What is the solution of the system ?Use substitution.<br> Y= -3x<br> X + y = -4

A brand of clay brick tiles has the dimensions 3 5 8 by 7 5 8 by 1 2 inch. These thin bricks are commonly used for floors. Estim

raketka [301]

Answer: The cost to tile the floor is $318.24.

Step-by-step explanation:

Since we have given that

Dimensions of floor is 12 by 17 foot.

So, Area of floor would be

$12\times 17\\\\=204\ sq.\ foot$

As we know that 1 foot = 12 inch

So, Area of floor would be

$204\times (12)^2\\\\=204\times 144\\\\=29376\ sq.\ foot$

Dimension of brick tiles is given by

$3\dfrac{5}{8}\ by\ 7\dfrac{5}{8}\ by\ \dfrac{1}{2}$

So, Area of brick tiles is given by

$2(lb+bh+lh)\\\\=2(\dfrac{29}{8}\times \dfrac{61}{8}+\dfrac{61}{8}\times \dfrac{1}{2}+\dfrac{29}{8}\times \dfrac{1}{2})\\\\=2(\dfrac{1769}{64}+\dfrac{61}{16}+\dfrac{29}{16})\\\\=2\times \dfrac{1769+244+116}{64}\\\\=\dfrac{2129}{32}$

So, Number of clay brick would be

$29376\div \dfrac{2129}{32}\\\\=29376\times \dfrac{32}{2129}\\\\=\dfrac{29376\times 32}{2129}\\\\=441.53\\\\\approx 442$

cost of each clay brick = $0.72

So, Total cost of flooring would be

$442\times 0.72\\\\=\$318.24$

Hence, The cost to tile the floor is $318.24.

7 0

2 years ago

A radio telescope has a parabolic surface, as shown below.

krek1111 [17]

OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0

Because the roots of the equation are 0 and 12, we know the formula is therefore of the form

y = ax(x - 12), for some a

So put in x = 6

-9 = 6a(-6)

9 = 36a

a = 1/4

So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x

The gradient of this is dy/dx = 0.5x - 3

The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8

Gradient of the parabolic mirror at x = 4 is -1

So the gradient of the normal to the mirror at x = 4 is therefore 1.

Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.

So the focal point is at y = -8, i.e. 1 metre above the back of the dish.

5 0

2 years ago

Help asap im in a quiz!

goldfiish [28.3K]

The answer should be b

5 0

2 years ago

Molly is raising cows. She has a pasture for them that is 0.65 square miles in area. One dimension of the pasture is 0.4 miles l

dem82 [27]

Answer:

The other dimension of the pasture (width) is $1.625\ mi$

Step-by-step explanation:

In this problem I assume that the pasture has the shape of a rectangle.

Let

x -----> the length of the pasture

y -----> the width of the pasture

we know that

The area of the pasture (rectangle) is equal to

$A=xy$

we have

$A=0.65\ mi^{2}$

$x=0.4\ mi$

substitute and solve for y

$0.65=0.4y$

$y=0.65/0.4$

$y=1.625\ mi$

5 0

2 years ago

Please check what i have Quickly

RUDIKE [14]

Break the figure into a triangle and a rectangle.

The triangle has a base of 6 and a height of 3, so the area is 6*3/2 = 18/2 = 9
The rectangle has a length of 5 and a height of 6, so 6*5 = 30 is the area of the rectangle.

The total area is 30+9 = 39

Answer: 39

5 0

3 years ago

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What is the solution of the system ?Use substitution. Y= -3x X + y = -4