Round 9.25327275426 to the nearest hundredth.

Answer:

-32

Step-by-step explanation:

Pal, it's M A T H

Answer:

-32

Step-by-step explanation:

x-2x-20=12

-x=32

x=-32

.....................

The general term of the function is y = 4000 + 100x

The given parameters are

Guaranteed = $4000

Monthly raise = $100

Let the number of months be x, and the total earning be y

So, we have:

y = Guaranteed + Monthly raise * x

This gives

y = 4000 + 100 * x

Evaluate

y = 4000 + 100x

Hence, the general term of the function is y = 4000 + 100x

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The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].

As per the question statement, two points lie (-2, 1) & (-5,5) on a line.

We are supposed to find the slope of the line.

To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].

Using these values into above mentioned formula, we get,

Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].

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The name of the segment in the scaled copy that corresponds to segment AB is segment EF

The given parameters are:

Polygon EFGH is a scaled copy of Polygon ABCD.

This means that the corresponding points are

E = A

F = B

G = C

H = D

Remove points C and D

So, we have

E = A

F = B

Hence, the name of the segment in the scaled copy that corresponds to segment AB is segment EF

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Answer:

Step-by-step explanation:

let x = 5, y = 0

so the equation is 4x+y>9

and put the value of x and y in the equation

4 (5) + 0 > 9

20 + 0 > 9

20 > 9, therefore the order pair ( 5,0) satisfies the condition. true

Answer:

118

Step-by-step explanation:

The key piece of information to focus on is that there are around 120 fruits. 15 is the biggest of the given divisors, and the gaps between multiples of 15 is the greatest (compared to 4 and 6) which will narrow down our options. Therefore we can first try approaching the problem by finding multiples of 15 that are close to 120.

The question says that when the number (let's call it A) is divided by 15, it leaves 13. Therefore we can express A as such:

A-13 = 15x OR 15x + 13 = A

Where 'x' represents a whole number showing that the number is divisible by 15.

The closest multiples of 15 to 120 are 105 (15*7), 120 (15*8), and 135 (15*9).

A is one of these numbers + 13, let's see which ones are closest:

105+13 = 118, 120+13 = 133, 135+13 = 148

118 is very close to 120, so let's check it with the other numbers:

118/4 = 29 r 2

118/6 = 19 r 4

The exact number of fruits is 118.

Hope this helped!

Answer:

118

Step-by-step explanation:

We are told that there are about 120 fruits.

Fruits divided equally among 4 students

Multiples of 4:  4, 8, 12, ... 112, 116, 120, 124, ...

Therefore, 116, 120 and 124 are closest to 120.

Add the given remainder of 2 to these numbers:

Fruits divided equally among 6 students

Multiples of 6:  6, 12, 18, ... 108, 114, 120, 126 ...

Therefore, 114, 120 and 126 are closest to 120.

Add the given remainder of 4 to these numbers:

Fruits divided equally among 15 students

Multiples of 15:  15, 30, 45, ... 105, 120, 135, ...

Therefore, 105, 120 and 135 are closest to 120.

Add the given remainder of 13 to these numbers:

Therefore, as the total of 118 fruits is common to all three groups the exact number of fruits is 118.

Check

Divide 118 by each group of students:

As the remainders concur with the given amount of fruit left over for each group of students, this verifies that the exact number of fruits is 118.

I have two answers depending on the format. I'm not sure if the entire function is to the 2ndpower or not. Either way, it's either 256 or 4.

Above given the the linear equations. Systems of liner equations in three variables using substitution method, the variables are (-3.2, -0.218, 0.06).

The standard form for the linear equations in two variables is Ax+ By =C. For example, 2x+3y=5 is a linear equation in the standard form. When an equation is given in this form, it's pretty easy to find the both intercepts (x and y). This form is also very useful when solving systems of the two linear equations.

Solve one of the equation for one of it's variables. From the given three variables, there is no incorrect choice so choose to solve for any variable.

x= y+ z -3

Substitute the value from the first variable we solved for into the other equation and solve for the next variable.

(y+z-3) +y +3z = -2

2y+4z= 1

y= [tex]\frac{1+4z}{2}[/tex]

Substitute the value from the two variables that we solved and plug it into the remaining equation and solve for the last remaining variable.

3([tex]\frac{1+4z}{2}[/tex]+z-3) - 2 ([tex]\frac{1+4z}{2}[/tex]) + 3z= -12

3([tex]\frac{1+4z+2z-6}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+ 3z= -12

3([tex]\frac{6z-5}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+3z = -12

[tex]\frac{18z-15}{2}[/tex]- 1+ 4z+ 3z= -12

18z-15-2+8z +6z= -24

32z-17=-24

32z=-24+17

z=[tex]\frac{-7}{32}[/tex]= -0.218

therefore, y= 0.06

Now substitute the values:

x= 0.06+(-0.218)-3= -3.2

The three variables are (-3.2, -0.218, 0.06)

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Answer:

#1 = -2

Step-by-step explanation:

First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.

you first multiply the whole number (ignoring the negative sign for now) by the denominator:

2*3=6

then you add the numerator:

6+2=8

finally you put that number over the denominator and then put the negative sign back:

-8/3

Next, you can use keep change flip to solve the division

You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:

-8/3 divided by 4/3 becomes -8/3 x 3/4

finally you multiply across as you would normally and simplify

-8/3 x 3/4= -24/12

-24/12 simplified is -2

:D

if you need help with the rest just comment on this response and I'll try to answer as soon as I can

Answer: A=32 B=19

Step-by-step explanation:

Answer:

Explanation

temperature in a town during day=12.5The temperature in a town is 12.5°F

temperature at night is -23.3°F

difference -23.3°F+12.5°F

=. -10.8

Answer:

Bar A : 266 calories; Bar B : 251 calories

Step-by-step explanation:

Assume bar A's caloric content is "a" and bar B's caloric content is "b".

1. a + 2b = 768

2. 2a + b = 783

Add both equations together.

3. 3a + 3b = 1551

Divide both sides by 3.

4. a + b = 517

Subtract equation 4 from equation 1.

5. a + 2b - a - b = 768 - 517

Evaluate.

6. b = 251

Subtract b's value from equation 2.

7. 2a + b - b = 783 - 251

Evaluate.

8. 2a = 532

Divide both sides by 2.

9. a = 266

The radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

We have that:

Radius of the water pipe = 0.74 cm

r = 0.74 cm

It fills a 12 L bucket in 4 minutes

1 L = 1000 cm³

12 L = 12,000 cm³

Volume of water put in the pool = 12,000 cm³

Height of the pool that rise = 5 mm = 0.5 cm.

H = 0.5 cm

Let the radius of the pool be R.

Volume = π r² h

Substituting the values, we get that:

12,000 = ( 22 / 7 ) R² ( 0.5 )

R² = 7636.36

R = 87.39 cm

Therefore, we get that, the radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

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Answer:  onever

Step-by-step explanation:

4x-8>1+4(x+3)

4x-8>1+4(x)+4(3)

4x-8>1+4x+12

4x-8>4x+13

4x-8-4x>4x+13-4x

-8>13

Hence, inequality is never true

The equation to represent the situation is given as $2h -$10 = 0

We have been given that

    Money earned by Shane for babysitting =  $8 per hour

    Money earned by Shane for walking dogs = $6 per hour

Let the number of hours spent by Shane be h hours

Tips she received for babysitting = $12

Tip she received for walking dogs = $10

Total amount earned by Shane for babysitting = $8*h + $12

Also Shane worked two more hours for walking dogs then the amount will be = 2*$6 = $12

Total amount earned by Shane for walking dogs = $6*h + $12 + $10

                                                                                  = $6h + $22

As she earned the same total amount of job the equation will be given as

  $8h + $12 = $6h + $22

  $2h -$10 = 0

Which is the required equation

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The inequality notation for the given interval is -∞ < x ≤ -11 and -8 ≤ x < ∞

Disclaimer:

Considering the given interval as (-∞, -11] ∪ [-8, ∞).

Given interval is a union of two intervals.

The first interval denotes the set of all real numbers which are less than or equal to -11.

And the second interval denotes the set of all real numbers which are greater than or equal to -8.

The inequalities can be written as below:

(-∞, -11] ⇒ x ≤ -11 (or) -∞ < x ≤ -11

[-8, ∞) ⇒ x ≥ -8 (or) -8 ≤ x < ∞

And there is a union symbol between these two intervals.

So, x should satisfy both inequalities.

x ≤ -11 and x ≥ -8

or the above can be written as

-∞ < x ≤ -11 and -8 ≤ x < ∞

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The mass of the isotope after 45 hours is 2.5 grams.

Given, from the table we can find that when time is 10 hours,

the mass is 12.6 grams;

when time is 25 hours the mass is 6.3 grams .

And 12.6 × 1/2 = 6.3

Also we can find when time is 15 hours the mass is 10 grams,

when time is 30 hours, the mass is 5 grams as:

10 × 1/2 = 5

so we know that half life period is:

25 - 10 = 30 - 15 = 15 hours.

When time is 45 hours,

45 = 15+115

= 3 half life periods, so the mass is :

20 × 1/2 × 1/2 × 1/2

= 2.5 grams.

Hence the mass of the isotope after 45 hours is 2.5 grams.

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The volume of the water filled in the cylinder A is 141.77  cm³.

A cylinder is a 3 solid that contains two parallel bases connected at a fixed distance by a curved surface.

The formula for the volume of the cylinder is;

Volume = πr²h

Where, π = 3.14,

radius r = 3 cm.

height h = 10 cm.

Put the values and obtain the volume.

Volume = (3.14)(3)²(10)

Volume = 282.74  cm³.

As, the cylinder is half filled with water;

Water volume = 282.74/2  cm³

Water volume = 141.77  cm³

Thus, the volume of water filled in cylinder A is 141.77  cm³.

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The correct question is-

Cylinder A has radius 3 cm and height 10 cm. Cylinder A is half full of water.

Work out the volume of water in Cylinder A.

Step-by-step explanation:

I think the answer is just no solution to begin with since the value of an absolute value will never be a negative number or in this case less than -2. therefore the equation is false

Answer:

Step-by-step explanation:

perimeter of rectangular: 2(a+b)

we know from the graph, assume that a = 2x b = x+ 3

so the perimeter (C) in terms of x is C = 2(2x + x +3) = 6x + 6

Using translation concepts, the correct option is given as follows:

The graph of f(x) is shifted to the right to create g(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the functions are given as follows:

That is, g(x) = f(x - 31), hence the function was shifted 31 units to the right and the correct option is given by:

The graph of f(x) is shifted to the right to create g(x).

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Answer:

Step-by-step explanation:

7(i)

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]

7(ii)

[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]

The mode of the data is 39 as it's frequency is highest .

Mode is a measure of central tendency . It is the no . which has highest frequency in data .

Data - Frequency

 40   -   6

 35   -   7

 37   -   7

39   -   12      ( max . )

 36   -   5

 38   -   6

 41   -   4

The value of frequency corresponding to 39 is maximum .

Therefore , as 39 occurs most of the time in the data , hence it is the mode of this data .

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Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

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The area of the triangle is 1200√5 cm².

Given that, the sides of the triangle are 70cm,80cm and 90cm.

We need to find the area of a triangle using Heron's formula.

As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as 's' is determined using the below-given formula:

Area of triangle = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2

Now, semi perimeter = (70+80+90)/2=120

Area of triangle=√120(120-70)(120-80)(120-90)

=√120×50×40×30

=√40×3×2×25×40×30

=40×5√3×2×3×2×5

=40×5×3×2√5

=1200√5 cm²

Therefore, the area of the triangle is 1200√5 cm².

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well, tis noteworthy that whenever we have an absolute value equation is really a piece-wise function in disguise, namely the absolute expression is really two in disguise.

[tex]8x=2|6x-2|\implies \cfrac{8x}{2}=|6x-2|\implies 4x=|6x-2|\implies \begin{cases} 4x=+(6x-2)\\ 4x=-(6x-2) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=+(6x-2)\implies 4x=6x-2\implies 0=2x-2 \\\\\\ 2=2x\implies \cfrac{2}{2}=x\implies \boxed{1=x} \\\\[-0.35em] ~\dotfill\\\\ 4x=-(6x-2)\implies 4x=-6x+2\implies 10x=2\implies x=\cfrac{2}{10}\implies \boxed{x=\cfrac{1}{5}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x= \begin{cases} 1\\[1em] \frac{1}{5} \end{cases}~\hfill[/tex]

Answer:

No

Step-by-step explanation:

If Q is the midpoint of PR, then PQ=QR.

[tex]5(x+2)=8x-3 \\ \\ 5x+10=8x-3 \\ \\ 3x=13 \\ \\ x=\frac{13}{3} \\ \\ \implies PQ=5\left(\frac{8}{3} +2 \right) \neq 36[/tex]

This means PQ + QR = PR isn't 72, and thus Q is not the midpoint of PR.

Answer:

A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.

C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1

What is sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given:

10/3, 4, 24/5, 144/25, ...

From the above sequence we can generate the formula,

f (x) = 10/3

Also, for f(x+1) we can have

x=1,

f(1)= 10/3

f(2)= 4

So, f(x + 1) = 6/5(f(x))

Step-by-step explanation: