Find the value of a that makes the ordered pair a solution of the equation. Y=3x+7; (-3, a)

Given functions f(x) = 2x² + 1 and g(x) = 7x - 8, then [tex]f[g(2) = 73\end{array}$[/tex].

A technical definitiοn οf a functiοn is: a relatiοn frοm a set οf inputs tο a set οf pοssible οutputs where each input is related tο exactly οne οutput.

This means that if the οbject x is in the set οf inputs (called the dοmain) then a functiοn f will map the οbject x tο exactly οne οbject f(x) in the set οf pοssible οutputs (called the cοdοmain).

The nοtiοn οf a functiοn is easily understοοd using the metaphοr οf a functiοn machine that takes in an οbject fοr its input and, based οn that input, spits οut anοther οbject as its οutput.

Given f(x) = 2x² + 1 and g(x) = 7x - 8

Then

a)

[tex]$\begin{array}{l c l}{f[g(2)]=f[(7*2-8)]=f(6)}\\ {f[g(2)]=2(6)^{2}+1=72+1}\\f[g(2) = 73\end{array}$[/tex]

b)

[tex]$\begin{array}{l}{{f[g(x)]=f(7x-1)=2[7x-8]^{2}+1}}\\ {{f[g(x)]=2(49x^{2}+64-112x)+1}}\\ {{f[g(x)]=98x^{2}-224x+129}}\end{array}$[/tex]

c)

[tex]$\begin{array}}{g[f(x)]=g[2x^{2}+1]=7[2x^{2}+1]-8}\\ {g[f(x)]=14x^{2}-1}\end{array}$[/tex]

d) (g · g)(x) = g{g(x)} = g(7x - 8)  

= 7(7x - 8) - 8

= 49x−64

e) (f · f)(-2) = f{f(-2)} = f(2(-2)²)

= 2(2(-2)²)²

= 128

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Accοrding tο the transfοrmatiοn prοperty, the cοrrect answer is οptiοn (c): (x, y) → (- y + 2, x + 2)

Transfοrmatiοn is a functiοn that maps οne set οf pοints tο anοther set οf pοints in a way that preserves sοme structure οr prοperties οf the οriginal set. The mοst cοmmοn types οf transfοrmatiοns are geοmetric transfοrmatiοns, which preserve distance, angle, and shape, and algebraic transfοrmatiοns, which preserve algebraic prοperties such as the sum, prοduct, οr symmetry οf functiοns.

Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. Therefοre, tο determine whether a transfοrmatiοn maps triangle ABC tο a similar, but nοt a cοngruent triangle, we need tο examine hοw the transfοrmatiοn affects the angles and sides οf triangle ABC.

Let's assume that triangle ABC has vertices A(a₁, a₂), B(b₁, b₂), and C(c₁, c₂).

a) (x, y) → (x + 2, - y - 2)This transfοrmatiοn is a translatiοn that mοves each pοint οf the plane twο units tο the right and twο units dοwn. Therefοre, this transfοrmatiοn dοes nοt change the size οr shape οf triangle ABC. It οnly changes its pοsitiοn in the plane. Hence, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

b) (x, y) → (- 4x, - 4y)

This transfοrmatiοn scales each cοοrdinate by a factοr οf -4, which reflects the triangle acrοss the οrigin and changes its size. Hοwever, this transfοrmatiοn alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

c) (x, y) → (- y + 2, x + 2)

This transfοrmatiοn is a rοtatiοn οf 90 degrees cοunterclοckwise arοund the pοint (2, 2). Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a rοtatiοn, it preserves the angles οf the triangle. Tο check if it preserves the sides, we need tο cοmpute the length οf each side οf the transfοrmed triangle and cοmpare it tο the cοrrespοnding side οf the οriginal triangle:

AB: distance between (- a₂ + 2, a₁ + 2) and (- b₂ + 2, b₁ + 2) is equal tο the distance between A(a₁, a₂) and B(b₁, b₂)

AC: distance between (- a₂ + 2, a₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between A(a₁, a₂) and C(c₁, c₂)

BC: distance between (- b₂ + 2, b₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between B(b₁, b₂) and C(c₁, c₂)

Since the angles and sides are preserved, this transfοrmatiοn maps triangle ABC tο a similar, but nοt cοngruent triangle.

d) (x, y) → (- y, - x)

This transfοrmatiοn is a reflectiοn acrοss the line y = x. Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a reflectiοn, it preserves the angles οf the triangle. Hοwever, it alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

Therefοre, the answer is οptiοn (c): (x, y) → (- y + 2, x + 2)

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The study that we have here is an observational study. The study is not retrospective in nature.

This study is observational because the researchers are observing and collecting data on a group without manipulating any variables.

It is not a retrospective study because the data is collected in real-time during the first year of college, rather than looking back on past experiences.

Therefore, there are no treatment or control groups, and there is no need for blinding. The study simply reports the percentage of first-year women students who experienced sexual assault during their first year at the regional college.

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Answer: 6

Step-by-step explanation:

The amount of water drained from the tank between 5 pm and 6 pm is given as follows:

143 liters.

An exponential function is modeled as follows:

y = ab^x.

In which the parameters are represented as follows:

The parameter values for this problem are given as follows:

Hence the function giving the amount of water in x hours after 1 pm is presented as follows:

y = 1870(0.86)^x.

At 5pm and 6 pm, the amounts are given as follows:

Hence the amount drained is of:

1023 - 880 = 143 liters.

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Answer: 1/3 or 1 divided by 3 is equivalent to 0.333333

Answer:

0,33

Step-by-step explanation:

this for sure.......

The values are given as;

1. The intercept, c = -1.5, Slope, m = -1/4

2. Intercept = 0. 5, Slope, m = -3/5

The general formula for the equation of a line is represented thus;

y = mx + c

Given that the parameter are;

For the first graph

The intercept, c = -1.5

The slope, m = y₂ - y₁/x₂ - x₁

Substitute the values as shown in the graph

Slope, m = -2-(-3)/- 3- 1

Slope, m = -2 + 3/-4

Slope, m = -1/4

For the second graph, we have

Intercept = 0. 5

The slope, m = y₂ - y₁/x₂ - x₁

Substitute the values

Slope, m = 2 - (-1)/3 - (-2)

Slope, m = -3/5

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Therefore , the solution of the given problem of function comes out to be  f(x) = -6x + 8 .

Numerous subjects, including numbers, numbers, as well as their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between variable elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.

Here,

The linear function with a slope of -6 can be written in slope-intercept form as:

=> f(x) = -6x + b

where "b" is the y-intercept. We are also given that f(0) = 8, so we can substitute those values in to solve for "b":

=> f(0) = -6(0) + b = 8

=> b = 8

Therefore, the linear function we are looking for is:

=> f(x) = -6x + 8

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When it happens, the ratio of their corresponding side will not change. The value of x is 8.

What are properties of triangle?

The sum of the interior angles of a triangle is always 180°.

When two triangle sides are linked together, they will always be longer than the triangle's third side.

Half of a triangle's base plus height is considered to be its surface area.

Already mentioned the ΔDEF and ΔXYZ are similar.

When it happens, the ratio of their corresponding side will not change.

So,

7/14=6/12=2x-5/22

We take last two,

6/12=2x-5/22

Or, 24x-60=132

Or, x= 192/24

Or, x=8

Hence, the value of x is 8.

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The area of the figure is 72 square meters

From the question, we have the following parameters that can be used in our computation:

A composite figure

The area of the figure is calculated as

Area = Sum of areas of the individual figures

From the figure, we have

Number of rectangles that make up the composite =3

Using the above as a guide, we have the following:

Area = 8 * 5 + 4 * 7 + 2 * 2

Evaluate

Area = 72

Hence, the area is 72 square meters

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Answer:

To prove that 7^7 - 7^6 is divisible by 6, we can factor out 7^6 from the expression:

7^7 - 7^6 = 7^6 (7 - 1)

Simplifying the expression, we get:

7^7 - 7^6 = 7^6 (6)

We can see that 7^6 is a common factor in the expression, and 6 is also a factor. Therefore, we can conclude that 7^7 - 7^6 is divisible by 6.

Step-by-step explanation:

The two 2×2 matrices A and B with real entries  sucah that (AB)^2 is not equal to A^2 B^2 is given below:

Let A = [[1, 0], [0, -1]] and B = [[0, 1], [1, 0]] be two 2x2 matrices with real entries. Then,

AB = [[0, 1], [-1, 0]] and AB^2 = [[-1, 0], [0, -1]]

A^2 = [[1, 0], [0, 1]] and B^2 = [[0, 1], [1, 0]]

So, A^2B^2 = [[0, 1], [1, 0]] and (AB)^2 = ABAB = [[0, 1], [-1, 0]][[0, 1], [-1, 0]] = [[-1, 0], [0, -1]]

Therefore, (AB)^2 is not equal to A^2B^2 for the matrices A and B defined above.

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Devaluation of 5%:

125+(125x5%)=187,5

Many US dollars can be bought if Nepali currency is devaluated by 5%=

62.500:187,5=333 dollar

A

i had this question it's right

If mDA =(23x -14), mDB =(9x-4), and mx=?Arc DA= ?

The equation of the graph is option (c) i.e. y = 0.5 csc [0.5(x + π/2)] - 1 which is solve below.

In elementary mathematics, term "graph" denotes a plot or a function graph. A graph, in the language of mathematicians, a set of points and connections between some subset of those points (which may empty).

If the equation y = A csc (B(x + C)) + D

Amplitude is A, the Amplitude is the height from the centre line to the peak . Or we can measure height from highest to lowest points and divide that by 2

Period is 2π/B, the Period goes from one peak to the next

Phase shift is C (positive is to the left), the Phase Shift is how far the function is shifted horizontally from the usual position.

Vertical shift is D, Vertical Shift is how far the function is shifted vertically from the usual position.

If y = csc(x), then A = 1 , B = 1 , C = 0 , D = 0

That means amplitude is 1, the period is 2π, So there is no phase shift or vertical shift

Now lets solve the problem from the graph

[tex]The\ amplitude = \frac{(-0.5 - (-1.5))}{2} = 0.5[/tex]

∴ [tex]A = 0.5[/tex]

The period is from 2.5π to -1.5π

∴ [tex]The \ period\ is\ 4\pi[/tex]

∵ [tex]The\ period = \frac{2\pi }{B}[/tex]

∴ [tex]4\pi = \frac{2\pi }{B}, by\ cross \ multiplication[/tex]

∴ [tex]B = \frac{2\pi }{4\pi } = \frac{1}{2} = 0.5[/tex]

There is only one answer which has value A = 0.5 and B = 0.5

∴ y = 0.5 csc[0.5(x + π/2)] - 1

So, The Correct equation of the graph is 0.5 csc[0.5(x + π/2)] - 1

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Answer:

The answer is c

Step-by-step explanation:

edge

Answer:

2.700 × 10-7

Step-by-step explanation:

Answer:  2.7*10^-4

step by step explanation:

1. Make the number a new number between 1 and 10

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Move the decimal point to make 0.00027 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.

0.00027 -> 2.7

Our new number is 2.7. We moved the decimal point 4 times.

2. Define the power of 10

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Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 4 times, so the exponent is negative 4

10^(-4)

3. Final result

2.7*10^(-4)

Answer:

Step-by-step explanation:

Answer:10-2= 8

Step-by-step explanation:

Answer:

please mark as brainliest

Answer:

B

Step-by-step explanation:

the graph of the function is a parabola

Answer:

I tried my best by helping

Step-by-step explanation:

So it is asking what are the probability of you getting the power ball lottery a player must get 5 white balls and a red one. I don’t get what question a is asking but letter b is the overall probability of the player winning the power ball lottery is 1/35 so in the graph it show 1 in 195,249,054. So that will be the answer of explaining the probability.

The numerator of the rational expression 7/V + 3/V is 10. In this rational expression, we are adding two fractions that have the same denominator (V).

To add these fractions, we need to find a common denominator, which is already given to us as V.

Then, we add the numerators of the two fractions, which are 7 and 3, to get:

7/V + 3/V = (7+3)/V

Simplifying the numerator by adding 7 and 3, we get:

10/V

The numerator for the rational expression 7/V + 3/V is:

7 + 3 = 10

Therefore, the numerator is 10.

Therefore, the numerator of the rational expression 7/V + 3/V is 10.

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Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.

What is congruency?

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

To write a congruence statement for two triangles, we need to identify their corresponding parts and ensure that they are congruent in both triangles.

The congruence statement can be written in the following form:

Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.

For example, if we have two triangles with vertices A, B, and C and P, Q, and R respectively, and we know that the following pairs of corresponding parts are congruent:

AB ≅ PQ

BC ≅ QR

AC ≅ PR

Then, we can write the congruence statement as:

Hence, Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.

The symbol ≅ means "is congruent to."

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Answer:

Kevin has 11 CDs.

Answer:

5divided by 14 is 2 with a remainder of 3

7

the first order pair is always x and the second is y

slope m =Y2_Y1 ÷ X2_X1

then 24_ 17 ÷3 _2= 7

The graph of the sinusoidal function shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters.

we can use a general form of sinusoidal function

h(t) = A sin(ωt + φ) + C

where:

A = amplitude (maximum displacement from the mean position)

ω = angular frequency (radians per second)

φ = phase angle (initial position of the oscillation)

C = vertical displacement (position of the mean or equilibrium position)

Since the mass is released from rest, we can assume that the initial displacement is zero, i.e., C = 0. Also, we know that the period of the oscillation is 1/f, where f is the frequency. Therefore, we can find the frequency from the given time period of 0.8 seconds.

Let's assume that the height of the mass oscillates with an amplitude of 0.1 meters and a frequency of 5π radians per second (corresponding to a period of 0.4 seconds), and the phase angle is 0.

h(t) = 0.1 sin(5πt)

We can plot this function for t ranging from 0 to 0.8 seconds using a graphing tool or by hand. Here is the resulting graph

    |

0.1 +                 . * .

    |             .*         *.

    |           .              .

    |         *                 *

    |        *                    *

    |      .                        .

    |     .                            .

    |   .*                                *.

    | .*                                      *.

-0.1 +----------------------------------------------

    0        0.2        0.4        0.6        0.8

The x-axis represents time in seconds, and the y-axis represents the height of the mass in meters. The graph shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters. The maximum height occurs at t = 0.1 seconds and t = 0.5 seconds, while the minimum height occurs at t = 0.3 seconds and t = 0.7 seconds. At t = 0.4 seconds and t = 0.8 seconds, the mass returns to the equilibrium position.

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Answer: 30 Child tickets 6 Adult tickets.

Step-by-step explanation:

Set up your system of equations to solve.

36 tickets are purchased, meaning a number of child tickets, and a different number of adult tickets add up to 36. We can write this as x+y=36.

The price of the tickets add up to 252 dollars. We can write this as 6 (the child price) times x + 12 (the adult price) times y = 252

So, x+y=36 and 6x+12y=252.

I will solve this using the substitution method.

So, first, we need to isolate a variable, I will choose the first equation to do so.

x+y=36 ---> x=36-y

Now, plug the value of x into the second equation.

6(36-y)+12y=252.

Distribute.

216-6y+12y=252

Combine like terms.

216+6y=252.

Subtract 216 from both sides.

6y=36

Divide by 6 on both sides.

y=6

Now plug this value of y into the previous equation to get x.

x+6=36

Subtract 6 from both sides.

x=30

Remember x was children's tickets and y was adult tickets. (It is better to use variables like C and A in this case).

The volume of the prism is 115.5 cubic centimeters.

A three-dimensional structure called a right rectangular prism has six rectangular faces, each of which has four right angles. The length, breadth, and height of a right rectangular prism are perpendicular to one another, and the opposing sides are congruent and parallel to one another. The prism's dimensions—also referred to as its length, breadth, and height—can be utilised to determine its volume. Multiplying the prism's length, width, and height yields the volume of a right rectangular prism.

The volume of the rectangular prism is given by the formula:

Volume = Length x Width x Height

Substituting the values we have:

Volume = 3.5 cm x 6 cm x 5.5 cm

Volume = 115.5 cubic centimeters

Hence, the volume of the prism is 115.5 cubic centimeters.

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Answer:

Since wave heights at Folly Beach are normally distributed with a mean of 4 feet and a standard deviation of 1.5 feet, we can use the normal distribution formula to find the probability of a wave having a height of exactly 3 feet.

The formula for the normal distribution is:

P(x) = (1 / (σ * sqrt(2π))) * e^(-(x - μ)^2 / (2 * σ^2))

where:

P(x) is the probability density function

σ is the standard deviation

μ is the mean

e is the base of the natural logarithm

x is the value of the variable

Substituting the values given in the problem, we get:

P(3) = (1 / (1.5 * sqrt(2π))) * e^(-(3 - 4)^2 / (2 * 1.5^2))

P(3) = 0.176

Therefore, the probability that a wave has a height of exactly 3 feet is 0.176 or approximately 17.6%.