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Marina CMI [18]
3 years ago
5

How many solutions can be found for the equation 4z + 2(z - 4) = 3z + 11

Mathematics
2 answers:
Novosadov [1.4K]3 years ago
5 0

Answer:

one

Step-by-step explanation:

i just took the test

Gnom [1K]3 years ago
4 0
4z+2(z-4)=3z+11  perform indicated multiplication on left side

4z+2z-8=3z+11  combine like terms on left side

6z/-8=3z+11  add 8 to both sides

6z=3z+19  subtract 3z from both sides

3z=19  divide both sides by 3

z=19/3 

z=6 1/3

So there is only one solution when z=6 1/3
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Geometry help please how do I do these?
trapecia [35]

Answer:

Question 7:

∠L = 124°

∠M = 124°

∠J = 118°

Question 8:

∠Q = 98°

∠T = 98°

∠R = 82°

Question 15:

m∠G = 110°

Question 16:

∠G = 60°

Question 17:

∠G = 80°

Question 18:

∠G = 70°

Step-by-step explanation:

The angles can be solving using Symmetry.

Question 7.

The sum of interior angles in an isosceles trapezoid is 360°, and because it is an  isosceles trapezoid

∠K = ∠J  = 118°

∠L = ∠M

∠K+∠J+∠L +∠M = 360°

236° + 2 ∠L = 360°

Therefore,

∠L = 124°

∠M = 124°

∠J = 118°

Question 8.

In a similar fashion,

∠Q+∠T+∠S +∠R = 360°

and

∠R = ∠S = 82°

∠Q = ∠T

∠Q+∠T + 164° = 360°

2∠Q + 164° = 360°

2∠Q = 196°

∠Q = ∠T  =98°.

Therefore,

∠Q = 98°

∠T = 98°

∠R = 82°

Question 15.

The sum of interior angles of a kite is 360°.

∠E + ∠G + ∠H + ∠F = 360°

Because the kite is symmetrical

∠E  = ∠G.

And since all the angles sum to 360°, we have

∠E +∠G + 100° +40° = 360°

2∠E = 140° = 360°

∠E  = 110° = ∠G.

Therefore,

m∠G = 110°

Question 16.

The angles

∠E = ∠G,

and since all the interior angles sum to 360°,

∠E + ∠G + ∠F +∠H = 360°

∠E + ∠G  + 150 + 90 = 360°

∠E + ∠G   = 120 °

∠E = 60° = ∠G

therefore,

∠G = 60°

Question 17.

The shape is a kite; therefore,

∠H = ∠F = 110°

and

∠H + ∠F + ∠E +∠G = 360°

220° + 60° + ∠G = 360°,

therefore,

∠G = 80°

Question 18.

The shape is a kite; therefore,

∠F = ∠H  = 90°

and

∠F +∠H + ∠E + ∠G = 360°

180° + 110° + ∠G  = 360°

therefore,

∠G = 70°.

3 0
3 years ago
Find the value of x.
kirza4 [7]
Hey there :)

Here we need to use Trigonometry!

The given angle is 61°
The opposite to the angle is 22 
So x is the adjacent

The trigonometric ratio that uses opposite and adjacent is tan
( I have uploaded a picture to help you )


tan α = \frac{opposite}{adjacent}
tan 61 = \frac{22}{adj}
adj = \frac{22}{tan(61)}
adj ≈ 12.19 ≈ 12

x = 12


5 0
3 years ago
Among all pairs of numbers whose difference is 6, find a pair whose product is as small as possible. What is the minimum product
kkurt [141]
Ummm if its multiply then its 1 and 6. is its addition then its 1 and 5 or 6 and 0. if its divide it would be 6 and 1. is its subtraction then it would be 7 and 1 or 6 and 0

3 0
3 years ago
write the equation in slope-intercept form of the line that has a slope of -3 and contains the point (4, -5).
Novosadov [1.4K]
You can answer this question by plugging the given values into point-slope form, which is y - y_{1} = m (x - x_{1}). M will represent slope and x_{1} and y_{1} will represent the x and y coordinates.

   y - y_{1} = m (x - x_{1})   Substitute in the values
y - (-5) = 4 (m - 4)   Cancel out the -(-5)
   y + 5 = 4 (m - 4)   Use the Distributive Property
   y + 5 = 4m - 16    Subtract 5 from both sides
       
         y = 4m - 21
 

3 0
3 years ago
A consumer report counted 72 low-quality, 112 medium-quality, and 711 high-quality computers based on a random sample. The repor
blsea [12.9K]

Answer:

high quality = 711/895

medium quality = 112/895

low quality = 72/895

Step-by-step explanation:

72 + 112 + 711 = 895

high quality = 711/895

medium quality = 112/895

low quality = 72/895

8 0
2 years ago
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