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3 years ago

What is the answer to 2/5(10p-15)=14?

Mathematics

1 answer:

satela [25.4K]3 years ago

8 0

Answer:

P = 5

Step-by-step explanation:

2/5(10p) - 2/5(15)= 14

20p/5 - 30/5= 14

4p - 6= 14

4p = 20

p=5

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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

Find the equation of this line.<br> Acellus

aalyn [17]

Answer:

Step-by-step explanation:

two points on the line are (-3,-2) and (5,4)

slope=(4+2)/(5+3)=6/8=3/4

eq. of line is

y+2=3/4 (x+3)

4y+8=3x+9

4y=3x+1

y=3/4 x+1/4

8 0

2 years ago

4+ a/5= 8<br> What is the solution to the equation?

den301095 [7]

A= 20 let me know if you need an explanation❤️, mark me branliest pls

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3 years ago

WILL GET A BRAINLIEST...!

Orlov [11]

X divided by 4, it's ur expression

4 0

3 years ago

What postulate or theorem can be used to prove that these two triangles are congruent?

kati45 [8]

Answer:

AAS postulate can be used to prove that these two triangles are congruent

Step-by-step explanation:

Let us revise the cases of congruence

SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ

In the given figure

∵ There is a pair of vertically opposite angles

∵ The vertically opposite angles are congruent ⇒ (1)

∵ There are two angles have the same mark

∴ These marked angles are congruent ⇒ (2)

∵ There are two sides have the same mark

∴ These two marked sides are congruent ⇒ (3)

→ From (1), (2), and (3)

∴ The two triangles have 2 angles and 1 side congruent

→ By using case 4 above

∴ The two triangles are congruent by the AAS postulate of congruency.

AAS postulate can be used to prove that these two triangles are congruent

5 0

2 years ago