What is the equation of the line that is perpendicular to
the given line and has an x-intercept of 6?
O y = -x + 8
O y = -x + 6
Oy=x-8
Oy=x-6

The function rule for f⁻¹ is f⁻¹(y)=(x/4)+4. And, the function rule for g⁻¹ is g⁻¹(v)=(4u-65)/2.

The inverse function is defined as the function that is considered "undo" or reverse of another function. For example, let us consider a function to be f. Then, the inverse function is written as f⁻¹.

a) Given f(x)=4x-16. Let's consider y=f(x)=4x-16. Then,

y=4x-16

4x=y+16

x=(y+16)/4

=(y/4)+4

To find the inverse function, then put x=y, we get,

f⁻¹(y)=(x/4)+4

b) Given g(u)=(2u+9)/4+14. Let g(u)=v=(2u+9)/4+14. Then,

v-14=(2u+9)/4

2u+9=4v-56

2u=4v-65

u=(4v-65)/2

To find the inverse function, then put u=v, we get,

g⁻¹(v)=(4u-65)/2

The required answers are f⁻¹(y)=(x/4)+4 and g⁻¹(v)=(4u-65)/2.

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The complete question is -

a. Given that f(a) = 4x-16 where f(x) = y, define a function rule for f⁻¹.

f⁻¹(y) =

b. Given that g(u) = (2u + 9)/4 +14 where g(u) = v, define a function rule for g⁻¹.

g⁻¹(v) =

Answer:

C: ST

Step-by-step explanation:

Perpendicular Lines

The four points R(-5, 3), S(-5, 4), T(-3, 4), and U(-3, 1) are shown in the image attached below.

The vertical line TU is also shown. The only possible line perpendicular to TU is ST because it's a horizontal line.

Horizontal lines have a slope of 0. Let's verify the slope between points S(-5,4) and T(-3,4):

\(\displaystyle m=\frac{4-4}{-3+5}=\frac{0}{2}=0\)

Once verified, the answer is C: ST

Answer:

  (x +5)(x +6)

Step-by-step explanation:

You're looking for two factors of 30 that total 11.

  30 = 1×30 = 2×15 = 3×10 = 5×6

5+6 = 11, so those are the numbers you want in the binomial factors.

  x^2 +11x +30 = (x +5)(x +6)

_____

Additional comment

You will notice that ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

The constant is the product of the factor constants, and the x-coefficient is their sum.

The percentage of value-added time in a trip to the emergency room is 15.83%.

Given the following data:

Time taken by triage nurse before assessment = 14 minutes

Average time taken for assessment by triage nurse = 5 minutes

Time taken before examination room = 79 minutes

Time taken in the examination room for vitals and notes by nurse = 11 minutes

Time taken before the doctor sees the patient = 22 minutes

Average time taken by the doctor for treatment = 17 minutes

Time taken for the nurse to come to discuss post-treatment instructions = 6 minutes

Time taken to review the instructions with the patient = 4 minutes

Let us first calculate the total time taken,

Total Time = Time before examination room + time in examination room + time after treatment + time taken by the triage nurse

Total Time = 79 + 11 + 22 + 17 + 6 + 4

                  = 139 minutes

Now, let us calculate the total time spent on assessment and treatment.

This will include the time taken by the triage nurse and the doctor.

Total Time Spent on Assessment and Treatment = Time taken by triage nurse + time taken by the doctor

Total Time Spent on Assessment and Treatment = 5 + 17

                                                                                  = 22 minutes

Now, we can calculate the percentage of value-added time as follows,

Percentage of Value-Added Time = Total Time Spent on Assessment and Treatment / Total Time * 100

Percentage of Value-Added Time = 22 / 139 * 100

Percentage of Value-Added Time = 15.83%

Therefore, the percentage of value-added time in a trip to the emergency room is 15.83%.

Rounding off this value to 2 decimal places, we get the final answer as 15.83%.

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Answer:

V = 13 65⁄72 ft3

Step-by-step explanation:

V = 13⁄4 ft × 7⁄3 ft × 11⁄6 ft

V = 1,001⁄72 ft3

V = 13 65⁄72 ft3

61 is the sum of two consecutive integers (-6,-5 ) and (5,6).

According to Pierr De Fermat any whole number writteen as the sum of four or less square numbers.

So 61 is the whole number so we can write in the sum of squares,

Now we know even+odd=odd so that let a and a+1 integer , according to Pierr De Fermat we can write,

a²+(a+1)²=61;

⇒a²+a²+2a+1=61

⇒2a²+2a-60=0

⇒a²+a-30=0 (∵divided by 2)

⇒a²+6a-5a-30=0

⇒a(a+6)-5(a+6)=0

⇒(a+6)(a-5)=0

⇒a+6=0 or a-5=0 ⇒a=-6 or a=5

If a=-6 then a+1=-6+1=-5.

if a=5 then a+1=5+1= 6.

so 61= (-6)²+(-5)² and 61= 6²+5².

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Answer:

5/18

Step-by-step explanation:

540/9=60

60x4=240(Alvin's money)

60x5=300(simon's money)

Alvin gives half so you divide 240 by 2 which is 120

Simon gives a tenth so you divide 300 by ten which is 30

120+30=150

150/540=5/18 ( simpliest form)

Theo have 5/18 fraction of total amount of money.

Given that, Alvin and Simon shared £540 in the ratio 4:5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Now, 4+5=9

So, share of Alvin = 4/9 × 540

= 4 × 60

= £240

Then Simon share = 540-240 = £300

Theo's share = 1/2 × 240

=£120

Theo's share 1/10 of 300

=1/10 × 300

=£30

Total Theo's share = 120+30 =£150

Now, fraction = 150/540

=5/18

Therefore, Theo have 5/18 fraction of total amount of money.

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For one course, there will be at least 10 students.

Given,

The number of students enrolling for a course = 37

Number of courses = 4

We have to find the number of minimum students will be at least for one course;

Here,

Number of students can be divided by number of courses = Anticipated Number of students enrolled for one course

That is,

37 / 4 = 9.25 ≈ 10

Therefore,

There will be 10 minimum students at least for one course.

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Answer:

Rational Numbers.

Step-by-step explanation:

Rational numbers ( these can be written as a/v where a and b are integers, b not 0)

Answer:

x + 2 + 3x = 30

Step-by-step explanation:

Both lengths are unknown, but Ginny's car length is described in terms of Zach's car length, so we choose a variable for Zach's car length.

Let x = Zach's car length.

Zach's car length is x.

"Ginny's car is 2 more than 3 times the length of Zach's car."

Ginny's car length is 2 + 3x.

Add the lengths:

x + 2 + 3x

"The sum of the lengths of both cars is 30 inches."

x + 2 + 3x = 30

Answer: x + 2 + 3x = 30

Step-by-step explanation:

x² - 4x + 6 = x + 2

x² - 5x + 4 = 0

(x - 4)(x - 1) = 0

Therefore x = 4 or x = 1.

Answer:

IK = 20

Step-by-step explanation:

If Point J is on the line segment IK, then;

IK = IJ + JK

Given that

IJ = 4

IK = 5x

JK = 4x

Substitute into the expression

5x = 4 + 4x

5x - 4x  = 4

x = 4

Get the value of IK

IK = 5x

IK = 5(4)

IK = 20

Hence the numerical length of IK is 20

Answer:

x=8 y=4

Step-by-step explanation:

eliminate x: make x of two equation equal to each other

2(-3x+9y=12) : -6x+18y=24 ___[1]

-3(2x-8y=-16) : -6x+24y=48 ___[2]

[2]-[1]= 6y=24

substitute y to any equation;

2x-8y=-16

2x-8(4)= -16

2x= -16+32

2x= 16

Answer:

x=14 and y=6

Step-by-step explanation:

-3x+9y=12.............(i)×2

2x-8y=-16..............(ii)×3

Multiplying equation (i) by 2 and equation (ii) by 3 and adding (i) and (ii)

-6x+18y=12

6x-24y=-48

-----------------

0-6y=-36

or, -6y=-36

So,y=6

From (i)

-3x+9y=12

or,-3x+9×6=12

or,-3x+54=12

or,-3x=12-54

or,-3x=-42

So,x=14

The measures of position that divide a set of data into four equal parts are called quartiles.

