Choose the correct zeros for the following quadratic function.
f(x) = x^2 + 5x - 14
A. {1,3}
B. {4, -3}
C. {2, -7}
D. {2, -1}

Answer:

Step-by-step explanation:

The sum of measures of angles in triangle is allways 180°

So:

   x + 53° + 60° = 180°  {subtract 113° from both sides}

   x = 67°

Answer:

The length of the shorter part of the wire is 24 centimeters.

Step-by-step explanation:

Let [tex]L[/tex] the total length of the piece of wire, where [tex]L-x[/tex] and [tex]x[/tex] are the perimeters of the greater and lesser squares. All lengths are measured in centimeters. Since squares have four sides of equal length, the side lengths for the greater and lesser squares are [tex]\frac{L-x}{4}[/tex] and [tex]\frac{x}{4}[/tex]. From statement we find that the sum of the areas of the two squares ([tex]A[/tex]), measured in square centimeters, is represented by the following expression:

[tex]A = \left(\frac{L-x}{4} \right)^{2}+\left(\frac{x}{4} \right)^{2}[/tex] (1)

And we expand this polynomial below:

[tex]A = \frac{L^{2}-2\cdot L\cdot x +x^{2}}{16} + \frac{x^{2}}{16}[/tex]

[tex]A = \frac{L^{2}-2\cdot L\cdot x +2\cdot x^{2}}{16}[/tex]

[tex]2\cdot x^{2}-2\cdot L\cdot x +L^{2}-16\cdot A = 0[/tex] (2)

If we know that [tex]L = 76\,cm[/tex] and [tex]A = 205\,cm^{2 }[/tex], then the length of the shorter part of the wire is:

[tex]2\cdot x^{2}-152\cdot x +2496 = 0[/tex]

By the Quadratic Formula, we determine the roots associated with the polynomial:

[tex]x_{1} = 52\,cm[/tex], [tex]x_{2} = 24\,cm[/tex]

The length of the shorter part of the wire corresponds to the second root. Hence, the length of the shorter part of the wire is 24 centimeters.

Answer:

Step-by-step explanation:

The answer would be 5 because 14/7=2 and 6/3=2 and 10/ 2 =5 so 5

Answer:

5/7

Step-by-step explanation:

5/7 is the simplified fraction for 30/42 by using the GCD or HCF method

Answer:

n can be a number less than 3

Step-by-step explanation:

Hope this helps!

Answer:

N<3

Step-by-step explanation:

parallel: g(x) = -5/3x + 1

perpendicular: h(x) = 3/5x - 5

neither: j(x) = 2x + 3

Answer: a. Lin's tank hold 20 cups and Elena's tank hold 20 gallons; I know this because gallons are greater than cups.

Step-by-step explanation:

Gallons are greater than cups so the fish tank that will hold 20 gallons would have to be the bigger one which in this case is Elena's.

With cups being lesser in quantity than gallons, the fish tank that will hold 20 cups of water will definitely have to be the smaller one which in the case is Lina's.

Answer:

lesser x: - 6

greater x: 2

Step-by-step explanation:

f(x) = (x + 2)² – 16

(x + 2)² – 16 = 0

(x + 2 + 4) (x + 2 - 4) = 0

(x + 6)(x - 2) = 0

roots (zero): x = -6 or x = 2

Answer:

2 k 3 − 3 k 2 − 2 k

Step-by-step explanation:

Answer: ...

2k^3−3k^2−2k

Answer:

-7/3

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -7/3x + 5

Step 2: Break Function

Identify Parts

Slope m = -7/3

y-intercept b = 5

Answer:

change/original price X 100

22/88 X 100 = 25%

Answer:

-8-x or -x-8 or x=-8

Step-by-step explanation:

Distribute the -8 to the (1+x)

-8-8x+7x

then add the -8x+7x

-8-x or -x-8

and if you want to solve for x

x=-8

Answer:

Positive, Upward Slope.

Step-by-step explanation:

Answer:

the slope of a line shows how steep a straight line is, or the direction of a straight line

Answer:

50,373 feet

Step-by-step explanation:

tan 15° = 13500 / x

.268 = 13500 / x

x = 50,373

Answer: x=9 1/3

Step-by-step explanation:

-5=-3x-33

-5+33=-3x

28=-3x

3x=-28

x=28/3

x=9 1/3

Answer: X=-28/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5=−3(x+11)

−5=(−3)(x)+(−3)(11)(Distribute)

−5=−3x+−33

−5=−3x−33

Step 2: Flip the equation.

−3x−33=−5

Step 3: Add 33 to both sides.

−3x−33+33=−5+33

−3x=28

Step 4: Divide both sides by -3.

-3x/-3= 28/-3

X=-28/3

have a nice day :)

Answer:

1/6

Step-by-step explanation: in a rate you need to make it a one so you double the 1/2 gallon to make it one gallon then since you doubled that you have to double the days to 6. So they drink 1 gallon per 6 days.

Answer:

[tex]\frac{dy}{dx}[/tex] = 8(2x + 3)³

Step-by-step explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)

Here

f(x) = [tex](2x+3)^{4}[/tex] ⇒ f'(x) = 4(2x + 3)³

g(x) = 2x + 3 ⇒ g'(x) = 2

Thus

[tex]\frac{dy}{dx}[/tex] = 4(2x + 3)³ × 2

    = 8(2x + 3)³

Answer:

5.567764363 or rounded off to two decimal places 5.57

Step-by-step explanation:

Calculator

Answer:

Hi! The correct answer is y = 5

Step-by-step explanation:

~Solve for the first variable in one of the equations, then substitute the result into the other equation~

Answer:

9

Step-by-step explanation:

if you have two negatives next to eachother, the equation now adds like 5+4. 5+4=9

Answer:

-2

Step-by-step explanation:

f(x) = –x– 5

f(x) = -(-3)– 5

f(x) = 3– 5

f(x) = -2

Answer:

Answer is -2 because - * - = + 3-5=-2

Answer:

do you have 12 as an answer?

Answer:

length, width, and height are (b+2), (b-2), (b+3)

Step-by-step explanation:

Doing what the problem statement tells you to do, you get ...

 (b^3 +3b^2) -(4b +12)

 = b^2(b +3) -4(b +3) . . . factor each pair of terms

 = (b^2 -4)(b +3) . . .  write as a product

 = (b -2)(b +2)(b +3) . . . use the factoring of the difference of squares

The three factors are (b-2) , (b+2) , and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.

The possible dimensions of the prism are:

Length: 9x, 5x + 7, or x + 3

Width: 5x + 7, x + 3, or 9x

Height: x + 3, 9x, or 5x + 7

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the possible dimensions of the prism, we need to factor the given volume expression into three factors, each representing the length, width, and height of the box.

We start by looking for common factors among the coefficients of the three terms:

45x³ + 198x² + 189x

= 9x (5x² + 22x + 21)

Now we can factor the quadratic expression inside the parentheses:

5x² + 22x + 21

= 5x² + 15x + 7x + 21

= 5x(x + 3) + 7(x + 3)

= (5x + 7) (x + 3)

The volume expression can be factored as:

45x³ + 198x² + 189x

= 9x (5x + 7) (x + 3)

Thus,

The possible dimensions of the prism are:

Length: 9x, 5x + 7, or x + 3

Width: 5x + 7, x + 3, or 9x

Height: x + 3, 9x, or 5x + 7

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ2

Answer:

x = t - p

Step-by-step explanation:

p + x = t

subtract p from both sides.

x = t - p

Answer:

Its XYW is half of LXYZ

Step-by-step explanation:

.

Answer:

this is the required solution

Answer:

There ya go

Step-by-step explanation:

Answer:

15/2

Step-by-step explanation:

goodluck on the rest! (: