Let f(x)=12x+7. Use algebra to find the inverse function f^-1(x).

Hello!

[tex]8.423 \texttt{ hours in hours, minutes, seconds}[/tex]

[tex]8.423=08:25:22[/tex]

Hope this helps!

The solution of the simultaneous equations is given by: x=0.60 and

y = 0.80 .

A system of equations or simultaneous equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.

The given pair of simultaneous equations are:

6 x + 8 y = 10

9 x + 6 y = 10.20

Now let us multiply the first equation by 6 and the second equation by 8 and subtract it from the first.

   36 x + 48 y = 60

   72 x + 48 y = 81.60

⇒ 36 x  = 21.60

⇒ x = 21.60 ÷ 36

⇒ x = 0.60

Substituting the value in the first equation we get:

y= 0.80.

Hence the solution of the simultaneous equation is x=0.60 and

y = 0.80 .

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The values in percentages will be 37.7% and the maximum will be: 45.3%

From the information, approximately 41.5% of city residents prefer local businesses over national chains and the survey had a margin of error of ±3.8%.

Therefore, the minimum number will be:

= 41.5% - 3.8%

= 37.7%

The maximum will be:

= 41.5% + 3.8%

= 45.3%

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Answer:

[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]

[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]

[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]

[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]

[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]

Step-by-step explanation:

Method: Extracting the Square Root

[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]

Method: Factoring

[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]

Method: Factoring

[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]

Method: Quadratic  Formula

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]

Given:

[tex]5x-4=-2x^2[/tex]

Rearrange into standard form by adding 2x² to both sides:

[tex]\implies 2x^2+5x-4=0[/tex]

Therefore:

[tex]a=2, \quad b=5, \quad c=-4[/tex]

Substitute the values into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]

[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]

[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]

Method: Quadratic  Formula

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]

Given:

[tex]5x^2-7x-13=0[/tex]

Therefore:

[tex]a=5, \quad b=-7, \quad c=-13[/tex]

Substitute the values into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]

[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]

[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]

The linear speed in miles per hour of the tip of a lawnmower blade spinning is 0.0601509076 miles per hour and angular velocity is 293.276 rad/hr.

The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an item along a straight line. It is the distance traveled along a linear path in the allotted amount of time.

2800 rotations per minute on a lawnmower blade.

Specifically, the frequency of the blade is 2800 revolutions per hour,

f = 2800 / 60, or 46.66.

The angular velocity is

ω = 2πf

where f = frequency

ω = 2 × 3.14 × 46.7

ω = 293.276 rad/hr

The diameter of the circle centered at the blade's middle determines the path's breadth.

26 inches in diameter

radius = 26 / 2 = 13

13 inch = 0.0002051 miles

Velocity is given by -

V = ωR

V = 293.276 × 0.0002051

Velocity = 0.0601509076 miles per hour

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Using proportions, it is found that Carl would have 60 more hits in 500 turns.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Billy's proportion is of 28/100, hence his amount of hits in 500 turns is:

500 x 28/100 = 140 hits.

Carl's proportion is of 1/2.5, hence his amount of hits in 500 turns is:

500 x 1/2.5 = 200 hits.

The difference is:

200 - 140 = 60 hits.

Carl would have 60 more hits in 500 turns.

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Answer:

g(0) = 3

Step-by-step explanation:

Hello!

Substitute 0 for x in the equation.

g(0) is 3.

The area of the region inside the rectangle that surrounds the square is; 162 square meters

We are given that;

Side length of square = 6 m

Width of rectangle = 11 m

Length of rectangle = 18m

Thus;

Area of rectangle = width * length = 11 * 18 = 198 square meters

Area of square = side * side = 6 * 6 = 36 square meters

Area of region inside rectangle not inside square = (area of rectangle) - (area of square) = 198 - 36 = 162 square meters

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Answer:

D:function, E:not a function

Step-by-step explanation:

We can figure this out using the line test. To do the line test you draw multiple straight, vertical lines along the graph, and if at any point the figure in question touches one of the lines multiple times, that figure is not a function.

:D

The volume 240 ml to oz is 8 oz.

The volume is in millilitres. Therefore, we have to convert to other units.

1 ml = 0.033814 oz

1 ml = 0.00175975 pints

1 ml = 0.00422675 cup

1 ml = 0.57 grams

Hence, lets convert the volume to the various units.

1 ml = 0.033814 oz

240 ml = ?

cross multiply

volume = 240 × 0.033814 = 8.11536 oz = 8 oz

1 ml = 0.00175975 pints

240ml = ?

volume = 0.00175975 × 240 = 0.42216 = 0.4 pints

1 ml = 0.00422675 cup

240 ml = ?

volume =  0.00422675 × 240 = 10.1442 cups

1 ml = 0.57 grams

240 ml = ?

volume = 0.57 × 240 = 136.8 grams

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Suppose [tex]x>0[/tex]; then the curves meet when

[tex]x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12[/tex]

By symmetry, they intersect at [tex]x=\pm\frac12[/tex].

We also see that [tex]\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}[/tex] and [tex]\max\left\{g(x):|x|\le\frac34\right\} = 2[/tex] at [tex]x=0[/tex]. [tex]f[/tex] and [tex]g[/tex] are continuous, so it follows that

[tex]\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}[/tex]

Compute the area [tex]\alpha[/tex]. Taking advantage of symmetry again, we have

[tex]\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23[/tex]

and it follows that [tex]9\alpha = \boxed{6}[/tex].

The value of AB that is 5x is equal to 30.

It is given that the points A, B and C are collinear. Collinear points may be defined as three or more points which lie on a straight line.

Here B lies between A and C and the three points A, B and C are collinear. Thus, according to property of collinear points:

AB+BC=AC

Now, according to question AB=5x, BC= 4x+12 and AC= 10x+6.

So, 5x+4x+12=10x+6

Taking the like terms on one side;

12-6 = 10x+9x

=> x=6

Now, AB=5x, thus AB= 5×5=30

Therefore, the value of AB is 30.

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Complete question:

Three points A, B and C are collinear. Point B is between points A and C. AC=10x+6, AB=5x, and BC=4x+12, Find AB.

The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

The amount of money Robert has left given the amount he started with and after deducting tax is approximately $7.34

Tax can be defined as the compulsory levy paid by citizens of a particular country on their income, goods and be services.

Amount of tax = Tax rate × Amount Robert spent before tax

= 7.25% × $30.45

= 7.25/100 × 30.45

= 0.0725 × 30.45

= $2.207625

Total amount Robert spent = Amount Robert spent before tax + Amount of tax

= $30.45 + $2.207625

= $32.657625

Amount Robert has left = Amount Robert started with - Total amount Robert spent

= $40 - $32.657625

= $7.342375

Approximately,

$7.34

Therefore, the amount Robert has left after deducting tax is $7.34

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Step-by-step explanation:

hmmm, it is all there, you only need to write it up.

so, please, let me know what you don't understand about such equations and variables.

(a)

2x + 5y = 45

8x + 3y = 44

(b)

to solve this we try to use either one equation to express one variable by the other. and solve for that remaining variable (and then drive the second one from that), or to combine both equations directly to eliminate one variable and solve.

I think the second option is best here.

so, we multiply the 1st equation by -4, and then we add both equations :

-8x - 20y = -180

8x + 3y = 44

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

0 - 17y = -136

-17y = -136

17y = 136

y = 8

2x + 5y = 45

2x + 5×8 = 45

2x + 40 = 45

2x = 5

x = 2.5

to rent a chair costs $2.50.

to rent a table costs $8.00.

Answer:

a) 9

b)3

c)22

Step-by-step explanation:

a)13+14/8-5 =27/3 =9

b) 9+9/4+2= 18/6 = 3

c) 12+16-6=22

Answer:

A- 9

B-3

C-22

Step-by-step explanation:

A-13+7*2/8-(3+2)

13+14/8-5

27/3

9.

B-9+3^2/2^2+2

9+9/4+2

18/6

3.

C-(10+2)+(4^2-6)

(12)+(16-6)

12+10

22

Answer:

C. & D.

Step-by-step explanation:

I believe it is C & D because, They both are in the same order just switched around, combine like like terms on both sides of the equation then if they are identical then they're equivalent.

Based on the fact that the larger room is twice as wide as the smaller room, the width of the larger room is 59¹/₂ inches.

The larger room is twice the width of the smaller room.

If the smaller room is 29³/₄ inches therefore, the width of the larger room will be:

= Width of smaller room x 2

Solving for the width of the larger room gives:

= 29³/₄ x 2

= 29.75 x 2

= 59.50

= 59¹/₂ inches

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Rita is left with $25

Rita has $300

She spent 1/3 of the money on notebook

= 1/3 × 300

= 100

Rita also spent 1/4 of the money on stationary item

1/4 × 100

= 25

Hence Rita is left with $25

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The 8 in Carla's number is 100 times the 8 in Travis' number.

Here you need to understand the concept of place value. For any number, each digit is always a order of magnitude of 10 larger than the digit in the left.

For example, in 88

The first 8 is 10 times larger than the second one.

There comes the concept of place value, the first digit at the left of the decimal point represents the units, the second represents the tens, the third one the hundresd, and so on.

So, in the two given numbers:

815,247 Here the 8 represents the hundreds of thousands.

638,571 Here the 8 is in the thousands place value.

Then the relation between the first 8 and the second one is:

100,000/1,000 = 100

The 8 in Carla's number is 100 times the 8 in Travis' number.

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Answer:

-6.23 is the answer

Answer:

-6.23

Step-by-step explanation:

The solution will be,

→ 2.67 + (−8.9)

→ 2.67 - 8.9

→ -6.23

So, the answer is -6.23.

The cost of a Token from the question is; $7.2

We are told that Jane and Jim spend the same amount of money today.

Now, Jim spent 5.25 dollars on food and rode the train 3 times, and Jane spent 12.45 dollars on food and rode the roller coaster twice.

Assuming cost of a token is T, the the algebraic expression formed is;

5.25 + 3T = 12.45 + 2T.

3T - 2T = 12.45 - 5.25

T = $7.2

Thus, we conclude that the cost of a Token is; $7.2

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Answer:

radious:10

height:7

volume:?

we know that

volume of cylinder:2pie×r²×h

=22/7×10²×7

=2200unit³

Answer:

48

Step-by-step explanation:

use a calculator

The value of a in the equation in the simplest form will be 17 / 6.

We are given an equation:

x³ / x^(1/6) = x^(a)

We need to evaluate the left hand side to find the value of a in the equation in simplest form.

We know that:

x^ (a) / x^ (b) = x^ ( a - b)

Using this, we get that:

x^ (3 - 1/6) = x^ (a)

x^ (17/6) = x^ (a)

By comparing the bases, we get the value of a as:

a = 17 / 6.

Therefore, the value of a in the equation in the simplest form will be 17 / 6.

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The solution of the equation c = kny, for y is y = c/kn

The equation is given as

c = kny

Divide both sides of the given equation by k

So, we have

c/k = kny/k

Evaluate the quotient on both sides of the above equation

So, we have

c/k = ny

Divide both sides of the above equation by n

So, we have

c/kn = ny/n

Evaluate the quotient on both sides of the above equation

So, we have

c/kn = y

Rewrite as

y = c/kn

Hence, the solution of the equation c = kny, for y is y = c/kn

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Answer:five more than y

Step-by-step explanation:

To two decimal places,

√70

must lie between 8.3

and 8.4