MATHEMATICS HIGH SCHOOL

5 cm 13 cm and 12 cm is a right triangle

Answers

Answer 1

Answer: I think its not a right triangle because of the cm.

Answer 2

Answer: Yep, it is because it follows Pythagoras theorem

5²+12²=13²

Answer with explanation:

Ques 1)

$x=(1)/(√(3)-√(2))$

Now we are asked to find the value of:

$√(x)-(1)/(√(x))$

We know that:

$(√(x)-(1)/(√(x)))^2=x+(1)/(x)-2$

Also:

$x=(1)/(√(3)-√(2))$ could be written as:

$x=(1)/(√(3)-√(2))* (√(3)+√(2))/(√(3)+√(2))\n\n\nx=(√(3)+√(2))/((√(3))^2-(√(2))^2)$

since, we know that:

$(a+b)(a-b)=a^2-b^2$

Hence,

$x=(√(3)+√(2))/(3-2)\n\n\nx=√(3)+√(2)$

Also,

$(1)/(x)=√(3)-√(2)$

Hence, we get:

$(√(x)-(1)/(√(x)))^2=√(3)+√(2)+√(3)-√(2)-2\n\n\n(√(x)-(1)/(√(x)))^2=2√(3)-2\n\n\n√(x)-(1)/(√(x))=\sqrt{2√(3)-2}$

Hence,

$√(x)-(1)/(√(x))=\sqrt{2√(3)-2}$

Ques 2)

$x=(√(a+2b)+√(a-2b))/(√(a+2b)-√(a-2b))$

on multiplying and dividing by conjugate of denominator we get:

$x=(√(a+2b)+√(a-2b))/(√(a+2b)-√(a-2b))* (√(a+2b)+√(a-2b))/(√(a+2b)+√(a-2b))\n\n\nx=((√(a+2b)+√(a-2b))^2)/((√(a+2b))^2-(√(a-2b))^2)\n\n\nx=((√(a+2b))^2+(√(a-2b))^2+2√(a+2b)√(a-2b))/(a+2b-a+2b)\n\n\nx=(a+2b+a-2b+2√(a+2b)√(a-2b))/(4b)\n\n\nx=(2a+2√(a^2-4b^2))/(4b)\n\n\nx^2=((2a+2√(a^2-4b^2))/(4b))^2\n\n\nx^2=((2a+2√(a^2-4b^2))^2)/(16b^2)$

Hence, we have:

$x^2=(4a^2+4(a^2-4b^2)+8a√(a^2-4b^2))/(16b^2)\n\n\nx^2=(4a^2+4a^2-16b^2+8a√(a^2-4b^2))/(16b^2)\n\n\n\nx^2=(8a^2-16b^2+8a√(a^2-4b^2))/(16b^2)\n\n\nbx^2=(8a^2-16b^2+8a√(a^2-4b^2))/(16b)\n\n\nbx^2=(8a(a+√(a^2-4b^2))-16b^2)/(16b)\n\n\nbx^2=(8a(a+√(a^2-4b^2)))/(16b)-(16b^2)/(16b)\n\n\nbx^2=(a(a+√(a^2-4b^2)))/(2b)-b\n\n\nbx^2=ax-b\n\n\ni.e.\n\n\nbx^2-ax+b=0$

1. x = 1/ ( $√(3) - √(2))$ = $√(3)+ √(2)$ ;
( $√(x) -1/ √(x) )^(2) = x + 1/x - 2 =$ =

AHH HELPPPP !!!!-In the following diagram, two parallel lines are cut by a transversal. The measure of which angle is equal to the measure of angle 1 ?
a - angle 2
b - angle 3
c - angle 4
d - angle 6

Answers

Final answer:

The correct option is c.

In the given diagram, angle 1 is equal to angle 4. Vertically opposite angles are formed when two lines intersect, and in this case, angle 1 and angle 4 are vertically opposite angles.

Explanation:

For question 1, in a diagram where parallel lines are cut by a transversal, the angles corresponding to each other are congruent. Therefore, the measure of angle 4 is equal to the measure of angle 1.

Vertically opposite angles occur when two lines intersect. The angles that are directly across from each other (i.e., vertically opposite to each other) are equal. Hence, in the case of angle 1 and angle 4, these are vertically opposite angles and are equal.

Learn more about angle equality and vertically opposite angles here:

brainly.com/question/29147905

#SPJ2

Answer:

angle 4

Step-by-step explanation:

1 and 4 are vertical angles

∠1 = ∠4

This according to the vertical angle theorem

Hope this helps!!

How to simplify square root of 72?

Answers

Answer: $\sqrt[6]{2}$

Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36 then recognise 36 as a perfect square, 6 · 6.

There is no need to factor further because the 6's pair up. So a 6 comes out of the radical leaving a 2 inside and our answer is $\sqrt[6]{2}$ .

As you make your factor tree, always be on the lookout for perfect squares such as 36.

I have shown my work in the image attached.

6√2

√72
= √8*9
= √(4*2*9)
= √4*√2*√9
= 2*3*√2
= 6√2

I need help with this math question on my study guide!Sadly, I do not remember how to do this and I would greatly appreciate any help you can offer.

Answers

Sadly is right. You must have practiced this stuff in middle school
until it was coming out of your ears. Fortunately, you have a chance
to relearn it now. You should do that ... it'll be important in any math
course you ever take.

'm' is the slope of the line on the graph.

The slope is

      (the change in 'y' between any two points on the line)
divided by
   (the change in 'x' between the same two points).

You can choose any two points on the line, and the slope is always the same.

To make it easy, look at the two points on this graph where the line crosses
the x-axis and the y-axis.

Going between these two points ...
-- the line goes up, from y=0 to y=4. The change in 'y' is 4 .
-- the line goes to the right, from x=-2 to x=0. The change in 'x' is 2 .

   'm' = the slope = (4)/(2) = 2 .

The "y-intercept" is the place where the line crosses the y-axis.
On this graph, that's the point where y=4 .

The equation of EVERY straight line on ANY graph is:

   Y = (the slope) times 'x' + (the y-intercept) .

So the equation of THIS line on THIS graph is

   Y = 2x + 4 .

Find 7% of 280
Find 12% of 300
Find 2% of $1250

Answers

percent means parts out of 100
7%=7/100=0.07
'of' means multiply so

7%=0.7
7% of 280=0.07 times 280=196

12%=0.12
12% of 300=36

2%=0.02
2% of $1250=$25

Other Questions

You arrive in Mexico City with $580. How many pesos can you buy?

Luis walked 2 3/4 miles in 2 hours. How many miles did he walk in one hour?

Carol sold twice as many magazine subscriptions as Jennifer. If Carol and Jennifer sold 90 subscriptions in all, how many subscriptions did Carol sell?

What is the property, transformation, or simplification used in each step of this problem? x-7=34 x-7+7=34+7 x+0=34+7 x=34+7 x=41