Find the y-intercept and slope of the function graph and find the equation for the function

Mathematics is a discipline that has a long and rich history. It has evolved over time from simple counting and measuring to a broad and complex subject that is used in many fields. The development of mathematics has been driven by the need to solve practical problems, as well as the desire to understand the underlying patterns and structures of the world around us.

Early forms of mathematics, such as counting and measuring, were developed by ancient civilizations to solve practical problems such as trade, construction, and agriculture. These early forms of mathematics were based on empirical observations and were often tied to the physical world.

As mathematics developed, it began to include more abstract concepts such as numbers, geometry, and algebra. These abstract concepts allowed for the development of more complex mathematical techniques and the ability to solve a wider range of problems.

Today, mathematics is used in a wide range of fields including science, engineering, economics, and even art. It is an essential tool for understanding and solving problems in the world around us.

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The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Step-by-step explanation:

The Mediterranean vegetation is dominated by evergreen shrubs and sclerophyllous trees adapted to the distinctive climatic regime of summer drought and cool moist winters with only sporadic frost.

Answer:

g'(1,-5)

Step-by-step explanation:

Rule

(x,y) → (y -x)

(-5,-1) → (-1,5)

Helping in the name of Jesus.

Answer:

For new coordinates of each point, we can use the following formula:

(x, y) \(\longrightarrow\) (y, -x)

To rotate a point 90 degrees clockwise about the origin, we swap the x and y coordinates and negate the x coordinate.

Therefore, the rotated points are:

G(-5,-1) \(\longrightarrow\) G'(-1, 5)

H(-3,-2) \(\longrightarrow\) H'(-2, 3)

J(-3,-5) \(\longrightarrow\) J'(-5, 3)

K(-5,-4) \(\longrightarrow\) K'(-4, 5)

Therefore, The vertex of G is (-1,5)

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

Step-by-step explanation:

Answer options, incorrect statements are underlined below:

1. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range.

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

3. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly two elements of the range.

4. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.

Answer:

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

Step-by-step explanation:

A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point.

Total number of ways to select 3 people from the 5 total: 5!/(3! (5 - 3)!) = 10

• Number of ways of picking 0 women:

\(\dbinom20\times\dbinom33 = 1\times1 = 1\)

• Number of ways of picking 1 woman:

\(\dbinom21\times\dbinom32 = 2\times3 = 6\)

• Number of ways of picking 2 women:

\(\dbinom22\times\dbinom31 = 1\times3 = 3\)

• Number of ways of picking 3 women: 0, since there are only 2 to choose from

Then X has the probability mass function

\(P(X=x) = \begin{cases}\frac1{10}&\text{if x=0}\\\frac6{10}=\frac35&\text{if }x=1\\\frac3{10}&\text{if }x=2\\0&\text{otherwise}\end{cases}\)

Answer:

x = -7

Step-by-step explanation:

The 2 horizontal lines are parallel as given ion the problem.

The x + 97 angle is congruent to the right angle.

x + 97 = 90

x = -7

Answer:

B

Step-by-step explanation:

Answer:

Starting time: 1:37

Step-by-step explanation:

Instead of proof to solve the problem, let us prove that the starting time above is correct;

1. There are 60 minutes in an hour, so 60 - 37 = the minutes 'till 2:00, or 23 minutes

2. Knowing that the time the truck stopped driving through the neighborhood was 5 minutes past 2:00, the minute difference being 23 + 5, or 28 minutes

Proved: 28 minutes

Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

Answer:

The inverse of a given function

d) \(g(x) = \frac{1}{4} x - 3\)

Step-by-step explanation:

Explanation:-

Given that f(x) = 4x + 12

  let y = 4 x + 12

     4 x = y - 12

        \(x = \frac{y-12}{4}\)

        \(x = \frac{1}{4} y - 3\)      

we know that   y = f(x)

                   ⇒  x = f⁻¹(y)

      \((f^{-1} y) = \frac{1}{4} y - 3\)

Put  replace 'y' in 'x'

    \((f^{-1} x) = \frac{1}{4} x - 3\)

Final answer:-

The inverse of a given function

\(g(x) = \frac{1}{4} x - 3\)

Answer:

D

Step-by-step explanation:

Right on edge

Answer:

A) \( \frac{8}{3} x - 6\)

Step-by-step explanation:

Let the width of the rectangle be x units.

