20y−25x=140 and y+5/4x=-5

The solution of the inequalities is x > 6 or x < -4

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

8 – 6x < −28 or 9x + 5 < −31

collect like terms and solve for x in both inequalities:

For 8 – 6x < −28:

8 – 6x < −28

-6x < -28 - 8

-6x < -36

-x < -36/6

-x < -6

x > 6

For 9x + 5 < −31:

9x + 5 < −31

9x < -31 - 5

9x < -36

x < -36/9

x < -4

Thus, the solution is x > 6 or x < -4

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Answer:

the answers are in the picture.. if you have any questions you can ask :)

An inverse of a relationship that is never a function and can be a function itself.

An inverse function or an anti-function is defined as a function, which can reverse into another function, which undoes the action of another function. A function is the inverse of a function if whenever y=f(x) then x=g(y).

Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function.

A one-to-one function not only passes the vertical line test, but it also passes a horizontal line test.

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The congruences given are the corresponding sides and angles of WZX and YZX. Segment ZX is congruent to itself, so SAS WZX YZX.

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Answer: The equation is y=2x

0, becous A (-1x2) can't be negative.

A. Peg is walking with a speed of 3 miles per hour.

B. The completed table is given below.

C. If Peg and Raj started at the same time from the same place on the

trail, they are 1.5 miles apart after 3 hours.

D. After 4 hours Peg and Raj will be 2 miles apart.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

From the graph it can be seen that -

In 1 hour Peg walks 3 miles.

In 2 hours Peg walks 6 miles.

In 3 hours Peg walks 9 miles.

In 4 hours Peg walks 12 miles.

Therefore, the speed of Peg is 3 miles/hour.

It is given that Raj walks 2.5 miles/hour.

So, to complete the table use the formula speed = distance/time.

distance = speed × time

When time = 0 hours

Raj (0) = 2.5 × 0

Raj (0) = 0 miles

When time = 1 hours

Raj (1) = 2.5 × 1

Raj (1) = 2.5 miles

When time = 2 hours

Raj (2) = 2.5 × 2

Raj (2) = 5 miles

When time = 3 hours

Raj (3) = 2.5 × 3

Raj (3) = 7.5 miles

Now, Raj and Peg started at the same time.

After 3 hours Peg reaches 9 miles and Raj reaches 7.5 miles.

The difference between their distance is -

9 - 7.5

1.5 miles

Now, when time = 4 hours

Raj (4) = 2.5 × 4

Raj (4) = 10 miles

After 4 hours Peg reaches 12 miles and Raj reaches 10 miles.

The difference between their distance is -

12 - 10

2 miles

Therefore, after 3 hours and 4 hours the difference between Pe and Raj is 1.5 miles and 2 miles respectively.

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The length of the banner is, 84 inch when the width is enlarged to 63 in.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A picture of a school's mascot is 18 in. wide and 24 in. long.

And, It is enlarged proportionally to banner size.

Now, Let the length of the banner when the width is enlarged to 63 in.

Hence, By definition of proportionality, we get;

⇒ Length / Width

⇒ 24 / 18 = x / 63

Solve for x as;

⇒ 24 × 63 / 18 = x

⇒ x = 84 inch

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The two functions be[tex]$f(x)=3 x-7$[/tex] and  [tex]$g(x)=\frac{x+1}{x-1}$[/tex] then the value of f(g(-3)) be -1.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).

If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.

Let the given two functions be

[tex]$$\begin{aligned}& f(x)=3 x-7 \\& g(x)=\frac{x+1}{x-1}\end{aligned}$$[/tex]

f(g(-3)) = f(g(x = 3)) = f(3 - 1) = f(4/2) = f(2)

f(x = 2) = 3 × 2-7 = 6 - 7 = -1

Therefore, the correct answer is option A. -1.

The complete question is:

Consider these functions:

[tex]$$\begin{aligned}& f(x)=3 x-7 \\& g(x)=\frac{x+1}{x-1}\end{aligned}$$[/tex]

What is the value of f g(3))?

A. -1

B. 0

C. 3

D. 5

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Answer:

5⁻³

Step-by-step explanation:

For categorical data, the mode is a particularly useful measure of central tendency it is a True statement.

A categorical variable in statistics is a variable that, based on some qualitative quality, can have one of a small, and typically fixed, number of potential values, designating each individual or other unit of observation to a certain group or nominal category.

Ordinal variables shouldn't be averaged because the gaps between the categories could not be uniform. Standard deviation and variance shouldn't be used to describe categorical data because they both depend on the mean. Instead, percentiles and range are used as metrics of spread for ordinal categorical data.

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Answer: Distributive property

Step-by-step explanation:

Therefore , the solution of the given problem of ratio comes out to be

5/14 is the ratio of sopranos to the entire chorus as a fraction.

A pair of equivalent variables "a" and "b" can be defined using the straightforward formula "a / b," where "b" could also be bigger than zero. Two ratios are combined to make one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. 3/4 of the group are girls, while 1/4 are boys. Parts can be a division between one or more items, a number, or a portion of the volume of a component.

Here,

given :

=>12 altos, 20 sopranos, 4 tenors, and 40 bass singers.

To find the ratio of sopranos to the entire chorus as a fraction

So,

Total singers leaving sopranos are :

=> 12 + 4 + 40 = 56

The ratio of sopranos and entire chorus is:

=> 20 /56

=> 10/28

=> 5/14

Therefore , the solution of the given problem of ratio comes out to be

5/14 is the ratio of sopranos to the entire chorus as a fraction.

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You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. f(x) = -27.

f(x) = 3x - 9

determine f(x) = 9

f(9) = 3(9) - 9

f(9) = 27 - 9

f(9) = 22

Hence, the answer is 22.

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The maximum area that Georgina Orwell can enclose is 10000 square feet.

The maximum area that Georgina Orwell can enclose with 200 feet of fencing is:

Let x be the length of the side of the pig pen along the barn and y be the width of the pig pen.

We know that:

x + 2y = 200

We can use this equation to find the value of one variable in terms of the other. For example, we can solve for y:

y = (200 - x) / 2

We can use this equation to find the area of the pig pen:

A = xy = x((200 - x) / 2)

= (200x - x^2) / 2

To find the maximum area, we need to find the value of x that maximizes A. To do this, we can take the derivative of A with respect to x and set it equal to zero:

A'(x) = (200 - 2x) / 2 = 0

200 - 2x = 0

x = 100

So the maximum area is:

A = (200x - x^2) / 2 = (200 * 100 - 100^2) / 2 = 10000 sq ft.

Therefore, the maximum area that Georgina Orwell can enclose is 10000 square feet.

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Since varies directly with y, the value of y when x= 10 is equal to -80/3.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = -8/3

When the value x = 10, the value of y can be calculated as follows;

y = kx

y = -8/3 × 10

y = -80/3

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The value of x for the given corresponding angles is, 7 degree.

What is corresponding angles?

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and similarity. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Given:

m || n

The angles (7x - 4) and (5x + 10) are corresponding angles.

We have to find the value of x.

Since, the angles are corresponding angles and corresponding angles are equal when the lines are parallel.

⇒ 7x - 4 = 5x + 10

Add 4 on both sides,

7x - 4 + 4 = 5x + 10 + 4

7x = 5x + 14

Subtract 5x on both sides,

7x - 5x = 5x + 14 - 5x

2x = 14

Divide both sides by 2

⇒  x = 7

Hence,  the value of x for the given corresponding angles is, 7 degree.

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Dividend ÷ Divisor = Quotient and Remainder

When a dividend is divided by a divisor, we get the value of the quotient in the result.

The quotient is the result of dividing one integer by another. For example, in 8÷ 4 = 2, the result of the division is 2, hence the quotient is 2. The dividend is 8 and the divisor is 4.

According to the Quotient Rule, the derivative of a quotient equals the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square.

This is the rule we employ when dividing one exponential equation by another. According to the quotient rule, we must subtract the exponent in the denominator from the exponent in the numerator, but the bases must be the same.

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The lengths of the sides of each array are factors of 8.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

Given here: The dimensions of the four arrays as (1,8), (4,2), (2,4), (8,1)

Now factors of 8 are given by 8=2⁰,2¹,2²,2³

Thus clearly all the sides are factors of 8

Hence, The lengths of the sides of each array are factors of 8

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Hey there!

Answer:

After solving for x, our final answer is x = 20.

1. Switch sides.

[tex]\frac{x}{5}-47=-43[/tex]

2. Move 47 to the right side.

[tex]\frac{x}{5}=4[/tex]

3. Multiply both sides by 5.

[tex]\frac{5x}{5}=4*5[/tex]

4. Simplify.

[tex]x=20[/tex]

___________________________

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5x+3y=450 is the equation to determine how many of each type of ticket they should sell.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

Let x be the number of adult tickets and y be the number of student tickets.

5x+3y=450

The equation to find the number of each type of ticket they should sell is 5x+3y=450.

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The angle formed by two chords intersecting inside a circle has a measure equal to the arithmetic mean of the intercepted arcs' respective lengths.

The products of the measures of the segments of the chords are equal if two chords cross in a circle. 

Theorem of intersecting chords. "The arithmetic mean of the measures of the two intercepted arcs is equal to the measure of an angle created by two chords that intersect inside a circle."

By intersecting the lines from two well-known ground landmarks, intersection is a technique for finding a location on a map. Fire lookouts employ a variety of techniques to locate fires, including intersections.

A tangent is a line that precisely crosses a circle at one point, and the junction is identified by the term "point of tangency" for the intersection. A radius drawn to the point of tangency always has the tangent perpendicular to it. A line that crosses a circle at precisely two different locations is known as a secant.

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The above conversation suggests that the area of the dilated image can be approximated as the sum of the areas of rectangles. If the original shape is dilated by a factor of k, the area of the dilated image would scale by a factor of k².

The area of the image based on the information will be 720 square inches.

The area of a circle with radius r is given by A = πr².

If the circle has an area of 20 square inches, then we can solve for the radius: 20 = πr² => r = sqrt(20/π). If the circle is dilated using a scale factor of 6, the radius would be 6 times larger, which means the area would be 6² times larger: A' = π(6r)² = 36πr²

= 36π(20/π)

= 720 square inches.

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a) 8780

b) i) 1159   ii) 1990

c) 9611

a) The total number of workers at the beginning is 2340 + 3455 + 675 + 960 + 1350 = 8780 workers.

b)

i) The first two companies laid off 1 worker for every 5 workers, so for the first company (2340 workers) this means 2340/5 = 468 workers lost their job. For the second company (3455 workers) this means 3455/5 = 691 workers lost their job.

In total, 468 + 691 = 1159 workers lost their job.

ii) The other three companies recruited 2 new workers for every 3, so for the third company (675 workers) this means 6752/3 = 450 new workers were recruited. For the fourth company (960 workers) this means 9602/3 = 640 new workers were recruited. For the fifth company (1350 workers) this means 1350×(2/3) = 900 new workers were recruited.

In total, 450 + 640 + 900 = 1990 new workers were recruited.

c) The total number of workers finally is 8780 - 1159 + 1990 = 9611 workers.

The complete question is -

Five companies employed 2340, 3455, 675, 960, and 1350 workers. The first two companies laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for every 3.

a) What was the total number of workers at the beginning?

b) How many people: i) Lost job ii) Got a job?

c) What was the total number of workers finally?

The option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.

In the given question, we have to determine which numbers could not be used to represent the probability of an event.

Let P be the probability.

It can accept any value [0,1] (inclusive of 0, 1), as well as [0%, 100%] (inclusive of 0% and 100%).

It is unable to accept negative values.

Because probability values cannot be larger than one or less than one, 64/25 and -1.5, respectively, cannot be used to indicate the likelihood of an evens.

So, the option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.

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If the quadratic expression with integer coefficients is factorable over the integers then its discriminant is a perfect square.

The term quadratic expression is defined as an expression with the variable with the highest power of 2.

Here we have to identify the way to know that  if a quadratic equation is factored.

As per the definition here we know that if it is a positive perfect square the equation can be factored fairly easily.

Where as here we have also know that not every quadratic equation can be solved by factoring or by extraction of roots.

And if the quadratic expression that is written as the product of a constant times two linear factors then it is said to be in factored form.

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The relation for time and distance  will be written as D = 40t miles.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that the speed of the eagel is 40 miles per hour. The relationship between the distance and the time will be calculated as,

Distance = Speed x Time

Distance =  40 x Time

D = 40t miles

Here t, is in hours.

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