The Smith family is driving to a vacation spot. The number of miles they have left is 540-60x, where x represents the number of driving hours. What does 60x represent?
a. the number of miles driven after 1 hour
b. the total distance to the state park
c. the number of miles driven after x hours

Answer:

x= 1; y= 0; z= -2 and w= 3.

Step-by-step explanation:

Given that,

1) x + 2y - z = 3

2) 2x - y + z - w = -3

3) y + 2z - w = -7

4) x + 3y + 2z + 2w = 3 ​

now, from 1) z = x + 2y -3 →→(5)

from 2) w = 2x -y + z +3

         ⇒w = 2x -y + x + 2y -3 +3  (from (5))

            w = 3x + y →→(6)

Now substitute (5) and (6) in 3), we get

y +2(x + 2y -3) - (3x + y) = -7

⇒ 4y - x = -1 →→→(7)

Now substitute (5) and (6) in 4), we get

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

⇒ 9x +9y = 9

⇒ x + y =1 →→→(8)

⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1

⇒ y = 0 and x = 1

substituting these values in

(5) and (6) gives, z = -2 and w = 3

⇒ x= 1; y= 0; z= -2 and w= 3.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates on the graph are (0, -3), (1, -1.8), (2, -0.6), (3, 0.6), (4, 1.8), and (5, 3).

The graph on option C best represents the function -5y = -6x + 15

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Function:

-5y= -6x + 15

We will find coordinates using this function.

For x = 0,

-5y = -6 x 0 + 15

y = -3

For x = 1,

-5y = - 6 x 1 + 15

-5y = -6 + 15

-5y = 9

y = -9/5 = -1.8

For x = 2,

-5y = -6 x 2 + 15

-5y = -12 + 15

-5y = 3

y = -3/5 = -0.6

For x = 3,

-5y = -6 x 3 + 15

-5y = -18 + 15

y = 3/5 = 0.6

For x = 4

-5y = -6 x 4 + 15

-5y = -24 + 15

-5y = - 9

y = 9/5 = 1.8

For x = 5

-5y = -6 x 5 + 15

-5y = -30 + 15

-5y = -15

y = 3

The coordinates on the graph are (0, -3), (1, -1.8), (2, -0.6), (3, 0.6), (4, 1.8), and (5, 3).

The graph of these coordinates is found on the graph on option C.

Thus,

The graph on option C best represents the function -5y = -6x + 15

Option C is the correct answer.

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Answer:

The answer is 3024

Step-by-step explanation:

you do 9!/(9-4)! which comes out to 3024

Answer:the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.

Step-by-step explanation:

Final answer:

Calculus is the mathematics of change, encompassing derivatives and integrals, which are fundamental for solving rates of change and accumulation problems in various fields, including engineering and economics.

Explanation:

Calculus is a branch of mathematics that focuses on the study of change. It is divided into two major areas: differential calculus and integral calculus. Differential calculus deals with the concept of a derivative, which measures how a function changes as its input changes. This can be visualized as the slope of the tangent line to a curve at a given point. Integral calculus, on the other hand, involves the calculation of an integral, which can be thought of as the area under a curve or the accumulation of quantities. Together, these concepts allow us to solve complex problems involving rates of change and accumulation.

Calculus is essential in many fields such as engineering, physics, economics, and even biology. For example, in engineering, calculus is used to model and solve problems related to motion, forces, and energy.

It's important to note that students who do not take calculus in high school can still pursue engineering by taking calculus in their first year of college. The understanding of dimensions and units within calculus also applies to physical quantities, exemplifying the principle that dimensions obey the rules of algebra.

If a student is planning to major in economics, a strong recommendation is to learn at least a little calculus. This math competency greatly facilitates the understanding of advanced economics and helps speed up the learning process, especially in constructing and analyzing algebraic models used to describe economic relationships and functions.

Answer:

A) x=2, 8

Step-by-step explanation:

abs(x-5)=3

x-5=3, x-5=-3

x=3+5=8,

x=-3+5=2

Final answer:

option A.  x=2, x=8

Explanation:

To solve the equation |x-5|=3, we need to consider both cases regarding the absolute value function. The absolute value of an expression is equal to 3 if the expression itself is 3 or -3. Therefore, we have two equations to solve:

Solving the first equation:

Solving the second equation:

Thus, the solutions for the equation |x-5|=3 are x=2 and x=8, which corresponds to option A.

Answer:

a. [tex]0.1\ miles[/tex]

b Slope: [tex]\frac{1}{10}[/tex] or [tex]0.1[/tex]

Step-by-step explanation:

The equation of a line that passes through the origin is:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

By definition, Direct variation equations have the following form:

[tex]y=kx[/tex]

Where "k" is the Constant of variation.

Then, you can conclude that:

[tex]m=k[/tex]

a. Let be "d" the distance in miles that the train travels per gallon.

You can observe in the graph that when the train travels 10 miles, it uses 100 gallons. Then, you can set up the following proportion:

[tex]\frac{10}{100}=\frac{x}{1}[/tex]

Solving for "x", you get:

[tex]x=\frac{1}{10}\\\\x=0.1[/tex]

Then, it travels 0.1 miles per gallon.

b. The slope is also [tex]\frac{1}{10}[/tex] or [tex]0.1[/tex]. To check this, you can subsitute the coordinates of the point (100,10) into [tex]y=mx[/tex] and solve for "m" in order to find its value.

This is:

[tex]10=m(100)\\\\m=\frac{1}{10}[/tex]

Answer:

36

Step-by-step explanation:

the data we have is:

coontainers of green dye        containers of water

                    6                        ⇒                 3

and we need to know how many containers of water he would use for 24 containers of green dye, and then sum this results to know how many containers did he used in total.

coontainers of green dye        containers of water

                    6                        ⇒                 3

                    24                      ⇒                 x

and we solve for x using rule of three: multiply cross quantities and divide by the remaining amount:

x = 24*3/6

x = 72/6

x = 12

so he used 12 containers of water for the 24 containers of green dye, which in total of containers is:

12 + 24 = 36

Answer: 36 containers in total.

Ronald used 12 containers of water, making the total number of containers used 36.

Ronald uses a ratio of 6 containers of green dye to 3 containers of water to get a particular shade of green. To find out the total number of containers used if he used 24 containers of green dye, we can use a proportion based on the given ratio.

For every 6 containers of dye, there are 3 containers of water:

6 containers of dye : 3 containers of water

So if Ronald used 24 containers of green dye:

24 containers of dye : x containers of water

We can set up a proportion to find the value of x:

6/3 = 24/x

Cross-multiply and solve for x:

6x = 24 * 3

6x = 72

x = 72 / 6

x = 12

Therefore, Ronald used 12 containers of water.

To get the total number of containers used, add the number of containers of dye and water:

24 containers of dye + 12 containers of water = 36 containers.

Thus, Ronald used a total of 36 containers.

Answer:

The function through which given point passes is f(x) = 24 x - 12 .

Step-by-step explanation:

Given as :

The points are

[tex]x_1[/tex] , [tex]y_1[/tex] = 1 , 12

[tex]x_2[/tex] , [tex]y_2[/tex] = 2 , 36

now, slope of the line

Let The slope of line = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Or, m = [tex]\frac{36 - 12}{2-1}[/tex]

Or, m = 24

So The slope of line = m = 24

Now, equation of line in point-slope form

y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex] )

Or, y - 12 = 24 × (x - 1 )

or, y - 12 = 24 x - 24

or, y = 24 x - 24 + 12

or, y = 24 x - 12

or , f(x) = 24 x - 12

So, The function through which given point passes is f(x) = 24 x - 12 . Answer

Answer:

Substitute the slope  and the coordinates of point D in the equation of the line  y=mx+b and then solve for b in each equation

Step-by-step explanation:

we know that

The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1

The second step is substitute the slope m2 and the coordinates of point D in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation

Answer:

26.82

Step-by-step explanation:

Answer:

$26.82

Step-by-step explanation:

Product Cost: $18

Markup: 49%

Selling Price = (49% / 100% * $18) + $18 = $8.82 + $18 = $26.82

This gives you a price markup of $26.82.

this is my first answer and it could very well be wrong, sorry ;(

Answer:

34/9

Step-by-step explanation:

3 7/9 = 9*3+7 =34

34/9

Answer:34/9

Step-by-step explanation:

9*3 = 27

27+7= 34 then add the denominator

Answer:

Step-by-step explanation:

The inequality is shown by [tex]g \geq 4.2[/tex].

