A water well drilling rig has dug to a height of -30 feet after one full day (24 hours),of continuous use. assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours (5/8 days)?

Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

As given in the question,

Speed of a truck=60mph

⇒60 minutes = 60miles

⇒14 minutes = (60/60)×14

                     = 14 miles

Car speed =67mph

67 miles=60minutes

⇒1miles = (60/67) minutes

⇒14miles = (60/67)×14

                ≈12.54 minutes (approximately)

Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

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The histogram for these data is given at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, there are 5 classes with a range of 30, as 59.5 - 29.5 = 30, hence the class width is of:

30/5 = 6.

From the data-set, we have that:

Considering this, the histogram is given at the end of the answer.

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Answer:

Step-by-step explanation:

2/5 or 4/10 or 8/20 or 16/40  

Answer:

$14 for 50 copies.

Step-by-step explanation:

Given that,

→ C(x) = 10.00 + 0.08x

Then the cost for 50 copies will be,

→ C(50) = 10.00 + (0.08 × 50)

→ C(50) = 10.00 + 4

→ [ C(50) = $14 ]

Hence, the total cost of $14.

Choosing different pairs of points we got different slopes, then we conclude that the 3 points don't lie on the same line.

Remember that if a line contains two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

a = (y₂ - y₁)/(x₂ - x₁)

Here the 3 points are on the same line if we get the same slope for any pair that we choose.

If we use the first two; (15, -12) and (28, 14), the slope is:

a = (14 - (-12))(28 - 15) = 8.67

If we use the second and third point (28, 14) and (32, 21), we get:

a = (21 - 14)/(32 - 28) = 6.125

We got different slopes, then we conclude that the 3 points don't lie on the same line.

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Answer: -26

Step-by-step explanation:

5 x -6 = -30

-30 + 4 = -26

5(-6) + 4 = -26

Answer:

1) 60 miles per hour (60.00, if rounded)

2) 152 customers per day (150, if rounded)

3) 3.5 meters per second (3.50, if rounded)

4) 1.48 dollars per pound (1.48, if rounded)

5)  0.4825 dollars per pair (0.48, if rounded)

( shown work in screenshots, 1-5; magnify it to see better :D )

7) (x, TU, TB) = (4, 8, 13)

9) (x, RS, MN) = (8, 41, 41)

11) (AB, BC, AC) = (42, 42, 84)

In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:

Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21

TB = TU + UB

21 = 2 · x + 3 · x + 1

21 = 5 · x + 1

5 · x = 20

x = 4

Then, the lengths of each line segment are:

TB = 21

TU = 2 · 4

TU = 8

UB = 3 · 4 + 1

UB = 13

The solutions are (x, TU, TB) = (4, 8, 13).

Case 9 - RS = 3 · x + 17, MN = 7 · x - 15

RS = MN

3 · x + 17 = 7 · x  - 15

4 · x = 32

x = 8

And the lengths of each line segment are:

RS = MN = 41

The solutions are (x, RS, MN) = (8, 41, 41).

Case 11 - AB = 2 · x - 8, BC = x + 17

AB + BC = AC

AB = BC

2 · x - 8 = x + 17

x = 25

And the lengths of each line segment are:

AB = 2 · 25 - 8

AB = 42

BC = AB

BC = 42

AC = 42 + 42

AC = 84

The solutions are (AB, BC, AC) = (42, 42, 84).

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Answer:

Step-by-step explanation:

it should be Venus

hmmm. im thinking its venus

The simple interest was $10.5 and the amount after 1 year would be $360.5 in her account.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as

Principal amount (P) = $350

Time (T) = 1 year

The rate of interest (R) = 3%

Simple interest= P × R × T

Simple interest = 350 × 3/100 × 1

Simple interest = $10.5

So the amount after 1 year would be P + S.I. = 350 + 10.5 = $360.5

Therefore, the simple interest would be $10.5 and the amount after 1 year would be $360.5.

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first off let's keep in mind that an absolute value is really a ± equation in disguise, so |5x -4| can pretty much be rewritten as ±(5x - 4), so is a dual equation, let's solve both for "x".

[tex]|5x-4|\leqslant 3x\implies \pm(5x-4)\leqslant 3x \\\\[-0.35em] ~\dotfill\\\\ +(5x-4)\leqslant 3x\implies 5x-4\leqslant 3x\implies 2x-4\leqslant 0\implies 2x\leqslant 4 \\\\\\ x\leqslant \cfrac{4}{2}\implies {\LARGE \begin{array}{llll} x\leqslant 2 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-(5x-4)\leqslant 3x\implies (5x-4)\stackrel{\stackrel{notice}{\downarrow }}{\geqslant} -3x\implies 8x-4\geqslant 0 \\\\\\ 8x\geqslant 4\implies x\geqslant \cfrac{4}{8}\implies {\LARGE \begin{array}{llll} x\geqslant \cfrac{1}{2} \end{array}}[/tex]

Check the picture below.

Answer:  C, I think is correct

The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

Luis has $420 to spend at a bicycle store for some new gear and biking outfits.

Therefore,

x = maximum number of outfits Luis can purchase while staying within his budget.

Hence, the inequality that can be used to represent the situation is as follows;

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.

