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2 years ago

I already solved this problem. I just need help with the HINT part.

1 answer:

8 0

$x+y=25 \\ y=25-x~~Other~number~in~terms~of~x \\ \\ x^2+y^2=313 \\ x^2+2xy+y^2=313+2xy \\ (x+y)^2=313+2x(25-x) \\ \frac{25^2-313}{2} =25x-x^2 \\ x^2-25x+156 \\ \\ \Delta =(-25)^2-4\times 1\times 156 \\ \Delta =625-624 \\ \sqrt{\Delta}=1 \\ \\ x= \frac{25 \pm 1}{2} \\ x= \left \{ {{x_1=13} \atop {x_2=12}} \right.$

The number "x" is given by:
$y= \left \{ {{y_1=25-13 \rightarrow~y_1=12} \atop {y_1=25-12 \rightarrow ~y_1=13}} \right.$

Therefore, we have:

$\boxed {S=({12,13})} \rightarrow~The~curly~braces~does~not~want~appear~here.$

You might be interested in

Which is the least common multiple of 4 and 12

spayn [35]

The answer is 12. My explanations is that LCM is the smallest number that both numbers can fit into. 12 fits into 12 once, and 4 fits into 12 3 times, so 12 is the answer.

3 0

2 years ago

A carpenter is making a rectangular form for a concrete pad she wants the length of the path to be 11 feet more than the width o

Basile [38]

Answer:

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Step-by-step explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

Given the following data;

Area of concrete pad, a = 80ft²

Translating the word problem into an algebraic equation, we have;

$l = 11 + w$

We know that, the area of rectangle, A = length * width

$A = l*w$

Substituting the values into the equation, we have;

$80 = (11 + w)w$

Expanding the bracket, we have;

$80 = 11w + w^{2}$

$w^{2} + 11w - 80 = 0$

*Solving the quadratic equation by using factorization method*

$w^{2} + 16w - 5w - 80 = 0$

$w(w + 16) - 5(w + 16) = 0$

$(w - 5)(w + 16) = 0$

Width, w = 5 feet or w = -16 feet.

Therefore, the width of the concrete pad is 5 feet or -16 feet.

To find its length, l;

$l = 11 + w$

When w = 5 feet

$l = 11 + 5$

Length, l = 16 feet

When w = - 16 feet

$l = 11 + (-16)$

$l = 11 - 16$

Length, l = -5 feet.

Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.

6 0

3 years ago

How to write composite number till 25 in set builder form Pls help

dimaraw [331]

All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers (1 and itself).

Example: factors of 12

12 ÷1 = 12

12÷ 2 = 6

12÷3= 4

12÷4 = 3

12÷6=2

12÷12 = 1

= {12,6,4,3,2,1}

Composite Number/ Its Factors

4 = {1,2,4}

6 = {1,2,3,6}

8 = {1,2,4,8}

9 = {1,3,9}

10 = {1,2,5,10}

12 = {1,2,3,4,6,12}

14 = {1,2,7,14}

15 = {1,3,5,15}

16 = {1,2,4,8,16}

18 = {1,2,3,6,9,18}

20 = {1,2,4,5,10,20}

21 = {1,3,7,21}

22 = {1,2,11,22}

24 = {1,2,3,4,6,8,12,24}

25 = {1,5, 25}

Hope it helps!

#MissionExam001

6 0

3 years ago

Nolan rides his bike 63 miles in 270 minutes. What is his average speed in miles per hour?

boyakko [2]

Here, to find the average rate of change, you would simply divide 270 by 63. And when that is done, you would get a long decimal. 4.285714285714286

And since you obviously can't put in such a long decimal as your answer, you would round it instead. Once rounded, you would end up with 4.29 (because the number after 8 is five, which rounds up, which would turn the 8 to 9.)

8 0

3 years ago

Calculator

Sedaia [141]

Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[-3-(-6)]^2+[6-3]^2}\implies d=\sqrt{(-3+6)^2+(6-3)^2} \\\\\\ d=\sqrt{9+9}\implies \boxed{d=\sqrt{18}} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=\sqrt{[-2-(-6)]^2+[-1-3]^2} \\\\\\ d=\sqrt{(-2+6)^2+(-1-3)^2}\implies d=\sqrt{16+16}\implies \boxed{d=\sqrt{32}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(\sqrt{18})(\sqrt{32})}\implies \sqrt{18\cdot 32}\implies \sqrt{576}\implies 24$

7 0

3 years ago