Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?

The vertex of the equation of the parabola y = 2( x - 3 )² + 1 is (3,1).

Given the equation of the parabola in the question:

y = 2( x - 3 )² + 1

To determine the vertex of the parabola, we use the vertex form of a parabola which is expressed as:

Vertex form: y = a(x - h)² + k

Where (h, k) represents the vertex of the parabola.

The given equation is already in the vertex form:

y = 2( x - 3 )² + 1

Hence, comparing the given equation, y = 2(x - 3)² + 1, with the vertex form, we can see that:

h = 3 and k = 1

Therefore, the vertex is (3,1).

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The value of x is 9

To find the value of x for which the rational expression is equal to zero, we need to set the numerator equal to zero:

x - 9 = 0

Solving for x:

x = 9

Therefore, the value of x = 9.

Looking at the denominator (x - 4)(x + 4), we see that it contains two factors: (x - 4) and (x + 4). For the entire expression to equal zero, either the numerator or one of the factors in the denominator must equal zero.

Setting each factor in the denominator equal to zero:

x - 4 = 0 or x + 4 = 0

x = 4 or x = -4

These are the valid values of x for which the rational expression is equal to zero.

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The values are x = 2 and NS = 3.5.

Given is a circle with center S, we need to find the missing measure,

K = 16, MP = 8, LP = 2x+4, and PS = 3.5, we need to find the measures of x and NS.

We know that the perpendicular drawn from the center of a circle bisect the chords into two halves,

And the perpendiculars are congruent.

Therefore,

MP = PL

2x+4 = 8

x+2 = 4

x = 2

Also,

NS = PS

So, NS = 3.5

Hence the values are x = 2 and NS = 3.5.

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The hands of an analog clock point at 1:27 is at 1o'clock position

At 1:27 on an analog clock, the hour hand focuses straightforwardly at the numeral "1" on the clock confront, demonstrating that it is within the 1 o'clock position.

The miniature hand, on the other hand, focuses between the numerals "2" and "3" on the clock confront, roughly midway between them.

Since there are 60 minutes in an hour and the diminutive hand moves around the clock confront at a consistent rate, it shows that 27 minutes have passed since the hour started.

Hence, the miniature hand is closer to the numeral "3" but not however at it. The moment hand may be anyplace on the clock confront, because it moves persistently.

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The reason for the fourth step to prove the congruence of [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex], based on the congruence of the triangles ΔABX and ΔCBX is the option C.

C. Corresponding parts of congruent triangles are congruent (CPCTC)

Congruent triangles are triangles that have the same shape and size.

The completed two column table to prove the congruence of the segment [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] can be presented as follows;

Statement [tex]{}[/tex]                                             Reasons

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] and ∠ABX ≅ ∠CBX [tex]{}[/tex]         Given

2. [tex]\overline{BX}[/tex] ≅ [tex]\ovderline{BX}[/tex]                                 [tex]{}[/tex]         Reflexive property of Equality

3. ΔABX ≅ ΔCBX [tex]{}[/tex]                                 SAS Triangle Congruence Theorem

4. [tex]\overline{AX}[/tex] ≅ [tex]\overline{XC}[/tex]                                [tex]{}[/tex]          CPCTC

The reason for the fourth step can be presented as follows;

CPCTC is an acronym for corresponding parts of congruent triangles are congruent. The triangles ΔABX and ΔCBX are congruent, therefore, CPCTC indicates that the segments [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] which are corresponding parts are therefore congruent.

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Answer:  D

Step-by-step explanation: -135

Answer:

Step-by-step explanation:

Area of parallelograph = bh

b=20  h =42

A=(20)(42) = 840 mm²

The value of the angle csc θ of the given problem is: 5/4

There are different trigonometric ratios such as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, we are given that:

cot θ = 4/3

We know that cot θ = 1/tan θ

Thus:

tan θ = 3/4

Since θ is an acute angle, it means it is less than 90 degrees. Thus, using Pythagoras theorem, we can find the third side which is the hypotenuse to be 5

Now, csc θ = 1/sin θ

Thus: sin θ = 4/5

csc θ = 5/4

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Answer:  A.   x=3     y= -1         z=4

Step-by-step explanation:

I plugged it into my graphing calculator.

>2nd Matrix

>Edit >A

>choose 3x3

>Enter all coefficients as they look

>2nd Matrix

>Edit >B

>Choose 3x1

>Enter answers as they look

Go to main page

[tex][A]^{-1} [B]\\[/tex]

Answers end up being 3, -1,  4

The expression which is equivalent to -32^3/5 is  -32768 / 125.

We are given that;

Expression=-32^3/5

Now,

To find an equivalent expression for -32^3/5 is to use the property of exponents that says [tex](a/b)^n = a^n / b^n.[/tex] Applying this property, we get:

-32^3/5 = (-32)^3 / 5^3

Now we can simplify the numerator and denominator by cubing them:

-32^3/5 = -32768 / 125

This is an equivalent expression for -32^3/5. There may be other ways to find equivalent expressions, such as factoring or using common denominators.

Therefore, by the expression the answer will be -32768 / 125.

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Answer:

18

Step-by-step explanation:

is a 1/3 scale

6-12-?

8-16-24

simple :)

Hello!

[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]

Based on the figure, if I and K are parallel lines, the value of x+y in degrees is 62°.

The correct answer choice is option A.

From the diagram

x + 149° = 180° (Sum of angle on a straight line)

x = 180° - 149°

x = 31°

Also,

y = 31° (alternate angles are equal)

Therefore,

x + y = 31° + 31°

= 62°

Hence, the sum of angle x and angle y is 62°.

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As per the given data, the area of the rectangular field is approximately 204 square meters.

To find the area of the rectangular field, we need to multiply its length by its width.

Given that the length is 18 2/5 m and the width is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the area of the rectangular field:

Area = Length * Width

     = (92/5) m * (255/23) m

     = (92 * 255)/(5 * 23) m^2

     = 23460/115 m^2

     = 204 m^2 (rounded to the nearest whole number)

Therefore, the area of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area. ​

Using binomial probability, the probability is 0.8897

Using binomial probability formula, we can determine the number of defective batteries

In this case, n = 1,200 (the sample size) and p = 0.006 (the probability of finding a defective battery).

We want to find the probability of finding 5 or fewer defective batteries, which is equivalent to finding the cumulative probability up to 5.

Let's calculate this probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial probability formula:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^(^n ^- ^k^)[/tex]

where C(n, k) represents the number of combinations of n items taken k at a time.

Plugging the values and solving;

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) =

[tex]C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]

To calculate these probabilities, we need to use a combination formula to determine the number of combinations. The combination formula is given by:

C(n, k) = n! / (k! * (n - k)!)

Now let's calculate the probability:

[tex]P(X \leq 5) = \\C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(^1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3^)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4^)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]

Using a calculator or statistical software to perform the calculations, we find that the probability is approximately 0.8897 when rounded to four decimal places

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The zeros of this expression are irrational, so it cannot be factored using integers.

When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.

In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.

In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)

= 144 - 52

= 92.

Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.

This means that the expression cannot be factored into two binomial factors with integer coefficients.

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To determine the radius of each wheel, we can use the formula for the circumference of a circle:

Circumference = 2πr,

where "Circumference" represents the circumference of the wheel and "r" represents the radius of the wheel.

Given that the circumference of each wheel is 22 inches, we can set up the equation as follows:

22 = 2πr.

To solve for the radius, we'll isolate "r" by dividing both sides of the equation by 2π:

22 / (2π) = r.

Using a calculator for the approximation, we get:

r ≈ 3.5 inches.

Therefore, to the nearest length, the radius of each wheel is approximately 3.5 inches.

Answer:

C) 3.5 inch

Step-by-step explanation:

The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

We have,

When reflecting a point across the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same.

Applying this transformation to each vertex, we get:

F' = (-(-2), -1) = (2, -1)

G' = (-(2), 2) = (-2, 2)

H' = (-(4), -3) = (-4, -3)

Therefore,

The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

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The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.

We can make use of the data given to determine the Burj Khalifa's floor count.

Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.

Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.

tan(39.62°) = h / d

h = d * tan(39.62°)

h = 1000 * tan(39.62°) ≈ 753.7 meters

So, as per this, Number of floors = h / floor height

Number of floors = 753.7 meters / 5.079 meters

Number of floors ≈ 148.4 floors or 148 floors.

Thus, 148 floors are there in Burj Khalifa.

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The solution to the system of equations is  x = 5.4 and y = -1.4

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

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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The 77th term of the given Sequence is 244.

The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.

The formula for the nth term of an arithmetic progression is:

_ = _1 + ( − 1),

where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.

