Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

For this case we must make a conversion. We have that by definition 1 liter equals 0.264172 gallons.

So, making a rule of three we have to:

1L ----------------> 0.264172 gallons

15L --------------> x

Where:

x: Represents gallons equivalent to 15 liters.

[tex]x = \frac {15 * 0.264172} {1}\\x = 3.96258[/tex]

Rounding out we have that 15 liters equals 3.96 gallons.

Answer:

3.96 gallons

15 liters is approximately 3.96 gallons.

Given that we need to calculate 15L is approximately how many gallons rounded two decimal places for final answer.

To convert liters (L) to gallons (gal), you need to know the conversion factor between the two units.

The conversion factor between liters and gallons is 1 L = 0.264172 gal.

Now, let's calculate how many gallons are approximately equal to 15 liters:

15 L x 0.264172 gal/L = 3.96258 gal

Rounding to two decimal places, the approximate value is 3.96 gallons.

Therefore, 15 liters is approximately 3.96 gallons.

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Answer:

325 mi

Step-by-step explanation:

We can write a proportion to solve, putting distance over inches

50 miles       x miles

------------- = -------------

1 inch            6.5 inches

Using cross products

50 * 6.5 = 1*x

325 = x

The distance is 325 miles

Answer:

The the vertex is: (2, 4)

Domain: all real numbers

Range: [tex][4 \infty)[/tex]

Step-by-step explanation:

Quadratic functions can be written vertically as follows

[tex]f(x) = a(x-h)^2 +k[/tex]

Quadratic functions can be written vertically as follows

Where the point (h, k) represents the vertex of the quadratic function.

For this type of functions the domain is always all real numbers and the range is [tex][k, \infty)[/tex] or if [tex]a <0[/tex] then the range is [tex](-\infty, k][/tex]

In this case the function is:

[tex]f(x) = (x - 2)^2 + 4[/tex]

So

[tex]h = 2\\k=4[/tex]

The the vertex is: (2, 4)

Domain: all real numbers

Range: [tex][4, \infty)[/tex]

Answer:

2i + 6

Step-by-step explanation:

4-2 = 2

6-3 = 3

2 * 3 = 6

2i

Answer:

9 - 12i

Step-by-step explanation:

Noting that i² = - 1

Expand the factors on the numerator and denominator

(4 - 2i)(6 - 3i) = 24 - 12i - 12i + 6i² = 24 - 24i - 6 = 18 - 24i

(1 - i)(1 + i) = 1 + i - i - i² = 1 + 1 = 2

The division reduces to

[tex]\frac{18-24i}{2}[/tex]

= [tex]\frac{18}{2}[/tex] - [tex]\frac{24}{2}[/tex] i

= 9 - 121i

Answer:

B

Step-by-step explanation:

B is incorrect.  Some systems have infinitely many solutions.

Answer: 36" = 3 feet

               18" = 1.5 feet

Explanation: 1 foot = 12 inches

Answer:

2) -81t² +16

Step-by-step explanation:

(9t -4)(-9t -4) = (9t x -9t) + (9t x -4) + (-4 x -9t) + (-4 x -4)

                     = -81t² - 36t + 36t + 16

                     = -81t² + 16

Answer:

- 81t² + 16

Step-by-step explanation:

Simply expand the equation by factoring

(9t-4)(-9t-4)    factor out negative sign

= -(9t - 4) (9t +4)

= -(9t + 4) (9t - 4)      recall a² - b² = (a+b) (a-b)

= - [ (9t)² - 4²]

= - ( 81t² - 16)

= - 81t² + 16

Answer:

Step-by-step explanation:

To solve this problem we need to solve a system of equations. We have two machines:

The machine "Paint Pro" is used for two hours.

The machine "Goldilocks" is used for an hour and a half.

When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall.

Therefore, we have the following system of equations:

P + G = 55 ft^2/m

120P + 90G = 5850 ft^2 → 4P + 3G = 195

Solving the system of equations we have that:

P = 25

G = 30

Therefore, the paint pro paints 30sqft per minute and Goldilocks paints 25 sqft per minute.

