Which functions show a negative rate of change?

Georgia  takes 24 minutes to clean the espresso machine by herself.

The correct answer is an option D.

The equation for the situation is:

[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}[/tex]

here, x is the number of minutes it takes Georgia to clean the machine by herself.

We need to find the value of x.

Consider the equation,

[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}[/tex]

(2x - 12) × 8 = x² - 12x

16x - 96 =  x² - 12x

x² - 12x -16x + 96 = 0

x² - 28x + 96 = 0

x²-24x-4x+96 = 0

(x - 24)(x - 4) = 0

x = 24 or x = 4

If x = 4, then x - 12 would be negative which is not possible.

Thus, it takes 24 minutes for Georgia.

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Find the complete question below.

According to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.

For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.

In option A:

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

The horizontal asymptote is none.

The vertical asymptote is -1 and 3.

Hence, this is the correct option.

Option B:

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

The horizontal asymptote is 0.

The vertical asymptote is 2, -1 , and 3.

Hence, option B is incorrect.

Option C:

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

The horizontal asymptote is none.

The vertical asymptote is 1 and -3.

Hence, option C is incorrect.

Hence, according to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

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Answer:

y =  [tex]\frac{1}{3}[/tex]x + 6

Step-by-step explanation:

The equation we currently have right now is y = -3x+2. Since we know that the line equation is y = mx + b, let's take out m to find the slope of a perpendicular line. M will be -3.

To convert a regular slope to a perpendicular one, we have to:

- reciprocal/flip it (this means that if m = 3, the perpendicular will be [tex]\frac{1}{3}[/tex])

- swap the signs (this will mean that if a number is positive, then it will become negative)

Therefore, if m = -3, the perpendicular slope will be [tex]\frac{1}{3}[/tex] (we flipped and changed signs)

Now, we are also given that this line passes through the point (6,8), so we can use this formula: [tex]y - y1 = m(x-x1)[/tex]

What do we know right now?

- y1 = 8 (from (6,8))

- x1 = 6 (from (6,8))

- m =  [tex]\frac{1}{3}[/tex]

Let's plug in what we know:

y - 8 =  [tex]\frac{1}{3}[/tex](x - 6)

y =  [tex]\frac{1}{3}[/tex](x-6) + 8

y =  [tex]\frac{1}{3}[/tex]x - 2 + 8

y =  [tex]\frac{1}{3}[/tex]x + 6

As, a = -49 is a negative number, so there is no real root for the integer.

What is square root?

A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.

The expression is given as - a = -49

The value for n is n = 2

Find the nth root value for the expression a.

Since a = -49 is a negative number there is no real square root for the number.

If it would have been a = 49, then there would have been one real square root.

n=2 which generates √49.

This gives the value as 7.

Therefore, there are no roots for -49.

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The scale factor of the dilation is equal to: B. 5.

In Geometry, a scale factor simply refers to the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor with respect to the origin is given by this mathematical expression:

(x, y)      →    (SFx, SFy)

Where:

Scale factor = 15/3 = -25/-5

Scale factor = 5.

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As per the given equation, the percentage of the whole chart that is yellow is 15%.

One quarter of the pie chart is blue, which is 25%.

15% of the pie chart is orange.

When we add the percentages of blue and orange sections, we get 25% + 15% = 40%. So, 40% of the pie chart is blue or orange.

As the other two sections, Yellow and Grey, are equal in size, we can assume that they make up half of the remaining 60% of the pie chart. So each of the Yellow and Grey sections make up 30%/2 = 15% of the pie chart.

Therefore, the percentage of the whole chart that is yellow is 15%.

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Answer:

16.6666666666667%

Step-by-step explanation:

17/102 = x/100

17*100/102 = x

x = 16.66666667

Answer:

The percent is:

16.667%

Step-by-step explanation:

17 / 102 = 0.16667

0.16667 * 100 = 16.667%

The required average speed of the train is calculated to be 60 mph, when the train travels certain distance and stops.  

Distance between station A and station B is given as 120 miles.

A train traveling from station A to station B travels exactly 1/3rd of the distance when it is held up and stops for 16 minutes.

Let, its average speed was x mph.

Then, total time taken if it didn't stop = 120/x h

Now, before stop it took time = ( 1/3 × 120)/x h = (40/x) h

After stop the time it took = 80/(x + 15) h

i.e, 40/x + 16/60 + 80/(x+15) = 120/x  

⇒ 80/(x + 15) + 8/30 = 80/x

⇒ 80(1/x - 1/(x + 15)) = 8/30

⇒ 10 × (15/x² + 15x) = 1/30

⇒ x² + 15x = 10 × 15 × 30

⇒ x² +15x - 450 = 0

⇒ x² +75x -60x - 450 = 0

⇒ (x+75)(x-60) = 0

⇒ x = 60 or, x = -75

As speed cannot be negative, the average speed is 60 mph.

