D) Linear Functions: Model from a Verbal Description - Quiz - Level H Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18 m every 3 s. After 5 s, the drone is at a height of 40 m. The drone's height in meters, y, is a function of the time in seconds, x. How many meters does the drone rise each second? Find the rate of change. 6 meters per second What is the height of the drone before Rebecca makes it rise? Find the initial value. 10 meters ◄» Write an equation to represent the function. y = ? x + ?​

Answer:

Step-by-step explanation:

To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:

Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.

Swap the x and y variables: x = 3y + 7.

Solve for y:

Subtract 7 from both sides to get x - 7 = 3y.

Divide both sides by 3 to get (x - 7) / 3 = y.

Write the inverse function using f^-1(x) instead of y:

f^-1(x) = (x - 7) / 3

So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.

The length of the both pieces are 1ft and 9ft respectively. Option C

We have from the information given that;

Now, substitute the values, we get

x + 6 + 3x =10

Collect the like terms

x + 3x = 10 -6

Add the like terms

4x = 10 - 6

Substract the like terms

4x = 4

Make 'x' the subject of formula by dividing both sides by 4, we get;

x = 4/4

divide the values

x = 1

Thus, the values are 1ft and 9ft

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Answer:

400 m walking

Step-by-step explanation:

sum the parts of the ratio , 2 + 13 = 15 parts

divide the distance covered by 15 to find the value of one part of the ratio.

3000 m ÷ 15 = 200 m

then

2 parts = 2 × 200m 400 m

400 m covered by walking

In the triangle, the nearest whole number of the side t is 28.

The sine rule states that the ratios of the sides to their corresponding opposite angles are equal to a particular value. This value gives the circumradius of that triangle.

The sum of three angles in a triangle is 180°.

Find the angle ∠T for ∠A=46° and ∠D=84°.

∠A+∠D+∠T=180°

46°+84°+∠T=180°

130°+∠T=180°

∠T=50°

The sine rule for triangle ABC is [tex]\[\frac{a}{{\sin A }} = \frac{{37}}{{\sin B }} = \frac{c}{{\sin C }} = 2R\][/tex], where R is the circumradius and a, b, and c are the opposite sides of the angles ∠A, ∠B, and ∠C, respectively.

On applying the sine rule to triangle ADT, the result becomes [tex]\[\frac{a}{{\sin 46^\circ }} = \frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }} = 2R\][/tex].

Take the equation [tex]\frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }}[/tex] and find t.

[tex]\[\begin{array}{l}t = \frac{{37\sin 50^\circ }}{{\sin 84^\circ }}\\ \approx 28.4997\\ \approx 28\end{array}\][/tex]

Therefore, the nearest round whole number of t is 28.

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Lowell's verbal representation of the equation y = x - 25 is "y is equal to x minus 25".

This verbal representation accurately describes the equation. In the equation, y is the dependent variable and x is the independent variable. The equation says that y is equal to x minus 25, which means that for every value of x, there is a corresponding value of y that is x minus 25.

So, Lowell has completed the task correctly.

STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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The area of the composite figure is 41 ft square.

The figure is a composite figure. A composite figure is a figure that has two or more shapes.

Therefore, the area of the composite figure is the sum of the individual area of the shapes.

Therefore,

area of the figure = area of rectangle 1 + area of rectangle 2

area of rectangle 1 = lw

where

Therefore,

area of rectangle 1 = 2 × 4 = 8 ft²

area of rectangle 2 = 11 × 3 = 33 ft²

Hence,

area of the figure =  = 8 + 33

area of the figure = 41 ft²

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Answer:

y = 2/3x + 4

Step-by-step explanation:

y-intercept (b) is 4

Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3

y = mx + b = 2/3x + 4

The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:

[tex]log a^b = blog a[/tex]

Using this rule, we can write the expression as:

[tex]r log a + y log c = log a^r + log c^y[/tex]

Now we can use the rule that says:

log a + log b = log ab

to combine the two logarithms:

[tex]log a^r + log c^y = log (a^r c^y)[/tex]

Therefore, the expression r log a + y log c simplifies to:

[tex]r log a + y log c = log (a^r c^y)[/tex]

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Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.

The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.

A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.

The average rate of change between x=x and a function f(x)

F(x₂) - F(x₁)/(x₂) - x₁

so,

f(x) = x²

average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10

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Solving provided question, we can say that The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.

The least common multiple, or the least common multiple of the two integers a and b, is the smallest positive integer that is divisible by both a and b. LCM stands for Least Common Multiple. Both of the least common multiples of two integers are the least frequent multiple of the first. A multiple of a number is produced by adding an integer to it. As an illustration, the number 10 is a multiple of 5, as it can be divided by 5, 2, and 5, making it a multiple of 5. The lowest common multiple of these integers is 10, which is the smallest positive integer that can be divided by both 5 and 2.

To compare the proportion of each notebook covered with stickers, we need to find a common denominator for the fractions.

The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.

So, Kayla covered more of her notebook with stickers, as 20/24 is greater than 15/24.

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The constant of proportionality is 0.60

The equation is y = $0.60x.

Here is the completed table

Number of lemons  Total cost

4                                  $2.40

7                                 $4.20

15                                 $9

18                                  $10.80

Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.

The equation that represents direct variation is:

y = kx

Where:

$1.80 = 3k

k = $1.80 / 3

k = $0.60

y = $0.60x

Total cost of 4 lemons=  $0.60 x 4 = $2.40

Total cost of 18 lemons=  $0.60 x 18 = $10.80

Number of lemons that cost $4.20 : 4.20 / 0.6 = 7

Number of lemons that cost $9 : 9 / 0.60 = 15

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The lengths of the pieces are 1ft and 9ft

From the information given, we have that;

The shorter side = x

The longer side of the board = 6 +3x

The total length = 10

Substitute the values, we have;

x + 6 + 3x = 10

collect the like terms

x + 3x = 10 -6

Add or substract the like terms, we have;

4x = 4

Now, make 'x' the subject of formula by dividing by 4, we get;

4x/4 = 4/4

x = 1 ft

The longer side = 9ft

Hence, the values are 1 and 9

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The given system of linear equations has a unique solution.

A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given that, a system of linear equations, ​ y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,

The rule for a system of linear equations, ​a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-

​a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.

a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.

Checking for the given equations,

y = 5x+1 and y = -2x-8

Converting into standard form of the linear equations,

5x-y +1 = 0 and 2x+y+8 = 0

5/2 ≠ -1

The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]

Hence, the given system of linear equations has a unique solution.

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Answer:

One solution

Step-by-step explanation:

Answer:

a) $4096 b) $1884,8 ■■ im not 100% sure

Step-by-step explanation:

a) 3200×0.064×2=$4096 in intrest

b) 12,400×0.076×2=$1884,8 in intrest

Answer:

E is a major arc

C is a minor sector

A is a major segment

Major segment is the portion (or part) of the circular region enclosed between a chord and the corresponding major arc.

Major arc is the longer arc connecting two endpoints on a circle.

A sector with a central angle less than 180° is called a minor sector.

Based on the 2021 federal income tax brackets, the gross pay of $49,946 puts you in the 22% tax bracket. For the fully filled tax bracket, you would owe $10,890.50 in federal taxes, and for the partially filled tax bracket, you would owe $4,994.60 in federal taxes.

In the experiment in which researcher randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention, this type of experiment design is a randomized block design where the pet types (dogs and cats) are the blocks.

Randomized block design is a type of experimental design that is used to control for the effects of extraneous variables. It involves dividing the subjects or treatments into groups, or blocks, that are similar with respect to the extraneous variable.

These blocks are then randomly assigned to the treatments being tested. By controlling for the extraneous variable in this way, the randomized block design can reduce error and increase the accuracy of the results.

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Answer:

answer B (Khan)

Step-by-step explanation:

A randomized block design where the pet types (dogs and cats) are the blocks

The rate of change of the function on the interval specified as in the task content is; 7.

It follows from the task content that the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h] is to be determined.

Since the function is a linear function, it follows that the rate of change is a constant and hence is given by;

f'(x) = 7.

Ultimately, the rate of change of the function on the given interval is; 7.

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Answer:

If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.

Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:

V = Bh

3/8 = (1/4)h

Multiplying both sides by 4, we get:

3 = h

So the height of the prism is 3 inches.

Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.

Answer:

[tex]sin(P)=\frac{\sqrt{55}}{10}[/tex]

Step-by-step explanation:

The sine function is defined as a ratio of sides: [tex]sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.

We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:

[tex]c^2=\sqrt{45}^2+\sqrt{55}^2\\c^2=45+55\\c^2=100\\c=10[/tex]

We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following: [tex]sin(P)=\frac{\sqrt{55}}{10}[/tex] and we can't simplify this any further as 45 has no factors which are perfect squares.

Answer:

perimeter of rectangle = 2(length +breadth)

=2(20+80) m

=200 m

∴perimeter of rectangle is 200 m

The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.

We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.

Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.

In a week there are 20 hours

So, in 4 weeks, there will be 80 hours

Take - home pay before deductions = 80 * $11.66 = $932.8

Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94

This is equal to ¢ 68094.

Hence, the monthly take-home pay is ¢ 68094.

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Answer:

Step-by-step explanation:

Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.

The total cost of the dinner including the tip was $61, so we can write the following equation:

f * 12.75 + t * f = 61

Expanding the left side of the equation:

12.75f + t * f = 61

Combining like terms:

13.75f + t = 61

Solving for t:

t = 61 - 13.75f

So, the equation that describes the situation is t = 61 - 13.75f.

Answer:

(-10, 12).

Step-by-step explanation:

A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).

So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).

So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).

1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

An expression is combination of variables, numbers and operators.

The given expression is 3/4a + 8 - 1/4a - 2

Three by four times of a plus eight minus one by four times of a minus 2.

In the given expression a is a variable and plus and minus signs are the operators.

3/4a + 8 - 1/4a - 2

3/4a and  - 1/4a are the like terms

Add the like terms

3/4a   - 1/4a +8 - 2

2/4 a +6

1/2a+6

Hence, 1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

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Answer:

20000*4*5/100=4000

Step-by-step explanation:

Hope this helps!

Answer:46

Step-by-step explanation:

180=104+30+x

134+x=180

x=46