Express 130 and 325 as the sum of two squares in two different ways.

Answers

Answer 1

Answer:

3^2 + 11^2 = 130

7^2 + 9^2 = 130

---

1^2 + 18^2 = 325

6^2 + 17^2 = 325

Step-by-step explanation:

We want to express 130 and 325 as the sum of two squares in two different ways.

Then, we want to find two integers a and b such that:

a^2 + b^2 = 130

There is not an analytical way to do this, we just need to try with different integers.

Let's start with 130.

So we start by defining a as a really small integer, for example 1, and try to find b.

1^2 + b^2 = 130

b^2 = 130 - 1

b^2 = √129 = 11.3

This is not an integer, so let's try with another value of a.

a = 2

2^2 + b^2 = 130

4 + b^2 = 130

b^2 = 130 - 4

b = √126 = 11.2

This can be discarded again.

Now let's try with a = 3

3^2 + b^2 = 130

9 + b^2 = 130

b^2 = 130 - 9

b = √121 = 11

Nice.

So we can express 130 as:

3^2 + 11^2 = 130

Now let's find another pair.

In the same way, we can see that for a = 7 we get:

7^2 + b^2 = 130

42 + b^2 = 130

b^2 = 130 - 49

b = √81 = 9

Then we can write:

7^2 + 9^2 = 130

Now for 325:

With the same reasoning than before, we want to find two integers such that:

a^2 + b^2 = 325

Then we start evaluating a by the smallest values:

a = 1

1^2 + b^2 = 325

b^2 = 325 - 1 = 324

b = √324 = 18

Then we can write 325 as:

1^2 + 18^2 = 325

Now to find the next pair we need to keep testing values for a, we will get for a = 6:

6^2 + b^2 = 325

36 + b^2 = 325

b^2 = 325 - 36 = 289

b = √289 = 17

Then we can write:

6^2 + 17^2 = 325.


Related Questions

What percent of 134 is 66? (To the nearest tenth of a percen t)

Answers

Answer: 49.25

Step-by-step explanation:

4.
2
Round off 14.9028 to the nearest
hundredths​

Answers

Answer:

14.9000 is the answer

Step-by-step explanation:

round it

Answer:

can you be more clear

Step-by-step explanation:

BRAINLY TO WHOEVER HELPS

Determine which of the following could NOT represent the sides of a right triangle.
A) 3,4,5
B) 1,2,3
C) 5,12,13
D) 6,8,10

Answers

Answer:

A, C and D

Step-by-step explanation:

B is left out because the hypotenuse of 1 and 2 will be appx 2.24 but the rest are good to go

Explain how to find the slope of the line.

Answers

Step-by-step explanation:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 3}{6 - 2} \\ = \frac{ - 2}{4} \\ = - \frac{1}{2} [/tex]

Even if x₁ = 6, y₁ = 1 and x₂ = 2, y₂ = 3 the result remains same.

#CMIIW

A student scores 88, 73, 81, 75 , and 78 on the first five science tests of the year. What is the minimum score the student needs to get on the sixth test in order to have a test average of at least

Answers

Answer:

84

Step-by-step explanation:

A credit card company advertises an APR of 17.2%, compounded daily. What is the effective interest rate

Answers

Answer:

18.76%

Step-by-step explanation:

effective interest rate = ( 1 + periodic interest rate)^m - 1

m = number of compounding = 365

Periodic interest rate = APR / number of compounding = 17.2 / 365 = 0.0471% = 0.000471

(1 + 0.000471) ^365 - 1 = 18.76%

In a race , Ram covers 5 km in 20 min. How much distance will he cover in 100 min

Answers

Answer:

25 km

Step-by-step explanation:

100/20=5

5*5=25

You can use proportion
Km Min
5 20
? 100

(5*100)/20
500/20
=25

Solve the simultaneous equations

y – x = 3
y = 7x

Answers

Answer:

x=1/2, y=3 1/2

Step-by-step explanation:

substitute y=7x into y-x=3

7x - x = 3

6x = 3

x=1/2

y=7(1/2)

y=3 1/2

Katie noticed that many of the students at her school ate fruit during lunch. She randomly chose 30 students and found that 18 of them ate fruit during lunch. If Katie sample is representative, which of the following is closest to the number of 1,560 students at her school who eat fruit at lunch?

