Solve the following system of equations, using any method. Express your answers in one decimal place.

Answer:

Step-by-step explanation:

Answer:

[tex]38[/tex] and [tex]68[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the smaller one of the two number.

[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].

The question states that the product of the two numbers is [tex]2584[/tex]. In other words:

[tex]x\, (x + 30) = 2584[/tex].

Rearrange this equation and solve for [tex]x[/tex]:

[tex]x^{2} + 30\, x - 2584 = 0[/tex].

The first root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].

Similarly, the second root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].

Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.

Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].

9514 1404 393

Answer:

  38 and 68

Step-by-step explanation:

Let x represent the average of the two numbers. Then their product is ...

  (x -15)(x +15) = 2584

  x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2

  x = √2809 = 53

Then the two numbers are ...

  53 +15 = 68

and

  68 -30 = 38

The two numbers are 38 and 68.

_____

Additional comment

Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 0.86

Step-by-step explanation:

9514 1404 393

Answer:

  D.  G(x) = (x+3)² -2

Step-by-step explanation:

G(x) is translated left 3 and down 2 from F(x). The transformation ...

  G(x) = F(x -h) +k

is a translation right h units and up k units. We have h=-3 and k=-2, so the function of interest is ...

  G(x) = F(x +3) -2

  G(x) = (x +3)² -2

Answer:

0

Step-by-step explanation:

You can't divide anything by zero

0÷0=

=0

Answer:

an emergency fund allows you to live for a few months if you lose your job or if something unexpected comes up that costs a fair chunk of money to cover

Answer:

If there ever was an emergency you will need money to pay/afford the injury

Step-by-step explanation:

Step-by-step explanation:

Q9 . y = x + 5

x= y-5

× the input

y the output

x= -3

Q10.

y = 2x -3

y+3 = 2x

x = (y+3) ÷ 2

× = 5/2

= 2.5

Q11.

y = 1/4x - 1

y+1 = 1/4 x

4y+4 = x

x = 12

Q 12 .

y = 2/3x + 4

y-4 = 2/3x

3(y-4) = 2x

x = 3(y-4)/2

x = -3

Answer:

1360

Step-by-step explanation:

there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.

a+1 = 3

(a - 1)^2

[tex] {a}^{2} - 2.a.b + {b}^{2} \\ \\ a - 2a + 1 \\ \\ 1 + 1 = 2[/tex]

answer: 9

Step-by-step explanation:

x = - 4; y = 3; z = 2;2 x² - 2 z^4 + y² - x² + z^4 = = 2 * (-4)² - 2 * 2^4 + 3² - ( -4)² + 2^4 == 2 * 16 - 2 * 16 + 9 - 16 + 16 = = 32 - 32 + 9 - 16 + 16 = 9

Answer:

ffffgggghhhuukufgnjsdhn

Answer:

∞

Step-by-step explanation:

since cos(0) = 1, you have 1/0

Equations are used to show the relationship between variables (usually x and y). The true statement about f(x) is that the range of f(x) is [tex]y \ge -8[/tex]

Given that:

[tex]f(x) = 2(x - 2)^2 - 8[/tex]

To identify the true statement, I will make use of graphical method.

See attachment for the graph of [tex]f(x) = 2(x - 2)^2 - 8[/tex]

From the attached graph, we can see that the graph as a minimum at:

[tex](x,y) = (2,-8)[/tex]

And it opens upward.

This implies that the minimum y-value of f(x) is at -8, and it has no maximum.

In other words, the range of the function is:

[tex]f(x) \ge -8[/tex]

Hence, the true statement is option (a):

The range of f(x) is [tex]y \ge -8[/tex]

Read more about equations at:

https://brainly.com/question/17995541

Answer:

=fx+5f

Step-by-step explanation:

=fx+5f

Answer:

1st box: 1

2nd box: 1

Step-by-step explanation:

1: 3 * 7 = 21, so only put the 1 and carry the 2.

2: 5 * 6 = 30, but we have a 1 from the previous answer given so 31, but only put the 1.

I hope this helps :)

Answer:

8/9

Step-by-step explanation:

5/6 x 2/3 = 10/18 (5/9 reduced)

5/9 x 8/5 = 40/45 ( 8/9 reduced)

The GCF of 10 and 6 is 2. May this will help you.

Answer:

c no is correct pls mark me branilest

Answer:

(x, y) = (y, x). Exercise 1.3.4. Let X,Y,Z and W be nonempty sets. Then, prove the following statements

Answer:

sq rt of 66 is 8.12 so 8.1 closest

Answer:

8.1

I hope it will help you a lot.

HOPE your day goes great.

Answer:

because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)

so we have:

[tex]\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{a=4} \atop {b=-16}} \right.[/tex]

=> [tex]P(x)=x^{4} + 4x^{3}-x^{2} -16x-12[/tex]

With P(x) = 0

=> [tex]x^{4}+4x^{3}-x^{2} -16x-12 = 0[/tex]

=> ........

Step-by-step explanation:

Answer:

5 + 8 × 4

Assuming "five and eight" means 5 + 8

Answer:

d

Step-by-step explanation:

i did this last year

Answer:

give brainliest please I need it to level up

Step-by-step explanation:

20 + 8

4(5 + 2)

100 + 75

25(4 + 3)

49 + 28

7(7 + 4)

32 + 24

8(4 + 3)

Answer:

Ans; 8 +20 —> 4(2+5)

Ans; 75+100 —> 25(4+3)

Ans; 28+49 —> 7(4+7)

Ans; 24+32 —> 8(3+4)

I hope I helped you^_^

Answer:

A. x≤2; B. wrong unequality after dividing by negative number.

Step-by-step explanation:

9x-18x≥ -18;

-9x≥ -18;

0≥ -18+9x;

18≥9x;

9x≤18;

x≤2.

Answer:

4 foot ribbon

Step-by-step explanation:

Answer:

544

Step-by-step explanation:

$7.68 x 540 = 4,147.2

Answer:

This given triangle is an equilateral triangle.

Answer:

3rd, y=-1/5x

Step-by-step explanation: