Dylan is evaluating the expression 13 + 19 + 7 + 10. At one step in his work, Dylan rewrites the equation as 13 + 7 + 19 + 10. Which property of addition must Dylan have used when he evaluated the expression?
associative property
commutative property
distributive property
identity property

Answer:

20 years approx

Step-by-step explanation:

Step one:

given data

Principal= $1000

rate= 6%

Final amount A= $3300

Required

Time t

Step two:

the expression for the compound interest is given data

A= P(1+r)^t

t = ln(A/P) / r

substitute

t= ln(3300/1000)/0.06

t= ln3.3/0.06

t= 1.193/0.06

t=19.88 years

t= 20 years approx

Answer:

y=68

x=12

Step-by-step explanation:

Variables= x and y

Lets make y the larger variable.

x+y=80

y=5x+8

substitution

x+5x+8=80

6x+8=80

x=12

plug 12 back in to find y

5(12)+8=68

y=68

x=12

Answer:

[tex]g(-3) = 5[/tex]

[tex]f(2) = 13[/tex]

[tex](f + g)(x) = x^2 +2x- 1[/tex]

Step-by-step explanation:

Solving (a):

[tex]g(x) = x^2 - 4[/tex]

Required

Determine g(-3)

[tex]g(x) = x^2 - 4[/tex]

Substitute -3 for x

[tex]g(-3) = (-3)^2 - 4[/tex]

[tex]g(-3) = 9- 4[/tex]

[tex]g(-3) = 5[/tex]

Solving (b):

[tex]f(x) = 3x + 7[/tex]

Required

Determine f(2)

[tex]f(x) = 3x + 7[/tex]

Substitute 2 for x

[tex]f(2) = 3*2 + 7[/tex]

[tex]f(2) = 6 + 7[/tex]

[tex]f(2) = 13[/tex]

Solving (c):

[tex]f(x) = 2x + 3[/tex]

[tex]g(x) = x^2 - 4[/tex]

Required

[tex](f + g)(x)[/tex]

In functions:

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = 2x + 3 + x^2 - 4[/tex]

Collect Like Terms

[tex](f + g)(x) = x^2 +2x- 4+3[/tex]

[tex](f + g)(x) = x^2 +2x- 1[/tex]

Answer:

Always

Step-by-step explanation:

We know that,

As every natural number n be represented in a rational form: n/1, any natural number can be represented in the form p/q, where q≠0. Hence, all natural numbers are rational numbers.

Answer:

C)  6 inches

Step-by-step explanation:

(√72)² = x² + x²

72 = 2x²

72/2 = x²

36 = x²

√36 = √x²

6 = x

x = 6 inches

Answer:

By Pythagoras theorem, we get

[tex] {x}^{2} + {x}^{2} = {( \sqrt{72}) }^{2} \\ 2 {x}^{2} = 72 \\ {x}^{2} = 36 \\ \boxed{x = 6}[/tex]

Answer: Choice E)

The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

=============================================================

Explanation:

x = amount of sugar (in grams)

y = number of calories in the juice

ŷ = estimate of y, so its the estimate of calories in the juice

The regression equation rearranges to ŷ = 2.5x + 57

This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.

The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5

The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.

All of these facts point to choice E as the final answer.

Answer:

e.

Step-by-step explanation:

calories is y or response variable and sugar is the explanatory variable, x.

if x(sugar) is 1

y = 57 + 2.5(1) = 59.5, a 2.5 increase.

if it is 2

y = 57 + 2.5(2) = 62, another 2.5 increase.

if zero grams of sugar x = 0

y = 57 + 2.5(0) = 57 calories.

Answer:

Step-by-step explanation:

Step-by-step explanation:

Side length = √Area = √(36x¹⁶y⁴)

= √[(6x⁸y²)²] = 6x⁸y².

Hence the expression for side length is 6x⁸y².

The length of the side of the table top will be 6x⁴y².

Based on the information given, it was stated that the area of the table top was given in the question.

It should be noted that the area of a square is gotten by squaring the sides. Therefore, the length of the side of the square will be 6x⁴y².

Learn more about squares on:

https://brainly.com/question/12831058

This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.

By Pythagoras theoram,

[tex] {p}^{2} + {b}^{2} = {h}^{2} [/tex]

where p is the perpendicular, b is the base and h is the hypotenuse.

Plugging the values,

[tex] {9}^{2} + {11}^{2} = {h}^{2} [/tex]

Then,

[tex]h = \sqrt{ {9}^{2} + {11}^{2} } [/tex]

[tex]h = 14.12(approx.)[/tex]

The x of the right angled ∆ = 14.12

Answer:

the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding

Answer:

I answered the first two Q but i dont know the third one sorryy

Step-by-step explanation: i put the answers as pics

_______________________________

1lbs = 30min

________________________________

Answer:

52 kilometers per hour

:)

-5+3d+6-4d

anwers is 12/-30

Answer:

is this free points. cuz why you said please and thank you?

Step-by-step explanation:

Answer:

m = -2 and n = 10

Step-by-step explanation:

If the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. Then;

x+ 3 = 0

x = -3

Substitute x =-3 into the polynomial and equate to -1

-1 = m(-3)³-3(-3)²+n(-3) + 2

-1 = -27m - 27 - 3n + 2

27m + 3n = -25 + 1

27m + 3n = -24 ... 1

Similarly, if it is divided by x - 2, the remainder is -4, then;

-4 =  m(2)³-3(2)²+n(2) + 2

-4 = 8m - 12- 2n + 2

8m -2n = -4 + 10

8m + 2n = 6 ... 2

Solve 1 and 2 simultaneously

27m + 3n = -24 ... 1 * 2

8m + 2n = 6 ... 2 * 3

______________________

54m + 6n = -48

24m + 6n = 12

54m - 24m = -48 - 12

30m = -60

m = -60/30

m = -2

Get n by substituting m = -2 into 1

From 1:  27m + 3n = -24

27(-2) + 3n = -24

-54 + 3n = -24

3n = -24 +54

3n = 30

n = 30/3

n = 10

Hence m = -2 and n = 10

Answer:

Step-by-step explanation:

(5-2i) ( 5+2i) = (5^2) - ((2i)^2) = 25 - 4i^2

= 25 - 4(-1) = 25 +4 = 29 + 0i

The Solution is 29 + 0i.

The sum of a real number and an imaginary number is called a complex number. A complex number is usually represented by z and has the form a + ib. Here, both a and b are real numbers. The real part, denoted by Re(z), is represented by the value "a," and the imaginary part, represented by "b," is represented by Im(z). Also known as an imaginary number, ib.

Given Expression (5 – 2i)(5 + 2i)

we know a² - b² = (a - b)(a + b)

(5 – 2i)(5 + 2i) = 5² - (2i)²

= 25 - 4i²

and i² = -1

= 25 - 4(-1)

= 25 + 4 = 29

since the solution has 0i

so the equation is 29 + 0i

where a = 29 and b = 0

Hence, equation is 29 + 0i.

Learn more about complex numbers;

https://brainly.com/question/20566728

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Answer:

16

Step-by-step explanation:

4x4 = 16

Answer:

Step-by-step explanation:

5x + y = 9

-10x + 7y = 18

10x + 2y = 18

-10x + 7y = 18

9y = 36

y = 4

5x + 4 = 9

5x = 5

x = 1

(1,4)

answer is D

Answer:

The answer is 245.7

Step-by-step explanation:

7 days in a week. 9 weeks. 9 x 7 = 63.

63 x 3.9 = 245.7

Answer: 54 in.

Step-by-step explanation:  So, the problem does something a little sneaky, and that is they ask for the TOTAL amount of wood needed for triangle DFG.  And to find that, we simply have to multiply side AC by 3 to get side DG.  We do this because triangle ABC is 3 times as small as triangle DFG.   Then, add your side DG that you just got, (21) to side FG and FD to get the total amount of wood needed, 54 in.

The length of wood needed for triangle DFG is 54 inches

Start by calculating the side length DG in triangle DFG

The side lengths of DFG are three times the corresponding side length of ABC

So, we have:

[tex]DG = 3 \times AC[/tex]

[tex]DG = 3 \times 7\ in[/tex]

[tex]DG = 21\ in[/tex]

The perimeter of triangle DFG is then calculated as:

[tex]P = DF + FG + DG[/tex]

This gives

[tex]P = 15 + 18 + 21[/tex]

[tex]P = 54[/tex]

Hence, the length of wood needed is 54 inches

Read more about perimeter at:

https://brainly.com/question/24571594

Answer:

131.2 ft

Step-by-step explanation:

12.8*10.25=131.2

Answer:

Step-by-step explanation:

The principal amount is

P=3000.

The time for which money is borrowed is ,

[tex]t=9 months[/tex]

The interest rate is ,

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

Determine the time in terms of year by division of time by 12.

[tex]t=\frac{9}{12} years\\= \frac{3}{4} years\\[/tex]

The formula for the interest is ,

[tex]I=\frac{P.r.t}{100}[/tex]

Substitute the known calues in the formula to obtain the value of interest.

[tex]I=\frac{3000.\frac{3}{4} .3\frac{1}{2} }{100} \\=\frac{3000.3.7}{2.4.100} \\=78.75\\[/tex]

So interest paid by the woman is $78.75

(b)

Determine the amount paid by the woman .

[tex]A=P+I\\=3000+78.75\\=3078.75[/tex]

So woman repay $3078.75 to the bank.

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Answer:

Domain: (-7, 4]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line's x-values span from -7 to 4. Since -7 is an open dot, it is exclusive in the domain. Since 4 is a closed dot, it is inclusive in the domain:

(-7, 4] or -7 < x ≤ 4

Answer:

C

Step-by-step explanation:

took the quiz and got it right