What is AAS postulate?

Answer:

AC = 28

Step-by-step explanation:

ΔADB ≈ ΔDBC

DC / BC = AD / 15

16 / 20 = AD / 15

cross-multiply:

20AD = 240

AD = 12

AD + DC = AC

12 + 16 = AC

28 = AC

Answer:

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

Step-by-step explanation:

[tex] \huge \frac{ {9}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ {( {3}^{2} )}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ { {3}}^{2 \times \frac{1}{2}b } }{ {3}^{a} } \\ \\ \huge = \frac{ {3}^{b} }{ {3}^{a} } \\ \\ \huge = \frac{1}{ {3}^{a - b} } \\ \\ \huge= \frac{1}{ {3}^{2} } \\ ( \because \: a - b = 2)\\ \\ \huge = \frac{1}{ 9 }[/tex]

The evaluation of the expression 9^((1/2)b)/3^a is 1/9

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]

Now, for this case, we are given that:

a - b = 2

The expression is:

[tex]\dfrac{9^\dfrac{1}{2}b}{3^a}[/tex]

Since we know that [tex]3^2 = 9[/tex], thus:

[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} = \dfrac{(3^2)^{\frac{1}{2}b}}{3^a} = \dfrac{3^{2 \times 1/2 \times b}}{3^a} = \dfrac{3^b}{3^a} = \dfrac{1}{3^{a-b}}[/tex]

Since a-b = 2, therefore, we get:
[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} =\dfrac{1}{3^{a-b}} = \dfrac{1}{3^2}} = \dfrac{1}{9}[/tex]

Thus, the evaluation of the expression 9^((1/2)b)/3^a is 1/9

Learn more about exponentiation here:

https://brainly.com/question/15722035

Answer:

$98

Step-by-step explanation:

Tablet

Divide 185 by 10 to get 18.5, this is 10% of the price.

Since it is 30% off, it is 70% of the price.

Multiply 18.5 by 7 to get the sale price, $129.50

Camcorder

Divide 140 by 10 to get 14, this is 10% of the price.

Since it is 30% off, it is 70% of the price.

Multiply 14 by 7 to get the sale price, $98

Answer:

15x²

Step-by-step explanation:

Given

f(x) = 5x² , then

3f(x) = 3 × 5x² = 15x²

Answer:

no association because they all are in plcace

Answer:

(a). 7√2

Step-by-step explanation:

Answer:

a) Please find attached the required travel graph with times increasing from (0:00) of the day of travel to the following day

b) The average speed of return journey = 880 km/(15.5 h) ≈ 56.77 km/h

Step-by-step explanation:

The given information includes;

The time of departure of the salesman, t₁ = 0800

The duration of travel of the salesman = 13 hours

The average speed with which the salesman travels = 60 km/h

The time duration in which he stops = 30 minutes

The speed with which he continues = 50 km/h

The time duration he travels at 50 km/h = 2 hours

The time he arrives home after he turns, t₂ = 16:00

The appropriate graph is a distance time graph

So as to show the given information in a travel graph, we calculate the distances as follows;

Time   [tex]{}[/tex]                                                                     Location

08:00   [tex]{}[/tex]                                                                   0

08:00 + 13 = 21:00  [tex]{}[/tex]                                                13 × 60 = 780

21:00 + 0.30 = 21:30  [tex]{}[/tex]                                             780

21:30 + 2:00 = 23:30  [tex]{}[/tex]                                            780 + 50 × 2 = 880

23:30 + 1:00 = 0:30 (24: hours )   [tex]{}[/tex]                          880

16:00  [tex]{}[/tex](40 hours from 0:00 the previous day)  

Therefore, we have;

Location; 0, 780, 780, 880, 880, 0

Time; 08:00, 21:00, 21:30, 23:30, 24:30, 40:00

To show the distance traveled over the given time periods graphically, we let 00:30 = 24.30 and the arrival time (the next day) 16:00 = 40.00 hours after midnight (0:00) the previous day                

Please find attached the required travel graph created with Microsoft Excel

b) The average speed of return journey = (Total distance of return journey)/(Total time)

The total distance going = 880 km

Therefore the return journey is also 880 km

∴ The total time taken on return journey Δt = (Time at arrival home) - (Time of start of return journey)

∴ Δt = 40 - 24.5 = 15.5

Δt = 15.5 hour

∴ The average speed of return journey = 880 km/(15.5 h) ≈ 56.77 km/h.  

Answer:

- 9q² - 3q - 6

Step-by-step explanation:

3C - 3D

= 3(q² - 2 + q) - 3(3q² + 2q) ← distribute parenthesis

= 3q² - 6 + 3q - 9q² - 6q ← collect like terms

= - 9q² - 3q - 6

The required expression is - 9q² - 3q - 6 which equals 3C - 3D in standard form.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question as follows:

3C - 3D  ....(i)

We have to determine the resultant expression that could represent the standard form.

As per the question, we have the equations

C = q² - 2 + q and D = 3q² + 2q

Substitute these equations into the expression (i):

3(q² - 2 + q) - 3(3q² + 2q)

Apply the distributive property of multiplication,

3q² - 6 + 3q - 9q² - 6q

Combine the likewise terms in the above expression,

- 9q² - 3q - 6

Thus, the resultant expression is - 9q² - 3q - 6.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ2

Answer:

-60

Step-by-step explanation:

Answer: Scale factor is 1.5

Step-by-step explanation:you get scale factor e.g F'G' : FG= 12:8 =1,5

Answer:

Please see the attachment, none of the graphs you showed was correct.

Step-by-step explanation:

Hope it helps :)

Answer:

3

Step-by-step explanation:

Answer:

∠A = 6x + 4

Step-by-step explanation:

Hello There!

We are given the exterior angle ∠ACD and an interior angle ∠B

If you didn't know this is the rule for exterior angles of a triangle:

An exterior angle is equal to the sum of its opposite interior angles

so ∠ACD = ∠A + ∠B ( ∠A and ∠B being the opposite interior angles)

So with the information that we are given we plug them into their corresponding angle

then we would have

8x+5 = ∠A + 2x + 1

now we solve for A

Well how do we solve for A?

Well we have to isolate the variable

To do so we want to get rid of 2x + 1

We do that by subtract each side by 2x and 1

8x + 5 - (2x + 1 ) = 6x + 4

we're left with

∠A = 6x + 4

Answer and Step-by-step explanation:

How to know if the side lengths can form a triangle:

Add together two of the lowest numbers. If it is greater than the largest number, it can form a triangle.

13. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9.

-- 9 is greater than 7, the largest length.

14. No, these side lengths can't form a triangle.

-- 2 + 3 = 6

-- 6 is equal to 6, not greater than.

15. Yes, these side lengths can form a triangle.

-- 2 + 4 = 6

-- 6 is greater than 5, the largest number.

16. Yes, these side lengths can form a triangle.

-- Don't get confused when you see that there are two side lengths that are the same (it means that this is an isosceles triangle); the rules still apply.

-- 2 + 8 = 10

-- 10 is greater than 8, the largest number.

17. Yes, these side lengths can form a triangle.

-- 5 + 6 = 11

-- 11 is greater than 9, the largest number.

18. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9

-- 9 is greater than 8, the largest number.

I hope this helps!!

#teamtrees #PAW (Plant And Water)

Answer:

Domain → (-∞, ∞)

Range → (-∞, 5)

Step-by-step explanation:

Domain of a function is a set of x-values (input values) for which the function is defined.

Function A is a quadratic function (in the form of a parabola) opening downwards.

This function is defined for every input value from negative infinity to positive infinity.

Therefore, domain of the given function A is (-∞, ∞).

Similarly, y-values (output values) vary from negative infinity to 5.

Therefore, range of the given quadratic function will be (-∞, 5).

Answer:

35.34 and 16.66

Step-by-step explanation:

Given data

let the numbers be x and y

the smaller number = x

the larger number = y

x+y=52--------1

The larger number is 2 less than twice the smaller number

y=2x-2-------2

put y= 2x-2 in eqn 1

x+2x-2=52

3x-2=52

3x=52-2

3x=50

x= 50/3

x= 16.66

put x=16.66 in eqn 1 to find y

x+y=52

16.66+y= 52

y=52-16.66

y= 35.34

Hence the numbers are

35.34 and 16.66

Check

35.34+16.66= 52

Basically, you are going to evaluate 5n - 4 from n = 1 to n = 18. Don't forget to add as you evaluate.

I will get you started.

Let n = 1 and then n = 2.

5(1) - 4 + 5(2) - 4 + the rest

5 - 4 + 10 - 4 + the rest

1 + 6 + the rest

7 + the rest

Just continue the pattern. You will then let n be 3, 4, 5, etc all the way to 18.

Answer:

x=0,-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

see you have to add something that equalles 0 so any questions like this you put a negitive infront of the 7.

Answer:

153.94 inches cubed

Step-by-step explanation:

plug in 7 as the radius

the formula is A = πr^2

Answer:

17.6

Step-by-step explanation:

9514 1404 393

Answer:

  EAGI

Step-by-step explanation:

Your choices are correct except for "B". Graph 3 has a dashed line, so the inequality symbol is <, not ≤.

Answer:

c) 6 ft

Step-by-step explanation:

3^2+5^2 = 9+25 = 34

sqrt34 = approx 6

Answer:

p<70

Step-by-step explanation:

Answer:

p < 70

Step-by-step explanation:

2(10 + p) - 20 < 140

20 + 2p - 20 < 140

2p < 140

p < 70

Answer:

6,y,5,

5,7,1,9,0 ok

tjis is a anwers

Answer:

37.69cm i might be wrong, u gonna have to check

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

From the above-given multiples of 4 and 6 is the multiple 12 is the smallest common multiple. Therefore, LCM. of 4 and 6 is 12.