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3 years ago

-5/6x = 20 2/3(x - 7) = -2 solve them and show your work! ASAP! I need this done fast!!

Mathematics

1 answer:

LenKa [72]3 years ago

3 0

Answer:

x=-24 & x=4.

Step-by-step explanation:

-5/6x=20

x=20/(-5/6)

x=(20/1)(-6/5)=-120/5=-24

-------------------------------------

2/3(x-7)=-2

2/3x-14/3=-2

2/3x=-2+14/3

2/3x=-6/3+14/3

2/3x=8/3

x=(8/3)/(2/3)

x=(8/3)(3/2)=8/2=4

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70/9 as a mixed number

Makovka662 [10]

70/9
Divide
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3 years ago

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Question:

aivan3 [116]

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

$\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}$

The scale factor is equal to

$z=\frac{CB}{C'B'}$

substitute

$z=\frac{4}{8}$

simplify

$z=\frac{1}{2}$

Part B) What is the ratio of the areas (small to large)?

Area of the small triangle

$A=\frac{1}{2}(2)(4)=4\ units^2$

Area of the large triangle

$A=\frac{1}{2}(4)(8)=16\ units^2$

ratio of the areas (small to large)

$ratio=\frac{4}{16}=\frac{1}{4}$

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

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3 years ago

Please help with #12 im confused that is the key but i dont get it

Svetllana [295]

Given Equation

$\boxed{ \tt \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})}$

Step by step expansion:

$\dashrightarrow \sf \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})$

$\\ \\$

$\dashrightarrow \sf \: (8 \sqrt{3})^{2} - (2 \sqrt{2} {)}^{2}$

Reason:

(a + b)(a - b) = a²- b²

$\\ \\$

$\dashrightarrow \sf \: (8 {}^{2} \times { \sqrt{3} }^{2} )- (2 \sqrt{2} {)}^{2}$

$\\ \\$

$\dashrightarrow \sf \: (64 \times 3 ) - (2 \sqrt{2} {)}^{2}$

$\\ \\$

$\dashrightarrow \sf \: (64 \times 3 ) - (2 {}^{2} \times \sqrt{2} {}^{2} {)}$

$\\ \\$

$\dashrightarrow \sf \: 192- 8$

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$\dashrightarrow \sf \: 184$

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~BrainlyVIP ♡

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2 years ago

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△QRS is rotated about point P to △Q′R′S′ . Which statements are true about the pre-image and image?

yuradex [85]

Note that rotation will not affect the shape and size of an object.

Rotation with respect to a point preserves the corresponding sides and the corresponding angles of the original image.

Hence, the statements

The corresponding angle measurements in each triangle between the pre-image and the image are preserved and

The corresponding lengths, from the point of rotation, between the pre-image and the image are preserved

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3 years ago

If Michael invests $2000 in the bank at a rate of 5.5% for 6 years how much interest will he make?

Natalija [7]

Answer:

intereste = 660

Step-by-step explanation:

$interest \: = \frac{2000 \times 5.5 \times 6}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{66000}{100} \\ \: \: \: \: \: \: \: \: \: \: \: = 660 \\$

plz..

mark it as a brilliant answer

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3 years ago