What is the Inverse of function ?
f(x) = (3-x)/7

Answer:

[tex]x_1=2; x_2=-1[/tex]

Step-by-step explanation:

The square term is [tex]x^2[/tex] so we expect the complete square to be of the form [tex](x-a) ^2=x^2+2ax+a^2[/tex].

Let's compare the first degree terms now: we have [tex]2ax[/tex] on one side and [tex]-1x[/tex] on the other. That would make [tex]a=- \frac12[/tex]. At this point we have still the second squared term, so we add and subtract [tex]\frac14 = (\frac12)^2[/tex]

Our equation becomes:

[tex]x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0[/tex]

(the [tex]\frac94[/tex] term comes from rewriting [tex]2= \frac84[/tex] and adding the terms out of the bracket).

At this point it's just solving the equation:

[tex](x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1[/tex]

An arithmetic sequence can be expressed as explicitly or recursively

The explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]

The recursive formula is given as:

[tex]a_n = a_{n -1} - 4[/tex]

[tex]a_1 = 7[/tex]

Substitute 2 for n in [tex]a_n = a_{n -1} - 4[/tex]

[tex]a_2 =a_1 - 4[/tex]

This gives

[tex]a_2 =7 - 4[/tex]

[tex]a_2 =3[/tex]

Calculate the common difference (d)

[tex]d = a_2 -a_1[/tex]

[tex]d = 3- 7[/tex]

[tex]d = -4[/tex]

The explicit formula is then calculated as:

[tex]a_n = a_1 + (n - 1)d[/tex]

This gives

[tex]a_n = 7+ (n - 1)*-4[/tex]

Expand

[tex]a_n = 7+4 - 4n[/tex]

[tex]a_n = 11 - 4n[/tex]

Hence, the explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]

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Answer:

[tex]\boxed{70 \ \text{units}^{2}}[/tex]

Step-by-step explanation:

I assume that the polygon is made up of a rectangle and two triangles. Thus, the area of the polygon is the area of the triangles and the rectangle.

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[tex]\text{Area of polygon} = \text{Area of rectangle} + \text{Area of triangle}_{1} } + \text{Area of triangle}_{2}[/tex]

➡ [tex]\text{Area of polygon}= 49 + 7 + 14[/tex]

➡ [tex]{\bold{Area \ of\ polygon = 49 + 21 = \underline{70 \ units}^{2}}[/tex]

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Percentage Calculator: What is the percentage increase/decrease from 72 to 63? = 12.5.  

Answer:

k > 13

Step-by-step explanation:

[tex]k+6 > 19\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k > 13\:\\ \:\mathrm{Interval\:Notation:}&\:\left(13,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}[/tex]

[tex]k+6-6 > 19-6[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]k > 13[/tex]

Thus, the answer is k > 13

[RevyBreeze]

Answer:

4(x² - x - 2)

Step-by-step explanation:

The highest common factor is 4 so factor it out.

Answer:

Step-by-step explanation:4x2−4x−84x2-4x-8Factor 44 out of 4x2−4x−84x2-4x-8.

Factor 44 out of 4x24x2.4(x2)−4x−84(x2)-4x-8Factor 44 out of −4x-4x.4(x2)+4(−x)−84(x2)+4(-x)-8Factor 44 out of −8-8.4(x2)+4(−x)+4(−2)4(x2)+4(-x)+4(-2)Factor 44 out of 4(x2)+4(−x)4(x2)+4(-x).4(x2−x)+4(−2)4(x2-x)+4(-2)Factor 44 out of 4(x2−x)+4(−2)4(x2-x)+4(-2).4(x2−x−2)

Factor x2−x−2x2-x-2 using the AC method

Consider the form x2+bx+cx2+bx+c. Find a pair of integers whose product is cc and whose sum is bb. In this case, whose product is −2-2and whose sum is −1-1.−2,1

Write the factored form using these integers.4((x−2)(x+1))4((x-2)(x+1))Remove unnecessary parentheses.4(x−2)(x+1)

The molar solubility of Ba₃(PO₄)₂ is its concentration of pure substance

The correct equation for the ksp is Ksp = 6x⁵

Start by writing the reaction for the solution of Barium phosphate

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Next, we make an ICE chart

Let "x" be the molar solubility of Barium phosphate

          Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp)

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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The molar solubility of Ba₃(PO₄)₂ is its concentration of a pure substance.

The correct equation for the ksp is Ksp = 6x⁵.

The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is denoted by the symbol Ksp.

Start by writing the reaction for the solution of Barium phosphate.

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Let "x" be the molar solubility of Barium phosphate

         Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp),

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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#SPJ4

Answer:

435 is the answer

Step-by-step explanation:

well first you can cut it up

9x7=63

than    8x15=120

than for the trangle

you do  24x 21= 504 than you do 504/2=252

than add all of them =435

Answer:

x = 9#

Step-by-step explanation:

need help with answer just ask me i got yall

Answer:

It is irrational

Step-by-step explanation:

Hope that helps!

Answer:

6:35.

Step-by-step explanation:

I start by adding the hours spent to the time leaving me with 5:50, I then add the 40 which brings it to 6:30 and the additional 5 minutes bringing the final answer to 6:35.

Answer:

6:35 PM

Step-by-step explanation:

When Harold got home, it was already 3:50 PM. Then he played games for an hour and five minutes. Adding on an hour, it made the time 4:50 PM, and then adding on the five minutes, made the time 4:55 PM. When he finished playing games, he took an hour and forty minutes to do his homework. 4:55 PM, adding on the hour makes it 5:55 PM, then adding the 40 minutes, makes it 6:45 PM.

- Educationist

to get the equation of any straight line, we simply need two points off of it, well, let's use the provided values hmmm

[tex]\begin{array}{ccll} \stackrel{toppings}{x}&\stackrel{cost}{y}\\ \cline{1-2} 3 & 7.50\\ 8& 10 \end{array} \qquad\implies \qquad (\stackrel{x_1}{3}~,~\stackrel{y_1}{7.50})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{7.50}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{3}}}\implies \cfrac{2.5}{5}\implies \cfrac{~~ \frac{25}{10}~~}{5}\implies \cfrac{25}{50}\implies \cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7.50}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{3})\implies y-\cfrac{750}{100}=\cfrac{1}{2}(x-3) \\\\\\ y-\cfrac{15}{2}=\cfrac{1}{2}x-\cfrac{3}{2}\implies y=\cfrac{1}{2}x-\cfrac{3}{2}+\cfrac{15}{2}\implies y=\cfrac{1}{2}x-6[/tex]

A 2 x 2 matrix has 2 rows and 2 columns

A specific 2 x 2 matrix a with no zero entries at all is [tex]\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right][/tex]

From the question, we understand that the matrix is a 2 x 2 matrix.

A 2 x 2 matrix is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d&\end{array}\right][/tex]

Also from the question we understand that the elements of the matrix are non-zero.

This means that:

[tex]a \ne 0\ , b \ne 0, \ c \ne 0, \ d \ne 0[/tex]

An example of such matrix is:

[tex]\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right][/tex]

Note that there are several matrices that fit the given construction requirement

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About 25 gallons of 20% mixture are needed to make the 80% mixture.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of gallons of 20% mixture needed, hence:

(20% of x) + (80% of y) = 65% of 100

0.2x + 0.8y = 65   (1)

Also:

x + y = 100    (2)

From both equations:

x = 25, y = 75

About 25 gallons of 20% mixture are needed to make the 80% mixture.

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Answer:

divide

Step-by-step explanation:

divide 26.216 and 128 to get ur anser

Answer:

Add 509 and 476; The Roman Era lasted for a total of 985 years from 509 B.C to 476 A.D.

Step-by-step explanation:

well, when we use the word "the function" we're referring to the dependent part, which depends on the independent, y,x wise, we're referring to the function "y" or f(x) if you wish.

so for an exponential function

is the function ever positive only? it can be

is it negative only?  it can be

can it be both?  sure thing, most of the time it's both

we can say a function f(x) is always positive when the independent values of "x" yield a positive value only, mind you that when we're talking about "the function" we're really referring to the resulting values in a set, so can the values of the output no matter what "x" we use be always positive? sure, can they also be negative only? sure, how about both? sure thing.

notice the template in the picture below, we can transform any exponential function like the one above 2ˣ with some vertical shift upwards, and is always positive, or -2ˣ with a vertical shift downwards and it's always negative, or we can stretch it about and have -2ˣ shifted upwards so sometimes is positive, and sometimes is negative.

above the x-axis is always positive, below is negative, but with transformations on the parent function it can be any of the three types.

Answer:

118

Step-by-step explanation:

62+x=180

x=180-62

x=118

Answer:

its cost 25 cents

in so will cost 275 cent so 2.75

Step-by-step explanation:

Answer:

A. 18

B. -3

C. 3

D. -9

Step-by-step explanation:

Simplify:

A. -9(-2) <== when multiplying two negatives, they make a positive

-9(-2) = 18

B. -9(+6)

-9(+6) = -3

C. -9/-3 <== when dividing two negatives, they make a positive

-9/-3 = 3

D. 9/-1​ <== when dividing a # with a negative, it makes a negative

9/-1​ = -9

Hope this helps!

What is k ? (k = y/x)

     If y is dollars earned and x is hours worked,

k = y/x

k = 150 dollars /20 hours

k = 7.50 dollars per hour

What is the equation for the direct variation situation? (y = kx)

y = kx

y = (7.50)(60)

y = 450

How much will she earn for working 60 hours?

y = $450

       She will earn $450 after working for 60 hours.

Answer:  x = -4 + y

Step-by-step explanation:

Subtract y from both sides y- x - y = 4 - y

Simplify -x = 4 - y

Divide by -1

-x ÷ -1,

4 ÷ -1,

y ÷ -1,

Simplify x = -4 + y

Answer: A Quadrilateral is a trapeziod with only 1 pair of parallel sides.

Hope this helps!

Answer:

The trapezoid itself, including quadrilaterals.

Trapezoids have 1 pair of parallel sides. See picture below.

Answer:

51 seats

Step-by-step explanation:

96 = 2 buses minus six seats

96 = 2x -6

102 = 2x

102/2 = x

51 seats

[tex]x^2+2x\\\\\text{If x = 3,}\\\\3^2 + 2(3) = 9 + 6 = 15[/tex]

Answer:

1.4 meters

Step-by-step explanation:

Given,

Volume of rectangular prism ( V ) = 18.144 cubic meters

Width ( w ) = 2.7 m

Length ( l ) = 4.8 m

To find : d

Here, d is Height ( h ).

Formula : -

V = whl

18.144 = 2.7 x 4.8 x d

18.144 = 12.96 x d

d = 18.144 / 12.96

d = 1.4 meters

[tex] \huge\fbox\green{ANSWER} [/tex]

[tex]v = l \times w \times h[/tex]

[tex]18.144 {m}^{3} = 4.8m \times 2.7m \times d[/tex]

[tex]18.144 {m}^{3} = 12.96 \times d[/tex]

[tex] \frac{18.144 {m}^{3} }{12.96 {m}^{2} } = \frac{12.96 {m}^{2} }{12.96 {m}^{2} } \times d[/tex]

[tex]1.4m = d[/tex]

Answer:

240 ft^2

Step-by-step explanation:

10*18=180

20*6=120

120/2 = 60

180+60=240

Answer:

A

Step-by-step explanation:

it aligns with the other dots, and you can do exactly 1-1

Answer:

C. (9,4.5)

Step-by-step explanation: