2. Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).

Answer:

Mpq= (

[tex] \frac{4 \times \frac{1}{3} + - 2 \times \frac{1}{5} }{2} and \frac{3 \times \frac{1}{6} + 3 \times \frac{2}{3} }{2} [/tex]

[tex] \frac{16}{15} \: and \frac{41}{12} [/tex]

midpoint for PQ is (16/15; 41/12)

Answer: y = 12/11 x + -12/11

Step-by-step explanation:

m = y2 -y1/x2 -x1

x1 = -4

x2 = 7

                  into m = y2 - y1/x2 -y1

y1 = -7

y2 = 5

m = 12/11

x = -4            into y = mx + b

y = -7

b = - 12/11

y = 12/11x + -12/11 into

y = mx + b :

y + 12/11x + -29/11

To the nearest cent, the amount she would have in 2 years is $44.10

What is future value of the deposit in savings account?

The future value of the savings account deposit is accumulated balance in the account after 2 years which includes the initial deposit plus interest earned over 2 years

FV=PV*(1+r)^N

FV=accumulated balance after 2 years=unknown

PV=initial deposit=$40

r=interest rate per year=5%

N=number of years that the deposit would last=2

FV=$40*(1+5%)^2

FV=$44.10

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The graphed function is decreasing on this following interval:

(-5, 5).

Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.

From this problem, there is only one interval, from x = -5 to x = 5, hence the interval is (-5, 5).

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Answer: A

Step-by-step explanation:

A. 2.6x 10^-7

Answer:

a

Step-by-step explanation:

because you move the decimal 7 times to the right to put it into scientific notation

The Domain of the given function is −2≤x≤2 and the range of the given function are −2≤y≤3.

The domain of a graphical function refers to all the input values which are shown or plotted on the x-axis. The domain of a function may be defined as the set of values that are assumed for the function.

The range of a graphical function refers to all the input values which are shown or plotted on the y-axis. The range of a function may be defined as the set of values that the function gives after assuming the input values for the function.

Here in the graph, the set of input values on the x-axis are from -2 to 2. Thus, the domain is −2≤x≤2. Also, the set of input values on the y-axis is from -2 to 3. Thus, the range is −2≤y≤3.

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The value of h in the given diagram is 72 ft. The correct option is the third option 72

From the question, we are to calculate h. h is the height of the triangle

First, we will the determine half the length of the base of the triangle.

Half the length of the base of the triangle = 42 ft/2

Half the length of the base of the triangle = 21 ft

Thus,

By the Pythagorean theorem, we can write that

75² = 21² + h²

5625 = 441 + h²

h² = 5625 - 441

h² = 5184

h = √5184

h = 72 ft

Hence, the value of h in the given diagram is 72 ft. The correct option is the third option 72

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Answer:

1e+21

Step-by-step explanation:

I believe this the answer

Answer:

LK = 7

Step-by-step explanation:

NK = NM + ML + LK ( substitute values )

23 = x - 6 + 9 + 2x - 19

23 = 3x - 16 ( add 16 to both sides )

39 = 3x ( divide both sides by 3 )

13 = x

Then

LK = 2x - 19 = 2(13) - 19 = 26 - 19 = 7

The inverse of the given linear function is of:

R^(-1)(x) = (x - 2)/3

The graph is given at the end of the answer.

A linear function is modeled by the following rule:

y = mx + b

In which:

For function R, in blue, we have that when x = 0, y = 2, hence the intercept is of b = 2 and:

R(x) = mx + 2.

When x = 1, y= 5, when x = 2, y = 8, that is, when x changes by 1 y changes by 3, meaning that the slope is of m = 3, and:

R(x) = 3x + 2.

To find the inverse function, we exchange x and y in the original function, then isolate y.

For function R(x), we have that:

y = 3x + 2.

Then the inverse is found as follows:

x = 3y + 2

3y = x - 2

y = (x - 2)/3

R^(-1)(x) = (x - 2)/3

The graph of R(x) in blue and of R^(-1)(x) in blackis given at the end of the answer. Since they are inverses, they are symmetric over the line y = x.

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Answer:

2

Step-by-step explanation:

What you do to one side, you must do to the other.

When you add the 2 on one side of the = sign then you have to add the 2 on the other side. when you do that you will get 7 + 2. so the number in the green is 2. hope this helped a little!

Answer: The total weights of the two animals is  11. 92 × 10² Ibs

Step-by-step explanation:

The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

According to question, number of favorable outcomes = 1, i.e., the number 3 shows up on the die

And the total number of outcomes = 6

Hence, The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].

