Find the midpoint M of the line segment joining the points S = (4,-2) and T = (-6,2).

Answer:

6cm by 1.5cm

18cm by 4.5cm

80cm by 20cm

Step-by-step explanation:

Using proportions, it is found that:

a) The graph for the distance-time journey is given at the end of the answer.

b) The average speed for the whole journey was of 25 miles per hour.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the rates of the variables.

Proportions are applied to find the relation between velocity, distance and time, as velocity is distance divided by time, that is:

v = d/t.

Then, applying cross multiplication, the distance is given by:

d = vt.

On the first interval of his trip, for the first 15 minutes = 1/4 of an hour, he traveled at a velocity of 40 mph, hence the distance is:

d = 40 x 1/4 = 10 miles.

During the second interval, of 25 minutes, from 15 minutes to 40 minutes, he stopped, hence his distance remained constant at 10 miles.

During the third interval, of 20 minutes = 1/3 of an hour, Tim completed the journey at a velocity of 45 mph, hence the complete distance is given by:

d = 10 + 45 x 1/3 = 10 + 15 = 25 miles.

The graph with these three intervals is given at the end of the answer.

He drove a distance of 25 miles in one hour, hence his average speed is given as follows:

v = d/t = 25/1 = 25 miles per hour.

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Answer:

22

Step-by-step explanation:

z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex] is in the form z = a+ ib, where a = 13/20 and b = 19/20

Exact value of |z| = 1.151

Argument of z = 55.6197

Consider the complex number z = (2+7i)/(6+2i)

6a. Here z is in a rational form and we need to simplify it to represent it in the form a+ ib.

Multiplying and dividing the conjugate of the denominator to z, we get,

z = [tex]\frac{2+7i}{6+2i} \times \frac{6-2i}{6-2i}[/tex]

⇒ z = [tex]\frac{12 +38i +14}{6^2+2^2}[/tex]

⇒ z = [tex]\frac{26+38i}{40}[/tex]

⇒ z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex]

is in the form z = a+ ib, where a = 13/20 and b = 19/20

6b.modulus of z = |z| = √(a²+b²)

                                  = [tex]\sqrt{\frac{13^2}{20^2} +\frac{19^2}{20^2} }[/tex]

                                  = [tex]\sqrt{\frac{530}{400}}[/tex]

                                  = √(53/40)

                                  = 1.151

6c. Argument of z = tan⁻¹(b/a)

                              = tan⁻¹((19/20)/(13/20))

                              = tan⁻¹(19/13)

                              = 55.6197

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Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=17

Step-by-step explanation:

The value of the function f(0) = 1, obtained from the graph.

For the given question;

The graph for the function is given.

For finding the value of function f(0), simply see the value of y with respect to x = 0.

f(0) = 1, taken from graph.

Thus, the value of function f(0) is found as 1.

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Answer: s= -4u/9  +  5t/9

Step-by-step explanation: Hope it helps

Step-by-step explanation:

First of all, we have to take -5t to the other side and after taking it to the other side it will be +5t, then we have to take (only) 9 to the other as it is 9s (multiplication) it will be division if u take it to the other side.

Done

The density of the material of mass 200 g and volume 10.4 ml is 19.2 g/ml.

According to the question,

We have the following information:

Density is defined as the mass per unit volume.

So, we have the formula of density:

Density = Mass/volume

Mass of the metal object = 200 g

Volume of the metal object = 10.4 ml

Density = 200/10.4 g/ml

Density = 19.231 g/ml

Now, we will round it off to nearest 1 decimal point.

We know that when the digit is greater than 5 then the number is increased by 1 and when the digit is less than 5 then the number remains same.

So, we have:

Density = 19.2 g/ml

Hence, the density of the metal object is 19.2 g/ml.

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Answer:

y = 3x - 1

Step-by-step explanation:

In order for lines to be parallel, they must have the same slope.

The slope of y = 3x - 8 is 3.

Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:

y − y₁ = m(x − x₁)

y - (-7) = 3(x - (-2))

y + 7 = 3(x + 2)

Distribute 3 and isolate y:

y + 7 = 3x + 6

y = 3x - 1

Step-by-step explanation:

your teacher gave you the law of sines already.

this was the only "trick" needed to solve this.

now, we just need to use it.

to be considered : a, b, c are always the sides opposite to the angles A, B, C.

so,

sin(28)/11 = sin(x)/22

sin(x) = 22×sin(28)/11 = 2×sin(28) = 0.938943126...

x = 69.87481894...° ≈ 69.9°

Answer: 28

Step-by-step explanation: 28

We can write the system of equations:

x = y + 15

x + y = 105

Solving the system, we will see that Robin has 45 apples and Linda 60 apples.

Here we can only solve the first part, as the second is incomplete.

Let's define the variables:

x = apples that Linda has.

y = apples that Robin has.

We know that Linda has 15 more apples than Robin, and that between the two there are 105 apples, so we can write the system of equations:

x = y + 15

x + y = 105

To solve this, we can replace the first equation into the second one, so we get:

(y + 15) + y = 105

2y + 15 = 105

2y = 105 - 15 = 90

y = 90/2 = 45

So Robin has 45 apples, and Linda has 15 more, so she has:

x = 45 + 15 = 60

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On a hot summer day, 606 people used the public swimming pool; daily admission prices are $1.75 for children and $2.50 for adults; admission receipts totaled $1357.50; 396 adults and 210 children swam at the public pool that day.

Therefore,

1.75C + 2.50A = 1357.50

C + A = 606

C = 606-A

1.75(606 - A) + 2.50A = 1357.5

1060.5 - 1.75A + 2.50A = 1357.5

1060.5 + 0.75 A = 1357.5

0.75 A = 297

A = 297/0.75

A = 396

No of adults = 396

Therefore children = 606-396

No of children = 210

396 adults and 210 children swam at the public pool that day

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28% is the correct answer because it is the closest to true value sine people are sensitive about information like this.

The error interval for the area will be expressed as 64.2< a < 63.93

Error intervals may be defined as the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated. According to the question, Area of circle = 78.1 cm² and Area of square = 21.4 cm². If we round the area to one decimal point, we get the Area of circle = 78.1 + 0.05   and = 78.1 - 0.05 that is 78.15 and 78.05. Also, the Area of square = 21.4 - 0.05 and = 21.4 + 0.05 we get 21.35 and 21.45. Now, Area of shaded region in the form m < a < n. So, n = 78.15 - 21.35

=> n= 56.8 and

m = 78.05 - 21.45

=> m = 56.6

Area of shaded region is 56.6< a < 56.8.

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The fraction 70 1/3% in simplest form is 24.67%.

Firstly converting mixed fraction to fraction. For conversion to fraction rewriting the fraction -

Fraction = (3×70 + 1)/3%

Then performing the multiplication in numerator of the fraction to find the fraction in simplest form

Fraction = (73 + 1)/3%

Performing addition in numerator of the fraction to find the fraction in simplest form

Fraction = 74/3 %

We have got the improper fraction as numerator is greater than denominator. Now performing division to find the fraction in simplest form

Fraction = 24.67%

Thus, the fraction in simplest form is 24.67%

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A zero function is a constant function for which, regardless of the inputs, the output value is always zero.A zero function's input can be any real number, but its output is always zero, hence it can take any value from the real numbers

Solve the problem ?

The function f (x) = x - 8  has zeros.

To make f (x) = x  -  8 = 0,   find x.

Start by factoring f (x),

then f(x) =(x-8)=0

f (8 )  =    0

x =  8

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The probability formula is given by:

The person selects one of six envelopes.

There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes

Then, the expected value is given by

A multi step equation with an answer of -8 can be expressed as: 2x + 20 = 4.

x = -8 when solved.

A multi step equation can be an equation that has variables or/and terms on both sides, of which we can solve for the variable in the equation by isolating the variable to one side of the equation using inverse operations.

For example, a multi step equation can be expressed as 2x + 20 = 4.

Solve for x in the equation:

2x + 20 - 20 = 4 - 20 [subtraction property of equality]

2x = -16

2x/2 = -16/2 [division property of equality]

x = -8

Thus, 2x + 20 = 4 is a multi step equation that has a solution of -8.

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Answer:

20002

Step-by-step explanation:

100*20=2000

2000*10=20000

20000+2=20002

The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

Denoting the distance in feet between the wall and the base of the ladder by x and the angle in radians between the ladder and the ground by y, it is noted;

cos(y) = x/10

which implies;

y = arccos(x/10)

Denoting time in seconds by t, it is further noted that;

[tex]\frac{dx}{dy} = \frac{dy}{dx} \frac{dx}{dt}[/tex]  (chain rule)

Noting (using a standard table of derivatives for convenience)

[tex]\frac{dy}{dx}= -\frac{1}{\sqrt{1-(0.1x)^2} }(0.1)[/tex] (also by chain rule)

The above equation changes as;

[tex]\frac{dy}{dx}= -\frac{0.1}{\sqrt{1-0.1x^2} }[/tex]

It is noted from the question that in this particular system;

[tex]\frac{dx}{dt} = 0.5[/tex]  feet per second

So (denoting the derivative as a function of x)

[tex]\frac{dy}{dt}(x)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01x^2} }[/tex]

At last;

[tex]\frac{dy}{dt}(8)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01(64)} }[/tex]

         = [tex]\frac{0.05}{\sqrt{1-0.64} }[/tex]

         = [tex]\frac{-0.05}{\sqrt{0.36} }[/tex]

         = -5/60

         = -1/12 radians per second

The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

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Answer:

3/4

Step-by-step explanation:

Probability

8 red marbles, 3 blue marbles, and 1 green marble = 12 total marbles

8 red marbles+ 1 green marble = 9 not blue marbles

P ( not blue ) = not blue marbles / total marbles

                     = 9/12 = 3/4

Answer:

9

Step-by-step explanation:

8+3+1=12

12-3=9

umm ok i think i got it wrong or overcomplicated it lol

hope this helped

The value of m = -10, which we get by solving the given equation

The given equation is

0.61m - 1.51m = 9

⇒-0.9m = 9                  (we get the minus sign because 0.61  is smaller than 1.51)

⇒-0.9m/(-0.9) = 9/(-0.9)       (dividing both sides of the equation by -0.9)

⇒m = -90/9

⇒m = -10

Thus on solving the given equation we get the value of m as -10

That is m=-10

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The graph of the coordinate plane is attached below.

Any point on a plane can be uniquely identified by a pair of numerical coordinates using a cartesian coordinate system, which employs signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length.

The graph of the line decreases between  (2.5, 2) and (4.5, 0.25) and the graph increases between (2.5, 2) and (4.5, 0.25)

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Should be B.

There is a nested function structure. Let's first look at the limit of the interior (f(0)). The point we need to pay attention here is to look at the limits from the right and left. If both values are equal, we can say that it has a limit at that point.

If we express it algebraically;

The left limit and the right limit of [tex]f(0)[/tex] are equal and equal to [tex]2.[/tex]

The left limit and the right limit of f(2) are equal and equal to 3.

As I have drawn with colored arrows in the graph below, we approach from the left and from the right, and if they both point to the same point, we can talk about the existence of the limit at that point. Otherwise, this function does not have a limit at that point.

As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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given that

consider the chances,

therefore x lies between -6 and 2

The amount that Georgina has invested in savings account and CD are $ 2500 each.

Given that:-

Total amount invested in savings account and CD = $ 5000.

APY in savings account = 0.6 %

APY in CD = 0.9 %

Total interest earned = $ 37.5

Let the amount invested in savings account be x.

Hence, according to the data given in the question, we can write,

Amount invested in CD = 5000 - x

Interest in savings account in a year = x*(0.6)*1/100 = 0.006x

Interest in CD in a year = (5000-x)*(0.9)*1/100 = (0.009)(5000-x) = 45 - 0.009x

Hence,

0.006x + 45 - 0.009x = 37.5

45 - 37.5 = 0.009x-0.006x

7.5 = 0.003x

x = 7.5/(0.003)

x = 7500/3 = 2500

Hence, Georgina has invested $2500 in each savings account and CD.

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ANSWER

y - 3 = -8/5 (x + 5)

EXPLANATION

The point-slope form of the equation of a line, that has a slope m and passes through point (x1, y1) is:

In this problem m = -8/5 and the given point is (-5, 3). The equation is: