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3 years ago

What is the next number in the pattern? 4, -12, 36, -108, k

Mathematics

1 answer:

Lunna [17]3 years ago

5 0

This is a geometric sequence where r = -3.

4 x -3 = -12

-12 x -3 = 36

36 x -3 = -108

-108 x -3 = 324

Answer: 324

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The midpoint of \overline{\text{AB}}

Schach [20]

Answer:

<em>The coordinates of b are: B=(-7,-8)</em>

Step-by-step explanation:

We are given the coordinates of the midpoint of $\overline{\text{AB}}$ as M=(-5,-2).

We are also given the coordinates of A=(-3,4). The question requires us to calculate the coordinates of the other endpoint B.

Let (xb,yb) the coordinates of B. The coordinates of the midpoint can be calculated as follows:

$\displaystyle x_m=\frac{x_a+x_b}{2}$

$\displaystyle y_m=\frac{y_a+y_b}{2}$

We know xa=-3 and xm=-5. Solve the first equation for xb:

$2x_m=x_a+x_b\Rightarrow x_b=2x_m-x_a$

Substituting:

$x_b=2\cdot (-5)-(-3)=-10+3$

$x_b=-7$

We can solve the second equation for xb and get:

$y_b=2y_m-y_a$

Since ya=4 and ym=-2, then:

$y_b=2\cdot (-2)-(4)=-4-4$

$y_b=-8$

Thus, the coordinates of b are: B=(-7,-8)

4 0

3 years ago

You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site

tino4ka555 [31]

Answer:

Equation: 810= (90 + 24y)

y = 30 hours

Step-by-step explanation:

Given:

Site visit = $45 per site

cost per hour worked = $24

for <u>each </u>work site, the total amount of money earned

= site visit fee + cost for working

But the question mentions TWO sites, hence there will be two site visits. Therefore for TWO sites, we have to account for TWO site visit fee.

Therefore for TWO sites, the total amount of money earned

= site 1 visit fee + site 2 visit fee + cost for working

= (2 x site visit fee) + cost for working ------ Equation 1

We are further given that we worked y hours at the hourly work rate of $24 per hour.

Hence the cost for working

= y hours x hourly rate

= y x $24

= $24y (substituting this into equation 1 above)

for TWO sites, the total amount of money earned

= (2 x site visit fee) + cost for working

= (2 x $45) + $24y

= $90 + $24y

= $(90 + 24y)

We are also given that we have to earn $810 for two sites, hence

810 = 90 + 24y

810 - 90 = 24y

24y = 720

y = 720/24

y = 30 hours

8 0

3 years ago

What is the slope of a line that is perpendicular to the graphed line?

Lemur [1.5K]

Answer:

Step-by-step explanation:

To find the slope of the graphed line, you take two points. I have chosen (0, 4) and (8, 0)

The formula of a slope is (y value of second point $-y$ value of first point) divided by (x value of second point $-x$ value of first point):

$\frac{0-4}{8-0} =-\frac{1}{2}$

------------------------------------------------------------------------

The slope for a perpendicular line is 2.

6 0

3 years ago

Min-Jee is planting two rectangular flower beds. One bed is 2.78 feet by 4.81 feet, and the other bed is 2.78 feet by 5.61 feet.

shusha [124]

Answer: $(2.78+4.81)(2.78+5.61)$

Step-by-step explanation:

<h3> The complete exercise is attached.</h3><h3></h3>

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

Then, you can notice that it can be obtained by multiplying the dimensions of the rectangle.

Knowing this, you can determine that the total area of the two flowers bed can be obtained by adding the products of their dimensions.

Since one of the rectangular flower bed is 2.78 feet by 4.81 feet and the other bed 2.78 feet by 5.61 feet, you can write the following expression to find the total area (in square feet)of the two beds:

$2.78*4.81 +2.78*5.61$

If you factor out 2.78:

$2.78(4.81 +5.61)$ or $(4.81 +5.61)2.78$

Therefore, the expression that does not represent the total area in square feet of the two beds, is:

$(2.78+4.81)(2.78+5.61)$

6 0

3 years ago

Read 2 more answers

What property is this (8x5) x 10=8x(5x10)

sertanlavr [38]

Answer:

Associative

you can change (8*5) *10 to (8*10) *5

You can change 8*( 5*10) to 10* (8*5)

8 0

3 years ago