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3 years ago

In the diagram below line m is parallel to line n

Mathematics

1 answer:

Dovator [93]3 years ago

3 0

You need to find the angle measurements of the triangle.
The angle supplementary to 128 measures (180 - 128 =) 52 degrees.

Using the corresponding and supplementary property because lines m and n are parallel, you know that the highest (in location) angle of the triangle measure 90 degrees.

A triangle's total angle measurements add up to 180 degrees. Subtract the other two known angles from 180. 180 - 52 - 90 = 38. The third (right side) angle of the triangle measures 38 degrees.

Now, using the supplementary angle theorem, you can find angle a, which is supplementary to the third angle on the triangle. 180 - 38 = 142.

Angle a measures 142 degrees.

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(2.2.5) In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, an

DaniilM [7]

Answer:

56 ways.

Step-by-step explanation:

This question is solved by using combinations and permutations chapters in the math book.

To put it simply, we need to find the number of 3 horse combinations we can make from 8 horses. This requires the combinations formula:

$C(n,r)=\frac{n!}{r!(n-r)!}$

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7 0

3 years ago

Let

Maksim231197 [3]

Answer:

3.3

Step-by-step explanation:

We determine the plane formed by $u_1$ and $u_2$ . The normal to the plane is given by their cross product:

$u_1\times u_2$

$\begin{pmatrix} - 2\\ - 4\\ 1 \end{pmatrix}\times\begin{pmatrix} - 4\\ 1 \\ - 4\end{pmatrix}=\begin{pmatrix} 15 \\ - 12\\ - 18\end{pmatrix}$

The equation of the plane is then given by

$15x-12y-18z=0$

The distance between a vector $\begin{pmatrix} x_1 \\ y_1 \\ z_1 \end{pmatrix}$ and a plane $Ax+By+Cz +D =0$ is given by

$d=\dfrac{|Ax_1+By_1+Cz_1 +D|}{\sqrt{A^2+B^2+C^2}}$

Comparing,

$A = 15,\ B = - 12,\ C = -18,\ D = 0,\ x_1=3,\ y_1 =-8, \ z_1 =3$

Substituting,

$d=\dfrac{|(15\times3)+(-12\times-8)+(-18\times3)+0|}{\sqrt{15^2+(-12)^2+(-18)^2}}$

$d=\dfrac{|45+96-54|}{\sqrt{225+144+324}}=\dfrac{87}{\sqrt{693}}$

$d =\dfrac{87}{26.32\ldots}\approx 3.3$

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3 years ago

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Mazyrski [523]

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Step-by-step explanation:

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4 years ago

Id like some help in this, thanks.

gogolik [260]

Answer:

80 cm²

Step-by-step explanation:

Given 2 similar figures with sides in the ratio a : b , then

ratio of areas = a² : b²

Here ratio of sides = 7 : 14 = 1 : 2

ratio of areas = 1² : 2² = 1 : 4

Thus area of B is 4 times area of A

area of B = 4 × 20 = 80 cm²

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3 years ago

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Sedaia [141]

Step-by-step explanation:

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3 years ago