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Prove: Every point on the perpendicular bisector of a segment is equidistant from the ends of the segment.

The correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

From the question, we are to solve the inequality

The given inequality is

–3(2x – 5) < 5(2 – x)

First, clear the brackets

–6x + 15 < 10 – 5x

NOTE: This is one of the correct representations of the inequality

Collect like terms

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1 and flip the sign

x > 5

Representing this on a number line, we get a number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right.

Hence, the correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

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Step-by-step explanation:

every point on the circle has the same distance from the center : r (radius).

we can see that radius right there on the x-axis : the distance of (3, 0) to (0, 0) is simply 3. that is our radius.

the distance formula is applied Pythagoras

distance² = (difference in x coordinates)² +

+ (difference in y coordinates)²

distance = sqrt( ... )

so,

(-2.5, - 2.5)

(-2.5 - 0)² + (-2.5 - 0)² = 6.25 + 6.25 = 12.5

that is not 3² = 9, so the point is NOT on the circle.

(1, 3)

(1 - 0)² + (3 - 0)² = 1 + 9 = 10

that is not 3² = 9, so the point is NOT on the circle.

(2, -sqrt(5))

(2 - 0)² + (-sqrt(5) - 0)² = 4 + 5 = 9

that IS 3² = 9, so, the point IS on the circle.

(-sqrt(3), -sqrt(7))

(-sqrt(3) - 0)² + (-sqrt(7) - 0)² = 3 + 7 = 10

that is not 3² = 9, so the point is NOT on the circle.

The interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.

It should be noted that the null hypothesis simply means a statical theory that suggests that there's no relationship between the variables given in the data set.

From the information given, it was stated that the proportion of blue beads in the container is 0.30. Here, the interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.

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Answer: 99M

Step-by-step explanation:

Rectangle area

A=LW

A = 11 x 9

A = 99

Mark as brainliest please TT. Thank you :D

Answer:

99 m

Step-by-step explanation:

width times length = area

11 ×9= 99m

Answer:

-2

Step-by-step explanation:

For a straight-line graph, pick two points on the graph.

The gradient of the line = (change in y-coordinate)/(change in x-coordinate)

             (x, y)

Point 1: (2, 0)

Point 2: (3, 2)

Gradient = (change in y)/(change in x)

= (2 - 0) / (3 - 2)

= 2 / 1

= 2

Note: gradient is basically slope where slope = rise / run

Answer:

help has arrived its -2

Step-by-step explanation:

Answer:

  66°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°.

__

  79° +x +35° = 180°

  x = 180° -114° . . . . . . . . subtract 114° from both sides

  x = 66° . . . . . simplify

The value of the expression f(5) + j(-2)  is -8 where f(x)=12-3x and j(x)=x² + 4x - 1

The expression is given as:

f(5) + j(-2)

Where f(x)=12-3x and j(x)=x² + 4x - 1

Calculate f(5) and j(-2)

f(5)= 12 - 3(5) = -3

j(-2) = (-2)² + 4(-2) - 1 = -5

So, we have:

f(5) + j(-2)  = -3 - 5

Evaluate

f(5) + j(-2)  = -8

Hence, the value of the expression f(5) + j(-2)  is -8

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Answer:

Step-by-step explanation:

Answer:

282.7miles

Step-by-step explanation:

334+514=848inch

12inch=4miles

848inch=x

[tex]x = \frac{818 \times 4}{12} = 282.7[/tex]

Total distances in miles

Now 12 in =4mi

3in=1mi

Total miles

If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

Tₙ = a + (n-1)d

(for all positive integer values of n)

Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,

4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........

Therefore,

Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,

a₃₆ = 4.54 + (36-1)4.54

a₃₆ = 163.44

Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

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Answer:

He read 10% of the book, so 90% remains to be read.  That 90% consists of 45 pages, so

45=0.90n

n= 45/0.90

n=50

There are 50 pages total in the book

Step-by-step explanation:

Answer:

144 inches in 12 feet.

Step-by-step explanation:

There are 12 inches in 1 foot.

Find inches when you have 12 ft.

[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]

Feet cancel out leaving inches.

There are 144 inches in 12 feet.

Answer:

B

Step-by-step explanation:

If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.

These roots are real and distinct, or choice B.

If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.

I hope that helps!

Answer:

[tex]3 < x < 5[/tex]

Step-by-step explanation:

Given inequality:

[tex]|2x - 8| < 2[/tex]

[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]

[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]

[tex]\implies -2 < 2x-8 < 2[/tex]

Therefore:

[tex]\implies -2 < 2x-8[/tex]

[tex]\implies 6 < 2x[/tex]

[tex]\implies 3 < x[/tex]

And:

[tex]\implies 2x-8 < 2[/tex]

[tex]\implies 2x < 10[/tex]

[tex]\implies x < 5[/tex]

Merge the overlapping intervals:  [tex]3 < x < 5[/tex]

Proof

Graph:  [tex]y=|2x-8|[/tex]

Add a line at  [tex]y=2[/tex]

The interval that satisfies  [tex]|2x - 8| < 2[/tex]  is the area under the points of intersection (shaded area on the attached graph).

The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.

So

Case-1

Case-2

So solution is

C. Vertex (x,y). The vertex is right in the middle of the quadratic graph.

The measure of all the angles is given below:

angle 1= 30

angle 2=  150

angle 3= 30

angle 4= 150

angle 5= 30

angle 6= 150

angle 7= 30

angle 8= 73.5

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

As,

angle 1= 30 (Vertically opposite angle)

angle 7= 30 (corresponding angle)

angle 4+30= 180 (linear pair)

 angle 4= 150

angle 4= angle 2= 150 (Vertically opposite angle)

angle 2= angle 6= 150  (corresponding angle)

angle 1= angle 5= 30  (corresponding angle)

angle (2x+3)= angle 4  (corresponding angle)

     2x+3= 150

      x= 73.5

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Answer:

2.  3.913 kg (3 dp)

3.  light cream

4.  240 CoffeeStops

5.  7 CoffeeStops per square mile

6.  2,861 cups of coffee each day

Step-by-step explanation:

Given:

Question 2

[tex]\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}[/tex]

Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)

---------------------------------------------------------------------------------------------

Question 3

Given:

[tex]\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}[/tex]

Therefore, the container holds light cream.

---------------------------------------------------------------------------------------------

Question 4

Given:

[tex]\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}[/tex]

Therefore, there are 240 CoffeeStops.

---------------------------------------------------------------------------------------------

Question 5

Given

[tex]\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}[/tex]

Therefore, the density of CoffeeStops is 7 per square mile.

---------------------------------------------------------------------------------------------

Question 6

Given:

[tex]\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}[/tex]

Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.

Answer:

47.14 cm

Step-by-step explanation:

Circumference :

The frequency of the data set that matches with the interval stated are:

50 - 54: 2

55 - 59: 6

60 - 64: 7

65 - 69: 3

70 - 74: 2

Frequency is the number of times a data point or a set of points within an interval appears often in a data set.

The corresponding frequency to each of the interval given for the data would be as follows:

50 - 54: 2

55 - 59: 6

60 - 64: 7

65 - 69: 3

70 - 74: 2

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Answer:

2900

Step-by-step explanation:

2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.

Answer:

Freshmen to sophomores - (17:19)

Sophomores to freshmen - (19:17)

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

Answer:

This equation has 2 solutions.

1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]

2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]

Answer: the other person is correct

Answer:

x+2

Step-by-step explanation:

x^2+x-7 = x+2

Answer:

The answer is 1/4!!

<3 love

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

Given that;

First, we substitute the value of p and b into the equation.

m = ( p-2b ) / 2

m = ( 57.4 - 2(8.7) ) / 2

m = ( 57.4 - 17.4 ) / 2

m = 40 / 2

m = 20

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

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Answer: 1/3x + 2/3

Step-by-step explanation:

f(x)= 3x - 2 =>

y= 3x - 2 =>

x= 3y - 2 =>

3y - 2= x =>

3y= x + 2 =>

y= 1/3x + 2/3 =>

f-1(x)=1/3x + 2/3

Answer:

I believe it's c because Greg downloaded 5 song which is 6.45 total then bought certain song at sale price Wich ended at 9.42

Answer:

[tex]\frac{72}{-x^{5} +9}[/tex]

Step-by-step explanation:

Let me know if that is not the same equation you wrote and if you have any questions !!