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kirill115 [55]
3 years ago
10

Need help please can you give answer with working out i can not answer as it is quite gard

Mathematics
1 answer:
Elis [28]3 years ago
4 0

Step-by-step explanation:

\text{Given:}\\\\AB=3x-4\\AC=2x+12\\BC=7x-2\\AB:AC=1:2\Rightarrow(3x-4):(2x+12)=1:2\\\\\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\qquad\text{cross multiply}\\\\(3x-4)(2)=(2x+12)(1)\qquad\text{use the distributive property}\\\\(3x)(2)+(-4)(2)=2x+12\\\\6x-8=2x+12\qquad\text{add 8 to both sides}\\\\6x-8+8=2x+12+8\\\\6x=2x+20\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\6x-2x=2x-2x+20\\\\4x=20\qquad\text{divide both sides by 4}\\\\\dfrac{4x}{4}=\dfrac{20}{4}\\\\x=5

\text{Put the value of}\ x\ \text{to}\ AC\ \text{and}\ BC:\\\\AC=2(5)+12=10+12=22\\\\BC=7(5)-2=35-2=33\\\\AC:BC=22:33=\dfrac{22}{33}=\dfrac{22:11}{33:11}=\dfrac{2}{3}=2:3

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A painter starts with a blank 24-inch by 12-inch piece of rice paper. The painter wants to leave a uniform border x inches wide
ddd [48]

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

<h2>a.</h2>

In this scenario, 'x' represents the width of the border. A "uniform border" means that the border has the same width all around.

The area of the paper that can be painted does not include the border. Since the border is on the original rice paper (not added to it), you subtract 'x' from each side of the rice paper.

The area of a rectangle is A = lw (Area is length times width). <u>Each length and width is reduced by 'x'.</u>

If the original rice paper's area is: 24 X 12, then,

the Area that can be painted is:

A = (24 - x) (12 - x)

A polynomial in standard form means the most expanded version of an expression, ordering the terms (numbers) from greatest to least degree. (The degree of a term is the value of its exponent).

Expand the expression. Multiply the numbers from each bracket in the order FOIL (first, outside, inside last):

A = (24 - x) (12 - x)

= 288 - 24x - 12x + x²        Collect like terms (-24x - 12x = -36x)

= 288 - 36x + x²        Rearrange ordering greatest to least exponent value

= x² - 36x + 288        Standard form polynomial

<h2>b.</h2>

The width of the margin is the same thing as the width of the border. Since 'x' is the width of the border,

x = 2

Using either the expanded or factored equation for area of that can be painted, substitute 'x' for 2.

I will use the factored form.

A = (24 - x) (12 - x)        Substitute x for 2

= (24 - 2) (12 - 2)          Solve inside each bracket first by subtracting

= (22) (10)             Multiply

= 220                 Area that can be painted

Remember to include the units: 220 in²

Therefore if the margin is 2 inches wide, then the area that can be painted in 220 square inches.

5 0
3 years ago
A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake
Andreas93 [3]

Answer: 12.5 cm

Step-by-step explanation:

Equation would be:

1:80

?:1000

So you'll just have the cross multiply the equation above to find ? ( scale drawing lake). It'll be 1000*1/80 which will be 12.5 cm.

                               

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