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3 years ago

Which expression correctly represents the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide?

Mathematics

2 answers:

Maurinko [17]3 years ago

5 0

Answer: $2(12\ cm)+2(7\ cm)$

Step-by-step explanation:

We know that the formula to find the perimeter of a rectangle is given b y:-

$P=2(l+w)$ , where l is length and w is width.

Then, the expression that correctly represents the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide will be :-

$P=2(12\ cm+7\ cm)\\\\=2(12\ cm)+2(7\ cm)$

Hence, D is the correct option.

iren2701 [21]3 years ago

3 0

D.
That is what i do 12 x 2 will equal 24 since the are 2 parallel sides like in a rectangle. and it will be the same concept on the other side 7 x 2 = 14 and 24 + 14 will equal 38
hope this helped and is how you are supposed to work it

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5. What is the range? Explain. (1 point)

pav-90 [236]

The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is [5, ∞).

To know more about Range here.

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3 0

1 year ago

zhenek [66]

Answer:

Step-by-step explanation:

length = x +x + 2 = 2x + 2

Width = 2+ x

Area of rectangle = length *width

(x +2)(2x + 2) = 110

Use FOIL method

x*2x + x*2 + 2*2x + 2*2 = 110

2x² + <u>2x + 4x</u> + <u>4 - 110</u> = 0 {Combine like terms}

2x² +6x - 106 = 0

a = 2 ; b = 6 ; c = -106

b² - 4ac = 6² - 4*2*(-106)

= 36 + 848

= 884

$\sqrt{b^{2}-4ac}=\sqrt{884}= 29.73$

$x =\dfrac{-b+\sqrt{b^{2}-4ac}}{2a} \ ; \ x==\dfrac{-b-\sqrt{b^{2}-4ac}}{2a}\\\\x = \dfrac{-6+29.73}{2*2} \ ; \ x =\dfrac{-6-29.73}{2*2} \ this \ is \ ignored \ as \ it \ is \ negative\\\\x=\dfrac{23.73}{4};$

x = 5.93 m

5 0

3 years ago

Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

$k = \frac{y}{x}$ (1)

Where:

$x$ - Input.

$y$ - Output.

If we know that $(x_{1}, y_{1}) = (13, 45.5)$ , $(x_{2}, y_{2}) = (14, 49)$ and $(x_{3}, y_{3}) = (15, 52.5)$ , then the constants of proportionalities of each ordered pair are, respectively:

$k_{1} = \frac{y_{1}}{x_{1}}$

$k_{1} = \frac{45.5}{13}$

$k_{1} = \frac{7}{2}$

$k_{2} = \frac{y_2}{x_2}$

$k_{2} = \frac{49}{14}$

$k_{2} = \frac{7}{2}$

$k_{3} = \frac{y_{3}}{x_{3}}$

$k_{3} = \frac{52.5}{15}$

$k_{3} = \frac{7}{2}$

Since $k_{1} = k_{2} = k_{3}$ , the constant of proportionality is 3.5.

8 0

3 years ago

Lilian has 42 feet of yarn. She wants to cut the yarn into 8 equal parts. How long will each part be?

GrogVix [38]

Answer:

A. Five and two eighths feet.

Step-by-step explanation:

42 (feet of yarn) ÷ 8 (equal parts) = 5.25 (feet of yarn that each part is)

5.25 =

$5 \frac{1}{4}$

$5 \frac{2}{8}$

because 1/4 = 2/8.

Hope this helps!

3 0

3 years ago

Read 2 more answers

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

3 years ago