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Black_prince [1.1K]
3 years ago
9

How would you explain triangle classifications in your own words?

Mathematics
1 answer:
balandron [24]3 years ago
8 0

Answer:

A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.

The sum of the length of two sides of a triangle is always greater than the length of the third side.

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Classify each conic section and write its equations in standard form. Show work.
svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0
2 years ago
Can someone explain how to do it aswell please and thank you
Paul [167]

Answer:

B: 24ft^2

Step-by-step explanation:

Area of triangle = (base x height)/2

Step 1: form an equation

a = (12ft x 4ft)/2

Step 2: solve equation

a = 48ft^2 / 2

a = 24ft^2

*the base is the measurement for the bottom of a triangle while height is the measurement of the length from the bottom to the top of a triangle*

8 0
3 years ago
Read 2 more answers
A rectangular window pane has an area of 15x^2 - 19x + 6. The width of the window pane is 3x - 2. What is the length of the wind
almond37 [142]
Length= 5x-2 because 15x^2-10x-9x+6 is (5x-2) and (3x-2) 
LW=A
L={(5x-2)(3x-2)}/(3x-2)=5x-2
7 0
3 years ago
A manager wants to determine the number of containers to use for incoming parts for a kanban system to be installed next month.
qwelly [4]

Answer:

2 containers should be used

As the system improves, neither more or fewer containers be required

Step-by-step explanation:

According to the given data we have the following:

D=83 pieces per hour.

T=80 minutes=1.33 hour

X=0.18

C=53

In order to calculate how many containers should be used we would have to use the following formula:

Number of containers=<u>DT(1+X)</u>

                                         C

Number of containers=<u>(83)(1.33)(1+0.18)</u>

                                                 53

Number of containers=2.45=2

2 containers should be used.

As the system improves, neither more or fewer containers be required

8 0
3 years ago
10 men and 5 women are meeting in a conference room. Four people are chosen at random from the 15 to form a committee. (a) What
nata0808 [166]

Answer:

Step-by-step explanation:

Given

There are 10 men and 5 women in a conference room

total People=15

(a)Probability that the committee consists of 2 men and 2 women

we have to select from 10 men and 5 women

P=\frac{^5C_2\times ^{10}C_2}{^{15}C_4}

(b)Bob and Jane end up on the same committee

as bob and Jane are necessary to include so there are 4 women and 9 men left to select remaining 2 person

P=\frac{^{13}C_2}{^{15}C_4}

(c)Bob is in the committee but Jane is not

9 men and 4 women left to choose other 3 person

P=\frac{^{13}C_3}{^{15C_4}}

7 0
3 years ago
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