Write the equation of the line passing through the point (a, b) and having a slope m.​

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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In the given diagram, the measure of arc QS is 168°

From the question, we are to determine the measure of arc QS

The measure of the arc is the angle subtended by the arc at the center of the circle.

From one of the circle theorems, we have that

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference

In the given diagram,

The angle subtended by arc at the circumference of the circle = 84°

∴ The angle subtended by the arc QS at the center = 2 × 84°

The angle subtended by the arc QS at the center = 168°

Hence, in the given diagram, the measure of arc QS is 168°

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Answer:  168°

Step-by-step explanation:  TRUST ME!!!  Answer is correct in Edge!  :)

The system of linear equations represents the situation is;

x + y = 125

x + y = 1255x + 8y = 775

Simultaneous equation is an equation in two unknown values are being solved for at the same time.

let

x + y = 125

5x + 8y = 775

From equation (1)

x = 125 - y

5x + 8y = 775

5(125 - y) + 8y = 775

625 - 5y + 8y = 775

- 5y + 8y = 775 - 625

3y = 150

y = 150/3

y = 50

x + y = 125

x + 50 = 125

x = 125 - 50

x = 75

Therefore, the number of quick washes and premium washes Monica’s school band had is 75 and 50 respectively.

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Answer:

A. 5x + 8y = 775 and x + y =125

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 > x² - 5x.

The answer for the inequality is -1 the greater than sign x greater than 6

The interval notation is ( -1,6)

Answer:

[tex]-1 < x < 6[/tex]

Step-by-step explanation:

Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.

Option ( C ) is correct for this expression . 100 inches Over 1 minute times × 1 foot Over 12 inches.

What is a basic expression?

Given that the expression 100 inches.

We need to convert 100 inches per minute to feet per minute.

Since, we know that 1ft = 12 inch

Then,

1 in = 1/12 ft

Now, we shall convert 100 inches per minute to feet per minute.

To convert in/min to ft/min, let us multiply by 1/12

Thus, we have,

[tex]\frac{100 in}{min} * \frac{1 ft }{12 in}[/tex]

Therefore, option ( c ) is correct for this expression .

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The complete question is -

Which expression converts 100 inches per minute to feet per minute?

A) Start Fraction #1 100 inches Over 1 minute End Fraction × Start Fraction 60 minutes Over 1 hour End Fraction

B) Start Fraction #2 100 inches Over 1 minute End Fraction × Start Fraction 1 hour Over 60 minutes End Fraction

C) 100 inches Over 1 minute times × Start Fraction 1 foot Over 12 inches End Fraction

D) 100 inches Over 1 minute times × Start Fraction 12 inches Over 1 foot End Fraction

Answer:

The answer is 1. This table is an example of the principle of independence.

Step-by-step explanation:

This means any Trade activity is performed without reliance on another party.

He got the perfect answer to his question and he can get his answer without any other information.

Answer:

i think this may help you

The diagram to show that the square root of 121 is 11 attached below

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]

Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).

Herewe are given the number as 121

It is perfect root then ;

√121 = 11

The solution that show that the square root of 121 is 11 attached below

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Answer:

B.) f⁻¹(x) = (1/9)x - 7/9

Step-by-step explanation:

Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.

f(x) = 9x + 7                            <----- Original function

y = 9x + 7                               <----- Substitute f(x) for "y"

x = 9y + 7                               <----- Swap variable positions

x - 7 = 9y                                <----- Subtract 7 from both sides

(x - 7) / 9 = y                           <----- Divide both sides by 9

(1/9)x - 7/9 = y                      <----- Divide each term individually by 9

The inverse function is represented by the symbol f⁻¹(x).

The domain of the function shown in the graph is x < 7

The complete question is added as an attachment

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is  x < 7

Hence, the domain of the function shown in the graph is x < 7

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Answer:

-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)  (the last choice).

Step-by-step explanation:

Im ignoring the 2^2 in the equation

The equation transforms to

2x^2 - 3x - 5 = 0    (standard form)

So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)

Answer:

C

Step-by-step explanation:

Let's review some sets of numbers.

Natural numbers: 1, 2, 3, 4, ...

The natural numbers are the counting numbers. You normally start counting with 1, not 0, and you only count whole numbers.

Whole numbers: 0, 1, 2, 3, 4, 5, ...

The whole numbers are the counting numbers with the addition of zero. There are no negative numbers in the whole numbers.

Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...

The integers are the natural numbers, plus zero, plus the negatives of the natural numbers. All numbers are whole with no decimal part.

