MATHEMATICS HIGH SCHOOL

Consider triangle QRS. The legs each have a length of 10 units. Triangle Q R S is shown. Angle Q S R is 90 degrees. The length of Q X is 10 and the length of S R is 10. What is the length of the hypotenuse of the triangle? 5 units 5 StartRoot 2 EndRoot units 10 units 10 StartRoot 2 EndRoot units

Answers

Answer 1

Answer:

Answer:

The correct answer would be D

Step-by-step explanation:

Answer 2

Answer:

Answer: D

Step-by-step explanation: :)

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about 60% of the normal human beings body weight is composed is water. How much of a 125 pound person is water weight?

Answers

60% of weight 60%=0.6 'of' means multipy 60% of 125 means 0.6 times 125=75 75 pounds

u do .6 x 125 = 75
Hope it right! and it helps u out!

A van travels 220 miles on 10 gallons of gas. Find how many gallons the van needs to travel 550 miles.31 gallons of gas
121 gallons of gas
25 gallons of gas
115 gallons of gas

Answers

The van will need 25 gallons of gas for it to travel 550 miles. This is calculated by dividing 10 gallons to 220 miles to get the miles per gallons, which in this case is 22 miles per gallon. Then we have to divide 550 miles by 22 miles per gallon to get the total gas consumption, which is 25 gallons.

Answer:

Step-by-step explanation:

To calculate how many gallons the van needs to travel 550 miles you should multiply the number of miles by the relationship between the number of gallons of gas it needs to travel 220 miles, (it is important to put the quantity in miles on the denominator) as follows:

$550miles*(10gallons)/(220miles)=25$

Therefore the van needs 25 gallons of gas to travel 550 miles

If you divide the mass of a substance by its volume, can you can find its density?

Answers

So the question is is it true or false that when you divide the mass of a substance by it's volume you will get its density. So from the definition of density we know that density=mass/volume or: D=m/V. So the answer is true, when you divide a mass of a sbstance by its volume, you get it's density.

The sum of the first 10 terms of an arithmetic sequence is 235 and thesum of the second 10 terms is 735. Find the first term and the common

difference.

Answers

If the sum of the first 10 terms of an arithmetic sequence is 235 and the sum of the second 10 terms is 735. The first term of the arithmetic sequence is -21.5 and the common difference is 10.

What is the arithmetic sequence?

Let's a represent the first term of the arithmetic sequence and the common difference as d

Formula for the sum of the first n terms of an arithmetic sequence is given by:

S_n = (n/2) * [2a + (n - 1)d]

So,

Sum of the first 10 terms: S₁₀ = 235

Sum of the second 10 terms: S₂₀ = 735

First 10 terms:

S₁₀ = (10/2) * [2a + (10 - 1)d]

235 = 5 * [2a + 9d]

47 = 2a + 9d

Second 10 terms:

S₂₀ = (10/2) * [2a + (20 - 1)d]

735 = 5 * [2a + 19d]

147 = 2a + 19d

Now we have a system of equations:

2a + 9d = 47

2a + 19d = 147

(2a + 19d) - (2a + 9d) = 147 - 47

10d = 100

d = 10

Substitute it into the first equation to solve for "a":

2a + 9(10) = 47

2a + 90 = 47

2a = -43

a = -21.5

Therefore the first term of the arithmetic sequence is -21.5 and the common difference is 10.

Learn more about arithmetic sequence here:brainly.com/question/6561461

#SPJ3

Answer:

$\bold{a_1 = -42.65}\n\n\bold{d=14.7}$

Step-by-step explanation:

The sum of the first 10 terms of an arithmetic sequence is:

$S_(10)=a_1+a_2+...+a_(10)=(a_1+a_(10))/(2)\cdot10=(2a_1+(10-1)d)/(2)\cdot10$

$(2a_1+(10-1)d)/(2)\cdot10=235\n\n(2a_1+9d)\cdot5=235\n\n2a_2+9d=47$

the sum of the second 10 terms is: a₁₁ + a₁₂+...+ a₂₀

And the sum of the first 20 terms of an arithmetic sequence is:

$S_(20)=a_1+a_2+...+a_(10)+a_(11)+...+a_(20)=(2a_1+(20-1)d)/(2)\cdot10$

so the sum of the second 10 terms is:

$a_(11)+a_(12)+...+a_(20)=S_(20)-S_(10)$

Therefore we have:

$(2a_1+(20-1)d)/(2)\cdot10-(2a_1+(10-1)d)/(2)\cdot10=735\n\n(2a_1+19d)\cdot5-(2a_1+9d)\cdot5=735\n\n2a_1+19d-(2a_1+9d)=147\n\n10d=147\n\nd=14.7$

and:

$2a_1+9\cdot14.7=47\n\n2a_1+132.3=47\n\n2a_1=-85.3\n\na_1=-42,65$

A fisherman can row upstream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the trip took 3 hours?

Answers

Answer:

Fisherman traveled 14.4 miles.

Step-by-step explanation:

A fisherman's downstream speed = 6 mph

and upstream speed = 4 mph

Let the fisherman traveled x miles he travels upstream.

Time spent in travelling x miles = $(x)/(4)$ hours [Since time = $\frac{\text{distance}}{\text{speed}}$ ]

Similarly when fisherman covers x miles down stream

Time spent in x miles = $(x)/(6)$ hours

Now total time in going upstream and downstream is 3 hours then

$(x)/(4)+(x)/(6)=3$

x $((3+2)/(12))=3$

$((5x)/(12))=3$

5x = 12×3

5x = 36

x = $(36)/(5)=7.2$ miles.

Since fisherman has traveled 2x distance so the answer will be 14.4 miles

Therefore, fisherman traveled 14.4 miles.

total time = upstream time + downstream time
he rowed the same distance both ways.
upstream time = D/4
downstream time = D/6
total time = D/4 + D/6 = 3D/12 + 2D/12 = 5D/12 = 3 hours
D = 3*12/5 = 36/5 or 7.2 miles
where D is the one-way distance. The total distance he rowed is 2*D = 72/5 or 14.4 miles

What is the intermediate step in form (x+a)^2=b as a result of completing the square of the following equation6x^2+72x-170=-2

Answers

Answer:

6x² + 72x - 170 = -2

<=> 6x² + 72x - 168 = 0

<=> x² + 12x - 28 = 0

<=> x² + 12x + 36 = 64

<=> (x+6)² = 64

Step-by-step explanation:

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