What number should be added to the expression x2 + 14x to change it into a perfect square trinomial?(Points : 1)
7
14
28
49

Answers

Answer 1

Answer: $(x+a)^2=x^2+2\cdot x\cdot a+a^2\ \ \ \Rightarrow \ \ \ \ 2\cdot x\cdot a=14x\ \ \ \Leftrightarrow\ \ \ 2a=14\ /:2\n\na=7\ \ \ \Rightarrow\ \ \ a^2=7^2=49\n\n\ \ \ \Rightarrow\ \ \ a\ perfect\ square\ trinomial=(x+7)^2$

Answer 2

Answer: # to be added to x² +14x to change it to a perfect square trinomial is
(14/2)² = 7²
= 49
the trinomial is x² + 14x + 49 = (x +7)²

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What is 8u + 9v + 3u -5v simplified

Answers

8u + 9v + 3u -5v can be simplified as 11u + 4v.

What is expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given expression

8u + 9v + 3u - 5v

Adding like terms

= 11u + 4v

Hence, 11u + 4v is simplified form of expression 8u + 9v + 3u -5v.

Learn more about expression here:

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8u + 9v + 3u -5v
= 11u + 4v ....simplified

hope it helps

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?{5, 8}
{-5, -8}
{3, 8}
{4, 7}
{4, 8}

Answers

Answer:

Hence, the domain of the function is:

{4,7}

Step-by-step explanation:

We are given the range of the function:

$f(k)=k^2+2k+1$ as {25,16}

The function f(k) could also be written as:

$f(k)=k^2+2k+1=k^2+k+k+1\n\nf(k)=k(k+1)+1(k+1)\n\nf(k)=(k+1)(k+1)\n\nf(k)=(k+1)^2$

The range is the value of the function at some k.

if f(k)=25 then we have to find the value of k.

$f(k)=25=5^2=(k+1)^2$

on taking square root on both side we have:

$k+1=5\n\nk=5-1\n\nk=4$

if f(k)=64 then we have to find the value of k.

$f(k)=64=8^2=(k+1)^2$

on taking square root on both side we have:

$k+1=8\n\nk=8-1\n\nk=7$

Hence, the domain of the function is:

{4,7}

The domain of a function contains the x-values of the function while the range of the function contains the y-values of the function. In this case, we substitute 25 and 64 to y. Then,
25 = k2 + 2 k + 1 (k-4) * (k+6) = 0
64 = k2 + 2 k + 1 (k-7) * (k+9) = 0
hence the domain is {-9,-6, 4,7}

What does the word pythagorean mean?

Answers

The Pythagorean Theorem is the mathematical concept that states a² + b² = c², where a and b are the sides of a right triangle and c is the hypotenuse. It was created by the Greek philosopher and mathematician Pythagoras.

Definition of PYTHAGOREAN. : of, relating to, or associated with the Greek philosopher Pythagoras, his philosophy, or the Pythagoreans. (from my book dictionary)

Write the equation of the line that passes through the given points. (0,-5) and (8,0)

Answers

Answer:

$y=(5)/(8)x-5$

Step-by-step explanation:

You're given two points, using that you can use the slope-finding formula:

$slope=((y^(2) - y^(1)) )/((x^(2) - x^(1)))$

After that, match up the y-coordinates with each other and the same goes for the x-coordinates. It should look something like this:

$slope = ((0-(-5)))/((8-0)) \n\n=(5)/(8)$

5/8 is your slope. Using the general slope formula y=mx + b, you know that m is the slope and b is the y-intercept. So now you know your slope, plug it into the formula, along with one of the given points. In this case, I will be using (8, 0) because it is easier to solve.

$m = (5)/(8)\n \ny = ((5)/(8) )x+b\n(8, 0)\n(0) = (5)/(8)(8) + b\n 0 = 5 + b\n\n-5 =b\n \ny=(5)/(8)x-5$

You can see I replaced the x and y with the given values accordingly. Then you simplify by subtracting the five on both sides and your y-intercept is -5. Then combine your slope and y-intercept to get your answer!

Hope that helped!

-Bob Ross

Find the domain and range of the relation. A. domain: {-3, -1.5, 1.5, 3}; range: {4, 3, 1.5} B. domain: {-3, -1.5, 0, 1.5, 3}; range: {4, 3, 1.5} C. domain: {4, 3, 1.5}; range: {-3, -1.5, 1.5, 3} D. domain: {4, 3, 1.5}; range: {-3, -1.5, 0, 1.5, 3}

Answers

the domain is the x values and the range is the y values

domain : { - 3, -1.5,0,1.5,3 }
range : { 4, 3, 1.5 }

It costs $3.56 to buy a pack of pencils. Which of the following equations shows the amount of money needed, x, to buy k packs of pencils?x = 3.56k
k = 3.56x
x = 3.56 + k
k = 3.56 + x