y is inversely proportional to x
when y = 7, x = 9
a) work out an equation connecting y and x
b) work out the value of y when x = 21

The opposite of the opposite of -2 is equal to: -2

This can be solved by using the concept of inverse.

This quantity is also referred to as the opposite (number), sign modification, and negation. It changes the sign of a real number so that the additive inverse of a positive number is negative and the additive inverse of a negative number is positive. Due to their ability to reverse mathematical processes, inverse techniques are crucial for solving equations. One of the most crucial issues to ask whenever a new mathematical method is presented is how to invert it.

The term inverse in mathematics refers to the inverse of another operation.

In this case firstly opposite of - 2 is 2 and next opposite of 2 is again -2.

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Answer:

Step-by-step explanation:

1/16=64^4x-3

1/4^2=(4^3)^4x-3

4^-2=(4^3)^4x-3

4^-2=4^3*(4x-3)

Since the bases are equal (to 4), the exponents must be equal to each other.

-2=3*(4x-3)

-2=12x-9

-2+9=12x

7=12x

7/12=x

x=7/12

So the answer is x=7/12

Answer:

x=4 and y=2

Step-by-step explanation:

You should use graph, point of intersection(for example point M(4,2) ) is solution

And we can conclude that x=4 and y=2

Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.

A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.

Here,

"Female doctors make up 22.2% of all registered doctors," the inquiry states.

Consider the entire number of doctors who are registered as x; 22.2% of those doctors are women.

and 47,200 divided by 22.2% of x

=>22.2/100 * x = 47,200

in math

264414 doctors were registered that year, or

x = 58700* 100/22.2 x.

Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.

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On solving the value of provided question we can say that - the value of the slope intercept y = -3.

The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.

as we can see from graph that,

line passes through origin, so x= 0

the, y = -5x - 3

y = -3

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The acceleration of the particle is 1 foot per second square

From the question, we have the following parameters that can be used in our computation:

Velocity function v(t) = −t2 + 5t − 3

Express properly

So, we have

v(t) = -t² + 5t − 3

At time t = 3 seconds, we have

v(3) = -(3)² + 5(3) − 3

Evaluate

v(3) = 3

So, we have

Acceleration = v(3)/3

This gives

Acceleration = 3/3

Evaluate

Acceleration = 1 foot per second square

Hence, the acceleration is 1 foot per second square

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Answer:

60cm

Step-by-step explanation:

given:

focal length (f) = 20cm

image height (v) = ½u

object height (u) = ?

(1÷v) + (1÷u) = (1÷20)

(1÷(½u)) + (1÷u) = (1÷20)

(2÷u) + (1÷u) = (1÷20)

(3÷u) = (1÷20)

u = 20 × 3

u = 60cm

Check the picture below.

Answer:

A.  x ≥ 21[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

81 - 1[tex]\frac{1}{5}[/tex] x ≤ 55

-1[tex]\frac{1}{5}[/tex] x ≤ 55-81

-[tex]\frac{6}{5 }[/tex] x ≤ -26

x ≥ -26(-[tex]\frac{5}{6}[/tex])       **flip the inequality when you divide by a negative number

x ≥ 21[tex]\frac{2}{3}[/tex]

As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

The formula is presented as

k(x) = x² + 9

The aforementioned equation is linear.

 the range is (-∝, ∝) and the domain is(-∝, ∝) 

Formula 2

The formula is presented as

y = (x + 5)² +3

The aforementioned equation is linear.

The range is (-∝, ∝), and the domain is (-∝, ∝).

As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).

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The 5 life examples are:

In all these life examples that are listed above, the number 100 is divided by 20 giving 5 as the result. which is said to be:

100/20

= 5.

Therefore, reason behind this is that the number 20, in these life examples, is a representative of a whole value and the number 5 represents the number of parts it is being divided into, so when you multiply 20 by 5, you get 100, which represents the total of these five parts. So, 100 is related to 20 in this context as the multiple of 20 and 5.

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Answer:

In geometry, a polygon can be defined as a flat or

plane, two-dimensional closed shape bounded with

straight sides. It does not have curved sides. The

sides of a polygon are also called its edges. The

points where two sides meet are the vertices (or

corners) of a polygon

1. polygon with four sides is called a Quadrilateral

2. polygon with six sides is called hexagon

3. polygon with five sides is called pentagon

Hope this helps?

Answer:

3.5m(3m + 1.8)

10.5m^2+6.3m

Step-by-step explanation:

On solving the provided  question, we can say that - the value of the  fraction will be 1/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here,

x + x = 1/2

2x = 1/2

x = 1/4

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Answer:

Step-by-step explanation:

To solve for r, you need to first find the values of x that make y equal to 24. These values of x are called the roots of the polynomial equation y = (x+3)(x-2)(x-r).

To find the roots of the equation, you can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation y = ax^2 + bx + c.

In this case, the coefficients are:

a = 1

b = -3

c = -24

Substituting these values into the quadratic formula, we get:

x = (3 +/- sqrt(9 - 96)) / 2

= (3 +/- sqrt(-87)) / 2

Since sqrt(-87) is not a real number, there are no real roots for this equation. Therefore, the value of r cannot be determined.

The two scenarios that can be represented by a ratio 4:5 are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons. ( option A and D)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For a scenario that will give ratio of 4:5, it means the first entity will be 4 and the second entity will be 5.

Therefore the two statements that obey this in the option are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons.

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The blanket that they should choose is the one for which the multiplication of dimensions result in the largest value.

The area of a rectangle of dimensions length and width is given by the multiplication of these dimensions, as follows:

Area = length x width.

Then, to obtain the area for each blanket, their dimensions must be multiplied.

Then the blankest with the greatest area is the one for which the multiplication of the dimensions will result in the largest value.

(applying the formula for the area of the rectangle).

The problem is incomplete, as the dimensions were not given, hence the answer is given in general terms.

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The Complete statement are:

The properties of polynomial addition include closure, commutativity, and associativity.

These properties of polynomial addition make it easy to perform arithmetic operations with polynomials because they have predictable results and the order in which the polynomials are grouped or ordered does not change the final result.

Therefore, In simple terms, closure property ensures that the sum of two polynomials is also a polynomial, commutative property ensures that the order of the polynomials does not change the sum and the associative property ensures that the grouping of the polynomials does not change the sum.

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Answer:

Step-by-step explanation:

Answer:

a = -20/13

Step-by-step explanation:

7 - 13a = 27

-13a = 20

a = -20/13

Let's check

7 - 13(-20/13) = 27

7 + 260/13 = 27

7 + 20 = 27

27 = 27

So, a = -20/13 is the correct answer!

The area is 8.84 sq. units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

To find the area we will find the product of 3.4 x 2.6, we can break each length into its base-ten units,

3.4 = 3+0.4

2.6 = 2+0.6

We can rewrite the product and solve it,

= (3+0.4) × (2+0.6)

= (3+0.4) × 2 + (3+0.4) × 0.6

= 3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6

This expression represents the partial product, each of the expression gives the area of sub rectangles (A, B, C and D). the sum of the partial product will give the area of the main rectangle.

Therefore,

3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6

= 6+0.8+1.8+0.24

= 8.84

Hence, the required area is 8.84 sq. units.

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Each position in base 10 is worth ten times the place to its right, and there are ten numbers (0–9). 49D2 in the base-ten system is equal to 204064.

When you come to "two," you discover that there isn't a single digit in base-two math that stands for "two." Instead, you enter a "1" for "1 two" and a "0" for "0 ones" in the twos and units columns, respectively.

[tex]49D2 in the base-ten system is 4916^3 + 1316^2 + 216^1 \\\\= (494096) + (13256) + (216) \\\\= 200704 + 3328 + 32\\ \\= 204064[/tex]

A binary counting system simply employs the numerals 0 and 1 in each place. Base 2 is another name for binary. In binary, a second place is required to represent a number greater than 1.

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The value of x on the line segment and the triangle is 17.3 units

From the question, we have the following parameters that can be used in our computation:

A triangle (see attachment for the triangle)

Also from the question, we understand that:

BD bisects ∠ABC

Using the bisector theorem, we have

x/13 = 20/15

Multiply both sides of the equation by 13

So, we have the following representation

13 * x/13 = 20/15 * 13

Evaluate the products

So, we have the following representation

x = 20/15 * 13

Evaluate the other products

So, we have the following representation

x = 52/3

This gives

x = 17.3

Hence, the length x is 17.3 units

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Answer: The matching jacket requires 1/6 yards less fabric than the dress, which is 3 1/4 - 1/6 = 3 1/4 - 2/12 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 3/12 yards of fabric.

To add these two amounts of fabric together, you need to add the yards and the inches separately.

For the dress: 3 1/4 yards = 3 + 1/4 = 3 + 0.25 = 3.25

For the jacket: 3 3/12 yards = 3 + 3/12 = 3 + 0.25 = 3.25

So, for both pieces, the required fabric is 3.25 + 3.25 = 6.5 yards

Step-by-step explanation:

The graph in the question is a parabola that opens downwards.

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions like print(), etc. but you can also create your own functions. These functions are called user-defined functions.

This means that the range of the function is all real numbers less than or equal to the y-intercept of the parabola, which is 0 in this case. Therefore, the range of the function is all real numbers less than or equal to 0.

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Therefore , in response to the given problem of triangle, we can state that the triangles ECD and PQR

A triangle is a polygon since it has four segments and three vertices. It is one of the basic geometric forms. The title given to that of a triangle with the vertex A, B, and C is Triangle ABC. A unique planes and trapezoid in Geometric forms are discovered once the three criteria are not collinear. Quadrilateral and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where its three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

=> EC = PQ (equal side)

=> CD = PR  (equal side)

=> ED = QR (equal side)

as a result, the SSS property compares both triangles.

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Answer:

  3.58

Step-by-step explanation:

You want to know the weekly growth factor if the daily growth factor is 1.2.

The weekly growth factor will be the growth factor over 7 days:

  (1.2)^7 ≈ 3.58

Every week, the number of locusts grows by a factor of 3.58.

__

Additional comment

The exponential model is ...

  number = (initial number)(growth factor)^t

The period of time associated with the growth factor is the units associated with t. Since 1 week = 7 days, the multiplier for 7 days is ...

  weekly growth factor = (daily growth factor)^7

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Answer:

−1 < y < 3

Step-by-step explanation:

The  value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.

In the equation we are given the value of y as: 1

[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

Therefore, we can say that the value of the given polynomial is: 8

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Complete question is: Find 6y2 + 3y - 1 4 for y = 1

Answer:

The tree is 44 feet

Step-by-step explanation:

[tex]\frac{8}{6}[/tex] is equivalent to [tex]\frac{4}{3}[/tex] (divide the numerator and denominator by 2)

[tex]\frac{4}{3}[/tex] = [tex]\frac{x}{33}[/tex]

3 x 1  = 33, so 4 x 11 = 44

Answer:

17.5 miles

Step-by-step explanation:

right!!