write a quadratic function whose zeros are 7 and 2

This looks like a system of differential equations.

[tex]\begin{cases}x' + 2y' + x = 0 \\ x' - y' + y = 0 \\x(0)=0, y(0)=1\end{cases}[/tex]

Eliminating x' gives

[tex](x'+2y'+x)-(x'-y'+y) = 0 - 0 \implies 3y' - y + x = 0[/tex]

and eliminating y' gives

[tex](x'+2y'+x) + 2(x'-y'+y)=0+2\times0 \implies 3x' + x + 2y = 0[/tex]

so that we can rewrite the system as

[tex]\begin{cases}3x' = -x - 2y \\ 3y' = -x + y\end{cases}[/tex]

or equivalently in matrix form as

[tex]\begin{bmatrix}x\\y\end{bmatrix}' = \dfrac13 \begin{bmatrix}-1&-2\\-1&1\end{bmatrix} \begin{bmatrix}x\\y\end{bmatrix}[/tex]

Compute the eigenvalues for the coefficient matrix:

[tex]\det\begin{bmatrix}-1-\lambda&-2\\-1&1-\lambda\end{bmatrix} = (-1-\lambda)(1-\lambda) - 2 = \lambda^2 -3 = 0 \implies \lambda=\pm\sqrt3[/tex]

Compute the corresponding eigenvectors:

[tex]\lambda=\sqrt3 \implies \begin{bmatrix}-1-\sqrt3&-2\\-1&1-\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1=(1-\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1-\sqrt3\\1\end{bmatrix}[/tex]

[tex]\lambda=-\sqrt3 \implies \begin{bmatrix}-1+\sqrt3&-2\\-1&1+\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1 = (1+\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]

We end up multiplying the matrix by 1/3, so the eigenvalues also get scaled by 1/3 and λ = ±1/√3. The eigenvectors stay the same.

Then the characteristic solution to the system is

[tex]\begin{bmatrix}x\\y\end{bmatrix} = C_1 e^{t/\sqrt3} \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 e^{-t/\sqrt3} \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]

Use the initial conditions to solve for the constants.

[tex]\begin{bmatrix}0\\1\end{bmatrix} = C_1 \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]

[tex]\implies \begin{cases}(1-\sqrt3) C_1 + (1+\sqrt3) C_2 = 0 \\ C_1 + C_2 = 3\end{cases}[/tex]

[tex]\implies C_1=\dfrac{3+\sqrt3}2, C_2=\dfrac{3-\sqrt3}2[/tex]

Then the particular solution is

[tex]\begin{bmatrix}x\\y\end{bmatrix} = \dfrac{3+\sqrt3}6 e^{t/\sqrt3} \begin{bmatrix}1-\sqrt3\\1\end{bmatrix} + \dfrac{3-\sqrt3}6 e^{-t/\sqrt3} \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]

or

[tex]\begin{cases}x(t) = -\dfrac1{\sqrt3} e^{\sqrt3 \, t} + \dfrac1{\sqrt3} e^{-\sqrt3\,t} \\\\ y(t) = \dfrac{3+\sqrt3}6 e^{\sqrt3\,t} + \dfrac{3-\sqrt3}6 e^{-\sqrt3\,t}\end{cases}[/tex]

Answer:D

Step-by-step explanation: Multiply the expression

Answer:

Step-by-step explanation:

$40 - $18.25 = $21.75

she has $21.75 to buy the paper with

21.75 divided by 0.34 is 63.971...

this means she only has enough money to buy 63 sheets of paper

leaving her with only 33 cents

Answer:

-7

Step-by-step explanation:

^

Answer:

-7

Step-by-step explanation:

Answer:

2*5*5

Step-by-step explanation:

50 ---> 25 * 2

25 = 5*5

50 = 2*5*5

Hope this helps :)

Have a nice day!

You can split up the length of AE into the lengths of the line segments connecting adjacent points:

AE = AB + BC + CD + DE

Plug in everything you know and solve for DE :

9 = (2 1/2) + (4 1/3) + (1 2/3) + DE

Rewrite the mixed numbers as improper fractions with a common denominator.

2 1/2 = 4/2 + 1/2 = 5/2 = 15/6

4 1/3 = 12/3 + 1/3 = 13/3 = 26/6

1 2/3 = 3/3 + 2/3 = 5/3 = 10/6

9 = 54/6

So we have

54/6 = 15/6 + 26/6 + 10/6 + DE

⇒   DE = (54 - 15 - 26 - 10)/6 = 3/6 = 1/2

(It looks as though you will need to enter 1 in the top box and 2 in the bottom one)

Answer:

The answer is 3x.

Step-by-step explanation:

I used a calculator

Answer:

2/3 × 2/5 = 4/15

Step-by-step explanation:

see image. If you just look at the horizontal lines the rectangle is divided into thirds. Two of the sections are highlighted indicating 2 out of 3, or 2/3.

If you then consider the vertical lines. There are 5 sections and 2 out of the 5 are highlighted indicating 2/5.

When you overlap both images (which is what the original image you posted was) you get a small section that is doubly highlighted. In your original image it is kind of purple (I marked them in yellow) In the double-layered image, there are 15 small sections. 4 are highlighted (double-highlighted) This is 4/15.

2/3 × 2/5 = 4/15

I supposed it could also be

2/5 × 2/3 = 4/15

Numerically, these are the same. They have the same result. I hope this helps!

