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iragen [17]
3 years ago
14

Find the value of a square + b square when a+b = 8 and ab = 10

Mathematics
1 answer:
Ne4ueva [31]3 years ago
5 0

As we know,

\boxed{ \boxed{(a + b) {}^{2}  =  {a}^{2}  +  {b}^{2}  + 2ab}}

now, let's plug the given values to find a² + b²

  • (8) {}^{2}  =  {a}^{2}  +  {b}^{2}  + (2 \times 10)

  • 64 =   {a}^{2}  +  {b}^{2}  + 20

  • {a}^{2} +   {b}^{2}  = 64 - 20

  • a {}^{2} +  b {}^{2}  = 44
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State whether the equation is true, false, or an open sentence. 9 = 5 + 4
Molodets [167]

Answer:

This equation is true because when you flip it 5+4=9 it is the same. and 5+4=9

Step-by-step explanation:

9=5+4   5+4=9  

4 0
3 years ago
Read 2 more answers
The sum of Eric’s and Bob’s weights is 9 times the difference of their weights. The positive difference of their weights is also
Pie

Answer:

<u>150</u>

Step-by-step explanation:

So I will shorten Eric, and Bob's names as E, and B.

So the equations are this

B-E = B+E - 240, E as Eric, and B as Bob, and this E+B=9(E-B)

Move the variables and you get

-2E =- 240

Just divide them both by -2

and E=120

So when we know the value of E we can just plug it into the 1st question

120+B=9B+1080

Moves the Variables and numbers to the other side

8B=1200

1200/8= 150

B=150

There is Bob's weight

6 0
2 years ago
What is the value of x?<br> 4 cm<br> 32 cm<br> 40 cm
Luba_88 [7]

Answer:

x=5

Step-by-step explanation:

Since 32 is 8 times 4 cm, then 40/8=5.

7 0
3 years ago
Read 2 more answers
Special right triangles.
Oliga [24]

QUESTION 9

The given right angle triangle has its two legs equal to x\:cm and the hypotenuse is 2\:units.


Using the Pythagoras theorem, we have

x^2+x^2=2^2


This implies that;

2x^2=2^2


2x^2=4


x^2=2


x=\sqrt{2}


x=1.414


x\approx1.4\:units


QUESTION 10


The given right angle triangle has its two legs equal to x\:units and the hypotenuse is 7\:units.


Using the Pythagoras theorem, we have

x^2+x^2=7^2


This implies that;

2x^2=7^2


2x^2=49


x^2=24.5


x=\sqrt{24.5}



x=4.95\:units


QUESTION 11

Sam divided the square backyard into two sections along the 40ft diagonal.

Let one of the sides of the garden be x\:units, then the other side of the garden is also  x\:units since it was a square backyard.


The diagonal is the hypotenuse which is 40ft and the two legs are  x\:units each.


Applying the Pythagoras Theorem, we have;

x^2+x^2=40^2


2x^2=1600


x^2=800


\Rightarrow x=\sqrt{800}


\Rightarrow x=28.28


The length of one side of the garden is approximately 28cm.


QUESTION 12

The hypotenuse of Nicole's right triangular support is 92cm long.


It was given that the two lengths of the triangular support are of equal length.


Let the two lengths of the triangular support be l\:cm each.


We then apply the Pythagoras theorem to obtain;

l^2+l^2=92^2


\Rightarrow 2l^2=8464


\Rightarrow l^2=4232


\Rightarrow l=\sqrt{4232}


\Rightarrow l=65.05cm


Therefore Nicole needs l+l=65.05cm+65.05cm\approx130cm of wood to complete the support.

The correct answer is A.


QUESTION 13

A 45-45-90 triangle is an isosceles right triangle.


Let the length of the two legs be m\:inches each.

It was given that the hypotenuse of this triangle is 12\:inches.


Applying the Pythagoras Theorem, we have;

m^2+m^2=12^2


\Rightarrow 2m^2=144


\Rightarrow m^2=72


\Rightarrow m=\sqrt{72}


\Rightarrow m=8.49


The length of one leg of the hypotenuse is approximately 8.5 inches to 1 decimal place.


QUESTIONS 14.

It was given that the distance from home plate to first base is 90 feet.


Since the baseball field form a square, the length of the baselines are all 90ft.

We want to calculate the distance from home plate to 2nd base,which is the diagonal of the square baseball field.

Let this distance be d\:ft, then using the Pythagoras theorem;

d^2=90^2+90^2


d^2=8100+8100


d^2=16200


\:d=\sqrt{16200}


\:d=127.279


Therefore the distance from home plate to second base is 127 ft to the nearest foot.


QUESTION 15.

The distance from third base to  first base is also 127 ft to the nearest foot.


The reason is that the  diagonals of a square are equal in length.


3 0
3 years ago
Help please!!!!
yanalaym [24]
18  The 2 trapezia formed by midpoint are similar so we can write

19/24 = x / 19

x = 19^2 / 24 = 15.04 

19.   360 degrees . This is true for all polygons
6 0
3 years ago
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