At first we need to find the point 4.2.

In order to do so, it needs to divide the distance between 4 to 5 in 10 equal parts.

Adjacent part of 4 is 4.1 and the next adjacent is 4.2.

Since, g is greater or equal to 4.2, the arrow will be towards the increasing side.

See the image.

Answer:

40° ( angle 2 and 3 are alternating angles, therefore angle 2=3)

Answer:

7<k+3+2

7<k+5

2<k

which is same as k>2

Answer:

To work this problem out you would do it as if it were just a simple equation

7x-19<16 (you would first have to add 19 to both sides)

7x<35 (then you would divide by 7 to get the variable by itself)

x<5 ( you answer would then be 5)

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

(8x+12)=76

8x=64

x=8

check

8(8)+12=104

64+12=76

76=76

Answer:

13.31803792

Step-by-step explanation:

Law of Cosines

a= 8

b= 18

c= ?

[tex]c^2=a^2b^2-2ab*cos(c)[/tex]

[tex]c^2=8^2-18^2-2*8*18*cos(43)[/tex]

c = 64 + 324 - 2 * 8 * 18 * cos(43)

cos(43) = 0.7313537016

Order of Operations

64 + 324 - 2 * 8 * 18 * 0.7313537016 = 177.3701339

Square Root the answer

[tex]\sqrt{177.3701339}[/tex] = 13.31803792

[tex]log_{x}(1/8)=-3/2[/tex]

This is equal to...

[tex]x^{-3/2}=1/8[/tex]

We want "x" so we need to isolate it using laws of exponents...

[tex]x^{(-1)(3/2)}=1/8[/tex]

[tex]x^{3/2}=8[/tex] because [tex]x^{-a}=1/x^{a}[/tex]

[tex]x=\sqrt[3]{8^{2}}[/tex] because [tex]x^{a/b}=\sqrt[b]{x^{a}}[/tex]

x = 4

answer: B

[tex] \frac{2}{3} x + 5 = 1[/tex]

[tex] \frac{2}{3} x = 1 - 5[/tex]

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

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

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

[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]

[tex]x = ( - 6)[/tex]

[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]

Answer: 36

Step-by-step explanation:

The legs are given to be :

3x - 1 and -x + 27

The base = 5x + 1

One of the properties of an isosceles triangle is that two sides are equal , that is the two legs are equal. This means that

3x - 1 = - x + 27

3x + x = 27 + 1

4x = 28

x = 7

To calculate the length of the base, substitute x = 7 into the length of the base given , that is

Length of the base = 5(7) + 1

L = 35 + 1

L = 36

Answer:

x=-1, y=6. (-1, 6).

Step-by-step explanation:

x+y=5

x-y=-7

---------

2x=-2

x=-2/2

x=-1

-1+y=5

y=5-(-1)=5+1=6

Answer:

Tuesday : Total = 30 : 72 = 5 : 12

Step-by-step explanation:

Monday: 42 miles

Tuesday: 42 - 12 = 30 miles

Monday + Tuesday: 42 + 30 = 72 miles

Tuesday : Total = 30 : 72 = 5 : 12

The amount spent at the movie store is $ 10.5

Given that Davis bought some candy for $ 35

This was seven dollars less than four times what he bought at the movie store

Which means that $ 35 is equal to seven dollars less than four times what he bought at the movie store

Let "m" be the amount spent at the movie store

$ 35 = seven dollars less than four times what he bought at the movie store

35 = 4m - 7

35 + 7 = 4m

42 = 4m

Thus the amount spent at the movie store is $ 10.5

Answer:

[tex]y=mx[/tex]

Step-by-step explanation:

[tex]y=mx[/tex]

where, y is the total cost of the erasers,

m is the numbers of erasers,

x is the cost of each erasers.