\( \therefore \: length \: of \: rectangle = \frac{1}{3} x - 3 \\ Perimeter \: of \: rectangle = 2(l + w) \\ = 2 \bigg( \frac{1}{3} x - 3 + x \bigg)\\ = 2 \bigg( x + \frac{1}{3} x - 3 \bigg)\\ = 2 \bigg( \frac{3x + x}{3} - 3 \bigg)\\ = 2 \bigg( \frac{4x}{3} - 3 \bigg) \\ = 2 \bigg( \frac{4x}{3} - 3 \bigg) \\ = \frac{2 \times 4x}{3} -2 \times 3 \\ \purple{ \bold{{Perimeter \: of \: rectangle = \frac{8}{3} x - 6}}}\)

If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.

We are required to find the database whose standard deviation is lower.

Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.

Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.

Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

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For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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\(\\ \sf\longmapsto 2(n-1)+47=2(3n-1)\)

\(\\ \sf\longmapsto 2n-2+47=6n-2\)

\(\\ \sf\longmapsto 2n+47=6n\)

\(\\ \sf\longmapsto 4n=47\)

\(\\ \sf\longmapsto n\approx 12\)

Answer:

n = 11.75

Step-by-step explanation:

2(n - 1) + 47 = 2(3n - 1)              Distribute the multiplier

2n - 2 + 47 = 6n - 2                 Combine terms

              47 = 4n                       divide

                n = 11.75

The number of Lexi is using for every bracelet and necklace include the following:

For her bracelet =329

For her necklace= 593

Addition is defined as one of the arithmetic parameters that can be used to combine various data together to arrive at a particular value.

For the family,

bracelet = 5

necklace = 9

Total jewelry made = 14

total number of beads used = 922 beads

The number of beads used for bracelet;

= 5/14×922

= 4610/14

= 329

The number of beads used for necklace;

= 9/14× 922

= 8298/14

=593

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According to John Locke, Experience is how we acquire basic knowledge.

What explains why, in many of the problems, historical data is used is; Information changes rapidly.

1) John Locke's theory simply means that all knowledge comes exclusively through experience. He argues that at birth the mind is a tabula rasa, that humans fill with ideas as they experience the world through the five senses.

Thus, the missing word in the question is "Experience".

2) The reason why historical data is used in may problems is because Information changes rapidly. The information being circulated currently may be different from that circulated 100 years ago.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

The next they will ring again is after 8 hours.

Step-by-step explanation:

Find the least common multiple of 3,6 and 8:

3,6,9,12,15,18,21,24

6,12,18,24

8,16,24

The least common multiple is 24 so all 3 bells will ring together every 24 minutes.

answer: 3:24

SOLUTION:

Step 1 :

We are meant to find the side x, ( round to the nearest tenth ).

We have the nut has side lengths of 2 cm and the nut is shaped like a regular hexagon.

Step 2 :

We also need to find the internal angle of a hexagon,

Each internal angle =

Step 3 :

To get x, we need to do the following :

CONCLUSION :

The value of x = 3. 5 cm ( to the nearest tenth )

Answer:

70÷100×200=140

Step-by-step explanation:

Because 70 is the percentage of 140

Answer:

9/8

Step-by-step explanation:

3/2*3/4

3*3=9

2*4=8

9/8

Answer:

9/8

Step-by-step explanation:

\(\frac{3}{2}\) x \(\frac{3}{4}\) = 9/8

Answer:

y= 13 is the answer for the question

There are 50 predicted rolls for 5 in 300 times of rolls.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Janet rolls a 6-sided number cube 300 times,

Probability = (Favourable Outcomes)/(Possible Outcomes)

Favourable Outcomes: 5 (1 total)

Possible Outcomes: 1,2,3,4,5,6 (6 total)

Probability of a 5 in any given roll of a die = 1/6

1/6x300 = 50 = 50 predicted roll with 5.

Hence, There are 50 predicted rolls for 5 in 300 times of rolls.

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Answer:

x = -3

Step-by-step explanation:

The two angles shown are corresponding angles, meaning that they have the same value. Because of this, we can create an equation to solve for the value of x.

2x + 9 = 7x + 24

Remember, those two angles are similar, and that's why we can make the two values equal to each other. First, let's remove 7x from both sides.

2x - 7x + 9 = 7x - 7x + 24

-5x + 9 = 24

Then, we'll remove 9 from both sides.

-5x + 9 - 9 = 24 - 9

-5x = 15

Finally, we'll divide both sides by -5 to isolate x and figure out what it is equivalent to.

-5x/-5 = 15/-5

x = -3

And there it is... the value of x. Hopefully that's helpful! :)

Answer: 5670

Step-by-step explanation:

Answer:

She received $18.11

Step-by-step explanation:

25.63-7.52= $18.11

Answer:

8. $18.11

10. 71

Step-by-step explanation:

25.63 - 7.52 = 18.11

90 - 19 = She is old. JK

90 - 19 = 71