5(x – 10) = 30 – 15x

After direct variation y =10 when x = 5.

So,

The initial statement is y = kx

Then to find y when x = 5.

When x = 5:

Therefore, after direct variation y =10 when x = 5.

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Answer:

  False

Step-by-step explanation:

You want to know "what is 3/4c - 1 = 1 + 3/4c?"

Subtracting the left-side expression from both sides, we get ...

  (3/4c -1) -(3/4c -1) = (1 +3/4c) -(3/4c -1)

  0 = 2 . . . . a False statement

__

Additional comment

Since the equation is written without parentheses, we have to assume that c is in the numerator in each expression, and that its coefficient is (3/4).

Answer:

just add more to the milk and another scoop of chocolate

Step-by-step explanation:

1.5 cups milk

6 scoops of chocolate

After factorization of the expression 9x²-25, the answer comes to:

So,

The given expression is: 9x²-25

Then,

Therefore, after factorization of the expression 9x²-25, the answer comes to:

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Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Marianne figured out that her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six. If her father is 42.

Let x be the Marianne age

(x + 5⁴ - 365 - 22) (1/6) = 42

x + 238 = 252

x = 14 years

Thus, Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.

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Step-by-step explanation:

1. -9x

2. 2(5x -3)

3.. -4x + 4y -9

4. 6x+18

5.-5x +42

6. (2x+5)

We need to use the concept of lines and slopes to solve the problem.The equation of the line that passes through (5,-2) and is perpendicular to y=[tex]\frac{5}{3} x-3[/tex] is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex].

We will be using the concept of lines and slopes to solve the question. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes equal to -1.

Here we know that the line passes through a point (5,-2) and is perpendicular to another line,we need to find out the slope of the line first.

Let slope of given line be m1 and slope of the line that we need to find out be m2.

[tex]y=\frac{5}{3} x-3[/tex]

slope is the coefficient of x, thus m1=[tex]\frac{5}{3}[/tex]

we know that m1xm2=-1

[tex]\frac{5}{3}[/tex]×m2=-1⇒m2=[tex]\frac{-3}{5}[/tex]

The formula that we need to find the equation of a line is

(y-y1)=m(x-x1)

here (x1,y1) is (5,-2) and m is m2

[tex]y-5=\frac{-3}{5} (x+2)\\y-5=-\frac{3}{5} x-\frac{6}{5} \\y=\frac{-3}{5} x+5-\frac{6}{5} \\y=\frac{-3}{5} +\frac{19}{5}[/tex]

Thus using the concept of lines and slopes we found out that the equation of line that has been asked for is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex]

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Step-by-step explanation:

to cross the y-axis x must be 0.

so,

y - 4×0 = 1

y = 1.

so, the point is

(0, 1)

The minimum number of weeks it will take for Eduardo to make a profit

850w > 7500 + 300w. Option D

This is further explained below.

Generally, the Total cost  is  mathematically given as

X= $7500+$300w

Where he is earning each week

=$850

Therefore,

He will be paid in n weeks=$850n

The information that has been presented states that the very bare minimum number of weeks that it will take for Eduardo to earn a profit is by.

Total revenue is more than total expenditures

850w > 7500 + 300w

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The expansion of the expression log₈8 √3a⁵ is

1+ log 3/2log 8 +5 log a/ log 8.

Given that the expression is log₈8 √3a⁵.

We are required to expand the expression.

The change of base formula is used to write a logarithm operation again as a fraction of logarithms with a new base.

The expression is log₈8 √3a⁵.

log₈8 √3a⁵= (log 8 +log [tex]\sqrt{3}[/tex] +log [tex]a^{5}[/tex])/log 8

=1+ log 3/2log 8 +5 log a/ log 8      (We know that log [tex]m^{n}[/tex]=n log m)

Hence the expansion of the expression log₈8 √3a⁵ is

1+ log 3/2log 8 +5 log a/ log 8.

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[tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.

Now,

[tex]2^{(x + 3)} = 512[/tex]

=> [tex]2^{(x + 3)} = 8^3 = (2^3)^3[/tex]

As [tex](a^b)^c = a^{bc}[/tex],

=> [tex]2^{(x + 3)} = 2 ^9[/tex]

=> x + 3 = 9

=> x = 6

Hence, [tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.

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If I were George Washington, I would have put two very different people to advise me because I would have a broader vision of government affairs.

George Washington (1732-1799) was an American politician and military man who stands out for being one of the most influential people in history and for having served as the first president of the United States between 1789 and 1797. He is considered the most important father of the Nation of the United States.

In 1789 he was unanimously elected by the other founding fathers as the first president of the United States. During his rule he tried to create a nation capable of maintaining peace with its neighboring countries, so he proclaimed neutrality to avoid any involvement in foreign conflicts.

For George Washington it was a challenge to occupy the position of the first president of the United States because he was going to lead a country that was just being formed. Due to the above, it was of vital importance to include all forms of thought and all visions in its government plan and way of governing.

Therefore, when assuming office as president of the United States, it would be of great importance to have advisers who would help him see from the point of view of other people so that his decisions would take into account the interests of all citizens to avoid uprisings and divisions.

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The equation of the line in point-slope form is y-1 = 3 ( x + 1)

Equation of a line:

The equation of a line, in point-slope form, is designated  using:

y-y0= m( x - x0)

In which the point is given by(x0,y0)  and m is the slope.

Slope of the line below is 3 (given in the question).

This means that m = 3

(-1,1)

This means x= -1 and y =1

equation of the line

y - y0 = m( x- x0)

y-1 =m(x-(-1))

y-1=m(x + 1)

substituting the value of m is 3

y-1= 3 ( x + 1)

Therefore, The equation of the line in point-slope form is y-1= 3 (x + 1)

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Answer:

Heya genial Gracia dispute

Answer:85.7 miles per hour

Step-by-step explanation:

If two water tanks are 50 inches tall and tank a is empty and for each minute the water increases by 3.7 inches and tank b is draining and the water decreases by 1.9 inches each minute, then the minutes after which the height of the water in each tank is the same is equal to 9.

The time in minutes after which the height of the water in each tank is the same can be determined by using a linear equation.

The equation for this problem can be given as,

0 + 3.7(x) = 50 - 1.9(x)

Here x is equal to minutes. To find the minutes after which the water level will be the same can be determined by calculating the value of x in this linear equation.

3.7(x) + 1.9(x) - 50 = 0

5.6(x) = 50

x = 50 / 5.6

x = 8.92 ≈ 9

Hence, the height of the water in tank a and tank b is equal after 9 minutes.

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Answer:

the area is 935 square inches, and the perimeter is 39 inches

Step-by-step explanation:

Hey there!

In order to find the perimeter and area of the board, we must first list out the information we already know

----------------------------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------------------------

There is a tiny pattern in here:

The original board has a length of 44 while the new one has the length of 11

This means that, the original board had dimensions 4 times the length of the new board

In order to find the area or perimeter, we need to know the width of the new board

To do this, we divide 1496 by 44

That gets us 34

This means that the width of the old board is 34

Now we divide 34 by 4 which gets us 8.5

This means, 8.5 is the width of the new board

Now that we know this, we can easily find the area and the perimeter of the new board

8.5 + 8.5 + 11 + 11 = 39

This means, the perimeter is 39

8.5 x 11 = 935

This means, the area is 935

This brings us to the conclusion that the area is 935 square inches, and the perimeter is 39 inches!

Answer:

2.61625

Step-by-step explanation:

209.3 divided by 80

Answer:

you are very very very correct

Answer: 2 11/24

Step-by-step explanation: First we have to subtract it, so 6 5/8 - 4 1/6 which is 2 11/24

Actual miles is [tex]\frac{2492}{13}[/tex]

According to the question,

Given that,

Map is 5.6 ft

scale of Map is 2.6 ft which is equal to 89 miles

Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]

                    = [tex]\frac{498.4}{2.6}[/tex]

multiply both the numerator and denominator with the same integer

                    =  [tex]\frac{4984}{26}[/tex]

                    =  [tex]\frac{2492}{13}[/tex]

Actual miles is [tex]191\frac{9}{13}[/tex]  ≈ 1.916923 ×[tex]10^{2}[/tex]

Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.

Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.

Convert Miles to Feet

Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.

Convert to Feet per Minute

Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.

Convert to Feet per Second

Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.

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a WHOLE is always simplified to "1", and we can use any denominator for that, so 5/5 is 1, and 7/7 = 1, and [tex]\cfrac{4}{4}\implies \cfrac{113}{113}\implies \cfrac{1000000}{1000000}\implies \text{\LARGE 1}whole[/tex]

so hmmm for this case we'll be use thirds or namely the denominator of 3, so a whole bunch of basketballs was originally 3/3 of "b", "b" was the whole amount, so originally we had 3/3, but then during the day we sold 2/3 of them, so we were left with 3/3 - 2/3 = 1/3, and then 8 came back, because they were deflated or something, now the store has a total of 38 basketballs.

[tex]\stackrel{whole}{\cfrac{3}{3}b}~~ - ~~\stackrel{sold}{\cfrac{2}{3}b}\implies \cfrac{3b-2b}{3}\implies \cfrac{b}{3}\implies \stackrel{\textit{remaining in store}}{\cfrac{1}{3}b} \\\\\\ \stackrel{in~store}{\cfrac{1}{3}b}~~ + ~~\stackrel{coming~back}{8}~~ = ~~\stackrel{new~total}{38} \\\\\\ \cfrac{b}{3}+8=38\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{b}{3}+8 \right)=3(38)}\implies b+24=114\implies \stackrel{originally}{b=90}[/tex]

Using the mass ratio, the spacecraft's velocity was determined to be 7.7025 km/s.

Here, c = 2.7 km/s, t = 30s, R = 20

On substituting the values of 'R', 't', 'v', we get:

v = -0.0098 ( 30) + 2.7 ( ln (20))

=> v = - 0.294 + 2.7 (2.995)

=> v = 7.7025 km/s

A spaceship is a machine or vehicle built to travel through space. Spacecraft are a form of artificial satellite used for a wide range of tasks, such as communications, Earth observation, meteorology, navigation, space colonization, planetary exploration, and cargo and person transfer.

Following are the main distinctions between spaceships and rockets: The spacecraft is launched into space by rockets, which then crash to Earth. Rockets are never manned, whereas spacecraft can be either manned or unmanned. Additionally, spacecraft cannot match the power of rockets.

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The domain of f(x) to be [0,∞).

If the domain R, f(x) is not one to one, so its inverse exists not a function.

If we restrict the domain of f(x) then we can define an inverse function.

An inverse function, even comprehended as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function exists denoted by ' f ' or ' F '.

In order to have an inverse function, a function must be one to one.

In the case of f(x) = x⁴ we find that f(1) = f(−1) =1.

If f(x) exists not one to one on its implicit domain R.

If we restrict the domain of f(x) to [ 0, ∞) then it does contain an inverse function, then [tex]f^{-1}(y)=\sqrt[4]{y }[/tex]

Let the given function be y = f(x) = x⁴

Taking the square root of both ends, then we get

± √y = x²

Let the real values be x, then

We require the left hand side to be non-negative, so assume the non-negative square root.

Take the square root of both sides of the equation then

±[tex]\sqrt[]{\sqrt{y} }[/tex] = x

⇒ x = ± [tex]\sqrt{\sqrt{y} }[/tex] = ± [tex]\sqrt[4]{y}[/tex]

It  does not give us a unique value of x in terms of y.

So the inverse function exists not defined, then x ≥ 0,  

i.e., restrict the domain of f(x) to be [0,∞).

If the domain R, f(x) exists not one to one, so its inverse exists not a function.

The domain of f(x) then we can describe an inverse function.

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1) Solve each inequality individually.

[tex]\dfrac{2x-3}5 - \dfrac{4x-9}6 > 1 \\\\ 6(2x-3) - 5(4x-9) > 30 \\\\ (12x-18) - (20x+45) > 30 \\\\ -8x > 3 \\\\ x < -\dfrac38[/tex]

and

[tex]5(x-1) + 7(x+2) > 3 \\\\ (5x-5) + (7x+14) > 3 \\\\ 12x > -6 \\\\ x > -\dfrac12[/tex]

Then the solution set is

[tex]-\dfrac12 < x < -\dfrac38[/tex]

since -1/2 = -4/8 is smaller than -3/8.

2)

[tex]\dfrac{x+1}2 - \dfrac{x+2}3 < \dfrac{x+12}6 \\\\ 3(x+1) - 2(x+2) < x+12 \\\\ (3x+3) - (2x+4) < x + 12 \\\\ x - 1 < x + 12 \\\\ -1 < 12[/tex]

This is true for all values of [tex]x[/tex].

For the second inequality, (I use periods in place of commas because it renders better as TeX)

[tex]0.3x - 19 \le 1.7x - 5 \\\\ -1.4x \le 14 \\\\ x \ge -10[/tex]

Taken together, the solution set is

[tex]\boxed{x\ge-10}[/tex]

3)

[tex](x-6)^2 < (x-2)^2 - 8 \\\\ x^2 - 12x + 36 < (x^2 - 4x + 4) - 8 \\\\ -8x < -40 \\\\ x > 5[/tex]

and

[tex]3(2x-1) - 8 < 34 - 3(5x-9) \\\\ (6x - 3) - 8 < 34 - (15x - 27) \\\\ 21x < 72 \\\\ x < \dfrac{72}{21} = \dfrac{24}7[/tex]

But [tex]x[/tex] cannot be both larger than 5 = 35/7 and smaller than 24/7, so there are no solutions.

4)

[tex]\dfrac{3x-2}3 - \dfrac{4x+1}4 \le 1 \\\\ 4(3x-2) - 3(4x+1) \le 12 \\\\ (12x-8) - (12x + 3) \le 12 \\\\ -11 \le 12[/tex]

This is true for all [tex]x[/tex].

[tex](x-1)(x-2) > (x+4)(x-7) \\\\ x^2 - 3x + 2 > x^2 - 3x - 28 \\\\ 2 > -28[/tex]

This is also true for all [tex]x[/tex].

Any value of [tex]x[/tex] is a solution.

Answer:

$46

Step-by-step explanation:

So, the principal amount, P = $460

Yearly simple interest, R = 2.5% which equals 0.025

Time(T) which is 4 years.

The interest(I) for the amount, P at the rate of R yearly, after T years,

Elena's account will earn $46.

Answer:

y = 3x² + 2

Step-by-step explanation:

I'm help to number on more this, thank for subject on help for today.

The composite functions of the model taking the 20 % discount and then the 15 % discount is (D ◦ E)(x) = 0.68x.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

Let D(x) = cost after applying the 15% discount,

E(x) = cost after applying the 20% employee discount, and x = cost of item(s).

Then D(x) = 0.80x and E(x) = 0.85x.

(D ◦ E)(x) = 0.68x.

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Answer: 3

Step-by-step explanation:

First substitute values in :

8(3)(1/2)/ 2(1/2)(4)

Then simplify :

12/ 4

3

Answer:

Mean - 67 inches

Median - 67 inches

Mode - 68 inches

Step-by-step explanation:

Definitions of the words:

Mean - The average number of the data set.

Median - The middle number in the data set when ordered from least to greatest.

Mode - The value that appears most frequently.

Mean:

We can add them up and divide by the number of values in the set, 7.

469 / 7 = 67

Median:

We can order them from least to greatest and see which one is the 4th one.

60, 62, 66, 67, 68, 68, 78.

67 is in the middle, so that is our median.

Mode:

Only 68 is repeated twice in the set, so 68 is the mode.

Hope this helped! Have a great day!