Given:- [tex]m=19, y=3[/tex]

by putting these value in the above equation,

i.e. [tex]y=mx[/tex]

we get,

[tex]3=19x[/tex]

[tex]x=\frac{3}{19}[/tex]

[tex]x=0.157[/tex]

Now for 45 erasers substitute the value of [tex]x=0.157[/tex]

so, we get [tex]y=45\times 0.157[/tex]

[tex]y=7.065[/tex]

cost of 45 erasers are $7.065

Answer:

All proofs are given in the explanation

Step-by-step explanation:

System Of Linear Equations

Given a system of equations of the form

[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]

The solution of the systems is a pair of values x,y such that both conditions are met, i.e. the equations become identities.

We are given the following system

[tex]\displaystyle \left\{\begin{matrix}x+y=7\\ 3x-2y=1\end{matrix}\right.[/tex]

Part A. If we replace x=3, y=4 into both equations we get

[tex]\displaystyle \left\{\begin{matrix}(3)+(4)=7\\ 3(3)-2(4)=1\end{matrix}\right.[/tex]

They are both now identities, so the solution is correct

Part B. If we multiply the first equation by 5 we get

[tex]\displaystyle \left\{\begin{matrix}5x+5y=35\\ 3x-2y=1\end{matrix}\right.[/tex]

Adding both  equations

[tex]\displaystyle 8x+3y=36[/tex]

Part C. The new system will be

[tex]\displaystyle \left\{\begin{matrix}x+y=7\\ 8x+3y=36\end{matrix}\right.[/tex]

If we try again x=3, y=4 in the new system we get

[tex]\displaystyle \left\{\begin{matrix}3+4=7\\ 8(3)+3(4)=36\end{matrix}\right.[/tex]

We can see both equations are now identities, so the solution holds also for this 'new' system

Part D. If we multiply or divide an equation by a constant, the conditions between the variables won't change, it's just another form to express the same relation. Adding two equations is exactly the same, it won't introduce any changes in the relationship between the variables, so the solution will always be the same

Answer:

1 : 80,000,000

Step-by-step explanation:

Convert each 12,000km to cm to match the model's unit:

12,000 * 100,000 = 1,200,000,000 cm

The scale is the ratio of the model's dimension to the planet's dimension:

15 : 1,200,000,000

Divide each by 15 to simplify the ratio:

1 : 80,000,000

Therefore, the model is at a scale of 1 : 80,000,000.

Answer:

The sports shop has 21 part-time employees.

Step-by-step explanation:

Solution:

What is 25% of 84?

.Y is 25% of 84

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 25% * 84

Converting percent to decimal:

p = 25%/100 = 0.25

Y = 0.25 * 84

Y = 21

Or another quicker way....

50% is half of the whole, and 25 is half of 50.

84/2/2

equals 21 too, I don't recommend to use it as row form.

The sports shop has 21 part-time employees, found by calculating 25% of 84.

The question asks how many part-time employees a sports shop with 84 employees has if 25% of them work part-time. To find the answer, we need to calculate 25% of 84 employees. The calculation is done as follows:

First, convert the percentage to a decimal by dividing it by 100: 25% = 0.25.

Then, multiply the total number of employees by this decimal: 84  times 0.25 = 21.

Therefore, the sports shop has 21 part-time employees.

Answer:

The answer is B. 6 and 8.

Answer:

B) 6 and 8

Step-by-step explanation:

[tex]3 \times 8 = 24[/tex]

[tex]4 \times 6 = 24[/tex]

[tex]2 \times 12 = 24[/tex]

Answer:

Option C

Step-by-step explanation:

The given polynomial is: 1280 x¹¹ - 405 x⁷.

The least power of the variable is taken common outside. So we get:

x⁷{1280 x⁴ - 405}

Now, 5 is a factor of both 1280 and 405.

So, it can be written as:

5x⁷{256x⁴ - 81}

We know that

Also, 256 = 16² and 81 = 9².

Therefore, this can be rewritten as:

Using the above formula, a = 16x² and b = 9.

Therefore, this becomes:

can again be factorized with a = 16x and b = 3.

Therefore, it would be:

Hence, OPTION C is the answer.

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