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Ahat [919]
3 years ago
11

An angle measures 114° less than the measure of its supplementary angle. What is the measure of each angle?

Mathematics
1 answer:
dezoksy [38]3 years ago
3 0

Answer:

66°

Step-by-step explanation:

x+114°=180°

x+114°-114°=180°-114°

x=66°

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Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely
navik [9.2K]

Answer:

Never

Never

Never

Step-by-step explanation:

The equations given are

2x1−6x2−4x3 = 6 ....... (1)

−x1+ax2+4x3 = −1 ........(2)

2x1−5x2−2x3 = 9 ..........(3)

the values of a for which the system of linear equations has no solutions

Let first add equation 1 and 2. Also equation 2 and 3. This will result to

X1 + (a X2 - 6X2) - 0 = 5

And

X1 + (aX2-5X2) + 2X3 = 8

Since X2 and X3 can't be cancelled out, we conclude that the value of a is never.

a unique solution,

Let first add equation 1 and 2. Also equation 2 and 3. This will result to

X1 + (a X2 - 6X2) - 0 = 5

And

X1 + (aX2-5X2) + 2X3 = 8

The value of a = never

infinitely many solutions. 

Divide equation 1 by 2 we will get

X1 - 3X2 - 2X3 =3

Add the above equation with equation 3. This will result to

3X1 - 8X2 - 4X3 = 12

Everything ought to be the same. Since they're not.

Value of a = never.

4 0
3 years ago
What is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2
satela [25.4K]

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

If y = 2\cdot x + 3 is a line <em>tangent</em> to the parabola y = c\cdot x^{2}, then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:

2\cdot c \cdot x = 2 (1)

Then, we have the following system of equations:

y = 2\cdot x + 3 (1)

y = c\cdot x^{2} (2)

c\cdot x = 1 (3)

Whose solution is shown below:

By (3):

c =\frac{1}{x}

(3) in (2):

y = x (4)

(4) in (1):

y = -3

x = -3

c = -\frac{1}{3}

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

We kindly invite to check this question on tangent lines: brainly.com/question/13424370

3 0
2 years ago
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
antoniya [11.8K]
10 cents, cause the {ball +$1.00=$1.10} subtract $1 from both sides the ball=$0.10
8 0
3 years ago
Read 2 more answers
1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually.
DaniilM [7]

Answer:

Step-by-step explanation:

a) We would use the formula for exponential growth model which is expressed as

y = b(1 + r)^t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 5655

r = 1.4% = 1.4/100 = 0.014

Therefore, the equation would be

y = 5655(1 + 0.014)^t

y = 5655(1.014)^t

b) in 2022, t = 2022 - 2010 = 12 years

y = 5655(1.014)^12

y = 6682

6 0
3 years ago
If Tina cuts a lawn by herself, she can finish in 5 hours. If bill cuts the same lawn by himself it takes him two hours longer t
shtirl [24]
Tina can finish in 5 hours
Bill takes two hours longer than Tina.
5+2=7
Bill takes 7 hours to cut the lawn.
7+5=12
It takes both of them working together 12 hours. Hope this helped!
8 0
3 years ago
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