Without graphing is each system independent dependent or inconsistent

2/3 is the slope of (2,4) and (5,6)

slope = [tex]\frac{2}{3}[/tex]

calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = ( 2, 4 ) and (x₂, y₂ ) = (5, 6 )

m = [tex]\frac{6-4}{5-2}[/tex] = [tex]\frac{2}{3}[/tex]

The equation of the tangent line at x=1 can be written in point-slope form as

... L(x) = f'(1)(x -1) +f(1)

The derivative is ...

... f'(x) = 4x^3 +4x

so the slope of the tangent line is f'(1) = 4+4 = 8.

The value of the function at x=1 is

... f(1) = 1^4 +2·1^2 = 3

So, your linearization is ...

... L(x) = 8(x -1) +3

or

... L(x) = 8x -5

Lines k and n are perpendicular

The slope of line k is -6

Fact: The product of slopes of two perpendicular lines = -1

So the slope of line n = -1 ÷ -6 = 1/6

The correct choice is 'D.'

If lines k and n are Slopes of Perpendicular Lines k is -6, then the slope of the perpendicular line n is 1/6.

In the study of Mathematics, especially when dealing with Geometry and Algebra, understanding the relationship between lines can be critical.

This particular question asks about perpendicular lines and their slopes. If lines k and n are perpendicular, knowing the slope of one can help deduce the slope of the other.

As per the properties of perpendicular lines, the product of their slopes is -1.

In the case where the slope of line k is -6, the slope of the perpendicular line n would be the Positive reciprocal, which is simply flipping the fraction and changing the sign.

Hence, the slope of line n would be 1/6.

So, ultimately the answer is Option d: 1/6, which is the slope of line n that is perpendicular to line k with a slope of -6.

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If you actually do what the problem statement tells you to do, the answer falls into your lap.

The attachment shows the triangle reflected across the y-axis (blue), then across the x-axis (red). The red triangle is clearly equivalent to the original being rotated 180° about the origin.

The appropriate choice is ...

... a 180° rotation about the origin

_____

Algebraically, reflection across the y-axis negates the x-coordinate:

... (x, y) ⇒ (-x, y)

and reflection across the x-axis negates the y-coordinate:

... (x, y) ⇒ (x, -y)

Then, reflection across first one axis then the other will result in both coordinates being negated:

... (x, y) ⇒ (-x, -y)

This is precisely what happens when a figure is rotated 180° about the origin.

Answer:

A 180 rotation about the origin

The median on any box plot is the little dot in the middle of the box so the answer is C)42. So where the line is in the middle of the box it is always going to be the median. The median is in the middle. You can also remember it like this Hey Diddle diddle the medians the middle you add and divide for the mean and the mode is the most.

Answer:  

B) 38  

Step-by-step explanation:

38 is the first (lower) quartile of the box-and-whisker plot.

The closet area is 1/9 of the bedroom area, so is (1/9)·(90 ft²) = 10 ft².

The width of the closet multiplied by the length is the area.

... length×(2 ft) = 10 ft²

... length = (10 ft²)/(2 ft) = 5 ft

The length of Jackson's closet is 5 ft.

The general expression for the change in temperature between 8am and 10am

[tex]\delta_{8-10}= \delta_{8-9} + \delta_{9-10}[/tex] where [tex]\delta[/tex] stands for change in the subscripted time interval.

For city A:

[tex]\delta_{8-10} = 4 - 7 = -3\enspace ^\circ F[/tex]

For city B:

[tex]\delta_{8-10} = -6 - 2 = -8\enspace ^\circ F[/tex]

In city A, there is an overall drop of 3 degrees (negative value). In city B, the temp drops 8 degrees.

Among A and B, city B has a greater change in temperature (8 vs. 3)

There could be a strong correlation between the proximity of the holiday season and the number of people who buy in the shopping centers.

It is known that when there are vacations people tend to frequent shopping centers more often than when they are busy with work or school.

Therefore, the proximity in the holiday season is related to the increase in the number of people who buy in the shopping centers.

This means that there is a strong correlation between both variables, since when one increases the other also does. This type of correlation is called positive. When, on the contrary, the increase of one variable causes the decrease of another variable, it is said that there is a negative correlation.

There are several coefficients that measure the degree of correlation (strong or weak), adapted to the nature of the data. The best known is the 'r' coefficient of Pearson correlation

A correlation is strong when the change in a variable x produces a significant change in a variable 'y'. In this case, the correlation coefficient r approaches | 1 |.

When the correlation between two variables is weak, the change of one causes a very slight and difficult to perceive change in the other variable. In this case, the correlation coefficient approaches zero

Most likely, there would be a strong correlation between the two.

A correlation is a measurement of the relationship between two variables. When two variables are strongly correlated, this means that a change in one variable has a strong impact on the other one. On the other hand, when the correlation between variables is weak, this means that the two variables are not strongly connected. In this example, the two situations are likely to be strongly correlated because the number of people is very likely to go up as the holiday season approaches.

Hi ArbogastMadyson,

Which type of triangle is shown here?

There are 6 types of triangle:

Since your triangle contains length in inches not degrees we will not use the 1st, 5th, and 6th clssifications.

Scalene Triangle - 3 unequal sides

Isosceles Triangle - 2 equal sides, 1 unequal,

Equilateral Triangle - 3 Equal Sides

In your image all 3 lengths are different.

Answer - Scalene Triangle

It would of been easier to search the definition of the answers up.

Answer:

The Answer is;

No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.

Step-by-step explanation:

You cannot make a valid inference of the preference of watching TV talk shows by only considering students in one class. You have to randomly select people from the whole population (i.e the total number of students in the school) and then make an inference.

Answer:

No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.

ANSWER

The number that fills in the blanks is 1

EXPLANATION

Two numbers are relatively prime if they have no common factor greater than 1.

For exam 12 and 17 have no common factor greater than 1.

This is equivalent to saying that the greatest common divisor (GCD) of the two numbers is 1.

[tex]gcd(12,17)=1[/tex]

This means that [tex]12[/tex] and [tex]17[/tex] are relatively prime.

But

[tex]gcd(12,16)=4[/tex]. This means 12 and 16 are not relatively prime or coprime

the point was reflected over the x- axis

note that for reflection in the x- axis

a point (x, y ) → (x, - y )

the x-coordinate remains unchanged while the y- coordinate of the image is the negative of the original y- coordinate

Answer:

Option B and C are correct.

Step-by-step explanation:

It is given that A point located at (1, 6) undergoes a transformation. Its image is at (1, -6).

[tex]P(1,6)\rightarrow P'(1,-6)[/tex]

If the point was reflected over the y-axis, then

[tex]P(x,y)\rightarrow P'(-x,y)[/tex]

[tex]P(1,6)\rightarrow P'(-1,6)\neq P'(1,-6)[/tex]

If the point was translated down 12 units, then

[tex]P(x,y)\rightarrow P'(x,y-12)[/tex]

[tex]P(1,6)\rightarrow P'(1,6-12)=P'(1,-6)[/tex]

If he point was reflected over the x-axis, then

[tex]P(x,y)\rightarrow P'(x,-y)[/tex]

[tex]P(1,6)\rightarrow P'(1,-6)[/tex]

If he point was translated up 12 units, then

[tex]P(x,y)\rightarrow P'(x,y-+12)[/tex]

[tex]P(1,6)\rightarrow P'(1,6+12)=P'(1,18)\neq P'(1,-6)[/tex]

Hence, the correct options are B and C.

the mode is the amount/s which occurs most frequently.

In this data set there are 2 values which occur twice

the mode is £254 and £180

The mode of staff wages is:

   £ 180   and    £ 254

The mode of a data set is a data value that exist or occur in the set most frequently (i.e. most of the times)

We are given data points as:

£254 £254 £310    £276     £116 £90     £312 £180    £180 £536 £350     £243     £221     £165   £239  £700

On arranging these data points along with their frequency we get:

      Data point                   Frequency

         £90                          1

        £116                                 1

        £165                                1

        £180                                2

        £221                          1

        £239                          1

        £243                                1

      £254                                 2

       £276                                  1

       £310                                   1

        £312                                  1

       £350                                  1

       £536                                  1

  £700                                   1

Two data points has highest frequency

   £180    and     £254

( since both have frequency 2)

Answer:

The correct answer is that the function starts high and ends low.

Step-by-step explanation:

First we need to check for the highest power in a term. Since it is 5, which is an odd number, we know that they start and end in different places.

Next, we determine where it finishes based on the coefficient of that term, which is -1. Since it is negative, we know it finishes down. Since they are different, this means it starts up

Answer:

A ) The graph of the function start high and ends low .

Step-by-step explanation:

Given  : f(x) = [tex]-x^{5} +x^{2} -x[/tex].

To find : Describe the end behavior of the following function.

Solution : We have given function

f(x) = [tex]-x^{5} +x^{2} -x[/tex].

We can see the Degree = 5  ( Odd) ,  Leading coefficient = negative  .

By the End Behavior Rule  : If  the degree odd and leading coefficient is negative then the left side of graph would be up and right would be down.

Therefore, A ) The graph of the function start high and ends low .

Try this option (answers: 5.53 and 3.22)

B

the average temperature rose by + 5°

this years average = - 19 + 5 = - 14°

Hello!

Given the function, f(x) = 5x, find the equation where the function f, is reflected over the x-axis.

There are two types of reflections. One reflection is over the x-axis (the most common) and over the y-axis.

Say for example, we are given the point (x, y), and we want to reflect it over the x-axis. If the point (x, y) is reflected over the x-axis, then the point is (x, -y). Why? It's because y-values above the x-axis are POSITIVE while x-values below are NEGATIVE.

So, an equation to show this is: y = -f(x).

To find it, we multiply the entire function, which is f(x), by a negative. Since f(x) = 5x, the transformed function is f(x) = -5x.

Therefore, the function rule for the function shown is -f(x).

The function rule for the function f(x) = 5x reflected over the x-axis is -f(x) = -5x. This is due to the reversal of the y-values when reflecting a function over the x-axis.

In Mathematics, when we reflect a function over the x-axis, it simply means reversing the signs of the y-values. For this given function f(x) = 5x, its reflection would get the y-values inverted, which would convert the positive to negative (or vice versa). Taking this into account, the function reflecting in the x-axis would be -f(x) = -5x.

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Answer:

C. k=68, t=52

Step-by-step explanation:

Let u, v, y represent the measures of the unmarked angles at the respective vertices. The angles of the equiangular triangle are all 180°/3 = 60°, so we have the relations ...

From these relations, we know that

... v = 180 -124 = 56 . . . . . 3rd equation above

... 56 +56 +k = 180 . . . . . . 2nd equation above, with y=v=56

... k = 180 -112 = 68 . . . . . above with 112 subtracted

... t = 180 -128 = 52 . . . . . 5th equation above with u=64 and 128 subtracted

Answer:

The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.

Step-by-step explanation:

Rearranging the two equations, you get ...

The above-listed answer is the only one that matches these solution counts.

_____

Testing the above values of x reveals they are, indeed, solutions to Equation 1.

(1) has solutions x = 3, x= - 1.5 and (2) has no solution

solving each equation

(1)

add 5 to both sides

|4x - 3 | = 9 ( remove bars from absolute value )

4x - 3 = 9 or 4x - 3 = - 9 ( by definition )

4x = 9 + 3 = 12 or 4x = - 9 + 3 = - 6

x = 3 or x = - 1.5

(2)

subtract 8 from both sides

|2x + 3 | = - 5

the absolute value cannot be equal to a negative quantity

thus |2x + 3 | = - 5 has no solution

Answer:

Erica

Step-by-step explanation:

Two lines with the same (defined) slope will only have infinite solutions if their y-intercepts are the same. Otherwise, the number of solutions (points on both lines) is zero.

Since the 2 lines have the same slope, then the lines are parallel and never intersect. Thus there is no solution to the system of equations

Neither Jake nor Erica are correct.

Answer:

Expression  Katrina drinks of water in 7 day = 8 *7 cups .

Step-by-step explanation:

Given  : Katrina drinks 0.5 gallons of water per day and There are 16 cups in a gallon.

To find : Which expression shows how to find the number of cups of water she drinks in a week.

Solution : We have given that

Katrina drinks of water per day = 0.5 galoons.

1 gallon  = 16 cup .

So,  Katrina drinks of water per day = 0.5 * 16 cups.

Katrina drinks of water per day = 8  cups.

1 week =  7 days .

Katrina drinks of water in 7 day = 8 *7 cups.

Katrina drinks of water in 7 day = 56  cups.

Therefore, Expression  Katrina drinks of water in 7 day = 8 *7 cups .

a gradient of a line that is parallel and perpendicular to this line with this gradient of -2

Gradient is the slope

So slope of the line =-2

Slope of parallel line is equal to the slope of the line

So slope of parallel line = -2

Slope of perpendicular line is equal to negative reciprocal of slope of the line

We know slope of line = -2

Negative reciprocal = [tex]\frac{1}{2}[/tex]

So , Slope of perpendicular line= [tex]\frac{1}{2}[/tex]

The answer would be A because the distance from 8 to 0 is 8 and the distance from 0 to -12 is 12 so 8+12 is 20

Answer:

Yes. (See below for explanation.)

Step-by-step explanation:

The number of servings is found by dividing the quantity available by the size of a serving. The quantity of punch is the sum of the quantities of the juices that go into the punch. The serving size of 3/4 cup is the same as 6 ounces, since a cup is 8 ounces. (3/4 × 8 oz = 6 oz)

The quantity available is (64 oz + 28 oz + 76 oz). The serving size is 6 oz. Since the units of numerator and denominator are the same, they cancel, leaving ...

... number of servings = (quantity available)/(serving size)

... = (64 +28 +76)/6 . . . . as shown in the problem statement

_____

It might not be obvious that the above ratio gives the number of servings. However, if you look at the real units, you see how it happens.

[tex]\dfrac{oz}{(\frac{oz}{serving})}= oz\dfrac{serving}{oz}=\dfrac{oz}{oz}serving=serving[/tex]

we have

[tex]f(x)=\frac{1}{2}x+2[/tex]

To graph the line find the x and y intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

so

Find the y-intercept

For [tex]x=0[/tex]

[tex]f(0)=\frac{1}{2}*0+2=2[/tex]

the y-intercept is the point [tex](0,2)[/tex]

Find the x-intercept

For [tex]y=0[/tex]

[tex]0=\frac{1}{2}x+2\\x=-4[/tex]

the y-intercept is the point [tex](-4,0)[/tex]

Using a graphing tool

Plot the points to graph the line

therefore

the answer in the attached figure

The graph of the linear function f(x) = 12x + 2 is attached below

The graph of a linear equation is a straight line when plotted on a coordinate plane. A linear equation can be written in the form:

y = mx + b

Where:

"y" represents the dependent variable (usually plotted on the vertical axis).

"x" represents the independent variable (usually plotted on the horizontal axis).

"m" is the slope of the line, which determines its steepness.

"b" is the y-intercept, which is the point where the line crosses the y-axis.

The graph of the linear equation f(x) = 12x + 2 is attached below;

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The x-coordinate of the intersection point of two perpendicular lines, one with equation y = mx + b and the other with equation y = -x/m - b, is given by x = 2b/(m + 1/m).

Given two perpendicular lines, one has the equation y = mx + b. The y-intercept of this line is b, and the slope is m. The equation of the second line, which is perpendicular to the first, will have a negative reciprocal slope, -1/m, and for opposite y-intercepts, we'll assume its y-intercept to be -b. Thus the equation of the second line is y = -x/m - b.

For the intersection point, equal the y-values of the two equations: mx + b = -x/m - b. Simplify to obtain the x-coordinate of the intersection point:

mx + x/m = 2b or x(m + 1/m) = 2b. Therefore, the x-coordinate of the intersection point is x = 2b/(m + 1/m).

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To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, set the equations of the lines equal to each other and solve for x.

To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, we need to find the equations of both lines. Let's assume the equation of one line is y = mx + b. Since the lines are perpendicular, the slope of the other line will be the negative reciprocal of m. Let's call the slope of the other line n. Therefore, the equation of the other line will be y = -nx + c, where c is the y-intercept of the second line. To find the x-coordinate of the intersection point, we can set the two equations equal to each other and solve for x:

mx + b = -nx + c

x(m + n) = c - b

x = (c - b)/(m + n)

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The greatest common factor of 60 and 48 is 12. If 12-student vans are used for transport, then (60+48)/12 = 9 vans will be needed.

_____

5 vans are needed for the 6th graders; 4 vans are needed for the 7th graders.