This table shows input and output values for a linear function f(x)
What is the difference of outputs for any two inputs that are three values apart.
Express your answer as a decimal.​

Using the Law of Cosines,

[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]

Using the Law of Sines,

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

So, as angles in a triangle add to 180 degrees,

[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

Answer:

[tex]\huge\boxed{\sf |AB|=10 \ units}[/tex]

Step-by-step explanation:

Coordinate of A = [tex](x_1,y_1)[/tex] = (-7,-6)

Coordinate of B = [tex](x_2,y_2)[/tex] = (1,0)

We will use distance formula to find the length of AB.

[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|AB|=\sqrt{(1-(-7))^2+(0-(-6))^2} \\\\|AB|=\sqrt{(1+7)^2+(6)^2} \\\\|AB|=\sqrt{(8)^2+36} \\\\|AB|=\sqrt{64+36} \\\\|AB|=\sqrt{100} \\\\\boxed{|AB|=10 \ units}\\\\\rule[225]{225}{2}[/tex]

Answer:

A ≈ 391.1 feet

formula to find the area of an octagon is shown below

[tex]area = 2(1 + \sqrt{2} )a { }^{2} [/tex]

The rate of change of the function the height of a plant is gotten as; D: 0.7

To find the rate of change, we will use the formula;

Rate of change = (y2 - y1)/(x2 - x1)

From the given table, we can solve for the rate of change by picking two consecutive points to get;

Rate of change = (9.6 - 8.2)/(2 - 0)

Rate of change = 1.4/2

Rate of change = 0.7

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Answer: The slope is 1/3

Step-by-step explanation:

m = y2-y1/x2-x1

m =9-7/4+2

m=2/6

m=1/3

Answer:

The slope is 1/3

Step-by-step explanation:

m=y2-y1/x2-x1

m=9-7/4-(-2)

m=2/6

m=1/3

Answer:

  g(x) = -√(x+6)

Step-by-step explanation:

The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).

__

  x = f(y)

  x = y^2 -6

  x +6 = y^2 . . . . . . add 6

  -√(x +6) = y . . . . . negative square root

The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).

The inverse of f is g(x) = -√(x +6).

_____

Additional comment

The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.

Answer:

  72 ft

Step-by-step explanation:

The perimeter of the concrete walk is the sum of the lengths of its outside edges. Each of those is two border-widths longer than the parallel pool dimension.

__

The border width is ...

  (10 ft) + 2(3 ft) = 16 ft

The border length is ...

  (14 ft) + 2(3 ft) = 20 ft

The perimeter is the sum of the lengths of the four sides. It can be found using the formula ...

  P = 2(L +W)

  P = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft

The perimeter of the concrete walk is 72 feet.

_____

Additional comment

The term "perimeter of the concrete walk" is actually somewhat ambiguous. It could refer to the total length of all of the edges of the concrete walk. If that is the case, then the 48 foot length of the inside edge must be added to the length of the outside edge for a total of 120 feet. That is, if one were to mark the edges of the walk with tape, for example, 120 feet of tape would be needed.

[tex] {5}^{3} \: \times \: {5}^{ - 5} [/tex]

[tex] {5}^{ - 2} [/tex]

[tex] \boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }[/tex]

[tex] {5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

[tex]\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

Ann and Bob's age is 21 years  and 28 years respectively and after 14 years the ratio will be 5:6.

What is Ratio ?

The comparison of one quantity to other is called a ratio and when two ratios are equal they are said to be in proportion.

It is given in the question that

The ratio of Ann's age to bob's age is 3:4

in 7 years time this ratio will be 4:5

their ages now = ?

Let the age of Ann and Bob is x and y

x:y = 3:4

x =(3/4)y

After seven years

(x+7):(y+7) = 4 :5

(x+7)/(y+7) = 4/5

((3/4)y +7)/(y+7) = 4/5

(3y +28)/(y+7) = 16/5

5*(3y+28)= 16(y+7)

15y +140 = 16y+112

y = 140-112

y =28 years

x = 21 years.

After x years suppose the ratio is 5 :6

(21+x)/(28+x) = 5:6

126 +6x = 140 + 5x

x = 14 years.

Therefore after 14 years the ratio will be 5:6.

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Answer:

x = 76.5

Step-by-step explanation:

[tex]\frac{x}{4.5}[/tex] = 22 - 5

[tex]\frac{x}{4.5}[/tex] = 17

x = 17 x 4.5

x = 76.5

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression

An extraneous solution is a solution that in obtained after completely solving an equation but it does not  work in the original given equation.

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression (Option D).

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Answer:

it's 8

Step-by-step explanation:

the lil hand is on the 8 and the big hand is on the 12

Answer:

The time is 8:00  but with out a question im not sure what your asking

Step-by-step explanation:

[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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Answer: 3ln4 + 3lna

Step-by-step explanation:

[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]

The error Kevin made was in step 2 when he added before he multiplied.

This question would be solved using the BODMAS rule. The BODMAS rule provides the order in which mathematical problems should be solved. The order is:

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Answer: 32

Step-by-step explanation: this is arithmetic sequence

general formula = a+(n-1)d

nth term = 5+(n-1)3

=5+3n-3

=2+3n

10th term = 2+3(10)

=32

The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean

The dot plot that completes the question is added as an attachment.

Start by calculating the mean of the data plot using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

Substitute the values on the dot plot

[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]

[tex]\bar x = 7[/tex]

This means that the population mean of the dot plot is 7

Next, we create another dot plot that has the same mean as 7.

There are no direct rules to this, so we make use of the trial by error method.

After several attempts, we have the following frequency table:

Data point      Frequency

2                                  1

3                                  2

4                                  0

5                                  4

6                                  5

7                                  2

8                                  5

9                                  0

10                                 2

12                                 3

The mean of the frequency table is:

[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]

Evaluate

[tex]\bar x = \frac{168}{24}[/tex]

Evaluate the quotient

[tex]\bar x = 7[/tex]

This means that the sample mean is 7 (same as the population mean)

Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)

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Answer:

13 and 30

Step-by-step explanation:

the smaller of the two numbers is 13.

If there is a 17 number difference, then that means that the second number is 30.

give brainliest, please!
hope this helps :)

Answer: The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height

Step-by-step explanation:

Area of ΔABC= 1/2 × Base × Height = 1/2 × h × BC

If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.

Thus, we have seen the formula and definition of the area of triangle ABC.

Answer:

can u make it in a sentence cause I don't understand ur question

Answer:

i don't know

Step-by-step explanation:

Answer: Hope this helps you.

1,3

Step-by-step explanation:

(6, 4) and (0,2)

4-2/6-0 =2,6 (1,3)

Step-by-step explanation:

please mark me as brainlest

Answer:

28

Step-by-step explanation:

▪︎ ADE and ABC are similar triangles (AAA)

▪︎ DA = DB + BA = 30 + 12 = 42

▪︎ k = DA / BA = 42 / 12 = 3.5

▪︎ DE = BC * k = 8 * 3.5 = 28

The value of the expression if x is equivalent to 12 is - 26

Given the expression

f(x) = 5/6(1/2x+6)-3x

If the value of x is 12, then;

f(12) = 5/6(1/2(12)+6)-3(12)

f(12) = 5/6(6+6) - 36

Simplify

f(12) = 5/6(12) - 36

f(12) = 10 - 36

f(12) = -26

Hence the value of the expression if x is equivalent to 12 is - 26

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[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]

Answer:

h(x) = 1/4 x

Step-by-step explanation:

h(x) = x + 4, h(x) = x – 4, h(x) = 3/4 x, h(x) = 1/4 x. Summary: The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.

Answer:

do the calculation below

Step-by-step explanation:

(4/52 ) *(3/51)

leave a comment if you need more help

The recursive formula of the sequence is [tex]a_n = -\frac{a_{n-1} }{5}[/tex] where a1 = 50

The sequence is given as:

50,−10,2,....

The above sequence is a geometric sequence, and it has the following parameters:

This means that the product of the current term and -1/5 gives the next term.

i.e.

[tex]a_n = -\frac{a_{n-1} }{5}[/tex]

Hence, the recursive formula of the sequence is [tex]a_n = -\frac{a_{n-1} }{5}[/tex] where a1 = 50

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Answer:

Step-by-step explanation:

Limits exist for:

[tex]\lim_{x \to4 \4} \frac{x^2 -x-12}{4-x}[/tex] = [tex]\frac{(x-4)(x+3)}{4-x}[/tex] = ( - 1 )( x + 3 ) = - 7

[tex]\lim_{x \to \ 2} \frac{x^2 +2x-8}{2-x}[/tex] = [tex]\frac{(x+4)(x-2)}{2-x}[/tex] = ( - 1 )( x + 4 ) = - 6

[tex]\lim_{x \to2 } \frac{x^2 +3x - 10}{x^2 -4}[/tex] = [tex]\frac{(x+5)(x-2)}{(x+2)(x-2)}[/tex] = [tex]\frac{x+5}{x+2}[/tex] = [tex]\frac{7}{4}[/tex]