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Darya [45]
2 years ago
10

i had 3 times as many rose bushes as holly bushes in my garden. Then i moved seven of my rose bushes to my grandfather’s garden,

and i planted 11 new holly bushes in my garden. Now my garden gas half as many rose bushes as holly bushes. How many rose bushes and holly bushes, in all, did i have initially
Mathematics
1 answer:
PIT_PIT [208]2 years ago
6 0

Total number of rose and holly bushes that I had initially = 20

<h3>System of linear equations</h3>

Let the initial number of rose bushes be r

Let the initial number of holly bushes be h

I had 3 times as many rose bushes as holly bushes in my garden

r  =  3h......................(1)

After moving seven of my rose bushes to my grandfather’s garden, the remaining number of rose bushes = r - 7

After planting 11 new holly bushes in my garden, the new number of holly bushes = h + 11

Now my garden has half as many rose bushes as holly bushes

r - 7   =  0.5(h  +  11)

r  =  0.5h  +  5.5 + 7

r  =  0.5h  +  12.5...............(2)

Compare equations (1) and (2)

3h  =  0.5h  +  12.5

3h - 0.5h  =  12.5

2.5h  =  12.5

h   =  12.5/2.5

h  =   5

Substitute h = 5 into equation (1)

r  =  3h

r  = 3(5)

r  =  15

Total number of rose and holly bushes that I had initially = h + r

Total number of rose and holly bushes that I had initially = 5 + 15

Total number of rose and holly bushes that I had initially = 20

Learn more on system of linear equations here: brainly.com/question/13729904

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bixtya [17]

The scale factor that was used to create triangle J’K’L’ is 1/3

<h3>How to determine the scale factor?</h3>

From the graph, we have the following highlights:

KL = 3

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The scale factor (k) from JKL to J'K'L is calculated as:

Scale factor = K'L'/KL

This gives

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5 0
1 year ago
3. Given ABCD ≅ FGHJ and mC = 9x - 7, mH = 5x + 13, find the value of x and the measures of angle C and angle H. Show all work
kondor19780726 [428]

Answers:

x = 5

m∠C = m∠H = 38 degrees

 

 

WORKINGS

 

Given that ABCD ≅ FGHJ

We know that corresponding angles of two congruent quadrilaterals are equal

Therefore,

m∠A = m∠F

m∠B = m∠G

m∠C = m∠H

m∠D = m∠I

 

Given,

m∠C = 9x – 7

m∠H = 5x + 13

 

Since m∠C = m∠H

9x – 7 = 5x + 13

 

Add 7 to both sides of the equation

9x – 7 + 7 = 5x + 13 + 7

9x = 5x + 20

 

Subtract 5x from both sides of the equation

9x – 5x = 5x – 5x + 20

4x = 20

 

Divide both sides of the equation by 4

4x/4 = 20/4

x = 5

 

 

To determine the measures of angle C and angle H

m∠C = m∠H

 

We know that m∠C = 9x – 7

Since x = 5

m∠C = 9(5) – 7

m∠C = 45 – 7

m∠C = 38

 

Therefore, m∠C = m∠H = 38 degrees
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Step-by-step explanation:

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Step-by-step explanation:

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