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The equation of the line that passes through the points (2, 1 ) and (4,5) in the Cartesian coordinate plane is y = (2/3)(x - 4) + 5.

By subtracting the y coordinates [5 - 1] = 4, we get

Subtract the x coordinates in the same order  [4 - (-2)]  = [4 + 2] = 6

The slope is given by  y-coordinate/x-coordinate = 4/6  = 2/3.

Now, just choose one point say (4,5), and substitute the coordinates in this formula-

y - [y-coordinate of our point] - (slope)* [ x - ( the  x-coordinate of our point)]

y - 5  = (2/3)(x - 4)      ...........(adding 5 to both sides)

y = (2/3)(x - 4) + 5    

Hence, the equation of the line in the "slope-intercept" form is y = (2/3)(x - 4) + 5.

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The complete question is -

what is the equation of the line that passes through the points (-2,1) and (4,5) in the cartesian coordinate plane?

Answer:

Step-by-step explanation:

Upper right graph meets both of the requirement, the line lays on both (0,9) on the y axis and (3,0) on the x axis

Answer:

c.philiippines

Step-by-step explanation:

exporting (present participle)

send (goods or services) to another country for sale:

The equation used to represent the distance between two points A and B is AB  =  x Cos 28°

The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.

As per the given question,

Let the hypotenuse be x

The two points A and B are on the base of the triangle so,

Base - length = AB

The distance between the two points is

⇒   cos Θ   =   base / hypotenuse

where,      base = AB

                hypotenuse = x

⇒   cos Θ   =   AB / x

⇒   AB   =   x cos Θ      →   1

Substitute Θ  =  28 in 1,

⇒   AB = x cos 28°

Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.

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The complete question is

When θ = 28° , which equation can be used to find the distance from point a to point b?

By using tangent chord angle formula, the measure of angle FGH is 50°.

What is tangent chord angle?
The angle formed by the chord in the alternate segment is equal to the angle formed by the tangent through the point of contact of the tangent for any circle, according to the theorem.

Another name for the tangent-chord theorem is the alternate segment theorem.
We have to find the m ∠FGH.
Since, by tangent - chord angle theorem, the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle.
GH = 2(m ∠FGH)⇒ m ∠FGH = 1/2(GH)
Here GH = 100° ⇒ m ∠FGH = 1/2(100°) m ∠FGH = 50°
Hence, by using tangent chord angle formula, the measure of angle FGH is 50°.

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volume of ball = 5421.85[tex]cm^{3}[/tex]

A sphere is a set of points in space that are a given distance r from the center.

The volume of a 3 -dimensional solid is the amount of space it occupies.  Volume is measured in cubic units( in3,ft3,cm3,m3 , et cetera).  Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a sphere is four-thirds times pi times the radius cubed.

V=4/3πr^3

The volume of a hemisphere is one-half the volume of the related sphere.

Given that

diameter of ball = 21.8 cm

now we need to find the volume of ball

volume of the sphere =[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]

diameter = 21.8cm

radius = diameter/2

         = 21.8/2

          =10.9

now substitute the value of radius in the volume formula

volume of ball =[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex](10.9)^{3}[/tex]

volume of ball = 5421.85[tex]cm^{3}[/tex]

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The count increase in the alien bacteria at the midnight is 31692.

Here we have to find the count of alien bacteria at midnight.

Data given:

Count of alien bacteria at 5 pm = 26,300

Percentage increase in bacteria per hour = 2.7%

increase = 1 + 2.7/100

               = 102.7

time = 12 - 5 = 7

The count of alien bacteria at midnight = 26,300 ×( 1.207 [tex])^{7}[/tex]

                                                                 =  31692

Therefore the alien bacteria at midnight is 31692.

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To dilate a rectangle means to either expand or contract the size of rectangle without changing it's shape .

Dilation is where the polygon grows or shrinks but keeps the same overall shape.

To dilate a rectangle means to either expanding or contracting the rectangle without changing it's shape .

For example: Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

To dilate this rectangle by factor 3 , then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The rectangle has enlarge it's size .

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Answer:

C) [tex]y=3x-8[/tex]

Step-by-step explanation:

[tex]y-16=3(x-8) \\ \\ y-16=3x-24 \\ \\ y=3x-8[/tex]

The required markup from the cost of $270 is 20% of the sale price.

The selling price of an item is ​$360. It is marked down by ​%10, but this sale price is still marked up from the cost of ​$270.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Selling price after 10% marked down,
= [1 - 0.10] × 360
= 324
Now,
Percentage marked up of cost price of $270
= 324 - 270 / 270 × 100
= 20%

Thus, as of the given condition markup cost of $270 is 20% of the sale price.

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Answer:

1,728 small cubes are needed to completely fill a larger cube with side lengths of 30 cm.

Step-by-step explanation:

Answer:

Figure 1 (The Star)

Step-by-step explanation:

Line symmetry is symmetry created by a line that divides a shape. Only the "star" (Figure 1) and the "A" (Figure 2) can be split through the center into two identical halves, therefore we can rule out Figures 3 & 4. Rotational symmetry is when a shape looks the same after a partial turn. Rotational symmetry is only true for the "star" (Figure 1) which will be symmetric every 72-degree (360/5) turn. However, the "A" (Figure 2) can only be flipped 180 degrees to remain symmetric.

Therefore Figure 1 is the only figure with both rotational and line symmetry.

Answer:

15/4

Step-by-step explanation:

[tex]\ell=5/2 \\ \\ w=1 \\ \\ h=3/2 \\ \\ V=lwh=(5/2)(1)(3/2)=15/4[/tex]

Answer:

3.75 so i believe the answer might be 15/4?

Step-by-step explanation:

im sorry if this is not the right answer

The limit of x/|x|  as x approaches 0 does not exists.

We need to find the limit of x/|x| as x approaches 0.

Consider left hand limit.

lim x -> 0- (x/|x|)

x/|x| = -1 for all negative values of x.

So, lim x -> 0- (x/|x|) = -1

Consider right hand limit.

lim x -> 0+ (x/|x|)

x/|x| = 1 for all positive values of x.

So, lim x -> 0+ (x/|x|) = 1

lim x -> 0- (x/|x|) ≠ lim x -> 0+ (x/|x|)

Therefore, the limit of x/|x| does not exists.

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The complete question is:

What is the limit of x/|x| as x approaches 0?

Answer:

19

Step-by-step explanation:

9 1/2 divided by 1/2 is 19

The inequality graphed on the given image is the one in option B, the inequality is:

x > -2.

On the graph, we can see an inequality. We can see a vertical line and all the region to the right of that line is shaded.

The vertical line is x = -2

If the right side of that is shaded, then all the points (x, y) with a value of x larger than -2 are solutions, then the inequality is just:

x > -2

Then the correct option is B.

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Answer:

325.6g

Step-by-step explanation:

weight of phone + weight of case

= 310 + 15.6

= 325.6g

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The two numbers whose difference is 86 and whose product is a minimum. The numbers are (43,-43) and therefore, the smaller number is  -43 and largest number is 43.

Given :

Two numbers whose difference is 86 and whose product is a minimum.

To find : The numbers

Let the largest number be x,

and smallest number be y.

According to question,

Two numbers whose difference is 86.

i.e.  x - y = 86                   -----------------------------(1)

Product of two number is minimum.

i.e.   xy = 86                     -------------------------------- (2)

where P is minimum.

Now substitute x from (1) in (2),

     x (x -86) = P

⇒ y(x) = x² - 86x = P               ------------------------------ (3)

Differentiating Equation (3), we get:

y'(x) = 2x - 86

and y'(x) = 0

After subtracting we get:

    2x - 86 = 0

⇒ x = 86 /2

⇒ x = 43

The vertex of the equation occur at x = 43.

Putting the value of x = 43 in equation (1) , we get:

    48 - y = 86

⇒ -y = 86 - 48

⇒ y = -43

So, the value of y is - 43.

Therefore, the numbers are (43,-43).

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The equation of a line with point (0,5) and gradient 3 in the form of y = mx + c is y = 3x + 5.

The point slope form of the equation to be used for finding the equation is -

y - [tex] y_{1}[/tex] = m (x - [tex] x_{1}[/tex] )

As per the mentioned information, m or slope is 3, [tex] y_{1}[/tex] is 5 and [tex] x_{1}[/tex] is 0. Keep the values in point slope form to find the equation.

y - 5 = 3 (x - 0)

Performing multiplication on Right Hand Side

y - 5 = 3x - 0

Shifting 5 to Right Hand Side

y = 3x + 5

Thus, the answer is y = 3x + 5.

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With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17[tex]\frac{1}{3}[/tex]

With one third of a serving remaining, there are 17 servings total.

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Answer: Acute Triangle

Step-by-step explanation:

Because when we look at it we can actually see each of the angles, they are less than 90 degrees then they are consider as acute angles, if it's greater than 90 degrees and smaller than 180 degrees then it will be consider as a obtuse, and if it's equal to 90 degrees then it's a right angle. This is not a equiangular, if it's then it should be have three 60degrees angles.

so,  -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

Polynomial function:

A polynomial function, in general, is also stated as a polynomial or polynomial expression, defined by its degree. The degree of any polynomial is the highest power present in it.

given that

Patricia is studying a polynomial function f(x). three given roots of f(x) are

-11-[tex]\sqrt{2}[/tex]i , 3 + 4i and 10 . Patricia concludes that f(x) must be a polynomial with degree 4.

so -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

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Answer: the answer is  -1

Answer:

they are equivalent when m = 1

Step-by-step explanation:

-5(3m-7) = -15+35

-5(3m-7) = 20

-15m+35 = 20

-15m+35 = 20

-15m = -15

m = 1

The equation of the graph is  f(x)=-2x+5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us take any two points from the graph to find the equation of the graph.

(-1, 3) and (2, -3)

Let us find the slope of line.

m=-3-3/2+1

m=-6/3=-2

Slope of line is -2 and now we find the y intercept.

y=-2x+b

3=-2(-1)+b

3+2=b

5=b

Hence, f(x)=-2x+5 is the equation of the graph.

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The coordinate of the circumcenter of a triangle is (1,3).

Here we have to find the coordinates of the circumcenter of a triangle.

Given data:

The vertices of the triangle are:

A = (0,1)

B = ( 2,1)

C= ( 2,5)

The formula to find the distance between the two points:

Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2-y1)^{2} }[/tex]

In the same manner distance between AB, BC, and AC are:

AB = [tex]\sqrt{(2-0)^{2} + (1-1)^{2} }[/tex]

    = 2

BC = [tex]\sqrt{(2-2)^{2} + (5-1)^{2} }[/tex]

      = 4

AC = [tex]\sqrt{(2-0)^{2} + (5-1)^{2} }[/tex]

     = 2√5

So by the Pythagoras, we get to know that the triangle is a right-angle triangle.

The circumcenter of a right-angle triangle is the midpoint of the hypotenuse.

Midpoint of AC = (0+2)/2 , (1+5)/2

                         = 2/2, 6/2

                         = 1,3

Therefore the coordinate of the circumcenter is (1,3).

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, that is, the INPUT never repeats, Check the picture below.

now, to check on the graph if it's a function or not, simply recall the vertical line test, if you can draw a vertical line on the graph and it only touches it ONCE, then it's a function, if however a vertical line touches it more than once, then is not.

The value of m∠IJK is 19.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

               I

            /    \

         /         \

      /               \

H /                      \ J                       K

Now,

m∠JHI = (x+12)

m∠HIJ = (x−3)

m∠IJK = (5x−6)

The sum of the angles in the triangle IHJ is 180 degrees.

m∠JHI + m∠HIJ + m∠IJH = 180

x + 12 + x - 3 + m∠IJH = 180

2x + 9 + m∠IJH = 180

2x + m∠IJH = 180 - 9

2x + m∠IJH = 171

m∠IJH = 171 - 2x ____(1)

Now,

m∠IJK = 180 - m∠IJH

5x - 6 = 180 - m∠IJH

m∠IJH = 180 - 5x + 6

m∠IJH = 186 - 5x _____(2)

Now,

From (1 ) and (2) we get,

186 - 5x = 171 - 2x

186 - 171 = 5x - 2x

15 = 3x

x = 5

Now,

The value of m∠IJK.

= 5x - 6

= 5 x 5 - 6

= 25 - 6

= 19

Thus,

m∠IJK value is 19.

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Step-by-step explanation:

convert, Keep Change Flip, convert back

[tex]\frac{23}{4} * \frac{2}{7}[/tex]

[tex]\frac{46}{28} \\[/tex]

[tex]1\frac{18}{28}[/tex]

the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square

When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.

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