Use this information for problems 1 and 2. When full, one of the pools at Sapphire Island will hold 43,000 gallons of water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute.



Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level.

a
\large 130+20000\left(60h\right)=43000

b
\large 60\left(130\right)+20000h=43000

c
\large 130\left(60h\right)-20000=43000

d
\large 130\left(60h\right)+20000=43000

Answer:

Step-by-step explanation:

Add like terms. 3x & 7x are like terms

3x +7x - 2 = 10x - 2

Answer:

0.2

Step-by-step explanation:

3x+7x-2

3x+7x-2=0

3x+7x=2

10x=2

x=2/10

x=[tex]\frac{1}{5}[/tex]

Answer:

0 < k < 2

Step-by-step explanation:

In the first quadrant both of x and y get positive values, so

And replacing x with 2k in the second equation:

Since y > 0:

Combining both k > 0 and k < 2, we get:

Answer:

  0 < k < 2

Step-by-step explanation:

The intersection will lie in the first quadrant when the solution has the characteristics: x > 0, y > 0.

For x > 0, we require ...

  x = 2k

  x > 0

  2k > 0 . . . . substitute for x

  k > 0 . . . . . divide by 2

__

For y > 0, we require ...

  y = (12 -3x)/2

  y = (12 -3(2k))/2 = 6 -3k . . . . . substituted for x and simplify

  y > 0

  6 -3k > 0 . . . . . . substitute for y

  2 -k > 0 . . . . . . . divide by 3

  k < 2 . . . . . . . . . add k

So, the values of k that result in the intersection being in the first quadrant are ...

  0 < k < 2

Answer:

Step-by-step explanation:

To find g-¹( 2) we must first find g-¹(x)

To find g-¹(x) equate g(x) to y

That's

y = g(x)

We have

y = - 2x + 7

Now interchange the terms that's x becomes y and y becomes x

We have

x = - 2y + 7

Make y the subject in order to find g-¹(x)

Move 7 to the left side of the equation

- 2y = x - 7

Multiply both sides by - 1

We have

2y = 7 - x

Divide both sides by 2 to make y stand alone

That's

So we have

Now to find g-¹(- 2) substitute the value of x that's - 2 into the expression

We have

We have the final answer as

Hope this helps you

Answer:

-10

-12

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The X-Values cannot repeat in a function.

Answer:

What is the change in y-values from

Point A to Point B?

50

What is the change in x-values from

Point A to Point B?

1

What is the rate of change of the linear function?

50

feet per second

Step-by-step explanation:

The change in y-values from Point A to Point B is from 0 to 50feet.  What is the change in x-values from Point A to Point B is 0 to 1 second. Rate of change of the linear function is given by y = 50x (feet per second).

" Linear function is defined as the algebraic expression which represents the relation between the variables with highest exponent equals to 1."

Formula used

[tex]\frac{y-y_{1} }{x-x_{1} } =\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

According to the question,

Given,

Speed of Red kangaroos can reach = 50 feet per second

Number of feet represent by y - axis

Time represent by x-axis

When

[tex]x_{1} = 0 seconds \\\\y_{1} = 0 feet[/tex]

When

[tex]x_{2} = 1 seconds \\\\y_{2} = 50 feet[/tex]

Change in y-values from point A to B  is given by [tex](y_{1}, y_{2} ) = (0,50)[/tex]

Change in x-values from point A to B  is given by [tex](x_{1}, x_{2} ) = (0,1)[/tex]

Rate of change of the linear function

[tex]\frac{y-0 }{x-0 } =\frac{50-0}{1-0}[/tex]

⇒[tex]y= 50x[/tex]

Hence, the change in y-values from Point A to Point B is from 0 to 50feet.  What is the change in x-values from Point A to Point B is 0 to 1 second. Rate of change of the linear function is given by y = 50x (feet per second).

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Answer:

Step-by-step explanation:

1). 6x + 7 - 18x + 4

  = (6x - 18x) + (7 + 4)

  = -12x + 11

2). 5x - 7x + 5x + 4 - 9

  = (5x + 5x - 7x) + (4 - 9)

  = 3x - 5

3). 3x + 8y - 5x + 3y

  = (3x - 5x) + (8y + 3y)

  = -2x + 11y

4). 17x² - 7x²- 5x + 3x + 14

  = (17x² - 7x²) + (-5x + 3x) + 14

  = 10x² - 2x + 14

5). 3xy - 9xy - 5x + 4x - 7 + 3

  = (3xy - 9xy) + (-5x + 4x) + (-7 + 3)

  = -6xy - x - 4

6). 9x + 7y - 15x + 4x - 9y

  = (9x - 15x + 4x) + (7y - 9y)

  = -2x - 2y

7). 3x + 7 - 5x - 8y + 4x - 2y + 7

  = (3x - 5x + 4x) + (-8y - 2y) + 14

  = 2x - 10y + 14

8). 3xy - xy + 15x + 4 - 11

  = (3xy - xy) + 15x + (4 - 11)

  = 2xy + 15x - 7

9). -8x + 3x + 7y - 5x + 4y - 2

  = (-8x - 5x + 3x) + (7y + 4y) - 2

  = -10x + 11y - 2

10). 3x² + 6x - 3y + 2x - 7

  = 3x² + (6x + 2x) - 3y - 7

  = 3x² + 8x - 3y - 7

Answer:

a)A=53

b)A=42.68

c)A=60

Answer:

Since there are no common factors, the only common factor for [tex]\frac{4}{x+5}[/tex] is  1

Answer:

40 feet

Step-by-step explanation:

We know that the area of a rectangle is represented as [tex]lw=a[/tex], where l is the length and w is the width.

We already know the width, and we know the area, so we can plug these values into the equation.

[tex]l\cdot 6 = 240[/tex]

Our goal is to now isolate the variable l, and to do this we can divide both sides by 6.

[tex](l\cdot6) \div6 = 240\div6\\\\l = 40[/tex]

Hope this helped!

Answer:

l=a/w

Step-by-step explanation:

Length equals area divided by width.

Answer: 117?

Step-by-step explanation:

Answer:

<o=180-132=48

so,<s=24(The angle at the circumference is half of its corresponding angle at center)

=========================================

Work Shown:

f(x) = x^2 - 2x

f(2) = 2^2 - 2*2 ... replace every x with 2

f(2) = 4 - 4

f(2) = 0

----------------------------

g(x) = 12-8x

g(3) = 12-8*3 ... replace every x with 3

g(3) = 12-24

g(3) = -24

----------------------------

Subtract the results of the previous two sections

f(2) - g(3) = 0 - (-24)

f(2) - g(3) = 0 + 24

f(2) - g(3) = 24

Answer:

75.9 km/hr

Step-by-step explanation:

Distance between the highway and farmhouse is given as = 2km = a

The distance after the intersection and the highway = b

Let the distance between the farmhouse and the car = c

Using the Pythagoras Theorem rule

c² = a² + b²

c² = 2² + b²

Step 1

Since distance is involved, time is required. Hence, we differentiate the equation above in respect to time

c² = 2² + b²

dc/dt (2c) = 4 + 2b

dc/dt =[ b/(√b² + 4)] × db/dt

We are told in the question that:

the car travels past the farmhouse on on the highway at a speed of 80 km/h.

We are asked to calculate the speed at which the distance between the car and the farmhouse kept increasing when the car is 6 km past the intersection of the highway and the road.

This calculated using the obtained differentiation above:

dc/dt = [ b/(√b² + 4)] × db/dt

Where b = 6km

db/dt = 80km/hr

[6/(√6² + 4)] × 80km/hr

6/√36 + 4 × 80km/hr

6 × 80/√40

480/√40

= 75.894663844km/hr

Approximately = 75.9km/hr

In this exercise we want to calculate the speed of the vehicle to reach the farm, in this way we will find a speed of approximately:

[tex]75.9 km/hr[/tex]

To start this exercise we have to use some data informed in the text, like this:

Since distance is involved, time is required. Hence, we differentiate the equation above in respect to time

[tex]c^2 = 2^2 + b^2\\\frac{dc}{dt} (2c) = 4 + 2b\\\frac{dc}{dt} =[ b/(\sqrt{b^2} + 4)] ( \frac{db}{dt})[/tex]

Calculate the speed at which the distance between the car and the farmhouse kept increasing when the car is 6 km past the intersection of the highway and the road. This calculated using the obtained differentiation above:

[tex]\frac{dc}{dt} = [ 6/(\sqrt{6^2} + 4)] (80)\\=6/\sqrt{36} + 4 * 80\\=6 * 80/\sqrt{40} \\=480/\sqrt{40} \\= 75.9km/hr[/tex]

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Solution:

x+9=13

then,

13-9=4

so the value of x is 4

Answer:

Step-by-step explanation:

X +9 equals 13

X+9 =13

X=13 - 9

X= 4

[tex]hope \: this \: helps[/tex]

[tex]have \: a \: nice \: life! :) [/tex]

Answer:

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

Step-by-step explanation:

Un par ordenado es un elemento de la forma [tex](x,f(x))[/tex], donde [tex]x[/tex] es un elemento del dominio de la función, mientras [tex]f(x)[/tex] es la imagen de la función evaluada en [tex]x[/tex]. Entonces, un par ordenado que está contenido en la citada función debe satisfacer la siguiente condición:

La imagen de la función existe para un elemento dado del dominio. Esto es:

[tex]x \rightarrow f(x)[/tex]

Dado que [tex]f(x)[/tex] es una función polinómica, existe una imagen para todo elemento [tex]x[/tex]. Ahora, se eligen elementos arbitrarios del dominio para determinar sus imágenes respectivas:

x = 0

[tex]f(0) = 0^{3}-2\cdot (0)^{2}-2[/tex]

[tex]f(0) = -2[/tex]

(0, -2) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 1

[tex]f(1) = 1^{3}-2\cdot (1)^{2}-2[/tex]

[tex]f(1) = -3[/tex]

(1, -3) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 2

[tex]f(2) = 2^{3}-2\cdot (2)^{2}-2[/tex]

[tex]f(2) = -2[/tex]

(2, -2) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 3

[tex]f(3) = 3^{3}-2\cdot (3)^{2}-2[/tex]

[tex]f(3) = 7[/tex]

(3, 7) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

Step-by-step explanation:

hi the answer is x= 3/5

i have added 2 methods of solving it in the above picture. ask me if you have any questions

Answer:

x = 3/5

Step-by-step explanation:

This equation can be solved with algebraic techniques. We will simplify the equation by combining like terms and then use algebraic techniques in order to solve for x.

2(x - 4) + 2x = -6x - 2 Use the distributive property.

2x - 8 + 2x = -6x - 2 Combine like terms (variable terms first).

4x - 8 = -6x - 2 Add 6x to both sides of the equation.

10x - 8 = -2 Add 8 to both sides of the equation.

10x = 6 Divide by 10 on both sides of the equation.

x = 6/10 Simplify the fraction.

x = 3/5

Answer:

I) y = 1/x

ii) y = 1/6

Step-by-step explanation:

inversely proportional just means that the right hand side is the inverse of the left hand side of an equation.

Answer:

10.58 feet

Step-by-step explanation:

Hello!

If you think about how it would look in life you will notice that it looks like a right triangle which means we can use the Pythagorean theorem to find the far the ladder needs to be from the house.

The Pythagorean theorem is [tex]a^{2}+ b^{2}= c^{2}[/tex]

a is a leg

b is the other leg

c is the hypotenuse

Since the ladder has to go from the ground to the window ledge it is the hypotenuse and the window ledge is a leg

Put in what we know

[tex]a^{2} +12^{2} =16^{2}[/tex]

Now we solve for a

Simplify

a^2 + 144 = 256

Subtract 144 from both sides

a^2 = 112

Take the square root of both sides

a = 10.583

The answer is 10.58 feet

Hope this helps!

Answer:

11 ft

Step-by-step explanation:

Try to imagine it or draw it out to help you. The ladder is 16 feet long and the window ledge is 12 feet high, so this is a right triangle.

The ladder is the hypotenuse, so use the given values in the pythagorean theorem.

a^2 + b^2 = c^2

12 + b^2 = 16

b = 11

12^2 + 11^2 = 16^2

1 44 + 121 = 265

√265 = 16

Answer:

= 40

Step-by-step explanation:

2 ( 3 (5 + 2) -1)

= 2 * 20

= 40

Answer:

Step-by-step explanation:

[tex]2\left(3\left(5+2\right)-1\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3\left(5+2\right)-1\right)\:\\\\:\quad 20\\\\=2\times \:20\\\\= 40[/tex]

Answer: False!

This equation is in slope - intercept form, where y = mx + b. B is the y - intercept and m is the slope. They got the location of the y - intercept right, but they forgot to add the negative. It's actually -8.

Hope this helps!

The y-intercept is -8 as the minus always stays with the number to the right of it

Answer:

[tex]96ft^{3}[/tex]

Step-by-step explanation:

Step 1: Find area of base

[tex]\frac{bh}{2}=\frac{(6)(8)}{2} =\frac{48}{2}=24ft^{2}[/tex]

Step 2: Find Volume

[tex]V=\frac{1}{3} (24)12\\V=\frac{1}{3} (288)\\V=96ft^{3}[/tex]

Therefore the volume of the triangular pyramid is [tex]96ft^{3}[/tex]

The volume of the triangular pyramid will be 96 cubic feet.

Let h be the height of the pyramid, l be the slant height and A be the base area of the pyramid.

Then the volume of the pyramid will be

Volume = (1/3) × A × h

The base area of the triangular pyramid is calculated as,

A = 1/2 x 6 x 8

A = 3 x 8

A = 24 square feet

Then the volume of the triangular pyramid is calculated as,

V = 1/3 x 24 x 12

V = 8 x 12

V = 96 cubic feet

The volume of the triangular pyramid will be 96 cubic feet.

More about the volume of the pyramid link is given below.

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Greetings from Brasil...

See the attached chart. The midpoint, M, has 8 units down on the Y axis. So the other half will also have 8 units after that point M. This is also true for the X axis.

Just make the difference between points T and M. For M and S they are the same quantities.

(0; 3) and (1; -5)

X: 1 - 0 = 1   (one unit until mid point)

Y: - 5 - 3 = - 8  (8 units until mid point)

To S:

S(W; Z)       M = center point coordinate value

W = M +  1 ⇒ W = 1 + 1 = 2

Z = M - 8 ⇒ Z = - 5 - 8 = - 13

Answer:

144%

Step-by-step explanation:

Complete question below:

Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016. What is Linnea's company's revenue in 2017 as a percent of its revenue in 2016?

Solution

Let

36x= Linnea's company revenue in 2017

25x=Linnea's company revenue in 2016

Percent of Linnea's company's revenue in 2017 as a percent of its revenue in 2016= 36x / 25x × 100

36x / 25x * 100

=1.44 × 100

=144%

Answer:

√29 units

Step-by-step explanation:

Find the distance between (-1,4) and (1,-1).

We'll use the Pythagorean Theorem:

The horizontal distance between the two points is 1 - (-1), or 2, and the vertical distance is 4 - (-1), or 5.

Thus, the distance squared is 2^2 + 5^2, or 29, and the distance between the two points is therefore

d = √29 units

Answer:

B

Step-by-step explanation:

Any number, regardless of its sign, raised to an even power will always be positive. Therefore, a⁷² will be positive. We know that -3/7 is negative, and since a positive times a negative is negative, the answer will be negative.

Answer:

The average rate of change for the given function in the interval (-5, -1) is 0 (zero)

Step-by-step explanation:

The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:

the average rte of change of h(t) in the interval (-5, -1) is:

[tex]\frac{h(-1)-h(-5)}{-1+5}[/tex]

so we find:

[tex]h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9[/tex]

then the average rate of change becomes:

[tex]\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0[/tex]

Answer:

never

Step-by-step explanation:

smith will run out by week 2

Answer:

After 17 weeks

Step-by-step explanation:

We can create a system of equations for this problem, where y is the total amount of money in their banks and x is the amount of weeks passed.

Mr. Smith's equation will be [tex]y = 12x+21[/tex].

Mr. Brown's equation will be [tex]y = 10x+55[/tex].

We can now solve for x by using substitution.

Let's substitute Mr. Brown's equation into Mr. Smith's equation.

This get us [tex]10x + 55 = 12x + 21[/tex].

We can now solve for x.

Let's subtract 12x from both sides:

[tex]-2x + 55 = 21[/tex]

And now let's subtract 21 from both sides:

[tex]-2x+34=0[/tex]

Now we subtract 34 from both sides:

[tex]-2x=-34[/tex]

And divide both sides by -2.

[tex]x=17[/tex]

Hope this helped!