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3 years ago

A picture is 2” x 1.5”. Scale is 1:40cm. What are dimensions of original painting

Mathematics

1 answer:

Ann [662]3 years ago

4 0

2*1.4=2.8
1.5*1.4= 2.1
New figure: 2.8 by 2.1

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Solve for x in the equation x squared + 2 x + 1 = 17.

Papessa [141]

Answer:

$x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\$

Step-by-step explanation:

given equation

$x^2 +2x +1 = 17$

subtracting 17 from both sides

$x^2 +2x +1 = 17\\x^2 +2x +1 -17= 17-17\\x^2 +2x - 16 = 0\\$

the solution for quadratic equation

$ax^2 + bx + c = 0$ is given by

x = $x = -b + \sqrt{b^2 - 4ac} /2a \\\\and \ \\-b - \sqrt{b^2 - 4ac} /2a$

________________________________

in our problem

a = 1

b = 2

c = -16

$x =( -2 + \sqrt{2^2 - 4*1*-16}) /2*1 \\x =( -2 + \sqrt{4 + 64}) /2\\x =( -2 + \sqrt{68} )/2\\x = ( -2 + \sqrt{4*17} )/2\\x = ( -2 + 2\sqrt{17} )/2\\x = - 1 + \sqrt{17}\\and\\\\x = - 1 - \sqrt{17}\\$

thus value of x is

$x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\$

3 0

2 years ago

Which of the following is an equation for the plane through the point (1, 1, −1) and parallel

Bas_tet [7]

The given plane, $x-y+z=3$ , has normal vector $\vec n = \langle1,-1,1\rangle$ . Any plane parallel to this one has the same normal vector.

Let $(x,y,z)$ be any point in the plane we want. The plane contains the point (1, 1, -1), so an arbitrary vector in this plane is

$\langle x,y,z\rangle - \langle 1,1,-1\rangle = \langle x-1, y-1, z+1 \rangle$

and this is perpendicular to $\vec n$ .

So the equation of the plane is

$\langle x-1, y-1, z+1 \rangle \cdot \vec n = 0 \implies (x-1) - (y-1) + (z+1) = 0 \implies \boxed{x - y + z = -1}$

or equivalently,

$\boxed{-x + y - z = 1}$

6 0

2 years ago

Explain your answer !! <br> Have a nice day <br><br> Will give braisnlt

Viktor [21]

Answer:

(3,-4) or x=3 and y= -4

Step-by-step explanation:

I'm going to solve this by substitution

We first need to get a variable by itself in one of the two equations (it doesn't matter which variable and the equation you do the work on doesn't matter either)

I'm going to solve for y in the second equation

-4x-4y=4

add 4y and subtract 4 from both sides to get

-4x-4=4y

Divide by 4 to get

-x-1=y

We can plug this value in for y into the first equation and get

4x+5(-x-1)= -8

Solve for x

4x-5x-5= -8

-x-5= -8

-x= -3

x=3

We can plug this value into one of the first two equations and solve for y

4(3)+5y= -8

12+5y= -8

5y= -20

y= -4

Therefore the solution is (3,-4) or x=3 and y= -4

8 0

2 years ago

Hot dogs come in packages of 8. hot dog buns come in packages of 12. if grace wants to have enough to serve 24 people and have n

OLga [1]

She would by 3 packages of hot dogs and 2 packages of hot dog buns. This is because 3*8 would be 24 and 12*2 is also 24. These would both be the minimum amount of packages.

5 0

3 years ago

A 72.9-foot rope from the top of a circus tent pole is anchored to the ground 44.9 feet from the bottom of the pole. What angle

Ilia_Sergeevich [38]

See the attachment.

It is in the attachment (photo)

4 0

3 years ago