Rocío y su hermano Rafael son aficionados al modelismo y tienen una colección de
barcos y aviones. Rocío comentó: "Si tuviéramos once barcos más, tendríamos el
mismo número de barcos y aviones”, a lo que Rafael respondió: “Pero si tuviéramos
doce aviones más, tendríamos el doble de aviones que de barcos”. ¿Cuántos barcos
y aviones tienen Rocío y Rafael?

We must write and solve a system of equations to see how many of each type of coin Carlos has.

The answer is:

We start by defining the variables:

We know there are 46 coins in total, thus:

x + y + z= 46

The number of pennies and dimes is the same, thus:

x = y

The total value of the coins in the box is $4.09, then:

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

So we can write the system of equations:

x + y + z= 46

x = y

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

First, we can replace x by y in the first and third equations (by using the second one) to get:

2y + z =  46

y*$0.11 + z*$0.25 = $4.09

Now we can isolate z in the first equation to get:

z = 46 - 2y

And replace that in the other equation:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

Now we can solve the equation for y:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

y*$0.11 + $11.50 - y*$0.50 = $4.09

y*($0.11 - $0.50) = $4.09 - $11.50

y*(-$0.39) = -$7.41

y = (-$7.41)/(-$0.39) = 19

if y = 19, then x = 19

By using the first equation:

x + y + z = 46

19 + 19 + z = 46

z = 46 - 19 - 19  = 8

We can conclude that:

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13997560

Answer:

1200

hello i love to help

Answer:

x=14

Step-by-step explanation:

2x+4=3x-10

Add 10 to both sides, leaving you with

2x+14=3x

Subtract 2x from both sides, leaving you with

x=14

Answer:

$ 43.25

Step-by-step explanation:

68 - 40% = 40.8

40.8 + 6% = $ 43.25

Answer:

  6∛3

Step-by-step explanation:

  [tex]\displaystyle 5\sqrt[3]{24}-\sqrt[3]{192}=5\sqrt[3]{2^3\cdot3}-\sqrt[3]{4^3\cdot3}\\\\=(5\cdot2-4)\sqrt[3]{3}=\boxed{6\sqrt[3]{3}}[/tex]

_____

The cubes under each radical can be brought out. Coefficients of like radicals can be combined.

Answer:

7/21=3/9

Step-by-step explanation:

7/21=3/9=1/3 - Ratios are basically the same as fractions

Answer:

[tex] \\ 7 \ratio21 = 3 \ratio9[/tex]

[tex] \\ \frac{7}{21} = \frac{3}{9} [/tex]

Answer:

[tex]\huge\boxed{D)\frac{3p}{p-3} }[/tex]

Step-by-step explanation:

The first thing that can help you here is factoring every term.

[tex]p^2-4p-12[/tex]

Factor.

[tex](p-6)(p+2)[/tex]

[tex]6p+12[/tex]

Factor.

[tex]6(p+2)[/tex]

18p

Factor, keeping in mind the denominator of the other term.

[tex]6(3p)[/tex]

[tex]p^2-9p+18[/tex]

Factor.

[tex](p-6)(p-3)[/tex]

Now you have simplified your original problem:

[tex]\frac{p^2-4p-12}{6p+12} *\frac{18p}{p^2-9p+18}[/tex]

into:

[tex]\frac{(p-6)(p+2)}{6(p+2)} *\frac{6(3p)}{(p-6)(p-3)}[/tex]

Now, after multiplying the numerator and denominator of the fractions:

[tex]\frac{(p-6)(p+2)(6)(3p)}{(6)(p+2)(p-6)(p-3)}[/tex]

Then, you can simplify the fraction by cancelling terms:

[tex]\frac{3p}{p-3}[/tex]

Hope it helps :) and let me know if you want me to elaborate.

Answer:

the answer is 5,746 = c

Step-by-step explanation:

Answer:

Proportional quantities can be described by the equation y = kx, where k is a constant ratio. You can tell that the relationship is directly proportional by looking at the graph. So yes it does equal a proportional relationship.

Hope this helps :)

Answer:

Proportional quantities can be described by the equation y = kx, where k is a constant ratio. You can tell that the relationship is directly proportional by looking at the graph. So yes it does equal a proportional relationship.

Step-by-step explanation:

Yw

Answer:

[tex]The\,\,equation\,\,will\,\,be\,\,2x+y=8[/tex]

Step-by-step explanation:

Let, A=(3,2)

      B=(-1,10)

So, The equation will be

[tex]\frac{x-x_{1} }{x_{1} -x_{2} } =\frac{y-y_{1} }{y_{1} -y_{2} } \\=>\frac{x-3 }{3-(-1) } =\frac{y-2 }{2-10} \\=>\frac{x-3 }{4} =\frac{y-2 }{-8}\\=>-8x+24=4y-8\\=>8x+4y=32\\=>2x+y=8[/tex]

Hope you have understood this.....            

ask me if you have any confusion.....            

if you liked it pls mark it as the brainliest

Answer:

y = - 2x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 1, 10 )

m = [tex]\frac{10-2}{-1-3}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 2 )

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of line

Among the fractions given in this question 11/18 and 5/14,  the largest fraction is: 3/5.

To find out which fraction is the largest, just divide the numerator by the denominator of the ratio and make the comparisons between them, thus defining which is the largest by decimal places or the largest number.

[tex]\large \sf \dfrac{11}{18} \rightarrow 11\div18\rightarrow 0{,}61111111111[/tex]

[tex]\large \sf \dfrac{5}{14} \rightarrow 5\div14\rightarrow 0{,}35714285714[/tex]

We can conclude that the largest fraction, being between 11/18 and 5/14, is 11/18.

Answer:

c = 58, d = 50

Step-by-step explanation:

c = 180 - 50 - 72 = 58

d = 180 - 72 - 58 = 50

Answer:

C = 58

D = 50

Step-by-step explanation:

C is 58 as all angles on a straight line add up to 180 degrees

D is 50 as all angles within a triangle add up to 180 degrees

(72+58 = 130, 180-130 = 50)

Answer:

Hope this helps

Step-by-step explanation:

A: Duane makes bowls faster.

B) 18 hours

C) About 19.92 hours

Answer: all real numbers

Step-by-step explanation:

The sum of 6 and x is less than or equal to - 20.

Answer:  (6+x) ≤ -20

Answer:

23.6

Step-by-step explanation:

Answer:

23.6 is the correct answer

Answer: 5 or 9

Find the factors of the number 45.

1, 5, 9, 15

The numbers must be greater than 1 and less than 10.

Now, we must take 5 and 9.

5 x 9 = 45

9 x 5 = 45

The answers are 5 & 9.

Step-by-step explanation:

Answer:

6 dollars

Step-by-step explanation:

Hope this helps. :))

Answer:

February: +10

March: -5

April: +50

May: -25

June: -20

Step-by-step explanation:

Subtract each value in column 2 by 1000. A positive number means exceeding the monthly goal of 1000 pounds, a negative number means not achieving the goal.

Answer:

  A. (8 2/5, 8 2/5)

Step-by-step explanation:

You want to find point P such that ...

  AP : PB = 2 : 3

  3AP = 2PB . . . . . . . . cross multiply

  3(P -A) = 2(B -P) . . . recognize length XY = Y - X

  5P = 3A +2B . . . . .  collect P terms

  P = (3A +2B)/5 = (3(2, 6) +2(18, 12))/5 = (6+36, 18+24)/5= (42, 42)/5

  P = (8 2/5, 8 2/5) . . . . matches choice A

Answer:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

Step-by-step explanation:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

[tex]90+60+ 7x -12 = 7x+138[/tex]

Step-by-step explanation:

f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.

y = 3x - 1

3x = y + 1

x = 1/3(y + 1)

and now we rename x to y and y to x, so that we get a normal function definition :

y = 1/3(x + 1) = (1/3)x + 1/3

now we create the first derivative d/dx of this function :

y' = 1/3

since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function.

so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.

therefore also d/dx f^-1(11) = 1/3.

y = 2×sqrt(x)

sqrt(x) = y/2

x = y²/4

again we rename the variables, so that we get a normal function definition for the inverse function :

y = x²/4

the first derivative is :

y' = 2x/4 = x/2

so, d/dx f^-1(6) = 6/2 = 3

Use the inverse function theorem: if f(x) is continuously differentiable at x = a, and given f(a) = b, then f is invertible around x = a, and

[tex]\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}[/tex]

Both the given functions f(x) meet the conditions above. Note that you don't need to actually compute the inverse function itself.

If f(x) = 3x - 1, then f(x) = 11 when

3x - 1 = 11   ⇒   3x = 12   ⇒   x = 4

Now if f(4) = 11, it follows from the inverse function theorem that

[tex]\left(f^{-1}\right)'(11) = \dfrac1{f'(4)} = \boxed{\dfrac13}[/tex]

since f'(x) = 3.

If f(x) = 2√x, then f(x) = 6 when

2√x = 6   ⇒   √x = 3   ⇒   x = ±9

But note that f(x) is defined only for x ≥ 0, so we must take x = 9. Now if f(9) = 6, the inverse function theorem says

[tex]\left(f^{-1}\right)'(6) = \dfrac1{f'(9)} = \dfrac1{\frac1{\sqrt9}} = \boxed{3}[/tex]

since f'(x) = 1/√x.

Answer:

4 significant figures are in the number 0.3368

E, C, F are the answers.

Answer:

a) answer is "a"

b) answer is "-2b"

c) answer is "-c"

d) answer is "3c"

Step-by-step explanation:

Absolute value is positive value of something.

a>0 then a must be positive so absolute value means nothing if a is already positive. Therefore answer is a.

b<0, so b must be negative. absolute value makes 2b positive but you know b is negative so answer is -2b.

c<0 same as a except sign is flipped so answer is negative instead of positive.

c>=0, C is either 0 or positive so absolute value does nothing yet again so answer is just 3c.

Sorry is explanation wasn't through i'm only in middle school

a. | a | > 0, a is greater than and less than zero.

b. | 2b | if b < 0, b is not less than zero not greater than zero.

c. | c | if c < 0, c is not less than zero not greater than zero.

d.  | 3c | if c ≥ 0, c is greater than zero and less than zero.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

Given,

| a | > 0

∴ a is greater than and less than zero.

| 2b | if b < 0

b is not less than zero not greater than zero.

| c | if c < 0

c is not less than zero not greater than zero.

| 3c | if c ≥ 0.

c is greater than zero and less than zero.

learn more about modulus functions here :

https://brainly.com/question/13103168

#SPJ2

Answer:

Step-by-step explanation: