In the first event, the eighth graders are running a baton relay race with three other classmates. The team’s top speed for each leg is 56.81 seconds, 59.22 seconds, 57.39 seconds, and 60.11 seconds. Use the information to predict the team’s best time for the race. (2 points)

Answer:

− 7n+18

Step-by-step explanation:

(10- 2n)- (5n- 8)

− 2n+10-5n+8

-7n+18

Answer:

First Q: The smallest value for which n works is 11.

Second Q: Smallest here is 17.

Third Q: I don't know this one, sorry!

Fourth Q: n is -10.

Step-by-step explanation:

For the first two questions, find the smallest common factor between the two numbers (subtract the remainder).

Q1:

First, subtract the remainders from the numbers (2149 - 4 = 2145; 1578 - 5 = 1573)

Then, list the factors

2145: 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145

1573: 1, 11, 13, 121, 143, 1573

These two numbers share 11 and 13 in common. 11 is the smaller of these, so it is the smallest value n can work.

Q2:

Repeat the steps from Q1.

12650 - 2 = 12648; 5800 - 3 = 5797

12648: 1, 2, 3, 4, 6, 8, 12, 17, 24, 31, 34, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 372, 408, 527, 744, 1054, 1581, 2108, 3162, 4216, 6324, 12648

5797: 1, 11, 13, 17, 31, 187, 341, 527, 5797

These two share 17, 31, and 527 in common. 17 is the smallest of these, so it is the smallest value n can work.

Q4 (I don't know how to do Q3 yet):

2n + 25 = n + 15

Subtract n from both sides

n + 25 = 15

n = 15 - 25

Subtract 25 from 15 to get -10

n = -10

Again, I don't know how to do Question 3 yet. Sorry for the inconvenience! Anyhow I hope the rest of this was helpful!

The least possible natural number n is 11.

Given that, when you divide 2149 by n, the remainder is 4. When you divide 1578 by n the remainder is 5.

The greatest common divisor (GCD) refers to the greatest positive integer that is a common divisor for a given set of positive integers.

Question 1:

First, subtract the remainders from the numbers (2149 - 4 = 2145; 1578 - 5 = 1573)

Then, list the factors

2145: 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145

1573: 1, 11, 13, 121, 143, 1573

11 and 13 are common factors. 11 is the smaller of these, so the smallest n value is 11.

Question 2:

First, subtract the remainders from the numbers

That is, 12650 - 2 = 12648; 5800 - 3 = 5797

List the factors:

12648: 1, 2, 3, 4, 6, 8, 12, 17, 24, 31, 34, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 372, 408, 527, 744, 1054, 1581, 2108, 3162, 4216, 6324, 12648

5797: 1, 11, 13, 17, 31, 187, 341, 527, 5797

17, 31, and 527 are common factors. 17 is the smaller of these, so the smallest n value is 17.

Therefore, the least possible natural number n is 11.

To learn more about the GCD visit:

https://brainly.com/question/27227228.

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Answer:

not similar

Step-by-step explanation:

similar means proportional

1, 1, and 0.5 are not proportional to 3.5, 3, and 2.25

As the two side lengths of the smaller triangle is the same but the ratio of those side in a larger triangle and the smaller triangle is different they are, D. Not similar.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

We know two triangles are similar if the ratios of their corresponding sides are equal.

The larger triangle has sides 3, 3.5, and 2.25.

And the smaller triangle has sides 1, 1, 0.5.

As the smaller triangle has side lengths 1, 1, and the ratio of the sides of the larger triangle and the smaller triangle is (2 + 1)/1 and (2.5 + 1)/1 which is equal to 3/1 and 3.5/1 3 and 3.5 but the smaller side has 1 and 1, therefore, they are not similar.

learn more about congruency here :

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Answer:

[tex]Amount = \$4500[/tex]

Step-by-step explanation:

Represent Swing Set with S and Fort with F

Given

[tex]S = \$900[/tex]

[tex]S = \frac{1}{4}\ of\ F[/tex]  --- S = one-fourth of F

Required

Determine the amount spent on both

Substitute 900 for S in [tex]S = \frac{1}{4}\ of\ F[/tex]

[tex]\$900 = \frac{1}{4} * F[/tex]

Multiply both sides by 4

[tex]4 * \$900 = \frac{1}{4} * F * 4[/tex]

[tex]4 * \$900 = F[/tex]

[tex]\$3600= F[/tex]

[tex]F = \$3600[/tex]

The total amount to be spent it:

[tex]Amount = F + S[/tex]

[tex]Amount = \$3600 + \$900[/tex]

[tex]Amount = \$4500[/tex]

Answer:

Step-by-step explanation:

sin A = [tex]\frac{35}{37}[/tex]

cos A = [tex]\frac{12}{37}[/tex]

Answer:

105

Step-by-step explanation:

all angles inside a triangle add up to equal 180, the inside angle at R is 75 degrees, the TP line is obviously a 180 degree angle, because it's just a straight line, so you subtract 75 from 180 to get 105

hope this helps :)

Answer:

raise a product to a power.

you first simplify the parenthesis in the numerator by raising 2 by the power of three and multiplying the exponents.

i suck at explaining, but after the first step the expression looks like:

[tex](\frac{8r^{6}t^{3} }{4t^{2} })^{2}[/tex]

Step-by-step explanation:

Answer:

A.)x=6

B.)x=16

did u mean to solve it or do something else if this is not the way u mean i can do another way if u like

Answer:

( -1, 0)

Step-by-step explanation:

(2 + -4)/2 = -1

(2 + -2)/2 = 0

Answer:

The area is -6/5 units

Step-by-step explanation:

We start by integrating the curve equation

1/x^2 = x^-2

So the integration will be;

x^-2+1/-2 + 1 = -1/x + k

So we have the area as;

-1/5 -1 = (-1 - 5)/5 = -6/5

-

Answer:

a. 73%

b. 73:100

c. 0.73

d. 73/100

Step-by-step explanation:

If you are only talking about the shaded part out of the total number of squares then these are your answers

73 out of 100 is 73%

73:100 is the ratio

73/100 = 0.73 is the decimal

73/100 is the fraction

Answer:

Option C is the correct answer

Step-by-step explanation:

C. Multiply both sides of the equation by 20

Answer:

The distance is....

5

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

106=2(x+x+5)

53=2x+5

48=2x

24=x

24+5=29

Answer:

2.355cm

Step-by-step explanation:

The answer is 4.2

The 9 is above 5 so it raises the one

Answer:

both are 75 degrees

Step-by-step explanation:

the angles add up to 180, as they are also vertical angles

Answer:

b=c since they are vertical angles, b=75 and c=75

Step-by-step explanation: The angle opposite of the given is the same (105) that gives you two measure. Add 105+105 to get 210. A set of vertical angles=360 degrees, take away 210 from 360 to get the measure of b+c. Divide that by two to get the measure of either b or c.

Answer:

4x²+20x+25

Step-by-step explanation:

(2x+5)² = (2x+5)(2x+5)

(2x+5) (2x+5) = 2x(2x) + 2x(5) + 5(2x) + 5(5)

= 4x² + 10x + 10x + 25

= 4x²+20x+25

Answer:

3/-2 is = to 30 degrees so..

Step-by-step explanation:  w=34

V=21

Answer:

280

Step-by-step explanation:

Answer:

look it up mf

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50).

Answer:

(5,0)

Step-by-step explanation:

Answer:

less - than is the answer

hope it helps you

Answer:

Answer above is correct

Step-by-step explanation:

Answer:

z = 3y + x

Step-by-step explanation:

z - x / 3 = y

multiply both sizes by 3

z - x = 3y

add x

z = 3y + x