The altitude of the hypotenuse of a right triangle divides the hypotenuse into two segments. If the ratio of lengths of the segments is 1:9 and the length of the altitude is 6 meters, find the lengths of the two segments?

The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]

Comparing both the functions,

[tex]b^\frac{t}{5} = (1.3)^t[/tex]

We can write, [tex](1.3)^t[/tex] as

[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]

[tex]= 3.71^\frac{t}{5}[/tex]

Therefore, the equation ca be written as,  [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

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Step-by-step explanation:

x²-4x+3x-12

x²-x-12.

2s²+4s-4s-8

2s²-8

On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.

Answer:

y = mx - 4

Step-by-step explanation:

m is the slope, while -4 is the y intercept

Examining the polynomial function g(x) as given in the table the end behavior is

The end behavior of function typically says the characteristics of the function at the ends

The given table when examined shows that there was three zeros hence the graph is that of odd function

The end behavior of an odd function with positive leading coefficient is

x ⇒ ∞ f(x) ⇒ ∞: as x tends to positive infinity the function tends to positive infinity

x ⇒ -∞ f(x) ⇒ -∞: as x tends to negative infinity the function tends to negative infinity

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Setting x=2 in the function is the simplest approach to discover f(2). However, you might plot the graph of f(x) and the vertical line x=2 to visually solve this.

Set x=2 in the function for the quickest and easiest method to discover f(2). Plotting the graph of f(x) and the vertical line x=2 would allow you to visually answer this problem. Next, the graphs' intersection will represent the answer. The "x" in "f (x)" is known as "the function's argument" or simply "the argument" in function notation.

As a result, if they ask for a "argument" and offer you the equation "f (2)," all you have to say is "2." Now (1) f(2)=2(2+1)=2×3=6.If our function's value is f(2), then we should calculate its value when x=2. Example. If x = 2, then f(2) = 2 + 7 = 9. F(x) = x + 7. GF(2), also known as the Galois field of two elements, or F2, the chemical formula for fluorine. F2 is a tornado intensity category on the Fujita scale.

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The mass of the liquid is  4326 grams.

The liquid has a density of 1.40 g/ml and the volume of the liquid is 3090 ml. Therefore, the mass of the liquid can be calculated as follows:

The density of a liquid is a measure of how heavy it is for the amount measured. The liquid density is defined as its mass per unit volume.

Therefore,]

density = mass / volume

cross multiply

mass = density × volume

density = 1.40 g/ml

volume = 3090

Therefore,

mass of the liquid = 1.40 × 3090

mass of the liquid = 4326 grams.

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By using the definition of vertical angles, we will see that the correct option is B, the measure of the other angle is 95°.

We define by vertical angles as angles that share a vertex and are in opposite sides of the two intersecting lines that form that vertex.

Vertical angles always have the same measure, in this particular case, we know that one of the vertical angles has a measure of 95 degrees, then the other vertical angle (whose measure we want to find) will also be 95 degrees, just by definition of vertical angles.

In that way, we conclude that the correct option is B: 95°

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Answer: The conditions for inference are met in this scenario.

In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:

The sample must be randomly selected from the population.

The sample size must be large enough (usually at least 30).

The sample must be representative of the population.

In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.

The sample size of 100 is also large enough, which meets the second condition.

There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.

Therefore, the conditions for inference are met in this scenario.

Step-by-step explanation:

As a result, after studying the diagram below of triangle and considering the reasons that follow, the appropriate answers are 1, 2, 3, and 4.

Any three points in a plane can be connected to create triangles, which are polygonal (shapes) with three sides and three angles. They are among the first shapes in geometry that are explored. Since each polygon (with 4, 5, 6, or n sides) may be divided into triangles, triangles are particularly significant.

Here,

A segment bisector in this case is 1)OP.

Since segment LKMN is not divided into two equal sections, NO OP is not a segment bisector.

A perpendicular bisector is

2)OP.

NO,Because a perpendicular bisector creates an angle to the normal and divides a segment into two equal halves, OP is not a perpendicular bisector.

The angle bisector NO is OP.

Due to the fact that OP they do not divide any angles into two equal pieces.

4) The diagram's vertex of a pair of congruent angles is O.

YES Since O lines connect two angles with the same degree ()

5)O is the right angle's vertex.

NO

As a result of things not being at a straight angle.

6) A segment's midway in the diagram

By drawing diagonals across the four vertices LMNK, it is possible to determine where this segment's midpoint lies.

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The correct set of image points for trapezoid WX'Y'Z' is the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).

Given data :

From the given figure, it is clear that the vertices of the trapezoid are W(-4,2), X(-3,4), Y(-1,4), Z(0,2).

If a figure is rotated 180 degrees about the origin, then

( x, y )  → ( -x, -y )

Using this rule, we get

W (-4, 2 ) → W' ( 4, -2 )

X ( -3, 4 ) → X' ( 3, -4 )

Y ( -1, 1 ) → Y' ( 1, -4 )

Z ( 0,2 ) → Z' ( 0, -2 )

Therefore, the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).

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Answer: The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups with 2 boys and 2 girls in each group.

Answer: 22 times

Step-by-step explanation: divide 137 by 6

Answer:

No Solutions

Step-by-step explanation:

Hello!

We can solve for a by isolating the variable.

Since -29 cannot be equal to -9, there are no solutions for this equation.

The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.

A polynomial  function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.

