a straight line passes through the point P(-1,5). Another line which passes through Q(-4,4) intersects the first line at point R( µ,5) where µ is a constant . If <PRQ = 90° find the value of R​

The rate of change of the given function is -1/2.

       [tex]$r(a) = {\frac {f(x+h)-f(x)}{h}}\\\\[/tex]

       [tex]$r(i) =\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}\end{aligned}}}[/tex]

Given is the function as follows -

y = - 12 - (1/2)x

We have the function f(x) as -

y = - 12 - (1/2)x

dy/dx = d/dx(12 - x/2)

dy/dx = 0 - 1/2

dy/dx = -1/2

Therefore, the rate of change of the given function is -1/2.

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Answer:

Step-by-step explanation:

1 times 28

2 times 14

4 times 7

7 times 4

14 times 2

28 times 1

Answer:quantitative

Step-by-step explanation:

Answer: 5,850

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf Mean = \$ \ 5850}[/tex]

Step-by-step explanation:

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data}[/tex]

Here,

Data: $7500, $6500, $5750, $4900, $6250, $4200

So,

[tex]\displaystyle Mean =\frac{Sum \ of \ all \ prices }{No. \ of \ prices} \\\\Mean =\frac{7500+6500+5750+4900+6250+4200}{6} \\\\Mean = \frac{35100}{6} \\\\Mean = \$ \ 5850\\\\\rule[225]{225}{2}[/tex]

17. (f-g)(x) = ( -x + 2x - 6 ) - ( -x + 5 ) = -2x + 11

18. (fg)(x) = ( -x - 9 )( x + 1 ) = -x² - x - 9

19. (f g)(x) = f(g(x)) = (x + 2x - 6)(-x + 5) = -x² + 6x - 30

20. (g o f)(x) = g(f(x)) = x + 5(x + 2x - 6) = x + 5x + 10x - 30

21. Domain: All real numbers

22. Domain: All real numbers

23. Range: Not given

24. Range: {6}

25. Range: All real numbers

26. Range: Not given

Specifically, it provides the difference, product, and composition of the given functions, as well as the domain and range of certain functions. The problems involve algebraic equations and simplifying expressions.

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Answer: True

Step-by-step explanation:

Answer:

|t - 101| ≤ 1.5

Step-by-step explanation:

The correct inequality to determine the range of body temperature for an adult dog is |t - 101| ≤ 1.5. This inequality states that the body temperature t can be as much as 1.5 degrees less than or 1.5 degrees more than 101 degrees Fahrenheit.

The graphing form of the function is,

⇒ (x - 8)² + (y + 5)² = 9²

And, The center of function = (8, - 5)

The radius of the function is,

⇒ r = 9

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ x² + y² - 16x + 10y + 8 = 0

Now,

Since, The function is,

⇒ x² + y² - 16x + 10y + 8 = 0

We can write as;

⇒ x² - 2 × 8 × x + y² + 2 × 5 × y + 8 = 0

⇒ x² - 2×8×x + 64 - 64 + y² + 2×5×y + 25 - 25 + 8 = 0

⇒ (x² - 2×8×x + 64) + (y² + 2×5×y + 25) - 64 - 25 + 8 = 0

⇒ (x - 8)² + (y + 5)² = 81

⇒ (x - 8)² + (y + 5)² = 9²

Thus, The graphing form of the function is,

⇒ (x - 8)² + (y + 5)² = 9²

Clearly, This represent the equation of circle with center (8, - 5) and radius 9.

And, The center of function = (8, - 5)

The radius of the function is,

⇒ r = 9

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A recursive algorithm to find a^2n, where a is a real number and n is a positive integer, is as follows:

This algorithm uses the property of exponentiation that a^(2n) = (a^n)^2, and divides the problem of finding a^2n into a smaller subproblem of finding a^n. It takes advantage of the recursive nature of the problem by calling the same algorithm with a smaller value of n.

The time complexity of this algorithm is O(log n) as it divides the problem into half at each recursive step.

It should be noticed that this algorithm assumes that the input value of n is positive, otherwise it would be necessary to add a check for a negative value or zero.

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Answer:

7704 R 2

Step-by-step explanation:

61634/8 = 7704.25

7704.25 = 7704 + 0.25  ==>

In order to find the remainder value, multiply 8 with 0.25:

8 * 0.25 = 2

Hence, the quotient is 7704 and the remainder is 2.

7704 R 2

The two numbers which are 14 and -5 give you -70 when multiplied but when added give you 9

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

Let x and y represent the unknown numbers

The two numbers give -70 when multiplied, hence:

xy = -70   (1)

The two numbers give 9 when added, hence:

x + y = 9   (2)

x = 9 - y

put x = 9 - y in equation 1:

(9 - y)y = -70

9y - y² = -70

y² - 9y - 70 = 0

y = -5 or 14

when y = -5; x = 9 - (-5) = 14

when y = 14; x = 9 - 14 = -5

The two numbers are 14 and -5

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equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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Answer: E' (2,6) F' (2,-2) G' (-5,-3)

Step-by-step explanation: To find the coordinates flipped over the y-axis the rule goes from (x,y) to (-x,y) *Just a reminder the negative sign doesn't necessarily mean negative. It just means the opposite sign, so negative numbers would turn positive.

The number of miles each car travels in 1 hour is 16 1/4 miles

From the question, we have the following parameters that can be used in our computation:

Given rate. 97 1/2 miles in 3/2 hours

The number of miles each car travels in 1 hour can be calculated as

Number of miles = 97 1/2 miles/3/2 hours * 1 hour

This gives

Number of miles = 97 1/2 miles/3/2

Evaluate the quotient

So, we have the following representation

Number of miles = 16 1/4 miles

Hence, the number of miles is 16 1/4 miles

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The system of equations that models the given situation are;

y = 10x + 35

y = 5x + 35

Let x denote the number of years since 2010

Let y denote the total members

The linear equation in slope intercept form is expressed as;

y = mx + b

where;

m is the slope or unit rate

b is the y-intercept or initial value

For the swim team, since  the team increased by an average of 10 members per year, then;

Slope = 10

In 2010, they had 5 members and so; y-intercept = 35

Thus, the equation is; y = 10x + 35

For the chorus team, we can deduce that;

Slope = 5 members per year

In 2010, they had 35 members and so; y-intercept = 35

Thus, the equation is; y = 5x + 35

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Complete question is;

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.

Answer:

g( [tex]\frac{3}{2}[/tex] ) = - [tex]\frac{35}{4}[/tex]

Step-by-step explanation:

substitute x = [tex]\frac{3}{2}[/tex] into g(x) , that is

g( [tex]\frac{3}{2}[/tex] )

= - 2( [tex]\frac{3}{2}[/tex] )³ - [tex]\frac{4}{3}[/tex] × [tex]\frac{3}{2}[/tex]

= - 2 × [tex]\frac{27}{8}[/tex] - 2

= = - [tex]\frac{27}{4}[/tex] - [tex]\frac{8}{4}[/tex]

= - [tex]\frac{35}{4}[/tex]

The amount of spacing needed to allow for expansion is 0.09 m

Length is the distance between two point.

To calculate the amount of spacing needed to allow for expansion, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1

Hence, the amount of spacing is 0.09 m.

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By using the given scale, we will find that the real distance between the two cities is 144 miles.

We know that in our map the scale is:

1/2 inch = 18 miles.

If we multiply that by 2 we get:

2*(1/2) inch = 2*18 miles.

1 inch = 36 miles

Now, if the distance in the map is 4 inches, then we need to multiply that by the scale:

4 inches = 4*( 1 inch) = 4*( 36 miles) = 144 miles.

The real distance is 144 miles.

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The correct option representing the function is f(t) = 30,303(0.85)t based on the deprivation rate.

Firstly calculating the depreciation rate -

30,303 - x%×30,303 = 25,757

x×303.03 = 30,303 - 25,757

Performing subtraction on Right Hand Side of the equation

x×303.03 = 4546

x = 4546/303.03

Performing division

x = 15%

The formula to be used for function is -

P = Po[tex] {(1+r)}^{t} [/tex], where P is the final value, Po is the original value, r is growth rate and t is time.

P = 30,303 [tex] {(1 - 0.15)}^{t} [/tex]

Performing subtraction on Right Hand Side of the equation

P = 30,303 [tex] {(0.85)}^{t} [/tex]

The value of car after t years is 30,303 [tex] {(0.85)}^{t} [/tex].

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The complete question is-

Jane bought a car for $30,303. The value of the car depreciated at a constant rate per year. The table below shows the value of the car after the first and second years:

Year 1 2

Value (in dollars) 25,757.55 21,893.92

Which function best represents the value of the car after t years?

f(t) = 25,757.55(0.85)t

f(t) = 30,303(0.85)t

f(t) = 30,303 (0.15)t

f(t) = 25,757.55 (0.15)t

Answer: £18704.32.

Step-by-step explanation:

To increase a value by a certain percentage, you can use the formula:

New value = Original value + (Original value x (Percentage increase/100))

In this case, to increase £16470.45 by 13.5%:

New value = 16470.45 + (16470.45 x (13.5/100))

New value = 16470.45 + 2233.8675

New value = 18704.3175

Rounded to 2 decimal places, the new value would be £18704.32.

Answer:

18704.32

Step-by-step explanation:

The down payment for the installment purchase for the $900 refrigerator is $300.

An installment purchase is a method of buying high value assets or goods on credit. A percentage of the total purchase price is paid immediately as a down payment, while the remaining amount is settled by paying periodic installments.

the good to be paid for installment after a down payment of 1/3 of the total amount is a refrigerator which cost $900

1/3 of $900 = 1/3 × $900

1/3 of $900 = $900/3

1/3 of $900 = $300

In conclusion, $300 will be the down payment for the installment purchase of the refrigerator.

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Each individual outcome of an experiment is called a sample point. So, the right answer is option(b).

The set of all possible outcomes of a random experiment is the sample space , S or the outcome space. An event always associated with a random experiment is a subset of the sample space. Each result in sample space is called a sample point. Also, it is called an element or member of the sample space. For example, there are possible two outcomes for tossing a coin, i.e., the sample space, S = {heads, tails}, or S = {H, T}. If we toss two coins, there are four outcomes : { HH, HT, TH , TT }, where the first letter refers to the outcome of the first tossing and the second to that of the second tossing, each outcome is called a sample point.

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Answer:

never

Step-by-step explanation:

because The union of a and b cannot be equal to the intersection of a and b

Step-by-step explanation:

In 8 hours temperature different is 20

so average rate is=20/8

2.5

Answer: $24

Step-by-step explanation: There were 4 people splitting the bill You, Ben, Carla, and David the bill was 96

divide 96 by four so that  you each pay the same amount

96 divided by 4 is 24 so everyone payed $24

24+24+24+24 equals 96 so it is the correct answer

On solving the provided question we can say that 1/4 means , 1 divides 4, so it its a division not expression.

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

darius says that 1/4 is a division expression

Badru says that 1/4 is a division

1/4 means , 1 divides 4, so it its a division not expression

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Answer:

B

Step-by-step explanation:

There are 6 roads connecting from a to b. You need to go to b, get back to a, and go back to b. There are 360 ways to complete this task.

Generally, If you need to go from a to b and back to a twice, you can think of this as going from a to b and back to a, and then from a to b and back to an again, without returning to b in between.

This means that you need to use two different roads for the first trip and two different roads for the second trip.

Since there are 6 roads to choose from, and you need to choose 2 roads for the first trip and 2 roads for the second trip, the total number of ways you can do this is

6 * 5 * 4 * 3 = 360ways

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Answer:

Step-by-step explanation:

Answer:

(8,000/10)=800