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2 years ago

How could Brent use a rectangle to model the factors of \large x^2-7x+6?

1 answer:

5 0

Answer:He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.

Step-by-step explanation:

He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.

He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.

He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.

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A tape manufacturer reduces the price of its heavy duty tape from $30 to $28 a reel, and the price of regular tape from $20 to $

juin [17]

3/5 of 1600 = $960 spent for heavy duty tapes
1600 - 960 = $640 spent for regular tapes

The company normally bought
960 ÷ 30 = 32 heavy duty tapes
640 ÷ 20 = 32 regular tapes

With the new prices, the company is paying
32 × 28 = 896 for the heavy duty tapes
32 × 19 = 608 for the regular tapes

The company is saving
960 - 896 = $64 for the heavy duty tapes
640 - 608 = $32 for the regular tapes

4 0

2 years ago

the area of a rectangular field is 18000m^2 if the ratio of length and breath is 5:4 find its perimeter

zavuch27 [327]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{540 \: m}}}}}$

Step-by-step explanation:

Let the length and breadth be 5x and 4x respectively.

Area of rectangular field = 18000 m²

Finding the value of x

Area of rectangle = $\sf{l \times b}$

Plug the values

⇒ $\sf{18000 = 5x \times 4x}$

Calculate the product

⇒ $\sf{18000 = 20 {x}^{2} }$

Swap the sides of the equation

⇒ $\sf{20 {x}^{2} = 18000}$

Divide both sides of the equation by 20

⇒ $\sf{ \frac{20 {x}^{2} }{20} = \frac{18000}{20} }$

Calculate

⇒ $\sf{ {x}^{2} = 900}$

Squaring on both sides

⇒ $\sf{x = 30}$

Replacing the value of x in order to find the value of length and breadth

Length = $\sf{5x = 5 \times 30 = 150 \: m}$

Breadth = $\sf{4x = 4 \times 30 = 120 \: m}$

Finding the perimeter of the rectangular field

Perimeter of rectangle = $\sf{2(l + b)}$

plug the values

⇒ $\sf{2(150 + 120)}$

Distribute 2 through the parentheses

⇒ $\sf{300 + 240}$

Add the numbers

⇒ $\sf{540 \: m}$

Hope I helped !

Best regards!!

8 0

2 years ago

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x^4 – 2x^2 – 3x + 4?

julia-pushkina [17]

Answer: $\pm1,\frac{\pm1}{3},\frac{\pm1}{9},\pm2,\frac{\pm2}{3},\frac{\pm2}{9},\pm4,\frac{\pm4}{3},\frac{\pm4}{9}$

Step-by-step explanation:

The rational theorem states that if f(x) has integer coefficients and $\frac{p}{q}$ is a rational zero, then q is the factor of leading coefficient and p is the factor of constant term.

Given polynomial= $9x^4-2x^2-3x+4$

Now, Factors of leading coefficient q= $\pm9,\pm3,\pm1$

factors of constant term p= $\pm4,\pm2,\pm1$

according to rational root theorem the rational roots are in the form

$\frac{p}{q}=\pm1,\frac{\pm1}{3},\frac{\pm1}{9},\pm2,\frac{\pm2}{3},\frac{\pm2}{9},\pm4,\frac{\pm4}{3},\frac{\pm4}{9}$

5 0

2 years ago

Read 2 more answers

Complete the steps to find all zeroes of the function f(x) = x4 − 4x3 − 4x2 + 36x − 45. This function has roots.

xxTIMURxx [149]

Steps?

A graph shows zeros to be ±3. Factoring those out leaves the quadratic
(x-2)² +1
which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.