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3 years ago

Determine o trigésimo termo da PA (6,17,28...)

Mathematics

1 answer:

zloy xaker [14]3 years ago

3 0

Answer:

Step-by-step explanation:

Dertemine o trigsímo termo da P.A 6,17,28

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In a triangle, the sum of the measures of the first two angles is 12 less than the measure of the third angle. In addition, the

USPshnik [31]

The measure of the three angles are 56, 28 , 192 degree

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

A triangle is a polygon with three sides , three vertices an three angles.

It is given to make system of equations

Let the measure of the first , second and third angle be x, y and z

the sum of the measures of the first two angles is 12 less than the measure of the third angle.

x +y = z -12 ----1

the measure of the first angle is twice as big as the measure of the second angle.

x = 2y

Now equation 1 will be

z - 3y = 12

x +y+z = 180

2y +y +z = 180

3y +z = 180 ----2

z - 3y = 12------3

On solving the system of equation 1, 2

2z = 192

z= 96 degree

3y = 180-96

y = 28

x = 56

Therefore the measure of the three angles area 56, 28 , 192 degree.

To know more about Triangle

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8 0

2 years ago

11. This picture shows a table in the shape of a regular hexagon.

disa [49]

Answer:

Sum of interior angles = 720°

One interior angle = 120°

Step-by-step explanation:

Sum of interior angles = 180°(n-2)

Where n is the number of sides in a polygon

Therefore, one angle in a regular polygon will be (180°(n-2))÷n

Hence

Sum of interior angles= 180°(6-2)

= 720°

One interior angle = 720°÷6

= 120°

3 0

3 years ago

The registration fees for the auto were determined from California's DMV website The registration fee is $182 plus 0.65% of the

dybincka [34]

We have to find 0.65% of 182

$\\ \rm\longmapsto 0.0065\times 182$

$\\ \rm\longmapsto 1.183\$$

Now total fee

$\\ \rm\longmapsto 182+1.183=183.183\$$

3 0

3 years ago

please help me, Prove a quadrilateral with vertices G(1,-1), H(5,1), I(4,3) and J(0,1) is a rectangle using the parallelogram me

mestny [16]

Answer:

Step-by-step explanation:

We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).

Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus

Join JH and GI such that they form the diagonals of the quadrilateral.Now,

JH= $\sqrt{(5-0)^{2}+(1-1)^{2}}=5$ and

GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$

Now, mid point of JH= $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

= $(\frac{5+0}{2},\frac{1+1}{2})=(\frac{5}{2},1)$

Mid point of GI= $(\frac{5}{2},1)$

Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.

Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.

Thus, From ΔGIJ, we have

$(GI)^{2}=(IJ)^{2}+(JG)^{2}$ (1)

Now, JI= $\sqrt{(4-0)^{2}+(3-1)^{2}}=\sqrt{20}$ and GJ= $\sqrt{(0-1)^{2}+(1+1)^{2}}=\sqrt{5}$

Substituting these values in (1), we get

$5^{2}=(\sqrt{20})^{2}+(\sqrt{5})^{2} }$

$25=20+5$

$25=25$

Thus, GIJ is a right angles triangle.

Hence, GHIJ is a rectangle.

Also, The diagonals GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$ and HJ= $\sqrt{(0-5)^2+(1-1)^2}=5$ are equal, thus, GHIJ is a rectangle.

6 0

3 years ago

Name a pair of fractions that use the least common denominator and are equivalent to 9/10 + 5/6

grin007 [14]

The smallest common denominator is 30 in so
<span>9/10=27/30 and 5/6=25/30 are your answers ; ]</span>

6 0

3 years ago

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