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likoan [24]
3 years ago
13

A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 19 inches per year. Type B is 7 feet tal

l and grows at a rate of 16 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Mathematics
1 answer:
iren [92.7K]3 years ago
7 0

it will take 8 months for these trees to be same height

Further explanation:

Let x be the number of years then,

Type A is 5 feet tall and grows at a rate of 19 inches per year

The expression for Type A is:

5+19x

Type B is 7 feet tall and grows at a rate of 16 inches per year

The expression for Type B is:

7+16x

Putting both of them equal will give us the time in which both to be same height

5+19x=7+16x\\Subtracting 16x from both sides\\5+19x-16x=7+16x-16x\\5+3x=7\\Subtracting 5 from both sides\\5+3x-5=7-5\\3x=2\\x=\frac{2}{3}\\Mutiplying\ numerator\ and\ denominator\ of\ fraction\ by\ 4\\x=\frac{8}{12}

Hence, it will take 8 months for these trees to be same height

Keywords: Rate of Change, Linear Equations

Learn more about linear equations at:

  • brainly.com/question/2116906
  • brainly.com/question/2131336

#LearnwithBrainly

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(60 points)
natka813 [3]

Answer:

<h2>2. D. 64</h2><h2>5. B. 1, -3/2</h2><h2>6. C. 0, 2</h2>

Step-by-step explanation:

2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56

5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-\dfrac{3}{2}}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}

6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}

8 0
3 years ago
Are they congruent? How do you know?
pogonyaev

Answer:

Yes, if you translate either plane, they will end up in the exact location.

5 0
3 years ago
Please actually help me. ill give brainliest if you explain your answer.
meriva

Answer:

subtract 11 from both sides

Step-by-step explanation:

-3x+11=44

-3x=33

x=-11

4 0
3 years ago
Read 2 more answers
10. Which of the following statements are TRUE?
Masja [62]

Answer:

A, C, D

Step-by-step explanation:

1) A triangular pyramid has the same number of faces as vertices: 5

2) C - The sum is 5 + 6 =11

3) D - Euler's Formula tells us that if we add the number of faces and vertices together and then subtract the number of edges, we will get 2 as our answer.

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Ba%5E2%20-2a-b%5E2%3D0%7D%20%5Catop%20%7B2b%2B2ab%3D0%7D%7D%20%5Cright
oksian1 [2.3K]

Given :-

  • a² - 2a - b² = 0
  • 2b + 2ab = 0

To find :-

  • Value of a and b .

Solution :-

<u>Taking</u><u> </u><u>second</u><u> </u><u>equation</u><u>:</u><u>-</u>

  • 2b + 2ab = 0
  • 2b ( 1 + a ) = 0
  • 2b = 0 or (1+a) = 0
  • b = 0 , a = -1

<u>Substitute</u><u> </u><u>in </u><u>first </u><u>equation</u><u> </u><u>:</u><u>-</u><u> </u>

  • a² - 2a - b² = 0

<u>When </u><u>b </u><u>=</u><u> </u><u>0</u><u> </u><u>,</u>

  • a² - 2a - 0² = 0
  • a² - a = 0
  • a( a -1) =0
  • a = 0 , 1

<u>When </u><u>a </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>,</u>

  • (-1)² - 2*(-1) - b² = 0
  • 1 + 2 - b² = 0
  • b² = 3
  • b = ±√3

<u>Answer </u><u>:</u><u>-</u><u> </u>

  • a = 0,1 ; b = 0
  • a = -1 , b = ±√3
8 0
2 years ago
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