Quartiles are statistical measures that divide a dataset into four equal parts, each containing approximately 25% of the data. These quartiles are denoted as Q1, Q2, and Q3.

Q1, also known as the first quartile or the 25th percentile, represents the value below which 25% of the data falls. It splits the lowest 25% of the dataset from the rest.

Q2, also known as the second quartile or the 50th percentile, is the median of the dataset. It represents the value below which 50% of the data falls, dividing the dataset into two equal parts.

Q3, also known as the third quartile or the 75th percentile, represents the value below which 75% of the data falls. It separates the highest 25% of the dataset from the rest.

These quartiles are useful in analyzing the distribution and dispersion of data, providing insights into the spread and central tendency.

They are commonly used in box plots, where the box represents the interquartile range (IQR), which is the range between Q1 and Q3, while the line inside the box represents the median (Q2).

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It will take Aidan approximately 9.70 years to save enough to buy the $29,000 speed boat.

To calculate the time it will take for Aidan to save enough for the speed boat, we can use the formula for compound interest. The formula is given by:

\(Future Value = Present Value * (1 + interest rate)^{(number of periods)}\)

In this case, Aidan currently has $2,600 saved, and he saves an additional $205 per month. The future value (FV) is $29,000, and the interest rate (r) is 1.7% per year. We need to find the number of periods (t) in years. Rearranging the formula, we get:

t = log(FV / PV) / log(1 + r)

Plugging in the values, we have:

t = log((29000 - 2600) / 205) / log(1 + 0.017)

≈ 9.70 years

Therefore, it will take Aidan approximately 9.70 years to save enough to buy the $29,000 speed boat.

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Answer:

\(Area = 24.8 cm^2\)

Step-by-step explanation:

Given

\(PQ = 4.9cm\)

\(RQ = 11 cm\)

\(<Q = 113\ degrees\)

Required

Find the area of the triangle

When presented with a triangle where two sides are known and an angle between the two sides; The area is solved as follows;

\(Area = \frac{1}{2}ABSinC\)

Where A and B are the two known sides and C is the angle between A and B

Having said that;

The area of the triangle is calculated as thus;

\(Area = \frac{1}{2} * RQ * PQ * SinQ\)

\(Area = \frac{1}{2} * 11 * 4.9 * Sin113\)

\(Sin113 = 0.9205\)

Hence, the equation becomes

\(Area = \frac{1}{2} * 11 * 4.9 * 0.9205\)

\(Area = \frac{11 * 4.9 * 0.9205}{2}\)

\(Area = \frac{49.6152}{2}\)

\(Area = 24.8076\)

\(Area = 24.8 cm^2\) --- Approximated

Answer:

a. El auto pesado ganará, ya que debido a su mayor masa tendrá una mayor fuerza de arrastre.

b. El auto ligero se detendrá en menos tiempo, debido a que su masa es menor, lo cual significa que tendrá una menor resistencia al movimiento.

Step-by-step explanation:

\(\text{Given that,}\\\\f(x) = 7x^2\\\\f'(x) = 7\cdot 2 x = 14x\\\\\text{At x = 12,}\\\\f'(12) = 14 \times 12 = 168\)

Graphing equations is a precious device in arithmetic and records evaluation. By plotting points and connecting them, we will visualize the behavior of features and identify key functions which include intercepts, local extreme factors, and inflection points.

