What are the 3 types of decays?

The ratio of 240 to 160 is part to part ratio.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The votes for Tigers outnumbered the votes for Lions by a ratio of 240 to 160.

⇒ 240 : 160.

Now,

We know that,

The ratio of part to part will be two different objects.

And, The ratio of part to whole will be the ratio of object to whole object.

Here, The ratio is given as;

⇒ 240 to 160.

⇒ 240 : 160

And, 240 > 160

So, The ratio is part to part ratio.

Thus, The ratio of 240 to 160 is part to part ratio.

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The domain and the range of this function shown in the graph are;

Domain = -5 ≤ x < 1

Range = -4 ≤ y < 7

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent -1 unit.

By critically observing the graph of this function shown, we can reasonably and logically deduce the following:

Domain = -5 ≤ x < 1 or [-5, 1].

Range = -4 ≤ y < 7 or [-4, 7].

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Answer:

  y = |x -4|

Step-by-step explanation:

You want the new function after the absolute value function is moved 4 units to the right.

When the function f(x) is translated to the right by h units, the new function is f(x -h).

When the function ...

  y = |x|

is translated right 4 units, the new function is ...

  y = |x -4| . . . . . . . x is replaced by x-4.

1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

[tex]a^2+b^2=c^2[/tex]

Making substitutions and applying the math results in:

[tex]15^2 + 36^2= 39^2[/tex]

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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To solve complex fractions addition the steps are elaborated below

Basically, a complex fraction is a rational expression that has a fraction in its denominator,  numerator or both, or we can simply state that there is at least one least fraction within the overall fraction.To solve complex fractions addition, the steps are first to convert the  denominators  and numerators  into single fractions and then simplify them, the next step is  to add the fractions with  the like denominators, then Simplify it again, then the step is to   Divide the complex fractions by multiplying the numerator by the reciprocal of the denominator.

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The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent.

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The sum must be greater than the longest side, not equal to it. The shorter two sides cannot angle up to form a triangle if they are precisely the same. When the sum of the two shortest sides equals the length of the longest side, it does not work.

The Triangle Inequality Theorem is simply a more formal way of expressing what we have just observed.

We discovered that the two short sides, which represent the sum of the two shortest sides, must be longer than the longest side in order for the theorem to hold.

The Triangle Inequality Theorem can be expressed in a variety of ways. It can also be said that any two sides of a triangle must have lengths that are greater than the length of the third side. The two shortest sides must be longer than the longest side when they are joined end to end in order for them to be able to tilt up to create a triangle.

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From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|

What is graph of a function?

The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.

Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.

Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|

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Simplify: [tex]5x^4 + 35x^3y -30x^2y^2[/tex]

I used distributive property to mulitply.

ie. [tex]5x^2*x^2[/tex]

Answer: 96

Step-by-step explanation:

The concurrency point for medians of a triangle is known as centroid.

A median is a line drawn from one of the vertices of a triangle that bisects the side opposite to the vertex. Since there are 3 vertices in a triangle, there are also 3 medians in a triangle. A median divides the triangle into 2 equal halves.

The 3 medians of a triangle intersect at a point inside the triangle. This point is known as the centroid of the triangle. It is the center point of a triangle and divides the medians in the ratio of 2 : 1.

Thus, the name of concurrency for medians of a triangle is centroid.

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Answer:

x=6, y=9

Step-by-step explanation:

1.) Since you are substituting, you plug 6 (X) in wherever you have X in the other equation. You will get y = 2*6 -3.
2.) Simplify. By simplification, you will get y=12-3=9. Therefore, x=6, y=9.

The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

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The most general interpretation of the linear equation 11 - y = 3 is:

"The difference between 11 and a number is equal to 3"

Here we have the following linear equation:

11 - y = 3

Which only depends on the variable y, that we assume it can take any real number as its value.

The linear equation says that if we subtract the number y from eleven, the outcome is 3.

Or we can use other words, like: "The difference between 11 and a number is equal to 3"

Where subtraction and difference are words that reffer to the same operation, which is the subtraction: A - B.

So that is the correct (and more general) interpretation of the linear equation.

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Answer:

42 :))

Step-by-step explanation:

The angles m∠ABC = (3·x - 2)° and m∠ABD formed by the ray [tex]\overrightarrow{BA}[/tex], which is an angle bisector of angle m∠CBD = (5·x + 18)°, indicates that m∠ABD is 64°

An angle bisector is a line, segment or ray that divides an angle into two congruent angles.

The information in the question are;

The ray that bisects ∠CBD = [tex]\overrightarrow{BA}[/tex]

The measure of angle, m∠CBD = (5·x + 18)°

The measure of angle, m∠ABC = (3·x - 2)°

Therefore;

(5·x + 18)° = 2 × (3·x - 2)° (definition of angle formed by an angle bisector)

(5·x + 18)° = (6·x - 4)°

(6·x - 5·x)° = (18 + 4)°

x = 22°

m∠CBD = m∠ABD + m∠ABC  (angle addition postulate)

m∠ABD = m∠ABC (angles formed by angle bisector [tex]\overrightarrow{BA}[/tex])

m∠ABC = (3·x - 2)°

Therefore; m∠ABC = (3 × 22 - 2)° = 64°

m∠ABD = m∠ABC = 64°

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A. Congruence means the same.

B. Angle addition postulate states that two angles side by side sum the measure of the two angles.

C. Linear pair theorem states that linear pair angles add up to 180 degrees.

D. Vertical angles theorem states that vertical angles are congruent.

Congruence in angles simply means the same or equals to.  Two angles are congruent when they are the same.

The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.

