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Sauron [17]
3 years ago
7

Which of the following would you add to each side of the equation x-9=12 to get the variable by itself?

Mathematics
1 answer:
VLD [36.1K]3 years ago
6 0
X-9=12
x-9+9=12+9
You need to add 9 to each side of the equation.
x=21
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A grocery store sells bags of oranges in two different sizes the 3 pound bag $4 the 8 pound bag cost $9 which cost less
timofeeve [1]

Answer:

The 8 pounds bag

Step-by-step explanation:

Case 1 :

a pound cost 4/3

case 2 :

a pound cost 9/8

4×8 > 9×3

then

\frac{4}{3} >\frac{9}{8}

Therefore the 8 pound bag costs less

7 0
3 years ago
X - 3y +3=0
Arte-miy333 [17]

Answer:

We know that for a line:

y = a*x + b

where a is the slope and b is the y-intercept.

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 =  y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3  = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y =  -(3/4)*(- (48/91)*a - 51/7) - (5/4)

  = (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 =  (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91)  + 51/7)^2 + ( -(36/91)*a  + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a  - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 +  a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) +  (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

a = \frac{-23.47  \pm  \sqrt{23.47^2 - 4*2.49*39.4}  }{2*2.49} \\\\a =  \frac{-23.47  \pm  12.57 }{4.98}

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98  = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

4 0
2 years ago
Find the inverse of h(x)=(2x-4)/3
Agata [3.3K]

Answer:

The inverse of the h(x) is h^{-1}(x)=\frac{3x}{2}+2           Step-by-step explanation:

Given : Expression h(x)=\frac{2x-4}{3}

To find : The inverse of the expression ?

Solution :

Expression h(x)=\frac{2x-4}{3}

Let, h(x)=y then  y=\frac{2x-4}{3}

For inverse we replace the value of x and y and find the value of y in terms of x.

Replace the value of x and y,

x=\frac{2y-4}{3}

Solve for y by cross multiply,

3x=2y-4

Adding 4 both side,

3x+4=2y

Dividing by 2 both side,

\frac{3x+4}{2}=y

Therefore, The inverse of the h(x) is h^{-1}(x)=\frac{3x}{2}+2

5 0
3 years ago
Read 2 more answers
9 times the quantity of 12 less than a number x is 24. Write in an algebraic expression.
kiruha [24]

Answer:

9(x-12)=24

Step-by-step explanation:

5 0
2 years ago
Terri owns a computer repair shop. Her revenue at the end of last month was $8,000. What is Terri's Run Rate?
Ilia_Sergeevich [38]

Based on the information given Terri's Run Rate is $96,000.

<h3>Run rate</h3>

Using this formula

Run rate=Revenue for the Period × Number of months in a year

Where:

Revenue for the Period =$8,000

Number of months in a year=12 months

Let plug in the formula

Run rate=$8,000×12 months

Run rate=$96,000

Inconclusion Terri's Run Rate is $96,000.

Learn more about run rate here:brainly.com/question/16134508

6 0
2 years ago
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