Rational numbers

The rational numbers are all numbers that can be written as a fraction of integers. For example, 1 can be written as 3/3, so 1 is a rational number. All natural numbers, whole numbers, and integers are rational numbers. Other rational numbers are numbers that are not whole, such as 2.5, 7/8, 1/4, etc. These numbers can be written as fractions of integers. Rational numbers written as decimal numbers will either be an integer, a terminating decimal, or a non-terminating, repeating decimal.

Up to here, each new set includes the previous set.

Now things change. If a number is rational, it is not irrational.

If a number is irrational, it is not rational.

Irrational numbers

Irrational numbers are always non-terminating, non-repeating decimals. They cannot be written as fractions of integers. Examples: √2, π

Now let's look at this problem.

We have a negative decimal number. The bar above the 12 means the digits 12 are repeating. This number can also be written as -0.121212...

Since our number is a non-terminating, repeating decimal, it is a rational number.

Answer: C

The answer is J.

The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.

The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.

The probability is equal to :

Answer:

J   [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

• First, let's find the probability of landing a letter B in Spinner 1.

We have a total of eight possibilities, and two of them are the letter B.

∴ [tex]P(B) = \frac{2}{8}[/tex]

            = [tex]\bf \frac{1}{4}[/tex]

• Next, let's find the the probability of landing the number 1 on Spinner 2.

There are a total of six possibilities, and two of them are the number 1.

∴ [tex]P(1) = \frac{2}{6}[/tex]

           = [tex]\bf \frac{1}{3}[/tex]

• Now we have to calculate the probability of spinning a letter B and the number 1:

[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]

                   = [tex]\bf \frac{1}{12}[/tex]

Answer:XDDXXDXD

DXDXXDXDDXDXDXDXXDDXDEDXXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-XDDXDXDXstep explanation:

seria tu cacá XDXDXDXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

The answer is 0.

The expression in algebraic form is :

We know subtracting a term from its equivalent term will be 0.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

“[tex]\textsf{x minus x}[/tex]”

[tex]\huge\textbf{Simplifying it: }[/tex]

[tex]\textsf{x minus x}[/tex]

[tex]\mathsf{= x - x}[/tex]

[tex]\mathsf{= 1x - 1x}[/tex]

[tex]\mathsf{= 0x}[/tex]

[tex]\mathsf{= 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak 0}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: x = 52 m

Step-by-step explanation:

     The formula we will use, which solves for the area of a trapezoid, is [tex]a=\frac{a+b}{2} h[/tex] where a is a base, b is a base, and h is the height.

    We will input the known values, then solve for x.

         [tex]\displaystyle a=\frac{a+b}{2} h[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=\frac{36\;\text{m}\;+x}{2}*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=(18\;\text{m}+\frac{x}{2})*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=486\;\text{m}+\frac{27x}{2}[/tex]

         [tex]\displaystyle 702\;\text{m}^2=\frac{27x}{2}[/tex]

         [tex]\displaystyle 1,404\;\text{m}^2=27x[/tex]

         [tex]\displaystyle x=52\;\text{m}[/tex]

The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

In this question,

The curves are y = 2/x, y = 2/x^2, x = 4

The diagram below shows the region enclosed by the given curves.

From the diagram, the limit of x is from 1 to 4.

The given curves are integrated with respect to x and the area is calculated as

[tex]A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx[/tex]

⇒ [tex]A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx][/tex]

⇒ [tex]A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx][/tex]

⇒ [tex]A=2[lnx-\frac{1}{x} ] \limits^4_1[/tex]

⇒ [tex]A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )][/tex]

⇒ A = 2[(1.3862-0.25) - (0-1)]

⇒ A = 2[1.1362 + 1]

⇒ A = 2[2.1362]

⇒ A = 4.2724 square units.

Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

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Answer:

Angle symbol

Angle ACB

Angle ACE

Angle DCE

Missing data:

Viewer's Age Group  Excellent Good Average Poor Marginal Total

16–25                          52                 42       12       7           113

26–35                          33                50         5       9          97

36–45                          58                 12       28      34         132

46–55                          25                17       22       12            76

56 +                               12                 5          3         8             28

Marginal Total             180               126      70      70           446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 [tex]*[/tex] 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

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The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

According to the statement

we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.

So, The given expression are:

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

And we have to prove the answer.

So, For this

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]

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

Then the equation become

[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]

Now solve it then

[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]

Now take 2 common from answer then equation become

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

Hence proved.

