What are 3 acute angles?

A pair of functions that are inverses of each other is: B. f(x) = 4x³ + 5 and g(x) = ∛[(x - 5)/4].

In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:

f(x) = y = ∛(x + 3) - 5

x = ∛(y + 3) - 5

x + 5 = ∛(y + 3)

Taking the cube of both sides of the function, we have:

(x + 5)³ = y + 3

g(x) = y = (x + 5)³ - 3 (Not inverse).

For the second option:

f(x) = y = 4x³ + 5

x = 4y³ + 5

x - 5 = 4y³

Dividing both sides of the function by 4, we have the following:

y³ = (x - 5)/4

Taking the cube root of both sides of the function, we have:

g(x) = y = ∛[(x - 5)/4] (Inverse)

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The most common method used for solving a pair of linear equations in two variables is the elimination method. This method involves adding or subtracting the equations to eliminate one of the variables so that the remaining equation can be solved.

The most common method used for solving a pair of linear equations in two variables is the elimination method. This method involves adding or subtracting the equations to eliminate one of the variables so that the remaining equation can be solved. Elimination is the simplest way to solve linear equations since it eliminates the need to do any complicated algebraic manipulations. With this method, one of the two equations is manipulated so that one of the variables is cancelled out. Once the equation is simplified, the remaining variable is solved for and can be substituted into the original equation to find the value of the second variable. The elimination method also allows for the simultaneous solving of more than one pair of equations. This is useful when solving more complex problems that involve multiple unknowns. The elimination method is a straightforward and effective way to solve linear equations in two variables and is one of the most commonly used methods for solving this type of problem.

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the complete question is

Which of the following method is used for the solution of pair of linear equations in two variables is  elimination method

The value of y = 18.75 if x and y have a proportional relationship, and y=15 when x=8 and when the value of x = 10 .

What is ratio ?

ratio can be defined as the given value divided by the total value called as the ratio.

Given ,

If x and y have a proportional relationship, and y=15 when x=8, what is the value of y when x=10

So , from the given given values,

8 / 15  = 10 / y

8*y = 15*10

y = 150 / 8

y = 75 / 4

y = 18.75

Hence, The value of y = 18.75 if x and y have a proportional relationship, and y=15 when x=8 and when the value of x = 10 .

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The value of the expression -6x + 1 - 3 -7 will be -6x - 9.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It should be noted that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The value of -6x + 1 - 3 -7 will be:

= -6x + 1 - 3 -7

= - 6x - 9

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Complete question

simplify fully.

-6x + 1 - 3 -7

Answer:

quantity supplied

Step-by-step explanation:

A log function can be translated by using a combination of operations such as addition, subtraction, multiplication and division to shift the function up or down, left or right on the graph.

For example, multiplying the log function by a constant (e.g. 3) will shift the graph up 3 units, while dividing the log function by a constant (e.g. 2) will shift the graph down two units. Another example would be adding a constant (e.g. 4) to the log function will shift the graph to the right 4 units, while subtracting a constant (e.g. 5) will shift the graph to the left 5 units on the graph.

Log functions can be translated by using a combination of operations such as addition, subtraction, multiplication and division to shift the graph up, down, left or right. Multiplying a log function by a constant will shift the graph up, while dividing the log function by a constant will shift the graph down. Adding a constant to the log function will shift the graph to the right, while subtracting a constant will shift the graph to the left.

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They are constructed like predators on the inside, though. According to a recent study, protein makes up about 50% of their daily caloric intake.

The cylinder, which is frequently a solid in three dimensions, is one of the most fundamental curved geometric forms. In simple geometry, this object is referred to as a prism with a circle as its base. A cylinder is also characterized as an infinitely curving surface in a number of modern domains of geometry and topology. The term "cylinder" refers to a three-dimensional object that has curved surfaces and circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles linked by a curved surface at the height of the cylinder, which is determined by the separation of the bases from the center. Cold drink cans and the wicks on toilet paper are examples of cylinders.

given

Giant pandas have a herbivorous appearance from the outside.

They consume bamboo almost constantly while awake.

They are constructed like predators on the inside, though.

According to a recent study, protein makes up about 50% of their daily caloric intake.

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A quadrilateral whose diagonals are parallel is referred to as a parallelogram. A parallelogram has equal angles on each side. A parallelogram has equal lengths on its opposing sides.

A parallelogram's diagonals cut through one another. Show: If a quadrilateral's one set of opposing sides is congruent and parallel, the quadrilateral is a parallelogram.

ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another. Having four sides in two dimensions, a quadrilateral. Square, rectangle, rhombus, trapezium, parallelogram, and kite are all examples of 2D shapes that are quadrilaterals.

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Answer:

There are multiple equivalent expressions for 3/4a(16b+24). The correct answers are:

(3/4)a(16b+24)

3/4(a16b+a24)

3/4*(16ba+24a)

Each of these three expressions are equivalent to 3/4a(16b+24) because they all multiply 3/4 by (16b+24) and (a) respectively, and all the operations of multiplication and addition are distributive.

Step-by-step explanation:

Answer:

3 √4096

Step-by-step explanation:

First we multiply them: 10 × 51.2 × 8 = 4096

Then (as there are three numbers) take the cube root: 3 √4096 = 16

Answer:

6000 students

Step-by-step explanation:

We know

30,000 students​ apply

The university accepts 50% of the students who apply.

50% of 30,000 students = 15,000 students

So, the University accepts 15,000 students

40​% actually enroll

40% = 0.4

15,000 times 0.4 = 6000 students

So, 6000 students actually enroll.

The system of equations which used to determine the length ,L, and the width , W, of the rectangular garden are, L + W = 21 and L - 2W = 5.

Let the length of rectangular garden

= L feet

and the width of rectangular garden

= W feet

We have , perimeter of a rectangular garden = 42 feet

As we know , the perimeter of a rectangle with length, L and width, W is = 2(L+ W)

so, 2(L+ W) = 42 feet

dividing by 2 both sides

=> L + W = 21 ---(1) , which is a linear equation. Now, it is say in problem that length of rectangular garden is 5 ft more than twice the width, i.e., L = 5 + 2W

=> L - 2W = 5 --(2)

To determine the dimensions, we have to solve the system of equations, (1) and (2)

Substract the equation (2) from (1),

L + W -( L - 2W) = 21 - 5

=> L + W - L + 2W = 16

=> 3W = 16

=> W = 16/3 feet

plugging the value of W in equation (1) ,

L = 21 - W = 21 - 16/3 = 47/3 feet

Hence, the required system of equations are L + W = 21 and L - 2W = 5.

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A cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7

When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

According to the conjugate root theorem, irrational roots of P(x) = 0 with the formula (a + √b) occur in conjugate pairs if P(x) is a polynomials with rational coefficients. This means that (a - √b) is likewise a root if (a + √b) is an irrational root and (a and b) are rational.

In this case, a cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7

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2y = x  -8 is the equation of line w.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Line v has an equation of y= – 2x+5.

also given Perpendicular to line v is line w

Slope of the perpendicular line w = -1/(Slope of the line v)

From Slope intercept form

y = mx + c

where m is the slope

Slope of the perpendicular line w = -1/ (-2)

The slope of the perpendicular line w = 1/2

Thus, the equation of a line:

y = 1/2x + c

Since, w passes through the point (6, – 5).

Thus,

-5 = 1/2 * 6 + c

c = -8

So, the equation of line y = 1/2x -8

Therefore, the Equation of line w is 2y = x  -8.

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Therefore , the solution of the given problem of  proportionality relationship comes out to be  it is not proportional relationship.

Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an airport and the number of apples in a harvesting of apples depend on the average number of apples produced by each tree. A linear relation between two number or variables is referred to as being proportional in mathematics. If the initial quantity doubles, the other amount also does so. Whenever one of the parameters is reduced to 1/100th of the its previous value, the other decreases as well.

Here,

Given :

=> y=75x-56

The proportional relationship says that the line of the given equation passes through origin ,

So , if we put x = 0,

We should get y=0.

So ,

=>  y=75(0)-56

=> y = 56

Thus , x =0 and y=56  because this line do not pass through origin it is not proportional relationship.

Therefore , the solution of the given problem of  proportional relationship comes out to be  it is not proportional relationship.

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From the figure, you can see that ∠3 and ∠4 are supplementary because they are linear pairs.

Answer:

Linear pair

Step-by-step explanation:

Angle 3 and angle 4 form a linear pair. The measure of angle 3 is four more than three times the measure of angle 4.

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The length of the femur + tibia.

Leg length (LL) is defined anatomically as the length of the femur plus the tibia. Because humans are bipedal, “leg length” is frequently measured as (femur + tibia + the height of the foot, from the tibia-talus articulation to the ground).

Leg lengths should be measured to see whether there is a discrepancy from one side to the other. It is critical to distinguish between genuine and perceived leg length deficiencies. A pelvic obliquity, contractures, or scoliosis may cause an apparent or functional leg length disparity. The majority of leg length discrepancies are normal. No one is exactly symmetrical, and adults often have a discrepancy of up to 2 cm.

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The range of the function f(x) = x² is [0, ∞).

The term function in math is defined as the term that define the relationship between two variables one is referred as dependent and the other is independent.

Here we have given that the function f(x) = x².

And we need to find the range of the function.

As we all know that the range is the set of all valid y  values.

So, here we have to use the graph to find the range.

When we plot the function on the graph then we get the graph like the following.

Then through the graph we have identified the Interval Notation, that is written as,

=> [0,∞)

And the Set-Builder Notation of the range is written as {y | y ≥ 0}

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Answer:

Step-by-step explanation:

(1/4) : (2 2/3) = 3/

32

= 0.09375

hope this helps :)

Answer:

The answer is 2721

Answer:

18 days

Step-by-step explanation:

You need to decide how many times 3 apples are more than ½: 3 / ½ = 6

So it will take 6 times more time: 3 x 6 = 18 days.

Answer:

The elevation of the bottom of the canyon is 85 4/5 feet below sea level. To convert it to the normal number, we can convert the fractional part to decimal by dividing the numerator by the denominator. So 4/5 can be converted to 0.8. Now we can add this decimal part to the whole number.

85 + 0.8 = 85.8

So the elevation of the bottom of the canyon is -85.8 feet below sea level.

The elevation of the bird's nest is 880 1/2 feet above sea level.

So the difference in elevation between the bottom of the canyon and the bird's nest is = 880 + 0.5 - (-85.8) = 880.5 - (-85.8) = 966.3

Therefore, the difference in elevation between the bottom of the canyon and the bird's nest is 966.3 feet

So, the bird flies 966.3 feet to reach the nest.

The equation x 5 x² 5 x³ 5, this is not a linear polynomial as the highest degree of the polynomial is 3.

A linear polynomial is a polynomial of degree one, and it is of the form ax + b. In this equation, a and b are constants, and x is the variable. In the case of the equation x 5 x² 5 x³ 5, this is not a linear polynomial as the highest degree of the polynomial is 3.

The expression x 5 X² 5 x³ 5 is not a linear polynomial. This expression is a third degree polynomial, which means that it is a polynomial with an exponent of 3 in its highest term.

The equation can be written as x + 5x² + 5x³, which is a polynomial of degree 3. To calculate the value of this equation, we can substitute any value for x and calculate the result. For example, if we substitute x = 2 the equation becomes 2 + 10 + 40 = 52. This is not a linear polynomial because it is an equation of degree 3.

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The point ( 3, 4) divides the given line segment formed by joining the points  ( 1,2) and ( 6,7) in the ratio of 2 :3.

As given in the question,

Given points to formed a line segment are :

(x₁ , y₁ ) = (1, 2)

( x₂ , y₂ ) =  (6, 7 )

Point that divides the given line segment is ( x , y ) = ( 3, 4 )

Standard formula to divide a line segment in the ratio m : n is given by :

( x ,y ) = [ (mx₂ + nx₁)/(m + n) ,  (my₂ + ny₁)/(m + n) ]

Substitute the value we get,

⇒ ( 3,4 ) =  [ (6m + n)/(m + n) ,  (7m + 2n)/(m + n) ]

⇒(6m + n)/(m + n)  = 3 or (7m + 2n)/(m + n) = 4

⇒ 6m + n = 3m + 3n or 7m + 2n = 4m + 4n

⇒ 3m = 2n or 3m = 2n

⇒ m : n = 2 : 3

Therefore, the required ratio that divides the given line segment at point (3,4 ) is equal to 2 :3.

The above question is incomplete, the complete question is :

In what ratio the point (3,4 ) divides the line segment joining the points (1 ,2) and (6 , 7) ?

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There are 10560 ways we form a subcommittee of 5 members that have at least one member from each party.