In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:

_77 = 16 + (77 − 1) × 3.

_77 = 16 + 76 × 3.

_77 = 16 + 228.

_77 = 244.

Therefore, the 77th term of the given sequence is 244.

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[tex]\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o[/tex]

Make sure your calculator is in Degree mode.

The equation of the circle is (x + 4)² + (y - 1)² = 81

Given is an equation of a circle we need to convert it in standard form,

x² + y² + 8x - 2y = 64,

To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.

The standard form of a circle equation is:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Let's convert the given equation to standard form step by step:

x² + y² + 8x - 2y = 64

Rearrange the equation to group the x-terms and y-terms:

x² + 8x + y² - 2y = 64

Now, complete the square for the x-terms.

Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:

x² + 8x + 16 + y² - 2y = 64 + 16

Simplify:

(x + 4)² + y² - 2y = 80

Complete the square for the y-terms.

Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:

(x + 4)² + y² - 2y + 1 = 80 + 1

Simplify:

(x + 4)² + (y - 1)² = 81

Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.

Hence the equation of the circle is (x + 4)² + (y - 1)² = 81

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The equation for the function shown is f(x) = (x + 1)² - 2. Option B

From the information given, we have the deductions;

The vertex of the parabola is given as (-1, -2)

Using the form;

f(x) = a(x - h)^2 + k

Such that (h, k) represents the vertex coordinates.

Substitute the vertex coordinates into formula, we get;

f(x) = a(x - (-1))² + (-2)

= a(x + 1)² - 2

Now, substitute the value for a, we get;

2 = a(-3 + 1)² - 2

find the square and collect like terms

4 = a(4)

a = 1

Put value back into the equation

f(x) = 1(x + 1)² - 2

Multiply the value, we get;

f(x) = (x + 1)² - 2

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==============================================

Explanation:

The formula to use is n*(n-1)/2

Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66

That formula is from the nCr combination formula when r = 2.

---------------------

Here's a visual way to see why that rule works.

Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]

In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]

Let's also cross out any cell below the main diagonal.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]

We do this because a mirrored copy is found above the diagonal.

We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.

Those 6 matchups are:

The order doesn't matter. A matchup like "A vs B" is the same as "B vs A".

We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.

Then we split that in half to get the formula n(n-1)/2.

Answer:

C. y + 4 = 4(x+3)

Step-by-step explanation:

Point slope form: y-y1 = m(x-x1)

Substitute the given slope 4 and point (-3, -4)

y-(-4) = 4(x - (-3))

Simplify

y + 4 = 4 (x+3)

The sum of Ethan and Calvin's current ages is approximately 45.65.

Let's assume Ethan's current age is represented by 'E', and Calvin's current age is represented by 'C'.

From the given information, we can establish the following equations:

The product of their current ages is 238:

E × C = 238

The product of their ages after four years is 378:

(E + 4) × (C + 4) = 378

We can solve this system of equations to determine the values of E and C, and then calculate their sum.

From equation 1, we can express E in terms of C:

E = 238 / C

Substituting this value of E into equation 2:

(238 / C + 4) × (C + 4) = 378

Expanding and simplifying the equation:

(238 + 4C) × (C + 4) = 378

[tex]238C + 952 + 4C^2 + 16C - 378 = 0\\4C^2 + 254C + 574 = 0[/tex]

Now, we can solve this quadratic equation for C using the quadratic formula:

C = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

a = 4, b = 254, c = 574

C = (-254 ± √([tex]254^2[/tex]- 4 × 4 × 574)) / (2× 4)

After solving, we find two possible values for C: C ≈ -73.85 and C ≈ -39.65

Since age cannot be negative, we discard the negative value. Thus, C ≈ 39.65.

Plugging this value of C back into equation 1:

E × 39.65 = 238

E ≈ 238 / 39.65

E ≈ 6

Therefore, Ethan's current age (E) is approximately 6 and Calvin's current age (C) is approximately 39.65.

The sum of their current ages is:

6 + 39.65 ≈ 45.65

Hence, the sum of Ethan and Calvin's current ages is approximately 45.65.

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In order to expand the properties of logarithms log981x:

log981x = log98 + log1x

One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.

Using this property, we can simplify the expression further:

log981x = log98 + log1x = log9 + log8 + log1 + logx

We know that log9 = 2 and log1 = 0, so we can simplify even further:

log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.

Therefore, the expanded value would be log981x to 2 + log8x.

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