1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ilya [14]
3 years ago
9

Factorise completely 3m^2-48​

Mathematics
1 answer:
Helen [10]3 years ago
3 0

Answer:

3 (m^2 - 16)

Step-by-step explanation:

factoring means taking out a common multiple of all the terms in the expression

in this case, if you multiply 3 and m^2, 3 and -16, you would get 3m^2-48​

so you take the three and put it outside of the parenthesis that contains the factored terms

this leaves you with 3 (m^2 - 16)

You might be interested in
PLEASEEE HELPPPP IM BEGGIN U
Anna71 [15]

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

  • the variables are omitted ("place value" is used instead)
  • the constant in the divisor is <em>negated</em> so its product with the partial quotient can be <em>added</em> to obtain the new dividend
  • the divisor binomial is assumed to have a leading coefficient of 1.

__

<h3>a) </h3>

The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

<h3>b)</h3>

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

__

<h3>c)</h3>

The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  \begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}

__

<h3>d)</h3>

The second attachment shows synthetic division by the factor (x+4).

_____

<em>Additional comment</em>

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

6 0
2 years ago
A radiator contains 15 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure anti
Annette [7]
<span>%Antifreeze=<span><span>V<span>Antifreeze</span></span><span>V<span>Fluid</span></span></span></span> <span><span>V<span>Fluid</span></span>=<span><span>V<span>Antifreeze</span></span><span>%Antifreeze</span></span></span> <span><span>V<span>Antifreeze</span></span>=<span>V<span>fluid</span></span>∗%Antifreeze</span> I want to find the amount of antifreeze in a 15 quart solution with 30% antifreeze <span><span>V<span>Antifreeze</span></span>=15∗0.30</span> =18/4 quarts of antifreeze Similarly, I want to find the amount of antifreeze in a 15 quart solution with 35% antifreeze first. <span><span>V<span>Antifreeze</span></span>=15∗0.35</span> = 21/4 quarts of antifreeze


<span>the difference between 21/4 and 18/4 is 3/4 quarts, which is the amount of pure antifreeze I've added in.
</span><span>
SO the V_fluid I replaced with 3/4 quarts of antifreeze is (3/4)/ 0.35</span>


5 0
3 years ago
Two friends Ana and Juan are buying books by joining the History Book
Travka [436]

Answer:

Ana  spent $17  per book on average.

Juan  spent $14.78  per book on average.

y = $15 + 17x--------- equation 1

y= $10 + 14.78 x------------- equation 2

Step-by-step explanation:

Ana has to pay a yearly fee of $15 to join.

She spends a total of $525 for 30 books.

The amount spent on books = Total amount - yearly fee

                                                 = $525- $15= $510

Price per book on the average = $510/30= $ 17

Ana  spent $17  per book on average.

Juan has to pay a yearly fee of $10 to join.

He spends a total of $350 for 23 books.

The amount spent on books = Total amount - yearly fee

                                                 = $350- $10= $340

Price per book on the average = $340/23= $ 14.78≅ $15

Juan  spent $14.78  per book on average.

The function can be established if y gives the total cost and x gives the number of books

y = $15 + 17x--------- equation 1

y= $10 + 14.78 x------------- equation 2

Juan has a better deal because the yearly fee is less also the price per book is less.

8 0
3 years ago
Divide. (4x^3+2x+1)÷(x+1)
stiks02 [169]

(4x^3+2x+1)\div(x+1)=4x^2-4x+6-\dfrac{5}{x+1}

8 0
3 years ago
In ΔNOP, the measure of ∠P=90°, NP = 12, PO = 35, and ON = 37. What ratio represents the cosine of ∠O?
Oxana [17]

Answer:

35/37

Step-by-step explanation:

In this question, we are to calculate the ratio that represents the cosine of angle O

Firstly, please check attachment for diagram of the triangle.

Mathematically, the trigonometric term Cos means the ratio of the length of the adjacent to that of the hypotenuse

The hypotenuse is the longest length which is 37 which represents the length ON

The side adjacent to angle O is the side OP which is 35

Thus, the ratio representing the cosine of angle O is 35/37

6 0
3 years ago
Other questions:
  • Who is Albert Einstein and i need for a essay so far i have
    9·1 answer
  • The following table shows the number of medals won in the 2008 Olympics for swimming by the top five countries. Country Number o
    10·1 answer
  • What are two whole numbers the square root of 96 lies between ?
    12·1 answer
  • Jim pays $75 per month for a cell phone plan plus $0.30 per minute beyond the first 1000 minutes. Write an equation for the cost
    14·2 answers
  • a storeowner buys a case of 144 pens for $28.80. Tax and shipping costs an additional $8.64. He sells the pens for $.59 each. wh
    10·2 answers
  • How do you write 2y=3(-x+5) in standard form ?
    9·1 answer
  • 20 POINTS PLEASE ANSWER!
    8·1 answer
  • Solve the inequality. a−2&gt;4
    8·2 answers
  • -5x + 12 - 7x = -3(5x + 8)​
    12·1 answer
  • X-5/-2=x-1/-3 help pls
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!