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3 years ago

The diagram shows a rectangle.

Mathematics

2 answers:

8090 [49]3 years ago

4 0

Answer:

To solve this we calcuclate the total are then we subtract the 4 rectangles area

total area = length × width =10.5 × 10.5 = 110.25 cm²

the rectangles drawn accurately = 2(.5 × 7)

7 cm²

the rectangles drawn not accurately 2(.5 × 10.5)

= 10.5 cm²

so the shaded area = 110.25 - 7 - 10.5 = 92.75 cm²

Taya2010 [7]3 years ago

4 0

Answer:

42 cm²

Step-by-step explanation:

We can see that the length of the blue rectangle is the same as the length of the smaller rectangle = 7 cm.

To calculate the width of the blue rectangle, we take the length of the smaller rectangle (7 cm) and substract two of the width (0.5 cm) of the smaller rectangle:

7 - (2 x 0.5) = 6 cm

Now we have the length and width of the blue rectangle.

Are of blue rectangle = l x w = 7 x 6 = 42 cm²

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Which is the approximate solution to the system y = 0.5x + 3.5 and y = − 2/3 x + 1/3 shown on the graph? (–2.7, 2.1) (–2.1, 2.7)

AlekseyPX

Answer:

The approximate solution to the system is $(-2.7, 2.1)$ .

Step-by-step explanation:

To solve the system of equations $\begin{bmatrix}y=0.5x+3.5\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$ you must:

$\mathrm{Rationalize\:equations}\\\\\begin{bmatrix}y=\left(\frac{1}{2}\right)x+\left(\frac{7}{2}\right)\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$

$\mathrm{Subsititute\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\begin{bmatrix}-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\\\\-\frac{2}{3}x=\frac{19}{6}+\frac{1}{2}x\\\\-\frac{7}{6}x=\frac{19}{6}\\\\6\left(-\frac{7}{6}x\right)=\frac{19\cdot \:6}{6}\\\\-7x=19\\\\x=-\frac{19}{7}\approx-2.7$

$\mathrm{For\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\mathrm{Subsititute\:}x=-\frac{19}{7}\\\\y=-\frac{2}{3}\left(-\frac{19}{7}\right)+\frac{1}{3}\\\\y=\frac{15}{7}\approx 2.1$

The approximate solutions to the system of equations are:

$x=-2.7 ,\:y=2.1$

5 0

3 years ago

Read 2 more answers

Re-write the quadratic function below in Standard Form y = -(x – 3)2 +8

lisov135 [29]

Answer:

y = -x² + 6x - 1

General Formulas and Concepts:

Algebra I

Standard Form: ax² + bx + c = 0
Expanding by FOIL (First Inside Outside Last)
Combining like terms

Step-by-step explanation:

Step 1: Define equation

y = -(x - 3)² + 8

Step 2: Rewrite

Expand [FOIL]: y = -(x² - 6x + 9) + 8
Distribute -1: y = -x² + 6x - 9 + 8
Combine like terms: y = -x² + 6x - 1

4 0

3 years ago

Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours o

OlgaM077 [116]

Answer:

Infotron should produce each day 13 hockey and 6 soccer games

Step-by-step explanation:

x = Number of hockey games Infotron should produce

y = Number of soccer games Infotron should produce

Number of labor-hours for assembly = 2x + 3y

Number of labor-hours for testing = 2x + y

Now we can write our equations system, this way:

2x + 3y = 44

2x + y = 32

*********************

Expressing y in terms of x in the 2nd equation:

2x + y = 32

y = 32 - 2x

********************

Substituting y and solving for x in the 1st equation:

2x + 3y = 44

2x + 3 * ( 32 - 2x) = 44

2x + 96 - 6x = 44

-4x = 44 - 96

-4x = - 52

x = -52/-4

x = 13

*****************

Solving for y in the 2nd equation:

2x + y = 32

2 * 13 + y = 32

26 + y = 32

y = 32 - 26

y = 6

Infotron should produce each day 13 hockey and 6 soccer games

7 0

3 years ago

What is the Square root of -3

zavuch27 [327]

The square root of -3 is 1.73205081

3 0

3 years ago

Vivian found data about her city's population and made a scatter plot the equation of the linebbest fit for. Her data is p= 637.

Andre45 [30]

Answer:

annual growth rate m = 637.5 people / year

Step-by-step explanation:

Solution:-

- The scatter plot displaying the city's population was modeled by a linear equation of the form:

y = m*x + c

Where, m and c are constants.

- The scatter plot displayed the following relation of the city's population (p):

p = 637.5*t + 198,368.1

Where, p : The population in t years after after 1990

t : The number of years passed since 1990.

- The slope of the graph "m = 637.5" denotes the rate of change of dependent variable with respect ot independent variable:

dp / dt = m = 637.5

- So the rate of change of population per unit time t since 1990 has been constant with a an annual growth rate m = 637.5 people / year

7 0

3 years ago