So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

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The volume of the figure in the attachment is 84 cubic yards

The volume of a figure or a three-dimensional shape is the amount of space inside the figure or the three-dimensional shape

The complete question is added as an attachment.

From the attached figure, we can see that the three-dimensional shape is a frustum

The volume is then calculated using the following formula

V = 1/2 * (Sum of the parallel bases) * height * side length

From the figure, we have:

Parallel bases = 2 yards and 6 yards

Height = 3.5 yards

Side length = 6 yards

Substitute the known values in the above equation

V = 1/2 * (2 + 6) * 3.5 * 6

Evaluate the product in the above equation

V = 1/2 * (2 + 6) * 21

Evaluate the sum in the above equation

V = 1/2 * 8 * 21

Evaluate the product in the above equation

V = 1/2 * 168

Evaluate the product in the above equation

V = 84

Hence, the volume of the figure in the attachment is 84 cubic yards

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Answer:

x = 18

y = 18

Step-by-step explanation:

We are given a right triangle (notice the 90 degree angle), with one of the angles being 45°.

We also know that the hypotenuse (the side opposite of the 90° angle) is 18√2.

We want to find the value of x and y.

First, let's figure out what the value of the other angle is.

The angles in a triangle all add up to 180 degrees.

Let's call the value of the angle we don't know s.
s + 45 + 90 = 180

Add 45 and 90 together.

s + 135 = 180

Subtract 135 from both sides.

s = 45

So the value of the other angle is 45 degrees.

When a right triangle is a 45-45-90 triangle (the numbers referring to the measures of the degrees), there is actually something special about it; if the legs (the sides that make up the 90 degree angle) have the value a (they would both be congruent because a 45-45-90 triangle is isosceles), then the hypotenuse will be a√2.

Keeping this in mind, let's solve for a.

Set 18√2 equal to a√2.

18√2=a√2

Divide both sides by √2.

18 = a

The value of a, aka the legs is a.

Both x and y would be equal to a in this case.

Therefore, x = 18, and y = 18.

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2

Last term an = [tex]2\frac{1}{2}[/tex] = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

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Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?

Answer:

13 square units

Step-by-step explanation:

We need to find the distance between the points using the  

Pythagorean Theorem, a² + b² = c²

(3,6) and (6,5); 6 - 3 = 3 and 6 - 5 = 1

3² + 1² = c²

9 + 1 = c²

c = √10

(6,5) and (5,1); 6 - 5 = 1 and 5 - 1 = 4

1² + 4² = c²

1 + 16 = c²

c = √17

√17 + √10 = 13.038

The desired measures for the data-set is given by:

The five number summary is composed by the measures explained below, except the IQR.

In this problem, we have that:

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The rate of change at 6 hours is -96

The function is given as:

P = 400 - 8t^2

Differentiate the function

P' = -16t

Set t = 6

P' = -16 * 6

Evaluate

P' = -96

Hence, the rate of change at 6 hours is -96

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Answer:

[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x=2(e-1)[/tex]

Step-by-step explanation:

Given definite integral:

[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x[/tex]

Integration by substitution:

Substitute u for one of the functions to give a function that's easier to integrate.

[tex]\textsf{Let }u=\sqrt{x}[/tex]

Find the derivative of u and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{2\sqrt{x}}[/tex]

[tex]\implies \text{d}x=2 \sqrt{x}\:\text{d}u}[/tex]

[tex]\implies \text{d}x=2u\:\text{d}u[/tex]

Use the substitution to change the limits of the definite integral from x-values to u-values:

[tex]\textsf{When }x=0 \implies u=\sqrt{0}=0[/tex]

[tex]\textsf{When }x=1 \implies u=\sqrt{1}=1[/tex]

Therefore, the limits are unchanged.

[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x+\text{C}$\end{minipage}}[/tex]

Substitute everything into the original integral and solve:

[tex]\begin{aligned}\implies \displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x & =\displaystyle \int^1_0 \dfrac{e^u}{u} \cdot 2u\:\:\text{d}u \\\\ & = \displaystyle \int^1_0 2e^u\:\:\text{d}u \\\\ & = 2 \int^1_0 e^u\:\:\text{d}u\\\\ & = 2 \left[ e^u\right]^1_0\\\\ & = 2 \left[e^1-e^0\right]\\\\& = 2(e-1)\end{aligned}[/tex]

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Answer:

Step-by-step explanation:

The vertical distance between the given points is:

Answer:

19,497m

Step-by-step explanation:

8,856-(-10,911)

=8856+10,911

=19,497m