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3 years ago

The length of a rectangle is twice its width. The perimeter of the rectangle is 126ft.

1 answer:

8 0

Alright, so let's make the length x and the width y. 2y=x, and xy=area. 2x+2y=perimeter. Plugging 2y=x into the perimeter equation, we get that 3x=perimeter=126, and x=126/3=42

Length=42ft, width=21ft

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Which of the values shown are potential roots of f(x) = 3x3 – 13x2 – 3x + 45? Select all that apply.

galina1969 [7]

Answer:

All potential roots are 3,3 and $-\frac{5}{3}$ .

Step-by-step explanation:

Potential roots of the polynomial is all possible roots of f(x).

$f(x)=3x^3-13x^2-3x+45$

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

p=All the positive/negative factors of 45

q=All the positive/negative factors of 3

$p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45$

$q=\pm 1,\pm 3$

All possible roots

$\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}$

Now we check each rational root and see which are possible roots for given function.

$f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0$

$f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32$

$f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144$

$f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}$

Similarly, we will check for all value of p/q and we get

$f(-5/3)=0$

Thus, All potential roots are 3,3 and $-\frac{5}{3}$ .

5 0

2 years ago

Read 2 more answers

4 + 5x = 3 (-x + 3) -11

Salsk061 [2.6K]

Answer:

4 + 5x = 3 (-x + 3) -11

4+5x=-3x+9-11

5x+3x=9-11-4

8x= -6

x= -0.75

8 0

3 years ago

Using the Triangle Sum Theorem, find x and the missing angles (2x +1) (5x +5) x= Angle (2x+1) = Angle (5x+5) =

Arte-miy333 [17]

Answer:

x = 12

(2x + 1)° = 25°

(5x + 5)° = 65°

Step-by-step explanation:

By the property of a triangle,

Sum of all angles of a triangle is 180°

In the given right triangle,

(2x + 1)° + 90° + (5x + 5)°= 180°

7x + 96 = 180

7x = 180 - 96

x = $\frac{84}{7}$

x = 12

Angle (2x + 1)° = 2(12) + 1 = 25°

Angle (5x + 5)° = 5(12) + 5 = 65°

Therefore, all three angles of the right triangle are 25°, 90° and 65°.

4 0

3 years ago

What is the sum of the first five terms of a geometric series with A1 equals 20 and R equals 1/4

sweet-ann [11.9K]

Sum = 20(1-(1/4)^5) / (1-1/4) = 26.64

6 0

3 years ago

2. Which of the following shows the correct area of the figure below rounded to the nearest hundredths place.

Lera25 [3.4K]

Answer:

the answer is 190.07 cm2

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3 years ago