Answer:

2.4

Step-by-step explanation:

for the edge question the answer is actually 0.5

Answer:

x=1

Step-by-step explanation:

-5 - (15x-1) = 2(7x-16) -x

Distribute the negative sign

-5-15x+1 = 2(7x-16)-x

Distribute the 2

-5-15x+1 = 14x -32-x

Combine like terms

-4-15x = 13x-32

Add 15x to each side

-4-15x+15x = 13x+15x-32

-4 = 28x-32

Add 32 to each side

-4+32 = 28x-32+32

28 = 28x

Divide each side by 28

28/28 = 28x/28

1 =x

Answer:

• The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

Step-by-step explanation:

We have to multiply the term  b2/4a2 by a in order to determine the value to add to the left side of the equation so as to balance both sides of the equation.

If we multiply the terms, we get;

[tex]\frac{b^{2} }{4a^{2} }*a=\frac{b^{2} }{4a}[/tex]

Therefore, we shall be adding the term [tex]\frac{b^{2} }{4a}[/tex] to the left side of the equation.

Answer: The answer is choice B.

Step-by-step explanation:

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx+b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0,1)\\(1, -2)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {-2-1} {1-0} = \frac {-3} {1} = - 3[/tex]

So, the equation is of the form:

[tex]y = -3x + b[/tex]

We substitute a point to find "b":

[tex]1 = -3 (0) + b\\1 = b[/tex]

Finally, the equation is:

[tex]y = -3x+1[/tex]

Answer:

Option C

Find the vertex:

[tex]\textrm{Use the formula } \frac{-b}{2a} \textrm{ to find the vertex}\\ \\ \frac{-10}{2} = -5\\ \\ \textrm{In order to find the y value plug in -5 back into the function}\\ \\ y=(-5)^2+10(-5)+16\\ y=-9\\\\ \textrm{The vertex of the function is} (-5,-9)[/tex]

Determine if the parabola will open up or down:

[tex]a > 0 \\ \\ 1>0[/tex]

Since the value of a is positive, the parabola will open upwards

Find the x and y intercepts:

Factor [tex]y = x^2+10x + 16[/tex] to find the x intercepts

(x+8)(x+2)

x + 8 = 0

x = -8

x + 2 = 0

x = -2

x intercepts:

x = -2

x = -8

Find the y intercept

[tex]y = 0^2+10(0) + 16\\\\ y=16[/tex]

Hence, C. Graph A best represents the quadratic function [tex]y = x^2+10x + 16[/tex]

[tex](-4qr)(-4qr)(-4qr)(-4qr)=(-4qr)^4=256q^4r^4[/tex]

To rewrite the expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we can rewrite it as (-4qr)^4 = 256q^4r^4.

To rewrite the given expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we need to understand that multiplying the same base with different exponents is equivalent to adding the exponents. In this case, the base is (-4qr) and the exponents are 1 for each occurrence. So, we can rewrite the expression as:

(-4qr)4 = -44q4r4 = 256q4r4

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Answer:

NO SOLUTION

Step-by-step explanation:

Let's actually solve the system

x-4y=1

5x-20y=4

Let's eliminate y.  To do this, multiply the first equation by -5, obtaining

-5x + 20y = -5

Now add this result to the second equation:

-5x + 20y = -5

5x -  20y =  4

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

           0   = -1

This result is never true.  Thus, this system of linear equations has NO SOLUTION.

The system of equations results in a false statement.

Let's solve the system of equation

x - 4y = 1 ......(1)

5x - 20y = 4 ........(2)

By using the elimination method

Eliminate y by multiplying (1) by -5

We have,

-5x + 20y = -5 ...........(3)

Adding (3) and (2), then we get

(x - 4y = 1) + (-5x + 20y = -5)

-5x + 20y = -5

5x - 20y = 4

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

      0 = -1

Therefore, the correct answer is option (a). The system results in a false statement.