The given question is incomplete. The complete question is 'Find the average speed of the train before it stopped for 16 minutes.'

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The rate of change of the function is: 2.

The y-intercept/initial value is: 3.

The rate of change is also the slope of a function, which is calculated as, m = change in y / change in x.

Given the points, (0, 3) and (2, 7):

Rate of change/slope (m) = (7 - 3) / (2 - 0)

m = 4/2

m = 2

To find the initial value/y-intercept (b), substitute m = 2 and (x, y) = (0, 3) into y = mx + b:

3 = 2(0) + b

3 = 0 + b

3 = b

b = 3

y-intercept = 3.

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The insect's length as seen via a microscope is found to be 56 millimeters.

For the stated question:

Then,

body length (under microscope) = 7*8 millimeters

body length (under microscope) = 56 millimeters

Thus, the insect's length as seen via a microscope is found to be 56 millimeters.

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Answer:

X = C - B

--------

A

Step-by-step explanation:

Solving for X is pretty much getting X alone on one side of the equal sign. That's when we would do the "opposite" of what the original equation is showing. And we do that to both sides.

For example, we see +b. The opposite of addition is subtraction, so we do just that. We do -b on BOTH sides of the equal sign. b -b = 0. It cancels it out. c-b is just as it says. So now we have ax = c-b.

Now we see ax are right next to each other with no symbol, which means they are being multiplied. The opposite of multiplication is division. So we'll do that exactly. We will divide A on both sides. ax/a gets rid of that a and leaves the x alone. Dividing c-b/a gives you just that, making the answer X = C-B/A

In quadrilateral ABCD, m∠C = 70°.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given:

ABCD is a quadrilateral.

m∠A =80°, m∠B = 100° and m∠D = 110°.

The sum of all the interior angles is 360°.

m∠A + m∠B + m∠C + m∠D = 360°.

80 + 100 + 110 + m∠C = 360

m∠C = 360 - 290

m∠C = 70°

Therefore, m∠C = 70°

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Step-by-step explanation:

In a quadrilateral, the sum of the measures of the angles is 360 degrees. Therefore, if we know the measures of three of the angles in a quadrilateral, we can use this information to find the measure of the fourth angle.

In this case, we know that:

m(<A) = 80 degrees

m(<B) = 100 degrees

m(<D) = 110 degrees

So, to find m(<C), we can use the equation:

m(<A) + m(<B) + m(<C) + m(<D) = 360

Substituting in the known values, we get:

80 + 100 + m(<C) + 110 = 360

Solving for m(<C), we get:

m(<C) = 360 - (80 + 100 + 110) = 360 - 290 = 70 degrees

So the measure of angle C is 70 degrees.

Answer:

$152

Step-by-step explanation:

160*.95 = 152

Answer:

Step-by-step explanation:

from the first ... 3y = 3x + 12 or

y = x + 4

This is the same as the second, so D

The y-intercept of the linear function 11x - 10y = 2 is given as follows:

y = -1/5.

The function for this problem is defined as follows:

11x - 10y = 2.

The y-intercept of a function is given by the value assumed by y when x assumes a value of 0.

Considering it's concept, the y-intercept of the function in this problem is obtained as follows:

-10y = 2

10y = -2

y = -2/10

y = -1/5.

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The amount for each berry are 5.60 and 1.60 respectively.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

Given that, Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60,

We will set a system of linear equations, to solve this,

Establishing the equation,

Let the amount of raspberries be x and that of blueberries be y,

x + y = 6

y = 6-x...(i)

2x + y = 11.60

y = 11.60 - 2x...(ii)

Equating eq(i) and eq(ii)

6-x = 11.60 -2x

x = 5.60

Put x = 5.60 in eq(i)

y = 6-5.60

y = 1.60

Hence, the amount for each berry are 5.60 and 1.60 respectively.

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Answer:

see below.

Step-by-step explanation:

1. g(x) = 2^(x-5) +3

2. g(x)= 1/3 * 2^x

3. f(x) was vertically stretched by 3.  K value is 3.  The Y intercept became augmented by 3 folds.

4. k value = 5, the curve basically got "lifted" up by 5 units.

The estimated weight of three containers weighing 1. 656 kg each =  5 kg

Let w represents the weight of each contaoner.

Here, each container weighs 1.656 kg

⇒ w = 1.656 kg

Here, the weight of all containers are the same.

To determine the estimated weight of three containers we us the Unitary method.

We simply multiply the given weight by the number of containers.

