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Elden [556K]
3 years ago
5

True or false: The solution, root, x-intercept, and zero of a problem are the same.

Mathematics
2 answers:
Solnce55 [7]3 years ago
7 0
The answer to your question is true
cluponka [151]3 years ago
3 0
This is true . Solution , root , x and zero all are the same thing
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Suppose that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job and a new roof. Further, 7% of al
ivann1987 [24]

Answer:

0.0105

Step-by-step explanation:

given that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job and a new roof. Further, 7% of all houses that need a new roof also need new windows.

If total houses are 100, then 30 require a paint along.  15 require both paint and new roof.

Out of 15 houses which require new roof 7% need new windows

i.e. no of houses which need new windows = 15*7%\\=1.05

If there are total 100 houses, 1.05 houses require a new window

So probability that a randomly selectede house needs a new window

= 0.0105

8 0
2 years ago
Now consider the expression 4.0×103+4×102. determine the values of a and k when the value of this expression is written in scien
natta225 [31]
Let`s say that the expression is written in the form:a * 10^k.4 * 10^3 + 4 * 10^2 = = 4 * 10 * 10^2 + 4 * 10^2 = = 40 * 10^2 + 4 * 10^2 = = 44 * 10^2 = 4.4 * 10^3.Answer:a = 4.4 and k = 3 and the expression in the scientific notation is:4.4 * 10^3.

6 0
3 years ago
Read 2 more answers
the sum of three number is 202, the second is three more than the first number, the third number is three times the second numbe
sertanlavr [38]

Answer:

x = 38

y = 41

z = 123

Step-by-step explanation:

x + y + z = =202

y = x + 3

z = 3y = 3(x + 3) = 3x + 9

<u>x</u> + <u>y</u> + <u>z</u> = <u>x</u> + <u>x + 3</u> + <u>3x + 9</u> = 5x + 12 = 202

5x + 12 = 202

5x = 190

x = 38

y = x + 3 = 41

z = 3y = 123

4 0
3 years ago
It is worth 50 points so please help
Vladimir [108]

Answer:

12 inches is the maximum length for each cloth because 60,48 and 72 are all multiples of 12.

you will have 5 pieces of blue cloth, 4 pieces of gold cloth and 6 pieces of white cloth.

4 0
3 years ago
1.) What are the zeros of the polynomial? f(x)=x^4-x^3-16x^2+4x+48.
Lerok [7]

Answer:

3.) \displaystyle [x - 2][x^2 + 2][x + 4]

2.) \displaystyle 2\:complex\:solutions → x^2 + 3x + 6 >> -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2}

1.) \displaystyle 4, -3, 2, and\:-2

Step-by-step explanation:

3.) By the Rational Root Theorem, we would take the Least Common Divisor [LCD] between the leading coefficient of 1, and the initial value of −16, which is 1, but we will take 2 since it is the <em>fourth root</em> of 16; so this automatically makes our first factor of \displaystyle x - 2.Next, since the factor\divisor is in the form of \displaystyle x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

2| 1 2 −6 4 −16

↓ 2 8 4 16

__________________

1 4 2 8 0 → \displaystyle x^3 + 4x^2 + 2x + 8

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x⁴ + 2x³ - 6x² + 4x - 16]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x³, the 4x² follows right behind it, bringing 2x right up against it, and bringing up the rear, 8, giving you the quotient of \displaystyle x^3 + 4x^2 + 2x + 8.

However, we are not finished yet. This is our first quotient. The next step, while still using the Rational Root Theorem with our first quotient, is to take the Least Common Divisor [LCD] of the leading coefficient of 1, and the initial value of 8, which is −4, so this makes our next factor of \displaystyle x + 4.Then again, we use Synthetic Division because \displaystyle x + 4is in the form of \displaystyle x - c:

−4| 1 4 2 8

↓ −4 0 −8

_____________

1 0 2 0 → \displaystyle x^2 + 2

So altogether, we have our four factors of \displaystyle [x^2 + 2][x + 4][x - 2].

__________________________________________________________

2.) By the Rational Root Theorem again, this time, we will take −1, since the leading coefficient & variable\degree and the initial value do not share any common divisors other than the <em>special</em><em> </em><em>number</em> of 1, and it does not matter which integer of 1 you take first. This gives a factor of \displaystyle x + 1.Then start up Synthetic Division again:

−1| 1 3 5 −3 −6

↓ −1 −2 −3 6

__________________

1 2 3 −6 0 → \displaystyle x^3 + 2x^2 + 3x - 6

Now we take the other integer of 1 to get the other factor of \displaystyle x - 1,then repeat the process of Synthetic Division:

1| 1 2 3 −6

↓ 1 3 6

_____________

1 3 6 0 → \displaystyle x^2 + 3x + 6

So altogether, we have our three factors of \displaystyle [x - 1][x^2 + 3x + 6][x + 1].

Hold it now! Notice that \displaystyle x^2 + 3x + 6is unfactorable. Therefore, we have to apply the Quadratic Formula to get our two complex solutions, \displaystyle a + bi[or zeros in this matter]:

\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = x \\ \\ -3 ± \frac{\sqrt{3^2 - 4[1][6]}}{2[1]} = x \\ \\ -3 ± \frac{\sqrt{9 - 24}}{2} = x \\ \\ -3 ± \frac{\sqrt{-15}}{2} = x \\ \\ -3 ± i\frac{\sqrt{15}}{2} = x \\ \\ -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2} = x

__________________________________________________________

1.) By the Rational Root Theorem one more time, this time, we will take 4 since the initial value is 48 and that 4 is the root of the polynomial. This gives our automatic factor of \displaystyle x - 4.Then start up Synthetic Division again:

4| 1 −1 −16 4 48

↓ 4 12 −16 −48

___________________

1 3 −4 −12 0 → \displaystyle x^3 + 3x^2 - 4x - 12

We can then take −3 since it is a root of this polynomial, giving us the factor of \displaystyle x + 3:

−3| 1 3 −4 −12

↓ −3 0 12

_______________

1 0 −4 0 → \displaystyle x^2 - 4 >> [x - 2][x + 2]

So altogether, we have our four factors of \displaystyle [x - 2][x + 3][x + 2][x - 4],and when set to equal zero, you will get \displaystyle 4, -3, 2, and\:-2.

I am delighted to assist you anytime.

3 0
3 years ago
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