The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value

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The zeros of the polynomial function represented by the graph is defined below.

Polynomial function:

Polynomial function refers the function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x.

Given,

Here we need to identify the zeros of the polynomial function represented by the graph.

As per the definition of the polynomial function,

Here the zeros of a function represent the x value(s) that result in the y value being 0.

And the zeros of a function represent the x-intercept(s) when the function is graphed.

Then the zeros of a function represent the root(s) of a function.

Finally, the zeros of a function represent the solution(s) of a function.

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Using the compound interest formula, if the account compounds at 4.8% monthly and he withdraws $500 monthly, it will take Steve 33 years, 7 months (403 months) to reduce $100,000 to a balance (future value) of $0.

The future value is the compounded present value, while the present value is the discounted future value.

However, with periodic withdrawals, a present value that compounds at an interest rate into the future can become $0 (future value) after some periods.

The time (period) Steve reduces his inheritance to $0 can be computed using an online finance calculator as follows:

I/Y (Interest per year) = 4.8%

PV (Present Value) = $100,000

PMT (Periodic Payment) = $-500

FV (Future Value) = $0

Results:

N (# of periods) = 403.164

Sum of all periodic payments = $-201,581.83

Total Interest $101,581.83

Thus, after 403 monthly withdrawals, Steve's inheritance will be reduced to a $0 future value.

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Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answering its the 2 one on the left

Step-by-step explanation:

Answer:

Step-by-step explanation:

The pressure is 38.5 Newton per square meter (N/m²)

Temperature can be defined as the quantity that is used to measure the degree of hotness or coldness of a body in °Kelvin or ° Celsius.

When the pressure of a glass varies directly with the temperature, this means that once there is an increase in temperature there should be an increase in pressure of the medium too.

To calculate the new pressure the gas formula is used;

Where,

P1 = 18.9N/m²

T1 = 90k

V1 = 20m³

T2 = 110k

V2 = 12m³

P2 = X

P1V1/T1 = P2V2/T2

Make P2 the subject of formula;

P2 = P1V1T2/T1V2

P2 = 18.9×20×110/90×12

P2 = 41580/1080

P2 = 38.5 N/m²

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The value of the solution is 6.6%

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation might be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

According to the above question :-

= (3 × 4)C3 × (52 — 3 × 4)C(5 — 3) / 52C5

= 12C3 × 40C2 / 52C5

= 12! × 40! × 47! × 5! / (52! × 9! × 3! × 38! × 2!)

= 12!/9! × 40!/38! × 47!/52! × 5!/(3!2!)

= ((10 × 11 × 12) × (39 × 40) / (48 × 49 × 50 × 51 × 52)) × (5 × 4 / 2)

= 10 × (1 × 11 × 1 × 3 × 40) / (4 × 49 × 5 × 51 × 4)

= (10 × 40 / (4 × 5 × 4)) × (11 × 1 / (49 × 17))

= 5 × 11 / (49 × 17)

= 55 / (17 × (50 — 1))

= 55 / (850 — 17)

= 55 / 833

≈ 6.6%

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We use substitution to solve systems of equations by plugging one equation into the other.

We're given:

y has already been isolated in the second equation. Plug this into the first one:

[tex]7x + (4x - 21) = 12[/tex]

Isolate x:

[tex]7x + 4x - 21 = 12\\11x - 21 = 12\\11x= 33\\x=3[/tex]

Therefore, x = 3. Plug this into the second equation to solve for y:

[tex]y = 4(3) - 21\\y = 12 - 21\\y = -9[/tex]

Therefore, y = -9.

x = 3

y = -9

After simplification, the solution of this system of linear equation is (6,3).

In the given question we have to find the solution to the system of equations below.

The given equations are:

x+3y=15………………(1)

4x+2y=30………………(2)

Multiply equation 1 by 4, we get;

4x+12y=60………………(3)

Subtract equation (3) and (2)

4x+12y-(4x+2y)=60-30

4x+12y-4x-2y=30

10y=30

Divide by 10 on both side, we get

y=3

Put the value of y in equation 1,

x+3*3=15

x+9=15

Subtract 9 on both side, we get

x=6

So the solution of system of equation is (6,3).

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The slope of the line, using two points (2, 2) and (-2, -3), is calculated as: 5/4.

Using two points on a line, the slope of a line can be calculated by applying the slope formula below:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Pick two points on the line in the graph given to find the slope of the line. The two points that are marked on the line are:

(2, 2) = [tex](x_1, y_1)[/tex]

(-2, -3) = [tex](x_2, y_2)[/tex]

Substitute the values into the slope formula:

Slope (m) = (-3 - 2) / (-2 - 2)

Slope (m) = -5/-4 = 5/4

The slope of the line is: 5/4.

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Step-by-step explanation:

1. The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

2. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The length of the line segment will be 4 units. Then the correct option is A.

The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,

D² = (2 - 2)² + (2 + 2)²

Simplify the equation, then we have

D² = (2 - 2)² + (2 + 2)²

D² = (4)²

D = 4 units

The length of the line segment will be 4 units. Then the correct option is A.

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The missing diagram is attached below.

We can represent a function in four ways: Algebraically, Numerically, Graphically, Visually.

In the given question we have to explain how we represent a function.

A function is a relationship between two sets of variables in which one variable depends on another. Different techniques can be used to portray various sorts of functions. Typically, functions are represented by diagrams or formulas. The four approaches for representing a function are as follows:

Algebraically

Numerically

Graphically

Visually

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Answer:   The solution set of the system using substitution for  3x + 2y       = 7y = -3x + 11 is ((5,-4).

       Hope this helps!