A scuba diver is practicing
in a marked pool. He
begins 3 feet below the
surface of the water and
then dives down to the 9
foot marker. How far did
he dive?

Answer:

9^4 * 2^4

Step-by-step explanation:

We know (a*b) ^c = a^c * b^c

(9*2) ^4

9^4 * 2^4

Answer:

[tex]9^{4} * 2^{4}[/tex]

Step-by-step explanation:

rule:

[tex](a*b)^{c} = a^{c} * b^{c}[/tex]

distribute the exponent to both bases:

[tex]9^{4} * 2^{4}\\\\[/tex]

A quotient is found by dividing two numbers and a quotient with a denominator of zero is infinity which is not a real number

The word that complete the sentence is therefore;

Each quotient must have a nonzero denominator

The reason by which the above word is selected is as follows;

The set of Real Numbers include;

Rational numbers; a/b, where b = nonzero number

Integers; Positive and negative whole numbers, including zero

Whole numbers; 0, 1, 2

Natural numbers; Positive whole numbers excluding zero

Irrational number; Numbers that cannot be expressed as a/b

A quotient is the outcome of dividing two numbers, x by y

Therefore;

Quotient = x/y

A quotient can be a rational or irrational number, however, a quotient that has a denominator of zero (y = 0) is infinity, which is not a real number

When y = 0, x/y = x/0 = ∞ (∞ is not a real number)

Therefore, from the properties of Real Numbers,

Each quotient must have a nonzero denominator to be a Real Number

Learn more about Real Numbers here;

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Answer:

6 (-5 + 6x)

Step-by-step explanation:

Rewrite the number 30 as 6×5 and 36 as 6×6

Factor out the common number, which is 6

so, 6 (-5 + 6x)

Answer:

-6(5-6x).

Just factor out -6 from the expression. Thank you!

Answer:

so your answer is (0.5,-1)

Answer:

A) 220.45%

B) 0%

Step-by-step explanation:

A) 220.45 / 100 = 2.2045 * 100 = 220.45%

B) Costs exceeded her paycheck, so 0% of her pay was leftover and put in the bank.

Answer: A) 22.045% , B) 75.16%

I guess its a typo and weekly salary was $1000

So weekly salary = 1000

Spent on shirt = $220.45

Spent on CD = $12.95

Spent on Gasoline = $15

A) 220.45/1000×100

= 22.045%

B) Total spent = 220.45 + 12.95 + 15

= $248.4

Total left with her = 1000 - 248.4

= $751.6

Total percent of pay she put in bank = 751.6/1000×100

= 75.16%

Must click thanks and mark brainliest

Answer:

1) 35 gallons by the first car 2) 40 gallons by the second car

Step-by-step explanation:

Suppose the first car used x gallons, when the second car used the rest- 75-x

If the first car's efficiency is 35 miles per galon, its milleage is 35*x, the second car's milleage is 15*(75-x). And the summary milleage is equal to 1825.

35x+15(75-x)=1825

35x+1125-15x= 1825

20x=700

x=35- gallons consumed by the first car,

75-35=40- gallons consumed by the second one

Answer:

52 dollars.

Step-by-step explanation:

2 ounces = 6.50

÷2 ÷2

1 ounce = 3.25

3.25 x 16 = 52 dollars.

Answer:

52 dollars per pound

Step-by-step explanation:

We can write a ratio to solve

6.50 dollars       x dollars

------------------- = ------------------

2 ounces            16 ounces

Using cross products

6.50 * 16 = 2x

Divide each side by 2

6.50 *16/2 = x

52 =x

Answer:

See below

Step-by-step explanation:

we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.

well, to do so let the two unequal positive numbers be [tex]\text{$x_1$ and $x_2$}[/tex] where:

the AM,GM and HM of [tex]x_1[/tex] and[tex] x_2[/tex] is given by the following table:

[tex]\begin{array}{ |c |c|c | } \hline AM& GM& HM\\ \hline \dfrac{x_{1} + x_{2}}{2} & \sqrt{x_{1} x_{2}} & \dfrac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } \\ \hline\end{array}[/tex]

[tex] \displaystyle \rm AM \times HM = \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } [/tex]

simplify addition:

[tex] \displaystyle \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]

reduce fraction:

