-2(3x + 4) + 7x = 10

john is cutting wood planks. He has a 3 foot plank. he needs to cut them in 3/8 length pieces. How many pieces will he have?

mojhsa [17]

Answer:

he will have 3 pieces

Step-by-step explanation:

3/8×8

=3

<h2>Mark me BRAINLIEST </h2>

4 0

3 years ago

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

Please help: linear algebra problem. (Linear combinations)

DochEvi [55]

Answer:

$\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]$

This tells us that:

$A=\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right]$

$b=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]$

Step-by-step explanation:

So we are saying we have scalars, c and d, such that:

$c\left[\begin{array}{ccc}5\\5\\ 3\end{array}\right]+d\left[\begin{array}{ccc}7\\-8\\-9\end{array}\right]=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]$ .

So we want to find a way to express this as:

Ax=b where x is the scalar vector, $\left[\begin{array}{ccc}c\\d\end{array}\right]$ .

So we can write this as:

$\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]$

3 0

3 years ago

You are given a list of students names and their test scores. Design a pseudocode that does the following:(a) Calculates the ave

Rashid [163]

Answer:

List_of_students = {}; //Structure array that contains the scores of students and Names

Number_of_students = size(List_of_students);

Average_score ; //Variable Stores average score

Below_Average = []; //That is initially filled with zeros

Highest_score ; //Initialize variable to store highest score

for ( i = 0 ; i < Number_of_students; i = i + 1)

{

Average_score = Average_score + List_of_students(i);

if ( i = 15)

{

Average_score = Average_score / Number_of_students;

}

for ( j = 0; j < Number_of_students ; i = i + 1)

{

if ( List_of_students(j) < Average_score)

{

print( "student %name got %score , List_of_students(j), List_of_students(j) )

}

Compare_Score = 0; //Variable to compare score

for ( k = 0; K < Number_of_students; k = k+1)

{

if ( List_of_students(k) => Compare_Score)

{

Compare_Score = List_of_students(k);

}

Highest_Score = Compare_Score;

Step-by-step explanation:

4 0

3 years ago

Ella and some friends are going to a movie. Each movie ticket costs $5. Create an equation that shows the relationship between h

Zarrin [17]

Answer:

Step-by-step explanation:

Cost of one ticket = $ 5

Cost of 'n' tickets = 5 * n = 5n

c = 5n

3 0

3 years ago

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