Titing Tunction Rune -3 -2 -1 3 2 1 7 ty A -2 1 2 3 g(x) X Determine the values of h and k in the equation of g(x). g(x)=√√x-h+k​

Answer:

Step-by-step explanation:

we will find the first angle in the larger triangle;

180⁰-60⁰= 120⁰

120⁰

the second angle will be;

120⁰+30⁰=150⁰

180⁰-150⁰=30⁰

30⁰ this means that the second triangle is isosceles triangle, when we find the hypotenuse of the smaller triangle it will be equal to x since the sides are equal

88/sin60⁰=x/sin90⁰

88sin 90⁰=xsin60⁰

88/0.8660=0.8660x/0.8660

x=101.62

Answer:

1/2 goes into 3/4 1 1/2 or 1.5 times

Step-by-step explanation:

The function has no vertical asymptotes and horizontal asymptotes are at y = 0.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels toward as it approaches infinity.

A straight line that serves as the asymptote of the curve y = f(x) or, in its implicit form, f(x,y) = 0, where the distance between the two lends to zero as the points on the curve approach infinity.

Given function,

f(x) = -7/(x² + 4)

in the given function the degree of the denominator is more than the numerator so The horizontal asymptote lies at y = 0 because, as we can see, the degree of the numerator is less than the denominator.

and there will be no vertical asymptote.

The graph of the equation is attached.

Hence horizontal asymptote lies at y = 0 and ni vertical asymptote.

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Option B: The domain of the function is the set of all real numbers, Option C: the range of the function is the set of all non-negative real numbers, Option D: the graph has an intercept at (0, 0), and option G: the graph is symmetric with respect to the y-axis are correct statements about the graph.

There are only real numbers in the domain, or collection of x-values. This is so because x holds true for all numbers. The set of all non-negative real numbers is known as the range or set of y-values. This is due to the fact that every value we obtain for y is a positive real number. The graph's x-intercept and y-intercept, also known as the intersection point, are located at (0, 0). Instead of the other way around, the graph increases on the interval x>0 and decreases on the interval x<0. Instead of a maximum, the graph shows a minimum at (0, 0). The graph is symmetric with respect to the y-axis because it may be folded in half along that axis.

As per the question, the function described below is an example of a polynomial function since it is a function of a single independent variable that has been raised to an integer power. Adding terms with a numerical coefficient multiplied by a specific power of the independent variables results in polynomial functions.

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Refer image for the complete question.

Answer:

Step-by-step explanation:

Let's say there are "x" students in class 6.

Since Anton got 0.2 of the votes, he got 0.2 * x votes.

Eva got 10% of the votes, which is equal to 0.1 * x votes.

Petra got 0.3 of the votes, which is equal to 0.3 * x votes.

Kofi got 9 votes.

So, the total number of votes in class 6 is x.

By adding up the number of votes each candidate received, we can write an equation:

0.2x + 0.1x + 0.3x + 9 = x

Simplifying the equation:

0.6x + 9 = x

Subtracting 0.6x from both sides:

9 = 0.4x

Dividing both sides by 0.4:

x = 22.5

Since the number of students must be a whole number, we round up to the nearest whole number:

x = 23

So there are 23 students in Class 6.

The length of side x is  √3 units.

We know that the larger triangle is an equilateral triangle, and it is divided into two equal right triangles.

Now, let's analyze these, we can see that the catheti are:

x and 3.

And the hypotenuse must have a length of 2x (if the triangle is equilateral).

Now we can use Pythagorean's theorem.

Then we will get:

(2x)^2 = x^2 + 3^2

4x^2 = x^2 + 9

4x^2 - x^2 = 9

3x^2 = 9

x^2 = 9/3 = 3

x = ± √3

We only care for the positive value, then:

x = √3

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The probability of the field mice having a weight greater than 33 g is 0.977, the field mice have a weight greater than 33 g.

The proportion of field mice with a weight greater than 33 g can be calculated using the formula for a standard normal distribution. This formula states that the probability of an event with a normal distribution occurring can be calculated by subtracting the area under the normal curve from the mean to the given value and dividing by the standard deviation.

In this case, the mean of the distribution is 25 g, the standard deviation is 4 g and the given value is 33 g.

Therefore, the probability of the field mice having a weight greater than 33 g is 0.977. This means that 0.977, or 97.7%, of the field mice have a weight greater than 33 g.

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The total length of the bolt should be 21/8 inches.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given the thickness of plate 1 = 7/8 inches

the thickness of plate 2 = [tex]1\frac{1}{4}[/tex] inches = 5/8 inches

total thickness of both plates = 7/8 + 5/4

5/4 is equaivalent to (5*2)/(4*2) = 10/8

the total thickness of both plates = 7/8 + 10/8

the total thickness of both plates = 17/8 inches

and the bolt must be at least 1/2 inch longer

total length of bolt = 17/8 + 1/2

convert 1/2 to the same denominator as 17/8

1/2 = (1*4)/(2*4) = 4/8

total length of bolt = 17/8 + 4/8

the total length of the bolt =  21/8 inches

Hence the bolt should be 21/8 inches longer.

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Answer:

y = -x+5

Step-by-step explanation:

Use point slope formula to find the equation of the line

First find the slope: (-1-4)/(6-1) = -5/5, slope = -1

Then, use the formula: y - y1 = m(x - x1)

y - 4 = -1(x - 1)

y - 4 = -x+1

y = -x + 5

The correct statement regarding the probability in this problem is given as follows:

D.) A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For each at bat, there are two possible outcomes:

There are four types of hits, which are given as follows:

Hence only statement D is correct, as the player can either be eliminated or get one of the four types of hits.

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To convert yards to feet we multiply the given value by 3.

A yard is one linear yard. "Yd" is the yard symbol. It is equivalent to 36 inches or 3 feet. 1 yard equals 0.9144 metres in metres when measured in metres. Both the imperial and US customary systems of measuring use this unit. The most common use of yards is to measure the length of a field, such a sports field.

A foot can also be used to measure length. The letter "ft" stands for the foot. Twelve inches and one third of a yard make up one foot. Additionally, one foot is equal to 0.3048 metres. We must divide the provided value by 3.281 to translate the given value from feet to metres. In aviation and elevation, the foot is typically used to measure height or altitude. The height of a person is also expressed in feet and inches.

Hence, to convert yards to feet we multiply the given value by 3.

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The number of points that Melissa scored would be = 89 points.

The competition was carried out by these two individuals that had different scores such as follows:

The total number of scores for Melissa = 50 point + Ron's score. That is , y = 50+X. ---> eq 1

The total number of Ron's score X = 4/9 × y --> 2

substitute y into equation 2.

X = 4/9× (50+X)

X= 22 + 0.44x

0.56x= 22

X= 22/0.56

X= 39.

substitute X into equation 1;

y= 50+39

y = 89

Therefore, the total number of points for Melissa = 89 point.

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Answer:

7x-43=5x+43

7x-5x=43+43

2x=86

x=86/2

x=43

An equation of a line in a slope-intercept format that is parallel to

y = (1/2)x - 3 line and goes through the point (4, 2) is y = (1/2)x

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know parallel lines have equal slopes.

The equation of the line given is y = (1/2)x - 3 and our required equation is parallel to it and passes through (4, 2).

So, 2 = (1/2)(4) + b.

2 = 2 + b.

b = 0.

Hence, y = (1/2)x is the required equation of the line.

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The model represent here gives the division problem is 3÷1/4.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have three section 1+ 1 + 1= 3.

and, Each section have the fraction

= 4/12

= 1/3

so, the model represent here gives the division problem

3÷1/4.

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Answer:

150 units (Option C)

Step-by-step explanation:

Perimeter of rectangle = Perimeter of triangle

= {2 × (Length + Width)} = Sum of all three sides

= {2 × [(2x) + (x + 12)]} = [(4x) + (2x) + (x + 3)]

The parenthesis are expanded using the Distributive Law:
= {2 × [2x + x + 12]}  = [4x + 2x + x + 3]

= {2 × [3x + 12]} = [7x + 3]
= 6x + 24 = 7x + 3

Bring all the like terms together and isolate x:

= 24 - 3 = 7x - 6x

= 21 = x

∴x = 21

Substitute this calculated value of x to determine the perimeter of rectangle:

6x + 24

= 6(21) + 24

= 126 + 24

= 150 units

∴Option C

Answer:

A(L) = - L²  + 215L

Domain
0 < L < 215

or

(0, 215) in interval notation

Step-by-step explanation:

Let  L represent the length and W the width

Perimeter of a rectangle = 2(L+W) and is given as 430 meters

Therefore 2(L + W) = 430

L + W = 430/2
L + W = 215

W = 215-L

The area A is given by L x W

Substituting for W in terms of L this becomes

A = L x(215 - L)

A = 215L - L²

which can be expressed as a function of in the form
A(L) = 215L - L² or in standard form(highest degree first)

A(L) = - L²  + 215L

The domain of this function are the values of L which result in a defined , real value for A

Without restrictions, the domain for L is -∞ < L < ∞. However real world facts coming into play

1. Area cannot be zero
So A(L) > 0 (upper bound on area)

-L² + 215L > 0

-L² > - 215L Move 215L to right side

L² < 215L   (dividing by -1 changes signs of variables and also inequality)

L < 215      (divide by L both sides)

2. Length cannot be negative
So lower bound on L is L > 0

Together the domain is
0 < L < 215

or

(0, 215) in interval notation

The total feet in altitude is given by the equation A = -790 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total feet in altitude be represented as A

Now , the equation will be

The hot air balloon descends 305 feet per minute for 4 minutes

So , the total descending will be a negative value , where

The feet in altitude descended = -305 x 4 = -1220 feet

Now , hot air balloon ascends 215 feet per minute for 2 minutes

So , the total ascending will be a positive value , where

The feet in altitude ascended = 215 x 2 = 430 feet

And , the total feet in altitude A = feet in altitude descended + feet in altitude ascended