[tex] \displaystyle x_{1} + x_{2} \times \frac{1}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]

simplify complex fraction:

[tex] \displaystyle x_{1} + x_{2} \times \frac{x_{1} x_{2}}{x_{1} + x_{2}} [/tex]

reduce fraction:

[tex] \displaystyle x_{1} x_{2}[/tex]

rewrite:

[tex] \displaystyle (\sqrt{x_{1} x_{2}} {)}^{2} [/tex]

[tex] \displaystyle AM \times HM = (GM{)}^{2} [/tex]

hence, PROVEN

[tex] \displaystyle x_{1} > x_{2}[/tex]

square root both sides:

[tex] \displaystyle \sqrt{x_{1} }> \sqrt{ x_{2}}[/tex]

isolate right hand side expression to left hand side and change its sign:

[tex]\displaystyle\sqrt{x_{1} } - \sqrt{ x_{2}} > 0[/tex]

square both sides:

[tex]\displaystyle(\sqrt{x_{1} } - \sqrt{ x_{2}} {)}^{2} > 0[/tex]

expand using (a-b)²=a²-2ab+b²:

[tex]\displaystyle x_{1} -2\sqrt{x_{1} }\sqrt{ x_{2}} + x_{2} > 0[/tex]

move -2√x_1√x_2 to right hand side and change its sign:

[tex]\displaystyle x_{1} + x_{2} > 2 \sqrt{x_{1} } \sqrt{ x_{2}}[/tex]

divide both sides by 2:

[tex]\displaystyle \frac{x_{1} + x_{2}}{2} > \sqrt{x_{1} x_{2}}[/tex]

[tex]\displaystyle \boxed{ AM>GM}[/tex]

again,

[tex]\displaystyle \bigg( \frac{1}{\sqrt{x_{1} }} - \frac{1}{\sqrt{ x_{2}}} { \bigg)}^{2} > 0[/tex]

expand:

[tex]\displaystyle \frac{1}{x_{1}} - \frac{2}{\sqrt{x_{1} x_{2}} } + \frac{1}{x_{2} }> 0[/tex]

move the middle expression to right hand side and change its sign:

[tex]\displaystyle \frac{1}{x_{1}} + \frac{1}{x_{2} }> \frac{2}{\sqrt{x_{1} x_{2}} }[/tex]

[tex]\displaystyle \frac{\frac{1}{x_{1}} + \frac{1}{x_{2} }}{2}> \frac{1}{\sqrt{x_{1} x_{2}} }[/tex]

[tex]\displaystyle \rm \frac{1}{ HM} > \frac{1}{GM} [/tex]

cross multiplication:

[tex]\displaystyle \rm \boxed{ GM >HM}[/tex]

hence,

[tex]\displaystyle \rm A.M>G.M>H.M[/tex]

PROVEN

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]

Answer:

-12

Step-by-step explanation:

√50-3√2(2√2-5) -5√32​

= 5√2 -12+15√2-5(4)√2

= 5√2 -12+15√2-20√2

= -12

Answer:

0.16

Step-by-step explanation:

Answer:

524cm^2

Step-by-step explanation:

Formula for Volume of sphere= 4/3 πr^2

We have,

r=5cm

Now,

Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599

Rounding to the nearest tenth,

Volume=524cm^2

Answer:

2y^3-7y^2+7y

Step-by-step explanation:

7y - 2y^3 + 5y^2 - (  12y^2 – 4y^3)

Distribute the minus sign

7y - 2y^3 + 5y^2 - 12y^2 + 4y^3

Combine like terms

2y^3-7y^2+7y

Answer:

y=-2x

Step-by-step explanation:

first find the slope: (-2-(-4))/(1-2)=2/-1=-2 so m=-2

now we have y=-2x+b, to find b we plug in any of the points

so the equation is y=-2x

Answer:

The answer would be D. DE

Step-by-step explanation:

same prob

Congruent triangles are exact same triangles, but they might be placed at different positions. The correct option is D.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes the length of line segment AB, and so on for others).

Given that ΔABC ≅ ΔDEF. Therefore, the given sentence can be completed as AB ≅ ΔDE.

Hence, the side AB ≅ ΔDE

Learn more about Congruent Triangles:

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#SPJ5

If an answer is not exact then that will be unequal.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

If a value is not equal to the answer of that value then that is called unequal.

