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Svet_ta [14]
3 years ago
10

Natalie did 87 sit-ups in 3 minutes.

Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

Answer:

19 sit-ups per minute ;

95 sit-ups

Step-by-step explanation:

Given that :

Number of sit-ups done in 3 minutes = 57

The unit rate of sit-ups done can be obtained thus :

Total Number of sit-ups done / total time taken

= 57 sit-ups /3 minutes

= 19 sit-ups per minute

. Number of sit-ups that can be done in 5 minutes :

Unit Rate of sit-ups * number of minutes

19 sit-ups / minute * 5 minutes

= 95 (sit-ups / minute * minute)

= 95 sit-ups

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Two altitudes of a triangle have lengths $12$ and $14$. What is the longest possible integer length of the third altitude
nataly862011 [7]

The longest possible altitude of the third altitude (if it is a positive integer) is 83.

According to statement

Let h is the length of third altitude

Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.

From Area of triangle

A = 1/2*B*H

Substitute the values in it

A = 1/2*a*12

a = 2A / 12 -(1)

Then

A = 1/2*b*14

b = 2A / 14 -(2)

Then

A = 1/2*c*h

c = 2A / h -(3)

Now, we will use the triangle inequalities:

  • a < b+c

2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

  • b < a+c

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

  • c < a+b

2A/h < 2A/12 + 2A/14

Solve it and get

h > 6.46

From all the three inequalities we get:

6.46<h<84

So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.

Learn more about TRIANGLE here brainly.com/question/2217700

#SPJ4

8 0
2 years ago
Jordon is looking for a job. She found one job that gave a $100 bonus plus paid $25 per hour. Another job gave no
maria [59]
It would be 20 hrs because if you put them both in an equation aka y=25x+100 and y=30x just plug in numbers into the x until they both have the answer which in this case is 20
5 0
3 years ago
Read 2 more answers
Jane drinks one-fourth of a gallon of soda every three days. If they continue to drink the same
zhenek [66]

Answer:

0.83 gallons of soda

7 0
3 years ago
Simplify the expression by combining like terms<br>5x + 5y - 3x​
Tcecarenko [31]

Answer:

2x+5y

Step-by-step explanation:

5x + 5y - 3x​

=2x+5y

8 0
3 years ago
Working her way through school, Julie works two part-time jobs for a total of 35 hours a week. Job A pays $6.10 per hour, and Jo
geniusboy [140]

Answer:

<u>Julie worked 18 hours at Job A and 17 hours at Job B.</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Rate per hour at Job A = US$ 6.10

Rate per hour at Job B = US$$ 7.40

Hours at Job A = x

Hours at Job B = 35 - x

Total of hours worked by Julie = 35 hours

Total weekly earnings = US$ 235.60

2. How many hours did she work at each job the week that she made $235.60?

For finding the result, we will use the following formula:

6.10x + 7.4 (35 - x) = 235.60

6.10x + 259 - 7.4x = 235.60

-1.3x = 235.60 - 259 (Subtracting 259 to both sides)

-1.3x = - 23.40

x = -23.4/-1.3 (Dividing by -1.3)

x = 18

<u>Julie worked 18 hours at Job A, so she worked 17 (35 - 18) hours at Job B.</u>

3. Proof that x = 18 is correct.

6.10x + 7.4 (35 - x) = 235.60

6.10 (18) + 7.4 (35 - 18) = 235.60

109.80 + 125.80 = 235.60

<u>235.60 = 235.60</u>

<u>It's proven that x = 18 is correct.</u>

6 0
3 years ago
Read 2 more answers
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