Does the function y=x have an inverse? If so does it pass the horizontal line test?

The y-intercept of the graph of the function g(n) represents the height of the flower.

We are given:

A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.

g(n) = 10(1.02)^n

which is an exponential function.

We need to find what the y-intercept of the graph of the function g(n) represents.

We have the exponential function;

g(n) = 10(1.02)^n

where,

x-coordinate of the graph represents the number of days.

y-coordinate of the graph represents the height of the flower.

Thus, the y-intercept of the graph of the function g(n) represents the height of the flower.

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Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]

[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]

Answer:

second number = (x + 7.5)

Since the product of the two numbers is double of their sum,

             x(x + 7.5) = 2(x + x + 7.5)

             x² + 7.5x = 2(2x + 7.5)

             x² + 7.5x = 4x + 15

x² + 7.5x - 4x - 15 = 0

      x² + 3.5x - 15 = 0

                      ∴ x = -6 or 2.5

∴ second number

= -6 + 7.5 or 2.5 + 7.5

= 1.5 or 10

∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.

Answer:45600

Step-by-step explanation: 3800x12

Answer: $42.60

Step-by-step explanation:

divide $35.50 by 5 and then add the quotient ---> $7.10, to $35.50, which equals $42.60.

Answer: HISFAVORITESUBJECTS

Step-by-step explanation:

The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).

What is internal division?

When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.

The division is internally because point P lies on the line as given in the question.

The formula for the internal division is as follows:

[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]

Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].

Substute all value to obtain the coordinates.

[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]

Hence, the first cordinate is (5,0).

As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.

Now, m=5 and n=1.

Again substitute all values in to find the new coordinate.

[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]

Hence, another coordinate is (-3,-4).

Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).

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The value after multiplying the given mixed fractions is 7/6   .

In the question ,

it is given that ,

the two mixed fraction are given as [tex]-2\frac{1}{4}[/tex]  and [tex]-1\frac{1}{3}[/tex]  ,

we need to find their value after multiplication .

we first convert the mixed fractions into improper fraction ,

So ,

[tex]-2\frac{1}{4}[/tex] = (-2×4+1)/4 = (-8+1)/4 = -7/4

and

[tex]-1\frac{1}{3}[/tex] = (-1×3+1)/3 = (-3+1)/3 = -2/3

So , the product of -7/4 and -2/3 is written as

= -7/4 × -2/3

= (-7 × -2)/(4 × 3)

= 14/12

after simplifying ,

= 7/6

Therefore , The value after multiplying the given mixed fractions is 7/6   .

The given question is incomplete , the complete question is

Find the value after multiplying the given mixed fraction [tex]-2\frac{1}{4} \times -1\frac{1}{3}[/tex]   .

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The two triangles are congruent.

So, their corresponding sides will be equal.

So, 2x+5 = 5x-19

3x = 24

x = 8 cm.

So, XZ = 2*8+5 = 21 cm

the slope of the given point is m=2/17

Answer:

A) 3

B) 2[tex]\sqrt{6}[/tex]

C) 3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

A

3x3 = 9

B

24 = 2x2x2x3  We can pull out a pair of 2 and are left with 6

C

18 = 2x3x3  We can pull out a pair of 3 and are left with 2

The quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].

According to the question,

We have the following information:

The sum of roots of a quadratic equation = 31

The product of roots of a quadratic equation = 210

We know that the standard form of the quadratic equation is given as follows:

[tex]ax^{2} +bx+c = 0[/tex]

Now, the sum of roots is -b/a and the product of roots is c/a.

So, we have the following expressions:

-b/a = 31

b = -31 and a = 1

c/a = 210

c = 210 and a = 1

So, the equation will be:

[tex]x^{2} -31x+210 = 0[/tex]

Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].

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Answer:

a) 1:25 b) 2:06 c) 5:00 d) 4:10

Step-by-step explanation:

The translation made from f(x) → f(x) + 6 is sliding it up

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.

A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Any translation in a Euclidean space is an isometry.

the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units

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The constant of proportionality for the relationship is 0.002.

We are provided that amount of chlorine needed is directly proportional to the volume of the pool .

So we can formulate the relation as

C = kV ... (1)                   ( where  C = amount of chlorine ,

                                              k = constant of proportionality

                                              V = volume of the pool  )

the sample ratio of chlorine to the the volume of pool , we have :

5 : 2500

10 : 5000

15 : 7500

So taking the first sample value and putting it in eqn (1)

we get

5 = k (2500)

therefore,

k = 5/ 2500

k = 0.002

So the constant of proportionality will be 0.002

Similarly if we take the other values also the constant of proportionality will remain the same.

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If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.

In the question ,

it is given that ,

the value of a - b = -5 and ab = 0

we need to find the value of the expression (a³-b³) ,

we know the identity that a³-b³ = (a - b)(a² + b² + ab)

we first need the value of a² + b² .

given that a - b = -5

squaring both the sides , we get

(a - b)² = 25

a² + b² - 2ab = 25

given ab = 0, so a² + b² = 25

Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,

we get ,

a³-b³ = (-5)(25 + 0)

a³-b³ = -5 × 25

a³-b³ = -125

the answer is -125 .

Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.

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Answer:

$134.86

Step-by-step explanation:

Let the original price before tax be x.

A whole amount is 100% of the amount, so x is 100% of the original price without tax.

The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.

106% of x = $142.95

106/100 × x = 142.95

1.06x = 142.95

x = 142.95/1.06

x = $134.86

Answer: $134.86

Jerry will able to make 3 pancakes if he has 4 1/2 cup of strawberry from which he make use of 3/4 strawberry to make breakfast smoothie and he need 1 1/4 cup of strawberries to make one pancake.

Total strawberry Jerry has = 4 1/2 cup = 9/2 cups

Strawberry used to make smoothies = 3/4 cup

Remaining strawberries

= 9/2 - 3/4

= (18-3)/4 = 15/4

To make one pancake, Jerry needs = 1 1/4 cup = 5/4 cup

Number of pancakes Jerry can make = 15/4/5/4 = 3 pancakes

Hence, the number of pancakes, Jerry can make is 3

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Answer:

  1, 2, 4, 5

Step-by-step explanation:

You want triangles congruent to triangle 4.

In this exercise, we can determine congruence using SSS congruence: the lengths of the sides in congruent triangles will match. (The order of appearance of the side lengths as you go around the triangle is irrelevant.)

The lengths of the sides are ...

Looking at the other triangles, we see side lengths of ...

All side lengths match: congruent to 4.

All side lengths match: congruent to 4.

One side is 6 grid squares: not congruent.

All side lengths match: congruent to 4.

One side is 6 grid squares: not congruent.

One side is the diagonal of a 3×2 rectangle: not congruent.

One side is the diagonal of a 4×1 rectangle: not congruent.

__

Additional comment

Triangles 3 and 6 are congruent to each other, but not to triangle 4.

The number of candy bar that she bought is 6

The total amount that she spend for soda and candy= $12

The cost of one soda = $3

The cost of one candy bar = $1.50

Number of soda that she bought = 1

Consider the number of candy bar that she bought as x

Then the equation will be

3×1 + 1.50 × x = 12
Multiply the terms

3 + 1.50x = 12

Move 3 to right hand side of the equation

1.50x = 12 - 3

1.50x = 9

Move 1.50 to the right hand side of the equation

x = 9 / 1.50

x = 6

Hence, the number of candy bar that she bought is 6

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The variable y varies directly with x and the variation equation is (b) y = -1/2x

The graph represents the given parameter

On the graph, we can see that:

The values of x are divided by -2 to get y

This means that the graph represents a direct variation

Recall that we stated that:

The values of x are divided by -2 to get y

This means that the constant of variation is -1/2

The direct variation equation is represented as:

y = kx

Where k represents the constant of variation i.e. k = -1/2

Substitute the known values in the above equation So, we have the following equation

y = -1/2x

Hence, the equation of variation is y = -1/2x

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Answer:

The registration fee is $28

Step-by-step explanation:

5,600/100=56 which is 1% of 5,600.

56/2=28 which is 0.5% of 5,600.

;)

Answer: $28

Step-by-step explanation:

you calculate what 0.5 percent is of 5,600  :)

The strength and relationships of the given data is verified as reasonable.

Given,

Determine the degree of the link (weak, moderate, or strong) in each of the six plots and if it is reasonable to fit a linear model to the data.

(a) There is a moderate relationship in the data. A linear model should not be reasonable.

→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.

(b) There is a strong relationship in the data. A linear model should be reasonable.

→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.

(c) There is a weak relationship in the data. A linear model should not be reasonable.

→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.

(d) There is a moderate relationship in the data. A linear model should not be reasonable.

→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.

(e) There is a strong relationship in the data. A linear model should be reasonable.

→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.

(f) There is a weak relationship in the data. A linear model should not be reasonable.

→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.

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anwser: she has 34 cookies left

Answer:

  A, B, E

Step-by-step explanation:

You want three true statements describing the circle whose equation is ...

  x² + y² – 2x – 8 = 0

A graphing calculator can plot this equation for you. The result is attached.

We see that ...

__

Additional comment

The standard form equation of a circle is ...

  (x -h)² +(y -k)² = r² . . . . . center (h, k), radius r

Rearranging the given equation to this form, we have ...

  (x -1)² +y² = 8 +1 = 9 . . . . . . . . r²=9 ⇒ r=3

This means the center is (1, 0), and the radius is 3. The point (1, 0) is on the x-axis.

The circle with equation x² + y² = 9 is centered at the origin and has radius 3.

Answer:

The slope (constant rate of change) is 5.

The ounces of the 50% mixture that the pharmacist should use is 6 ounce.

From the information, we need two equations to solve this problem.

equation 1:

x + y = 10

equation 2:

.5x + .75y = 10(.6)

set y = 10 - x

.5x + .75(10-x) = 6

.5x + 7.5 - .75x = 6

.5x -.75x = 6 - 7.5

-.25x = -1.5

Divide

x = -1.5/-.25

x = 6

Therefore, 6 ounce of the 50% sorghum are required.

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The number of coins that the pirates collect is A. 10.

From the information, the pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins and there are 38 pirates on the ship.

The number of coins that way person will get will be:

=>Total coins / Number of pirates

= (253 + 127) / 38

= 380 / 38

= 10

Each person gets 10 coins.

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Answer:

Below

Step-by-step explanation:

a(x-p)(x-q)        p = -2    q = 5

a ( x- - 2)(x - 5)         sub in the values of the point given (3,6) to calculate 'a'

6  = a (3+2)(3-5)

a = -6 /10 = - 3/5

y = -3/5 (x+2)(x-5)  

Answer:

[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]

[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-2, 0) and (5, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-2))(x-5)[/tex]

[tex]\implies y=a(x+2)(x-5)[/tex]

To find a, substitute the given point on the curve P (3, 6) into the equation:

[tex]\implies 6=a(3+2)(3-5)[/tex]

[tex]\implies 6=a(5)(-2)[/tex]

[tex]\implies 6=-10a[/tex]

[tex]\implies a=\dfrac{6}{-10}[/tex]

[tex]\implies a=-\dfrac{3}{5}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]

[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]

Answer:   A) 0.05%

Step-by-step explanation:  Converting the shaded area of the hundredths grid to a fraction would be 5/100 (or 1/20 simplified). Then convert 5/100 to a percentage by calculating 5 ÷ 100, which is 0.005%, therefor the answer is A.