For example 2 and 3 then 2 is not equal to 3 so it will be inequal i.e. 2<3.

Hence "If an answer is not exact then that will be unequal".

For more about inequality?

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#SPJ2

[tex](B)\:\:35.8\:\text{m/s}[/tex]

Step-by-step explanation:

[tex]80\:\dfrac{\text{mi}}{\text{hr}}×\left(\dfrac{1609\:\text{m}}{1\:\text{mi}}\right)×\left(\dfrac{1\:\text{hr}}{3600\:\text{s}}\right)[/tex]

[tex]= 35.8\:\text{m/s}[/tex]

Answer: b

Step-by-step explanation:

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

Explanation:

The interval [tex]40 \le x < 50[/tex] has the midpoint (40+50)/2 = 90/2 = 45 which represents the average value from this interval. We don't know what the exact 21 values are from this interval, but the best guess we can make is each value is on average 45.

Similarly, the interval [tex]50 \le x < 60[/tex] has the midpoint (50+60)/2 = 110/2 = 55 which represents the average value in this interval.

The set of all midpoints is: {45, 55, 65, 75, 85}. You start at 45 and add 10 to each term to get the next term. Let's say x represents the midpoint. We'll multiply each x value with its corresponding frequency (f) to get a new column of values you see in the table below.

For example, in the first row, we have 45*21 = 945

Add up everything in the x*f column and we'll get this sum:

945+2145+2600+2550+2380 = 10,620

We'll divide this over the total frequency, which is the sum of the frequency column (21+39+40+34+28 = 162)

We then arrive at this estimated final answer: (10,620)/(162) = 65.55555... where the '5's go on forever. This rounds to 65.56

Answer:

i.)1,2,3,4,6,12

ii).the number itself

iii.)1

Answer:

this answer requires that you do a little solving to find all the dimensions we need for the volume.

We know that H (height) = 2m

Diameter = 5 x height, so

Diameter = 5 x 2m = 10m

If you have the formula for finding the volume of a cylinder, it is basically the area of the circular base x cylinder height. You may know already that the area of a circle is (pi) x radius2

So this will be 2 (the height) x (pi) x r2

As we just figured out, the DIAMETER is 10, so the radius is half the diameter = 5.

This brings our volume to 2 x (pi) x 52

= 2 x (pi) x 25

2x25 = 50, so we have 50 x (pi).

Pi = 3.14

50 x 3.14 = 157

And don't forget your units = 157 m3

Answer:

330 cm^3

Step-by-step explanation:

Volume of figure=Volume of the cuboid+Volume of the other cuboid

Volume of figure=240+90=330

Answer:

hey mate ...

105 + JID = 180 ( STRAIGHT LINE )

JID = 75

NOW APPLY ANGLE SUM IN TRIANGLE JID

75 + 39 + IJD = 180

IJD = 66

x = IJD by vertically opposite angles

x = 66

Answer:

36 is the answer

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

72: 2×2×2×3×3

108: 2×2×3×3×3

180: 2×2×3×3×5

here, common factors are 2,2,3 and 3 ..

so.. HCF: 2×2×3×3

•°•HCF=36 ..

Answer:

it is  D.

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

-4x-3=-x-30

-4x+x=-30+3

-3x=-27

x=9

Answer:

1.)149800

2.)75.9820

3.)49990

4.)29.900

Answer:

let us do one night

Step-by-step explanation:

Agg-77182882

(#(+2+

There are 6 DIFFERENT POSSIBLE arrangements as obtained using the factorial method and they are :

DMC, CMD, DCM, MDC, CDM, MCD

Given :

DETECTIVE STORY = D

MYSTERY STORY = M

COMIC BOOK = C

To use the factorial method, we find the factorial value of the number of books to be arranged

Number of different possible arrangements = (number of books)!

Number of books = 3

Hence, 3! = 3 * 2 * 1 = 6 ways

The sample space :

DMC

CMD

DCM

MDC

CDM

MCD

THEREFORE, there are 6 different samples on the SAMPLE SPACE.

learn more :

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[tex]\\ \sf\longmapsto 3x-4y=-12[/tex]

[tex]\\ \sf\longmapsto 3x+12=4y[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{3x+12}{4}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{3}{4}x+\dfrac{12}{4)[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{3}{4}+3[/tex]