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4 years ago

Write two equivalent expressions to represent the area of this rectangle.

Mathematics

1 answer:

KengaRu [80]4 years ago

6 0

Answer:

The two expression to represent area is (5 x - 10) sq. units or 5( x- 2) sq. units

Step-by-step explanation:

Here, the length of the rectangle = (x-2) units

The width of the rectangle = 5 units

Now, AREA OF A RECTANGLE = LENGTH x WIDTH

So, here AREA = 5 ( x- 2)

= (5 x - 10) sq. units

( as by Distributive property: A (B-C) = AB - AC)

Hence, the two expression to represent area is (5 x - 10) sq. units or 5( x- 2) sq. units

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The sides of △FGH are FG = 6 x+ 7, GH = 8x - 5, and FH = 10x - 11. If the perimeter of △FGH is 87, list the angles in order from

irga5000 [103]

Answer:

From largest to smallest: FG, FH, GH

Step-by-step explanation:

Given

$FG = 6x + 7$

$GH = 8x - 5$

$FH = 10x - 11$

$Perimeter = 87$

Required

Order the sides in descending order

First, we need to solve for x.

Perimeter of FGH is calculated as thus:

$Perimeter = FG + GH + FH$

Substitute values for FG, GH, FH and Perimeter

$87 = 6x + 7 + 8x - 5 + 10x - 11$

Collect Like Terms

$87 - 7 + 5 + 11= 6x + 8x + 10x$

$96= 24x$

Reorder

$24x = 96$

Divide through by 24

$x = 96/24$

$x = 4$

Substitute 4 for x in FG, GH and FH

$FG = 6x + 7$

$FG = 6 * 4 + 7$

$FG = 24 + 7$

$FG =31$

$GH = 8x - 5$

$GH = 8 * 4 - 5$

$GH = 32 - 5$

$GH = 27$

$FH = 10x - 11$

$FH = 10*4 - 11$

$FH = 40 - 11$

$FH = 29$

In order of arrangement in descending order, we have:

$FG =31$ $FH = 29$ $GH = 27$

4 0

3 years ago

Simplify 1/4-7i to get a complex number in standard a + bi form.

Romashka [77]

Answer:

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

Step-by-step explanation:

we are given

$\frac{1}{4-7i}$

Firstly, we will get rid of imaginary term from denominator

so, we will multiply conjugate to both top and bottom term

$\frac{1}{4-7i}=\frac{1\times (4+7i)}{(4-7i)\times (4+7i)}$

$\frac{1}{4-7i}=\frac{4+7i}{4^2-(7i)^2}$

$\frac{1}{4-7i}=\frac{4+7i}{16+49}$

$\frac{1}{4-7i}=\frac{4+7i}{65}$

we can also write as

so, we get

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

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3 years ago

Sergeu [11.5K]

Answer:

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Step-by-step explanation:

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