Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 i) (21 5i)?

Answer:

The correct answer is option D, 20ft

Step-by-step explanation:

After drawing the picture below, you can just use pythagorean theorem to solve for the diagonal, or the hypotenuse in this case;

(Length)² + (Width)² = (Diagonal)²

(16)² + (12)² = (Diagonal)²

256 + 144 = (Diagonal)²

400 = (Diagonal)²

[tex]\sqrt{400}[/tex] = [tex]\sqrt{Diagonal^{2} }[/tex]

20 = Diagonal

Hope this helps!

Answer:

D. 20 ft

Step-by-step explanation:

Use pythagorus! We can imagine the rectangle is split into 2 equal triangles, one side of the triangle being 12, and the width being 16.

Pythagorus theorum is used to calculate the hypotenuse (long side) of a right-angled triangle. This is the formula:

[tex]\sf{a^{2}+b^{2} = c^{2} }[/tex]

So, we do 12^2 (squared) + 16^2 =

144 + 256 = 400

Now, we have to find the square root of 400, which is equal to

20

So our answer is 20ft

Hope this makes sense! If you need further explanation, do let me know...

- profparis

Answer:

C

Step-by-step explanation:

As properties are preserved

Answer:

80%

Step-by-step explanation:

We can find this by dividing 4 by 5 to get 0.8. Then we can convert this to a percent.

Answer:

use a calculator and you can find:

3. 3.9342208 x 10^(-6)

4. 162/3125

5. 1/60

Answer:

Step-by-step explanation:

Exponent Law:

[tex]\sf \left(\dfrac{a}{b} \right)^{m}=\dfrac{a^{m}}{b^n}\\\\a^m *a^n =a^{m+n}\\\\\dfrac{a^{m}}{a^n}=a^{m-n}[/tex]

In exponent law, in multiplication, if bases are same add the powers and in division, if the bases are same, subtract the powers.

3)

[tex]\sf \left(\dfrac{7}{3} \right)^{-2}*\left(\dfrac{1}{7}\right)^{5}*\left(\dfrac{3}{5} \right)^{2}=\dfrac{7^{-2}}{3^{-2}}*\dfrac{1}{7^5}*\dfrac{3^2}{5^{2}}[/tex]

                                    [tex]= \dfrac{7^{-2-5}*3^{2-[-2]}}{5^2}\\\\= \dfrac{7^{-7}*3^{2+2}}{5^{2}}\\\\=\dfrac{3^{4}}{7^7*5^{2}}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~```

4)

[tex]\sf \left(\dfrac{2}{5}\right)^3*\left(\dfrac{2}{3}\right)^{-2}*\left(\dfrac{3}{5}\right)^2=\dfrac{2^3}{5^3}*\dfrac{2^{-2}}{3^{-2}}*\dfrac{3^2}{5^2}[/tex]

                                     [tex]= \dfrac{2^{3-2}*3^{2-[-2]}}{5^{3+2}}\\\\=\dfrac{2*3^{2+2}}{5^{5}}\\\\=\dfrac{2*3^4}{5^5}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`````

5)

[tex]\sf \left(\dfrac{3}{10}\right)^4*\left(\dfrac{10}{15}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2*5}{3*5}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}[/tex]

                                     [tex]=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2}{3}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}\\\\=\dfrac{3^4}{2^4*5^4}*\dfrac{2^2}{3^2}*\dfrac{5^3}{3^3}\\\\=3^{4-2-3}*2^{2-4}*5^{3-4}\\\\=3^{-1}*2^{-2}*5^{-1}\\\\=\dfrac{1}{3*2^{2}*5}\\\\=\dfrac{1}{3*4*5}\\\\=\dfrac{1}{60}[/tex]

Answer:

⅜

Step-by-step explanation:

We want to find the cube root of 27/64.

∛(27/64)

We know that;

3³ = 27 and 8³ = 64

Thus;

∛(27/64) = ⅜

Answer:

[tex]\textsf{Perpendicular to given line}:y=-3x+14[/tex]

[tex]\textsf{Parallel to given line}: y=\dfrac13x-\dfrac83[/tex]

Step-by-step explanation:

Rewrite the given equation to make y the subject:

[tex]\begin{aligned}-3x+9y &=5 \\ \implies 9y &=3x+5 \\ \implies y &=\dfrac13x+\dfrac59\end{aligned}[/tex]

Therefore, the slope of the given equation is [tex]\frac13[/tex].

If two lines are perpendicular to each other, the product of their slopes will be -1.  Therefore, the slope (m) of the line that is perpendicular to the given line is:

[tex]\begin{aligned}m \times \dfrac13 & =-1\\ \implies m & =-3\end{aligned}[/tex]

To find the equation of the line, substitute the found slope (-3) and the point (5, -1) into the point-slope form of a linear equation:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(-1) &=-3(x-5) \\ y+1 & =-3x+15 \\ y &=-3x+14\end{aligned}[/tex]

If two lines are parallel to each other, their slopes will be the same.  Therefore, the slope (m) of the line that is parallel to the given line is [tex]\frac13[/tex]

To find the equation of the line, substitute the slope ([tex]\frac13[/tex]) and the point (5, -1) into the point-slope form of a linear equation:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\ \implies y-(-1) &=\dfrac13(x-5) \\\\ y+1 & =\dfrac13x-\dfrac53 \\\\ y &=\dfrac13x-\dfrac83\end{aligned}[/tex]

Slope =m=1/3

Note that perpendicular lines have slopes negative reciprocal to each other .

Equation in point slope form

And

parallel lines have equal slope

Equation of parallel line

Answer:

128 square cm

Step-by-step explanation:

2 x 8 x 8 x = 128 cm

Hope this Helps

The number of cookies left in the basket after everyone has eaten out of the cookies is 7.

The first step is to convert the fractions to percentages.

1/6 x 1000 = 16.67%

1/5 x 100 = 20%

Now determine the sum of the percentages of the cookies eaten : 10% + 30% + 16.67 + 20% = 76.67%

Determine the percentage of cookies left = 100 - 76.67 = 23.33%

Number of cookies left = (23.33 / 100) x 30 = 7

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

Answer:

30 leaps

Step-by-step explanation:

Equation of rabbit:

y=7x+150

Equation of kangaroo:

y=12x

To solve the system of equations, use substitution

12x=7x+150

5x=150

x=30

please mark brainliest!

Answer:

217.1 lbs

Step-by-step explanation:

I did set up cross multiplication using the height/weight ratio.

68/205 and 72/?.

72*205=14760

14760/68=217.05

Then I rounded to get 217.1 lbs

Answer:

how do u do that....I have never did this before

Answer:

-8

Step-by-step explanation:

with the way the table is it makes sense

Answer:

tell the full question

Step-by-step explanation:

bro

Considering the volume of the cube, it is found that it has a diagonal with a length of 12 inches.

The volume of a cube of side length a is given by:

V = a³.

The diagonal is given by:

[tex]D = \sqrt{3}a[/tex]

In this problem, the volume is of 340 in³, hence:

[tex]a³ = 340 \rightarrow a = \sqrt[3]{340} \rightarrow a = 6.98[/tex]

Hence, the diagonal is given by:

[tex]D = \sqrt{3} \times 6.98 = 12[/tex]

The cube has a diagonal with a length of 12 inches.

More can be learned about the volume of a cube at https://brainly.com/question/13030328

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Answer:

it would be 4200 ore

Step-by-step explanation:

because 882/.21

Answer:

For the first question, your answer would be 65 degrees. The reason for this is that complementary angles add up to 90 degrees. So, 90-25= 65 degrees.

Step-by-step explanation:

For supplementary angles- 180-the angle given= ?

The additional interest Benson pay each month is $750 if he invested at the rate of 2% for one year, option (b) is correct.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

We know the formula for the simple interest is given by:

I = PRT

Where I is the simple interest.

P is the principal amount

R is the rate of interest

We have in the question:

I = $180

R = 2% = 0.02

T = 1  year

Put the above values in the formula, we get:

180 = P(0.02)(1)

P = $9000

The additional interest Benson pay each month is:

= 9000/12

= $750

Thus, the additional interest Benson pay each month is $750 if he invested at the rate of 2% for one year option (b) is correct.

Learn more about the simple interest here:

https://brainly.com/question/22621039

Answer:

k=9

Step-by-step explanation:

K=9, because if you plug in 9 as k(2(9)=18)the equation is true.

Answer:

k=9

Step-by-step explanation:

2 × 9 = 18 which is the same as 9 + 9=18

Step-by-step explanation:

14(3.8) ×3 + 2(1/2)×3×4

= 159.6 + 12

= 171. 6

Reason:

There are 6 angles shown. If they are all the same measure, then they must be 360/6 = 60 degrees each. This is because the angles all glue together to form a full 360 degree rotation. There are no gaps or overlaps.

Answer:

541.9344 square centimeters

Step-by-step explanation:

one square inch is 6.4516 square centimeters

that means that you can multiple 84 by the above number

that gives you

541.9344

Answer: The graph will appear as a parabola opening downwards with a maximum point. It will cut the y-axis at -11.

Step-by-step explanation:

The coefficient of x^2 is negative, thus the graph will look "sad" ie. max a maximum point and open downwards. And bc it's x^2, it's a parabola.

Sub. x=0 and you'll get -11. Or just inspect and get the ans from the eqn.

to get the roots. ( x-intercepts). Just sub y=0 and solve.

The length and width of the rectangle are (4x - 1) and (x + 10) then the perimeter of the rectangle is 10x + 18. Then the correct option is C.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The polynomial of the rectangle will be given below.

4x² + 39x – 10

The factor of the polynomial will be

(4x - 1)(x + 10)

Then the perimeter of the rectangle will be

Perimeter = 4x - 1 + 4x - 1 + x + 10 + x + 10

Perimeter = 10x + 18

More about the factorization link is given below.

https://brainly.com/question/6810544

Answer:

-903,670

Step-by-step explanation:

-725628

- 178042

—-------------

_903,670

Answer:

p(blue)=0.14

p(not red)=0.9

p(green)=0.6

Step-by-step explanation:

p(blue)=12/84=0.14

p(not red)=74/84=0.9

p(green)=50/84=0.6

Hope it helps

Answer:

See below ~

Step-by-step explanation:

Q23)

Q24)

Q25)

Answer:

a=9, b=45, c=31.5, d=18, f=27

Step-by-step explanation:

To find the value of a, you can take 72-54=18 and do 18/2=9

a=9

To find the value of b, you can multiply the three a's. 27 is the product of the 3 a's. Next, you will do 72-27 to find the value of b

b=45

To find the value of c, you can take 9 and subtract it from 72, or in other words: 72-9=63. You will then divide 63/2 to find the value of c

c=31.5

To find the value of d, you can multiply (9*4)=36. You can then take 72-36 and get 36. To find the value of d, you will then divide 36/2.

d=18

To find F, you are given a clue that 1 a and 1 d together=f.

9+18=f

f=27

Answer:

a=9

b=36

c=45

d=31.5

f=40.5

Step-by-step explanation:

Phew! that was pretty tough. But I solved it! Your welcome! :)

Answer:

P = 91/990

Step-by-step explanation:

first red marble:    [tex]\frac{14}{45}[/tex]

second red marble: [tex]\frac{13}{44}[/tex]

The probability

[tex]P=(\frac{14}{45})(\frac{13}{44} )=\frac{(14)(13)}{(45)(44)} =\frac{182}{1980} =\frac{91}{990}[/tex]

Hope this helps