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satela [25.4K]
3 years ago
13

What is the solution to the equation 2/3 x + 1 = 1/6 x -7

Mathematics
1 answer:
slamgirl [31]3 years ago
3 0

Answer:

x = -16

Step-by-step explanation:

2/3 x + 1 = 1/6 x -7

Multiply both sides of the equation by 6 to eliminate the fraction

6*(2/3 x + 1) =6( 1/6 x -7)

4x +6 = x -42

Subtract x from each side

4x-x +6 = -42

3x +6= - 42

Subtract 6 from each side

3x+6-6 = -42-6

3x = -48

3x/3 = -48/3

x = -16

You might be interested in
From a point 100 m from a building the angles of elevation of the top and bottom of a flagpole atop a building are 54.5 degrees
AnnZ [28]

Answer:60ft

Step-by-step explanation:The height of the flagpole is approximately  

60

feet.

Explanation:

Always try to draw a diagram.

enter image source here

We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.

Since the angle in the corner of the larger right triangle measures  

42

˚

, the top angle in this triangle measures  

180

˚

−

90

˚

−

42

˚

=

48

˚

.

By basic trig ratios, we can find the height of the building with the flag pole on top, call it  

H

.

tan

42

˚

1

=

H

500

H

=

500

tan

42

˚

I would keep it in exact form until the last step.

We now devise an expression for the height of the building (without the flag pole). Call it  

a

tan

38

˚

1

=

a

500

a

=

500

tan

38

˚

We can now state that

h

=

H

−

a

h

=

500

tan

42

˚

−

500

tan

38

˚

h

≈

59.559

≈

60

feet

Hopefully this helps!

Answer link

EET-AP

Apr 10, 2017

The flagpole is  

60

f

t

in height to the nearest foot.

Explanation:

1) The flagpole is on top of a building.

2)Angles of elevation both measured from point  

500

f

t

from building

3) Angle of elevation to the top of building is  

38

d

e

g

4) Angle of elevation to the top of flagpole is  

42

d

e

g

The information above will provide us with two right angle triangles, one smaller one inside a larger one.

Both will have a base of  

500

f

t

.

The smaller triangle will have a base angle  

β

of  

38

deg opposite the  

90

deg, and the larger triangle will have a base angle  

β

of  

42

deg.

From this information we can find the heights of the building and the building + pole using the definition of the tangent of the two base angles  

β

:

tan

(

β

)

=

o

p

p

a

d

j

where the  

o

p

p

is the height and the  

a

d

j

is the  

500

f

t

o

p

p

(

b

u

i

l

d

)

=

tan

(

38

)

⋅

(

500

f

t

)

=

390.6

f

t

=

height of building

o

p

p

(

f

l

a

g

)

=

tan

(

42

)

⋅

(

500

f

t

)

=

450.2

f

t

=

height of building + pole

Then to the nearest foot the height of the flagpole is:

450.2

f

t

−

390.6

f

t

=

60

f

t

4 0
3 years ago
What si the value of X?
Licemer1 [7]

Answer:

this is a required answer.

4 0
2 years ago
2. In right triangle RST with right angle S the m4R = 24°. What is the
const2013 [10]

Sum of the interior angles of any triangle equal 180° ;

So :

90° + 24° + T = 180°

114° + T = 180°

subtract both sides 114

T = 180° - 114°

T = 66°

_________________________________

And we're done....

♥️♥️♥️♥️♥️

8 0
3 years ago
Read 2 more answers
Sketch a graph that represents the situation.
Marysya12 [62]

Answer:

$620

Step-by-step explanation:

 20 x 10 = 200 + 420 = 620

hope this helped. :)

p.s. can I get brainliest?

5 0
3 years ago
Solve the equation by completing the square m^2+6m-77=-5
Grace [21]
Maybe you thought about this:
m^2+6m-77+5=0 => m^2+6m-72=0 => m^2+ 2*3*m+3^2-3^2-72=0
=> m^2+2*3*x+3^2= (m+3)^2 this is the complete square of the binomial, we will still keep it =>
(m+3)^2 -9 -72=0 => (m+3)^2 - 81 = 0 => (m+3)^2 - 9^2 = 0
Now we got the difference squares, it mean a^2 - b^2 = (a-b) (a+b)
In according to this => (m+3-9) (m+3+9) = 0 =>
(m-6) (m+12)=0 => m-6=0 or m+12=0 => m1=6 or m2= -12 !!!!
Are you satisfied with this solution?

6 0
3 years ago
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