Identify the parent function.
• A. Square root
B. Cube root
• C. Absolute value
D. Reciprocal

The exponential decay model is found by solving for the time constant in the exponential decay equation.

The exponential decay equation is y(t)=y0e^{-kt}, where y0 is the initial value, k is the rate constant, and t is the time. The time constant is found by solving for t when y(t)=y0/2. This gives t=-ln(2)/k.

In mathematics, exponential decay refers to the process of decreasing an amount by a constant percentage rate over time. It can be expressed as y=a(1-b)x, where y is the final amount, an is the original amount, b is the decay factor, and x is the time elapsed.

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The fraction of the distance from Mrs. Thompson's house to the library that she biked was 2/3.

A fraction is a small part of a larger whole.

A fraction can represent a proportion of a larger number of units.

Fractions are quotients resulting from division operations.  Where the numerator is less than the denominator, it is called a proper fraction.  Otherwise, it is an improper fraction.  There are also complex fractions.

Fractions can be converted to decimals and percentages.

Total distance from Mrs. Thompson's house to the library = 3/4 kilometers

The distance biked by Mrs. Thompson = 1/2 kilometer

The fraction of the distance from the home to the library biked = 2/3 (1/2 ÷ 3/4)

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the orginal price is really "x", which oddly enough is the 100%, but we also know that 260 is 35% off that, so 260 is really 100% - 35% = 65% of the original price, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 260& 65 \end{array} \implies \cfrac{x}{260}~~=~~\cfrac{100}{65} \\\\\\ \cfrac{ x }{ 260 } ~~=~~ \cfrac{ 20 }{ 13 }\implies 13x=5200\implies x=\cfrac{5200}{13}\implies x=400[/tex]

The new coordinates of C is (-2, 2).

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

The coordinate of C is (1, -2).

A point (x, y) when reflected over the X axis becomes (x, -y).

C becomes (1, 2) when reflected over the X axis.

Translation is done 3 units left.

Translation of a point towards left and right changes the x coordinate and translation towards up and down changes the y coordinate.

New coordinate of C is (1 - 3, 2) = (-2, 2).

Hence the coordinates of C is option B (-2, 2).

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The solution for the give differential equation is y = c1e⁻ˣ+c2e⁻²ˣ·e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]coseˣ

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable

Given that, solve the differential equation by variation of parameters. y'' + 3y' + 2y = sineˣ

AE = m²+3m+2 = 0

Where, m1 = -1, m2 = -2

CF = y = c1e⁻ˣ+c2e⁻²ˣ

PI = y1 = eˣ and y2 = e⁻²ˣ

W = -e⁻³ˣ

W1 = -e⁻²ˣsineˣ

W2 = e⁻ˣsineˣ

u'1 = W1/W = eˣsineˣ;

u1 = ∫eˣsineˣ dx = ∫sint dt [put t = eˣ]

= -cost = -coseˣ

Similary,

u'2 = W2/W =  -e²ˣsineˣ;

u2 = -∫e²ˣcoseˣ dx = -∫tcost dt [put t = eˣ]

= -(tsint+cost) = -(eˣsineˣ+coseˣ)

PI: y = u1y1 + u2y2 = e⁻ˣ[-coseˣ] + e²ˣ[-(eˣsineˣ+coseˣ)]

= -e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]cose²ˣ

Hence, the complete solution is y = c1e⁻ˣ+c2e⁻²ˣ·e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]coseˣ

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Answer: x > 3

Step-by-step explanation:

Step 1: Subtract 5x from both sides.

−2x+9−5x<5x−12−5x

−7x+9<−12

Step 2: Subtract 9 from both sides.

−7x+9−9<−12−9

−7x<−21

Step 3: Divide both sides by -7.

−7x/−7 < −21/−7

x > 3

On a line graph it would look like this:

Answer:

2,112 [tex]ft^{3}[/tex]

Step-by-step explanation:

Volume of the cube

(12)(12)(12) = 1728

Volume of the pyramid

1/3(12x12x8) = 384

1728 + 384 = 2112

The length, width, and height of the box is 23 inches, 24 inches, and 25 inches.

