⦁ Find the distance between the two numbers

When measuring the length a and the width b of a rectangle, it was found that 5.4< a< 5.5 and 3.6< b< 3.7 (in centim

leva [86]

Answer:

The possible values of the perimeter of the rectangle is between 18 and

18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm

Step-by-step explanation:

* Lets explain how to solve the problem

- The perimeter of any quadrilateral is the sum of the length of its

four sides

- The rectangle is a quadrilateral with each two opposite sides are

equal in lengths, then its perimeter = 2l + 2w, where l, w are its

length and width

∵ The the length of the rectangle is a

∵ 5.4 < a < 5.5 cm

∵ The perimeter of the rectangle = 2a + 2b

- Lets multiply the inequality by 2

∴ 5.4 × 2 < a × 2 < 5.5 × 2

∴ 10.8 < 2a < 11 ⇒ (1)

∵ The width of the rectangle is b

∵ 3.6 < b < 3.7 cm

- Lets multiply the inequality by 2

∴ 3.6 × 2 < b × 2 < 3.7 × 2

∴ 7.2 < 2b < 7.4 ⇒ (2)

- <u><em>Add inequalities (1) and (2)</em></u>

∵ 10.8 < 2a < 11

+ 7.2 < 2b < 7.4

∴ 18 < 2a + 2b < 18.4

∵ 2a + 2b represents the perimeter of the rectangle

∴ The possible values of the perimeter of the rectangle is between

18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm

7 0

3 years ago

The temperature at noon on Monday

Effectus [21]

Answer:

There was a 5% change

Step-by-step explanation:

On Monday, the temperature was 80.

On Tuesday, the temp was 77

On Wednesday, the temp was 84

there was a difference of 4

4 is 5% of 80

3 0

2 years ago

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

3 years ago

Read 2 more answers

A carton can hold 1000 unit cubes that measure 1 inch by 1 inch by 1 inch. Describe the dimensions of the carton using unit cube

navik [9.2K]

The dimensions of the carton are:

10 x 10 x 10 [inch OR unit cubes - it's the same since cubes' dimensions are 1 x 1 x 1 inch)

I attach the explanation below.

6 0

3 years ago

I need help with the problem

Kobotan [32]

There are 99 miles left. 43(7)=301. 400-301=99.

7 0

3 years ago

Read 2 more answers