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3 years ago

If the ratio of b to a is equal to 6 and the difference of b and a is 12, what is the value of a?

Mathematics

1 answer:

Reil [10]3 years ago

3 0

Answer:

a = 2.4

Step-by-step explanation:

The problem statement tells you ...

b/a = 6

b - a = 12

Using the first equation, we can write an expression for b:

b = 6a . . . . . . . multiply both sides by "a"

This can be substituted into the second equation to find a value for "a":

6a -a = 12

5a = 12

a = 12/5 = 2.4

The value of a is 2.4.

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Solve the system of equations 5x+9y+9z=5 4x+9y+6z=10 2x+2y+5z=9

erma4kov [3.2K]

Answer:

{x,y,z} = {-116,28,37}

Step-by-step explanation:

// Solve equation [3] for the variable z

[3] 5z = -2x - 2y + 9

[3] z = -2x/5 - 2y/5 + 9/5

__________________________________________________________

// Plug this in for variable z in equation [1]

[1] 5x + 9y + 9•(-2x/5-2y/5+9/5) = 5

[1] 7x/5 + 27y/5 = -56/5

[1] 7x + 27y = -56

__________________________________________________________

// Plug this in for variable z in equation [2]

[2] 4x + 9y + 6•(-2x/5-2y/5+9/5) = 10

[2] 8x/5 + 33y/5 = -4/5

[2] 8x + 33y = -4

__________________________________________________________

// Solve equation [2] for the variable y

[2] 33y = -8x - 4

[2] y = -8x/33 - 4/33

__________________________________________________________

// Plug this in for variable y in equation [1]

[1] 7x + 27•(-8x/33-4/33) = -56

[1] 5x/11 = -580/11

[1] 5x = -580

__________________________________________________________

// Solve equation [1] for the variable x

[1] 5x = - 580

[1] x = - 116

__________________________________________________________

// By now we know this much :

x = -116

y = -8x/33-4/33

z = -2x/5-2y/5+9/5

__________________________________________________________

// Use the x value to solve for y

y = -(8/33)(-116)-4/33 = 28

__________________________________________________________

// Use the x and y values to solve for z

z = -(2/5)(-116)-(2/5)(28)+9/5 = 37

╦────────────────────────────╦

│Hope this helped _____________________│

│~Derelis ____________________________ │

╨___________________________________╨

4 0

3 years ago

1.What is the equation of the line perpendicular to that passes through ? Write your answer in slope-intercept form. Show your

Juliette [100K]

Answer:

1. Use a compass to make arc marks which intersect above and below then connect.

2. $y=\frac{1}{3}x + 2$

Step-by-step explanation:

1. To construct a perpendicular line, use a compass to draw arc marks from one end of the segment through point P. Then repeat this again at the other end. This means at point P there will be two intersecting arc marks. Repeat the process down below with the same radius as used above. Then connect the two intersections.

2. The point slope form of a line is $(y-y_1)=m(x-x_1)$ where $x_1=-3\\y_1=1$ . We write

$(y-1)=m(x--3)\\(y-1)=m(x+3)$

Since the line is to be perpendicular to the line shown it will have the negative reciprocal to the slope of the function 3x+y =-8. To find m, rearrange the function to be y=-8-3x. The slope is -3 and the negative reciprocal will be 1/3.

$(y-1)=\frac{1}{3}(x+3)$

Simplify for slope intercept form.

$(y-1)=\frac{1}{3}(x+3)\\(y-1)=\frac{1}{3}x+1\\y=\frac{1}{3}x + 2$

3 0

3 years ago

What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

3 years ago

The number part when a number and a variable are multiplied together in a term is called the _____.

77julia77 [94]

Answer:

Coefficient

Step-by-step explanation:

-Usually a combination of variables and constants are multiplied to get a product.

-The constant or number part in the multiplication process is called the Coefficient

7 0

2 years ago

The New Shanghai Restaurant offers a choice of two appetizers, three choices of soups, and eight choices of entrees for its lunc

lesya [120]

48 different <span>lunches can be ordered from the restaurant's lunch special menu</span>

4 0

3 years ago