Explain how to solve 2x + 1 = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer:

Se fabricaron:

1000 balones de los que cuestan $20

75 balones de los que cuestan $30

50 balones de los que cuestan $40

Step-by-step explanation:

Vamos a definir las variables:

x = número de balones de $100.00 vendidos.

y = número de balones de $120.00 vendidos

z = número de balones de $160,00 vendidos.

Sabemos que se producen 1125 balones, entonces:

x + y + z = 1125

y el costo de producción es $24,250, conociendo el costo de cada balón podemos escribir:

x*$20 + y*$30 + z*$40 = $24,250

Y también sabemos que la ganancia mensual es $92,750

Ganancia es la diferencia entre el dinero total recibido y los costos, entonces:

x*$100 + y*$120 + z*$160 - $24,250 =  $92,750

x*$100 + y*$120 + z*$160 = $92,750 + $24,250

x*$100 + y*$120 + z*$160 = $117,000

Entonces tenemos un sistema de 3 ecuaciones:

x + y + z = 1125

x*$20 + y*$30 + z*$40 = $24,250

x*$100 + y*$120 + z*$160 = $117,000

Para resolver esto debemos comenzar por aislar alguna variable en alguna de las ecuaciones, yo comenzare aislando x en la primera ecuación:

x = 1125 - y - z

Ahora podemos reemplazar esto en las otras dos ecuaciones para obtener:

(1125 - y - z)*$20 + y*$30 + z*$40 = $24,250

(1125 - y - z)*$100 + y*$120 + z*$160 = $117,000

Si simplificamos esto obtenemos:

$22,500 + y*$10 + z*$20 = $24,250

$112,500 + y*$20 + z*$60 =  $117,000

Ahora de vuelta, debemos aislar una variable en una de las ecuaciones, si aislamos y en la primera ecuación obtenemos:

y*$10 = $24,250 - $22,500 -  z*$20

y = ($1,750 - z*$20)/$10

y = 175 - 2*z

Reemplazando esto en la otra ecuación obtenemos:

$112,500 + (175 - 2*z)*$20 + z*$60 =  $117,000

Ahora podemos resolver esto para z.

(175 - 2*z)*$20 + z*$60 =  $117,000 - $112,500

(175 - 2*z)*$20 + z*$60 = $4,500

$3,500 - z*$40 + z*$60 = $4,500

$3,500 + z*$20 = $4,500

z*$20 = $4,500 - $3,500 = $1,000

z = $1,000/$20 = 50

Entonces tenemos 50 balones de los que cuestan $40.

Usando la ecuación y = 175 - 2*z podemos encontrar el valor de y.

y = 175 - 2*50 = 75

Entonces tenemos 75 balones de los que cuestan $30.

Usando la ecuación x = 1125 - y - z podemos encontrar el valor de x.

x = 1125 - 75 - 50 = 1000

tenemos 1000 balones de $20.

Answer:

Step-by-step explanation:

y = -3(x-3)^2 + 4

Answer:

8.7 feets

Step-by-step explanation:

As obtained frommthe diagram attached :

Base, b of triangle = 6 feets

Height of triangle, h = 12 feets

Volume of a Triangular Prism is obtained using the relation :

Base Area * Width

Base area of prism :

0.5 * base * height

0.5 * 6 * 12 = 36ft²

Width, w of the ramp =x

Volume, V = 313.2 ft³

V = base area * width

313.2 = 36 * x

313.2 = 36x

x = 313.2 / 36

x = 8.7 feets

Answer:

360 learners

Step-by-step explanation:

One way to solve these types of problems is that you could set up a proportion

learners/teachers = learners/teachers

Let x = no. of learners to enrol

30/1 = x/12

12(30) = x

x = 360 learners

Answer:

Complementary

x = 55

Step-by-step explanation:

Complementary angles add up to 90°, while supplementary angles add up to 180°.

In this situation, the two angles add up to 90° (the little box means that an angle is a 90° angle) So, the angles are complementary.

Now, we can write this equation.

x + x - 20 = 90

Simplify.

2x - 20 = 90

2x = 110

x = 55

Just in case, let's check the answer.

Substitute x = 55 into (x + x - 20 = 90)

55 + 55 - 20 = 90

110 - 20 = 90

90 = 90

This is true, so x = 55 is correct.

I hope this helps! Feel free to ask any questions!

Answer:

= 3.5 x 10^ -12

Step-by-step explanation:

i hope this helps :)

Answer:

35 * [tex]10^{-13}[/tex]

Step-by-step explanation:

Answer:

n=1.5

Step-by-step explanation:

distribute: 1.2n-5.4= 3.4-2(3n-1)

Add numbers]: 1.2 n - 5.4= 5.4-6n

Move terms: 1.2n+6n- 5.4=5.4

Add like terms: 7.2n= 5.4+5.4

Divide both sides of equation by 7.2

Answer n= 1.5

Answer:

C,D,A,B

Step-by-step explanation:

C - $24.74

D - $25.93

A - $26.92

B - $26.98

Answer:

8m = d

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

120-57=63

Answer:

73

Step-by-step explanation:

Answer:

C) 12.75

Step-by-step explanation:

4x=51

x=51/4

x=12.75

Answer:

The relationship between AB and CD

Answer:

because a trapezoid is a quadrilateral and abcd has four sides further a trapezoid has 1 one parallel side with both sides equal

Answer:

y - 8 = 4(x - 2)

Step-by-step explanation:

Note that as we increase any x value by 1, the corresponding y value increases by 4.  Thus, the slope is 4.

Using the slope-intercept formula, we get:

y - 8 = 4(x - 2)

Check:  If x = 5, does this formula result in y = 20?

y = 8 + 4(x - 2) with x = 5 comes out to y = 8 + 4(3)  =  8 + 12 = 20.  YES

Answer:

14.444444 but i dont know for sure so wait for someone else to respond

Step-by-step explanation:

Answer:

Y=130/9

Step-by-step explanation:

Answer:

-28.84

Step-by-step explanation:

-6π - 10

-6(3.14) - 10

-18.84 - 10

-28.84

Answer:

− 28.85

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

you have to subtract 26 on both sides.

so then the equation turns into 7t = 35

then you dive both sides by 7, leaving the equation as t=5

Step-by-step explanation:

So looking at this question, we have two variables (1 - a glass of milk; 2 - a snack bar) and two equations to use to solve for the two variables. Remember that for any number of variables, you need that same number or more equations to solve for the variables.

Let's say that a glass of milk is represented by g and a snack bar is represented by s.

So we essentially have two equations here:

4 glasses of milk + 3 snack bars = 88 carbs, or:

4g + 3s = 88

2 glasses of milk + 4 snack bars = 74 carbs, or:

2g + 4s = 74

Now that we have this, we can solve for our equations. There are two ways to do this:

SUBSTITUTION - solve for one variable, then substitute it in

Let's solve for g using the second equation. First, we'll isolate g by subtracting 4s from both sides.

2g = 74 - 4s

Next, we can divide the whole equation by 2 to solve for g.

g = 37 - 2s

Now, we can substitute this into the first equation for g and solve for s.

4g + 3s = 88

4(37 - 2s) + 3s = 88

148 - 8s + 3s = 88

148 - 5s = 88 (now subtract 88 from both sides and add 5s to both sides)

60 = 5s

s = 12

Now we can use this to solve for g in the original equation

g = 37 - 2s

g = 37 - 2(12) = 37 - 24 = 13

ELIMINATION - eliminate one variable to solve for the other, then use that to solve for the first

Let's look at our two equations

4g + 3s = 88

2g + 4s = 74

Let's eliminate the variable g first by multiplying the second question by -2.

4g + 3s = 88

-4g - 8s = -148

If we add these two equations together, we get

-5s = -60

Divide both sides by -5 and we get

s = 12

Now, we can plug s into either equation to solve for g as we did above.

Answer:

Step-by-step explanation:

It's rational because it doesn't have a continuous decimal. -51/2 is -25.5

Answer:

I believe it is ration since a rational number is any interger, fraction, or repeating decimal.

Step-by-step explanation:

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

Answer:

1. 12

2. 15

3. 16

4. 12

5. 21.333 ...

6. 29

7. 13

8. 11

9. 14

10. 24

6. (Assuming..) 68 / 4 = 17

Step-by-step explanation:

These are a lot so I will not be doing a explanation if you do not need it.

Hope this helps :)

Answer:

tomatoes in a plant in flip flop for sure

Answer:

-1.5

Step-by-step explanation:

Answer:

Your question is not correct.

By using basic meaning of percentage we got that the originally puppy's weight  was 50 pounds

Percentage is a number or ratio expressed as a fraction of 100.

Here given that Juan's puppy currently weighs 80 pounds and his is a 60% increase in weight from when he got her.

Let's suppose original weight of puppy was x pounds

We can calculate x as

[tex]x+ \frac{60}{100} \times x=80\\\\x+ \frac{6}{10} \times x=80\\\\x+ 0.6\times x=80\\\\\\1.6x=80\\\\x=\frac{80}{1.6} \\\\x=\frac{800}{16} \\\\\\x=50[/tex]

By using basic meaning of percentage we got that the originally puppy's weight  was 50 pounds .

To learn more about Percentage visit :brainly.com/question/24304697

Answer:

see explanation

Step-by-step explanation:

In math, when a number is squared, it means it has been multiplied by itself. For instance, two squared equals two times two, or four.

In this same case x^2---> x * x

x times x ---> x^2

Answer:

your answer will be option A.

The function is continuous.

Step-by-step explanation:

hope it helps you

have a great day!!!

Answer:

i've just been looking at different answers and I am 75% sure its

"The function is increasing over its entire domain"

Step-by-step explanation:

Answer:

He sold 10 hangers and 10 neclesses

Step-by-step explanation:

Given data

Let the number of door hanger be x

and the number of neckless be y

so

x+y= 20---------1

also,

2.25x+3.75y= 60---------2

Solve 1 and 2 together

From 1

x= 20-y

put this in place of x in 2

2.25(20-y)+3.75y= 60

45-2.25y+3.75y= 60

1.5y= 60-45

1.5y= 15

y= 15/1.5

y= 10

Put y= 10 in 1

x+10= 20

x= 20-10

x= 10

Answer:

$4 off

New price is $36

Step-by-step explanation:

Answer:

$4 discount.

$36 new price.

Step-by-step explanation:

40 x .10= 4

40- 4= 36