Please help I dont understand how to get the length of segment DF

the displacement is 23.14m and the velocity is 21.28m/s

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation y  = 25t - 1.86t²

at t =  1

So the displacement y = 25-1.86 = 23.14

to find velocity dy/dt = 25- 2(1.86)t

v = 25 - 3.72 = 21.28m/s

Hence the displacement is 23.14m and velocity is 21.28m/s

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The total area of the quilt is: 112.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 5 inches and height: 5.18 inches

The rectangle at the bottom:

Base: 16 inches with a height of 7.5 inches

So, we have the total area of the figure to be

Area of figure = 1/2 * 5 * 6 + 13 * 7.5

Area of figure = 112.5

Based on the parameters, the total area is 112.5 square inches

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The copy machine make 44 copies per minute.

The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;

We are given that Time copy machine take= 4min 15sec

Number of copies=187

Now, 1min=60sec

4min=240sec

Total time=240+15 =255sec

Therefore, 255sec=187copies

60sec= 187 x 60/255

=44

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Answer:

Step-by-step explanation:

12 x 3 =36

The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.

The system of equations that represent the information in the question is:

a + b = 20,000 equation 1

0.07a + 0.08b = 1540 equation 2

Where:

a = amount invested in the account that earns 7% interest

b = amount invested in the account that earns 8% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.07

0.07a + 0.07b = 1,400 equation 3

Subtract equation 3 from equation 2

0.01b = 140

Divide both sides of the equation by 0.01

b = 140/ 0.01

b = 14,000

Substitute for b in equation 1:

a + 14,000 = 20,000

a = 20,000 - 14,000

a = 6,000

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Answer:

Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:

Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.

Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.

Simplify the equation: On simplifying the equation, we get: y = 2x - 2.

Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.

Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.

Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.

That's it! You have successfully graphed the equation -3y + 6x = 6.

Answer:



Step-by-step explanation:

The solution is, the equation of the line is y = 2x/3 + 2, that is, The correct option is A.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept(This is the point where the line cut across the y axis.

The first step is to find the slope. The formula is

Slope, m = (y2 - y1)/(x2 - x1)

From the given points on the graph,

when x1 = 0, y1 = 2

when x2 = 3, y2 = 4

m = (4 - 2)/(3 - 0)

m = 2/3

Looking at the graph, at the point where the line cuts the y axis, y = 2. Thus, c = 2

We would substitute m = 2/3 and c = 2 into the slope intercept equation. Thus, the equation of the line is

y = 2x/3 + 2

The correct option is A.

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The evaluation of the function expressions gives:

(q + f)(5) = 1

(f - q)(2) = -2

(q f)(4) = 9

(f /q)(0) = 1

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

From the graph, when c = 5, q(5) = 0, f(5) = 1. Thus:

(q + f)(5) = 0 + 1 = 1

From the graph, when c = 2, f(2) = 0, q(2) = 2. Thus:

(f - q)(2) = 0 - 2 = -2

From the graph, when c = 4, q(4) = 3, f(4) = 3. Thus:

(q f)(4) = 3 * 3 = 9

From the graph, when c = 0, f(0) = 4, q(0) = 4. Thus:

(f /q)(0) = 4/4 = 1

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Answer:

3/400 per min

Explanation:

Divide the rate at which he can walk by the number how mins he can walk at that rate

The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)

Thus, the required equation among the option is y = -3x + 2.

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The range of set 1 is 11. The range of set 2 is  208

The wider range of set 2, set 2 contains a wider spread of the given data.

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

The set is given in the question, as follows:

Set 1: 1, 4, 6, 8, 10, 12

The maximum value = 12

The minimum value = 1

The range of the set 1 = maximum value - minimum value

Substitute the values in the above formula,

The range of the  set 1  = 12 - 1

Apply the subtraction operation to get the answer

The range of the set 1 = 11

Set 2: 230, 24, 33, 22, 41

Now, the range of the  set 2  = 230 - 22 = 208

Data set 1 has a range of 11, whereas data set 2 has a range of 208.

Therefore, the wider range of set 2, set 2 contains a wider dispersion of data.

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Note that the complete steps of the Flow Chart Proof is given as follows:

1) RS = TS, QR = UT [Given]

2) QR + RS = QR + RS [Reflexive Property of Equality]

3) QR + RS = RS + UT  [Substitution Property of Equality]

4) QR + RS = QS, TS + UT = US [Segment Addition Postulate]

5) QS = US [Substitution Property of Equality]

6) Line Segment QS is congruent to  Line segment US [Definition of Congruent Segments].

A flow chart proof is a type of proof that uses symbols and diagrams to show the logical flow of a proof.

It is a visual way of representing a mathematical argument that can be helpful for organizing and presenting complex ideas in a clear and concise manner.

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The elements of the set A are given as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The set A in the context of this problem is defined as follows:

A = {x | x is a month of the year.}

Hence the set A is composed by 12 elements, which are all the months of an year, as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The problem asks for all the elements of the set A, given as follows:

A = {x | x is a month of the year.}

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The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the probability of a tornado in any given year is 0.08,

the probability of no tornado in any given year is;:

=  1 - 0.08

= 0.92.

Let X be the number of tornadoes in a 22-year period.

X follows a binomial distribution with n = 22 and p = 0.08.

We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.

This can be written as:

P(X < 2) = P(X = 0) + P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038

P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214

So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.

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Answer:

Mrs. Morris drove a total of 1989 miles in June. This can be calculated by adding 873 miles (the amount she drove in May) to 1116 miles (the amount she drove more in June). Therefore, 873 + 1116 = 1989 miles.

Answer:

[tex]\frac{1}{22}[/tex]

Step-by-step explanation:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:

[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

[tex]\frac{1}{\sqrt{x}+11}[/tex]

and now we can directly plug in 121

[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]

Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

The kite is flying approximately 76.118 feet high.

What is ratio ?

Ratio can be defined as the given value divided by the total value.

We can use trigonometry to solve this problem.

Let's call the height of the kite h. Then, we have a right triangle, with one angle equal to 80 degrees and the adjacent side equal to 77 feet. We can use the sine function to find the height of the kite:

sin(80) = h/77

So, h = 77 * sin(80).

Using a scientific calculator or a trigonometry table, we can find the value of sin(80) to be approximately 0.98

Therefore, the height of the kite is:

h = 77 * 0.98 = 76.11

Hence, The kite is flying approximately 76.118 feet high.

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Answer:

1.8 quintillion or 1,800,000,000,000,000,000

Step-by-step explanation:

Answer: a

Step-by-step explanation: it's increasing and it's a line

The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 75x + 0.55y = 125.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute x=0, 1, 2, 3, 4, 5,....

When x=0

75(0)+0.55y=125

0.55y=125

y=125/0.55

y=227

When x=1

75(1)+0.55y=125

0.55y=50

y=50/0.55

y=91

When x=2

75(2)+0.55y=125

0.55y=-25

y=-25/0.55

y=-45.45

Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

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Answer:

This is not math...

Step-by-step explanation:

Answer:

C. No real factors

Step-by-step explanation:

Not factorable

Answer:

2489

Step-by-step explanation:

it would be 30+ 1,000+29+30+400+1,000+ 2489

I really hope this helps

Proverbs 4:6-7

Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)

Answer:

2489

Step-by-step explanation:

The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".

A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.

In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.

In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.

As an example of how this might be used in practice, consider the differential equation

=> "dy/dt = -3y".

In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".

However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:

=> "dsolve(diff(y,t) == -3*y)".

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19.375 pounds is the weight of bike.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that the  frame of a bike weighs16 pounds.

each tire weighs 9 ounces.

In a bike there are 2 tires, so total weight of tires is 2×9=18 ounces.

The seat weighs 12 ounces

The handlebars weigh 24 ounces.

Convert the ounces to pounds.

We know that 1 pound=16 ounces

So The total number of weight in ounces is 18+12+24=54 ounces

Divide by 16 to convert 54 ounces to pounds

54/16=3.375

Now total weight=16+3.375 pounds

=19.375

Hence, 19.375 pounds is the weight of bike.

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Answer:

Step-by-step explanation:

Here is a step-by-step explanation of the independence of the pair of events of choosing a number between 1000 and 5000 and flipping a coin:

Understanding the definition of independent events: Independent events are events that have no influence on each other. The outcome of one event does not affect the outcome of the other.

Event 1: Choose a number between 1000 and 5000: This event involves randomly selecting a number within the specified range.

Event 2: Flip a coin: This event involves flipping a coin and observing whether it lands on heads or tails.

Check for influence: To determine whether the events are independent, we need to check if the outcome of one event affects the outcome of the other. In this case, the outcome of the coin flip has no effect on the number you choose, and your choice of number has no effect on the outcome of the coin flip.

Conclusion: Since the outcome of one event does not affect the outcome of the other, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are considered independent.

So, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are independent events.

The amount of federal state tax Selina owes if her gross pay for two weeks is $840 is  $14.11, which is closest to option A: $16.17. so the best answer is A as it is the closest.

To calculate Selina's federal tax contribution, we first need to determine her taxable income. From her gross pay of $840, we can subtract the biweekly standard deduction for a single person, which is $191.15 (based on the federal tax table provided). This gives us a taxable income of $648.85.

Using the federal tax table for biweekly earnings of a single person, we can see that the federal tax on this amount is $67.25.

Selina's state tax deduction is 21% of her federal tax contribution, which is 0.21 x $67.25 = $14.11.

Therefore, the amount of state tax Selina owes is $14.11, which is closest to option A: $16.17. However, none of the given options match the calculated amount exactly, so the best answer is A as it is the closest.

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The distance from point A to point B measures is 1,269.9 feet.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

The horizontal distance= 1196ft

Angle of elevation to the lighthouse’s=13°

Angle of elevation from point B =3 °

Now,

Distance from A to B = D;

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet;

Therefore, by the trigonometric ratios the distance from point A to point B, D will be 1,269.9feet;

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