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3 years ago

How many solutions does 4(y-30)=4y+12

1 answer:

8 0

$\text{Solve for y:}\\\\4(y-30)=4y+12\\\\4y-120=4y+12\\\\\text{Subtract 4y from both sides}\\\\-120=12\\\\\text{You would see that the y variable is now non-existent}\\\\\text{This means that there are no solutions}\\\\\boxed{\text{No solutions}}$

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Dom josin is paid 18 as a pastry chef for regular 35hours week over rate is 1.5 times regular hourly rate he work 5 overtime hou

Nonamiya [84]

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5 0

3 years ago

The perimeter of the rectangle is 22 meters, and the perimeter of the triangle is 12 meters. Find the dimensions of the rectangl

lianna [129]

Answer:

Length:8 m

Width:3 m

Step-by-step explanation:

The complete question is

If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.

step 1

Perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

we have

$P=22\ m$

$22=2(L+W)$

Simplify

$11=L+W$ -----> equation A

step 2

Perimeter of triangle

The perimeter of triangle is equal to

$P=\frac{L}{2}+W+5$

$P=12\ m$

$12=\frac{L}{2}+W+5$

Multiply by 2 both sides

$24=L+2W+10$

$L+2W=14$ ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (8,3)

see the attached figure

therefore

The dimensions of the rectangle are

Length:8 m

Width:3 m

3 0

3 years ago

If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by

PIT_PIT [208]

Answer:

The family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

$\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}$ (1)

Where:

$\theta$ - Angle between vectors, in sexagesimal degrees.

$\|\vec a\|, \|\vec b \|$ - Norms of vectors $\vec {a}$ and $\vec{b}$

If $\theta$ is acute, then the cosine function is bounded between 0 a 1 and if we know that $\vec {a} = (p, 3, -7)$ and $\vec {b} = (p, -p, 4)$ , then the possible values for $p$ are: