Which is the scale factor of the dilation?

Answer:

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled [tex]\triangle OBT[/tex])

with [tex]\angle B =90^\circ[/tex]

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

[tex]\angle O = 55^\circ[/tex]

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]

So, height of building is 57.12 m.

Answer: No its not a Function

Step-by-step explanation:

ITs not a function because

{(1,3),(1,2),(3,-2),(3,-2),(3,2)}

The codomain is being repreted

for example if you look here (1,2),(3,2)}

The 2 is being repreted which shows its not a function

Hope this helps :)

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6

Answer:

3, 12, 27 and 300

Step-by-step explanation:

Plug n as 1, 2, 3 and 10.

3(1)² = 3

3(2)² = 12

3(3)² = 27

3(10)² = 300

Answer:

f(x) = (x + 5)² - 21.5

Step-by-step explanation:

Step 1: Subtract both sides by 7

2x² + 20x = -7

Step: GCF and divide

2(x² + 10x) = -7

x² + 10x = -7/2

Step 3: Complete the Square

x² + 10x + 25 = -7/2 + 25

(x +5)² = 43/2

Step 4: Subtract 43/2 to both sides

(x + 5)² - 43/2

And we have our equation!

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

f(-7)=224

Step-by-step explanation:

[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]

Answer:

x = -1/8

Step-by-step explanation:

The greater than sign can be replaced with an equal sign to solve.

5x + 4 < 3 – 3x =>

5x + 4 = 3 - 3x =>

+3x  -4    +3x - 4

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

8x = -1

x = -1/8

Answer:

[tex](C) \dfrac{x+3}{x}[/tex]

Step-by-step explanation:

We want to determine an  equivalent expression to:

[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]

Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.

[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]

Step 2: Change the division sign to multiplication

[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]

Step 3: Cancel out common terms and simplify

[tex]= \dfrac{x+3}{x}[/tex]

The correct option is C.

The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Given expression is,

                        [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]

Use factorization,   [tex]x^{2} -9=(x-3)(x+3)[/tex]

Now simplify the given expression.

                       [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]

Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Learn more:

https://brainly.com/question/1280754

Answer:

-9=-9

8=8

-48=-48 or -8(-6)=-48

-6=-6 or 18/-3=-6

Step-by-step explanation:

Answer:

Simplify each expression involving signed numbers.

-7 – 2 =

✔ –9

12 + (-4) =

✔ 8

-8(-6) =

✔ 48

StartFraction 18 over negative 3 EndFraction =

✔ –6

can I have some brainiest

Step-by-step explanation:

Answer:

36 toilet rolls

Step-by-step explanation:

1 pack consist of 4 rolls

So,

1 pack = 4 toilet rolls

Multiplying both sides by 9

=> 1×9 = 4×9

=> 9 packs = 36 toilet rolls

Answer:

For the first one,

x=6 and y=16

Step-by-step explanation:

If I think of any more then I will tell you

Answer:

believe its 2x cause 1 was wrong

Answer:

Step-by-step explanation:

Answer:

[tex]9\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{3} \div \frac{1}{4}[/tex]

[tex]\frac{7}{3} \div \frac{1}{4}[/tex]

[tex]\frac{7}{3} \times \frac{4}{1}[/tex]

[tex]\frac{7 \times 4}{3 \times 1}[/tex]

[tex]\frac{28}{3}[/tex]

[tex]9\frac{1}{3}[/tex]

[tex]9 \frac{1}{3} \\ solution \\ 2 \frac{1}{3} \div \frac{1}{4} \\ = \frac{7}{3} \times \frac{4}{1} \\ = \frac{7 \times 4}{3 \times 1} \\ = \frac{28}{3} \\ = 9 \frac{1}{3} [/tex]

Hope it helps...

Good luck on your assignment....

Answer: £107.08

Step-by-step explanation:

27% of 396.58

= 396.58 x 0.27

= 107.08

Answer:

11

Step-by-step explanation:

the answer is 11

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

#SPJ2

Answer:

(i) 12.25

(ii) 12.25.

Step-by-step explanation:

(1) cot^2 O = (7/2)^2 = 49/4

= 12.25.

(2) (1 - sin O) ( 1 + sin O)         1 - sin^2 O          cos^2 O

     ----------------------------  =     -------------   =       --------------

    (1 - cos O)(1 + cos O)         1 - cos^2 O         1 - cos^2 O

As cot O = 2/7, tan O = 1 /2/7 = 7/2.

Hypotenuse of the right  triangle = √( 2^2 + 7^2)

= √53

So cos O = 7/√53

Therefore  the original function = cos^2 O / (1 - cos^2 O)

= (7/√53)^2 / (1 -  (7/√53)^2 )

= 49/53 / 4/53

= 49/4.

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0                        x² + x + b = 0

a*1² +a*1 + 2 = 0                        1² + 1 + b = 0

a +a + 2 = 0                                 1 + 1 + b = 0

2a + 2 = 0                                    2 + b = 0

2a = -  2                                         b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:the answer I’m is C trust me

Step-by-step explanation: I just took the test

Answer:(-4,7)

Step-by-step explanation:

Edg 2021

Answer:

8 x^6  y^3

Step-by-step explanation:

(2x^2y)^3

(ab)^c = a^c  * b^c

2^3  * x^2^3  * y^3

8  * x^2^3  * y^3

We know that a^b^c = a^(b*c)

8  * x^(2*3)  * y^3

8  * x^(6)  * y^3

8 x^6  y^3

Hey there! :)

Answer:

D, e - 2b.

Step-by-step explanation:

Check each answer choice using the pattern given:

A. e - c = d because c + d = e. This is correct.

B. b + c = d. This is correct.

C. a + 2b = d because c = a + b. This is correct.

D. e - 2b ≠ d. This is incorrect.

E. f - e = d because d + e = f. This is correct.

Therefore, the only answer that does not equal "d" is D, e - 2b.

Answer:

[tex](2, 17)[/tex]

Step-by-step explanation:

A parabola has the general function: [tex]f(x)=ax^2+bx+c[/tex]

In this case we have: [tex]f(x) = x^2 - 4x + 21[/tex]

where

[tex]a=1[/tex]

[tex]b=-4[/tex]

[tex]c=21[/tex]

the vertex of a parabola is in the coordinates:

[tex](\frac{-b}{2a}, \frac{-b^2+4ac}{4a} )[/tex]

substituting all of the known values, we get the following:

[tex](\frac{-(-4)}{2(1)} ,\frac{-(-4)^2+4(1)(21)}{4(1)} )\\\\(\frac{4}{2} ,\frac{-16+84}{4} )\\\\\\(2 ,\frac{68}{4} )\\\\\\(2,17)[/tex]

the vertex of  [tex]f(x) = x^2 - 4x + 21[/tex] is at the point (2,17) which is the second option.

Answer:

2,17

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the figure attached,

Given : LM ≅ OP

            PQ ≅ MN

            NL ≅ QO

To Prove : ΔLMN ≅ ΔOPQ

In the triangles LMN and OPQ,

             Statements              Reasons

1). LM ≅ OP                       1). Given

2). PQ ≅ MN                     2). Given

3). NL ≅ QO                      3). Given

4). ΔLMN ≅ ΔOPQ            4). By SSS property of congruence

Answer:

Step-by-step explanation:

We will make a table with the values for both a 6% account and a 9% account.

The formula for this problem is Prt = I, where P is the amount invested in each account, r is the interest rate each carries in decimal form, t is the time in years, and I is the interest earned from the multiplication of the 3 previous values. We don't know how much is invested in either account, but we do know that no matter how much is invested in the 6% account, there is 6 times that in the 9% account. We know that the 6% account has a decimal rate of .06 and that the 9% account has a decimal rate of .09. "Annual" means 1 year, so the time is 1 year. Filling in the table, then:

                     P  *    r     *     t     =     I

Acct 6%         x     .06         1

Acct 9%       6x    .09          1

What we do with those number is multiply them straight across each row to get the amount of interest earned from each:

                    P     *     r     *     t     =     I

Acct 6%       x      *  .06    *    1      =   .06x

Acct 9%      6x     *  .09    *    1      =   .54x

The amount of Interest for both ADDS UP to 800; therefore:

.06x + .54x = 800 and

.6x = 800 so

x = 1333.33

That's how much was invested in the account that earned 6% interest annually.  

Answer:

B

Step-by-step explanation:

The coordinates are (1, 9).

x = 1

y = 9

Put x as 1, and the output should be 9.

g(1) = ( 3 (1) )²

g(1) = (3)²

g(1) = 9

Answer:

b

Step-by-step explanation:

B is correct since you could use a graphing calculator  to solve this by plugging each answer choice into the calc.

another way is to plug 1 or x into each of the equations and see which choice has 9 as y