Combinations are defined as the selections made by taking some or all of a number of objects, irrespective of their arrangements.

The number of combinations of n different things taken r at a time, denoted by nCr and it is given by,

[tex]^nC_{r} =\frac{n!}{r!(n-r)!}[/tex]

where 0 ≤ r ≤ n.

The given information is committee has 8 republicans and 6 democrats.

we have to form a subcommittee of 5 members with at least one from each group.

Hence we need to select one from each and then the remaining 3 can be of any type.

No of ways =  ⁸C₁*⁶C₁*¹²C₃

                    = 48*220

No of ways=10560 ways.

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It is a point where all the angle bisectors of a triangle meet.

The point of concurrency for angle bisectors is a point where the angle bisectors of a triangle intersect. In other words, it is a point where all the angle bisectors of a triangle meet.

When we construct the angle bisectors of a triangle, they will always intersect at a single point, this point is known as the incenter of the triangle.

The incenter is the center of the inscribed circle, which is the circle that is tangent to all three sides of the triangle.

It is also important to note that the incenter is always inside the triangle and it is equidistant from all three sides of the triangle.

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The probability that Dan holds his breath for less time than Glenn on any given dive is 0.359.

The probability that on any given dive Dan holds his breath for less time than Glenn would be equal to the probability that X (D-G) is less than zero. Since X is the difference between two independent random variables (D and G), the mean of X is equal to the difference between the means of D and G and the standard deviation of X is equal to the square root of the sum of the variances of D and G. Therefore, the mean of X is 6 seconds and the standard deviation of X is approximately 13.3 seconds.

To calculate the probability that X is less than zero, we can use the standard normal distribution and calculate the cumulative probability of X being less than zero. Using a standard normal table or a calculator with a standard normal distribution function, we can find that P(X < 0) = P(Z < (0 - 6) / 13.3) = P(Z < -0.45) = 0.3589, or approximately 0.359.

Therefore, the probability that Dan holds his breath for less time than Glenn on any given dive is 0.359.

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250 km is approximately 3 hours and 15 minutes of driving time.

The time it takes to drive 250 km (155 miles) depends on the speed at which you are driving. If you are driving at an average speed of 80 km/h (50 mph), then it will take approximately 3 hours and 15 minutes to drive 250 km (155 miles). However, if you are driving at higher speed, such as 90 km/h (56 mph), it will take slightly less time - around 2 hours and 50 minutes. The time it takes to drive 250 km will also depend on the traffic situation and other factors such as the number of stops you make along the way. Generally, it is recommended to allow at least 3 hours and 15 minutes to drive 250 km.

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The formula for km per hour is used to calculate the speed of an object in kilometers per hour. It is calculated by dividing the distance in kilometers by the time in hours .Km per hour (km/h) = distance (km) / time (h) For example, if an object travels 30 kilometers in 2 hours, the speed of the object is 15 km/h.

Km per hour (km/h) is a unit of speed which measures the distance an object travels in one hour. The formula for km per hour is used to calculate the speed of an object in kilometers per hour. It is calculated by dividing the distance in kilometers by the time in hours. For example, if an object travels 30 kilometers in 2 hours, the speed of the object is 15 km/h. The formula for km per hour is an important tool to measure the speed of vehicles, and is commonly used in navigation and transport systems. It is also useful in determining the rate at which work is being done, or the rate at which someone needs to travel to reach a certain destination. The formula for km per hour is also beneficial in determining the average speed of an object, which is the total distance traveled divided by the total time taken to travel that distance. This can be used to measure the efficiency of a vehicle or any other form of transportation. In conclusion, the formula for km per hour is an invaluable tool for measuring speed and efficiency.

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The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

[tex]D(h)=25 {e}^{ - 0.4 h}[/tex]

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

[tex]6 = 25 {e}^{ - 0.4h} [/tex]

[tex] \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} [/tex]

[tex]0.24= {e}^{ - 0.4h} [/tex]

Taking logarithm both sides of above equation , we get,

[tex] \ln(0.24) = \ln( {e}^{ - 0.4h)} [/tex]

Using the properties of natural logarithm,

[tex] \ln(0.24) = - 0.4h[/tex]

[tex] - 1.427116356 = - 0.4h[/tex]

[tex]h = \frac{1.42711635}{0.4} = 3.56779089[/tex]

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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