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3 years ago

Compare and contrast Converse and Inverse. Explain.

1 answer:

max2010maxim [7]3 years ago

5 0

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. ... To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”

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2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

| 0 -1 -9 -26 -24

1 9 26 24 0

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

| 0 -2 -14 -24

1 7 12 0

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

| 0 -3 -12

1 4 0

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

A line passes through (1,-1) and (3,5) . What is the equation of the line in slope-intercept form?

Mumz [18]

(1,-1) and (3,5)

Find slope first

y=mx+b

slope is also m

b is y-intercept

slope = y2-y1/x2-x1

x1=1

x2=3

y1=-1

y2=5

5-(-1)/(3)-(1)

6/2=3

y=3x+b

use (1,-1) into y=3x+b ( using substitution method)

-1=3(1)+b

-1=3+b

Move 3 to the other side

Sign changes from +3 to -3

-1-3+3-3+b

b=-4

Answer: C.) Y = 3x-4

3 0

3 years ago

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Maggie volunteered to bake a cake she decided to double the recipe if the original recipe calls for 3/4 cup brown sugar how much

zlopas [31]

Answer:

3/2

Step-by-step explanation:

3/4 * 2 = 6/4 = 3/2

7 0

3 years ago

What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function?

bonufazy [111]

The correct answer is:

Any real number for x except 5, and any real number for y.

Explanation:

A function is a relation in which each element of the domain, or x-value, is mapped to one element of the range, or y-value. This means that no x can be mapped to more than one y, so if we have the same number used twice for x, we do not have a function.

This means that 5 cannot be used for x in the other ordered pair.

Since there is no restriction on y in order to be a function, y can be any real number.

8 0

3 years ago

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Amy wants to buy a pair of jeans that cost $65. Today the store is offering a straight discount of 25%. Calculate her savings an

galben [10]

Answer: she will save $16.25

Step-by-step explanation:

If you do 65 divided by 4 you will see how much 25 percent of 65

3 0

3 years ago

Read 2 more answers