Since Mars is smaller than Earth, a projectile near the surface of Mars accelerates downward at a rate of only 3.8 meters per second every second. Suppose that an astronaut on the surface of Mars throws a ball upward at time t=0 such that the ball reaches a maximum height of 15 meters. Let h(t) be the height of the ball in meters t seconds after being thrown. Using the method of scaling and shifting from In-Class Activity 9.A, derive a formula for h(t)

On solving the provided question, we can say that the equation will be  distance = distance 36t + 18 = 63t distance = 63t = 63(2/3) = 42 miles

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the two sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

the equatiοn will be

distance = distance

36t + 18 = 63t

27t = 18

t = 18/27 = 2/3 hr

distance = 63t = 63(2/3) = 42 miles

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The two integers are 1 and 2.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so they are positive integer.

A number is negative if it is less than zero, so they are negative integer.

A number line is a visual representation of numbers on a straight line. This line is used for comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

x be a positive number

x + 1 = y

The sum of reciprocal of the smaller and twice the reciprocal of the larger number

Substitute

[tex]\frac{1}{x} + \frac{2}{y} = 2[/tex]

[tex]\frac{1}{x} + \frac{2}{x + 1} = 2[/tex]

[tex]\frac{x+ 1 + 2x}{x(x +1)} = 2[/tex]

[tex]x + 1 + 2x = 2x^2 + 2x[/tex]

Subtracting 2x on both sides, we get

x + 1 + 2x - 2x = 2x² + 2x - 2x

x + 1 = 2x²

2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

2x(x - 1) + 1(x - 1) = 0

(2x + 1)(x - 1) = 0

x = -1/2 and x = 1

But x = -1/2 is not possible. Becuase x is a positive number.

So, x = 1

y = x + 1

y = 2

The two integers are 1 and 2.

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The set of ordered pairs of option A does not represent a function. The solution has been obtained using the properties of function.

What is a function?

A relationship between a number of inputs and one output per input is referred to as a function. Typically, a function is denoted by the notation f(x), where x is the input. Typically, a function is represented as y = f(x).

We know that for one input, a function can have only one output.

But, in option A, for the same input value 2, there are two output values 2 and 7. Whereas in other options, each input has only one output.

Hence, the set of ordered pairs of option A does not represent a function.

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Answer: D Im doing the quiz

Answer:D:the range is 5, and the IQR is 10.

Step-by-step explanation:

7/12 can be written as a mixed number as follows:

7/12 = 7 ÷ 12/12 = 0 and 7/12.

So 7/12 can be expressed as "zero and seven twelfths" or simply "seven twelfths."

The percentage decrease for the sale of the house is 0.27%.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given that the initial cost of a home is  369,000.

The cost of a house decreases from 369,000 to 368,000.

The formula of percentage change is

(Final value - initial value)/ initial value × 100

= [(368,000 - 369,000)/369,000] × 100

= (-1000)/369,000 × 100

= 0.27

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The solution to the equation 16^{2x - 3} · 4^{-2x} = 4^2 include the following: C. x = 4.

In Mathematics, laws of indices can be defined as the standard principles or rules that are used for simplifying an equation or expression that involves powers (exponents) of the same base.

By rewriting the mathematical expression and applying the multiplication law of indices, we have the following:

16^{2x - 3} · 4^{-2x} = 4^2

4^2{2x - 3} · 4^{-2x} = 4^2

2{2x - 3} + {-2x} = 2

4x - 6 - 2x = 2

2x = 2 + 6

2x = 8

x = 8/2

x = 4.

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The expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.

The expression "log[a*b.c]" can be rewritten using the properties of logarithms as follows:

Use the logarithmic property log(a * b) = log a + log b:

log[a * b.c] = log (a * b) + log c

Apply logarithmic property log(a^n) = n * log a:

log[a * b.c] = log (a^2 * b) + log c = 2 * log a + log b + log c

So, the expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.

Therefore, the correct answer is as given above. It could then be concluded that the rewritten expression will then be 2 * log a + log b + log c.

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The area of the larger hexagon in discuss as required in the task content is; Choice B; b. 18√3 square units.

It follows from the task content that the area of the larger hexagon be determined.

Recall from the concept of similar shapes; if the ratio of side lengths of two similar shapes is; k, therefore the ratio of their perimeters is k and the ratio of their areas is; k².

On this note, since the larger hexagon is √2 times the side length of the smaller hexagon;

It follows that the area of the lager hexagon is (√2)² times the area of the smaller one.

Therefore, Area of larger hexagon = √2² × 9√3

= 18 √3.

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One thing that was not an impact of the Crusades was B. End of the Roman Empire.

The Crusades were a series of religious wars fought between Christians and Muslims in the 11th, 12th, and 13th centuries. The main objective of the Crusades was to recapture the Holy Land, which was considered the birthplace of Christianity, from Muslim rule.

The Crusades had a significant impact on the medieval world, but the end of the Roman Empire was not one of them. The Roman Empire ended several centuries before the start of the Crusades in the 11th century.

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The area of the shape given which is a circle is; 38.465 in²

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².

Area = πr²

The parameters are;

radius; r = 3¹/₂ inches = ⁷/₂ inches

Thus;

Area = π * (⁷/₂)²

Area = π * 49/4

Area = 3.14 * 49/4

Area = 38.465 in²

That's the area of the circle shape given.

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a. The composite function is N(T(t)) = 290t² - 380t + 386.44

b. the number of bacteria after 5.3 hours is 6519 bacteria.

A function is a mathematical equation that shows the relationship between two variables.

A composite function is a function which contains another function.

Since the number of bacteria in a refrtgerated food product is given by N(T) = 29T² - 76T + 30 , 3 < T < 33 where T is the temperature of the food.

Also, when the food is removed from the refrigerator, the temperature is given by T(t) = 5t + 1.4 where t where t is the time in hours.

So, to find the composite function N(T(t)), we substitute T(t) into N(T).

So,

N(T) = 29T² - 76T + 30

N(T(t)) = 29(5t + 1.4)² - 76(5t + 1.4) + 30

Expanding the brackets, we have that

N(T(t)) = 29(10t² + 14 + 1.96) - 76(5t + 1.4) + 30

N(T(t)) = 290t² + 406 + 56.84 - 380t - 106.4 + 30

N(T(t)) = 290t² - 380t + 406 + 56.84 - 106.4 + 30

N(T(t)) = 290t² - 380t + 386.44

So, the function is N(T(t)) = 290t² - 380t + 386.44

Since N(T(t)) = 290t² - 380t + 386.44 is the number of bacteria after t hours.

To find the number of bacteria after 5.3 hours, we substitute t = 5.3 into the equation.

So,

N(T(t)) = 290t² - 380t + 386.44

N(T(5.3)) = 290(5.3)² - 380(5.3) + 386.44

N(T(5.3)) = 290(28.09) - 380(5.3) + 386.44

N(T(5.3)) = 8146.1 - 2014 + 386.44

N(T(5.3)) = 6518.54

N(T(5.3)) ≅ 6519 bacteria

So, the number of bacteria after 5.3 hours is 6519 bacteria.

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Answer:

what is that maybe l can be of help to u

On solving the provided question, we can say that the slope intercept equation is 12x + 3y = -3 and slope, m = -4

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

the slope intercept equation is

12x + 3y = -3

3y = -12x - 3

y = -4x - 1

also, y = mx + c

so, slope, m = -4

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Answer:

Let's call the number of white boards that Mr. Kelso purchased "W", the number of sharpies "S", and the number of glue sticks "G". We know the following information:

W = 5G

S = G + 10

And we also know the total cost of the items:

0.79W + 1.56S + 0.85G = 91.92

We can use the first equation to substitute for W in the second equation:

0.79(5G) + 1.56(G + 10) + 0.85G = 91.92

Expanding and simplifying the equation:

4.95G + 1.56G + 16.6 + 0.85G = 91.92

7.36G + 16.6 = 91.92

7.36G = 75.32

G = 10.25

So Mr. Kelso purchased 10 glue sticks. Using the first equation, we can find that he purchased 5 * 10.25 = 51 white boards. And using the second equation, we can find that he purchased 10.25 + 10 = 20.25 sharpies.

Since the number of each item must be a whole number, we round up or down to the nearest integer. In this case, it would make sense to round up the number of sharpies to 21. So Mr. Kelso purchased 51 white boards, 21 sharpies, and 10 glue sticks.

The next number in this sequence is 63, which is the result of multiplying the previous number (39) by 2 and then adding 6.

Answer: T=Q/p+1

Step-by-step explanation:

Rearrange

The total amount of the single payment will be $6,924.95.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The rate of interest is given as,

r = 0.0775 / 2

r = 0.03875

The amount for 2 years is given as,

A = $1,300 × (1 + 0.03875)⁴

A = $1513.52

The amount for 5 years is given as,

A = $3,700 × (1 + 0.03875)¹⁰

A = $5,411.43

The total amount of repayment is given as,

Total amount = $1513.52 + $5411.43

Total amount = $6,924.95

The total amount of the single payment will be $6,924.95.

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Hi there, here's your answer:

Given:

The quotient of twice the difference of five less than a number and six.

Let the number be x.

By this, it is understood that the algebraic equation is in a fractional form, with the numerator being

Twice the difference of five less than a number, i.e.

2(x - 5)

And the denominator is 6.

