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3 years ago

Triangle abc (a- 12cm b- 6cm) is similar to ayz, whats the value of x

Mathematics

1 answer:

GrogVix [38]3 years ago

3 0

Answer:

26cm

Step-by-step explanation: we want a triangle with shorter sides (smaller perimeter) and we got 2 similar triangles , since triangles are similar the corresponding sides would be in ratio.

To get triangle of shorter perimeter we have to use the longest side of

△

put 6cm side corresponding to 12cm side.

Let

△

6cm side corresponding to 12 cm side .

therefore,

So the perimeter of ABC is half of the perimeter of DEF .

perimeter of DEF =

(

)

answer 26 cm.

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Prove the divisibility of the following numbers: 51^7-51^6 by 25

vampirchik [111]

To prove the divisibility lets expand each number first to get the complete picture of the problem

51^7 = 8.974106779 . 10^11

51^6 = 1.75962878 . 10^10

(51^7 - 51^6) = 8.974106779 . 10^11 - 1.75962878 . 10^10

= 8.798143901. 10^11

$\frac{8.798143901. 10^11}{25}$

= 3.51925756. 10^10

That is the answer expressed in scientific notation

= 35192575600

Which means the divisibility is proven

8 0

2 years ago

Read 2 more answers

Let Y1 and Y2 be independent exponentially distributed random variables, each with mean 7. Find P(Y1 > Y2 | Y1 < 2Y2). (En

ArbitrLikvidat [17]

Y₁ and Y₂ are independent, so their joint density is

$f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}$

By definition of conditional probability,

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = P((Y₁ > Y₂) and (Y₁ < 2 Y₂)) / P(Y₁ < 2 Y₂)

Use the joint density to compute the component probabilities:

• numerator:

$P((Y_1>Y_2)\text{ and }(Y_1$

$=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1$

$=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty$

$=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16$

• denominator:

$P(Y_1$

(I leave the details of the second integral to you)

Then you should end up with

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = (1/6) / (2/3) = 1/4

5 0

2 years ago

Question 1 (1 point)

Pavlova-9 [17]

Answer: 5

Step-by-step explanation: itswhere the 2 lines meet at the X

7 0

2 years ago

"three times a number is greater than or equal to 12 and less than 21"

Diano4ka-milaya [45]

Answer:

The required inequality is: 12 ≤ 3x < 21

Step-by-step explanation:

We are given: three times a number is greater than or equal to 12 and less than 21

We need to answer following questions:

1) The inequality translated in numerical form

Let number = x

12 ≤ 3x < 21

2) Your work solving the inequality

We need to find value of x. Divide the inequality by x

4 ≤ x < 7

3) The solution graphed on a number line

It is shown in figure attached.

4) The solution in set notation

The set notation is: Considering x belongs to natural numbers N

{∀ x|x∈N, 4 ≤ x < 7}

5) The solution in interval notation

The interval notation is: [4,7)

because we have 4 less than equal to x and x is less than 7

8 0

2 years ago

The lowest temperature ever recorded at Oymyakon in Russia was 96.2°F below 0°F. The lowest temperature ever recorded at Prospec

Alekssandra [29.7K]

Answer:

Thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F

Thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F

Step-by-step explanation:

If the temperature is x° F below 0° F then the thermometer reading is -x° F

It is given that the Lowest temperature recorded at Oymyakon in Russai was 96.2°F below 0°F

So the thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F

Also it is given that the Lowest temperature recorded at Prospect Creek in Alaska was 80°F below 0° F

So the thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F

7 0

2 years ago

Triangle abc (a- 12cm b- 6cm) is similar to ayz, whats the value of x​

Triangle abc (a- 12cm b- 6cm) is similar to ayz, whats the value of x