Find the area of the shaded region of the graph

Answer: first option

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The Standard form of the equation of the line is:

[tex]Ax + By = C[/tex]

Where A is a positive integer, and B, and C are integers.

You can observe in the graph that the line intersects the y-axis at [tex]y=-2[/tex], then, "b" is:

[tex]b=-2[/tex]

Find the slope of the line with this formula:

 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose two points of the line and substitute values.

Points:(-3,0) and  (3,-4)

Then:

 [tex]m=\frac{-4-0}{3-(-3)}=-\frac{2}{3}[/tex]

Substituting values into  [tex]y=mx+b[/tex], you get the equation of the line in Slope-intercept form:

 [tex]y=-\frac{2}{3}x+2[/tex]

To write it in Standard form, make the addition indicated:

[tex]y=\frac{-2x+6}{3}[/tex]

Multiply both sides of the equation by 3:

[tex]3(y)=(3)(\frac{-2x+6}{3})[/tex]

[tex]3y=-2x+6[/tex]

And finally add 2x to both sides:

[tex]2x+3y=-2x+6+2x[/tex]

[tex]2x+3y=6[/tex]

Answer:

1. P(A) = 0.6826

2. P(B) = 0.13591

Step-by-step explanation:

the first graph is given just as an example to show the percentage distribution values for bell shaped curve

Answer:

68.3%, 33.3%

Step-by-step explanation:

PLATO answer!! pls mark brainliest :)))

Answer:

in this problem we do a comparison case t i.e if 1/12 he writes 1/6 of page what about 1 page

     1/12minute  =   1/6

      ?    ×    1          then we cross multiply

(1*1/12)    ÷  1/6     =1/12*6  =  1/2 minute

The net of a cylinder is best described by a circle and one rectangle.

A cylinder is a three-dimensional solid, the most basics of curvilinear shapes which is considered as a prism with circle as its base.

A cylinder has a base radius and the height from its base to top .

Formula of surface area of cylinder is =  2πr(r + h)

Formula of Volume of cylinder is = [tex]\pi r^{2} h[/tex]

The net of the cylinder should have one side open such that it can be inserted within the cylinder.

As the top of the cylinder is circle, thus the net should have one circular top . Also the body of the cylinder is in the form of a rectangle which ensures the net should have also one rectangular body.

Therefore the net of a cylinder is best described by a circle and one rectangle.

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The net of a cylinder is comprised of 'one rectangle and two circles', which represent the lateral surface and the two equal-sized circular bases of the cylinder, respectively.

The net of a cylinder consists of two equal-sized circles and one rectangle that wraps around to form the curved surface. The two circles represent the top and bottom (or base) of the cylinder, and they are identical in size because the top and the bottom of a cylinder have the same cross-sectional area. The rectangle represents the lateral surface area of the cylinder, which, if 'unrolled', resembles a rectangle whose length is equal to the circumference of the circles (the perimeter of the base) and whose height is equal to that of the cylinder. The correct option that describes the net of a cylinder is thus 'one rectangle, two circles'.

The answer is x=17. Since it says that the plot point is the answer to square root 4.1^2 = 16.81 which is closest to 17.

Hope this helps and hope you have a great day and brainiest is always appreciated

Answer:

T= 200+45m

Step-by-step explanation:

m= months

T=total money

Answer:

  y = -(1/3)x -2

Step-by-step explanation:

For each horizontal "run" of 3 units, the "rise" of the line is -1 unit. Hence the slope is ...

   rise/run = -1/3

The y-intercept is where the line crosses the y-axis, at y = -2. So, the slope-intercept form of the equation of the line is ...

  y = (slope)·x + (y-intercept)

  y = -1/3x -2

The expression that represents the statement is (56 - 14) ÷ 8.

To represent the given statement, "Subtract 14 from 56 and divide the result by 8," we need to follow these steps:

Step 1: Subtract 14 from 56: 56 - 14 = 42

Step 2: Divide the result by 8: 42 ÷ 8 = 5.25

So, the expression that represents the statement is (56 - 14) ÷ 8.

The correct answer is: (56 - 14) ÷ 8.

The complete question is here:

Which expression represents the statement shown? Subtract 14 from 56 and divide the result by 8. (56/ 8)-14 (14-56)/ 8 14-(56/ 8) (56-14)/ 8.  

ANSWER

[tex]f(0) = g(0)[/tex]

EXPLANATION

From the graph we

[tex]g(0) = - 2[/tex]

because this is where the line x= 0 meets the graph of g(x).

Also

[tex]f(0) = - 2[/tex]

because this is where the line x= 0 meets the graph of f(x).

This implies that,

[tex]f(0) = g(0)[/tex]

The correct choice is A.

[tex]

3x^2y^5\cdot(4xy^2)^3 = 3x^2y^5\cdot(64x^3y^6) = \boxed{192x^5y^{11}}

[/tex]

Answer:

  D. [tex]f^{-1}(x)=\log_2{(x-6)}[/tex]

Step-by-step explanation:

Solve x = f(y) for y:

  x = 2^y +6

  x -6 = 2^y . . . . subtract 6

  log2(x -6) = y . . . . take the log base 2 . . . . matches choice D

Answer:

The answer is D

Step-by-step explanation:

In order to find out the inverse of the function, you have to express a new function where the independent variable must be "y" instead of "x".

So, you have to reorganize the base function and then free the variable "x".

[tex]f(x)=2^x+6\\f(x)=y\\y=2^x+6\\2^x=y-6\\log_2(2^x)=log_2(y-6)\\x*log_2(2)=log_2(y-6)\\log_2(2)=1\\x=log_2(y-6)\\[/tex]

Then, we recall "y" as "x" and [tex]x=f^-^1(x)[/tex]

Finally, the answer is:

[tex]f^-^1(x)=log_2(x-6)[/tex]

Answer:

Step-by-step explanation:

Let's call the ages D for daughter and S for son.

We know that the son is twice as old as the daughter, so:

S = 2D

We also know that in 15 years, their ages add up to 100, so:

(40+15) + (S+15) + (D+15) = 100

55 + S + 15 + D + 15 = 100

85 + S + D = 100

S + D = 15

Substituting the first equation:

2D + D = 15

3D = 15

D = 5

Therefore:

S = 2D = 10

The son is 10 and the daughter is 5.

Answer:

son = 10

daughter  = 5

Step-by-step explanation:

Let the daughter = d

Let the son =          s

s = 2*d

there ages in 15 years

Mother = 40 + 15 = 55

Son = s + 15

daughter = d + 15

Total: s + 15 + d+15 + 55 = 100    Combine the like terms.

s + d + 85 = 100                            Subtract 85 from both sides.

s + d = 100 - 85

s + d = 15

s = 2*d                                            Substitute for son

2d + d = 15

3d = 15

d = 15/3

d = 5

son = 2*5

son = 10

Check

son = 15 =           25

daughter + 15 =  20

Mother + 15    =   55

Total                   100 just as it should be.

Answer:

• The function is a linear function

• The function changes at a constant rate

Step-by-step explanation:

A graph of the function shows it to be a straight line (linear function). Such a function always changes at a constant rate. The line goes downward to the right, so the function is a decreasing function.

___

"changes at a constant rate" and "linear function" are two different ways of saying the same thing: the graph of the function is a straight line.

The answer is:

They will be 10 miles apart after 3 hours.

To calculate how long after they start will they be 10 miles apart, we need to assume that after 1 one hour, they were at the same distance (5 miles), then, calculate the time when they are 10 miles apart, knowing that Paul increased its speed two times, running first at 5mph and then, at 10 mph.

The time that will pass to be 10 miles apart can be calculated using the following equation:

[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]

Calculating the time to reach 5 miles for both Larry and Paul, at a speed of 5 mph, we have:

[tex]x=xo+v*t\\\\5miles=0+5mph*t\\\\t=\frac{5miles}{5mph}=1hour[/tex]

We have that to reach a distance of 5 miles, they needed 1 hour. We need to remember that at this time, they were at the same distance.

If we want to know how many time will it take for them to be 10 miles apart with Paul increasing its speed to 10mph, we need to assume that after that time, the distance reached by Paul will be the distance reached by Larry plus 10 miles.

So, for the second moment (Paul increasing his speed) we have:

For Larry:

[tex]x_{L}=5miles+5mph*t[/tex]

Therefore, the distance of Paul will be equal to the distance of Larry plus 10 miles.