I can manually you through the system of graphing the equation and identifying the essential factors.

To graph the equation y = \(2x^3 - 12x^2 + 18x\), you may comply with the steps:

Determine the dimensions you want to use for every axis. Choose appropriate values that assist you in clearly representing the characteristic's behavior.

Plot points on the graph by way of substituting unique x-values into the equation and calculating the corresponding y-values. Make positive to include enough points to appropriately represent the shape of the characteristic.

Connect the plotted factors to create an easy curve that represents the graph of the equation.

To become aware of the crucial points (local extreme factors and inflection factors), you'll need to apply calculus strategies:

Find the derivative of the equation with admire to x. The derivative will come up with the slope of the function at any given factor.

Set the by-product equal to zero and remedy for x to find the essential factors in which the slope is 0 or undefined.

Use the second spinoff to take a look to determine whether or not each critical factor is a nearby maximum, neighborhood minimal, or inflection factor. Evaluate the second spinoff at each important point.

Once you have discovered the critical points, you could decide their corresponding y-values with the aid of substituting the x-values into the unique equation.

Please comply with those steps and use suitable equipment to graph the equation and decide the essential factors.

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Answer:

9 hours.

Step-by-step explanation:

31 + 5.9*t < 84.10.

To solve it, collect the constant terms on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10%2F5.9 = 9 hours.

Answer:

7 hours

Step-by-step explanation:

99.10-34=65.1

65.1 divide by 9.30=7

Hope this helps!!

Answer:

0.128

Step-by-step explanation:

The emphasis is on the Counting and Cardinality standard in the early childhood years according to the National Council of Teachers of Mathematics.

The National Council of Teachers of Mathematics emphasizes the following standards in the early childhood years:

- Counting and Cardinality

- Operations and Algebraic Thinking

- Number and Operations in Base Ten

- Measurement and Data

- Geometry

The National Council of Teachers of Mathematics recognizes that all five math standards are important in the early childhood years. However, they place a particular emphasis on the standards related to counting and cardinality. This includes developing skills in counting, understanding numbers, and recognizing numerical relationships.

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Answer:

3

Step-by-step explanation:

Answer:Computer Store sells DVDs for a day =    110

No. of days the store works                 =    266

No. of DVDs saled in 266 days          =    266 days  x   110DVDs

                                                             =    29,260 DVDs

Step-by-step explanation:

The maximum area that the 60 m can enclose is 225m², the dimensions of the maximal region are 15m x 15m, and the height as an fcn of the base is 30 - b.

Let the base of the rectangular region be "b",

and the height be "h" and,

it is given that the perimeter of the rectangular region = 60m

(a) write height as an fcn of base

by using the formula of the perimeter of a rectangle,

2(h+b) = 60m

we can write, h = 30 - b

⇒Area of the rectangular region

area(A) = height × base

substituting the value of h.

= (30 - b) × b

thus, A(b)= 30b - b²

to find the maximum area that the 60 m can enclose

\(\frac{dA(b)}{db}\) should be equal to 0.

substituting the value of A(b).

30 - 2b = 0

thus, b = 15

maximum area = 30b - b²

substituting the value of b.

= (30 × 15) - 15²

thus, maximum area = 225m².

dimensions of the maximum region,

for maximum area height = base = 15m

thus, the dimensions of the maximum rectangular region are 15m x 15m.

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Answer:

a

Step-by-step explanation:

8+(-8)+a=?

8-8+a=0+a=a

Answer:

0

Step-by-step explanation:

8 + ( - 8 ) + a

= 8 - 8 + a

= 0 + a

= a

a = 0

The value of x from the given expression is 5/6

Given the expression to expand expressed as:

15 = 3/5(6x + 20)

We are to determine the value of x

15(5) = 3(6x + 20)

Expand

75 = 18x +60

Collect like terms

18x = 75 - 60

18x = 15

x = 15/18

x = 5/6

Hence the value of x from the given expression is 5/6

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