The area of a garden can be represented by the expression x2 - 6x - 27. What are the dimensions of the rectangle in terms of x?

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos²A - sin²B = cos(A + B) . cos(A - B)

Here A = [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] , B = [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex]

Consider the left side

cos²([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] ) - sin²( [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] )

= cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] + [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] ) × cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] - [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] )

= cos ([tex]\frac{\pi }{4}[/tex] ) × cos ( A)

= [tex]\frac{1}{\sqrt{2} }[/tex] cosA

=  right side , thus proven

Answer:

Step-by-step explanation:

exponent on 1 is 9

Answer:

x = 12

Step-by-step explanation:

(x + 42)° + 3x° = 90°

x + 3x + 42 = 90

4x = 90 - 42

4x = 48

x = 12

Answer:

[tex]y=\frac{5}{9}[/tex]

Step-by-step explanation:

For the graph of [tex]y=f(x)[/tex],

the horizontal asymptote becomes [tex]y=\frac{5}{9}[/tex]

Answer:

12

Step-by-step explanation:

here's your solution

=> area of rectangle = length*width

=> area 4*3 = 12.squnit

=> area of square = side^2

=> area = 1.squnit

=> Number of square = area of rectangle/area of square

=> no of square = 12/1

=>. 12

Answer: The probability is 5/6

Step-by-step explanation:

Answer:

We have a triangle rectangle here.

We know that:

AC =  15

BC = 8

AB = 17

We know that in a triangle rectangle the longest side is the hypotenuse.

In the image we can see that the shorter side is the base, then BC is the base.

AC is the height.

AB is the hypotenuse.

Such that:

A is the top vertex.

B is the bottom right vertex

C is the bottom left vertex.

Now you need to remember the relations:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Cos(θ) = (adjacent cathetus)/(hypotenuse)

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

then:

Sin (A) = (AC)/(AB) = 15/17 = 0.88

Cos(B) = (AC)/(AB) = 15/17 = 0.88

Tan(B) = (AC)/(CB) = 15/8 = 1.875

Now we want to find the measure of angle A.

We know that:

Sin(A) = 0.88

Then if we apply the Asin( ) function in both sides, we get:

Asin( Sin(A)) = Asin(0.88)

A = Asin(0.88) = 61.6°

(the Asin() function is the inverse of the sin() function)

Now we have:

sin(x) = 0.906

We do the same thing as before.

Asin(sin(x)) = Asin(0.906)

x = Asin(0.906) = 65°

And:

Sin(87°) = 0.999

Answer:

is there supposed to be a picture connected to this?

Answer:

what is the question?

Step-by-step explanation:

please let me know.

thanks

Answer:

Pretty sure it’s D

Step-by-step explanation:

Answer:

The square root of 192

Step-by-step explanation:

It's just the Pythagoras theorem p much

Answer:

the probability of rolling a number greater than 2 is 2/3

Step-by-step explanation:

because 3 4 5 and 6 are greater than two we have 4 numbers greater than 2 so 4/6 is 2/3 when simplified

Answer:

two expressions that are equivalent to 7x10^-4

=7/10000or 7/10^4

Answer:

Step-by-step explanation:

we know that the angle is less than 90,  so there is only one choice for that , the 75° choice.   that also seems about right.  

Answer:

C.

Step-by-step explanation:

It follows the rule

[tex]a {}^{2} + b {}^{2} = c {}^{2} [/tex]

Therefore that is the reason why it is called "a squared + b squared equals c squared"

Answer:

[tex]∠ACB=40°[/tex]

Step-by-step explanation:

[tex]∠APB=80°[/tex]

[tex]=>∠APB= 2×∠ACB[/tex]

[In Circle, the angle subtend at the centre is double angle subtend at the circumference.]

