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3 years ago

What is the domain and range of f(x)=2|x-4|

1 answer:

8 0

Domain is all the numbers you can use for x, it's the input
range is the numbers you get from inputting the domain, it's te output

we can use all real numbers because no square roots of negatives or division of zero occur

domain is all real numbers

notice that when x goes to positive infinity, f(x) goes to positive infinity
when x goes to negative inifnity, f(x) goes to positive inifinty
but, as x approaches 4, the value of f(x) approaches 0

the lowest point on range is 0 and max is negative infinity

domain=all real numbers
range= from 0 to infinity

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What is the range for a x intercept of (5,0) and a y intercept of (0,3)

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Answer:

(5,0)=x1,y1

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3 years ago

Find the distance between the two points in simplest radical form.<br> (-1, -5) and (4,7)

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3 years ago

Factor f(x) = 4x3 + 15x2 – 24x + 5 into linear factors given that - 5 is a zero of f(x).15f(x) = 4x3 + 15x2 - 24x + 5 =(Factor c

Basile [38]

If x=-5 is a zero, then the first factor of the polynomial would be (x + 5 )

To find the other two factors we can divide the polynomial by the expression (x+5).

Using synthetic division, we have:

-5 I 4 15 -24 5 (Coefficients of the dividend)

I -20 25 -5 (Multiplying each coefficient by the results of the substraction and adding)

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4 -5 1 0 (Coefficients of the quotient)

The result of the division is 4x^2 - 5x + 1. Factoring it, we have:

4x^2 - 4x -x + 1 (Separating -5x into -x and -4x)

4x (x - 1) - (x -1) (Factoring each pair of terms)

(x-1)(4x-1) (Factoring using the common factor)

So the answer would be:

(x + 5 )(x-1)(4x-1)

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1 year ago

In Exercises 10 and 11, points B and D are points of tangency. Find the value(s) of x.<br>

Lemur [1.5K]

In both cases,

$AB^2=AD^2$

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So we have

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$(4x+7)^2=(6x-3)^2$

$16x^2+56x+49=36x^2-36x+9$

$20x^2-92x-40=0$

$5x^2-23x-10=0$

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(omit the negative solution because that would make at least one of AB or AD have negative length)

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$(4x^2-18x-10)^2=(x^2+x+4)^2$

$16x^4-144x^3+244x^2+360x+100=x^4+2x^3+9x^2+8x+16$

$15x^4-146x^3+235x^2+352x+84=0$

$(x-7)(3x+2)(5x^2-17x-6)=0\implies\boxed{x=-\dfrac23\text{ or }x=7}$

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3 years ago

In a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35. The followi

Naddika [18.5K]

Answer:

112

Step-by-step explanation:

Given that in a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35.

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Let us obtain regression equation of y on x.

Let y be the scores at age 35 and x at age 18

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The line passes through (100,100) being average of x and y

Hence regression line would be

$y-100=0.8(x-100)\\y = 0.8x+20$

a) Here given that x =115

Hence $y=0.80(115)+20\\=112$

the average score at age 35 for all the individuals who scored 115 at age 18, would be 112.

b) Prediction also would be the same 112.

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3 years ago