For Paul:

[tex]x{L}+10miles=xo+10mph*t\\\\5miles+5mph*t+10miles=5miles+10mph*t\\\\5miles+10miles-5miles=10mph*t-5mph*t\\\\10miles=5mph*t\\\\t=\frac{10miles}{5mph}=2hours[/tex]

Then, there will take 2 hours to Paul to be 10 miles apart from Larry after both were at 5 miles and Paul increased his speed to 10 mph.

Hence, calculating the total time, we have:

[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]

[tex]TotalTime=1hour+2hours=3hours[/tex]

Have a nice day!

Answer:

The exact value of 2 sin(120°) cos(120°) is -√3/2

Step-by-step explanation:

* Lets revise the trigonometry functions of the double angle

# sin(2x) = 2 sin(x) cos(x)

# cos(2x) = cos²(x) - sin²(x) OR

  cos(2x) = 2 cos²(x) - 1 OR

  cos(2x) = 1 - 2 sin²(x)

# tan(2x) = 2 tan(x)/(1 - tan²(x))

* Now lets solve the problem

∵ 2 sin(120°) cos(120°)

- Put sin(120°) = sin(2×60°)

∵ sin(2x) = 2 sin(x) cos(x)

∴ sin(120°) = 2 sin(60°) cos(60°)

∵ sin(60°) = √3/2 and cos(60°) = 1/2

∴ sin(120°) = 2 (√3/2) (1/2) = √3/2

∴ sin(120°) = √3/2 ⇒ (1)

- Put cos(120°) = cos(2×60°)

∵ cos(2x) = cos²(x) - sin²(x)

∴ cos(120°) = cos²(60°) - sin²(60°)

∵ cos(60°) = 1/2 and sin(60°) = √3/2

∴ cos(120°) = (1/2)² - (√3/2)² = 1/4 - 3/4 = -2/4 = -1/2

∴ cos(120°) = -1/2 ⇒ (2)

- Substitute (1) and (2) in the expression 2 sin(120) cos(120)

∴ 2 sin(120°) cos(120°) = 2 (√3/2) (-1/2) = -√3/2

* The exact value of 2 sin(120°) cos(120°) is -√3/2

Answer:

  Factor pairs of 36 are ...

     1×36, 2×18, 3×12, 4×9, 6×6 . . . and the reverse of these

There is nothing in the problem statement limiting the dimensions to integer numbers of feet, so any dimensions x and 36/x will do. (x in feet)

Step-by-step explanation:

Area is the product of length and width. The desired dimensions are the length and width of the floor, so any pair of numbers resulting in a product of 36 will be a possible set of dimensions.

If the dimensions are supposed to be integer numbers of feet, then the possibilities for length×width are ...

  1×36, 2×18, 3×12, 4×9, 6×6, 9×4, 12×3, 18×2, 36×1

_____

As a practical matter, the tree house probably needs to be wider than 2 feet, leaving 3×12, 4×9, and 6×6 as possible dimensions (length×width or width×length). Depending on the flooring material and the difficulty of cutting it, there may be other limitations on the dimensions.

The possible dimensions for the floor of the tree house that Matt and his dad are building are 1 ft x 36 ft, 2 ft x 18 ft, 3 ft x 12 ft, 4 ft x 9 ft, and 6 ft x 6 ft. These pairs are derived by identifying the factors of 36 square feet.

To determine all possible dimensions of the floor that Matt and his dad need to cover, we need to find pairs of whole numbers that multiply to 36 square feet. This is a classic problem in mathematics involving factors.

Here are the pairs of whole numbers that multiply to 36:

Each of these pairs represents a possible dimension for the tree house floor.

the answer in decimal form is .25 but in fraction form is 1/4

The value of cos(75°)cos(15°) is 0.25.

To solve the expression cos(75°)cos(15°), we use the identity cos(a)cos(b) = 0.5[cos(a+b) + cos(a-b)]. Applying this identity, we have:

cos(75°)cos(15°) = 0.5[cos(75°+15°) + cos(75°-15°)].

Using the values of cos(90°) = 0 and cos(60°) = 0.5, we can simplify the expression:

cos(75°)cos(15°) = 0.5[cos(90°) + cos(60°)] = 0.5[0 + 0.5] = 0.25.

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Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Answer:Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Step-by-step explanation:

The answer is B. It is the most reasonable answer that I see.

Answer:

[tex]704 in^2[/tex]

Step-by-step explanation:

The figure is a parallelogram.

The area of a parallelogram is

[tex]=base\:\:\times\:\:height[/tex]

The base is 22 inches and the height is 32 inches.

We multiply to obtain:

[tex]22\times 32=704in^2[/tex]

the correct answer is B

Answer:

So first, we need to find the area of the whole circle since we already had the radius:

A = πr² = 3.14 . 7.53² = 178.040826 (cm²)

Now our next job is to find the area of the square inside the circle.

Looking at the picture, we can see that the radius of the circle is also half of the diagonal of the square, so the whole diagonal of the square should be: 7.53 . 2 = 15.06 (cm)

*Now this is where things get a little bit more complicated:

Imagine that x is the length of the side of the square.

Using Pythagorean theorem, knowing that d is the diagonal of the square and also the hypotenuse of the right triangle inside the square, we have the equation:

a² + a² = d²

2a²      = d²

a²        = d²/2

a²        = 226.8036/2 = 113.4018

So a², which is also the area of the square, is 113.4018 (cm²)

So the are of the yellow region is: 178.040826 - 113.4018 ≈ 64.6 (cm²)

*I could be wrong though

Answer:

  (-x +5) -5/(3x)

Step-by-step explanation:

Divide term by term.

  = (3x^2)/(-3x) +(-15x)/(-3x) +(5)/(-3x)

  = -x +5 -5/(3x)

1962 - 2003 = 41 years

In 2003 it’s value increased to = $435,000

$435,000 / 41 years

Per year’s value = $10,609.7561

B. 1950 - 1960 = 12 years

$60,000 / 12 years = $5000

Value of the house @ 1950 = $5000

Using proportions, it is found that:

Item a:

From an initial value of $60,000, the house increased in value by $375,000, as 435000 - 60000 = 375000.

The percent increase is given by:

[tex]\frac{375000}{60000} \times 100\% = 625\%[/tex]

In 2003 - 1962 = 41 years, hence:

[tex]r = \frac{625}{41} = 15.24[/tex]

The annual rate of increase in the value of the house was of 15.24%.

Item b:

The value increases 15.24% a year, hence, in t years after 1962, considering an initial value of $60,000, the value is:

[tex]V(t) = 60000(1.1524)^t[/tex]

1950 is 12 years before 1950, hence the value is V(-12), that is:

[tex]V(-12) = 60000(1.1524)^{-12} = \frac{60000}{(1.1524)^{12}} = 4029[/tex]

In 1950, the house was valued at $4,029.

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Answer:

Step-by-step explanation:

Givens

Cyclist A

r = r_a - 3

t = 5 hours.

d = ?

Cyclist B

r = r _a

t = 5 hours - 1/2 hour = 4.5 hours.

d = d - 31.5

Formula

(r - 3)*5 + 5*r = d

r*4.5 = d - 31.5

Explanation

The rate of A is 3 less than the rate of B. Together, they bicycle the entire distance (d). That's the first equation

The second equation is a lot harder. That equation has to do with the one starting off from B. His useful cycling time is 4 1/2 hours because he starts off 1/2 hour later.

He travels d - 31.5 which A travels 31.5

Solution

The total distance is the same. We will use that fact to solve for r first.

(r - 3)*5 + 5r = d

4.5r + 31.5 = d

Remove the brackets in the top equation.

5r - 15 + 5r = d

10r - 15 = 4.5r + 31.5             Add 15 to both sides

10r -15+15 = 4.5r + 31.5+15

10r = 4.5r + 46.5                   Subtract 4.5 r from both sides.

10r-4.5r = 46.5

5.5r = 46.5

r = 8.45 mph

====================

4.5r + 31.5 = d

4.5*8.45 + 31.5 = d

d = 69.53 miles

====================

If this proves to be incorrect, and you have choices, please list them.

n+5=2n-1

5=n-1

6=n <— Answer

Answer:

C 1/2

Step-by-step explanation:

There are 4 suits, 2 suits are  red (hearts and diamonds) while 2 are black (clubs and spades)

Since 13 cards are in each suit, 26 cards are red ( 2 * 13)  

There are 52 total cards

P (red) = red cards/ total cards

           = 26 / 52

           = 1/2

Answer:x=4 , y=-1

Step-by-step explanation:

X-y=5

X+y=3

If 1 and 2 are added then y will be eliminated

(1)+(2) gives : 2x=8 then x=4

Now substitute this value of x into either of the 2 equations and solve for y.

Let x=4 in (1) =4-y=5 = y=-2

Answer:

  D.  37.22%

Step-by-step explanation:

One of my favorite probability z-table websites calculates the fraction as 0.3722 = 37.22%.

___

Your graphing calculator or spreadsheet can probably do the same for you.

Using the concepts of the normal distribution and z-scores, you calculate the z-scores for $25,000 and $40,000. Then, looking up these z-scores in a standard normal distribution table, and subtracting these, you get the percentage 37.17%, making the closest answer option D: 37.22%.

This question requires understanding of both normal distribution and z-scores. A Z-score measures how many standard deviations an element is from the mean. To solve this, we calculate the z-scores for $25,000 and $40,000, respectively, using the formula: z = (X - μ) / σ where X is the value, μ is the mean, and σ is the standard deviation.

Then, look up these z-scores in a standard normal distribution table (also known as a Z table). The values corresponding to -1.35 and -0.10 are 0.0885 and 0.4602, respectively. Substract these to find the percentage of homeowners with incomes between $25,000 and $40,000. That is, (0.4602 - 0.0885) * 100 = 37.17%. The closest answer is then option D: 37.22%

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Answer:2006

Step-by-step explanation:

[tex]A = 118e^{0.024t}[/tex]

When A = 140:

[tex]140 = 118e^{0.024t}[/tex]

[tex]\frac{140}{118} = e^{0.024t}[/tex]

[tex]ln(\frac{140}{118}) = 0.024t[/tex]

[tex]\frac{1}{0.024} ln(\frac{140}{118}) = t[/tex]

Plugging into a calculator, t is approximately 7.12.  Since t represents years since 1998, we round up to the nearest whole number: t=8.  So the population of the city will reach 140 thousand in the year 2006.

The population of the city reach 140 thousand will be after 7.123 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The equation models the number of inhabitants in a specific city, in thousands, t years after 1998 is given below.

[tex]\rm A = 118 \times e^{0.024 \times t}[/tex]

The number of years when the population becomes 140 thousands is given as,

[tex]\rm 140 = 118 \times e^{0.024 \times t}[/tex]

Take natural log on both sides, then we have

0.024 t = ln (140 / 118)

0.024 t = 0.170957

t = 7.123 years

The population of the city reach 140 thousand will be after 7.123 years.

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Answer:

20

Step-by-step explanation:

9/15 = 3/5

3*4=12

5*4=20

Answer:

20 shots

Step-by-step explanation:

First round

basket = 9

Total shots = 15

Percentage = 9/15 x 100 = 60%

Second round

baskets = 12

Total = x

(12/x) x 100 = 60%

12/x = 0.6

x = 12 ÷ 0.6

x = 20

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1 - (- 7)} {2-0} = \frac {-1 + 7} {2} = \frac {6} { 2} = 3[/tex]

Thus, the equation is:

[tex]y = 3x + b[/tex]

Substituting a point we find b:[tex]-7 = 0 + b\\b = -7[/tex]

Finally the equation is:

[tex]y = 3x-7[/tex]

ANswer:

The missing value is 3

Answer:

The value of missing is 3

Step-by-step explanation:

* To form an equation of a line from two points on the line, you

  must find the slope of the line at first

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope of a line passes through point (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* Lets solve the problem

∵ (0 , -7) and (2 , -1) are tow points on the line

- Let (0 , -7) is the point (x1 , y1) and (2 , -1) is the point (x2 , y2)

∴ m = (-1 - -7)/(2 - 0) = (-1 + 7)/2 = 6/2 = 3

- Lets write the equation

∴ y = 3x + c

- c is the y-intercept means the line intersect the y-axis at point (0 , c)

∵ Point (0 , -7) on the line

∴ The line intersect the y-axis at point (0 , -7)

∴ The y-intercept is -7

∴ The equation of the line is y = 3x - 7

* The value of missing is 3