Calculate and express your answer in decimal form: 1/2 x 17 *

Quadrilateral QRST, with vertices Q (1, 2), R (3, 4), S (5, 6), and T (2, 7), is dilated by a factor of 2 with the center of dil

bija089 [108]

Answer:

Step-by-step explanation:

Given

Quadrilateral QRST

Q (1, 2), R (3, 4), S (5, 6), and T (2, 7)

Dlated Factor = 2

Required

Coordinates of quadrilateral Q′R′S′T′

<em>Provided that a quadrilateral is dilated with the center of dilation at the origin; the new dilated shape is simply the multiplication of the dilation factor by the coordinates of the original shape;</em>

<em />

In other words,

Q'R'S'T' = Dilation factor * QRST

When Q = (1,2)

Q' = 2 * (1,2)

Q' = (2,4)

When R = (3,4)

R' = 2 * (3,4)

R' = (6,8)

When S = (5,6)

S' = 2* (5,6)

S' = (10,12)

When T= (2,7)

T' = 2 * (2,7)

T' = (4,14)

Hence, the coordinates of Q'R'S'T' is

Q' = (2,4); R' = (6,8); S' = (10,12); T' = (4,14)

6 0

3 years ago

Find the base of a parallelogram with a slant height of 7cm and an perimeter of 63 cm2

vlada-n [284]

Base of parallelogram b = 24.5 cm

Step-by-step explanation:

We are given:

Perimeter =P= 63 cm^2

Slant Height =a= 7 cm

Base of Parallelogram =b= ?

The formula used is:

$Perimeter = 2(a+b)$

where a is height and b is base

Putting values:

$Perimeter = 2(a+b)\\63=2(7+b)\\63=14+2b\\2b=63-14\\2b=49\\b=\frac{49}{2}\\b=24.5$

So, Base of parallelogram b = 24.5 cm

Keywords: Perimeter of Parallelogram

Learn more about Perimeter of Parallelogram at:

#learnwithBrainly

5 0

3 years ago

The first table that Cory designs will seat 8 people. If the diameter is 5 feet, what is the area? The area in terms of pi is Pi

frutty [35]

Answer: 19.6

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S.

sweet-ann [11.9K]

Answer:

2.794

Step-by-step explanation:

Recall that if G(x,y) is a parametrization of the surface S and F and G are smooth enough then

$\bf \displaystyle\iint_{S}FdS=\displaystyle\iint_{R}F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})dxdy$

F can be written as

F(x,y,z) = (xy, yz, zx)

and S has a straightforward parametrization as

$\bf G(x,y) = (x, y, 3-x^2-y^2)$

with 0≤ x≤1 and 0≤ y≤1

So

$\bf \displaystyle\frac{\partial G}{\partial x}= (1,0,-2x)\\\\\displaystyle\frac{\partial G}{\partial y}= (0,1,-2y)\\\\\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y}=(2x,2y,1)$

we also have

$\bf F(G(x,y))=F(x, y, 3-x^2-y^2)=(xy,y(3-x^2-y^2),x(3-x^2-y^2))=\\\\=(xy,3y-x^2y-y^3,3x-x^3-xy^2)$

and so

$\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2$

we just have then to compute a double integral of a polynomial on the unit square 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\int_{0}^{1}\displaystyle\int_{0}^{1}(2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2)dxdy=\\\\=2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}ydy+6\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^4dy+\\\\+3\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}x^3dx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}y^2dy$

=1/3+2-2/9-2/5+3/2-1/4-1/6 = 2.794

5 0

3 years ago

Miss groves has trays of paint for students In her art class each tray has 5 colors one of the colors is purple what fraction of

Simora [160]

Answer:

1/5

Step-by-step explanation:

If each tray has 1 purple in 5 colors, it doesn't matter how many trays there are. The fraction of colors that is purple is 1/5.

4 0

3 years ago