if p(q) = q^2 4q- 12 then what is p(-1)

Answers

Answer 1
the solution:

(1): "q2" was replaced by "q^2".

Step by step solution :

STEP
1
:
Trying to factor by splitting the middle term

1.1 Factoring q2-4q-12

The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

-12 + 1 = -11
-6 + 2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization

Equation at the end of step
1
:

(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : q+2 = 0

Subtract 2 from both sides of the equation :
q = -2

Solving a Single Variable Equation:

2.3 Solve : q-6 = 0

Add 6 to both sides of the equation :
q = 6

Supplement : Solving Quadratic Equation Directly

Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = q2-4q-12

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000

Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}

Related Questions

why do you need to find the number that is halfway between 1 and 1 1/2

Answers

Answer:

Lets just say we are finding the halfway point is very needful because; it means that we can find the amount of flour used for 1 while egg.

We are told there is a need to find the Number that is halfway between 1 and 1½.

Step-by-step explanation:

Given that D, E, and F are the midpoints of their respective sides, which of the following is a true statement?

Answers

Answer:

I'm pretty sure its the 1st one.

Step-by-step explanation:


Evaluate the function.
f(t)=-2t - 1; Find f(-9)

Answers

Answer:

17

Step-by-step explanation:

substitute t = - 9 into f(t) , that is

f(- 9) = - 2(- 9) - 1 = 18 - 1 = 17

1 point
15.) Vincent pays $202 in advance on his account at the health spa. Each
time he uses the spa, $6 is deducted from the account. Write an equation
that represents the value remaining in his account after x visits to the spa.
Find the value remaining in the account after 18 visits. *
O V = 6 - 202x; $94
O V = 6 - 202x; $1,216
O V = 202 - 6x; $94
O V = 202 - 6x; $1,230

Answers

Answer:

O V=202-6x; $94

Step-by-step explanation:

202 needs to be placed before the 6, eliminating options 1 and 2. It can't be option 4 because thats more than 202, leaving us with option 3. Check you answer by replacing x with 18. O V=202-6(18) ->O V=202-108 -> 202-108=$94.

help please and NO LINKS

Answers

Answer:

B

Step-by-step explanation:

A trapezoid has only two parallel sides while a parallelogram has 2 pairs of parallel sides.

The first modern humans appeared on Earth about 200,000 years ago. Would it be possible to measure that number in terms of feet on the football field? Explain your answer.

Answers

hi um i know this answer is 79

How do I solve this triangle?

Answers

Answer:

check the length and the angles and check the height of it

Bruno and Amelia have 112 newspapers to deliver. Bruno delivers three fourths of the news papers, Amelia delivers one seventh pf the papers. How many papers are left to be deliverd

Answers

Answer:

f

Step-by-step explanation:

Change 7 1/4 to an improper fraction

Answers

Answer:

29/4

Step-by-step explanation:

7 x 4 = 28

28 + 1

hope that helps!

Answer:

29/4

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

4 × 7 = 28

Step 2

Add the answer from Step 1 to the numerator

28 + 1 = 29

Step 3

Write answer from Step 2 over the denominator

29/4

Hope this helps!:)

the students at Walden Middle school are selling tins of popcorn to raise money for new uniforms. they sold 42 tins in the first week. how much money did they make in the first weeks

Answers

Answer:

$388.50

Step-by-step explanation:

9.25 *  42  = $388.50

Which would be the most suitable viewing window to solve the system below?

Answers

The solution of the system belongs to -1 ≤ x ≤ 1, -1 ≤ y ≤ 1.

Given a system of the equations:

x/3 + y/2 = 1/3  .... (1)

(5x)/6 - (3y)/4 = 1/6  ....(2)

Multiply 5/2 to equation (1) then subtract from equation (2), we get,

(5y)/4 + (15y)/8 = 5/6 - 1/6

(10y + 15y)/8 = 4/6

(25y)/8 = 4/6

25y = 4/6 x 8

y = 32/150

y = 0.21

To find the value of x,

x/3 + 32/300 = 1/3

x/3 = 1/3 - 32/300

x = 3(1/3 - 32/300)

x = 1 - 32/100

x = 0.68

From the given choices,

-1 ≤ x ≤ 1, -1 ≤ y ≤ 1.

To learn more about the system of equations;

brainly.com/question/13729904

#SPJ1

Elizabeth lives on a straight road that goes east and west. She starts from a point 5.8 miles west of her home and drives a certain distance to the store. The store is more than 434 miles east of her home.

Let d represent the distance Elizabeth drove.

Which inequality represents this situation?

Answers

Answer:

−5.8+d>43/4

Step-by-step explanation:

The inequality represents the situation as −5.8+d>434.

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given that Elizabeth lives on a straight road that goes east and west. She starts from a point 5.8 miles west of her home and drives a certain distance to the store. The store is more than 434 miles east of her home.

The inequality will be written as the algebraic sum of the distance d and 5.8 is greater than the 434 miles.

Inequality: -5.8 > 434

To know more about inequality follow

https://brainly.com/question/24372553

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The number of hours required to paint a house varies indirectly to the number of painters. If 5 painters painted a house in 120 hours, how many painters would be required to paint a similar house in 50 hours?

Answers

The answer is 2 workers coz there can't be 2.08333... workers

6x-36+120=180
what is the value of x, in degrees?

Answers

X=16


Mark brainpower plz

Which statement is an example of the transitive property of congruence?
A. If A EFG = AHJK, then AHJK = A MNP.
B. AEFG = AEFG
C. If A EFG : AHJK, and AHJK = AMNP, then A EFG = AMNP.
D. If A EFG - AHJK, then AHJK - A EFG.

Answers

Answer:

my answer was d. 90 percent sure .

Step-by-step explanation:

The statement which is an example of the transitive property of congruence is C. If A EFG : AHJK, and AHJK = AMNP, then A EFG = AMNP.

Meaning of the transitive property of congruence

This transistive property holds congruent figure. it is states that: If Figure A is equal to figure B and Figure B is equal to Figure C, then Figure A will be equated to Figure C.

For example: AB = CD; CD = EF, then AB = EF

if angle A is equivalent to angle B and angle B is equivalent to angle C; then angle A will be equivalent to angle C

in conclusion, The statement which is an example of the transitive property of congruence is C. If A EFG : AHJK, and AHJK = AMNP, then A EFG = AMNP.

Learn more about transitive property of congruence : https://brainly.com/question/7042091

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I need help with this !!

Answers

Answer:

  -27

Step-by-step explanation:

It looks like you're trying to evaluate ...

  [tex]\displaystyle 5^{\log_5{8}}-3^{\log_3{5}+\log_3{7}}=8-3^{\log_3{35}}=8-35=\boxed{-27}[/tex]

__

The relevant rules are ...

  b^(log_b(x) = x

  log(a)+log(b) = log(ab)

If the sales tax in a town is 5% and Amanda pays $10 in tax on her purchase what was the cost of the item?

Answers

Answer:

$200

Step-by-step explanation:

If the tax is 5%, then she pays $5 for every $100. If she paid $10 in tax, her purchase was $200.

Can someone please take the time out of their day and help me with this

Answers

it is rotated 180°, it needs to be rotated another 90°, so it will go in the III quadrent i believe

Write the slope-intercept form of the equation with the given point and slope. Through (2,5) and m=1/2

Answers

Answer:

y=1/2x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-5=1/2(x-2)

y=1/2x-2/2+5

y=1/2x-1+5

y=1/2x+4

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

If you're satisfied with the answer, then please mark me as Brainliest. Thank you.

Help me out please number 10 and if you can answer 13 please

Answers

10. 25/100 and 25%
25 divided by 25 /100 divided by 25 = 1/4

TI
Assessment
Vhich table of values can be used to graph the function y = - 4x +3?
x
y
-1
-1
0
3
1
7
2
11
X
y
3
O
-1
-9
-1
7
1
3
15
x
0
1
3
-1
-5
-9
2
3
3
X
Y
3
7
11
15
3
or False
function's graph may include solutions that do not appear in its table of

Answers

Answer:

B, y=X. Hope it works

Step-by-step explanation:

what is the answer to (x-2)^5 ?

Answers

Answer:

x² - 4x + 4  

Step-by-step explanation:

(x -2)(x - 2)                

x² - 2x - 2x + 4          Expand using FOIL.

x² - 4x + 4                 Simplify.

The next term in the geometric sequence -1, -2, -4 __ is -6.


True or False

Answers

Answer:

False

Step-by-step explanation:

It is multiplied by 2 so the next answer would be -8 not -6 hope this helps!:)

tbh this question confusing the **** outta me​

Answers

Answer:

[tex]8^6[/tex]

Step-by-step explanation:

Powers are defined as the number of times you multiply a number by itself. For example, 2 to the 3rd power is 2 multiplied by itself 3 times. 2 * 2 * 2 = 8. You also know that if you multiply two powers of the same base, you add the exponent, and if you raise a power to a different power, you multiply the exponents.

e.g:

[tex]2^2\cdot2^2=2^{2+2}=2^4\\(2^2)^3=2^{2\cdot3}=2^6[/tex]

Now, we are asking to use grouping to write 2 to the power 18 as a power of 8. We know 2 to the power 8 is 2 to the power 3, so we have the following equation:

[tex]2^{18}=(2^3)^x[/tex]

We know this is now 2 to the power 3x = 2 the power 18, and therefore x = 6, because 3 times 6 is equal to 18. Now, we can just simplify 2 to the third as 8 and we now have:

[tex]8^6[/tex]

(2 + 10) × 5 = (2 × 5) + ( __ × 5)

Answers

Answer:

10

Step-by-step explanation:

We can use the distributive property to get:

[tex]5(2+10)=5(2)+5(10)[/tex]

Therefore, the blank is 10.

i need help asap)))))))))))))))))))))

Answers

Answer: a

Step-by-step explanation:

u do 1+1

PLEASE HELP ME OUT I WILL GIVE BRAINLIEST

Metallic blocks X, Y, and Z were placed in the graduates A,B,C the initial volume of liquid in the equal sized graduates was 40 ML. Which block was placed in which graduate?

Answers

Answer:

Answers are B-Y, C-Z, A-X

Joyce's mother buys some shares of Company A on Day 0.
On Day 7, the share price of Company A is $4.60.
If she sells all her shares of Company A and A buys 2000 shares of Company B on Day 7, she would receive $7400.
On Day 12, the share price of Company A is $4.80 and the share price of Company B is $0.50 less than that on Day 7.
If she sells all her shares of Company A and buys 5000 shares of Company B on Day 12, she would have to pay $5800. Find
(i) the number of shares of Company A Joyce's mother has,
(ii) the share price of Company B on Day 12.

Please help aNd thank you!!!​

Answers

Answer:

(i) 4000

(ii) $5.00

Step-by-step explanation:

Let no. of shares of Company A be X

Let share price of Company B on Day 7 be $y

Share price of Company B on Day 12 = $(y-0.50)

(i)

Consider Day 7:

4.60x - 2000y = 7400................ (1)

Consider Day 12:

4.80x - 5000(y-0.50) = -5800

4.80x - 5000y + 2500 = -5800

4.80x - 5000y = -8300............... (2)

(1)*2.5:

11.5x - 5000y = 18500................. (3)

(3)-(2):

11.5x - 4.80x - 5000y + 5000y = 18500 + 8300

6.70x = 26800

x = 4000

(ii)

Sub. x = 4000 into (1):

4.60(4000) - 2000y = 7400

-2000y = 7400 - 18400

-2000y = -11000

y = 5.5

Share price of Company B on Day 12

= 5.50 - 0.50

= $5.00

Jake drew a scale drawing of a house. He used the scale 10 inches = 6 feet. What is the scale factor of the drawing?

Simplify your answer and write it as a fraction.

Answers

Answer:

5:36

Step-by-step explanation:

12 inches = 1 foot, so 6 feet = 72 inches

10:72, reduces to 5:36


The equation A = 1/2bh (one halve) gives the area A of a triangle, where b is the length
of the base and h is the height. Solve this equation for h.

Answers

Answer:

h= (2a)/b

Step-by-step explanation:

solved for equation

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