2y = x + 3 5y = x - 7 What is the solution set of the given system? {(-1/3, -4/3)} {(1/3, 4/3)} {(-29/3, -10/3)} {(29/3, 10/3)}

Suppose that ABCD is a trapezoid, with AB parallel to CD, and diagonals AC and BD intersecting at P. Explain why (a) triangles A

lora16 [44]

Answer:

A trapezoid ABCD is show below,

AB || CD

AC and BD are diagonals intersecting at P.

(a)

In Δ ABC and ABD,

Area of triangle ABC = Area of triangle ABD

Because,

Area of triangle ABC = 1/2 × Base × Height

Base = AB

Height = h, which is same for both the triangle that's why,

Area of triangle ABC = Area of triangle ABD

(b)

As we know that,

Area of triangle ABC = Area of triangle ABD

On subtracting the area of triangle ABP from both the triangles, we get

Area of triangle ABC - area of triangle ABP = Area of triangle ABD - area of triangle ABP

⇒ area of triangle BCP = area of triangle DAP

Hence, triangles BCP and DAP have the same area.

(c)

In triangle ABP and CDP,

∠ABP = ∠CDP (opposite interior angles are equal between two parallel lines)

∠APB = ∠CPD (opposite angles are equal)

∠BAP = ∠DCP (opposite interior angles are equal between two parallel lines)

Therefore,

By AAA similarity

Triangles ABP and CDP are similar.

(d)

In triangle BCP and DAP,

Only ∠BCP = ∠APD (opposite angles are equal).

Therefore,

Triangles BCP and DAP need not be similar.

8 0

3 years ago

Match the equivalent expressions 3x+5x+8, 4x+4x, 4x+4x+4x+4x, -7x + 4 + 3x, 8x, 16x, -4x + 4 and 8x + 8

FrozenT [24]

Answer:

Combine like terms; 3x + 5x= 8x

Since you don't have any like terms for +8, it's going to remain the same and not change.

Answer : 3x + 5x + 8 = 8x + 8

Again with combining like terms, 4x + 4x = 8x

Answer: 4x + 4x = 8x

The third expression is going to be very similar to the last problem. 4x + 4x + 4x + 4x. We're going to add the terms together. 4+4+4+4 is equal to 16. Bring the x down and you get...

Answer: 16x

Lastly, we have -7x + 4 + 3x. Do the exact same thing we did to the other problems, combining like terms, shocking, I know. -7x + 3x= -4 and since there's no other like terms for +4, it stays the same. Therefore

Answer: -7x + 4 + 3x = -4 + 4

I hope this helps, mark as brainliest, please? :)

4 0

3 years ago

PLEASE CHECK MY ANSWERS (PART 2)

Anna007 [38]

3 is incorrect, should be 28.9

16^2 + 18^2 = EG^2
256 + 324
580 = EG^2
EG ≈ 24.08

16^2 + 24.08^2 = AG^2
256 + 580 = AG^2
836 = AG^2
AG ≈ 28.9

5 is incorrect:

The base is 8.
Draw an altitude the base.
Since the triangle is isoceles, it divides the base in half.
Half of that base is 4.
Two right triangles have been formed with one leg 4 and hypotenuse 8.
4^2 + b^2 = 8^2
16 + b^2 = 64
b^2 = 48
b ≈ 6.93

The height of the triangle is 6.93, the base is 8.
A = bh/2 = 8*6.93/2 ≈ 27.7 ≈ 28

3 0

4 years ago

Solve by graphing<br> X+Y=3<br> Y=2x

ZanzabumX [31]

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3 years ago

A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the

almond37 [142]

Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.

5 0

3 years ago