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3 years ago

What expression is equivalent to 4(n- 3^2) + n? Thats 3 squared with 2

Mathematics

1 answer:

Lelechka [254]3 years ago

6 0

Given that,

An expression : 4(n- 3²) + n

To find,

The equivalent expression.

Solution,

We have,

4(n- 3²) + n

As 3²= 9

= 4(n- 9) + n

Opening the brackets,

= 4n-4(9) + n

= 4n-36 +n

= 5n-36

Hence, the equivalent expression is 5n-36.

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60 nails cost m dollars
60nails = m dollars
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so for 24 (m/60) * 24 = 2m/5

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3 years ago

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Write the word sentence as an inequality. the sum of a number w and 2.56 is at least 10.24

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w + 2.56 ≥ 10.24

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The length of a rectangle is represented by the polynomial 2x - 5xº + 8 and the width is represented

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Step-by-step explanation:

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3 years ago

What is the solution to this system of equations 3x+y=17 and x+2y=49

11Alexandr11 [23.1K]

Answer:x=-3 y=26

Step-by-step explanation:

3x+y=17.............(1)

x+2y=49..............(11)

From (11) x=49-2y

Substitute x=49-2y in 3x+y=17

3(49-2y) + y=17

Open bracket

147-6y+y=17

147-5y=17

Collect like terms

5y=147-17

5y=130

Divide both sides by 5

5y/5=130/5

y=26

Substitute y=26 in x+2y=49

x+2(26)=49

x+52=49

Collect like terms

x=49-52

x=-3

7 0

3 years ago

A quadrilateral has vertices at A(–5, 5), B(1, 8), C(4, 2), D(–2, –2). Use slope to determine if the quadrilateral is a rectangl

lianna [129]

With the properties of rectangle in mind we must perform two verification. Verify to see if opposite sides are parallel and adjacent sides are perpendicular.

We need to determine the slope of each side, using the formula,

$m=\frac{y_2-y_1}{x_2-x_1 }$

Slope of AB

$m_{AB}=\frac{8-5}{1--5}$

$\Rightarrow m_{AB}=\frac{8-5}{1+5}$

$\Rightarrow m_{AB}=\frac{3}{6}$

$\Rightarrow m_{AB}=\frac{1}{2}$

Slope of BC

$m_{BC}=\frac{2-8}{4-1}$

$\Rightarrow m_{BC}=\frac{-6}{3}$

$\Rightarrow m_{BC}=-2$

Slope of CD

$m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-4}{-6}$

$\Rightarrow m_{CD}=\frac{2}{3}$

Slope of AD

$m_{AD}=\frac{-2-5}{-2--5}$

$\Rightarrow m_{AD}=\frac{-2-5}{-2+5}$

$\Rightarrow m_{AD}=\frac{-7}{3}$

Verify Parallel sides

If the quadrilateral is a rectangle, then opposite sides should have the same slope. But

$m_{AD} = \frac{-7}{3} \neq m_{BC}=-2$

$m_{AB}=\frac{1}{2} \neq m_{CD}=\frac{2}{3}$

Verify Perpendicularity

And also the product of slopes of all sides with a common vertex should be -1. But

$m_{AB} \times m_{BC}=\frac{1}{2} \times -2=-1$

$m_{AB} \times m_{AD}=\frac{1}{2} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{AD}=\frac{2}{3} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{BC}=\frac{2}{3} \times -2 \neq -1$

Since the quadrilateral fails to satisfy all these conditions, the quadrilateral is not a rectangle

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3 years ago