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3 years ago

Aa criterion : if two corresponding angles of two triangles are congruent then the two triangles are similar

1 answer:

7 0

The angle-angle-angle postulate states that if two corresponding angles of two triangles are the same, the triangles are similar.
This is simply because the triangle's sides are not known but they are at the same angle to one another so the triangles must be similar.

You might be interested in

Which value is NOT a solution of 8x3 – 1 = 0?

Tpy6a [65]

<u><em>Note: As you may have unintentionally missed to add the value choices. But, I would make sure to explain the concept so that you may improve your understanding in terms of solving these type of questions.</em></u>

Answer:

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Step-by-step explanation:

Considering the equation

$8x^3\:-\:1\:=\:0$

Steps to solve the equation

$8x^3-1=0$

$\mathrm{Add\:}1\mathrm{\:to\:both\:sides}$

$8x^3-1+1=0+1$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

$\mathrm{Divide\:both\:sides\:by\:}8$

$\frac{8x^3}{8}=\frac{1}{8}$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

$\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

$x=\sqrt[3]{\frac{1}{8}},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1-\sqrt{3}i}{2}$

So,

$x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$

Therefore,

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Keywords: solution, value

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7 0

3 years ago

-7(n - 2) + 2n = -5(n + 6)

skad [1K]

Given the expression below

$-7(n-2)+2n=-5(n+6)$

To find n

Open the brackets

$\begin{gathered} -7(n-2)+2n=-5(n+6) \\ -7n+14+2n=-5n-30 \\ -7n+2n+14=-5n-30 \\ -5n+14=-5n-30 \end{gathered}$

Collect like terms

$\begin{gathered} -5n+14=-5n-30 \\ -5n-(-5n)=-30-14 \\ 0\ne-44 \end{gathered}$

Since, the sides are not equal,

Hence, there is no solution

7 0

1 year ago

If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal

lorasvet [3.4K]

Answer:

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

The probability is $P(Z > 2.5 ) = 0.0062097$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 800$

The variance is $var(x) = 1600 \ kg$

The range consider is $x_1 = 778 \ kg \ x_2 = 834 \ kg$

The value consider in second question is $x = 900 \ kg$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{var (x)}$

substituting value

$\sigma = \sqrt{1600}$

$\sigma = 40$

The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as

$P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )$

Generally $\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)$

$P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )$

$P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)$

From the z-table the value for $P(z_1 < 0.85) = 0.80234$

and $P(z_1 < -0.55) = 0.29116$

$P(x_1 < X < x_2 ) = 0.80234 - 0.29116$

$P(x_1 < X < x_2 ) = 0.51118$

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

The probability of cucumber give the crop exceed 900 kg is mathematically represented as

$P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )$

substituting values

$P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )$

$P(X > x ) = P(Z >2.5 )$

From the z-table the value for $P(Z > 2.5 ) = 0.0062097$

7 0

3 years ago

The subject of the formula below is y.<br>a=4x/t - p<br>Rearrange the f make x the subject.

Crazy boy [7]

Answer:

x = t(a+p)/4

Step-by-step explanation

Given the expression

a=4x/t - p

We are to make x the subject of the formula

a=4x/t - p

Add p to both sides

a+p = 4x/t - p+p

a+p = 4x/t

Cross multiply

t(a+p) = 4x

Rearrange

4x = t(a+p)

Divide both sides by 4

4x/4 = t(a+p)/4

x = t(a+p)/4

4 0

2 years ago

Ermias and Jeremiah both leave the bookstore at the same time, but in opposite directions. If Jeremiah travels 8 mph faster than

leva [86]

Using proportions, it is found that Ermias is traveling at a rate of 11 mph and Jeremiah at a rate of 19 mph.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Jeremiah travels 8 mph faster than Ermias, hence their velocities are:

x, x + 8

They travel in opposite directions, hence in one hour they are 2x + 8 apart.

In eight hours, the distance is 8(2x + 8), which is of 240 miles, hence:

8(2x +8) = 240

2x + 8 = 30

2x = 22

x = 11.

Then:

x = 11 -> Ermias.

x = 11 + 8 = 19 -> Jeremiah.

More can be learned about proportions at brainly.com/question/24372153

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3 0

1 year ago