MATHEMATICS MIDDLE SCHOOL

4(3a + 7) + 3(2a + 5)

Answers

Answer 1

Answer:

Answer: 18a + 43 is the simplest form

Step-by-step explanation:

4(3a + 7) + 3(2a + 5)

4 * 3 a= 12a

4 * 7 = 28

3 * 2a = 6a

3 * 5 = 15

12a + 28 + 6a + 15

12a + 6a = 18a

28 + 15 = 43

18a + 43

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At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height , x of the tree ?

Answers

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of $x-49$ meters and the distance from the top of the tree to the end of the shadow is $x+1$ meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

$x^(2)+(x-49)^(2)=(x+1)^(2)$

Expanding, we get,

$2 x^(2)-98 x+2401=x^(2)+2 x+1$

$2 x^(2)-98 x+2400=x^(2)+2 x$

$2 x^(2)-100 x+2400=x^(2)$

$x^(2)-100 x+2400=0$

Solving the equation using the quadratic formula $x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}$ , we get,

$x=\frac{-(-100)\pm\sqrt{(-100)^(2)-4 \cdot 1 \cdot 2400}}{2 \cdot 1}$

Simplifying, we have,

$x=(100\pm√(10000-9600))/(2)$

$x=(100\pm√(400))/(2)$

$x=\frac{100\pm{20}}{2}$

Thus,

$x=(100+20)/(2) \nx=(120)/(2) \nx=60$ and $x=(100-20)/(2) \nx=(80)/(2) \nx=40$

where the value $x=40$ is not possible because substituting the value $x=40$ in $x-49$ results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

Can someone help me . Thanks . Work is due tomorrow

Answers

1 = 4 angles
2 = perpendicular

Hope that helped ;)

There are 15 violinists in the orchestra this year. Next year, two violinists will leave and some new violinists will join the orchestra. If v is the number of violinists who will join the orchestra, write an expression to represent the number of violinists in the orchestra next year.

Answers

13+v=x
This is the easy way I know. I hope I helped.

(15-2)+v=x would be one way that you could put your answer!

What is the debate among scientists on how new species form?

Answers

Answer:

read explanation

Step-by-step explanation:

Like most areas of Evolutionary Biology, research related to the formation of new species - 'speciation ' - is rich in historical and current debate.

Final answer:

Scientists have different models explaining how new species form. This includes 'Gradual Speciation' and 'Punctuated Equilibrium' models which describe the pace of speciation. Additionally, they consider 'allopatric' and 'sympatric' speciation describing the mechanisms of speciation.

Explanation:

The debate among scientists on how new species form revolves around different models and patterns observed in nature. Two main models of speciation that scientists explore are the 'Gradual Speciation' model and the 'Punctuated Equilibrium' model.

Gradual Speciation proposes that species evolve slowly over an extended period due to slight genetic changes from generation to generation. On the other hand, Punctuated Equilibrium suggests that species remain unchanged for many generations and then undergo rapid changes to form new species in a relatively short period.

Another aspect of the debate involves the mechanisms of speciation, including 'allopatric' and 'sympatric' speciation. Allopatric speciation involves a geographical separation of populations from a parent species and subsequent evolution, while Sympatric speciation is speciation that occurs within a parent species while in one location.

Learn more about Speciation here:

brainly.com/question/33392376

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Half of the candies in a jar are gumdrops. One-fourth of the candies are chocolates. There are 4 lollipops. There is an equal number of lollipops and chocolates. How many gumdrops are there?

Answers

If there is and equal amount of lollipops and chocolates, we know that 4 is 1/4 of the whole jar so,
1/4=4
Then,
2/4 which is 1/2 is 8
There are 8 gumdrops

If -4m+20=50, then what is M equal to?

Answers

-4m+20=50
add 4m to both sides because I dislike negatives
20=50+4m
subtract 50 from both sides
-30=4m
divide both sides by 4
-30/4=m
-15/2=m
-7 and 1/2=m

-4m + 20 = 50
-20 -20

50 - 20 = 30

-4m = 30

-4m/-4 = 30/-4

m = -7.5

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