A flower bed is in the shape of a trapezoid.

A trapezoid with base lengths of 6 feet and 8 feet, and height 4 feet.

What is the square footage of the flower bed?

28 ft2
56 ft2
96 ft2
192 ft2

The matrix for the combined rotation transformation of 45° and dilation

of [tex]\sqrt{2}[/tex] gives the matrix for the transformation as follows;

[tex]Matrix \ for \ the \ rotation \ and \ dilation \ is;\left[\begin{array}{cc}1 &-1\\1&1\end{array}\right][/tex]

The angle by which the transformation rotates about the origin = 45°

The dilation following the rotation = A factor of √2

Required:

The matrix for the transformation

Solution:

The dilation matrix for a scale factor of [tex]\mathbf{\sqrt{2}}[/tex] is presented as follows;

[tex]\mathbf{\left[\begin{array}{cc}\sqrt{2} &0\\0&\sqrt{2} \end{array}\right]}[/tex]

[tex]The \ transformation \ for \ a \ rotation \ of \ 45^{\circ} \ is; \left[\begin{array}{cc}cos(45^{\circ})&-sin(45^{\circ})\\sin(45^{\circ})&cos(45^{\circ})\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}cos(45^{\circ})&-sin(45^{\circ})\\&\\sin(45^{\circ})&cos(45^{\circ})\end{array}\right] = \mathbf{\left[\begin{array}{cc}\dfrac{\sqrt{2} }{2} &-\dfrac{\sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} }{2} &\dfrac{\sqrt{2} }{2} \end{array}\right]}[/tex]

Which gives;

[tex]\left[\begin{array}{cc}\dfrac{\sqrt{2} }{2} &-\dfrac{\sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} }{2} &\dfrac{\sqrt{2} }{2} \end{array}\right] \times \left[\begin{array}{cc}\sqrt{2} &0\\0&\sqrt{2} \end{array}\right] = \left[\begin{array}{cc}\dfrac{\sqrt{2} \times \sqrt{2} }{2} &-\dfrac{\sqrt{2} \times \sqrt{2} }{2} \\&\\ \dfrac{\sqrt{2} \times \sqrt{2} }{2} &\dfrac{\sqrt{2} \times \sqrt{2} }{2} \end{array}\right] = \left[\begin{array}{cc}1 &-1\\1&1\end{array}\right][/tex]

The required matrix for the transformation is therefore;

Learn more about other forms of transformation matrices here:

https://brainly.com/question/10212935

Answer:

B

Step-by-step explanation:

Divide 243.46 by 37 to solve for t

Step-by-step explanation:

37t means 37 x t. We are solving for t.

First, we need to divide 243.46 by 37.

243.46÷37=6.58

t=6.58

Now we need to check and make sure our answer is correct.

Since we are solving for t, we need to multiply 37 by 6.58 to make sure our answer is correct.

37 x 6.58= 243.46. We got 243.46 which means it is correct.

Answer:

x=2

Step-by-step explanation:

used simultaneous equation to work it out but i cba to explain because i need the points. i can explain to you if u want me to. just reply to this answer

Answer:

2

Step-by-step explanation:

[tex] \quad{\rule{300pt}{1.5pt}}\quad[/tex]

We are given that :

We know that :

[tex]\qquad\bull{\boxed {\mathfrak{Circumference = 2 \pi r }}}\bull[/tex]

Therefore,

[tex] \quad\dashrightarrow\quad \sf { 6.28 = 2 \pi r }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = \dfrac{6.28}{2\pi} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = \dfrac{6.28\times 7}{22\times 2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r =\cancel{\dfrac{43.64}{44}} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {r = 0.9989 }[/tex]

As we know,

[tex] \quad\dashrightarrow\quad \sf { Diameter = 2\times radius}[/tex]

[tex] \quad\dashrightarrow\quad \sf { Diameter = 2\times 0.9989}[/tex]

[tex] \quad\dashrightarrow\quad \sf { Diameter = 1.98 }[/tex]

[tex] \quad\dashrightarrow\quad {\pmb{\sf {Diameter = 2 mm ( approx ) }}}[/tex]

[tex] \rule{300pt}{2pt}[/tex]

Answer:

175/48

Step-by-step explanation:

Convert 8 6/8 and 2 2/5 to fractions
8 6/8 = 70/8 ; 2 2/5 = 12/5

Now, we have : 70/8 : 12/5
= 70/8 x 5/12
= 70x5/8x12

=350/96
Simplify the fraction, we get 175/48

Answer:

12π meters

Step-by-step explanation:

Area of circle = Pi*r^2 -> 36*Pi = Pi*r^2

So, radius of circle (r) = 6 m

Circumference of circle = 2*Pi*r = 2*Pi*6 = 12Pi m

Answer:

20.3

Step-by-step explanation:

10+4+2π I think!!!

Answer:

1

Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

2
1)( x^2+6x+9)/18  /  (x+3)^2/36

    x^2+6x+9=(x+3)^2

   (x+3)^2/18  *  36/(x+3)^2=36/18=2

2) I'll factor the terms for you.

  (2x+3)(x-4)/2(3+2x)  *  2/(x-4)(x+4)

Do you see the common factors ?

3
start fraction, 1, divided by, 2, end fraction unit. As the volume of n cubes will be equal to volume of rectangular prism. Therefore, a rectangular prism will take 48 cubes with each side 1/2 units to fill the prism.

Hope this is helpful

Answer:

(x+5)^2+(y-8)^2=4^2

Step-by-step explanation:

I used a website called desmos.

Answer:

(x + 5)² + (y - 8)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 5, 8 ) and r = 4 , then

(x - (- 5) )² + (y - 8)² = 4² , that is

(x + 5)² + (y - 8)² = 16

Answer:

D) y = 4

Step-by-step explanation:

It is a horizontally straight line, meaning it is parallel to the x-axis.

Answer:

Yes

Step-by-step explanation:

one X value yields only one Y value.

Answer:

$2.16

Step-by-step explanation:

To find the tip amount, you multiply the price by the tip percentage.

14.40*0.15 = 2.16

So...

Tip = $2.16

Hope this helps!

Answer:

16 years old

Step-by-step explanation:

let Gastas age be g

since Gasta is four years older

g=12+4

g=16 years old

Answer:

a^2 + b^2 = c^2, where c is the hypotenus and a and b are the legs

Step-by-step explanation:

Answer:

Jane spent the most money, while Anne spent the least.

Step-by-step explanation

Anne spent less because Jane spent 0.888 in decimal form, whereas Anne spent 0.875 in decimal form.

Answer:

(14, 23)

area = 400 square units

Step-by-step explanation:

Part (a)

To find the point where two equations meet (the point of intersection), equal the equations to each other, then solve for x.  Substitute the found value of x into one of the equations (it doesn't matter which) and then solve for y.  (x, y) is the point of intersection.

Equation 1:  y = 2x - 5

Equation 2:  y = 23

Equate the equations:

            y = y

⇒ 2x - 5 = 23

⇒       2x = 23 + 5

⇒       2x = 28

⇒          x = 28 ÷ 2

⇒          x = 14

Usually we'd substitute the found value of x into one of the equations and solve for y, however, as one of the equations is literally the y value, we don't need to do that.

So y = 23

Therefore, the point of intersection is (14, 23)

Part (b)

The vertices of the triangle will be the points where each pair of lines meet each other.  We have already determined that one pair of lines meets at point (14, 23).

y = 2x - 5 is a diagonal line, y = 23 is a horizontal line, and x = -6 is a vertical line.

So x = -6 and y = 23 meet at (-6, 23)

Now we just need to determine where y = 2x - 5  and  x = -6 meet.

Simply substitute x = -6 into y = 2x - 5:

⇒ y = 2(-6) - 5

⇒ y = -17

Therefore, the point of intersection is (-6, -17)

So we have three points of intersection which are the three vertices of the triangle:

(14, 23)  (-6, 23) (-6, -17)

As y = 23 is a horizontal line and x = -6 is a vertical line, their point of intersection (-6, 23) is a right angle.

Therefore the can determine that the height of the triangle is the difference between the y-coordinates of (-6, 23) and (-6, -17).

Similarly, the base (width) of the triangle is the difference between the x-coordinates of (-6, 23) and (14, 23).

Therefore, the height = 23 - -17 = 23 + 17 = 40

Therefore, the base = 14 - -6 = 14 + 6 = 20

Area of a triangle = 1/2 x base x height = 1/2 x 20 x 40 = 400 square units

see attached diagram

Answer:

The answer is 5.5

Step-by-step explanation:

6 x 6 = 36

2x2x2 = 8

36 + 8 =    44

2 + 6 = 8

44/8 = 5.5

Therefore, the answer to this problem is 5.5

I hope I helped! ^-^

Answer:

d. two and one fourth

Step-by-step explanation:

3 3/4 - 1 2/4 = 2 1/4

2 1/4

i hope this helps! have a wonderful rest of ur day :)

and if its not too much to ask could you mark me as brainliest pls

im trying to rank up and i only need 1 more, if not its ok! ty and let me know if you need help with anything else!!

Answer:

Multiply the numerator by the reciprocal of the denominator. Multiply x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=1x f - 1 ( x ) = 1 x is the inverse of f(x)=1x f ( x ) = 1 x .

Step-by-step explanation:

:)

Hi! I can help you with joy! :)

Answer:

2 terms

Hope it helps!

[tex]\rm{Stargazing{\bold{WithJoy:D}[/tex]

Answer:

(0,-2)

Step-by-step explanation:

The y axis is the axis that is up and down

The y intercept or where it cuts the y axis is at the point -2

The x value is 0 and the y value is -2

The y intercept is (0,-2)

Answer:

it's 0,-2

Step-by-step explanation:

Look where it touches the y axis (going up and down)

Answer:

5 < third side < 21

Step-by-step explanation:

Let the length of the third side be [tex]x[/tex].

We know that [tex]x[/tex] must be smaller than the sum of the lengths of the two other sides. Thus [tex]x < 21[/tex].

We also know that

[tex]x+8 > 13\\x > 5[/tex]

And

[tex]x+13 > 8\\x > -5[/tex]

So, in conclusion, [tex]5 < x < 21[/tex].

Answer:

25. hope this helped you brother!

Answer:

14 un cracked

Step-by-step explanation:

three-fifths of 60= 36

one-sixth of 60= 10

36+10=46

60-46=14

14 un cracked eggs