Jorge’s monthly bill from his Internet service provider was $25. The service provider charges a base rate of $15 per month plus $1 for each hour that the service is used. Find the number of hours that Jorge was charged for that month.

Greetings from Brasil...

2X/(X + 2) = 6/(X + 4)

2X(X + 4) = 6(X + 2)

2X² + 2X - 12 = 0     ÷2

2X²/2 + 2X/2 - 12/2 = 0/2

Δ = 25

S = {-3, 2}

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given

[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]

⇒ 2x(x + 4) = 6(x + 2)

⇒ [tex]2x^{2} +8x = 6x + 12[/tex]

⇒ [tex]2x^{2} +8x-6x-12=0[/tex]

⇒ [tex]2x^{2} +2x -12=0[/tex]

Divide above equation by 2, we get

⇒ [tex]x^{2} +x -6=0[/tex]

⇒ [tex]x^{2} +2x-3x-6=0[/tex]

⇒ [tex]x(x+2)-3(x+2)=0[/tex]

⇒ [tex](x+2)(x-3)=0[/tex]

⇒ x = -2, 3

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

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Answer:

9:45 A.M.

Step-by-step explanation:

First, add the time that took him to hike:

6:30 + 2 hours and 15 minutes = 8:45 A.M.

Next, add the 1 hour that he played volleyball for:

8:45 + 1 hour = 9:45 A.M.

So, he finished playing volleyball at 9:45 A.M.

Answer:

9:45 am

Step-by-step explanation:

He went at 6:30 am to a hike.

It took him 2 hours 15 minutes

=> 6 : 30

+  2    15

=> 8 : 45

He came back from the Hike at 8:45 am

He played volleyball for 1 hour.

=> 8 : 45

+  1

=> 9 : 45

He finished playing volleyball at 9:45 am

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer:

Step-by-step explanation:

3) G

Step-by-step explanation:

Q(-1,-1) R(3,1) S(2,-4)

x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)

Q -1+2 -1+3 (1,2) (-1,-2)

R 3+2 1+3 (5,4) (-5,-4)

S 2+2 -4+3 (4,-1)

It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:

[tex]\sin60^\circ=\dfrac{h}{4}[/tex]

and

[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]

so

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]

Answer:

h = √12

Step-by-step explanation:

use the Pythagorean

h² = 4² - 2²

h² = 16 - 4

h = √12

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.

We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.

We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.

Answer:

Theres more than one answer so b and a

Step-by-step explanation:

Answer:

135 units²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

To calculate h use Pythagoras' identity on the right triangle on the left

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = [tex]\sqrt{225}[/tex] = 15 , thus

A = 9 × 15 = 135 units²

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids.

A sphere is a solid shape.

Given data

radius of sphere = 17 units

The volume of a sphere can be expressed as below

[tex]volume = \frac{4}{3}\pi r^3[/tex]

Substituting our data into the expression we have

[tex]volume = \frac{4}{3}*3.142*17^3[/tex]

[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]

The volume of the sphere is given as

20582.195 units

Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

The function is given :

f(x) = 4x + 15

For f(-3), the input for the function f(x) is -3.

Replace the x variable with -3.

f(-3) = 4(-3) + 15

Evaluate.

f(-3) = -12 + 15

f(-3) = 3

The output for f(-3) is 3.

Answer: f(-3) = 3

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(-3).

We find f(-3) by plugging -3 in for x,

everywhere that x appears in the function.

So we have 4(-3) + 15.

4(-3) is -12 so we have -12 + 15 which is 3.

So f(-3) is 3.

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

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Answer:

By using The Pythagorean Theorem:

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

Step-by-step explanation:

The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]

[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]

The length of the hypotenuse for the given example will be 5m.

This is how to find the length of an hypotenuse.

Answer:

  2n+2 ways to win

Step-by-step explanation:

You generalize by observing patterns in the way you solve the smaller problems.

The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.

For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.

Answer:

1522km^2

Step-by-step explanation:

To solve this, first convert the percentage to a decimal. That would be .0475.

Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525

Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2

Answer:

The area will be 1292.98 km² after 11 years.

Step-by-step explanation:

To find what decreases by 4.57% each year in kilometers:

2600 × 4.57/100 = 26 × 4.57

= 118.82 km²

To find the area after 11 years:

118.82 × 11 = 1307.02

2600 - 1307.02 = 1292.98 km²

1292.98 km² is the answer.

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 12

The opposite is x

Substitute the values into the above formula and solve for x

That's

[tex] \sin(60) = \frac{x}{12} [/tex]

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

[tex]x = \frac{ \sqrt{3} }{2} \times 12[/tex]

We have the final answer as

Hope this helps you

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Answer:

3438.

Step-by-step explanation:

6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)

= 6³ ÷ 4 + 2 × 9 (256 - 68)

= 6³ ÷ 4 + 2 × 9 × 188

= 216 ÷ 4 + 2 × 9 × 188

= 54 + 2 × 9 × 188

= 54 + 3384

= 3438

3438 is the answer.

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Answer:

156.6 square yards

Step-by-step explanation:

To find the surface area of the pyramid, find the area of each surface and add them together.

formula for area of a triangle = 1/2(b·h)

1. There are three triangles with a base of 9 and a height of 9

1/2(9·9) = 40.5

Multiply by the three triangles

40.5 · 3 = 121.5

2. There is one triangle with a base of 9 and a height of 7.8

1/2(9·7.8) = 35.1

3. Add the areas of all surfaces

121.5 + 35.1 = 156.6

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

The number of measles vaccines that Dr. Potter give than polio vaccines is 30

Step-by-step explanation:

The parameters given are;

The number of doses given in a polio vaccine = 6 doses

The number of doses given in a measles vaccine = 3 doses

The number of vaccinations given by Dr. Potter last year = 60 vaccinations

The number of doses given in the 60 vaccinations = 225 doses

Let the number of polio vaccine given last year by Dr. Potter = x

Let the number of measles vaccine given last year by Dr. Potter = y

Therefore, we have;

6 × x + 3 × y = 225.......................(1)

x + y = 60.......................................(2)

From equation (2), we have;

x = 60 - y

Substituting the derived value for x in equation (1), we get;

6 × x + 3 × y = 225

6 × (60 - y) + 3 × y = 225

360 - 6·y + 3·y = 225

360 - 225 = 6·y - 3·y

135 = 3·y

y = 45

x = 60 - y = 60 - 45 = 15

Therefore;

The number of polio vaccine given last year by Dr. Potter = 15

The number of measles vaccine given last year by Dr. Potter = 45

The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.

The number of measles vaccines that Dr. Potter give than polio vaccines =  30 vaccines.

Answer:

Step-by-step explanation:

Volume = 1/3πr²h

Surface Area = πr(r+√(h²+r²))

V = 1/3π(10)²(34) = 3560 .5 cm³

SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²

Answer:

when you simplify you continue until you get to the simplest form but when you solve you continue until you get an answer. Solving gives you a value for a variable. You mean simplify and get 2x - 10 but when you solve you continue until you get x as 5

Step-by-step explanation:

Answer: ok, so simplifying is when you make something less complex or complicated. Solving means an expression can be used for representating  the solutions. for Example, say if you have the equation x+y=2x-1 is solved for the unknown x by the expression x=y+1. solving gives you the value for the variable. you know the difference by when you are simplifying you are trying to make the problem less complicated or less complex. and when you are solving you are trying to find the answer to the problem..

Step-by-step explanation:

Answer:

(-9,2)

Step-by-step explanation:

The rule for reflecting over the x axis is

(x,y)→(x,−y)

(-9, -2) becomes ( -9, - -2) = (-9,2)

Answer:

(-9,2)

Step-by-step explanation:

It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

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

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Answer:

Step-by-step explanation:

Answer:

Hey there!

The answer would be C. 4/15.

4/5(1/3)=4/15

Let me know if this helps :)

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.