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Answer:

25

Step-by-step explanation:

x/5-4=1

x/5=1+4

x/5=5

x=5×5

x=25

Two hikers are 22 miles apart and walking toward the each other, they meet in 4 hours. The rate of each hiker if one hiker walks 3.3 mph faster than the other are 2.2mph, 2.2mph, 3.3mph.

Distance divided by time is the dimension of speed. The SI measure of speed is the meter per second (m/s), although the most widely used unit in daily life is the kilometer per hour (km/h), or miles per hour in the US and the UK (mph). The knot is a popular choice for air and sea travel.

The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The distance traveled by an object during a period of time divided by the length of the period gives the average speed of an object throughout that period. Velocity and speed are not the same thing.

Time divided by distance are the speed-related metrics. The kilometer per hour (km/h), or miles per hour in the US and UK, is the unit of speed that is most frequently used in daily life. The meter per second (m/s) is the metric unit of speed (mph). The knot is often used in air and sea transportation.

Since the hikers are moving at varying speeds, they collide in a location other than the center.

Let the distance travelled by Hiker A (slower) be x at speed s.

So, the distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1).

s = x / 4

s + 1.1 = 22 - x / 4

After resolving equations 1 and 2, we obtain:

x = 8.8m and s = 2.2mph

Therefore,

Speed of the Hiker A = 2.2 mph

Speed of the Hiker A = 2.2 mph

Speed of the Hiker B = 3.3 mph

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Answer: the answer is c!

Step-by-step explanation:

If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x

Given,

The initial fee of taxi cab = $2.85

The charges per mile = $2.70

Consider the number of miles as x

Then,

The equation of the fare = 2.85+2.70x

Hence, If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x.

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To solve the equation, divide both sides by 5. The solution is c = 4.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

The given problem:

Solve 5c = 20

Notice that the variable, c, is already isolated on the left side.

Divide both sides by 5:

5c : 5 = 20 : 5

c = 4 (solved)

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Answer:

Step-by-step explanation:

Given that

To find

So, according the question,

We have

So, the money he loss to don't sell that Jackets in 30 days is the total cost of all jackets.

∴     The Total cost of all Jackets    = 75 × 5

                                                           = $375.

Answer: Retailer will loss $375.

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The standard form of a line is simply a special way of writing the equation of a line. You are probably already familiar with the slope-intercept form of a line, y = mx + b. The standard form is just another way to write this equation and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements). As you will see in the lesson below, every line can be expressed in this form.

Note that the requirements on A, B, and C vary a bit from textbook to textbook. While they technically can be any real numbers, it is most common to write them as integers and to keep A positive. It is also common to require that A, B, and C share no common factors.

Ax+By=C

THE STANDARD FORM OF A LINE: Ax+By=C

The result is referred to as the standard form of the line: Ax+By=C. We should always be able to convert from one form of an equation to another. For example, if we are given a line in the slope-intercept form, we should be able to express it in the standard form, and vice versa

he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations

Now ,

A=0

B=0

A and B are not both zero, the graph of Ax + By = C is always a line.

when ,

The graph of Ax + By = C, where A and B are not both zero

A[tex]\neq[/tex]0

B[tex]\neq[/tex]0, is a line.

Divide both sides by B. Because the form Ax + By = C can describe any line,

it is called the standard form of an equation for a line.

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The equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex] is [tex]y=6[/tex]

As per the question statement, we are supposed to find the equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex].

Before solving that, we need to know that the given line [tex]x = 11[/tex] is parallel to the y-axis as no point is passing through y axis hence the slope [tex]m_{1}[/tex] of the given line will be [tex]\frac{1}{0}[/tex].

The required line is perpendicular to the given line, so it will be parallel to the x-axis and hence it's slope would be slope [tex]m_{2}[/tex] = [tex]0[/tex]

We know the equation of the line passing through a some point [tex]x_{1}[/tex] and [tex]y_{1}[/tex] having slope m is given by:

[tex]y-y_{1} =m_{2} (x-x_{1})[/tex]

Here the required line is passing through (7,6), hence substituting the values of [tex]x_{1}, y_{1} ,m_{2}[/tex], we get

[tex]y-6=0(x-7)[/tex]

or [tex]y-6=0[/tex]

or [tex]y=6[/tex]

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The fraction of the brownies left is 1/12.

We need to find out what fraction of the brownies is left.

Let " r " denote the fraction that is left.

Then we have r + 1/4 + 2/6 + 1/3 = 1

⇒ r + 1/4 + 1/3 + 1/3 = 1 (Writing the fraction 2/6 in the simplest form)

⇒ r + 1/4 + 2/3 = 1

⇒ r + (3 + 8)/12 = 1 (taking LCM of 4, 3 and adding the fractions 1/4 and 2/3)

⇒ r + 11/12 = 1

⇒ r = 1 - 11/12

⇒ r = (12 - 11)/12

⇒ r  = 1/12.

Therefore, the fraction of the brownies left is 1/12.

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Disclaimer:

The fractions provided in the question are not clear.

Assuming the following to answer the given question.

Molly ate 1/4 of the brownies,

Milo ate 2/6 of the brownies, and

Morgan ate 1/3 of the brownies.

Answer:

What's f(x)?

Step-by-step explanation:

The two points that also lie on the circle are:

A (-3,-4) and D (5,0)

We know that a all the points on a circle are equidistant to the center of the circle, and in this case, the center is the origin (0, 0).

We know that the point (4, -3) lies on the circle, so the radius of the circle is:

R = √( (4 - 0)^2 + (-3 - 0)^2) = √25 = 5

So, any point that is at 5 units of the origin will also lie on the circle.

These points are:

A: (-3, -4)

R = √(  (-3 - 0)^2 + (-4 - 0)^2) = √25 = 5

And the point D: (5, 0)

R = √( (5 - 0)^2 + (0 - 0)^2) = √25 = 5

So the correct options are A and D.

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Answer:

The change in direction or bending of a light wave passing from one transparent medium to another; caused by the change in wave's speed is known as “Refraction”. Pencil appears bent in water because of the refraction of light rays

Step-by-step explanation:

Answer:

Both Choice C, D

Step-by-step explanation:

A: Choice A cannot be the correct answer due to it being negative.

B: Choice B also cannot be part of the correct answer because 8 x 3 = 24

C: Choice C is part of the correct answer

D: Choice D is also part of the correct answer

a) [tex]x^{2}[/tex]+8kx +k=0,   b) k=1/16

Here we have equation is 2x -y = 1 , [tex]x^{2}[/tex]+4ky+5k=0

To show that [tex]x^{2}[/tex] +8kx +k =0, we have two equation 2x-y=1 and [tex]x^{2}[/tex] +4ky + 5k=0

So from the equation 2x - y = 1 we can find y

Therefore y = 2x-1

Now we will put the value of y in the equation [tex]x^{2}[/tex] + 4ky + 5k =0

a) We have [tex]x^{2}[/tex] + 4k(2x-1) +5k=0

              [tex]x^{2}[/tex] + 8kx -4k + 5k=0

             [tex]x^{2}[/tex] +8kx +k=0

b) Now we have to find the value of k, and as from the question it is given that [tex]x^{2}[/tex] + 8kx +k =0 have equal roots

Therefore we get [tex]b^{2}[/tex] + 4ac = 0 is the condition of the linear equation in two equal roots.

So from this we have b= 8k, a = -1, c= k

           [tex](8k)^{2}[/tex] - 4× 1×k =0

           64[tex]k^{2}[/tex] -4k =0

           4k(16k -1) =0

           16k-1=0

            k = 1/16

As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.

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The complete question is:

Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.

The comparison of the mean and median of the data set of the dot plot in the first part and the variability and outlier of the dataset in the box and whiskers plot in the second part are;

First part;

1. The median is greater than the mean.

2. Both the mean and median will increase

Second part;

1. School 1 has greater variability

2. The maximum value of school 1 is not an outlier

3. The new athlete needs to spend 21 hours or more

First part;

1. The value in the dot plot are;

10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19

The number of data points = 36

The mean = The sum of the above data divided by 36

Using an online calculator of data sets, we have;

Therefore;

2. The addition of 60 to the dataset will increase the number of data points from 36 to 37, thereby changing the median, which is the middle value to the 19th number, which is 16, while the mean value will also increase to 16.405, therefore;

Second part;

1. A measure of variability of a box plot is the range, which is the difference between the largest and smallest values.

The range of school 1 is; 16 - 1 = 15

The range of school 2 is; 14 - 1 = 13

Therefore;

2. The maximum value of school 1 is 16

The inter quartile range of school 1 is; IQR = 10 - 4 = 6

An outlier = Q3 + 1.5 × IQR

Which gives;

An outlier ≥ 10 + 1.5 × 6 = 19

3. Q3 for school 2 = 12

IQR for school 2 = 12 - 6 = 6

Which gives;

Outlier for school 2 ≥ 12 + 1.5 × 6 = 21

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