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3 years ago

Express (x + 10)^2 as a trinomial in standard form.

Mathematics

1 answer:

nydimaria [60]3 years ago

5 0

Answer:

x2-20x+100

Step-by-step explanation:

You have to factor the expression in order to get your answer

Do this by expanding out the expression: (x-10)(x-10) Then factor by multiplying each of the components! Use the FOIL acronym to help you. FOIL stands for First, Outer, Inner, Last. Meaning multiply the first numbers of the expressions together, then the outers, then the inner two numbers, then the last two numbers of the expression.

Multiply x and x to get , multiply x and -10 to get -10x, multiply -10 and x to get -10x, multiply -10 and -10 to get 100. Add them all together: . Then combine like terms

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The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lun

Luden [163]

Answer:

The expected value for a student to spend on lunch each day = $5.18

Step-by-step explanation:

Given the data:

Number of students______$ spent

2 students______________$10

1 student________________$8

12 students______________$6

23 students______________$5

8 students_______________$4

4 students_______________$3

Sample size, n = 50.

Let's first find the value on each amount spent with the formula:

$\frac{num. of students}{sample size} * dollar spent$

Therefore,

For $10:

$\frac{2}{50} * 10 = 0.4$

For $8:

$\frac{1}{50} * 8 = 0.16$ l

For $6:

$\frac{12}{50} * 6 = 1.44$

For $5:

$\frac{23}{50} * 5 = 2.3$

For $4:

$\frac{8}{50} * 4 = 0.64$

For $3:

$\frac{4}{50} * 3 = 0.24$

To find the expected value a student spends on lunch each day, let's add all the values together.

Expected value =

$0.4 + $0.16 + 1.44 +$2.3 + $0.64 + $0.24

= $5.18

Therefore, the expected value for a student to spend on lunch each day is $5.18

7 0

2 years ago

Find an n^th degree polynomial with real coefficients satisfying the given conditions. n = 3; -2 and 2 i are zeros; f(-1) = 15.

Ira Lisetskai [31]

So, n = 3, is a 3rd degree polynomial, roots are -2 and 2i

well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too

so, the roots are -2, 2i, -2i

now... $\bf \begin{cases}
x=-2\implies x+2=0\implies &(x+2)=0\\
x=2i\implies x-2i=0\implies &(x-2i)=0\\
x=-2i\implies x+2i=0\implies &(x+2i)=0
\end{cases}
\\\\\\
(x+2)\underline{(x-2i)(x+2i)}=0\\\\
-----------------------------\\\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
(x+2)[x^2-(2i)^2]=0\implies (x+2)[x^2-(2^2i^2)]=0
\\\\\\
(x+2)[x^2-(4\cdot -1)]=0\implies (x+2)(x^2+4)=0
\\\\\\
x^3+2x^2+4x+8=0$

now, if we check f(-1), we end up with 5, not 15
hmmm

so, how to turn our 5 to 15? well, 3*5, thus

$\bf 3(x^3+2x^2+4x+8)=f(x)\implies 3(5)=f(-1)\implies 15=f(-1)$

usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15

6 0

3 years ago

A triangle has a base of 17 inches and a area of 127.5 square inches. What is the height of the triangle?

zmey [24]

We know that area=0.5*base*height.

Thus, the equation would look like:
127.5=0.5*base*height

That means, 255 = base*height.
We know base is 17
Then, we divide 255 by 17. That gets us the height.
The height equals 15.

8 0

3 years ago

Which of the following shapes have an area of 48 square feet? Select all that apply.

yKpoI14uk [10]

I think 2,3,4 or B,C,D would be correct.

The area of a triangle is (b•h)/2
And the area of a rectangle and parallelogram would just be b•h

1) 8(6) = 48/2 =24

2) 9(10 2/3) = 96/2 =48

3) 19.2(2.5) = 48

4) 16(3) = 48

Hope this is right and hope it helps. Have a good day

4 0

3 years ago

One difference between an assembly line process flow and a continuous process flow is that on the assembly line the flow is disc

IgorLugansk [536]

Answer:

True

Step-by-step explanation:

Assemble line is a production process in which parts are joined to the products produced as a partially finished product.

Here the process flow is discreet that is assembled one at a time.

Continous process flow is a type of manufacturing products without disruption of the flow process.

As the name implies,it is continous.

6 0

3 years ago