Answers

Answer:

52 / 1,560

Step-by-step explanation:

18 / 30

? / 1,560

1,560 / 30 = 52

52 / 1,560

1.
Kenneth's garden is in the shape of a rectangle. The length is
20 feet and it has a perimeter of 70 feet, How long is the
diagonal of his garden.

Answers

Answer: I'm pretty sure it's 25

Step-by-step explanation:

Use Pythagorean theorem to find diagonal.

Mike is 6.2 feet tall and casts a shadow that is 10.7 feet long. At the same time, a tree casts a shadow that is 37.5 feet long. How tall is the tree to the nearest tenth of a foot?

Answers

Answer:

I think it's 38

plz help me pls
8 hr = _________ min

30 min = _________ s

15 hr = ___________ min

5 yr = ____________d

7 d = ____________ hr

24 hr = __________ min

600 s = __________ min

60,000 min = __________ hr

Answers

Answer:

8hr=480min

30min=1800sec

15hr=900min

5yr=1825d

Step-by-step explanation:

How can you determine the part of an hour that is 15 minutes?

Answers

Answer:

You'll need to convert the minutes part to hours. 15 minutes times 1 hour per 60 minutes will make the conversion to hours and minutes will cancel out. 0.25 hours times 60 minutes per 1 hour = 0.25 hr × (60 min/ 1hr) = (0.25 × 60) min = 15 minutes.

Step-by-step explanation:

Mhanifa can you help this is due soon!!

Answers

Answer:

Question 1

Given pentagon

Sum of interior angles:

S = (5 - 2)*180° = 540°

Sum of exterior angles is same for any polygon:

360°Question 2

Given hexagon

Sum of interior angles:

S = (6 - 2)*180° = 720°

Sum of interior angles of a given hexagon:

x + 120° + 156° + 145° + x + 9° + 90° = 720°2x + 520° = 720°2x = 200°x = 100°

And pleaseee This too

Answers

Answer:

the correct option is 75

Step-by-step explanation:

The standard notation for how to write tables is in the next way.

[tex]\left[\begin{array}{ccc}inpt&outpt\\x_1&y_1\\x_2&x_2\end{array}\right][/tex]

Where the input values are represented in the x-axis (the horizontal one) and the output values are on the y-axis (the vertical one).

In this case, we want to find the number of (x-value) for the height of 250.

Then we need to look at the vertical axis and find the value y = 250.

Now let's move to the right until you meet with the point.

Once you reach the point, move down to the axis, the value at which you intersect the axis is the x-value.

We can see that the point is on the middle of the x-values:

x = 70 and x = 80

Then the x-value of the point is x = 75

This means that the correct option is 75

Urgent!!!!
Can someone please give me the correct answer to this question
The answers are in the picture.
I will mark you brainliest for the correct answer.
Please help!!

Answers

Answer:

2x=80°

x=40°

40°+20°=60°

Step-by-step explanation:

all triangles are 180°

Marco mixed 2 teaspoons of sugar and 1 teaspoon of milk into his coffee. What is the ratio of teaspoons of sugar
to teaspoons of milk?

Answers

Answer:

2 : 1

Step-by-step explanation:

teaspoons of sugar : teaspoons of milk

= 2 : 1

hope this helps :)

Suppose that y varies directly with x
and y=
= 10 when x = 20. What is y
when x = 15?
Be sure to simplify your answer.

Answers

Answer:

[tex]10 \times 2 = 20 \\ 5 \times 3 = 15[/tex]

answer:10×2=20

5×3=15

Answer:

y = 7.5

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 10 when x = 20

10 = 20k ( divide both sides by 20 )

[tex]\frac{1}{2}[/tex] = k

y = [tex]\frac{1}{2}[/tex] x ← equation of variation

When x = 15 , then

y = [tex]\frac{1}{2}[/tex] × 15 = [tex]\frac{15}{2}[/tex] = 7.5

The solid shown below is made by combining two rectangular prisms. What is the total volume of the solid?

Answers

Answer:

The question has a picture attached of both rectangular prisms which I have attached and solved.

Answer:   1320 cm³

Step-by-step explanation:  

top prism = 5×12×10=600  

lower prism = 15×12×(15-10) = 720

Adding both volumes

720 + 600 = 1320 cm³

10.
Use the tangent ratio to find the size of the angle marked x, correct to the nearest degree.

Answers

36 using the angles replaceable to multiple bc it’s needed

i NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:7

Step-by-step explanation:

Answer:

I shall help

Step-by-step explanation:

11. The answer is 96 because 12 times 8 is 96

12. The answer is B.

13. The answer is also B because you need to count. BIG BRAIN

14 The answer is 8.

Next time please think a little harder

BRain;liest pls

I NEED HELP WITH THIS

Answers

72 degrees
........................

Answer:

∠HGJ + ∠KJG = 180°

So, ∠KJG = 62°

PLEASE HELP FAST!!!!!!!!!

Answers

Answer:

132 degrees

Step-by-step explanation:

To solve this problem, you need to know a couple of rules

1) Inscribed angle theroem: when an angle is inscribed in a circle and touches the other end (as opposed to ending at the diameter of the circle), the measure of this angle is half of the measure of the arc.

2)Angles of a quadrilateral shape add up to 360 degrees.

3) The angles inside a circle and the angles of the circles arclength adds up to 360 degrees.

So first, solve angle S with inscribed angle theorem. 126/2 = 63

Then, use the rule that all arc angles in a circle add up to 360 degrees to find the arc angle from Q to S. 360-90-126 = 144. Now find angle P with inscribed angle theorem by doing 144/2 = 72.

Now, use the rule that all angles in a quadrilateral add up to 360 to find R. 360-93-72-63 = 132.  

Let me know if this doesn't work, I'll look at it again.

Tell me which lines to which plz

Answers

Answer:

cereal bowl- 2 cups

baby food jar- 4 fluid ounces

soda can- 12 fluid ounces

swimming pool- 1000 gallons

large can of paint- 1 gallon

Are there any properties that hold for base - 10 logarithms that would not be valid for the logarithm base e ? Why ? Are there any properties that hold for base - 10 logarithms that would not be valid for some positive base b, such that b ≠ 1 ?

Answers

Answer:

.

nhuxu

Step-by-step explanation:

vxxgfx

SECTION A:
QUESTION 1
MULTIPLE CHOICE (10 MARKS)
1.1 The way we see, think and feel about ourselves it includes all knowledge we have
about ourselves.
Self esteem
Self-awareness
Self-confidence

Answers

Answer:

Self esteem hope this helps

Pleas help will give brainliest

Answers

Answer:

8 steps can be cut

Step-by-step explanation:

20 ÷ 2.5 = 8


How many WNBA athletes played in China in the 2018-
19 season?
A. 4
C.11
B.8
D. 20"

Answers

Answer:

C. 11

I hope it's right and helpful

Answer:

c 11

Step-by-step explanation:

c 20 hg ch gggggghubydyh

HELP PLEASE! THANKS :)

Answers

Answer:

If im not wrong, it has to be "How much does your dog weigh"

Step-by-step explanation:

x^(2)-4x-17=0
Please show work step by step

Answers

Step-by-step explanation:

It seems here that they are asking us to solve for x

to do this we first need to factor

Since we can't factor this using the normal method we can instead do this

x^2 -4x-17=0

add 4 to both sides as it is a perfect square

x^2 - 4x + 4  = 17 +4

(x-2)^2 = sqrt 21

x-2 = ±  4.58

x -2 = 4.58    x-2 = -4.58

x= 6.58          x=-2.58

Or just say x=2+√21 or x=2−√21

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