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4 years ago

Which ratios form a proportion

Mathematics

1 answer:

nata0808 [166]4 years ago

4 0

I'm pretty sure it's <em>C</em>

Step-by-step explanation:

2/3=8/12

8/12 ....divided both by 4=2/3

2/3=2/3

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David is watching maria and alma race electric trains around track. Maria train can go around the track in 10 seconds. Almas tra

Nady [450]

Answer:

60 seconds.

Step-by-step explanation:

We have been given that Maria train can go around the track in 10 seconds. Alma train can go around the track in 12 seconds.

To find the number of seconds after which both trains will cross the finish line together the first time we will find LCM of 10 and 12. LCM will give us the smallest positive integer that is divisible by both 10 and 12.

Multiples of 10 are: 10, 20, 30, 40, 50, 60, 70,...

Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,..

We can see that least common multiple of 10 and 12 is 60, therefore, it will take 60 seconds for both trains to cross the finish line together the first time.

6 0

3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

4 years ago

Linh has obtained scores of 82, 79, and 75 on her midterm algebra exams. If the final exam counts twice as much as a midterm, wh

OLga [1]

Answer:

She must make a score of 42 in the final exam to obtain an average of 80.

Step-by-step explanation:

Hi there!

Let x be the score of the final exam, the equation will be as follows (remember that the score of the final counts double):

(82 + 79 + 75 + 2x)/4 = 80

Let´s solve the equation for x multiplying each side of the equation be 4:

82 + 79 +75 + 2x = 320

Substract 82, 79 and 75 to both sides of the equation:

2x = 320 - 82 - 79 -75

2x = 84

x = 84/2

x = 42

She must make a score of 42 in the final exam to obtain an average of 80.

Have a nice day!

8 0

4 years ago

The product of two numbers is -72. One of the factors is -9, what is the other factor?

Anna007 [38]

Answer:

Step-by-step explanation:

lets find out 9 times ? = 72

to do this, simply divide: 72/9 = 8

Since the end product is a negative and the factor is a negative, 8 will be a positive number

-9 times 8 equals -72

hope this helped ;)

3 0

3 years ago

What is the slope of the ordered papers (-4,8) (2,6)

makkiz [27]

Answer:-3

Step-by-step explanation:

m=y2 - y1

m= x2-x1

-4= y1

2=y2

2--4=6

x2=6

x1=8

6-8=-2

6/-2=-3

<u>Slope is -3!!</u>

Look up the wikihow on how to find slope, helped me a ton

5 0

2 years ago