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2 years ago

6

Gerry is making flower arrangements. She has 24 lilies and 40 orchids. Each

1 answer:

erica [24]2 years ago

8 0

Answer:

8 arrangements

Step-by-step explanation:

The highest common factor of 24 and 40 is 8

So

40 / 8 = 5

24 / 8 = 3

5 orchids and 3 lilies per arrangement makes 8 arrangements

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?

irga5000 [103]

The equivalence $n \equiv 5 \pmod{12}$

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5

for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)

we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009

The last k which produces n<5000 is 416

For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.

Answer: 417

6 0

3 years ago

If you help me I will love you forever

joja [24]

Answer:

I think the answer would be 22.15 but I'm not really sure.

7 0

3 years ago

Read 2 more answers

Need math help (last one wouldn't let me upload pic)

Scrat [10]

Answer:

$\text{Area of the figure}=54\text{ unit}^2$

Step-by-step explanation:

Please find the attachment.

Let us divide our given image in several parts and then we will find area of different parts.

First of all let us find the area of our red rectangle with side lengths 6 units and 7 units.

$\text{Area of rectangle}=\text{Length*Width}$

$\text{Area of red rectangle part}=6\text{ units}\times 7\text{ units}$

$\text{Area of red rectangle part}=42\text{ units}^2$

Now let us find area of yellow triangle on the top of red rectangle. We can see that base of triangle is 6 units and height is 1 unit.

$\text{Area of triangle}=\frac{1}{2}\times \text{Base*Height}$

$\text{Area of triangle}=\frac{1}{2}\times \text{6 units *1 unit}$

$\text{Area of triangle}=3\text{ unit}^2$

Let us find the area of green triangle.

$\text{Area of green triangle}=\frac{1}{2}\times \text{3 units *2 units}$

$\text{Area of green triangle}=3\text{ unit}^2$

Now we will find the area of blue triangle, whose base is 6 units and height is 2 units.

$\text{Area of blue triangle}=\frac{1}{2}\times \text{6 units *2 units}$

$\text{Area of blue triangle}=6\text{ units}^2$

Let us add all these areas to find the area of our figure.

$\text{Area of the figure}=42\text{ units}^2+3\text{ unit}^2+3\text{ unit}^2+6\text{ unit}^2$

$\text{Area of the figure}=(42+3+3+6)\text{ unit}^2$

$\text{Area of the figure}=54\text{ unit}^2$

Therefore, area of our given figure is 54 square units.

3 0

3 years ago

What value of x satisfies the equation x + 3 = -(x + 1)? a. x = 8

ludmilkaskok [199]

Answer:

-2

Step-by-step explanation:

x + 3 = -(x + 1)

open the bracket

x + 3 = -x -1

x+x= -1-3

2x= -4

X = -4/2= -2

8 0

3 years ago

Multiply and simplify: (2b2+2b)2

sveta [45]

Answer:

4b^2+2b (b^2 means b squared)

Step-by-step explanation:

4 0

3 years ago