Therefore, we get the algebraic equation to be:

[tex]\frac{2(x-5)}{6}[/tex]

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The data in the table represents a linear function, as when x is increased by one, y is subtracted by a constant amount of 9.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, the function is classified as linear, as the difference between consecutive terms is 9, while the ratios are different.

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Answer:

f-g= 3x²+1-(1-x)

3x²+1-1+x

3x²+x=0

x(3x+1)=O

x=0, 3x+1=0

So, x=0 or -1/3

The number of containers needed is given as follows:

3 containers.

The number of containers needed is obtained applying the proportions in the context of this problem.

She has 2 cups, hence the number of fluid ounces that she has is given as follows:

16 fluid ounces.

Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:

16/6 = 3 containers.

(rounding up).

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We can see here that simplifying, we have:

a. h²

b. h³

c. 1/(1 + h)

d. 3h

e. 3h/(64 + 4h)

f. h/(4h + 2h²)

Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.

In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.

We see here that the below gives us the workings:

a. (5 + h)³ - 125/ h = h³ +  5³ - 125/h = h²

b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]

c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h

d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h

e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h

f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²

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Answer:

Step-by-step explanation:

To find the number of solutions for a system of linear equations, we can use the method of substitution or elimination. Here, we'll use the method of substitution.

We'll start by solving for x in one of the equations and then substitute that expression into the other equation. If the resulting equation has a unique solution, then the system has a unique solution. If the resulting equation has no solution, then the system has no solution. If the resulting equation has infinitely many solutions, then the system has infinitely many solutions.

Let's start by solving the first equation for x:

y = -7/2 x + 11

To solve for x, we'll isolate x by subtracting 11 from both sides of the equation:

y - 11 = -7/2 x + 11 - 11

y - 11 = -7/2 x

Next, we'll multiply both sides of the equation by -2/7 to cancel out the fraction on the right side:

-2/7 (y - 11) = -2/7 (-7/2 x)

-2/7 y + 22/7 = 7/2 x

Now, we have an expression for x in terms of y. We can substitute this expression into the second equation:

7x + 2y = 20

7 (-2/7 y + 22/7) + 2y = 20

Substituting -2/7 y + 22/7 for x, we get:

7 (-2/7 y + 22/7) + 2y = 20

Expanding the left side of the equation, we get:

-2y + 22 + 2y = 20

0y = -2

Since 0y is never equal to -2, this equation has no solution.

Therefore, the system of equations has no solution, and there are no values of x and y that satisfy both equations simultaneously.

So, the system of equations y = -7/2 x + 11 and 7x + 2y = 20 has no solutions.

The graph of the quadratic function y = x² - 5 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function is given as follows:

y = x².

Which is concave up with vertex at the origin.

The translated function is given as follows:

y = x² - 5.

Meaning that the function was translated 5 units down, hence the vertex is at (0,-5) and the roots are plus/minus square root of 5.

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Answer:

40 meters per hour.

Step-by-step explanation:

How many seconds are in an hour? 3600. Divide 3600 by 90 to get 40.

a. The possible range of values in this row is from 210 to 219, inclusive.

To see why, note that the stem value is 21, so each leaf represents a number that should be added to 21. The smallest possible value is when the leaf is 0, which gives 21 + 0 = 210. The largest possible value is when the leaf is 9, which gives 21 + 9 = 219.

b. There are 6 data values in this row.

c. The actual values in this row are 210, 211, 213, 215, 217, 219.

In statistics, a leaf is the last digit or digits of a data point in a stem-and-leaf plot. A stem-and-leaf plot is a graphical display of data that shows the distribution of values by separating each value into two parts: a stem, which consists of the leading digits of the value, and a leaf, which consists of the final digit or digits of the value. The stem values are listed in a vertical column, and the leaves are listed in a row next to the corresponding stem. This type of plot allows us to see the shape of the data and the distribution of values within it.

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Organizar la riqueza a través de la pro- ducción de bienes y servicios es una característica de la empresa que se relaciona con su A) fin lucrativo.

Las empresas tienen como objetivo principal la maximización de sus ganancias y el crecimiento económico a través de la producción y venta de bienes y servicios. La obtención de ganancias es el fin lucrativo de la empresa y es a través de él que se organiza la riqueza generada por la empresa.

Sin embargo, las empresas también tienen una serie de responsabilidades sociales y éticas, por lo que pueden combinar su fin lucrativo con una cierta responsabilidad social o económica.

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The amount of protein in Peanut butter is 209.5g.

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the amount of protein in  838g of peanut butter.

Contents of peanut butter: 35%

Carbohydrates - 25%

Protein - 40% Fat

Now 25% of protein in 838g.

25/100×838

0.25×838

209.5 g of protein in peanut butter

Hence, 209.5 g of protein in peanut butter

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