MATHEMATICS HIGH SCHOOL

For the values a = 3.4 and b = 2.6, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth.A. 4.3

B. 2.4

C. 2.2

D. 4.8

Answers

Answer 1

Answer: The length of the hypotenuse is 4.3. This is calculated as the square root of 3.4 squared plus 2.6 squared.

Answer 2

Answer:

Answer:

Using Pythagoras theorem.

In any right angle triangle:

$\text{Hypotenuse side}^2 = \text{Sum of the square of side}$

As per the statement:

For the values a = 3.4 and b = 2.6, which are legs of a right triangle.

We have to find c, the hypotenuse:

Apply the Pythagoras theorem, we have;

$c^2 = a^2+b^2$

Substitute the values we have;

$c^2=3.4^2+2.6^2 = 11.56+6.76 = 18.32$

then;

$c=√(18.32) = 4.28018691$

Therefore, the value of c, the hypotenuse, to the nearest tenth is, 4.3 units

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Question A coast guard patrol boat and a fishing boat leave a dock at the same time on the courses shown. The patrol boat travels at a speed of 15 nautical miles per hour (15 knots), and the fishing boat travels at a speed of 2 knots. After 1 hour, the fishing boat sends a distress signal, which is picked up by the patrol boat. If the fishing boat does not drift, how long will it take the patrol boat to reach the fishing boat at a speed of 15 knots? Round the intermediate result to three decimal places and the final answer to the nearest thousandth. A diagram shows a triangle labeled Uppercase D Uppercase F Uppercase P. The side Uppercase D Uppercase F measures two. The side Uppercase D Uppercase P measures fifteen. The side Uppercase F Uppercase P is labeled as Lowercase d. A vertical dashed line extends up from the vertex D to a point N, forming an angle with side Uppercase D Uppercase P measuring twenty degrees. Angle Uppercase F Uppercase D Uppercase N measures one hundred five degrees. Enter the correct value in the box.

Answers

Let’s use the law of cosines to solve this problem. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds: c^2 = a^2 + b^2 - 2ab cos. In our case, we know that the patrol boat travels at a speed of 15 knots and the fishing boat travels at a speed of 2 knots. After 1 hour, the fishing boat sends a distress signal, which is picked up by the patrol boat. If the fishing boat does not drift, we can assume that it has traveled 2 nautical miles in one hour . Let’s call the distance between the patrol boat and the fishing boat “d”. We can use the law of cosines to solve for “d” as follows:

d^2 = 15^2 + 2^2 - 2(15)(2)cos(105°) d^2 = 225 + 4 - 60cos(105°) d^2 = 229.8 d ≈ 15.16 nautical miles

Therefore, it will take the patrol boat approximately 1.011 hours to reach the fishing boat at a speed of 15 knots .

write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 to 56

Answers

Answer:

5/7

Step-by-step explanation:

A common factor of 8 can be canceled from numerator and denominator.

40/56 = (5·8)/(7·8) = (5/7)·(8/8) = (5/7)·1 = 5/7

_____

Since you know your multiplication tables, you know that 40 and 56 are both multiples of 8.

If you don't know your multiplication tables, you can find the greatest common divisor (GCD) of the two numbers and divide each by that. The GCD can be found using Euclid's algorithm. For that, you divide the larger by the smaller and use the remainder as the new smaller number. The original smaller number is now the larger number. For these numbers, that looks like ...

56 ÷ 40 = 1 r 16

40 ÷ 16 = 2 r 8

16 ÷ 8 = 2 r 0 . . . . . the zero remainder signals that the divisor (8) is the GCD

Now, your fraction is ...

(40/8) / (56/8) = 5/7

Answer:

5/7

Step-by-step explanation:

40/56 both divided by 8 and that is how to get your answer because you can not simplify further

From midnight to 6:00 am, the temperature rose 1.05°C each hour. If the temperature at 6:00 am was -5.7°C, what was the temperature at midnight?

Answers

Answer:

13.2 C

Step-by-step explanation:

6am the temp is at -5.7

from 6am to 12pm is 18 hours apart

so if the temp rises at 1.05 every hour you multiply 1.05*18= 18.9

18.9-5.7=13.2

A skier has decided that on each trip down a slope, she will do 3 more jumps than before. On her first trip she did 5 jumps. Derive the sigma notation that shows how many total jumps she attempts from her third trip down the hill through her tenth trip. Then solve for the number of total jumps from her third to tenth trips.

Answers

Since we are already given the amount of jumps from the first trial, and how much it should be increased by on each succeeding trial, we can already solve for the amount of jumps from the first through tenth trials. Starting from 5 and adding 3 each time, we get: 5 8 (11) 14 17 20 23 26 29 32, with 11 being the third trial.

Having been provided 2 different sigma notations, which I assume are choices to the question, we can substitute the initial value to see if it does match the result of the 3rd trial which we obtained by manual adding.

Let us try it below:

Sigma notation 1:

10
Σ (2i + 3)
i = 3

@ i = 3

2(3) + 3
12

The first sigma notation does not have the same result, so we move on to the next.

10
Σ (3i + 2)
i = 3

When i = 3; 3(3) + 2 = 11. (OK)

Since the 3rd trial is a match, we test it with the other values for the 4th through 10th trials.

When i = 4; 3(4) + 2 = 14. (OK)
When i = 5; 3(5) + 2 = 17. (OK)
When i = 6; 3(6) + 2 = 20. (OK)
When i = 7; 3(7) + 2 = 23. (OK)
When i = 8; 3(8) + 2 = 26. (OK)
When i = 9; 3(9) + 2 = 29. (OK)
When i = 10; 3(10) + 2 = 32. (OK)

Adding the results from her 3rd through 10th trials: 11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 = 172.

Therefore, the total jumps she had made from her third to tenth trips is 172.

Answer:d

Step-by-step explanation:test

The sum of 2 numbers is 16, and the sum of their squares is 146. find the 2 numbers

Answers

Step-by-step explanation:

x + y = 16 (*)

x^2 + y^2 = 146 (**)

(*) <=> x= 16-y

substitute x = 16 - y

(**) <=> (16-y)^2 + y^2 = 146

<=> y^2 - 2.16.y + 16^2 + y^2 = 146

<=> 2y^2 - 32y + 110 = 0

<=> y^2 - 16y + 55 = 0

<=> (y-11)(y-5) = 0

<=> y=11 or y= 5

For y = 11, we have x= 16-11=5

For y=5, we have x= 16-5=11

Answer: (x,y) = (11,5) ; (5,11)

Select the factors of x^2 -10x+25? A.(x+5)(x+5) B.(x-5)(x-5) C.(x+25)(x+1) D.(x-25)(x-1)

Answers

The correct answer is option B which is the factors are (x-5)(x-5).

What is a quadratic equation?

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The quadratic equation will be solved as follows:-

x² -10x + 25 = x² -5x - 5x + 25

= x ( x- 5 ) - 5 ( x-5 )

= ( x - 5 ) ( x - 5 )

The factors of the equation are 5 and 5.

Therefore the correct answer is option B which is the factors are (x-5)(x-5).

To know more about quadratic equations follow

brainly.com/question/1214333

#SPJ2

a²-2ab+b²=(a-b)²

x²-10x+5=x²-2×5×x+5²=(x-5)²=(x-5)(x-5)

B.(x-5)(x-5)

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