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3 years ago

Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.

Mathematics

1 answer:

777dan777 [17]3 years ago

6 0

If two triangles are similar then the corresponding sides are in proportion. Thus,

AB / AU = BC / UV = AC / AV

AB / (20x+108) = 703 / 444

Where AB is equivalent to:

AB = AU + UB

AB = 20x + 108 + 273

AB = 20x + 381

Therefore going back to the first equation:

(20x + 381) / (20x + 108) = 703/444

444 (20x + 381) = 703 (20x + 108)

8880x + 169164 = 14060x + 75924

14060x - 8880x = 169164 – 75924

5180 x = 93240

x = 93240 / 5180

<span>x = 18 (ANSWER)</span>

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This cuboid is made from 6 small cubes.<br> Write how many small cubes there are in this cuboid

Alexxx [7]

Answer:

30 cubes

Step-by-step explanation:

To find the number of small cubes in the larger cuboid, you can multiply the number of cubes that make up the length, width and height together.

There are 5 cubes along the bottom, 2 along the side and 3 going up. The volume would be 5 × 2 × 3 which is 30 cubes.

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2 years ago

A toy manufacturer wants to know how many new toys children buy each year. A sample of 601 children was taken to study their pur

Lilit [14]

Answer:

The confidence interval is 6.6<μ<6.8.

Step-by-step explanation:

We have:

Number of observations = 601

Mean = 6.7

Standard deviation σ = 1.5

The z-score for a 95% confidence interval is 1.96.

The limits of the confidence interval can be calculated as

$X \pm z*\frac{\sigma}{\sqrt{n}}\\\\LL=X-z*\frac{\sigma}{\sqrt{n}}=6.7-1.96*\frac{1.5}{\sqrt{601} } =6.7-0.1199=6.6\\\\UL=X+z*\frac{\sigma}{\sqrt{n}}=6.7+1.96*\frac{1.5}{\sqrt{601} } =6.7+0.1199=6.8$

The confidence interval is 6.6<μ<6.8.

7 0

3 years ago

Nuts.com sells raw almonds for $10 per pound and roasted pistachios for $12 per pound. Christopher spends $70, before taxes and

sp2606 [1]

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Step-by-step explanation:

Cost of almonds per pound = $10

Cost of roasted pistachios = $12

Total amount spent = $70

Weight of nuts = 6.3

Let,

Weight of almonds = x

Weight of roasted pistachios = y

According to given statement;

x+y=6.3 Eqn 1

10x+12y=70 Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=6.3)\\10+10y=63\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2;

$(10x+12y)-(10x+10y)=70-63\\10x+12y-10x-10y=7\\2y=7$

Dividing both sides by 2

$\frac{2y}{2}=\frac{7}{2}\\y=3.5$

Putting y=3.5 in Eqn 1

$x+3.5=6.3\\x=6.3-3.5\\x=2.8$

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Keywords: linear equations, elimination method

Learn more about elimination method at:

#LearnwithBrainly

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3 years ago

How find derivative of function: y=arcsin(2x+1)<br> ...?

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$( \arcsin{x})'= \frac{1}{ \sqrt{1-x^2} } 
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3 0

3 years ago

A student estimates that it takes 2 hours to read 25 pages. At this rate, how many hours will she need to read 425 pages?

wolverine [178]

Answer:

34 hours

Step-by-step explanation:

2:25 = x:425

25/2 = 12.5

425/12.5 = 34

so it is 34:425

She will need to read for 34 hours to read 425 pages

7 0

3 years ago

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