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2 years ago

Madeline is standing 2x- 4 feet from the base of a tree. The height of the tree is 5x + 6 feet. Find the equation that shows

Mathematics

2 answers:

galben [10]2 years ago

6 0

Answer:

Madeline is standing 2x - 4 feet from the base of a tree, and the height of the tree is 5x + 6

Now we want to know the distance from Madeline's feet to the top of the tree.

You could picture it as a triangle rectangle, where the cathetus is the distance between Madeline and the tree and the distance between the floor and the top of the tree, in this case the distance between Madeline's feet and the top of the tree is the hypotenuse of such triangle rectangle, and can be obtained using the Pythagorean theorem: "the square of the hypotenuse is equal to the sum of the square cathetus"

then:

$H^2 = (2x - 4)^2 + (5x + 6)^2$

$H^2 = (4x^2 -16x + 16) + (25x^2 + 60x +36)$

$H^2 = (29x^2 + 44x + 52)$

$H = \sqrt{ (29x^2 + 44x + 52)}$

this is the distance from Madeline's feet to the top of the tree in terms of x.

kumpel [21]2 years ago

5 0

Answer:

c = sqrt( 29x^2 + 44x + 52)

Step-by-step explanation:

This is an application of the Pythagorean theorem

c = sqrt(a^2 + b^2)

a = 2x - 4

b = 5x + 6

c = sqrt( (2x - 4)^2 + (5x + 6)^2 ) Substitute and expand

c = sqrt( 4x^2 - 16x + 16 + 25x^2 + 60x + 36) Collect like terms

c = sqrt( 4x^2 + 25x^2 - 16x + 60x + 16+36) Combine the like term pairs.

c = sqrt( 29x^2 + 44x + 52)

This does not factor into anything very nice.

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A retaining wall requires 36.8 cu yd of concrete. The combined amounts of cement, sand, and gavel should be 1 1/2 times the of c

svet-max [94.6K]

Using proportions, it is found that the total amount of cement, sand, and gavel required is of 55.2 cubic yards.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The decimal equivalent to the mixed number 1 1/2 is given by:

1 + 1/2 = 1 + 0.5 = 1.5.

1.5 times 36.8 cubic yards is:

1.5 x 36.8 = 55.2.

The total amount of cement, sand, and gavel required is of 55.2 cubic yards.

More can be learned about proportions at brainly.com/question/24372153

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9 months ago

Triangles SLB and DOG are similar with <S=<D and <L =<O. If SL, LB and SB are 3,4,5 respectively and DO=5 find OG an

xeze [42]

All the side measures of ΔDOG will have the same relationship to their corresponding ΔSLB measures that DO has to SL.

OG/LB = DO/SL
OG/4 = 5/3
OG = 20/3

DG/SB = DO/SL
DG/5 = 5/3
DG = 25/3

In summary,
OG = 20/3 = 6 2/3
DG = 25/3 = 8 1/3

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2 years ago

1.) Is this number rational or irrational?

Setler79 [48]

Answer:

1) Irrational.

2) Irrational.

Step-by-step explanation:

We have been given two numbers. We are asked to determine whether the given numbers are rational or irrational.

We know that a number is a known as rational number, when we can represent it as a fraction or it has terminating decimals.

A number is a known as rational number, when it has non-repeating and non-terminating decimals.

1). $-\frac{\sqrt{3}}{5}+10.8$

$-0.3464101615137755+10.8=10.4535898384862245$

Since our given number has non-repeating or non-terminating decimal, therefore, given number is an irrational number.

2) $\sqrt{3}=1.7320508075688773$

Since our given number has non-repeating or non-terminating decimal, therefore, given number is an irrational number.

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2 years ago

Select the equation that most accurately depicts the word problem. Jim weighs 30 pounds less than Tom, and together they weigh 2

Amiraneli [1.4K]

<span>n=toms weight

(n-30)=jims weight

and together they weigh 210

so it would be (n - 30) + n = 210</span><span>
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2 years ago

Define the variables and write a system of equations to represent the given situation do not solve

Kaylis [27]

Answer: 28x + 15y = 131 and x + y = 7 where x is the number of Dress shirt and y is the number of T-shirt.

Step-by-step explanation:

We will represent the number of Dress shirt he bought by x and we will represent the number of T-shirt he bought by y.

We know that he spent 131 so the cost of each dress shirt plus the cost of each T-shirt has to equal 131. Also, he bought 7 total shirts so x plus y has to equal 7.

28x + 15y = 131

x + y = 7

Note: it says don't solve so I didn't solve but if you want to solve use these equations.

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2 years ago