The distance from O to A is 3 and the distance from A to A prime is 3. The diagram shows a dilation. Which dilation does it represent? What is the scale factor?.

Modeling of a situation is getting its properties held in another system, usually mathematical. The equation for given situation is [tex]C = 2T + 5[/tex]

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case the number of t-shirts brought is not known, so let we take it as T

Since each t-shirt costs $2, thus, T t-shirts will cost: T × $2

Since, cost of using the service of the t-shirt company is $5 flat rate, thus,

Total cost for purchasing T t-shirts = T × $2 + $5

Let total cost be denoted by C, then:

[tex]C = 2T + 5[/tex]

(we usually  don't write multiplication sign usually, and write the quantities close to each other, denoting that they're in multiplication.)

(we usually don't write symbols like $ etc in equations. It is known from context like what type of currency is in discussion(if multiple currency, then we can do some modification to variable symbols).

Thus,

The equation for given situation is [tex]C = 2T + 5[/tex]

Table for it, using values of T from 1 to 5, we get:

[tex]\begin{array}{cc}T&C\text{(In dollars)}\\1&7\\2&9\\3&11\\4&13\\5&15\end{array}[/tex]

Plotting them in graph, we get the following attached graph.

Learn more about forming equations here;

https://brainly.com/question/12279939

Answer:

True

Step-by-step explanation:

3² = 9  ⇒ odd

7² = 49 ⇒ odd

9² = 81 ⇒ odd

Therefore, the square of an odd number is always odd.

Proof

If n is an odd number, it can be written as n = 2k + 1, for some integer k.

Therefore, n² = (2k + 1)²

                      = 4k² + 4k + 1

                      = 2(2k² + 2k) + 1

As 2(2k² + 2k) + 1 is odd, this proves that the square of an odd number is always odd.

Answer:

  55 ft

Step-by-step explanation:

The mirror is 10 times as far to the dinosaur as it is to Amir: 40 ft = 10×4 ft.

The triangles shown in the diagram are similar, so the height of the dinosaur will be 10 times Amir's eye height. In feet, Amir's eye height is 5 6/12 feet, or 5.5 feet. Ten times that is 55 feet.

The dinosaur is 55 feet tall.

Answer:

55ft

Step-by-step explanation:

Answer:The height is 12ft

The length of the rug is 10ft and the height of the parallelogram is 12ft

The width of the rug is 6ft wide and the parallelogram is 9ft wide

Yes the rug will fit

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)5^1/3*3 = 5^3/3 = 5

2) 5+x=2 =>x=2-5 => x=-3

3)2*1/2^2*4^4 => 2*1/4*256 => 0,5*256 = 128

4) Rule!Any number to the power 0 is equal to 1; and 1 to any power will always give 1. => 1^5 =1.

5)x^(-6)-(-4) => x^-2 ; x^(-2)+3=x

y^5-8=y^-3

=>z^3/ x^2*y^3
z^0=1

x/y^3

Answer:

Both type of  numbers have a decimal point but the decimal numbers can contain digits other than 0 so you have to worry for these numbers when you're multiplying and the placement of the decimal point in the answer.

A way think about it is sum the total numbers after the decimal point, this work because the numbers can be represented as fractions (explanation below) so If one factor has 2 decimal places and another factor has 1 decimal place the answer have 3 decimal places.

Step-by-step explanation:

A whole can be represented as 2 and so on, while a decimal number is represented as 3.14 when the numbers after the decimal point can be different of 0.

So when you multiply two decimal numbers check the total number of number after the decimal point and sum these amounts.

Where the total number of numbers after the decimal point is equal to the power of 10 in the denominator that's mean equal to 3. However this method takes more time, so is more simply to say that the total of numbers after the decimal point is the sum of the total of numbers after the decimal point of each decimal number.

Answer:

It's correct

Step-by-step explanation:

(θ‿θ)(θ‿θ)(θ‿θ)

Answer: They sold each book at a price of 143.75 birr

Step-by-step explanation:

1500 divided by 12 is 125 and 15% of 125 is 18.75 so add it together and you got your answer. hope this helps <3

Answer:

C. 1725

Step-by-step explanation:

We can find the selling price by adding the cost price and the profit made

As the merchant has made 15% of profit on 1500 birr . So ,

15% of 1500 is 225 birr

[tex] \frac{x}{1500} \times 100 = 15 \: percent[/tex]

Adding the cost price and profit made we get ,

Selling Price = 1500 birr + 225 birr

Sp = 1725 birr

Answer:

24x + 72

Step-by-step explanation:

Answer:

hi is this correct please let me know

Step-by-step explanation:

4x

4

+91x

2

−225=0

Substitute t for x

2

.

4t

2

+91t−225=0

All equations of the form ax

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±

b

2

−4ac

​

​

. Substitute 4 for a, 91 for b, and −225 for c in the quadratic formula.

t=

2×4

−91±

91

2

−4×4(−225)

​

​

Do the calculations.

t=

8

−91±109

​

Solve the equation t=

8

−91±109

​

 when ± is plus and when ± is minus.

t= 49

​

t=−25

[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]

[tex]\bold{\underline{ Given}}[/tex]

[tex]\bold{\underline{To \: Find :- }}[/tex]

[tex]\bold{\underline{Let's \: Begin :- }}[/tex]

The coordinates of G = ( -6 , 5 )

The coordinates of H = ( 2 , - 7 )

According to the distance formula, we get :-

[tex]\purple{\bigstar}\boxed{\sf{Distance\:\:GH=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}[/tex]

Subsitute the required values in the above formula

[tex]\sf{ Distance \:GH = √( -6 - 2)² + ( 5 -(-7))²}[/tex]

[tex]\sf{Distance\:GH= √(-8)^2+(5 + 7)^2}[/tex]

[tex]\sf{Distance\:GH=√(-8)^2+(12)^2}[/tex]

[tex]\sf{ Distance \:GH =√64 + 144 }[/tex]

[tex]\sf{ Distance \:GH =√ 208}[/tex]

[tex]\sf{ Distance\: GH = √ 2 × 2 × 2 × 2 × 13}[/tex]

[tex]\sf{ Distance \:GH = 4√13}[/tex]

[tex]\sf{\red{ Hence\: the \: length\:of \: GH \: is \: 4√13 \: units}}[/tex]

1)

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to \frac{6.4}{100}\dotfill &0.064\\ t=years\dotfill &18 \end{cases} \\\\\\ I = (2000)(0.064)(18)\implies I=2304[/tex]

2)

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to \frac{6.4}{100}\dotfill &0.064\\ t=years\dotfill &30 \end{cases} \\\\\\ A=2000[1+(0.064)(30)]\implies A=2000(2.92)\implies A=5840[/tex]

Answer:

after 18 years : $477,685.19

after 30 years: $661,353.82

Step-by-step explanation:

interest formula: A=P(1+r/n)^nt

so...

2000(1+6.4/18)^18 = 477685.1913 rounds to $477,685.19

2000(1+6.4/30)^30 = 661353.8157 rounds to $661,353.82

Answer:h

Step-by-step explanation:

j

Answer:

The variables are F, G and H

Answer:

F,g,h Good luck!

Step-by-step explanation:

Answer: 5n nickels

Step-by-step explanation:

Since Casey has n nickles and Megan has 4 times as much, Megan has 4*n nickels = 4n nickels. The total ampunt = n+4n = 5n nickels.

Answer  The awnser is the 2x69, by 75 and 35 by 39x4 and 3 5ths .

Step-by-step explanation:

Answer:

I THINK ( A ) IS CORRECT ANSWER

I THINK ( A ) IS CORRECT ANSWERHOPE THIS HELPS U!!!

Answer:

20/100=1/5 the fraction of students who prefer apples is 1/5

Answer: The slope of the graph is -2

Step-by-step explanation:

Take any two points from the graph, and do rise/run

For example, we take (1,3) and (2,1)

Apply rise/run... rise: 2, run: -1

2/-1 = -2

m = -2

For the next question, the slope is 4

And the last question, the slope is 1 1/2

Hope this helped!

Answer:

118

Step-by-step explanation:

150+16%=174

174 - 32% = 118.32

118.32=118(to nearest whole number)

Answer:118

Step-by-step explanation:

Answer:

3.6 ft = 43.2 inches  

3.6 ft = 1.2 yards

Explanation:

Every foot is 12 inches. 3.6 * 12 = 43.2

To find yards, divide the feet by 3.

3.6 / 3 = 1.2

1. observe problem

The Full price is:

The Subtotal + the Subtotal*tax

so,

34.50+34.50*0.06=

36.57

The Full price plus tip is

Full price + Full price * tip percentage

so,

36.57+36.57*0.15

Which is

$42.0555

Rounded to is

$42.06

Answer:

AC = 18

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{12\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2 AC = 12[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 12 × 3 = 36 ( divide both sides by 2 )

AC = 18

∠ACB=90° ⇒ ΔABC is right triangle

AB is hypotenuse, ∠BAC=30° ⇒

[tex]CB=\dfrac{AB}{2}=\dfrac{12\sqrt{3} }{2} =6\sqrt{3}[/tex]

Let's use Pythagorean theorem

[tex]AB^2=BC^2+AC^2\\AC^2=AB^2-BC^2\\AC^2=(12\sqrt{3})^2-(6\sqrt{3} )^2\\AC=\sqrt{(12\sqrt{3}-6\sqrt{3})(12\sqrt{3}+6\sqrt{3}))} \\AC=\sqrt{6\sqrt{3}\times18\sqrt{3} } \\AC=\sqrt{3\times6\times18} \\AC=18[/tex]

Answer:

c. It would decrease

Step-by-step explanation:

When you increase the sample size, you decrease the standard/marginal error since you have a bigger representation of the population. However, this would take time and money to collect data for these big samples.

Answer:

1.) 60

2.) 36

3.) -9

4.) 74

5.) -36

6.) [tex]\frac{2}{6} =\frac{1}{3}[/tex]

Step-by-step explanation:

1.) 2×3[7+(6÷2)]

2×3[7+3]

2×3×10

2×30

60

2.) 3[-3(2-8)-6]

3[-3(-6)-6]

3[18-6]

3×12

36

3.) 3×3[2-(9÷3)]

3×3[2-3]

3×3[-1]

3×3×-1

9×-1

-9

4.) 2[-5(4-12)-3]

2[-5(-8)-3]

2[40-3]

2×37

74

5.) [(3×3)-(30÷6)]+(-27)-13

[9-5]+(-27)-13

4-27-13

4-40

-36

6.) 2÷[(4÷2)+(32÷8)]

2÷[2+4]

2÷6

[tex]\frac{2}{6} =\frac{1}{3}[/tex]

Hope this helps!

Answer:

3/4

Step-by-step explanation:

Since we have two points, we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 5 - -1)/( 4 - -4)

   = ( 5+1)/(4+4)

   = 6/8

   = 3/4

Answer:

All in order:

YES

NO

NO

NO

Step-by-step explanation:

-54 ≤ 7(-7) - 5 YES because the sign says greater than or equal to (in the image)

-54 ≤ 7(5) - 5 NO

-54 ≤ 7(7) - 5 NO

-54 ≤ 7(-9) - 5 NO