1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Allushta [10]
3 years ago
14

An angle measures 46° more than the measure of its supplementary angle. What is the measure of each angle?

Mathematics
1 answer:
Alona [7]3 years ago
6 0

Answer:

67 degree

113 degree

Step-by-step explanation:

Supplementary angles are angles that measure up to 180 degrees. For example, if one angle measures 60 degree, the other angle would measure (180 - 60) 120 degrees

Let x represent the smaller angle

The bigger angle = x + 46

We know that both the smaller and the bigger angle would add up to 180, thus this equation can be written :

x + 46 + x = 180

2x + 46 = 180

Collect like terms

2x = 180 - 46

2x = 134

Divide both sides by 2

x = 67 degrees

the bigger angle = 67 + 46 = 113 degree

You might be interested in
What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the uni
puteri [66]

Answer:

We have two rates, A and B.

If we want that the units of A can be converted into the units of B, then we must have that the units of A represent the same measure that the units of B.

What does this mean?

For example, if A is written in distance over time, then B must also must have units of distance over time.

An example would be:

units for distance = meter, kilometer, feet, etc.

units for time = hour, minute, second, etc-

Then we could have:

[A] = [km/h]

[B] = [m/min]

Then the units of A could be converted into the ones of B, because both of them have the same physical meaning.

Concluding, you only can convert units that represent the same physical quantity, for example, if you have one quantity in meters, for example:

10m

You only can convert this to other units of distance, remember to do the correct conversion, if we would want to write this in cm, you should remember that:

1m = 100cm

Then, 10 times one meter is 10 times 100 cm

10m = 10*(1m) = 10*(100cm) = 1000cm

7 0
3 years ago
1) Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given
neonofarm [45]

Answer:

Check below, please

Step-by-step explanation:

Hello!

1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

x_{1}=2\\x_{2}=2-\frac{f(2)}{f'(2)}=2.5\\x_{3}=2.5-\frac{f(2.5)}{f'(2.5)}\approx 2.4166\\x_{4}=2.4166-\frac{f(2.4166)}{f'(2.4166)}\approx 2.41421\\x_{5}=2.41421-\frac{f(2.41421)}{f'(2.41421)}\approx \mathbf{2.41421}

2)  Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.

We can rewrite it as: x^2-2x-4=0

x_{1}=-1.1\\x_{2}=-1.1-\frac{f(-1.1)}{f'(-1.1)}=-1.24047\\x_{3}=-1.24047-\frac{f(1.24047)}{f'(1.24047)}\approx -1.23607\\x_{4}=-1.23607-\frac{f(-1.23607)}{f'(-1.23607)}\approx -1.23606\\x_{5}=-1.23606-\frac{f(-1.23606)}{f'(-1.23606)}\approx \mathbf{-1.23606}

As for

x_{1}=3.2\\x_{2}=3.2-\frac{f(3.2)}{f'(3.2)}=3.23636\\x_{3}=3.23636-\frac{f(3.23636)}{f'(3.23636)}\approx 3.23606\\x_{4}=3.23606-\frac{f(3.23606)}{f'(3.23606)}\approx \mathbf{3.23606}\\

3) Rewriting and calculating its derivative. Remember to do it, in radians.

5\cos(x)-x-1=0 \:and f'(x)=-5\sin(x)-1

x_{1}=1\\x_{2}=1-\frac{f(1)}{f'(1)}=1.13471\\x_{3}=1.13471-\frac{f(1.13471)}{f'(1.13471)}\approx 1.13060\\x_{4}=1.13060-\frac{f(1.13060)}{f'(1.13060)}\approx 1.13059\\x_{5}= 1.13059-\frac{f( 1.13059)}{f'( 1.13059)}\approx \mathbf{ 1.13059}

For the second root, let's try -1.5

x_{1}=-1.5\\x_{2}=-1.5-\frac{f(-1.5)}{f'(-1.5)}=-1.71409\\x_{3}=-1.71409-\frac{f(-1.71409)}{f'(-1.71409)}\approx -1.71410\\x_{4}=-1.71410-\frac{f(-1.71410)}{f'(-1.71410)}\approx \mathbf{-1.71410}\\

For x=-3.9, last root.

x_{1}=-3.9\\x_{2}=-3.9-\frac{f(-3.9)}{f'(-3.9)}=-4.06438\\x_{3}=-4.06438-\frac{f(-4.06438)}{f'(-4.06438)}\approx -4.05507\\x_{4}=-4.05507-\frac{f(-4.05507)}{f'(-4.05507)}\approx \mathbf{-4.05507}\\

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.

x_{n+1}=x_{n}-\frac{f'(n)}{f''(n)}

f(x)=x^6-x^4+3x^3-2x

\mathbf{f'(x)=6x^5-4x^3+9x^2-2}

\mathbf{f''(x)=30x^4-12x^2+18x}

For -1.2

x_{1}=-1.2\\x_{2}=-1.2-\frac{f'(-1.2)}{f''(-1.2)}=-1.32611\\x_{3}=-1.32611-\frac{f'(-1.32611)}{f''(-1.32611)}\approx -1.29575\\x_{4}=-1.29575-\frac{f'(-1.29575)}{f''(-4.05507)}\approx -1.29325\\x_{5}= -1.29325-\frac{f'( -1.29325)}{f''( -1.29325)}\approx  -1.29322\\x_{6}= -1.29322-\frac{f'( -1.29322)}{f''( -1.29322)}\approx  \mathbf{-1.29322}\\

For x=0.4

x_{1}=0.4\\x_{2}=0.4\frac{f'(0.4)}{f''(0.4)}=0.52476\\x_{3}=0.52476-\frac{f'(0.52476)}{f''(0.52476)}\approx 0.50823\\x_{4}=0.50823-\frac{f'(0.50823)}{f''(0.50823)}\approx 0.50785\\x_{5}= 0.50785-\frac{f'(0.50785)}{f''(0.50785)}\approx  \mathbf{0.50785}\\

and for x=-0.4

x_{1}=-0.4\\x_{2}=-0.4\frac{f'(-0.4)}{f''(-0.4)}=-0.44375\\x_{3}=-0.44375-\frac{f'(-0.44375)}{f''(-0.44375)}\approx -0.44173\\x_{4}=-0.44173-\frac{f'(-0.44173)}{f''(-0.44173)}\approx \mathbf{-0.44173}\\

These roots (in bold) are the critical numbers

3 0
2 years ago
I need help with this! Quick ASAP?
sp2606 [1]

Answer:

a) F

b) B, E, D

Step-by-step explanation:

a) The segment with the greatest gradient has the largest change in y-values per unit change in x-values

From the given option, the rate of change of the <em>y </em>to the<em> </em>x-values of B = the gradient = (4 units)/(2 units) = 2

The gradient of F = (-3units)/(1 unit) = -3

The gradient of A = 4/4 = 1

The gradient of C = -2/5

The gradient of D = 2/6 = 1/3

The gradient of E = 3/4

The segment with the greatest gradient is F

b) The steepest segment has the higher gradient

From their calculated we have;

The gradient of segment B = 2 therefore, B is steeper than E that has a gradient of 3/4, and E is steeper than D, as the gradient of D = 1/3

Therefore, we have;

B, E, D.

6 0
3 years ago
What is in the middle of 0 and 1
Mashcka [7]

Answer:

.5

Step-by-step explanation:

That 0 between 1 is .5

8 0
3 years ago
Read 2 more answers
Which of the following options are solutions to the inequality f≥ 100
Klio2033 [76]

Answer:

f=100

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • Solve for x <br> - 4x + 5 = -2x-1
    6·2 answers
  • I need help simplifying this expression ( 7y - 8 + 6y - 3) please explain thanks !
    7·2 answers
  • What is the slope-intercept equation of the line below?​
    13·1 answer
  • How do you draw a triangle that has no right side
    12·1 answer
  • A piece rate worker is paid ____.
    10·2 answers
  • Can someone help me with this ​
    11·2 answers
  • 1 of 6
    13·1 answer
  • Calculator
    15·1 answer
  • I will give brainliest if answered correctly :D 5/1 (the fraction) MINUS 6!
    12·2 answers
  • Find the area of a regular octagon with an apothem length of 10 and a side length of 6.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!