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3 years ago

Can someone please help me with this!

Mathematics

2 answers:

Virty [35]3 years ago

5 0

The answer for number 3 is 3.c

lyudmila [28]3 years ago

4 0

The answer for 2 is 32

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He vertices of square pqrs are p -4,0 q 4,3 r 7,-5 and s -1,-18.Show that the diagonals of square pqrs are congruent perpendicul

Anit [1.1K]

Answer:

Step-by-step explanation:

The vertices of the square given are P(-4, 0), Q(4, 3), R(7, -5) and, S(-1, -18)

For this diagonal to be right angle the slope of the diagonal must be m1=-1/m2

So let find the slope of diagonal 1

The two points are P and R

P(-4, 0), R(7, -5)

Slope is given as

m1=∆y/∆x

m1=(y2-y1)/(x2-x1)

m1=-5-0/7--4

m1=-5/7+4

m1=-5/11

Slope of the second diagonal

Which is Q and S

Q(4, 3), S(-1, -18)

m2=∆y/∆x

m2=(y2-y1)/(x2-x1)

m2=(-18-3)/(-1-4)

m2=-21/-5

m2=21/5

So, slope of diagonal 1 is not equal to slope two

This shows that the diagonal of the square are not diagonal.

But the diagonal of a square should be perpendicular, this shows that this is not a square, let prove that with distance between two points

Given two points

(x1,y1) and (x2,y2)

Distance between the two points is

D=√(y2-y1)²+(x2-x1)²

For line PQ

P(-4, 0), Q(4, 3)

PQ=√(3-0)²+(4--4)²

PQ=√(3)²+(4+4)²

PQ=√9+8²

PQ=√9+64

PQ=√73

Also let fine RS

R(7, -5) and, S(-1, -18)

RS=√(-18--5)+(-1-7)

RS=√(-18+5)²+(-1-7)²

RS=√(-13)²+(-8)²

RS=√169+64

RS=√233

Since RS is not equal to PQ then this is not a square, a square is suppose to have equal sides

But I suspect one of the vertices is wrong, vertices S it should have been (-1,-8) and not (-1,-18)

So using S(-1,-8)

Let apply this to the slope

Q(4, 3), S(-1, -8)

m2=∆y/∆x

m2=(y2-y1)/(x2-x1)

m2=(-8-3)/(-1-4)

m2=-11/-5

m2=11/5

Now,

Let find the negative reciprocal of m2

Reciprocal of m2 is 5/11

Then negative of it is -5/11

Which is equal to m1

Then, the square diagonal is perpendicular

6 0

4 years ago

Original Price $60 Percent of Discount Sale Price $45

Brums [2.3K]

Answer:

Step-by-step explanation:

8 0

3 years ago

Identify the phrase that cannot be described by the same absolute value as the other three. Explain your reasoning.

r-ruslan [8.4K]

The answer would probably be 18 degrees below normal because the absolute values of the rest are 8 not 18 which is the absolute value of 18 degrees below normal.

6 0

4 years ago

Factor the expression completely.

evablogger [386]

Answer:

Factoring the expression $xy^4+x^4y^4$ completely we get $\mathbf{xy^4(x+1)(x^2-x+1)}$

Step-by-step explanation:

We need to factor the expression $xy^4+x^4y^4$ completely

We need to find common terms in the expression.

Looking at the expression, we get $xy^4$ is common in both terms, so we can write:

$xy^4+x^4y^4\\=xy^4(1+x^3)$

So, taking out the common expression we get: $xy^4(1+x^3)$

Now, we can factor the term (1+x^3) or we can write (x^3+1) by using formula:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

So, we get:

$xy^4(1+x^3)\\=xy^4(x^3+1)\\Applying\:the\:formula\;of\:a^3+b^3\\=xy^4(x+1)(x^2-x+1)$

Therefor factoring the expression $xy^4+x^4y^4$ completely we get $\mathbf{xy^4(x+1)(x^2-x+1)}$

6 0

3 years ago

The lines y=3x-1 and y=ax+2 are perpendicular if a=___

mezya [45]

Answer:

$a = \frac{-1}{3}.$

Step-by-step explanation:

The equation of line in the form .

y = mx + c

Where m is the slope and c is the y- intercept .

As given

The lines y=3x-1 and y=ax+2 are perpendicular .

Here 3 is slope for equation of line y=3x-1 and a is slope for equation of line

y=ax+2 .

Now by using properties of the perpendicular lines property .

When two lines are perpendicular than slope of one line is negative reciprocal of the other line .

Thus

$a = \frac{-1}{3}$

Therefore $a = \frac{-1}{3}.$

8 0

3 years ago

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