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4 years ago

What is the measure of angle A in the triangle?

Mathematics

2 answers:

Ilya [14]4 years ago

8 0

Answer:

m<A = 50

Step-by-step explanation:

2x - 10 + 70 + x + 30 = 180

3x + 90 = 180

3x = 90

x = 30

* plug back in*

m <A = 2(30)-10

m <A = 50

musickatia [10]4 years ago

3 0

Answer:

A = 50

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

A+B+C =180

2x-10 + 70 + x+30 = 180

Combine like terms

3x +90 = 180

Subtract 90 from each side

3x +90-90 = 180-90

3x= 90

Divide each side by 3

3x/3=90/3

x =30

We want to find A

A =2x-10

= 2*30 -10

=60-10

=50

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Given: -7x < -21. Choose the solution set. {x | x < -3} {x | x > -3} {x | x < 3} {x | x > 3}

blondinia [14]

First, simplify the inequality by getting the x term with a coefficient of 1.

Divide both sides by -7. When you multiply or divide an equality by a negative number, you flip the inequality sign the opposite way.

-7x / -7 < -21 / -7
x > 3

In set build notation is would look like this: {x | x > 3}

Which would be read as "the set of all x, such that, x is greater than 3".

5 0

4 years ago

The center of an ellipse is (−9,3) . One focus is (−13,3) . The major axis is 18 units long. What is the equation of the ellipse

Montano1993 [528]

The equation of the ellipse in standard form is:

$\frac{(x+9)^{2}}{81}+\frac{(y-3)^{2}}{65}=1$

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h , k)

and major axis parallel to x-axis is $\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

1. The length of the major axis is 2a

2. The coordinates of the vertices are (h ± a , k )

3. The coordinates of the foci are (h ± c , k), where c² = a² - b²

∵ The center of the ellipse is (-9 , 3)

∴ h = -9 , k = 3

∵ One focus is (-13 , 3)

∴ Major axis parallel to x-axis

∵ The length of the major axis = 2a

∵ The length of the major axis = 18

∴ 2a = 18

- Divide both sides by 2

∴ a = 9

∵ The coordinates of the foci are (h ± c , k)

∵ One focus is (-13 , 3)

∴ h ± c = -13

∵ h = -9

∴ -9 - c = -13

- Add 9 to both sides

∴ -c = -4

- Divide both sides by -1

∴ c = 4

∵ c² = a² - b²

∵ c = 4 and a = 9

∴ (4)² = (9)² - b²

∴ 16 = 81 - b²

- Subtract 81 from both sides

∴ -65 = -b²

- Divide both sides by -1

∴ b² = 65

- Substitute the values of a² and b² in the equation of the ellipse

∵ a² = (9)² = 81

∵ b² = 65

∵ h = -9 and k = 3

∵ $\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

- Substitute the values in the equation

∴ $\frac{(x+9)^{2}}{81}+\frac{(y-3)^{2}}{65}=1$

The equation of the ellipse in standard form is:

$\frac{(x+9)^{2}}{81}+\frac{(y-3)^{2}}{65}=1$

Learn more:

You can learn more about equations of conics equations in brainly.com/question/3333996

brainly.com/question/9390381

#LearnwithBrainly

8 0

3 years ago

In a plan for area codes, the first digit could be any number from 3 though 9, the second digit was either 0 or 4, and the third

Tanya [424]

<h2>Answer:126 ways</h2>

Step-by-step explanation:

Given that the first digit could be any number from $3$ though $9$ .

So,there are $7$ ways to choose the first digit.

Given that the second digit was either $0$ or $4$ .

So,there are $2$ ways to choose the second digit.

Given that the third digit could be any number except $0$ .

So,there are $9$ ways to choose the third digit.

The number of different codes possible is the product of number of ways of choosing first digit,number of ways of choosing second digit and number of ways of choosing third digit.

Total ways are $7\times 2\times 9=126$ ways