Graph: y < 1/3x + 1/2

The equation of the line is y=x+12.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The points are

(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

We have to Write the equation of the line.

According to given question we have,

Equation of line passing through the point (-3,9) and  (-9,3).

Slope of the line=

[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]

⇒y−9=1(x+3)

⇒y-9=x+3

Add 9 on both sides we get,

y=x+12

∴ y=x+12 which is in the form y=mx +c is the required equation.

Therefore, the equation of the line is y=x+12.

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y = x + 12

What is equation of a line?

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.

y-y₁=m(x-x₁)

mm₁=-1

Points (-3,9) and  (−9,3).

Slope of the line m = (y₂ - y₁)/(x₂ - x₁)

m = (3-9)/(-9+3)

m = 1

Now  equation of line passing through two points

(y - y₁)/(y₂ - y₁) = m*(x - x₁)/(x₂ - x₁)

(y - 9)/(3-9) = 1*(x - 3)/(-9+3)

y - 9 = x + 3

y = x + 12

Therefore, the equation of line is y = x + 12

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Answer: x < √3 - x

Step-by-step explanation:

-x^2+x-3<0

= x^2+x < 3

= x^2 < 3 - x

= x < √3 - x

Answer: d=12

Step-by-step explanation:

[tex]\displaystyle\\\frac{3d-2}{8} =-d+16\frac{1}{4} \\\\\frac{3d-2}{8} =-d+\frac{16*4+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{64+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{65}{4}[/tex]

Multiply both parts of the equation by 8:

[tex]\displaystyle\\3d-2=(-d+\frac{65}{4} )(8)\\\\3d-2=-8d+65*2\\\\3d-2=-8d+130\\\\3d-2+2=-8d+130+2\\\\3d=-8d+132\\\\3d+8d=-8d+132+8d\\\\11d=132\\[/tex]

Divide both parts of the equation by 11:

[tex]d=12[/tex]

Answer:

The [tex]y[/tex]-coordinate of this midpoint is [tex]5[/tex].

Step-by-step explanation:

Let [tex]{\sf A}[/tex] and [tex]{\sf B}[/tex] denote two points in the cartesian plane.

If point [tex]{\sf A}[/tex] is at [tex](x_{a},\, y_{a})[/tex] while point [tex]{\sf B}[/tex] is at [tex](x_{b},\, y_{b})[/tex], the midpoint of [tex]{\sf AB}[/tex] would be at:

[tex]\begin{aligned}\left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2} \right)\end{aligned}[/tex].

In other words, the [tex]y[/tex]-coordinate of the midpoint of [tex]{\sf AB}[/tex] would be the average of the [tex]y\![/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex].

In this question, the [tex]y[/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex] are [tex]3[/tex] and [tex]7[/tex], respectively. The [tex]y\![/tex]-coordinate of the midpoint of [tex]{\sf A}\![/tex] and [tex]{\sf B}[/tex] would be the mean [tex](3 + 7) / (2) = 5[/tex].

Answer:

The type of polygon that is formed is a Hexagon because of its 6 sides.

Step-by-step explanation:

When you graph all of these points into a coordinate grid it should look like this:

Amount of shampoo in the original bottle is 15.0376 ounces.

Larger bottle of shampoo contains = 20 ounces

Let, amount of shampoo in the original bottle = x ounces

33% of amount of shampoo in the original bottle = ((33x)/100)

According to the question, amount of shampoo in the larger bottle is 33% more of amount of shampoo in the original bottle. So, mathematically we can write

20 = x + ((33x)/100)

⇒ 20 = x + 0.33x

⇒ 20 = 1.33 x

⇒ x = 20/1.33

⇒ x = 15.0376

Amount of shampoo in the original bottle is 15.0376 ounces.

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Answer:

9

Step-by-step explanation:

The number 9 is in the hundredths place!

From left to right starting from the right side of the decimal, it goes tenths, hundredths, thousandths, etc!

If three friends ate at a restaurant. They ordered nachos for $18.85 and jalapeno poppers. Each friend paid $9.98, not including sales tax or tip, which was one third of the total. The cost of the jalapeno poppers is: $11.09.

First step is to calculate the amount that the three friend paid

Amount=$9.98×3

Amount=$29.94

Now let calculate the cost of the jalapeno poppers

Cost=$29.94-$18.85

Cost=$11.09

Therefore If three friends ate at a restaurant. They ordered nachos for $18.85 and jalapeno poppers. Each friend paid $9.98, not including sales tax or tip, which was one third of the total. The cost of the jalapeno poppers is: $11.09.

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The value of 'b' written in inequalities is: 8 > b > -8.

Inequalities are mathematical declarations that include the symbols > and <.

Some rules for solving the inequalities are-

For the given inequality;

48 < -6b < 48

Divide the inequality by -6; By the rule four when negative number is used for division of multiplication, the sign reverse.

Thus,

8 > b > -8 which defined the limits for the b values.

Therefore, the interval for the value of 'b'  are obtained as  8 > b > -8.

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The 82nd Percentile is 89.784

The formula n = (P/100) x N, where P is the percentile, N is the number of values in a data collection (ordered from least to largest), and n is the ordinal rank of a particular value, can be used to determine percentiles. In order to comprehend exam scores and biometric measurements, percentiles are routinely utilized.

The values' percentiles as determined by the formula are displayed below.

Percentile Value 0th = 51.7 5th = 68.1 10th = 69.36 15th = 71.24 20th = 72.92 25th = 74.6 30th = 75.86 45th = 80.38 60th = 84.34 65th = 85.38 70th = 87.12 75th = 88.4 80th = 89.4 85th = 90.84 90th = 92.44 95th = 95.2 100th = 100.1

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1.545 is  the riemann sum of the function .

What does Riemann sum do?

f(x) = x

p = { 1, 1.2 , 1.7 , 2}

c = { 1.1, 1.45,2}

fpr the interval  ( 1, 1.2) Δx = 0.2

                          ( 1.2, 1.7 ) Δx = 0.5

                           ( 1.7 , 2 )  Δx = 0.3

R(f, p,c ) = f(1.1) 0.2 + f( 1.45)0.5 +  f(0)0.3

             = (1.1) × 2  + ( 1.45) ×( 0.5) +  2 × 0.3

             = 0.22 + 0.725 + 0.6

             = 1.545

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Answer:

Step-by-step explanation:

So we know that 22000+(-480t)

And we know that T is the minutes so we just gonna apply the number of minutes into that

if 5 minutes we going to write 22000+(-480 x 5)

and so on

Good luck :)

Answer:

15.9p-13

Step-by-step explanation:

Answer:

15.9p-13

Step-by-step explanation:

i had this question and got it right

The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

Team A won 3 more medals than two times the medals won by Team B.

If the number of medals won by team B is x, than;

Number of medals won by team A = 3 + 2x

Number of medals won by team B = x

Also, we are told that Team A won 9 more medals than Team B.

Thus;

(3 + 2x) = x + 9

2x - x = 9 - 3

x = 6

3 + 2x = 3 + 2(6) = 15 medals

Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

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The correct option is C. Connect every intersection of an arc and the circle with a segment.

When constructing an inscribed regular hexagon, the steps come after six arcs are created on the circle is connect every intersection of an arc and the circle with a segment.

A hexagon is a two-dimensional geometric shapes shape with six sides that have the same or different length dimensions. A hexagonal flooring, pencil cross-section, honeycomb, and other real time of the hexagon shape include.

Some key features related to regular hexagon are-

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It is the location of the center of an equal distance point traced from the center. A circle's radius is the distance among its center and its circumference.

When building an engraved regular hexagon.

Following the creation of six arcs on the circle, the following steps will be taken.

A segment should be connected to every intersection of an arc and a circle.

The correct question is -

When constructing an inscribed regular hexagon, what steps come after six arcs are created on the circle?

A. Connect every other intersection of an arc and the circle with a segment. B. Connect the intersections of the diameters and the circle with a segment.

C. Connect every intersection of an arc and the circle with a segment.

D. Connect the midpoint of the radius to the endpoint of the diameter.

Answer: (C) Connect every intersection of an arc and the circle with a segment.

Step-by-step explanation: butter

When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

We need to find the type of correlation when two variables vary along with each other but the data points are loosely scattered around the line of best fit.

A scatter plot helps find the relationship between two variables. This relationship is referred to as a correlation. Based on the correlation, scatter plots can be classified as follows.

A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.

Therefore, when two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

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Answer:0.757

Step-by-step explanation:

Answer:

Step-by-step explanation:

So in your account you got $175.29

Then you deposit mean increase the amount of money in your account by $48.75

So: 175.29+48.75 = 224.04

The price is $249.99

So: 249.99 - 224.04 = $25.95

You need to save $25.95 in order to buy your cell phone

To buy the cellphone of worth $249.99, additional $25.95 are required.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

The price of cellphone = $249.99

The amount in saving account = $175.29

Additional amount deposit in account = $48.75

Total amount in account after deposit = 175.29 + 48.75 = 224.04

Since, the price of cellphone is $249.99

And the amount in account = 224.04

So the more amount required = 249.99 - 224.04 = 25.95

To buy the cell phone $25.95 are required.

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The plumber has enough handles to install the entire 9 sinks

A plumber needs to install handles in 9 sinks

Each sink has a hot water handle and a cold water handle, that means each sink will require 2 handles. This means the multiplication of 9 and 2

= 9 × 2

= 18

The plumber has a total of 19 handles and 18 handles are required for the installation. This means that he has enough handles and he will be left with one handle.

Hence, there will be enough handles for the installation.

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An equation of the tangent line to the curve [tex]x e^y+y e^x=4[/tex] at the point (0, 4) is [tex]y=-(4+e^4) x+4[/tex].

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  [tex]\left.y^{\prime}\right|_{x=0, y=4}[/tex] as-

Consider the given equation;

[tex]x e^y+y e^x=4[/tex]

Differentiate both side with respect to x;

[tex]\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}[/tex]

Now apply product rule;

[tex]\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}[/tex]

Applying exponential and power rule;

[tex]\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}[/tex]

Solve the value of y'

[tex]y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}[/tex]

Now, find the value of slope m.

[tex]m=\left.y^{\prime}\right|_{x=0, y=4}[/tex]

[tex]\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4[/tex]

Now, using the point-slope formula, obtain the line equation as follows.

[tex]\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}[/tex]

Therefore, an equation of the tangent line to the curve is   [tex]y=-(4+e^4) x+4[/tex].

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Answer:

y = x + 3

Step-by-step explanation:

The difference between 1 and 4 is 3

The difference between 2 and 5 is 3

The difference between 3 and 6 is 3

The difference between 4 and 7 is 3

So our answer will either be x= y-3 or y=x+3

Since y=x+3 is the only option that matches the table it must be the answer

Hope this helped and have a good day

Answer:

-13, -7.9, -7.7, -3.3, 0.1, 2.4

Step-by-step explanation:

The amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

Let x represent the amount of water

Hence,

15% = .18(30)/(30+x)× 100          

Solve for x

.15 = 5.4/(30+x)

.15(30+x) = 5.4

30 + x = 5.4/.15= 36

x = 36 - 30

x = 6 ml

Therefore the amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

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Answer:

it would be A since the plus sign is canceled by the minus sign for the equation.

The class size is 10.

The upper limit of the class interval 40 - 50 is 50/

The lower limit of the class interval 20 - 30 is 20.

The frequency of class interval 10 - 20 is 10.

A class interval is a group of values that are put together for computation in a frequency distribution. An example of a class interval is 20 - 30. The class size is the difference between the upper limit and the lower limit of a class interval. The class size is the same for all the data set.

Class size = upper limit - lower limit

50 - 40 = 10

The upper limit is the biggest number in a class. The lower limit is the smallest number in a class. For example in the class 20 - 30, the  upper limit is 30 and the  lower limit is 20. The frequency of a distribution is the number of times that data within a class appears in the data set. For example, the class 40 -- 50 appears 7 times in the data set.

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The correct responses for the points, segments, lines, planes, are as follows;

1. M, S, X, and Y

2. Two lines are; [tex] \overleftrightarrow{SX}[/tex], [tex] \overleftrightarrow{YR}[/tex]

3. [tex] \overline {MX}, \overline{MY}, \overline {MS}, \overline{MR}[/tex]

4. [tex]\overrightarrow{MT}[/tex]

5. S, M, T

6. T

7. [tex] \overline{MT}[/tex]

8. [tex] \overleftrightarrow{SX}[/tex]

9. [tex] \overleftrightarrow{SX}[/tex]

10. [tex] \overline{MR}[/tex]

11. A line

12. A plane

13. A point

14. A plane

15. A ray

16. A segment

Please find attached the drawing for the figures in questions 17, 18, 19,and 20

1. A point in Euclidean geometry is a location in space.

Four points are; M, S, X, and Y

2. A line has no thickness and extends indefinitely in both directions.

Two lines are;

[tex] \overleftrightarrow{SX}[/tex]

[tex] \overleftrightarrow{YR}[/tex]

3. Four segments are;

[tex] \overline {MX}, \overline{MY}, \overline {MS}, \overline{MR}[/tex]

4. A ray that has M as an endpoint is \overrightarrow{MT}

5. Three collinear points are; S, M, T

6. A point not on [tex] \overline{YR}[/tex] is T

7. A segment with points T and M as its endpoints is [tex] \overline{MT}[/tex]

8. A line that does not contain R is [tex] \overleftrightarrow{SX}[/tex]

9. A line containing M is; [tex] \overleftrightarrow{SX}[/tex]

10. A segment of lies on [tex] \overleftrightarrow{YR}[/tex] is MR

11. A toothpick suggests a line

12. A floor suggests a plane

13. The tip of a pin suggests a point

14. The water surface of a swimming pool suggest a plane

15. A beam of light from a laser suggests a ray

16. A fence pole suggests a segment

Please find attached the drawing for the figures in questions 17, 18, 19, and 20

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Answer:

x=11

Step-by-step explanation:

4x + 17 = 5x + 6

Solve for x

Subtract 4x from each side

4x-4x + 17 = 5x-4x + 6

17 = x+6

Subtract 6 from each side

17-6 = x+6-6

11 =x

Answer:

[tex] \sf \: x = 11[/tex]

Step-by-step explanation:

[tex] \sf \: 4x + 17 = 5x + 6[/tex]

Subtract both sides by 4x to remove 4x.

[tex] \sf4x + 17 - 4x = 5x - 4x + 6 \\ \sf 17 = x + 6[/tex]

Subtract both sides by 6 to remove 6 .

[tex] \sf17 - 6 = x + 6 - 6 \\ \sf11 = x[/tex]

Answer:

2. All real numbers

Step-by-step explanation:

Hope this helps!

Please mark as brainliest if correct!

Answer:

63,756 ft / 70 min