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andreyandreev [35.5K]
3 years ago
9

Lanie's room is in the shape of a parallelogram. The floor of her room is shown below and has an area of 108 square feet. Lanie

has a rectangular rug that is 6 feet wide and 10 feet long. Will the rug fit on the floor of her room? Use the drop‐down menus to explain and show your answer.
Mathematics
1 answer:
dsp733 years ago
7 0

Answer:

Yes it would

Step-by-step explanation:

Lanie's room is in the shape of a parallelogram.

Lanie has a rectangular rug that is 6 feet wide and 10 feet long.

Area of a rectangle = Length × Width

Area of the rectangular rug = 10 feet × 6 feet

= 60 square feet

We are told that:

The floor of her room is shown below and has an area of 108 square feet.

Hence, the rug would fit on the floor of her room because it's area is within the area of the floor of her room.

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Solve the system of equations below by graphing.
algol [13]

ANSWER


The correct answer is B

<u>EXPLANATION</u>

The first function is


x^2-2x+y-3=0


We make y the subject to obtain;


y=-x^2+2x+3


Let us quickly write this in the vertex form.


y=-(x^2-2x)+3


y=-(x^2-2x+(-1)^2)+3+(-1)^2


y=-(x-1)^2+4


Since the a is negative, the graph opens up.


The vertex is at (1,4)


The y-intercept is -3


The x-intercept is found by equating the function to zero.


-(x-1)^2+4=0


\Rightarrow (x-1)^2=4


\Rightarrow (x-1)=\pm 2


\Rightarrow x=1 \pm2

\Rightarrow x=-1,3


With these information we can quickly sketch the graph as shown in the attachment(the red graph).


For the second function,


x^2+y=0


we again make y the subject to obtain,


y=-x^2


This is a basic quadratic function that can be graphed easily. Note that it is also a maximum graph.


From the graph the solution to the two functions is


(-1.5,-2.25)





3 0
3 years ago
How to differentiate this
Art [367]

y=t^3\,\,\,x=\sqrt{2t}+1\rightarrow t=\frac{(x-1)^2}{2}\\\rightarrow y=\frac{1}{8}(x-1)^6\\\frac{dy}{dx}=\frac{3}{4}(x-1)^5

6 0
3 years ago
Katrina is asked to simplify the expression Negative 3 a minus 4 b minus 2 (5 a minus 7 b).
lara31 [8.8K]

Answer:

oofyios

Step-by-step explanation:

5 0
3 years ago
Circle the expression(s) that shows a sum or difference equivalent to -0.9(3x - 2.6 )
mel-nik [20]
It’s c i think sorry if i’m wrong
8 0
3 years ago
AC is tangent to circle O at point C. What is the length of AB?
DochEvi [55]

The length of AB is 9.

Solution:

Given data:

Radius OC = 8

Tangent AC = 15

The angle between the tangent and radius is always right angle.

∠C = 90°.

Hence OCA is a right triangle.

Using Pythagoras theorem,

<em>In a right triangle square of the hypotenuse is equal to the sum of the squares of the other two sides.</em>

OA^2=15^2+8^2

OA^2=225+64

OA^2=289

OA^2=17^2

Taking square root on both sides of the equation, we get

OA = 17

OB is the radius of the circle.

⇒ OB = 8

AB = OA – OB

     = 17 – 8

     = 9

AB = 9

Hence the length of AB is 9.

4 0
4 years ago
Read 2 more answers
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