Translate the following verbal phrase into a mathematical expression.

What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b square

geniusboy [140]

Answer:

$x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

A quadratic can generally be expressed as: $y=ax^2+bx+c$

So using the equation you gave: $0=x^2-5x-1$

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

$x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

5 0

1 year ago

Four congruent isosceles right triangles are cut from the 4 corners of a square with a side of 20 units. The length of one leg o

yanalaym [24]

Answer:

368 sq. units.

Step-by-step explanation:

We have a square of side lengths 20 units and we cut four congruent isosceles right triangles from the corners of the square.

Now, the four isosceles right triangles have one leg equal to 4 units.

Therefore, the area of four triangles = $4 \times ( \frac{1}{2} \times 4 \times 4) = 32$ sq. units.

Now, we have the area of the given square is (20 × 20) = 400 sq. units.

Therefore, the area of the remaining octagon will be (400 - 32) = 368 sq. units. (Answer)

7 0

2 years ago

Which of the following lists of orders pairs is a funtion

nordsb [41]

Answer:

D

Step-by-step explanation:

For it to be a function, every x value must have 1 unique y value ONLY.

In option A, you can see that the x value of 1 has 2 y values, 1 & 5. So it's not a function.

In option B, you can see that the x value of 0 has 2 y values, 0 & -4. Moreover, the x value of 4 also has 2 y values, 2 & -2. So it's not a function.

In option C, you can see that the x value of -2 has 2 y values, 4 & -4. This is not a function as well.

In option D, each x value has a unique y value that are different. So this is a function.

Answer is option D.

5 0

2 years ago

Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Vilka [71]

Answer: Choice B) 1/3, 1/4, 1/5, 1/6

=============================================

Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

a_1 = ( 2! )/( 3! )

a_1 = ( 2*1 )/( 3*2*1 )

a_1 = 2/6

a_1 = 1/3

The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

------------

Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

a_2 = 6/24

a_2 = 1/4

The second term is 1/4

------------

Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

a_3 = 1/5

The third term is 1/5

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Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

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The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

4 0

2 years ago

What is the area of the figure? Use 3.14 for π. Round to the nearest hundredth if necessary.

vfiekz [6]

Answer:

81.12 cm²

Step-by-step explanation:

The area for a semicircle can be figured with this formula: (πr²)/2. The triangle's area formula is bh/2.

(3.14 * 4²)/2 + (14 * 8)/2 (Work the operations in parentheses first.)

(3.14 * 16)/2 + 112/2

50.24/2 + 112/2 (Divide 50.24 by 2. Do the same for 112.)

25.12 + 56 (Add 25.12 & 56.)

81.12 cm²

The area of the figure is 81.12 cm².

7 0

2 years ago