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3 years ago

14

The figure below is made up of two rectangles.

1 answer:

Dmitry [639]3 years ago

7 0

Answer:

Total area of figure = [3x² + 7x + 6] feet²

Step-by-step explanation:

By dividing both rectangle by vertical line;

Given:

Length of big rectangle = (x + 3) feet

Width of big rectangle = (x + 2) feet

Length of small rectangle = 2x feet

Width of small rectangle = (x + 1) feet

Find:

Total area of figure

Computation:

Area of rectangle = Length x width

Total area of figure = Area of big rectangle + Area of small rectangle

Total area of figure = [(x + 3)(x + 2)] + [(2x)(x + 1)]

Total area of figure = [x²+ 2x + 3x + 6] + [2x² + 2x]

Total area of figure = [3x² + 7x + 6] feet²

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Amelie is shopping for children's books and puzzle books. She wants to purchase at least 2 more children's books than puzzle boo

oksano4ka [1.4K]

X = 9
y = 6

Step by step:

Divide 15 by 2: 15 ÷ 2 = 7.5
Subtract 0.5 from 7.5 (this will later be added back): 7.5 - 0.5 = 7
Subtract 1 from 7 (she wants to buy at least 2 more children books): 7 - 1 = 6
Subtract 6 from 15 (6 being the number of puzzle books, 15 being the total number of items): 15 - 6 = 9 (number of children books)

6 0

3 years ago

Having a small brain moment, can you please help and show work

ankoles [38]

Answer:

The value if x is 0.9875.

Step-by-step explanation:

First, we have to get rid of brackets by expanding :

$0.5(2x + \frac{3}{4} ) - \frac{1}{3} (0.1 + x) = 1$

$0.5(2x) + 0.5( \frac{3}{4} ) - \frac{1}{3} (0.1) - \frac{1}{3} (x) = 1$

$x + \frac{3}{8} - \frac{1}{30} - \frac{1}{3} x = 1$

Next you have to collect like terms :

$x - \frac{1}{3} x + \frac{3}{8} - \frac{1}{30} = 1$

$\frac{2}{3} x + \frac{41}{120} = 1$

Lastly, you can solve x :

$\frac{2}{3} x = 1 - \frac{41}{120}$

$\frac{2}{3} x = \frac{79}{120}$

$x = \frac{79}{120} \div \frac{2}{3}$

$x = \frac{79}{80}$

$x = 0.9875$

8 0

3 years ago

Which of the following are square roots of —8 + 8i/3? Check all that apply.

8090 [49]

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, $\sqrt{-8+8i\sqrt{3}}=(a+bi)$

$(\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2$

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = $\frac{4\sqrt{3}}{b}$

By substituting the value of a in equation (1),

$(\frac{4\sqrt{3}}{b})^2-b^2=-8$

$\frac{48}{b^2}-b^2=-8$

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = $\frac{4\sqrt{3}}{b}$

For b = ±2i,

a = $\frac{4\sqrt{3}}{\pm2i}$

= $\pm\frac{2i\sqrt{3}}{(-1)}$

= $\mp 2i\sqrt{3}$

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = $\frac{4\sqrt{3}}{\pm 2\sqrt{3}}$

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

6 0

3 years ago

Please help I need it asap!!!!! The equation of line k is y=ax+b. Which could be the equation of line l?

Reika [66]

Answer:

Option D

Step-by-step explanation:

See attached image

3 0

2 years ago

Yesterday's afternoon temperature was 21*F. It plunged overnight to 3*F. How many degrees did the temperature drop? I think the

Igoryamba

Answer: its D) 24

Step-by-step explanation:

For your answer i have checked and it is correct it is D) 24

7 0

3 years ago