Solve the inequality. Graph the solution. |8x−8|≤24

Answer: Quotient 142

Remainder 12

Step-by-step explanation:

The quotient is 142 and  the remainder is 12.

The long division method is as follows :

                                             [tex]142[/tex]

                                      [tex]39\sqrt{5550}[/tex]  

                                          -39                        

                                             165                       (3rd 5 taken down )

                                           -156    

                                                 90                     ( 0 taken down )

                                                -78  

                                                  12

step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.

step 2 : write the number on top and subtract the answer from 55.

step 3 :  Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.

step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.

step 5 : write that number on top after the previous number and subtract the answer from 165.

step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.

step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.

step 8 : write that number on top after the previous number and subtract the answer from 90.

We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.

Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.

Hence the quotient is 142 and the remainder is 12.

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Answer:

y = 12x + 18

Step-by-step explanation:

Equation of line in slope-intercept form: y =mx +b

Here, m is the slope and b is the y-intercept.

  m = 12

Substitute m =12 in the above equation,

        y = 12x + b

This line passes through (-2,-6). So, plugin the point in the above equation.

       -6 = 12*(-2) + b

      -6 = -24 + b

-6 + 24 = b

         b = 18

Equation of the line:

         [tex]\sf \boxed{\bf y = 12x + 18}[/tex]

The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]

The inverse of a matrix is given by

[tex]A^{-1} = \frac{1}{|A|} adjA[/tex]                   ...(1)

Now, determinant of matrix A is

|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]

= (3)(2) - (2)(1)

= 6 - 2

= 4

Now, adjoint A will be

[tex]A_{11}[/tex] = 3

[tex]A_{12}[/tex] = -1

[tex]A_{21}[/tex] = -2

[tex]A_{22}[/tex] = 2

AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]

Now, substituting the values of |A| and AdjA in equation (1), we get

[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]        

Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

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After evaluating the given fraction, the resultant answer is (C) 1¼.

So, 8 ÷ 6⅖:

Now, evaluate as follows

Which can also be written as 1¼.

Therefore, after evaluating the given fraction, the resultant answer is (C) 1¼.

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Answer:

Step-by-step explanation:

The attached graph is NOT a function, since it doesn't pass the vertical line test.

If a vertical line cuts the graph more than once, then this relation is not a function.

The length of the pole is 19.15 feet.

The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.

Given:

Angle made by straight road = 15°

Angle of elevation of the sun = 57°

Length of the shadow = 75 feet

∠ACB = 90° - 57° = 33°

∠CAB = 57° - 15° = 42°

Using Sine Law to find BC i.e.length of the pole.

[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]

[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]

[tex]BC= \frac{75sin 42}{sin 33}[/tex]

BC ≅ 19.15 feet (to the nearest hundredth.)

Hence, the approximate length of the pole is 19.15 feet.

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Given,

To find g(f(-2)). we first find the value of f(-2).

The value of f(-2) is,

So now to find the value of g(f(-2)),

So the value of g(28) is,

So the value of g(f(-2)) is 51.

Answer:

the  next year population is 122,689      

Step-by-step explanation:

The computation of the next year population is as follows:

= This year population × increase percentage

= 119,000 × (1 + 0.031)

= 119,000 × 1.031

= 122,689

Hence, the  next year population is 122,689

The above formula is applied so that the correct value of the population could come

and the same is relevant

The expression gives the cost of fuel for this journey is option H mp / 100 fx

Given,

The total distance of a car journey = m miles

One kilometer = x miles

The amount of petrol needed to travel a distance of f kilometers = 1 liter

Cost of the fuel = p pence/ liter

Now we have to find the expression which gives the cost of fuel for this journey in pounds.

1 pound = 100 pence

So,

The distance in miles we can travel with 1 liter of petrol = fx

Total liter of petrol needed for the journey = m/fx

Total cost of petrol for the journey = mp / fx100

That is,

The expression gives the cost of fuel for this journey is option H mp / 100 fx

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The question is incomplete. Completed question is given below:

A car journey is m miles long.

One kilometre is equivalent to x miles.

The car uses one litre of fuel to travel a distance of f kilometres.

Fuel for the car costs p pence per litre.

Which of the following expressions gives the cost of fuel for this journey, in pounds?

(There are 100 pence in one pound.)

A. 100fmpx

B. 100fmp/x

C. 100mpx/f

D. 100mp/fx

E. fmpx/100

F. fmp/100x

G. mpx/100f

H. mp/100fx

Answer:

Step-by-step explanation:

[tex]\displaystyle\\A=\left[\begin{array}{ccc}-1&6\\-2&2\\4&9\\-5&-11\end{array}\right] \ \ \ \ \ \ \ \ \ B=\left[\begin{array}{ccc}-4&-1\\-8&8\\2&-7\\-6&5\end{array}\right] \\\\A+B=B+A\ (commutativity)\\\\\Rightarrow B+A=\left[\begin{array}{ccc}-4+(-1)&-1+6\\-8+(-2)&8+2\\2+4&-7+9\\-6+(-5)&5+(-11)\end{array}\right] \\\\\\ \Rightarrow B+A=\left[\begin{array}{ccc}-5&5\\-10&10\\6&2\\-11&-6\end{array}\right][/tex]

The temperature in the evening is 79.5 degrees Fahrenheit.

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

Jesse recorded a temperature in the morning of 75 degrees Fahrenheit

The temperature increased by [tex]4\frac{1}{2}[/tex] degrees Fahrenheit in the afternoon

75 +  [tex]4\frac{1}{2}[/tex] =[tex]\frac{159}{2}[/tex]

=79.5 degrees Fahrenheit

Before decreasing by 2.6 degrees Fahrenheit in the evening. The temperature in the evening is 79.5 degrees Fahrenheit.

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Answer:

72 and 12

Step-by-step explanation:

substitute x = 3 into the expressions

2(x + 3)²

= 2(3 + 3)²

= 2(6)²

= 2 × 36

= 72

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

3(x - 1)²

= 3(3 - 1)²

= 3(2)²

= 3 × 4

= 12

123°

180°-57°=<6=123°

Answer:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome

Answer:

The answer is really option A. x^2 - x +2-5/x-1

Step-by-step explanation:

I just took the test and got it right :)

     The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

     Then, add or subtract 50% from the first total and then, I believe, add (or it might be the other way around) to get your actual total. We would want it because it shouldn't affect the cost of the first machine. I'm sorry, but I haven't done any math in a long. use a calculator if necessary

    Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price + profit margin = selling price.

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Answer:

Step-by-step explanation:

x = 39

C. 39 Cars

Step-by-step explanation:

2x+(-8x) +5-5

-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know

The scientific notation is 6.3 × [tex]10^{-3}[/tex]

The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])

Calculate the product or quotient

=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])

Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]

=63 × [tex]10^{-2-2}[/tex]

=63 ×[tex]10^{-4}[/tex]

= 6.3 × [tex]10^{-3}[/tex]

Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].

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Answer:

x = 9

Step-by-step explanation:

given g(x) = - x and g(x) = - 9 , the equate right sides

- x = - 9 ( multiply both sides by - 1 )

x = 9

the ratio of action movies to all movies is 2: 5 .

In mathematics, a ratio illustrates how frequently one number appears in another. On a fruit tray, the ratio would be eight to six if there were eight oranges and six lemons.

Let Brayden has x number of  movies in total.

Total number of action movies in  his collection = 40% of x = 0.4 x

Other movies = 1 - 0.4x = 0.6 x

Ratio of action movies to all movies = 0.4x : x = 2: 5

Therefore the ratio of action movies to all movies is 2: 5 .

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Answer:

10x^2 + 47.2x - 84.18

Step-by-step explanation:

You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible

Answer:

11

Step-by-step explanation:

If you input the number and then solve, you should get that #=#

2(11)+9=4(11)-13

22+9=44-13

31=31

Answer: 11

Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31

By 6.2 miles per hour, Sheri commutes more quickly.

We are given that,

John travels to work = 20km/hr

Sheri travels to work = 500m/min converting this into km/hr we get ,

1.61km/hr or 1 mile

John travels to work at the following rate:

[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]

Sheri travels work at the following rate:

[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]

Computing the difference between the two,

18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr

thus, by 6.2 miles per hour, Sheri commutes more quickly.

What are conversions in maths?

An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.

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As a result, the cone's volume is equal to three times its radius √343/π .

The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.

So with respect to the information provided to us :

Height of a cone =3* radius of the base

let height be h and radius be r

h=3r

The Formula for volume of cone is:

V=1/3hπr²

Putting the value we get:

343=1/3*π*r²*3r:

r= √343/π

Therefore ,

the volume of the cone whose height is three times its radius is:

√343/π

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The robot will take 0.15 hours to complete one task.

What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.

Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.

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Answer:

u = 115

Step-by-step explanation:

35 = u/5 + 12

35 - 12 = u/5

(35 - 12) * 5 = u

u = (35 - 12) * 5

u = 115

a) The x-intercepts of y=f(x) is (-3,0) (4,0)

b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.

Here to determine the x-intercept put y=0,

Given f(x)=(x-4) (x+3)

a) y=(x-4) (x+3)

Replacing y by 0 we get,

(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)

b) y = -2(x-4) (x+3)

Replacing y by 0 we get,

-2(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)

Replacing y by 0 we get,

(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0

By solving the above equation

(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0

-1/2x=4 and -1/2x=-3

x=-1/8 and x=1/6

Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) y=(-(x+1)-4) (-(x+1) +3)

Replacing y by 0 we get,

(-(x+1)-4) (-(x+1) +3) =0

By solving the above equation

(-(x+1)-4) =0 and (-(x+1) +3) =0

-(x+1) =4 and -(x+1) =-3

x=-5, 2

Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

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