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Answer:

x^2 +3

Step-by-step explanation:

f(x) = 2x^2 + 2

g(x) = x^2 - 1

(f - g)(x) = 2x^2 + 2 -( x^2 - 1)

     Distribute the minus sign

              2x^2 +2 -x^2 +1

              x^2 +3

[tex](f-g)(x)=2x^2+2-(x^2-1)=2x^2+2-x^2+1=x^2+3[/tex]

Answer:

[tex]176 \leq x \leq 321[/tex]

Step-by-step explanation:

Let

x -----> the number of steaks the restaurant owner can order

we know that

[tex]x\geq 176[/tex] ----> inequality A

[tex]x\leq 321[/tex] ----> inequality B

so

the compounded inequality is equal to

[tex]176 \leq x \leq 321[/tex]

Answer:

FLVS

a

Step-by-step explanation:

x ≥ 176 and x ≤ 321

Since you work as a cashier you must have a source of income, so you must pay taxes, because when you have an income you MUST pay taxes

Answer:

1)

Law of Detachment

If you have an income, then you must pay taxes.

You have an income.

You must pay taxes.

Law of Syllogism

If you have an income, then you must pay taxes.

If you must pay taxes, then you have a job.

If you have an income, then you have a job

2)

Law of Detachment

If you work as a cashier in a convenience store then you have a job.

You work as a cashier in a convenience store.

You have a job.

Law of Syllogism

If you work as as a cashier in a convenience store then you have a job  

If you have a job then you must pay taxes

If you work as as a cashier in a convenience store then you must pay taxes

Step-by-step explanation:

To answer it properly we need to remind those Laws in Mathematical Logic.

The Law of Detachment says that if a Logical Implication and the second Statement is true, we can derive a true conclusion

1. If p→q (True)

2) p (True)

3) q (True)

On the other hand, The Law of Syllogism says:

1) If p→q (True)

2) If q→r (True)

Subsequently, we can conclude by derivation as true this Logical Implication:

3) If p→r (True)

-----

If you have an income, then you must pay taxes.

If you have a job, then you have an income.

Law of Detachment

If you have an income (p), then you must pay taxes. (q)

If you have a job(r), then you have an income.

1)If you have an income, then you must pay taxes. (T) If p→q (True)

2)You have an income (T) p (True)

3) You must pay taxes q (True)

Law of Syllogism

If you have an income (p), then you must pay taxes. (q) If p→q (True)

If you must pay taxes (q), then you have a job. (r) If q→r (True)

If you have an income (p), then you have a job (r) If p→r (True)

--

If you work as a cashier in a convenience store (p) then you have a job (q)

If you must pay taxes (r) then you have an income

Law of Detachment

If you work as a cashier in a convenience store (p) then you have a job (q) If p→q (True)

You work as a cashier in a convenience store (p) p (True)

You have a job (q) q (True)

Law of Syllogism

*If you work as as a cashier in a convenience store(p) then you have a job (q) If p→q (True)

*If you have a job (q) then you must pay taxes (r) If q→r (True)

If you work as as a cashier in a convenience store (p) then you must pay taxes (r) If p→r

Answer:

S(x)=42000 * 1.04^x

Step-by-step explanation:

now = 42000

in 1 year = 42000 *1,04, because 4% increase is to multiply 1,04

in 2 years = 42000 *1,04*1.04 = 42000*1.04^2

in x years = 42000 * 1.04^x

Answer:

[tex]S(x)=42,000*(1.04)^{x}[/tex]

Step-by-step explanation:

We have as data

a = $42,000 (salary during the first year)

x = number of years

i = 4% = 0.04 (annual increase interest)

S(x) = Salary based on the years elapsed

"a" and "i" are constant for each year, while "x" increases one each year.

The function S(x) can be calculated like this:

[tex]S(x)=a*(1+i)^{x}[/tex]

Substituting constant values, we have

[tex]S(x)=42,000*(1+0.04)^{x}[/tex]

Simplifying, we have

[tex]S(x)=42,000*(1.04)^{x}[/tex]

Hope this helps!

Answer:

The values of y are -33 , -15 , -5 , -5 ⇒ answer C

Step-by-step explanation:

* We will use the substitution method to solve the problem

- The quadratic equation is y = -x² + x - 3

- The values of x are -5 , -3 , -1 , 2

- We will substitute the values of x in the equation to find the

  values of y

# At x = -5

∵ y = -x² + x - 3

∵ x = -5

∴ y = -(-5)² + (-5) - 3 = - 25 - 5 - 3 = -33

∴ y = -33

# At x = -3

∵ y = -x² + x - 3

∵ x = -3

∴ y = -(-3)² + (-3) - 3 = - 9 - 3 - 3 = -15

∴ y = -15

# At x = -1

∵ y = -x² + x - 3

∵ x = -1

∴ y = -(-1)² + (-1) - 3 = - 1 - 1 - 3 = -5

∴ y = -5

# At x = 2

∵ y = -x² + x - 3

∵ x = 2

∴ y = -(2)² + (2) - 3 = - 4 + 2 - 3 = -5

∴ y = -5

* The values of y are -33 , -15 , -5 , -5 ⇒ from left to right

Answer:

The answer is (B)

Step-by-step explanation:

Try out each of the situations. It can't be A, since the 0.9 is less than 1, so it has to be decreasing. This leaves only B and C. Since decreasing by 90 percent is the same as multiplying by 10 percent, the only possible answer left is B.

Hope this helps!

Answer:

the number of employees is decreasing by 10% every year

Step-by-step explanation:

[tex]f(t)=1.5(.90)^t[/tex]

In the given function 1.5 represents the initial number of employees

Exponential  function in the form of [tex]f(x) = a(b)^x[/tex]

When the value of b is less than 1 then it is exponential decay

When the value of b is greater than 1 then it is exponential growth

Exponential decay factor is 0.90

[tex]1-0.90= 0.10[/tex]

0.10 times 100 = 10%

So the number of employees is decreasing by 10% every year

Answer:

c=1`8h

Step-by-step explanation:

Answer: 279.4 centimeters hope this helped

Step-by-step explanation: 110 x 2.54 = 279.4

Answer:

one

Step-by-step explanation:

y = 1/2x + 4

x + 2y = -8

x + 2(1/2 x + 4) = -8

x + x + 8 = -8

2x = -16

x = -8

y = 1/2 (-8) + 4

y = 0

solution: (-8, 0)

Answer: one

The given linear system has a single solution at the point (-8, 0) after solving the equations by substitution.

To determine how many solutions the given linear system has, we can substitute y from the first equation into the second equation:

y =  rac{1}{2}x + 4

x + 2(rac{1}{2}x + 4) = -8

x + x + 8 = -8

2x = -16

x = -8

Then, substituting x into the first equation:

y =  rac{1}{2}(-8) + 4

y = -4 + 4

y = 0

The linear system has a single solution, which is (x, y) = (-8, 0).

Answer:

x=110592

Step-by-step explanation:

[tex]log_{48}x=3 \text{ means } 48^3=x\\\\[/tex]

So x=110592

Answer:

60000/4 pr 15000

Step-by-step explanation:

Rate of change = change in population / change in time

80000 - 20000 = 60000

January to April is 4 months

so the rate of change will be 60000/4 or 15000

Answer:

195

Step-by-step explanation:

y varies directly with x means y=kx

k is a constant of proportionality (meaning no matter what the variable pair (x,y) is k will forever remain the same value)

we have while x=6, y=90

so plug in  90=k(6)

Solve for k: k=90/6=30/2=15

So no matter (x,y) you have the equation y=15x for this problem

Now what is y when x=13

plug in and find out

y=15(13)

y=   45+150= 195