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3 years ago

Match each polynomial function w/ one of its factors.

Mathematics

2 answers:

gladu [14]3 years ago

8 0

Answer:

See below in bold.

Step-by-step explanation:

The first one looks like x + 3 might be a factor. By the Factor Theorem :To check we plug in x = -3 to see if the f(3) = 0.

f(3) = -27 - 27 + 39 + 15 = 0

So x+3 is a factor of x^3 - 3x^2 - 13x + 15.

x^3 - 2x^2 - x + 2

Because of the last term +2 , it looks like x - 2 might be a factor of this so we evaluate f(2)

f(2) = 8 - 8 - 2 + 2 = 0

So x - 2 is a factor of x^3 - 2x^2 - x + 2 .

x^4 + 3x^3 - 8x^2 + 5x - 25.

Because of the - 25 x + 5 could be a factor so try f(-5)

= (-5)^4 - 3* -125 - 8*25 + 5 * -5 - 25 = 0

So x + 5 is a factor of x^4 + 3x^3 - 8x^2 + 5x - 25.

Finally we check if (x + 4) is a factor of -x^3 + 13x - 12 :

f(-4) = - (-4)^3 + 13*-4 - 12 = 0.

So x + 4 is a factor of -x^3 + 13x - 12.

ololo11 [35]3 years ago

4 0

Answer: 1 goes with 2 4 goes with 3

Step-by-step explanation:

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Describe the characteristics of each set of numbers that make up the set of integers

Alex73 [517]

They have to correlate to each other
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3 years ago

What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

The multiplicative inverse of 5 in $Z_{13}$ is 8.

8 0

3 years ago

Solve 4e^2x-3=12 please help

Anestetic [448]

$4*e^{2x} -3 = 12$

Step 1:

Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.

$4*e^{2x} = 12+3$

$4*e^{2x} = 15$

Step 2:

Next we have 4 in multiplication on left side, so dividing right side by 4,

$e^{2x} = 15/4$

$e^{2x} = 3.75$

Step 3:

taking log on both sides

$ln ( e^{2x}) = ln(3.75)$

${2x} =ln 3.75$

Step 4:

Dividing right side by 2,

x= ln (3.75) /2 = 0.66088

Answer : x = 0.66088..

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3 years ago

Read 2 more answers

Iris wants to buy sneakers at $15 each and high heels at $30 each. Write an algebraic expression to find the total cost of the s

kogti [31]

Answer: 30y + 15x

If x is for sneakers, and y is for high heels, plug 15 in for a and 30 in for b. This means that x is how many sneakers she buys, and y is how many high heels she buys. The equation altogether represents the total amount of her purchases.

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3 years ago

a dime is dropped from a building at 1.024 ft . if the equation for height as a function of time is h(t)=-16t^2+ initial height

babunello [35]

Answer:

The dime hits the ground after 8 sec.

Step-by-step explanation:

Set h(t) = -16t^2 + h(0) equal to 0: -16t^2 + 1,024 ft = 0, or:

16t^2 = 1,024 ft, or:

t^2 = 64 ft^2

Then t = +8 sec

The dime hits the ground after 8 sec.

7 0

2 years ago