[tex]=>80° = 2× ∠ACB[/tex]

[tex]=>∠ACB=\frac{80°}{2}[/tex]

Answer:

yo did anyone have the answer

Step-by-step explanation:

Answer:

132 degrees

Step-by-step explanation:

To solve this problem, you need to know a couple of rules

1) Inscribed angle theroem: when an angle is inscribed in a circle and touches the other end (as opposed to ending at the diameter of the circle), the measure of this angle is half of the measure of the arc.

2)Angles of a quadrilateral shape add up to 360 degrees.

3) The angles inside a circle and the angles of the circles arclength adds up to 360 degrees.

So first, solve angle S with inscribed angle theorem. 126/2 = 63

Then, use the rule that all arc angles in a circle add up to 360 degrees to find the arc angle from Q to S. 360-90-126 = 144. Now find angle P with inscribed angle theorem by doing 144/2 = 72.

Now, use the rule that all angles in a quadrilateral add up to 360 to find R. 360-93-72-63 = 132.  

Let me know if this doesn't work, I'll look at it again.

Answer: x = -3/4

Step-by-step explanation:

Remember:

[tex]\sqrt{a}=b\\\\a=b^2[/tex]

-----------------

[tex]\frac{\sqrt{4x + 19} }{2} = 2\\\\\sqrt{4x + 19} = 4\\\\(4x+19)=4^2\\\\4x +19 = 16\\\\4x=16-19\\\\4x = -3\\\\x =\frac{-3}{4}[/tex]

Answer:

B one

They only cross once on the graph

Answer:

Step-by-step explanation:

Equation is below

Step 1

(3x^2 y^5)^4  

Step 2

(3x^2 y^5)^4  Simplify

81x^8y^20

Step 3

81x^8y^20  check

Answer

81x^8y^20

Hope this helped

Answer:

23

Step-by-step explanation:

20 - 3(-1)

20 - (-3)

20 + 3 =

23

Hello!

This is a problem about relating circle theorems to line lengths.

We can first see that both line segment MK and CM are secants within the circle that come from a common point K.

This means that the Intersecting Secant Theorem applies here.

The Intersecting Secant Theorem states that if two secants are formed from a common point outside the circle, the length of each secant multiplied by the length of its corresponding external secant are equivalent.

We can set up the following equation.

[tex]8(8+x+5)=7(7+2x+1)[/tex]

[tex]8(x+13)=7(2x+8)[/tex]

[tex]8x+104=14x+56[/tex]

[tex]6x=48[/tex]

[tex]x=8[/tex]

Using this value, we can find the length of line segment MK.

[tex]MK=x+5+8[/tex]

[tex]MK=8+5+8[/tex]

[tex]MK=21[/tex]

Hope this helps!

Answer:

the first one is 4.03 and the second one os 4.33

Answer:

4.03 and 4.33 is the answer.

Step-by-step explanation:

The numbers increase by +0.1

∴ 4.03, 4.13, 4.23, 4.33, 4.43, 4.53

Answer:

7) is $1.70

8) is 8 miles per hour

9) is Store A is the better buy

10) is 222

11) is the area is 6

12) is the range is 14

8.)8 miles per hour

20 = 150

X = 60

20 x 60 = 150x

1200 = 150x

X = 8

9.)better buy number A

44.68 /16 = 2.7925

31.57 /11 = 2.87

11.) The area of this figure is 6

3 X 2 = 6

12) Range of the data set is 14

15 - 1 = 14

Answer:

A it skews the data to the right

Step-by-step explanation:

A

Answer: B is 44 degrees.

Step-by-step explanation:

(6x+22)=(7x+16)=90.

x=4

(7(4)+16)=44

Answer:

110 minutes or 1 hour 50 minutes

Step-by-step explanation:

44 divided into 4 since we want to find out how much time it takes to run 1 mile, so 44 divided into 4 is 11

then simply multiply 11 with 10 and the answer is 110

: )

Answer:

choice 2) y ≤ 1

Step-by-step explanation:

Answer: B I think!

Step-by-step explanation: