Help me please- there's only 11 questions!

Using triangle A B C as the pre-image and the origin as the center of dilation, which coordinate point is not a coordinate of a

Ostrovityanka [42]

Answer:

The correct option is:

begin ordered pair 4 comma 12 end ordered pair i.e. (4,12).

Step-by-step explanation:

We are given the coordinates of the point A,B and C of the triangle ΔABC as:

A(-1,3) , B(2,1) and C(-2,-1).

Now it is given that there is dilation of this triangle about the origin with a scale factor of 4.

This means that the change in the coordinates after the transformation is given by the rule:

(x,y) → (4x,4y)

As A → A' , B → B' and C → C'

Hence the coordinates A',B' and C' are given by:

A' are (4×-1,4×3)=(-4,12)

B' are (4×2,4×1)=(8,4)

and C' are (4×-2,4×-1)=(-8,-4).

Hence the coordinate point which is not a coordinate of dilation is:

begin ordered pair 4 comma 12 end ordered pair i.e. (4,12)

3 0

3 years ago

Examine this algebraic expression:

fomenos

Answer:

x = variable (a symbol, usually a letter, representing possible inputs)

4 = constant (numbers that stand alone and have a fixed value)

3 = coefficient (number multiplied by variable)

3 0

3 years ago

Read 2 more answers

70% of a number is what fraction of that number?

sdas [7]

Answer:

7/10

..................

4 0

3 years ago

A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the po

astra-53 [7]

Answer:

a. See Attachment 1

b. $PT = 12.3\ m$

c. $HT = 31.1\ m$

d. $OH = 28.4\ m$

Step-by-step explanation:

Calculating PT

To calculate PT, we need to get distance OT and OP

Calculating OT;

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

$tan50 = \frac{OT}{20}$

Multiply both sides by 20

$20 * tan50 = \frac{OT}{20} * 20$

$20 * tan50 = OT$

$20 * 1.1918 = OT$

$23.836 = OT$

$OT = 23.836$

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

$tan30 = \frac{OP}{20}$

Multiply both sides by 20

$20 * tan30 = \frac{OP}{20} * 20$

$20 * tan30 = OP$

$20 * 0.5774= OP$

$11.548 = OP$

$OP = 11.548$

$PT = OT - OP$

$PT = 23.836 - 11.548$

$PT = 12.288$

$PT = 12.3\ m$ (Approximated)

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

Calculating the distance between H and the top of the tower

This is represented by HT

HT can be calculated using Pythagoras theorem

$HT^2 = OT^2 + OH^2$

Substitute 20 for OH and $OT = 23.836$

$HT^2 = 20^2 + 23.836^2$

$HT^2 = 400 + 568.154896$

$HT^2 = 968.154896$

Take Square Root of both sides

$HT = \sqrt{968.154896}$

$HT = 31.1\ m$ (Approximated)

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

Calculating the position of H

This is represented by OH

See Attachment 2

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

$tan50 = \frac{OH}{OT}$

Multiply both sides by OT

$OT * tan50 = \frac{OH}{OT} * OT$

$OT * tan50 = {OH$

$OT * 1.1918 = OH$

Substitute $OT = 23.836$

$23.836 * 1.1918 = OH$

$28.4= OH$

$OH = 28.4\ m$ (Approximated)

5 0

3 years ago

The current (2015) population of Eugene is approximately 155,000 people. a) If the population growth rate remains at 4% per year

Olegator [25]

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &500,000\\
I=\textit{initial amount}\to &155,000\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
t=\textit{elapsed time}\\
\end{cases}$

$\bf 500000=155000e^{0.04t}\implies \cfrac{500000}{155000}=e^{0.04t}\implies \cfrac{100}{31}=e^{0.04t}
\\\\\\
\textit{now, we take \underline{ln} to both sides}
\\\\\\
ln\left( \frac{100}{31}\right)=ln(e^{0.04t})\implies ln\left( \frac{100}{31}\right)=0.04t\implies \cfrac{ln\left( \frac{100}{31}\right)}{0.04}=t$

so it will have 500,000 approximately "t" years after 2015.

4 0

3 years ago