Substituting the values in the equation , we get

The total feet in altitude A = -1220 + 430

On simplifying the equation , we get

The total feet in altitude A = -790 feet

Hence , the equation is A = -790 feet

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Answer:

- 8.5

Step-by-step explanation:

The value of the 25th percentile for this data set is 26.25. This means that 25% of the data is below 26.25 and 75% of the data is above 26.25

The 25th percentile, also known as the lower quartile, is a value that separates the lowest 25% of the data from the rest of the data. To find the 25th percentile of an ordered data set, we first need to determine the position of the 25th percentile, which can be calculated using the formula:

position = (n+1) * p

where n is the number of observations in the data set and p is the percentile (in decimal form). In this case, n = 8 and p = 0.25. Put values:

position = (8+1) * 0.25 = 2.25

Since the position is not a whole number, we know that the 25th percentile falls between the second and third observations in the data set. In this case, the second observation is 24 and the third observation is 27. To find the exact value of the 25th percentile, we use the formula:

value = L + (position - i) * h

where L is the value of the lower observation, i is the integer part of the position, and h is the difference between the two observations. In this case, L = 24, i = 2, and h = 27 - 24 = 3. Put values:

value = 24 + (2.25 - 2) * 3 = 24 + 0.75 * 3 = 24 + 2.25 = 26.25

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Answer:

x = 1

Step-by-step explanation:

2/3 (2x + 4) + 6 = 10

2/3 (2x + 4) = 10 - 6

1⅓x + 2⅔ = 4

1⅓x = 4 - 2⅔

1⅓x = 1⅓

x = 1

Answer: 9

Step-by-step explanation:

12-3=9 or count up from 3 until you get too 12

Answer: 6k + 31

Step-by-step explanation:

19 - (-6k - 2(6))

19 - (-6k - 12)

19 + 6k + 12

6k + 31

Answer: 6k + 31

Step-by-step explanation:

=  19-6(-k-2)

= 19+6k +12

= 6k + 31

Answer:

$21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

$30 subtracted by 30% is equal to $21

9 × 3 = 27 +10% (3) = $30

The only 2-digit multiple of 2, 3, 4, 6, and 8 is the number 24.

Multiple is a term that refers to an amount that is greater than one or a collection of two or more items. It is often used to describe a quantity of objects, people, or events that are distinct from each other. For example, a multiple of five would be five, ten, fifteen, twenty, etc. Similarly, a multiple of three would be three, six, nine, twelve, etc.

Therefore, all five people are thinking of the same number: 24.

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The quantity of type A coffee will be 37 pounds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound.

The quantity of Type A coffee will be calculated as:-

B = 4A

4.20A + 5.6B = 984.20

4.20A + 4 x 5.6 x A = 984.20

4.20A + 22.4A = 984.22

26.6A = 984.22

A = 37

Therefore, the amount of each type of 37 pounds will equal one coffee.

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The terms which is not an impact of American consumerism is -

Option C: Cash generators for several nations.

What is consumerism?

The tendency to continuously consume is known as consumerism. It is the need to acquire more possessions and establish one's identity via them. Consumer spending and GDP growth are seen as benefits of consumerism by economists.

The American consumerism includes -

Debts : Due to introduction of credit cards the consumers have ore and more debt on their credit cards whilst they spend on materialistic goods.

Lack of Unemployment : Economists point out that a decline in product demand causes an economic downturn or even depression, which is accompanied by high unemployment.

Stress:  Due to debt, recession and unemployment people are constantly under stress for surviving.

Since, consumerism helps in GDP growth of a country it does not help generate cash for other nations.

Therefore, " Cash generators for several nations" is not an impact.

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A. The length of each segment of the rope is 5 m.

B. The mass of the middle segment is the length of the segment 10 kg.

C. The y values of the bottom of each segment are y₀ = 0, y₁ = 5 m, and y₂ = 10 m.

D. The distance d₂ the middle segment must be moved is 15,

Acceleration is a measure of the change in velocity over time. In physics, acceleration is defined as the rate of change of velocity, or the second derivative of position with respect to time. Acceleration is a vector quantity that has both magnitude and direction, and its unit is meters per second squared (m/s²).

A positive acceleration indicates an increase in speed, while a negative acceleration indicates a decrease in speed or a change in direction. In everyday life, we encounter examples of acceleration in movements such as starting a car, stopping a car, or changing direction while driving.

A. The length of each segment of the rope is 15 m / 3 = 5 m.

B. The mass of the middle segment is the length of the segment multiplied by the density of the rope: M2 = 5 m × 2 kg/m = 10 kg.

C. The y values of the bottom of each segment are y0 = 0, y1 = 5 m, and y2 = 10 m.

D. The distance d2 the middle segment must be moved is 25 m - 10 m = 15 m.

Therefore, the work required to move the middle segment can be approximated using the formula W = M2 × g × d2, where g is the acceleration due to gravity. The exact value of the work required to move the entire rope would need to take into account the different distances that each segment must be moved.

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