if p(q) = q^2 + 4q − 12,then what is p(−1)?

Answers

Answer 1
Answer: p(-1) = -15

Step-by-step:

Plug -1 into the equation in place of q.

p(-1) = (-1)^2 + 4(-1) - 12

p(-1) = (-1)^2 - 4 - 12

p(-1) = (-1)^2 -16

p(-1) = 1 - 16

p(-1) = -15
Answer 2
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

Related Questions

If 3 cans of beans cost 90¢, how many can you buy for $2.70?



If you can buy 10 juice packs for $3.00, how much will you spend to buy 4 juice packs?

please answer asap

Answers

9 cans of beans and spend around 13.25 dollars

Answer:

Step-by-step explanation:

1. 3 cans cost 90 cents

3=0.90 & x=2.7

by ratio:

3/0.9 = x/2.7

0.9x=8.1

x= 9

So you can buy 9 cans for 2.7 dollars

2. 10 Juice cost 3 dollars

by ratio:

10/3 = 4/x

10x=12

x=1.2

so you will spend 1.2 dollars to buy 4 juice packs

= 82.2×3.6 Show your working out

Answers

The answer would be 295.92

Five times the difference of a number and 8 is 19.

Answers

19 divided by 5 is 3.8 Therefore the difference between a number and 8 is 3.8 so the missing number could be 8 - 3.8 which is 4.2

PLEASEEEEE HELPPPP ASAPPP

Answers

Answer:

  40.5°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

In this triangle, that means ...

  tan(x°) = 4.7/5.5

The angle is found using the inverse function:

  x° = arctan(4.7/5.5) ≈ 40.5°

Solve (x 3)2 (x 3) â€"" 2 = 0. Let u =.

Answers

The solution to the original equation will be -2 and -6

Given the function [tex](x + 3)^2 + (x + 3) - 2 = 0.[/tex]

If u = x + 3, the function in terms of "u" will be;

[tex]u^2+u-2=0[/tex]

Factorize the resulting equation as shown:

[tex]u^2+u-2=0\\u^2+2u-u-2=0\\u(u+2)-1(u+2)=0\\(u-1)(u+3) = 0\\u=1 \ and \ -3[/tex]

Since x + 3 = u

x = u - 3

If u  = 1

x = 1 - 3  = -2

If u  = -3

x = -3 - 3  = -6

Hence the solution to the original equation will be -2 and -6

Correct question:

Solve (x + 3)^2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?

Learn more on factorization here: https://brainly.com/question/25829061

regular price: $225.75
Precent of discount: 30%

Answers

Answer:

$156.63

Step-by-step explanation:

223.75 - (223.75 x .3) = 156.625

question 4 algebra maths

Answers

Answer:

30

Step-by-step explanation:

4(3)^2 +(3*-2)

4*9-6=36-6=30

Answer:

30

Step-by-step explanation:

Substitute x = 3 and y = - 2 into the expression

4x² + xy

= 4(3)² + 3(- 2)

= 4(9) - 6

= 36 - 6

= 30

PLEASE HELP

Jed has 352 stickers in his sticker collection. He wants
to put them in an album. The album holds 8 stickers per
page. How many pages will Jed need? *Show your work
for full credit using any method to solve the problem.

Answers

352 divided by 8 =44 pages
Hope my answer helped!

Subtract
-
Iw +
W + 4 from įw + 3
1w -
- 1
- 1w + 1
1w7
w + 7
- 1w + 7
aro

Answers

Answer:

what grade are u in so I know

YO ANYONE WHO IS REALLY GOOD AT MATH THAT COULD HELP ME ?

Answers

Im good at math, what do you need help with?

a train goes 25 kilometers in 45 minutes, how fast would it go in 27 minutes?

Answers

Answer:

15km

Step-by-step explanation:

45mins = 25km

1 min =25/45

=5/9

27mins=5/9×27

=15km

At a restaurant, the amount of your bill before taxes and tip is $19.83. A 6% sales tax is applied to your bill, and you leave a tip equal to 19% of the original amount. Use mental math to estimate the total amount of money you pay to the nearest dollar.

Answers

Answer:

First, round $19.83 to make the mental math easier.  Then round the tip as well.  Then you can easily multiply the two rounded numbers to find the value.

Step-by-step explanation:

) f) 1 + cot²a = cosec²a​

Answers

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

[tex]\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}[/tex]

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

[tex]\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}[/tex]

Another identity is:

[tex]\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}[/tex]

Therefore:

[tex]\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}[/tex]

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

[tex]\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}[/tex]

Another identity:

[tex]\displaystyle \large{\sin^2x+\cos^2x=1}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}[/tex]

Hence proved, this is proof by using identity helping to find the specific identity.

The Bill of Rights was ___.
A) all of these
B) demanded by those considering ratification of the Constitution
C) none of these
D)the first ten amendments to the Constitution
E) added by the first Congress after the ratification of the Constitution

Answers

Answer: The answer is D, the first ten amendments to the constitution.

4.Cost of 10 book is ₹800.What is the cost of 50 such books

Answers

Answer:

₹4000

Step-by-step explanation:

₹800/10 books

₹80/1 book

(₹80/1 book)*(50) = ₹4000

Simplify the radical expression. Select all that apply. (There are two answers I believe) √−36
a. 6
b. -6i
c. 6i
d. -i√6
please dont send links, i will give you brainliest

Answers

Based on the graphs of f (x) and g(x), in which interval(s) are both functions increasing? Polynomial function f of x, which increases from the left and passes through the point negative 5 comma negative 4 and goes to a local maximum at negative 4 comma 0 and then goes back down through the point negative 3 comma negative 2 to a local minimum at the point negative 2 comma negative 4 and then goes back up through the point negative 1 comma 0 to the right, and a rational function g of x with one piece that increases from the left in quadrant 2 asymptotic to the line y equals 1 passing through the points negative 6 comma 2 and negative 3 comma 5 that is asymptotic to the line x equals negative 2 and then another piece that is asymptotic to the line x equals negative 2 and increases from the left in quadrant 3 passing through the point negative 1 comma negative 3 and 2 comma 0 that is asymptotic to the line y equals 1 (–°, °) (–°, –4) (–°, –4) ∪ (–2, °) (–°, –4) ∪ (2, °)

ALGEBRA
GIVE THE EXPRSSION FOLLOWING CASE
1. Y IS MULTIPLIED BY -8 AND THEN 5 IS ADDED TO THE RESULT

Answers

Is there a picture that I can see so I can hopefully help you out?

x² + 3x + k = 0
pls help​

Answers

Answer:

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{9}{4}\right),\:p=-\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]x^2+3x+y=0[/tex]

[tex]4\left\bigg(-\frac{1}{4}\right)\left\bigg(y-\frac{9}{4}\right)=\left\bigg(x-\left\bigg(-\frac{3}{2}\right)\right)^2[/tex]

[tex]\bold{\mathrm{Therefore\:parabola\:properties\:are:}}[/tex]

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{9}{4}\right),\:p=-\frac{1}{4}[/tex]

can you please answer this question asap
x-1/3-x+3/4=-1

Answers

= -1
It has no solution

The value of x is [tex]\mathbf{8\dfrac{1}{3}}[/tex]

The objective of this question is to evaluate and determine the value of x. The fraction given in the question consists of algebraic expressions and, we need to solve it through following process;

[tex]\mathbf{\dfrac{x-1}{3-x} + \dfrac{3}{4}=-1 }[/tex]

Collect like terms

[tex]\mathbf{(\dfrac{x-1}{3-x})=-1 -\dfrac{3}{4}}}[/tex]

[tex]\mathbf{(\dfrac{x-1}{3-x})=-(\dfrac{7}{4}})}[/tex]

-4(x - 1) = -7(3 -x)

-4x + 4 = -21 + 7x

4x -7x = -21 - 4

-3x = - 25

[tex]\mathbf{x= \dfrac{25}{3}}[/tex]

[tex]\mathbf{x= 8\dfrac{1}{3}}[/tex]

Learn more about evaluating fractions here:

https://brainly.com/question/12023322

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

What should you do to both sides of the inequality in order to solve x + (-2) > 3?
A) Subtract 3
B) Subtract 2
C) Add 3
D) Add 2

Answers

x+(-2) >3

open the bracket

x-2>3

collect the like terms by taking 2 to the other side

x>3+2

x>6

What is the solution to the 2nd degree equation below?x² + 2x + 4 = 0​

Answers

Answer:

x = (−2 ± √−12)/2

Step-by-step explanation:

Using the quadratic formula (search it up if you don't know what it is, but it's basically the first thing in the pic):

PLEASE HELP URGENTLY!!

The sum of three numbers is 96 . The second number is 3 times the third. The third number is 9 more than the first. What are the numbers?

Answers

Answer:

12, 63 and 21 sum to 96

.....

1 A recipe uses 1 - cups of milk to make 10 servings. If the same amount of milk is used each serving, how many servings can be made using 1 gallon of milk? Show your work​

Answers

Answer:

160 servings

Step-by-step explanation:

Step One:

1 gallon=16 cups

1 cup=10 servings

Step Two:

Multiply 16 by 10

which gives you your answer 160

What expression is equivalent too 3(-6h - 4) + 5h?

Answers

Answer:

-13h - 12

Step-by-step explanation:

3(-6h - 4) + 5h

-18h - 12 + 5h

-13h - 12

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

How to find a and b in the equation below.
3(a+b)=28

Answers

Answer:

a equals  and b equals 7

Step-by-step explanation

divide both side by 3 getting a+b=(28/3)

subtract b from both sides getting a=(28/3)-b

to solve for b its the same way so b=(28/3)-a

you can then substitute

Pleaseeeee helpppp asapp

Answers

Ok done. Thank to me :>

How many solutions does 9 - 5x = 8 - 3x - 1 -2x have?
A. One
B. Two
C. Infinite
D. Zero

Answers

Answer:

D) Zero solutions

Step-by-step explanation:

9 - 5x = 8 - 3x - 1 - 2x

9 - 5x = 7 - 5x

9 = 7

Zero solutions

i took the quiz its D. Zero

Holly has a credit limit of $2,500 on her credit card. She had a previous balance of $103.23
and made a $100 payment. The total of her purchases is $45.34. What is her available
credit?

Answers

Step-by-step explanation:

$103.23

$100

$45.34

+_____

=248.57


Brainliest reward need brief working out

Answers

Answer:

  1. 125 cm³; 88.8 cm³; 1650 cm³; 0.11 m³

  2. about 1.47 kg

  3. can't tell what the volume of 1 jar is

Step-by-step explanation:

The relationship between volume, mass, and density is ...

  mass = volume × density

Solving for volume, we find ...

  volume = mass ÷ density

__

(a) 50 g/(0.4 g/cm³) = 125 cm³

(b) 770 g/(8.67 g/cm³) ≈ 88.8 cm³ . . . (rounded to 3 significant figures)

(c) 4000 g/(2.42 g/cm³) ≈ 1650 cm³ . . . (rounded to 3 significant figures)

(d) 80 kg/(720 kg/m³) ≈ 0.11 m³ . . . (rounded to 2 significant figures)

_____

The volume of the cylinder is ...

  V = πr²h

  V = π(4 cm)²(15 cm) = 240π cm³ ≈ 754.0 cm³

Using the above relation, we find the mass to be ...

  mass = (754.0 cm³)(1.95 g/cm³) ≈ 1470 g = 1.47 kg

_____

We cannot tell if the volume of each jar is 360 liters, or if that is the total volume of all 6 jars. Either way, we suspect a units problem, as the jars would have to be extremely large and unusually thin relative to what we usually think of as a jar for jam (0.77 m diameter; 0.2 mm thick). The density of the jam would be roughly 10 times the density of air, if that is the volume of all 6 jars. The problem would be more sensible if the units of volume were mm³, and the given volume is that of one jar.

The mass of jam in one jar is (5400/6 -200) = 700 g. Divide that by what you think the volume of one jar is in cm³ to find the density in g/cm³. (For comparison, the density of air is about 0.0012 g/cm³.)

_____

Additional comment

We have rounded the answers to 2 or 3 significant figures. In most cases, this is more than would be justified by the number of significant figures in the given measurements. For purposes of ongoing calculations, it is useful to keep intermediate results to at least 1 more significant figure than required for the answer.

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