What is the scale factor from ABC to DEF?

Answer:

12 yrs.

Step-by-step explanation:

let present age of girl=x

age of mother=x+18

after 6 yrs

age of girl=x+6

age of mother=x+18+6=x+24

according to the condition of question

(x+6)+(x+24)=54

2x+30=54

2x=54-30=24

x=24/2=12

Answer:

Hi,

[tex]u_{20}=30[/tex]

Step-by-step explanation:

[tex]u_n=u_1+(n-1)*r, \ r= commun\ ratio.\\u_4=u_1+3*r=6\\u_6=u_1+5r\\(u_6)^2=u_1^2+10ru_1+25r^2\\s_n=u_1+u_1+r+u_1+2r+...+u_1+10r=11*u_1+55r\\s_{11}=(u_6)^2+18\ \\\Longrightarrow\ u_1^2+10ru_1+25r^2+18=11u_1+55r\\\Longrightarrow\ 4r^2+2r-12=0\\\Longrightarrow\ 2r^2+r-6=0\\r=\dfrac{3}{2} \ or\ r=-2\ (excluded)\\\\u_1=6-3r=\dfrac{3}{2} \\\\\\\boxed{u_{20}=u_1+19*r=30}\\[/tex]

The value of the 20th term of the arithmetic series will be 30

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Un  =  u₁+(n-1) x r

u₄  =  u₁  +(3 x r)=6

u₆ = u₁ +5r

u₆²=u₁²+10ru₁+25r²+18=11u₁+55r

Sn= u₁+u₁+r+u₁+2r+.............u₁+10r= (11 x u₁) +55 r

4r²+2r-12=0

2r²+r-6=0

r=3/2

u₁=6-3r=3/2

u₂₀=u₁+(19 x r)= 30

Hence the value of the 20th term of the arithmetic series will be 30

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Answer: 318 km²

Let's find the areas of the triangles

Formula: base x height / 2

9 x 6 = 54

54/2 = 27

Multiply by 2 since there are two triangles (I know, we already got the areas from 9 x 6)

27 x 2 = 54

Now let's try to find the areas of all the rectangular sides

Formula: length x width

9 x 11 = 99

8 x 11 = 88

7 x 11 = 77

99 + 88 + 77 = 264

Add up all the areas

264 + 54 = 318

Answer:

3√13

Step-by-step explanation:

3√13

This expression cannot be simplified because you cannot take any common factor outside the root.

Answer:

the answer will be

184.31

Answer:

13

Step-by-step explanation:

(fog)=3(x-1)+1

ie puting the function of g in f

so (fog)= 3x-3 + 1= 3x-2

finding fog

(fog)(5)= 3(5)-2

ie sub stitute 5 in x

(fog)(5)=15-2=13

Answer:

1 : 5

Step-by-step explanation:

3 students zoo

15 students aquarium

zoo : not zoo

3: 15

Divide each side by 3

3/3 : 15/3

1 : 5

Answer:

[tex] {x}^{2} - 36 \\ = (x + 6)(x - 6)[/tex]

Step-by-step explanation:

x^2-36

(x+6) ( x-6)

it's helpful to you

Answer:

[tex](x-6)(x+6)[/tex]

Step-by-step explanation:

In order to simplify this equation, one must use the quadratic factoring patterns. These patterns are as follows:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

This pattern works because, if one is to distribute the terms in the parenthesis by multiplying each term in one of the parenthesis by every term in the other, the result is the original equation:

[tex](a-b)(a+b)\\\\=(a)(a)+(a)(-b)+(a)(b)+(b)(-b)\\\\=a^2-ab+ab-b^2\\\\=a^2-b^2[/tex]

One can apply this pattern to the given equation, remember (6) times itself equals (36). Therefore, one can state the following: ([tex]36=6^2[/tex]), thus one can apply it to the given equation:

[tex]x^2-36\\\\=x^2-6^2\\\\=(x-6)(x+6)[/tex]

Answer:

Hello,

Step-by-step explanation:

Formula used (a+b)^2=a²+2ab+b²

[tex](12-9i)^2=3^2*(4-3i)^2\\\\=9*(16-9-24i)\\\\=9*(7-24i)\\\\=63-216i\\[/tex]

Answer: 2.31

Step-by-step explanation:

Answer:

30 quarts

Step-by-step explanation:

4 quarts = 1 gallon

7.5 gallons * 4 quarts/ 1 gallon = 30 quarts

Answer:

12/17

Step-by-step explanation:

Let

Numerator of the fraction = x

Denominator of the fraction = x + 5

The fraction is

x / (x + 5)

if both the numerator and denominator are increased by 3, the the resulting fraction becomes 3/4.

x + 3 / (x + 5) + 3 = 3/4

x + 3 / x + 8 = 3/4

Cross multiply

(x + 3)4 = (x + 8)3

4x + 12 = 3x + 24

4x - 3x = 24 - 12

x = 12

Recall,

x / (x + 5)

= 12 / (12 + 5)

= 12/17

The original equation = 12/17

Answer:

$55.20 is Mrs. Barker hourly overtime rate.

Step-by-step explanation:

The term "time and a half" in your question means that Mrs. Baker's overtime rate is 1.5 times her usual hourly rate.

So, ----> $36.80 times 1.5 = $55.20

Answer:

130

Step-by-step explanation:

65/50*100= 130

Answer:

x=4

Step-by-step explanation:

(x-1+5)×5=(2+x+4)×4

or, 5×(x+4)=4×(x+6)

or, 5x+20=4x+24

or, 5x-4x=24-20

or, x=4

Answer:

Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.

Answer:

1) 6а-9b=3(2a-3b)

2)8a-12b=4(2a-3b)

3) 5ab-5ac=5a(b-c)

4) 6ax+6ay=6a(x+y)

Answer:

B). 34.85°

Step-by-step explanation:

From trigonometric ratios:

[tex] \sin(C) = \frac{opposite}{hypotenuse} [/tex]

Opposite = 16

Hypotenuse = 28

[tex] \sin(C) = \frac{16}{28} \\ \\ C = { \sin}^{ - 1} ( \frac{16}{28} ) \\ \\ C = 34.85 \degree[/tex]

Answer:

2ax(y-2ay^2+3a^2x)

Step-by-step explanation:

2axy-4a^2xy^2+6a^3x^2

Given data

we have the following expression

2axy-4a^2xy^2+6a^3x^2

let us factor this expression

we have

2ax(y-2ay^2+3a^2x)

The common factor is 2ax

And the factorized expression is 2ax(y-2ay^2+3a^2x)

The ratio is (J/W) = 7/6. Or. J= (7/6)• W .

Second line: J= (7/6)• 24. J= 28.

Third line: J= (7/6)• 18. J= 21

Answer:

either 5 or 6

Step-by-step explanation:

I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.

15 divided by two is 7.5 and ten plus 7.5 is 17.5…. It says less than half the cost so I would round down to get $17 for the pain of pants

The cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15.

Let x be the cost of the pair of pants.

The value of x can be found as follows:

x = 15/2 + 10

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

x = $17.5  

Thus, the cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.

Learn more about the linear equation here:

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Answer:

37500

Step-by-step explanation:

pattern is multiplying by -5.

-7,500*-5 = 37,500

Have a nice day! :-)

Answer:

With the formula of lwh/3 the answer is 305.37

Step-by-step explanation:

l×w×h /3 =305.37

Answer:

916.11 ft³

Step-by-step explanation:

(9×6)×7.83/2×13/3

= 211.41×13/3

= 916.11 ft³

Answered by GAUTHMATH

Answer:

29 feet

Step-by-step explanation:

14 × 3 = 42

100 - 42 = 58

58 ÷ 2 = 29

One of the longer chains is 29 feet long.

Hope this helps.

Answer:

Does the answer help you?

Answer:

i don't know

( lol )

heheeeee

Let y = √x, so the limit can be rewritten as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]

Now,

[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]

so we can rewrite the limit further as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]

Combine the rational terms:

[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]

Then in the limit, we get

[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]

Answer:

-5.82

Possible by long devison and the rule that if there is one negitive then the answer is negitive