Answer:

55°

Step-by-step explanation:

I hope that helps

Answer:

14.58

Step-by-step explanation:

x\27 = 54/100 cross multiply then divide by 100% x=Original price

so then you'll get 14.58

To find the missing angle's measure

 ⇒ important to understand the sum of the angles of a triangle

    ⇒ the sum of every angle of any triangle in all cases equal to 180

         degrees

What is the information given:

 ⇒ one angle is of 94 degrees and the other of 46 degrees

Using the information in the first section and the information given in the diagram, let's set up an equation:

  [tex]94+46+x = 180\\140+x = 180\\x = 40[/tex]

The measure of the missing angle is 40 degrees

Hope that helps!

Answer: i think the answer is 116. if it is not i am terribly sorry.

Step-by-step explanation:

Answer:

the answer for this one it should be the probability or chances that the event b occurs when the event a has occured.

Step-by-step explanation: I hope this help you pal or folk and have a great day.

Answer:

sin (α )= 72 5sin (α) = 725

​

Step-by-step explanation:

Answer: im pretty sure it would be in the 2nd quadrant. cause its -1.9, -2 so that i think is in 3rd quadrant so reflected woud be in 2nd quadrant

hope this makes sense

Answer:

Quadrant 1

The since both of the coordinates are negative, they'll take place in Quadrant 3, so if it was the opposite (mirrored), they would both be positive making them be in Quadrant 1.

Answer: Heat pollution.

If you are to search up

heat pollution occurs because?

the answer that will pop up is:

The main reasons of thermal pollution are industries and power plants, withdrawing water (a powerful sink for heat waste) from streams for cooling their generators and machines, and then releasing back into the water bodies, which elevates the temperature of freshwater habitats (Miara et al., 2018).

Answer: I believe B and F

Step-by-step explanation:

3.375

hope it helps...!!

1. m∠5 = 75° (corresponding angles theorem)

2. Sum of angles in a triangle = 180°

3. m∠3 = 55°

4. Straight line angle = 180°

5. m∠2 = 50°

If two corresponding angles are formed when a transversal intersect parallel lines, they are both congruent based on the corresponding angles theorem.

1. m∠5 = m∠1 (corresponding angles theorem)

m∠5 = 75°

2. Sum of angles in a triangle = 180°

3. m∠3 + m∠4 + m∠5 = 180° (sum of triangle)

Substitute

m∠3 = 180 - 50 - 75 = 55°

4. Straight line angle = 180°

5. m∠2 = 180 - m∠3 + m∠1 (straight line angle)

m∠2 = 180 - 55 - 75

m∠2 = 50°

Learn more about corresponding angles theorem on:

https://brainly.com/question/5221905

Answer:

42

Step-by-step explanation:

40^2+13^2=x^2

1600+169=x^2

1769=x^2

1769−−−−√=x2−−√

±42≈x

Answer:

vertex = (- 5, - 13 )

Step-by-step explanation:

given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the turning point ( vertex) is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 10x + 12 ← is in standard form

with a = 1, b = 10 , then

x = - [tex]\frac{10}{2}[/tex] = - 5

substitute x = - 5 into the equation and evaluate for y

y = (- 5)² + 10(- 5) + 12 = 25 - 50 + 12 = - 13

turning point = (- 5, - 13 )

Answer:

the answer your looking for would be 14, 48, 50.

Step-by-step explanation:

Hope this helps!

Answer:

14, 48, 50 have a good day

Step-by-step explanation:

Answer:

[tex]\frac{2y-1}{3y+1}[/tex]

Step-by-step explanation:

[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] ( multiply numerator and denominator by y to clear the fractions )

[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] × [tex]\frac{y}{y}[/tex]

= [tex]\frac{2y-1}{3y+1}[/tex]

Answer:

Side length ( perpendicular = 60 cm)

Hypotenuse = 61 cm

Base length

By Pythagoras theorem ,

Hypotenuse² = Perpendicular² + Base²

61² = 60² + base²

3721-3600 = Base²

√121 = base

11cm = base

Answer:

Step-by-step explanation:

In the question we are given ,

And we have asked to find the length of base that is denoted by x .

Solution : -

According to Pythagoras Theorem ,

[tex] \longrightarrow \purple{\boxed{H {}^{2} = P {}^{2} + B {}^{2} }} \longleftarrow[/tex]

Where ,

Now , substituting value of hypotenuse, perpendicular and base :

[tex] \hookrightarrow \: 61 {}^{2} = 60 {}^{2} + x {}^{2} [/tex]

Now by squaring 61 and 60 , we get :

[tex] \hookrightarrow \:3721 = 3600 + x {}^{2} [/tex]

Now transposing 3600 to left hand side :

[tex] \hookrightarrow \:3721 - 3600 = x {}^{2} [/tex]

Now subtracting 3600 from 3721 :

[tex] \hookrightarrow \:121 = x {}^{2} [/tex]

[tex] \hookrightarrow \: \sqrt{121} = x[/tex]

We know that 11 × 11 is equal to 121 that means square root of 121 is 11 . So :

[tex] \hookrightarrow \: \red{ \boxed{11 \: cm = x}}[/tex]

Answer:

B) -2⅛

Step-by-step explanation:

All other options are irrational

Isolate the absolute value term:

4 |x + 5| + 8 = 24

4 |x + 5| = 16

|x + 5| = 4

By definition of absolute value,

• if x + 5 ≥ 0, then |x + 5| = x + 5, and so

x + 5 = 4

x = -1

• otherwise, if x + 5 < 0, then |x + 5| = -(x + 5), and so

-x - 5 = 4

-x = 9

x = -9