6. then divide 6 by 3 so you get y = 2

then substitute 2 into the y in the equation x - y = 1 and you get x = 3

METHOD OF ELIMINATION:

Given pair of linear equations are:

x+2y= 7 – – – Eqn(i)

On comparing with a1x+b1y+c1 = 0

x-y = 1 – – – Eqn(ii)

On comparing with a2x+b2y+c2 = 0

a1/a2 = 1/1 = 1

b1/b2 = 2/-1 = -2

c1/c2 = -7/-1 = 7

We have,

a1/a2 ≠ b1/b2 ≠ c1/c2

So, Given pair of linear equations in two variables have a unique solution.

Now,

On Subtracting eqn(ii) from eqn(i) then

x+2y = 7

x-y = 1

(-)

_______

0 +3y = 6

_______

⇛ 3y = 6

⇛ y = 6/3

⇛ y = 2

On Substituting the value of y in (1) then

⇛ x-2 = 1

⇛ x = 1+2

⇛x = 3

Answer: Therefore , the value of x and y with be (3,2) respectively.

Additional comment:

Answer:

The answer is 6 cause khan acadamy

Step-by-step explanation:

Answer:

The slope would be 13/20

Step-by-step explanation:

10-(-3) is 13 (numerator) and 6-(-14) is 20 (denominator)

hope this helps!!

Answer:

Step-by-step explanation:

h≈1.91cm

Answer:

x = − 3 y + 7

Step-by-step explanation:

Reorder  7  and  − 3

Answer:

65.214

Step-by-step explanation:

0x100=0

6x10=60

5x1=5

2x(1/10)=0.2

1x(1/100)=0.01

4x(1/1000)=0.004

add all of these values up. hope this helps!