Let W be the estimated weight of three containers.

Using Unitary method,

W = 3 × w

W = 3 × 1.656

W = 4.968

W ≈ 5 kg

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Answer:

1 = 18

Step-by-step explanation:

The dimensions of the the garden are 8 x 12

What is Quadratic Equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).

A = l x w

l = 2w-4

A = w (2w-4)

A = 2w² -4w

96m² = 2w² - 4w

0 = 2w² - 4w - 96 divide both sides by 2

0 = w² - 2w -48

(w-8) ( w +6) = 0

w = 8 since it can't equal -6

length therefore = 2w-4 = 16-4 = 12

Hence, the dimensions of the garden are 8 x 12

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Full question:

A rectangular garden has a length that is 4 meters less than twice its width. Can you set up a quadratic equation to find the dimensions of the garden if its area is 96m^2?

      Statement                                                Given

1. X is the midpoint of VY              1. Given

2. WV ║ YZ                                     2. Given

3. VX = XY                                       3. X is midpoint

4. ∠WXY = ∠YXZ                            4. Corresponding Angle Theorem

5. ∠WVX = ∠XYZ                            5. Vertical Angle Theorem

6. △YXZ = △VWZ                           6. AA Similarity

7. WV ≅ YZ                                      7. Prove

We know that WV ║ YZ, X is the midpoint of VY.

If X is the midpoint of VY. So VX = XY

The corresponding angles in the two regions of intersection are congruent when a line intersects two parallel lines.

From the Corresponding Angle Theorem

∠WXY = ∠YXZ

When two straight lines cross, the Vertical Angle Theorem states that they create two sets of linear pairings with congruent angles.

From the Vertical Angle Theorem

∠WVX = ∠XYZ

According to the AA similarity theorem, two triangles are similar if two of their triangles' triangles are congruent with two of their other triangles' angles.

By AA Similarity

△YXZ = △VWZ

Hence, WV ≅ YZ

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The complete question is given below:

The time it took for Devin to catch Antonio is given as follows:

50 seconds.

The position functions for each of Antonio and Devin can be modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

Antonio starts 50 meters in front of Devin, hence the functions, considering their velocities, are given as follows:

(these two equations compose the system of equations).

Devin will catch up to Antonio when:

D(x) = A(x).

Hence:

9x = 50 + 8x

x = 50 seconds.

(which is shown by the point of intersection of the graph).

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Answer:

[tex]\frac{2A}{h}[/tex] = b

Step-by-step explanation:

A = [tex]\frac{1}{2}[/tex] bh   Multiply both sides by [tex]\frac{2}{h}[/tex]

[tex]\frac{2}{h}[/tex]  x [tex]\frac{A}{1}[/tex] = [tex]\frac{2}{h}[/tex] x  [tex]\frac{h}{2}[/tex] x b

[tex]\frac{2A}{h}[/tex] = b

Answer:

Step-by-step explanation:

ok so with triangle sum theorem the equation we use for this is n-2•180 (n equals number of sides, for 3*180 is 540, 540-all non variable numbers leave us with 165, divide 165 by 13 and that’s your answer, if anything round. Please lmk if this is wrong

Answer:

Step-by-step explanation:

I DON'T KNOW

Answer:

see below

Step-by-step explanation:

h = 6

r = 8 ==> area = πr² = 3.14*8² = 3.14 *64 =201.0

top & bottom = 2*200.96 = 401.9

r=8 ==> perimeter = 2πr = 2*3.14 *8 = 16* 3.14 =50.2

lateral area = h*perimeter = 6*50.24 = 301.44

so it's about 100 sq inch less

The number of miles that Tyee will travel in 8 hours, given the speed is 216 miles

To find the number of miles that Tyree would drive in 8 hours, given the speed he is going, you first need to find the speed Tyree is going which is:

= Number of miles travelled / Number of hours

= 54 / 2

= 27 miles per hour

The number of miles that Tyree would travel in 8 hours is:

= Number of hours of travelling x Speed travelled

= 8 x 27

= 216 miles

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The explicit equation for this arithmetic sequence is: aₙ =  9 + (n-1)(-8).

An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,... The basic distinction of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

The formula for an arithmetic sequence is given as an=a1+(n1)d, where an a n is a broad term, a1 a 1 is the initial term, and d is the huge distinction. This is done in order to locate the general phrase in the list.

The general form of the explicit equation for an arithmetic sequence is:

an = a1 + (n-1)d

Given that the first term is 9 and the second term is 1,

d = a2 - a1 = 1 - 9 = -8

So the explicit equation for this arithmetic sequence is:

aₙ = 9 + (n-1)(-8)

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The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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