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One diagonal of a rhombus has endpoints (-11, -9) and (-5, -3).

valina [46]

Answer:

(-10, -8) and (-6, -4)

Step-by-step explanation:

we know that

The diagonals of a rhombus are perpendicular

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

step 1

Find the slope of the given diagonal

we have

(-11, -9) and (-5, -3)

m=(-3+9)/(-5+11)

m=-6/6=-1

Find the slope of the other diagonal

we have

m1=-1

Find m2

m1*m2=-1

(-1)*m2=-1

m2=1

step 2

Verify the slope of each of the endpoints of the other diagonal

The slope of the other diagonal must be equal to 1

so

case a) (-10, -4) and (-6, -8)

m=(-8+4)/(-6+10)

m=-4/4=-1

therefore

The points of case a) cannot be the end-points of the other diagonal

case b) (-8, -3) and (-5, -6)

m=(-6+3)/(-5+8)

m=-3/3=-1

therefore

The points of case b) cannot be the end-points of the other diagonal

case c) (-8, -4) and (-8, -8)

m=(-8+4)/(-8+8)

m=-4/0 -----> undefined

therefore

The points of case c) cannot be the end-points of the other diagonal

case d) (-10, -8) and (-6, -4)

m=(-4+8)/(-6+10)

m=4/4=1

therefore

The points of case d) can be the end-points of the other diagonal

6 0

3 years ago

As a salesperson, you are paid $100 per week plus $3 per sale. This week you want your pay to be at least $160. Write an inequal

Svet_ta [14]

First, you would need to create an equation for this problem. Let x represent the number of sales made.
$100 + $3x = $160

Next, you would need to isolate the x.

Subtract $100 from both sides.
$3x = $60

Now, all you would need to do is divide both sides by $3.
x = 20

You would need to make at least 20 sales.

I hope this helps!

3 0

4 years ago

Solve the system of equations.

morpeh [17]

Answer:

y=3,x=1.3,z=6.2 :)

Step-by-step explanation:

y=3,x=1.3,z=6.2 :)

So, we have:

: x+y+z=10 [equation 1]

: 5x+3y=14 [equation 2]

: x−2y+z=2.5 [equation3]

(I'm going to assume that you know how to solve equations with 2 variables)

1. eliminate a variable to get 2 variables

Let's reverse equation 2:

-x+2y-z= -2.5

and take equation 1, to try to eliminate "z"

x+y+z=10

add up the 2 equations to get:

3y=7.5

and solve to get

y=2.5

2. substitute what we already solved into another equation

Luckily, equation 2 only has 2 variables, and one is y, so we can sub it in.

5x+3y=14 --> 3x+3(7.5)=14

solve to get

x=1.3

3. Substitute both of our variables in to get the final variable: z

Let's take the first equation.

x+y+z=10 --> 1.3+2.5+z=10

solve to get

z=6.2

I hope this helps you!

3 0

3 years ago

Roget Factory has budgeted factory overhead for the year at $4,640,000. It plans to produce 2,000,000 units of product. Budgeted

Finger [1]

Answer:

$15.4

Step-by-step explanation:

3 0

3 years ago

A new youth sports center is being built in pagosa springs. The permitted of the rectangular playing field is 524 yards. The len

padilas [110]

Answer:

Length = 208 yards

Width = 54 yards

Step-by-step explanation:

Let the length of the field be "x" yards and the width be "y" yards. Its given that the length is 8 less than quadruple(4 times) the width. So x is 8 less than 4y. We can write this in equation as:

x = 4y - 8 Equation 1

Perimeter of the field is given to be 524 yards. Since, the field is rectangular, its perimeter is calculated as:

Perimeter = 2 (Length + Width)

Using the values, we get:

2(x + y) = 524 Equation 2

Substituting the value of x from Equation 1 into Equation 2, we get:

2(4y - 8 + y) = 524

2(5y - 8) = 524

5y - 8 = 524/2

5y - 8 = 262

5y = 262 + 8

5y = 270

y = 54 yards

Substituting the value of y in Equation 1, we get:

x = 4y - 8 = 4(54) - 8 = 208 yards

Thus, the length of the playing field is 208 yards and its width is 54 yards.

6 0

3 years ago