What is the number between 8.1 and 8.24?

Answer:

The correct answer is the third option: y = 4x - 20

Step-by-step explanation:

To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.

slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4

Therefore, the slope of the line of best fit is 4.

To find the y intercept, we can use our equation for slope and plug in one of our points.

y = mx + b

y = 4x + b

40 = 4(15) + b

40 = 60 + b

b = -20

Therefore, the y intercept is -20.

If we put both our slope and y intercept into one equation, we get:

y = mx + b

y = 4x - 20

The correct answer is the third option.

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The value of x from the given data is 2

Mean is the ratio of sum of numbers to the total samples. Given the following data

15,19,23,41, and Z

The mean is calculated as

Mean = 15+19+23+41+z/5

Since the mean the of the data is given as 20. Substitute

20 = 15+19+23+41+z/5

Cross multiply

20*5 = 15+19+23+41+z

100 = 15+19+23+41+z

100 = 98 + z

z = 100- 98

z = 2

Hence the value of x from the given data is 2

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Answer:

Since the graph looks like this, I would say solid line

In quadrant I, [tex]\cos(A)[/tex] is positive. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]

Since the product of the slope is -1, hence the lines are perpendicular

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1

Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;

Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3

Similarly for the coordinate points (-1, -7) and (1, -1).

Slope = -1+7/1+1
Slope of line 2 = 6/2

Slope = 3

Take the product of the slopes

Slope = -1/3 * 3
slope = -1

Since the product of the slope is -1, hence the lines are perpendicular

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A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.

Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.

A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).

An equidistant locus is one that is at the same distance to a reference point or a line.

In question 14, the required locus should be at the same distance to points A, B, C, and D.

In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.

The required construction is herewith attached to this answer.

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▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]

▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

» [tex] \tt{For \: \: y,}[/tex]

[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]

[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]

» [tex] \tt{At \: \: x = 2,}[/tex]

[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]

[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]

[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]

[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]

The characteristic that  is necessary to create a table that compares two functions  is D. Choose the same values for each functions .

The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation  and these can have  varying arguments.

It should be noted that when necessary to creating a table that compares two functions it  is important to Choose the same values for each functions .

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Answer:

angle a = [tex]\boxed{154}^{\circ}[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠a + 13° + 13° = 180°

⇒ ∠a + 26° = 180°

⇒ ∠a = 180° - 26°

⇒ ∠a = 154°

Answer:

Angle a equals= 154°

Step-by-step explanation:

you have two angles which add up to 26°

remember that triangle always adds up to 180°

so you calculate 180-26 and you get 154

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

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The answers to the questions are as follows:

We have E = {1, 3,5, 7, 9, 11, 13, 15, 17, 19}

A= { 3, 7, 9, 11, 15}

B = {5, 7, 11, 13}

We have A n B = numbers that are contained in both of the sets

= 7, 11

a.) We have to count the total number in the dataset. That is the total number of odd numbers that are less than 20.

Hence total numbers in the set = 10

b. The probability that the number is in set AnB

= 7, 11

= 2/10

= 1/5

We can conclude that the probability that the number is in A intersect B = 1/5

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The last one because the other ones only go to the positive side and not the negative too since the cube root

In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.

Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:

Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)

Slope (m) = 2/1

Slope (m) = 2

To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b

3 = 1(2) + b

3 = 2 + b

Subtract 2 from both sides

3 - 2 = 2 + b - 2

1 = b

b = 1

Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

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Using a system of equations, it is found that one large jar holds 6 ounces and one small jar holds 4 ounces.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One large jar and five small jars can hold 26 ounces of jam, hence:

l + 5s = 26, which is the first equation in matrix form.

Then:

l = 26 - 5s.

One large jar minus one small jar can hold 2 ounces of jam, hence:

l - s = 2, which is the second equation in matrix form:

Then:

l = 2 + s = 26 - 5s

2 + s = 26 - 5s

6s = 24

s = 4.

l = 26 - 5s = 6.

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Answer:

distributive property

Step-by-step explanation:

The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point  (-6,8) is -6x+8y=100.

Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]

and point at which the tangent meets the circle is (-6,8).

A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.

Linear equation looks like y=mx+c.

Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:

xz+ty=[tex]a^{2}[/tex].

We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex]  at (-6,8).

It will be as under:

x(-6)+y(8)=100

-6x+8y=100

Hence the equation of tangent to the circle at the point  (-6,8) is -6x+8y=100.

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The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

In solving for the values of 'x' we need to:

Given the expression;

1/x =x+3/2x^2

Cross multiply

x ( x+ 3) = 2x² ( 1)

Expand the bracket

x² + 3x = 2x²

collect like terms and equate all the variables to zero, we have ;

2x² - x² - 3x = 0

We then subtract the like terms, we getv

x²- 3x = 0

Now, let's find the common factor

Factor out 'x':

x ( x - 3 ) = 0

Equate each of the factors to zero and find the value of 'x' for each

So,

x = 0

And

x - 3 = 0

x = 3

Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

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[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{Last \: option \: (D.)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Write the equation in slope-intercept form. Then solve y.

▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]

Identify the x-intercept,

[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]

[tex]\small\longrightarrow \sf{3x=-4}[/tex]

[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]

[tex]\small\longrightarrow \sf{x = -1.33}[/tex]

The graph has the next properties:

[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]

[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]

[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]

Answer:

-3

Step-by-step explanation:

(-3, -1), (-5, 5)

Each point is (x, y).

slope = (difference in y)/(difference in x)

slope = (-1 - 5)/(-3 - (-5)) = -6/(-3 + 5) = -6/2 = -3

The slope is -3

The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

Volume of a rectangular prism = Base area × height

Height = Volume of a rectangular prism ÷ Base area

3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h

h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units

h = (3x³ + 16x² + 5x) / (x² + 5x) units

Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

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Answer: I believe the answer would be as follows:

8.431 grams

5.46 seconds

980 meters

900 miles

Step-by-step explanation:

it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.

Hope this helped!

The events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)

The probability values are given as:

P(A) = 0.3

P(B) = 0.6

P(A or B) = 0.8

For mutually exclusive events, we have:

P(A or B) = P(A) + P(B)

Substitute the known values in the above equation

P(A or B) = 0.3 + 0.6

Evaluate the sum

P(A or B) = 0.9

From the given parameters, we have

P(A or B) = 0.8

Hence, the events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)

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Answer:

D

Step-by-step explanation:

edge 2023

The sum of P(A) and P(B) is not equal to P(A or B).

Answer:

[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question

Step-by-step explanation:

Simplify

[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]

Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]

We get

[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]

[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]

So

[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]

Multiplying numerator and denominator by [tex]ab^2[/tex] gives

[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]

= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER

Hint:

We can eliminate first choice since negative exponents still remain

We can eliminate third choice because the expression has a minus sign which is not possible

That just leaves second and fourth choices to work with

Answer: 12 square units

Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.

Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.

Answer:

In standard form x^2/64 + y^2/100 = 1

Step-by-step explanation:

The major axis is the y axis because 10 has a larger value than 8.  

8x8 = 64

10 x10 = 100

The solution to the system of equations is x = 1, y = 10 and z = 4

The system of equations is given as:

3x +2y +4z = 11

2x -y +3z = 4

5x -3y +5z = -1

Multiply the second equation by 2

So, we have

4x - 2y + 6z = 8

Add this equation to the first equation

3x + 4x + 2y - 2y + 4z + 6z = 11 + 8

Evaluate the like terms

7x + 10z = 19

Multiply the second equation by 3

So, we have

6x - 3y + 9z = 12

Subtract this equation from the third equation

6x - 5x - 3y + 3y + 9z - 5z = 12 + 1

Evaluate the like terms

x + 4z = 13

Make x the subject

x = 13 - 4z

Substitute x = 13 - 4z in 7x + 10z = 19

7(13 - 4z) + 10z = 19

Expand

91 - 28z + 10z = 19

Evaluate the like terms

-18z = -72

Divide

z = 4

Substitute z = 4 in x = 13 - 4z

x = 13 - 4 * 4

Evaluate

x = 1

We have:

2x -y +3z = 4

This gives

2(1) - y + 3 * 4 = 4

Evaluate

2 - y + 12 = 4

This gives

y = 10

Hence, the solution to the system of equations is x = 1, y = 10 and z = 4

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Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

To plot the value(s) on the number line where the given function is equal to zero:

The equation is written as: y = (x+5)(x-1)

This is further written as:

The highest point occurs when x = 0, which is (5)(-1) = -5

Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

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The correct question is given below:

Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).

The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.

We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore

L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min

The least common multiple of 12, 15, and 18 is 180.

Convert the minutes to hours, for this we apply the rule of 3:

As the bells all together ring at 6 am, so we add

Answer: The bells are rung together again at 9 in the morning.