All categories

4 years ago

What is the maximum number of possible solutions for the system shown below?

1 answer:

7 0

$\bf \begin{cases} 3x^2+y^2=4\\[-0.5em] \hrulefill\\ x^2+y=5\implies \boxed{y}=5-x^2 \end{cases} \\\\\\ \stackrel{\textit{substituting \boxed{y} in the 1st equation}}{3x^2+\left( \boxed{5-x^2} \right)^2=4}\implies 3x^2+25-10x^2+x^4=4 \\\\\\ x^4-8x^2+21=0\impliedby \begin{array}{llll} \textit{the degree of this polynomial}\\ \textit{is 4, and by the fundamental}\\ \textit{theorem of algebra, it can}\\ \textit{have \boxed{4} solutions at most} \end{array}$

You might be interested in

Which of the following numbers is proportional to 84/108?

lara [203]

Proportional numbers are numbers with the same equivalent ratio

98/126 is proportional to 84/108

The number is given as:

$Number = \frac{84}{108}$

Reduce fraction to the lowest term

$Number = \frac{7}{9}$

Reduce 86/110 to the lowest term

$Number = \frac{86}{110}$

Divide by 2/2

$Number = \frac{43}{55}$

43/55 is not equivalent to 7/9

Reduce 98/126 to the lowest term

$Number = \frac{98}{126}$

Divide by 14/14

$Number = \frac{7}{9}$

7/9 is equivalent to 7/9.

Hence, 98/126 is proportional to 84/108

Read more about proportional numbers at:

brainly.com/question/1781657

8 0

2 years ago

Find the area on the shaded region

mars1129 [50]

Answer:

83.2 cm^2

Step-by-step explanation:

To solve this we're going to find the area of the bigger triangle (the shaded and unshaded parts together) and then the area of the smaller triangle (the unshaded part) and then subtract that from the area of the bigger triangle. We're going to use the equation: Area=1/2 x base x height. So the base of the big triangle is 16, and the height is (10.4+8.6 = 19). Put into the equation this looks like this: Area=1/2 x 16 x 19, so by multiplying we find that the area is 152 cm^2. Next we find the small triangle's area, Area=1/2 x 16 x 8.6, so the area is 68.8. Then to find the area of the shaded part, we subtract the unshaded area (68.8) from the whole area (152), 152-68.8=83.2.

4 0

3 years ago

A number line contains points Q, R, S, and T. Point Q is on the coordinate 24, R is on the coordinate 28, S is on the coordinate

const2013 [10]

$|\Omega|=QT=42-24=18\\ |A|=ST=42-29=13\\\\ P(A)=\dfrac{13}{18}\approx72.2\%\Rightarrow \text{D}$

7 0

4 years ago

Read 2 more answers

What is the value of x in the equation 1,331x with the exponent of 3 -216 =0

dimulka [17.4K]

The answer is x=6/11.
Tiger Algebra is a really good tool for algebra if you need some help.
Hope that helped! :)

4 0

3 years ago

PLEASE HELP ME!!!!!

solong [7]

The full workings for the house purchase you made on a mortgage are as follows:

1. Price of House = $499,000 (given)

2. Down Payment = $99,800 ($499,000 x 20%)

3. Amount Financed (Mortgage principal) = $399,200 ($499,000 - $99,800).

4. Monthly Payment = $2,522.94 (given)

5. Number of monthly payments = 360 months (30 x 12)

6. Total Payback = $908,258.40 ($2,522.94 x 360)

7. Total Interest = $509,058.40 ($908,258.40 - $399,200)

8. Assessed Valuation = $199,600 ($499,000 x 40%)

9. Real Estate Taxes (annual) = $6,047.88 ($199,600 x $3.03/$100)

10. Escrow Payment Per month (taxes & insurance) = $628.99 ($6,047.88 + $1,500)/12

11. Monthly Payment to lender (escrow + mortgage) = $3,151.93 ($628.99 + $2,522.94)

<h3>What is a mortgage?</h3>

A mortgage is a loan arrangement that allows a borrower to buy some property, usually a house, without paying for the full cost immediately.

The borrower then makes a monthly payment, which includes the principal and its interest.

Learn more about mortgage payments at brainly.com/question/22846480

#SPJ1

3 0

2 years ago