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AnnyKZ [126]
2 years ago
6

Jill planted two flowers in her garden. The first flower is 2 inches tall, and it is growing 2.25 inches each week. The second p

lant is 5.75 inches tall, and it is growing 1.5 inches each week. How many weeks will it be until the two plants are the same height?
Mathematics
1 answer:
Nadya [2.5K]2 years ago
4 0

Answer:it will take the two plants 6 weeks before the heights are the same

Step-by-step explanation:

Jill planted two flowers in her garden.

The first flower is 2 inches tall, and it is growing 2.25 inches each week. Since the growth rate is in an arithmetic progression, we will apply the formula for finding the nth term of the series

Tn = a + (n - 1)d

Tn = the nth height of the first flower

a = the initial height of the first flower

d = the common difference in height of the first flower weekly

n = number of weeks

From the information given,

For the first flower,

a = 2

d = 2.25

Tn ?

n ?

Tn = 2 + (n - 1)2.25

For the second flower,

a = 5.75

d = 1.5

Tn ?

n ?

Tn = 5.75 + (n - 1)1.5

To determine the number of weeks that it will take until the two plants are the same height, we would equate Tn for both flowers. It becomes

2 + (n - 1)2.25 = 5.75 + (n - 1)1.5

2 + 2.25n - 2.25 = 5.75 + 1.5n - 1.5

Collecting like terms

2.25n - 1.5n = 5.75 - 1.5 - 2 + 2.25

0.75n = 4.5

n = 4.5/0.75

n = 6 weeks

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Fred orders pictures from a photographer. Each picture costs $5.50. A one-time shipping fee of $4.25 is added to the cost of the
Alexus [3.1K]

Answer:

Fred ordered 12 pictures

Step-by-step explanation:

70.25-4.25 (one time shipping fee) =66

then you take 66 and divide it by the cost of each picture

66/5.50= 12 pictures

3 0
3 years ago
Read 2 more answers
Find the difference of(ab+8a+1)-(-6ab+4)
vagabundo [1.1K]
Hey there!

When finding the difference of expressions like these, there's a few things you should keep in mind. 

1. When finding the difference of two polynomials, multiply the polynomial that implied to be "negative" by –1 to expand the problem and make it easier to solve. 

2. You combine terms based on their unknown terms, like x, y, x², ab, etc. You cannot combine the terms x and x², but you can combine the terms 6b and 8b by adding them. 

3. You can rearrange your terms however you see fit. If a polynomial is implied as "positive", you can multiply that entire polynomial by +1 to get rid of the parentheses. 

With all that in mind, you can go ahead and solve for your difference, like so:

(ab+8a+1)-(-6ab+4)

(ab+8a+1) (-1(-6ab+4))

(ab+8a+1) + (6ab-4)

ab+6ab+8a+1-4

7ab+8a-3

7ab+8a-3 will be your difference. 

Hope this helped you out! :-)
8 0
3 years ago
PLZ HELP ME I WILL BRAINLIST YOU
AURORKA [14]

Answer:

B.   15 units^{2}

Step-by-step explanation:

4 0
3 years ago
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism i
vesna_86 [32]

ANSWER

211.2 {in}^{2}

EXPLANATION

The surface area of a triangular prism is

equal to the area of two triangular faces

plus the area of the three rectangular faces.

The area of the equilateral triangle is calculated using the formula:

= 2 \times \frac{ \sqrt{3} }{4}  {s}^{2}  + 3 \times  \: bh

where s=6 is the length of one side.

and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.

Surface area

= 2 \times \frac{ \sqrt{3} }{4}  \times  {6}^{2}  + 3 \times  \: 6 \times 10

= 18\sqrt{3} + 180

=211.2square inches.

8 0
3 years ago
Suppose you inherited a house that was purchased in 1950 for 20,000. It is now 2015 and the value of the house has increased by
sleet_krkn [62]
This deals with exponential growth.
house value = 20,000 * (1.05)^years
(where years is # of years from 1950 - so 1950 = 0, 1951 = 1, etc)
house value = 20,000 * (1.05)^65
house value = 20,000 * <span> <span> <span> 23.8399005592 </span> </span> </span>
<span><span><span>house value = 476,798.01</span>


</span> </span>

7 0
3 years ago
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