If x2 + mx + m is a perfect-square trinomial, which equation must be true?
x2 + mx + m = (x – 1)2
x2 + mx + m = (x + 1)2
x2 + mx + m = (x + 2)2
x2 + mx + m = (x + 4)2

Answers

Answer 1

Hello!

The answer is:

The third option,

[tex]x^{2}+mx+m=(x+2)^{2}[/tex]

Why?

We are looking for an equation that establishes a relationship between the perfect-square trinomial and the givens notable products.

So, we are looking for a notable product that gives us a value of "m" that is the coefficient of the linear term (x) and it's also the constant term.

- Trying with the two first options, we have:

[tex](x+1)^{2}=x^{2}+2x+ 1\\\\(x-1)^{2}=x^{2}-2x+ 1[/tex]

We can see that for these first two options, the value of m has not the same value for the coefficient of the linear term and the constant term since m is equal 2 and the constant number is not 2.

- Trying with the third option, we have:

[tex](x+2)^{2}=x^{2}+2*(2*x)+2^{2}=x^{2} +4x+4[/tex]

Now, we can see that the value of m is the same for the coefficient of the linear term and the constant term, we can see that m is equal to 4.

So, the correct option is the third option, because

[tex]m=4[/tex]

[tex]x^{2} +mx+m=(x+2)^{2}=x^{2} +4x+4=x^{2} +mx+m[/tex]

Have a nice day!

Related Questions

WILL GIVE BRAINLIEST

Which describes a uniform probability model?
A) flipping a coin and rolling a six sided die
B) selecting a ball from 2 baseballs and 3 softballs
C) the number of heads and tails from flipping two coins
D) a spinner with five equal sections: 2 blue, 2 red, 1 yellow

Thank You! :)

Answers

Answer:

Step-by-step explanation:

sorry just a little confused

Answer:

A) Flipping a coin and rolling a six sided dice.

Step-by-step explanation:

Lets use a process of elimination in order to find the correct answer.

We are looking for a uniform probability model. This means that every outcome in this situation has the same chance of occurring.

D) This cannot be the right answer as the chances of probability are [tex]\frac{2}{5} ,\frac{2}{5} ,\frac{1}{5}[/tex]

As these are not all equal, this cannot be the right answer.

B) This cannot be the right answer as the chances of probability are [tex]\frac{2}{5} ,\frac{3}{5}[/tex]

As these are not equal, this cannot be the right answer.

C) Lets look at every outcome that could occur in this situation.

You could have 2H, 2T, HT, and TH. As HT and TH are the same, their probability can be written together.

This means that the probabilities would be

[tex]\frac{1}{4} ,\frac{1}{4} ,\frac{1}{2}[/tex]

This means that A must be the correct answer as we have ruled out every other option.

the graph below has the same shape. what is the equation of the graph?

Answers

C; A and B are incorrect because the shift is not vertical, it is horizontal. This is because 3 is in parenthesis or a 'grouping' (same thing if it is in an exponent) and is being modified. Since the graph is being translated down 3 units, D is incorrect since it is a translation up 3 units. The answer is C.

write an equation in slope-intercept form when the y-intercept is 0 and the slope is -4

Answers

Answer: Y=mx+b

B is the y intercept and the slope is M

So the answer is Y= -4x+ 0

Step-by-step explanation:

Answer:

y = - 4x

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 4 and c = 0, hence

y = - 4x ← is the equation of the line

Find the slope of the line through (2, -3) and (-4, 3).

-1
0
1

Answers

ANSWER

-1

EXPLANATION

The slope formula is given by

[tex]m = \frac{y_1-y_2}{x_1-x_2} [/tex]

The slope of the line through (2, -3) and (-4, 3) is found by substituting the points into the above formula;

[tex]m = \frac{ - 3 - 3}{2 - - 4} [/tex]

This simplifies to

[tex]m = \frac{ - 6}{ 6} = - 1[/tex]

The slope is -1

Answer:

-1

Step-by-step explanation:

The slope of a line is the ratio of its change in rise to its change in run. In the -xy-plane, this is the same as the ratio of the change in y coordinate to the change in x coordinate. In notation, we write this as

[tex]\frac{\Delta y}{\Delta x}[/tex]

and calculate it by finding the difference between y coordinates and dividing it by the difference between x coordinates. Here, our y coordinates are 3 and -3, and our x coordinates are -4 and 2, so our slope would be

[tex]\frac{3-(-3)}{-4-2}=\frac{3+3}{-6}=\frac{6}{-6}=-1[/tex]

Evaluate 3/2y - 3 + 5/3z when y=6 and z=3

Answers

Answer: 11

Step-by-step explanation:

3/2(6) - 3 + 5/3(3)= 11

What is the truth value for the following conditional statement? p: false q: true ∼q → ∼p

Answers

Answer:

p false

Step-by-step explanation:

Answer:

Truth value of ~p → ~q will be False.

Step-by-step explanation:

If the truth value of conditional statement p is false then the truth value of

~p will be True

If the truth value of other statement q is True then the truth value of ~q will be False

We know truth value of the implication of two conditional statements a → b is False only when a is true and b is false.

Therefore, ~p → ~q will be False.

13 divide 32,708 what is the answer

Answers

Answer:

0.00039745627

13 / 32708 is 0.004

I got this answer by using Long Division.

Hope this helps

Which expression simplifies 2/5 ? A) (-1/10)-(-1/2) B) (-1/10)+(-1/2) C) (-1/10)×(-1/2) D) (-1/10)÷(-1/2)

Answers

[tex]\bf -\cfrac{1}{10}-\left( -\cfrac{1}{2} \right)\implies -\cfrac{1}{10}+\cfrac{1}{2}\implies \stackrel{\textit{using the LCD of 10}}{\cfrac{-(1)1~~+~~(5)1}{10}}\implies \cfrac{-1+5}{10} \\\\\\ \cfrac{4}{10}\implies \stackrel{simplified}{\cfrac{2}{5}}[/tex]

Help please what is the answer?

Answers

Answer:

C) 5.6

Step-by-step explanation:

AC = sqrt(11^2 + 2^2) = sqrt(125)

(1/2)AC = (1/2)sqrt(125)

(1/2)AC = 5.6

Answer: C) 5.6

Answer:

C, 5.6

Step-by-step explanation:

A midsegment is half of the side it is parallel to. This means that it is half of BC. They give us the coordinates for B and C so we can just use the distance formula (the square root of the change in x squared plus the change in y squared)

If you simplify it, you get root 125 which is about 11.2. 11.2 divided by 2 is 5.6, so your answer would be C.

Solve the equation. y-6/y =5

Answers

Answer:

-3/2

Step-by-step explanation:

multiply both sides by y:

y-6 = 5y

subtract y from both sides:

-6 = 4y

divide both sides by 4:

-6/4 = y

y = -3/2

Answer:

[tex]\frac{y-6}{y}=5\quad :\quad y=-\frac{3}{2}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}y\\\frac{y-6}{y}y=5y\\\mathrm{Simplify\:}\frac{y-6}{y}y:\quad y-6\\y-6=5y\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\y-6+6=5y+6\\y=5y+6\\\mathrm{Subtract\:}5y\mathrm{\:from\:both\:sides}\\y-5y=5y+6-5y\\-4y=6\\\mathrm{Divide\:both\:sides\:by\:}-4\\\frac{-4y}{-4}=\frac{6}{-4}\\y=-\frac{3}{2}[/tex]

[tex]y-\frac{6}{y}=5\quad :\quad y=6,\:y=-1[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}y\\yy-\frac{6}{y}y=5y\\y^2-6=5y\\\mathrm{Solve\:}\:y^2-6=5y:\quad y=6,\:y=-1[/tex]

Hope this helps!!!!

A sweater is marked down 35% off the original price. The original price was $40. What is the sale price of the sweater before sales tax?

Answers

Answer: $26

$40*.35=$14 off price of sweater

40-14=$26 sale price

$40*.65=$26 sale price

Answer:

The correct answer is $26.

Step-by-step explanation:

Well, we must first analyze the information we have.

We have a sweater that was marked down 35% off.

We know that the original price of the sweater is $ 40. Now we just have to find out the final price.

But to know that, we must first know what the discount was applied.

And we find out as follows:

[tex]Tax= 40 . 0,35[/tex]

[tex]Tax= 14[/tex]

In this way we show that the price discounted to the sweater was $ 14

Now we just have to make a subtraction between the original price and the discount :

40-14=26

The final price of the sweater is $ 26

Martin can run 1 mile in 7 minutes. What proportions can be written from this information?

Answers

Answer:

[tex]\frac{1}{7}=\frac{3}{21}[/tex]

[tex]\frac{7}{1}=\frac{21}{3}[/tex]

Step-by-step explanation:

Verify each case

case 1) [tex]\frac{1}{7}=\frac{3}{21}[/tex]