The desired length of the diagonal of the box d ≥ 41.5 inches

The length of the box = l

The width of the box = w

The height of the box = h

The formula for the diagonal of the box, obtained using the  Pythagorean Theorem is:

                                     d = [tex]\sqrt[]{l^{2}+w^{2}+h^{2} }[/tex]

So, the square of the diagonal of the box, d² ≥ 41.5² = 1722.25

                                     [tex]d^{2} = l^{2} + w^{2} + h^{2}[/tex]

                                   l² + w² + h² ≥ 1722.25

Since,20² = 400

21² = 441

22² = 484

23² = 529

24² = 576

25² = 625

26² = 676

27² = 729

Hence, 23² + 24² + 25² = 1730 > 1722.25

20² + 20² + 27² = 1529 < 1722.25

21² + 24² + 26² = 1693 < 1722.25

20² + 21² + 26² = 1517 < 1722.25

So, the box's possible length is 23 inches.

                                      width is 24 inches.

                             and height is 25 inches.

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The maximum number of comparisons in a bubble sort if there are 5 elements in the array = 10

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity is quite high.

Due to its simplicity, bubble sort is often used to introduce the concept of a sorting algorithm.

In computer graphics, it is popular for its capability to detect a tiny error (like a swap of just two elements) in almost-sorted arrays and fix it with just linear

complexity (2n).

Example: It is used in a polygon filling algorithm, where bounding lines are sorted by their x coordinate at a specific scan line (a line parallel to the x-axis), and with incrementing y their order changes (two elements are swapped) only at intersections of two lines

Calculating total number of comparison required to sort the array

= (n-1) + (n-2) +  (n-3) + . . . 2 + 1

= (n-1)*(n-1+1)/2  { by using sum of N natural Number formula }

= n (n-1)/2    

= 5(4)/2

=20/2

=10

The maximum number of comparisons in a bubble sort if there are 5 elements in the array = 10

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The fundamental theorem of algebra states that every polynomial equation of degree n, where n is a positive integer, has at least one root in the complex number system.

The Fundamental Theorem of Algebra states that any polynomial equation of degree n, with real or complex coefficients, has at least one root (real or complex).

In the case of the equation 2x^2 - 4x + 16 = 0, the Fundamental Theorem of Algebra implies that there is at least one real or complex root. In fact, this equation has two real roots: x=4 and x=-2.

This theorem provides an important foundation for many branches of mathematics, as it proves that solutions to equations exist.

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The data in a table indicate the exponential function f(x) = 3(2)x.The formula for an exponential function is: y = abx, where y and x are variables .

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. If your function has the formula y = a b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.

given

From the table, at point (0, 3):

3 = ab°  , a = 3

At point (2, 12):

12 = ab²

12 = 3b²

b² = 4

b = 2

f(x) = 3(2)ˣ

The data in a table indicate the exponential function f(x) = 3(2)x.

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The length should be x ≥ 3 inch and 4x ≥ 12 square inches.

What is linear inequality?

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression. Polynomial inequality, rational inequality, and absolute value inequality are the various kinds of mathematical inequalities.

Given a rectangle, length  = 4 inches

area is at least 12 square inches

inequality equation for area

A ≥ 12

area  = l x b

where l = length = 4 inches and b = breadth = x

A ≥ 12

4x ≥ 12

x ≥ 3 inches

Hence the breadth should be x ≥ 3 inches and equation of area is

4x ≥ 12 square inches.

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Answer:

y - 1 = -6( x - 2)

Step-by-step explanation:

(2,1)  The x is 2 and the y is 1.

Therefore , the value of the given problem of linear equation comes out to be  x = -250.

In algebra, a mathematical model is just one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since x and y are variables, the previous sentence is frequently referred to as a "mathematical expression with 2 variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many different situations. Once an issue has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.

Here,

Given : 70.50 - 45.50 + 0.15x - 0.09x =0

To find the value of x,

Thus,

We do : 70.50 - 45.50 + 0.15x - 0.09x =0

=> 15 + 0.06x =0

=> 6/100 *x = -15

=> 6x = -1500

=> x = -1500/6

=> x = -250

Therefore , the value of the given problem of linear equation comes out to be  x = -250.

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After solving, the exact value of tan5π/8 = -2.425

In the given question we have to find the exact value of tan5π/8.

The angles and sides of a right-angle triangle are measured using these trigonometric values. Cotangent, secant, and cosecant are the other three significant values in addition to sine, cosine, and tangent.

To find the value of tan5π/8 we simplify the values.

Rephrase 5π/8 as the angle divided by two where the values of the six trigonometric functions are known.

tan5π/8 = tan[(5π/4)/2]

Now applying the tangent half-angle identity.

tan5π/8 = ±√[{1-cos(5π/4)}/{1+cos(5π/4)}]

The tangent is negative in the second quadrant, so change the ± to -.

tan5π/8 = -√[{1-cos(5π/4)}/{1+cos(5π/4)}]

We know the value of cos(5π/4) = -1/√2

Now putting the value

tan5π/8 = -√[{1-(-1/√2)}/{1+(-1/√2)}]

tan5π/8 = -√[{1+1/√2}/{1-1/√2}]

tan5π/8 = -√[{√2+1}/√2/{√2-1}/√2]

tan5π/8 = -√(√2+1)/(√2-1)

As we know that, √2 = 1.41. So

tan5π/8 = -√(1.41+1)/(1.41-1)

tan5π/8 = -√(2.41)/(0.41)

tan5π/8 = -√5.88

tan5π/8 = -2.425

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The exact value of tan (5π/8) is 1.7320508076.

The exact value of tan (5π/8) can be calculated using the tangent of a sum formula. The formula states that tangent of (A+B) can be calculated by the formula:

tan(A+B) = (tan A + tan B) / (1 - tan A tan B).

Therefore, we can calculate the tan (5π/8) as follows:

tan (5π/8) = tan (3π/4 + π/8)

           = (tan (3π/4) + tan (π/8)) / (1 - tan (3π/4) tan (π/8))

           = (√2 + 0.3826834) / (1 - √2 * 0.3826834)

           = 1.7320508076

Therefore, the exact value of tan (5π/8) is 1.7320508076.

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The graph is attached in the solution.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Given that, a function f(x) = 3√x

Let x = 0,

f(0) = 3√0 = 0

Let x = 1,

f(1) = 3√1 = 3

Let x = 2

f(2) = 3√2 = 4.24

Plotting the graph, we get, (attached)

Hence, the answer is the graph attached to the solution.

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An equation that simplifies to the square root of -18 can be written as y = 3{√2}i.

The {i} in a complex number z = a + ib stands for -

i = [tex]$\sqrt{-1}[/tex]

i² = - 1

Given is the square root of -18.

An equation that simplifies to the square root of -18 can be written as -

y = √(- 18)

y = √(- 1) x √18

y = √(i)² x 3√2

y = 3{√2}i

Therefore, an equation that simplifies to the square root of -18 can be written as y = 3{√2}i.

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According to the word problem states that they must string at least 31 beads per day.

Math word problems require students to apply their arithmetic abilities in a "real-life" setting and are mathematical questions that are described in one or more sentences. Kids must therefore be familiar with the vocabulary associated with the mathematical symbols they are used to in order to comprehend the word problem.

given the string's existing 70 beads They intend to string 1000 beads by both the start of class in just 30 more days.

The minimal number of beads that must be strung each day is calculated by dividing the remaining beads by the number of days:

The quantity of beads needed to reach 1000 = 1000 - 70 = 930

Now, putting the values,

= (1000 - 70)/30

= 930/30

= 31

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The amount in quarts of liquid soap that Charlie use to make the cleaning solution is 3/4 quarts

From the problem we have the following information

Charlie makes 6 quarts of a cleaning solution

The solution is 3/4 water and 1/4 soap mixture

The soap mixture is 1/2 liquid soap and 1/2 vinegar

The soap mixture is 1/4 of the solution, and the solution is 6 quarts

= 1/4 * 6

= 3/2 quarts

The liquid soap is 1/2 soap mixture which is solved to be 3/2 quarts

= 1/2 * 3*2

= 3/4 quarts

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The digit which the letter A represents as required in the task content so that the given problem is true is; 5.

As evident in the task content; it follows that the digit which the letter A represents in the given task content is to be determined.

On this note, first, 47 can be subtracted from 137 so that we have;

137 - 47 = 90.

On this note, it can be inferred that;

A A + 3 A = 90

Therefore, by using the place value concept, it follows that we have;

( 10 × A ) + ( 1 × A ) + ( 3 × 10 ) + ( 1 × A ) = 90

10A + A + 30 + A = 90

12A = 90 - 30

12A = 60

A = 5.

On this note, the letter A as represented in the task content represents the digit; 5.

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1. The value of -5.1m + 2.3m is -2.8m.

2. The value of 3/5y + (-6/5y) is -3/5y

3. The value of 3.1n + 1.5 - 1.1n - 2.9 is 2n - 1.4

4. The value of -2.6c - 0.8 - 2.8c + 3.4 is 5.4c + 2.6.

5. The value of -3x - 2.6y + 1.2 + 1.2x - 4.7 is -1.8x - 2.6y - 3.5

6. The value of -4/22t - 5/22t + 15 + (-5) is -9/22t + 10.

7. The expression equivalent to -2.3v + (-4.2) + 8.8 + (-3.2v) is -5.5v + 4.6.

8. The expression equivalent to 3/14x + (-1) + (-4) - 2/7x is -1/14x - 5.

It should be noted that expression is used to show the relationship that the variables have in a data or based on the question given.

Here, the value of -5.1m + 2.3m is will be:

= -5.1m + 2.3m

= -2.8m.

The value of 3/5y + (-6/5y) is:

= 3/5y + (-6/5y) is:

= 3/5y - 6/5y) is:

= -3/5y

The value of 3.1n + 1.5 - 1.1n - 2.9 is:

= 2n - 1.4

The value of -2.6c - 0.8 - 2.8c + 3.4 is:

= -2.6c - 0.8 - 2.8c + 3.4

= -5.4c + 2.6

The value of -3x - 2.6y + 1.2 + 1.2x - 4.7 is:

= -3x - 2.6y + 1.2 + 1.2x - 4.7

= -1.8x - 2.6y - 3.5

The value of -4/22t - 5/22t + 15 + (-5) is:

= -4/22t - 5/22t + 15 + (-5)

= - 9/22t + 10

The expression equivalent to -2.3v + (-4.2) + 8.8 + (-3.2v) is:

= -2.3v + (-4.2) + 8.8 + (-3.2v)

= -5.5v + 4.6

The expression equivalent to 3/14x + (-1) + (-4) - 2/7x is:

= 3/14x + (-1) + (-4) - 2/7x:

= - 1/14x - 5

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1. Michael is a better grader.

2. Catherine received the better grader.

3. Sam received the better grader.

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Answer:

Below

Step-by-step explanation:

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The horizontal asymptote is y = 0 because m = n. A function's graph has a line known as a horizontal asymptote.

A horizontal asymptote is a line that the graph of a function approaches as x tends to either positive or negative infinity. If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote of the function is the line y = a/b, whereThe leading coefficients in the denominator and numerator, respectively, are a and b. Therefore, if m = n, then the horizontal asymptote is y = a/b, which reduces to y = 0.

The statement that defines the horizontal asymptote is that if m = n, then the horizontal asymptote is y = 0.

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The price of gasoline next year will be 4.575.

The function of the price of gasoline next year will be a function of the current price and the percentage increase.

Price of gasoline next year = (1 + percent increase/100) x current price

Price of gasoline next year = 3.75 x (1 + 22/100)

Price of gasoline next year = 3.75 x (1 + 0.22)

Price of gasoline next year = 3.75 x 1.22

Price of gasoline next year = 4.575

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The probability that both cards will be red cards is P(A⋅B) = 25/102

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The first event, random drawing of a red card (event A), has a sample space of an entire deck with 52 different elementary events occurring with equal probabilities of 1/52. Out of them only 26 events are "good" (that is, the card we randomly pick is red). Therefore, the probability of picking a red card equals to

P(A) = 26/52

P(A) = 1/2.

The second event, random drawing of a red card from a deck of only 51 remaining cards (event B), is dependent on the results of the first event. If the first event (event A) occurs (red card is drawn), the deck for the second drawing contains 25 red and 26 black cards and the conditional probability of picking red card is

P(B/A) = 25/51.

Now we can use the concept of conditional probability and a formula that describes the probability of a combined event through the probability of one and conditional probability of another:

P(A⋅B) = P(A) * P(B/A)

In our case P(A) = 1/2 and P(B/A) = 25/51

Therefore,

P(A⋅B) = (1/2) * (25/51)

P(A⋅B) =25/102

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Answer:

y = 11

Step-by-step explanation:

It is just an equation with one variable ( 'y') which you can solve

-7y + 2 = - 75     subtract 2 from both sides of the equation

-7y = -77             divide both sides by -7

y = 11  

Answer:

-7y+2=-75

-7y=-75-2

-7y=-77

y=11

Answer:

Step-by-step explanation:

Answer:

63 students

Step-by-step explanation:

sorry bro i don't know the answer

The data represents the linear equation.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

We have the table:

x → y

-9 →  -71

-8 → -63

-7 → -55

-6 →  -47

-5 →  -39

To prove that the data represents in the tables are from the linear equation:

If a first difference of the table of values shows a constant rate of change,

then the function is a linear equation.

So,

y₂-y₁ = -63 + 71 = 8

y₃ - y₂ = -55 + 63 = 8

y₄ - y₃ = -47 + 55 = 8

y₅ - y₄ = -39 + 47 = 8

Here, 8 is the constant rate of change.

So, the data represents the linear equation.

Therefore, the data represents the linear equation.

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