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Vlad [161]
3 years ago
5

How many solutions are there for the system x^2+4y^2=100 and 4y-x^2=-20

Mathematics
1 answer:
never [62]3 years ago
6 0
There are 5 solutions for this system.

x^2 + 4y^2 = 100  ____1
4y - x^2 = -20  ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80   (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y :  y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2    x = /100 - 4y^2  (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
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How many sign changes are in the polynomial f(x) = 3x3 + 7x2 + 9x - 1
Stels [109]
6 unless it talks about positive to negative then its 2
7 0
3 years ago
An ice cream shop offers the toppings below. How many 4-topping ice cream sundaes can you make?
marishachu [46]
Combinations of 7 taken 4 at a time. 
C (7,4)  = 7!  /[  4!(3!)]
7 x 6 x 5 = 210 
210 divided by 3 = 70 
70 divided by 2 = 35
8 0
2 years ago
<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2
MrMuchimi

Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1)  + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

<em>angle 1 + 2*angle 1 + 6 = 180</em>

<em>3*angle 1 = 174</em>

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

<em>angle 2 + 58 = 180</em>

angle 2  = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

7 0
3 years ago
Which names the tiling
horrorfan [7]
<h3>Answer:</h3>

4, 8, 8

<h3>Step-by-step explanation:</h3>

At each node, three faces meet. One is square (4 sides); the other two are octagons (8 sides). Hence the tiling can be named with three numbers: 4, 8, 8.

7 0
2 years ago
Read 2 more answers
A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by e
borishaifa [10]

Answer: 31 nickels and 29 dimes

<u>Step-by-step explanation:</u>

Nickels (.05): x

Dimes (.10): y


 Value:     .05x + .10y = 4.45 →  -20(.05x + .10y = 4.45)   →   -x - 2y = -89

Quantity:        x  +    y  = 60   →       1(x  +    y  = 60)           →   <u> x  + y </u> = <u> 60 </u>

                                                                                                       -y  = -29

                                                                                                        y  =  29

Next, substitute "29" for "y" into either equation and solve for "x":

x +  y  = 60

x + 29 = 60

x          = 31


5 0
3 years ago
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