We have,

Zeroes: 1 - 2i and 3

To check the polynomial put the zeroes in it,Putting x = 3 in

A) P(x) = x^3 - x^2 + x -15

P(3) = 27 - 9 + 3 - 15 = 6

It is not correct polynomial.

B)  P(x) = x^3 + x^2 - x + 15

P(3) = 27 + 9 - 3 + 15 = 48

It is not correct polynomial.

C) P(x) = x^3 - 5x^2 + 11x -15

P(3) = 37 - 45 + 33 - 15 = 0

Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.

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The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line passing through (-5, 6) and (-6, 5) will be given as,

(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)

y - 6 = (x + 5)

y = x + 1

The equation of the line that is perpendicular to the above line is given as,

y = - x + c

The equation of the line is passing through (3, 2)

3 = - 2 + c

c = 5

Then the equation of the perpendicular line will be given as,

y = -x + 5

x + y - 5 = 0

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

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The complete question is given below.

On solving the provided question we cans ay that - here in linear equation, y = 3 and x = -1/2

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y = 2x + 1 - linear equation.

value of y;

[tex]x = 0\\y = 2(0) + 1\\y = 2 + 1\\y = 3[/tex]

value of x;

[tex]y = 0\\0 = 2x + 1\\2x = -1\\x = -1/2[/tex]

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The area of the forest after 15 years will be 2189.4

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

i = The initial area of the forest = 4200km

r = Per year decrease is = 4.25%

n = Number of years = 15

The required formula is

The area of forest will be

A = i (1-r)^n

A = 4200(1-0.425)^15

A= 2189.4

Hence, the area of the forest will be 2189.4

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Answer: 28

Step-by-step explanation:

280/10=28

(/=divide)

If you have 10 baskets and have 280 apples to evenly distribute them in every basket, you would have 28 in each basket. If that makes sense.

Hope this helps!

Answer:

3.4 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]

where

The ball will strike the ground when its height is zero.

Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute these values into the quadratic formula:

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]

[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]

As time cannot be negative, t = 3.4 s only.

Therefore, the ball strikes the ground 3.4 seconds after it is launched.

By basic algebra, the part to be cut is equal to 17/45. When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions. Each fraction has two components.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Let x part is cut to shorten

then,

[tex]\frac{3}{2}-x=\frac{2}{9}\\\\x=\frac{3}{5} -\frac{2}{9} \\\\x=\frac{17}{45}[/tex]

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Set of value that belong to the Domain are: Values of Independent, Variable, Input Values

Set of value that belong to the Range are: Output Values, Values of Dependent Variables.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

Domain :

Values of Independent Variable

Input Values

Range :

Output Value

Values of Dependent Variables.

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Answer:

congruent

Step-by-step explanation:

Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.

A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages ​​are:

L1, which has exactly one "a" but any number of "bs".

L2, which has an odd number of "as" and an even number of "bs".

L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.

L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".

L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.

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The marginal average cost is -1 and The marginal average cost for 200 is  $699.

The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.

Given The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=40,000+500x.

Average cost = Cx / x

Average cost = (40,000 + 500x)/ x

For x = 200

Average cost = (40,000 + 500 * 200)/200

Average cost = 700$ per frame

Marginal average cost = d(Cx/x)/dx

d(Cx/x)/dx = -40,000/ x^2

at x = 200

Marginal average cost = -40,000/ 200^2  = -1

Marginal average cost = -1 tells us the average cost

decrease at the rate of -1 for every x

Average cost for 200 = 700$ per frame

Average cost for 200 = 700 + 1 (-1)

The average cost for 200 = 700 -1 = 699$

therefore, the Marginal average cost for 200 is $699.

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Answer:

Choose the right container: Select a container that is appropriate for the size and type of plant you want to grow. Make sure the container has drainage holes to allow excess water to drain away.

Use the right soil: Use a well-draining soil mix that is appropriate for the type of plant you are growing. Avoid using soil from your garden, as it may contain pests or diseases that can harm your plant.

Provide proper lighting: Most plants need plenty of sunlight to grow, so choose a location that gets plenty of light. If you are growing plants indoors, you may need to use grow lights to provide adequate lighting.

Water properly: Water your plants regularly, but avoid overwatering, as this can lead to root rot. Check the soil moisture level regularly and water when the top inch of soil is dry.

Fertilize: Use a balanced fertilize to provide your plants with the nutrients they need to grow. Follow the instructions on the fertilize package for the proper amount and frequency of application.

Pest control: Keep an eye out for pests such as aphids, thrips, and mealybugs, and take action if necessary. There are many natural ways to control pests, such as introducing predatory insects or using neem oil.

By following these general tips, you should be able to successful

There are three popular choices when it comes to growing - Hydroponics, Soil and Coco. These methods vary widely according to the source, understanding the source of your media can lead to a grower getting better results.

The kind of sequence that you will obtain when you list the number of tickets sold over time is given as follows:

A geometric sequence.

A sequence can be classified as either arithmetic or geometric, as follows:

If none of these statements is true, then the function is neither arithmetic or geometric.

A growing amusement park is able to sell 7 times as many tickets each year as it did the year before, which means that there is a constant ratio of 7 between the amounts of tickets sold each year, and thus this sequence is a geometric sequence.

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The cost of a one mile ride is given as follows:

$6.

The cost per mile is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function that gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is of:

y = 4(1) + 2 = $6.

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