As given,

Regular pay per hour = $14

Overtime work payment= 2 × ($14)

Total hours work done last week = 44hours

Let regular timing be 8 hours per day 5 days a week

Total regular working hours = 8 × 5

                                           = 40 hours

Over time = 44-40

                = 4 hours

Payment check = (40 × 14)+ (4 × 28)

                         = $672

Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.

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The equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.

The equation represents the relationship of two expressions on either side of the sign.

We have,

The hottest temperature = 98°F.

And that this was 25°F colder than 3 times the coldest temperature.

If we let the coldest temperature be denoted by T

We can write an equation as:

98°F + 25°F = 3T

Subtracting 25° on both sides.

98°F = 3T - 25°F

3T - 25°F = 98°F

The coldest temperature recorded in key west:

3°T - 25°T = 98°F

3°T = 123°F

T = 103°F / 3

T = 41°F

Thus the equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.

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Answer:1.c 2.b 3.a

Step-by-step explanation:

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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It looks like the system of ODEs is

[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]

Differentiate both sides of both equations with respect to [tex]t[/tex].

[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]

Eliminating the exponential terms, we have

[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]

[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]

Now we can eliminate [tex]y[/tex] and it derivatives.

[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]

Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is

[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]

Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives

[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]

The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is

[tex]y(t) = C_3 e^{-t}[/tex]

Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form

[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]

Substituting into the ODE gives

[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]

so that the general solution is

[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]

Answer:

10x + x^4/x-2

Step-by-step explanation:

Combine like terms

(10x + x^4)/(x-2)

Answer:

x = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

4x - 10 = - 6x - 2 ( add 6x to both sides )

10x - 10 = - 2 ( add 10 to both sides )

10x = 8 ( divide both sides by 10 )

x = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

Yes Jake is correct we the scales are accurately represented.

From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.

Therefore, the original length will be:

= 8 ÷ 1/90

= 8 × 90

= 720 inches

Therefore, Jack is correct.

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The formula for the general term and of the sequence is ±8.

To find the formula for the given sequence:

Therefore, the formula for the general term and of the sequence is ±8.

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P= 3

b=4

By using pythagorus therom,

h^2=p^2+b^2

=3^2+4^2

=9+16

=25

h =5

now,

sin(theta)= p÷h

=3÷5

You can add and subtract radicals by ensuring that they have same radical parts.

It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.

The necessary steps to add or subtract radicals include:

Identify the radical parts.

Add them together.

If there's unlike radical parts, one will manipulate the parts involved before solving.

Example: Add ✓63 + 5✓7

It should be noted that ✓63 = ✓9 × ✓7 = 3✓7

Therefore, ✓63 + 5✓7 will be:

= 3✓7 + 5✓7

= 8✓7.

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Answer:

21g

Step-by-step explanation:

12 + 9 = 21 then add the variable.

After Simplify this expression 12 g + 9 g. We get, 21g.

To simplify this expression

12 g + 9 g,

Add ( 12 + 9) ,which is 21

So, 12 g + 9 g = 21 g.

Therefore, the final answer is 12 g + 9 g = 21 g.

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Step-by-step explanation:

the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction does not matter, but it is essential that once a direction is picked for one coordinate, we use the same one then also for the other.

I prefer to go from left to right, so (-5, 0) to (-4, 2) :

x changes by +1 (from -5 to -4).

y changes by +2 (from 0 to 2).

so, the slope is +2/+1 = 2/1 = 2.

The table which represents the function g(x) is: answer option A.

x                g(x)

1                  -3

2                  3

3                  9

In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values and output values of a data set, as well as showing how the elements in a table are paired (mapped).

When x = 1, the function f(x) is given by:

f(x) = 2x − 3

f(1) = 2(1) − 3

f(1) = 2 - 3

f(1) = -1.

Therefore, the function g(x) = f(3x) = 3 × -1 = -3.

When x = 2, the function f(x) is given by:

f(x) = 2x − 3

f(2) = 2(2) − 3

f(2) = 4 - 3

f(2) = 1.

Therefore, the function g(x) = f(3x) = 3 × 1 = 3.

When x = 3, the function f(x) is given by:

f(x) = 2x − 3

f(3) = 2(3) − 3

f(3) = 6 - 3

f(3) = 3.

Therefore, the function g(x) = f(3x) = 3 × 3 = 9.

In conclusion, the table which represents the function g(x) is as follows:

x                g(x)

1                  -3

2                  3

3                  9

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Answer: A

Step-by-step explanation:

rxl ontop

1) d - c is calculated as; -4

2) Simplifying ³/₄ - ²/₅ gives; 7/20

1) We are given;

c = 12 and d = 8. Thus;

d - c is calculated as;

8 - 12 = -4

2) We want to simplify ³/₄ - ²/₅

Factoring out 1/20 gives;

1/20(15 - 8) = 7/20

3) Number of pencils purchased = 888 pencils

Number of pencils in a box = 12

Thus;

Number of boxes purchased = 888/12 = 74 boxes

4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6

5) √64 = 8

6) (30 - 4 * 2)/(2 * 2²)

= (30 - 8)/8

= 22/8 = 11/4

7) 11 = x + 19

x = 11 - 19

x = -8

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