HELP ASAP 30 PTS
determine the range of the following graph:

It would take 2.69 minutes for both machines to complete the project at the same time

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Machine A completes a project every 5.5 minutes. Machine B completes a project every 5.25 minutes.

Let t represent time it would take both machines to complete the project, hence:

(1/5.5 + 1/5.25)t = 1

86t/231 = 1

t = 2.69 minutes

It would take 2.69 minutes to complete

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Answer:

they are both negative numbers and -14 < -8 (less than)

Step-by-step explanation:

The circumference of this circle is 2π

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

The arc is the circumference.

C = 2πr

C = 2x πx 6

C = 12π

A circle is 360 degrees.  The  arc is covering 60 degrees

60/360 = 1/6

The arc is 1/6 of the circle, so it will be 1/6 of the circumference

1/6 C = 1/6 (12π)

arc = 2π

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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Answer:

  a) -900 L/min

  b) 63000 L

  c) v = -900t +63000

  d) 7200 L

Step-by-step explanation:

a) You are given two points on the curve of volume vs. time:

  (t, v) = (20, 45000) and (70, 0)

The rate of change is ...

  Δv/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 . . . . liters per minute

__

b) In the first 20 minutes, the change in volume was ...

  (20 min)(-900 L/min) = -18000 L

So, the initial volume was ...

  initial volume -18000 = 45000

  initial volume = 63,000 . . . . liters

__

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form:

  v = -900t +63000

__

d) Put the number in the equation and do the arithmetic.

When t=62, the amount remaining is ...

  v = -900(62) +63000 = -55800 +63000 = 7200

7200 L remain after 62 minutes.

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To find the value of 'x', we can use the property of parallel lines that states when a transversal intersects two parallel lines, the corresponding angles are equal.

In triangle ABC, we have DE parallel to BC. Therefore, we can conclude that triangle ADE is similar to triangle ABC.

Using the property of similar triangles, we can set up the following proportion:

\(\displaystyle\sf \dfrac{AD}{DB} = \dfrac{AE}{EC}\)

Substituting the given values:

\(\displaystyle\sf \dfrac{6x - 7}{4x - 3} = \dfrac{3x - 3}{2x - 1}\)

To solve this proportion for 'x', we can cross-multiply:

\(\displaystyle\sf (6x - 7)(2x - 1) = (4x - 3)(3x - 3)\)

Expanding both sides:

\(\displaystyle\sf 12x^{2} - 6x - 14x + 7 = 12x^{2} - 9x - 12x + 9\)

Combining like terms:

\(\displaystyle\sf 12x^{2} - 20x + 7 = 12x^{2} - 21x + 9\)

Moving all terms to one side:

\(\displaystyle\sf 12x^{2} - 12x^{2} - 20x + 21x = 9 - 7\)

Simplifying:

\(\displaystyle\sf x = 2\)

Therefore, the value of 'x' is 2.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that AD=4x−38, BD=3x−1, AE=8x−7 and CE=5x−3. Let AC=x

Using the basic proportionality theorem, we have

BD

AD

​

=

AC

AE

​

⇒

3x−1

4x−3

​

=

x

8x−5

​

⇒x(4x−3)=(3x−1)(8x−5)

⇒4x

2

−3x=3x(8x−5)−1(8x−5)

⇒4x

2

−3x=24x

2

−15x−8x+5

⇒4x

2

−3x=24x

2

−23x+5

⇒24x

2

−23x+5−4x

2

+3x=0

⇒20x

2

−20x+5=0

⇒5(4x

2

−4x+1)=0

⇒4x

2

−4x+1=0

⇒(2x)

2

−(2×2x×1)x+1

2

=0(∵(a−b)

2

=a

2

+b

2

−2ab)

⇒(2x−1)

2

=0

⇒(2x−1)=0

⇒2x=1

⇒x=

2

1

​

Hence, x=

2

1

​

.

After how many minutes will the two pools have the same amount of water? 36 min.

How much water will be in each pool when they have the same amount? 2638 liters.

Explanation:

y=1900+20.5x

y=1351+35.75x

Let the time be t

\(\\ \sf\longmapsto 1900(1+\dfrac{20.5}{100})^t=1351(1+\dfrac{35.75}{100})^t\)

\(\\ \sf\longmapsto 1900(\dfrac{120.5}{100})^t=1351(\dfrac{135.75}{100})^t\)

\(\\ \sf\longmapsto 1900(1.2)^t=1351(1.35)^t\)

\(\\ \sf\longmapsto \dfrac{1900}{1351}=\left(\dfrac{1.35}{1.2}\right)^t\)

\(\\ \sf\longmapsto 1.4=(1.125)^t\)

\(\\ \sf\longmapsto (1.125)^2.9=(1.125)^t\)

\(\\ \sf\longmapsto t=2.9h\)

\(\\ \sf\longmapsto tanC=\dfrac{AB}{BC}\)

\(\\ \sf\longmapsto tan17=\dfrac{AB}{206}\)

\(\\ \sf\longmapsto AB=0.3(206)\)

\(\\ \sf\longmapsto AB=61.8ft\)

The correct sentences in the passage are option A, option B, and option E.

Let's check all the options, then we have

Any two squares are either similar or congruent. The statement is true.

If two lines are parallel, they never intersect. The statement is true.

If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.

The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.

A line can be drawn through any two distinct points. The statement is true.

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Answer:

I believe it should be A

Step-by-step explanation:

Answer:

Answer:A. gross pay − deductions = net income

Step-by-step explanation:

Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Complete Question  

Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = 12e^x, [−6, 6] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)

Answer:

The  average is  

  \(AV  =  403\)

The value of  x is

   \(x =  4\)

Step-by-step explanation:

From the question we are told that

  The equation is  \(f(t) =  12e^x\)

  The  points consider is  [-6 , 6]

Generally the average value of the function over the given interval is mathematically represented as

          \(AV  =  \frac{1}{z-w} \int\limits^ z_w {f(x)} \, dx\)

          \(AV  =  \frac{1}{ 6 - (-6)}  \int\limits^{6}_{-6} { 12e^x} \, dx\)

          \(AV  =  \frac{1}{12 } e^x| \left 6} \atop {-6}} \right.\)

          \(AV  = e^6 -e^{-6}\)

          \(AV  =  403\)

Generally when the function equal the average we have that

        \(f(x) =  12e^{x} =  403\)

        \(e^{x} =  34\)

          \(x =  ln(34)\)

        \(x =  4\)

Answer:

  C  86

Step-by-step explanation:

You want the measure of the angle marked x° where chords cross. The angle marked x° intercepts an arc of 104° and one that is unmarked. The remaining arcs of the circle are marked 111° and 77°.

The measure of angle x is half the sum of the arcs it intercepts. One of those is given as 104°. The other will be ...

  360° -111° -104° -77° = 68°

Then the value of x is ...

  (104 +68)/2 = 172/2 = 86

The value of x is 86, choice C.

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The area of this triangle is 21 square units.

From the graph:

The length of the base = 4 + 3 units

= 7 units

The length of the height = 3 + 3

= 6 units

Area of the triangle = 1/2 b *h

= 1/2*7*6

= 1*42/2

= 42/2

= 21 square units.

Therefore the area of this triangle is 21 square units.

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Answer:

$23,465

$4,693

Step-by-step explanation:

To find a percent of a number, multiply the percent by the number.

6.5% of $361,000 = 0.065 × $361,000 = $23,465

20% of $23,465 = 0.2 × $23,425 = $4,693

Answer:

14t

Step-by-step explanation:

the answer is 14t hope this helps

Answer:

There are 12 boys at the movie.

Step-by-step explanation:

Key skills needed in order to solve: Proportions, Ratios, and Multiplication

1) The ratio is 4 boys : 5 girls --> It can be written as a fraction --> 4/5

2) If there are 15 girls, we need to find the number of boys. let's say x is the number of boys when there are 15 girls. The ratio would then be x/15

3) Make a proportion --> \(\frac{4}{5}\) = \(\frac{x}{15}\)

You have to cross multiply here. You do the first fraction's numerator times the second fraction's denominator, and the first fraction's denominator times the second fraction's numerator.

4) This means you have to do: 4(15) = 5(x)

5) Multiply it out --> 60=5x

6) Divide by 5 and you will get x=12

Therefore there are 12 boys at the movie.

Hope you understand and have a nice day!! :D

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

25

Step-by-step explanation:

Answer:

8.5 × 10-5

Step-by-step explanation:

moving decimal place -5 times

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

D

Step-by-step explanation:

the y-intercept is nothing else than the y-value when x = 0 (the point where the graph intersects the y-axis, which is the vertical line at x=0).

for x = 0 we need to use the middle definition

f(x) = -x + 1

because -2 <= x < 3, and that is the interval, where we find 0 (larger than -2 and smaller than 3).

so,

f(0) = -0 + 1 = 1

so, D is the correct answer

Answer:

The motorist's rate is:

rate = distance / time

where distance is measured in kilometers and time is measured in hours.

We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:

rate = distance / time = 228 km / 6 hours = 38 km/hour

To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:

time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours

Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.

Answer:

\(116^o\)

Step-by-step explanation:

All triangles equal \(180^o\). Therefore, in order to find the value of \(x^o\), all you will have to do is subtract \(64^o\) from \(180^o\).

\(180^o-64^o=116^o\)

\(x^o=116^o\)

9514 1404 393

Answer:

  3t -4

Step-by-step explanation:

If t represents their normal travel time (in hours), Anna and Tamara traveled 2t on the third day, and t-4 on the fourth day.

The number of hour traveled in the last two days (day 3 and day 4) are ...

  2t +(t-4) = 3t-4

Dimension of smaller garden :

l = 1/2 ft.

b = 2/3 ft.

Dimension of bigger garden :

L = 4 ft.

Let , breadth be x ft.

We know , area is given by :

Area = L×B.

Area of small garden = \(\dfrac{1}{2}\times\dfrac{2}{3}=\dfrac{1}{3}\ ft^2\)

Area of big garden \(=4\times x=4x\ ft^2\)

Hence, this is the required solution.