Sam can paint an apartment living room in 3 hours, and Pam can paint the same room in 2 hours. The solution to the equation §+ £ = 1 describes how long it will take them to paint the living room if they work together. Before solving this problem, make a guess about the answer. Then solve the equation. How did your guess compare?

Flossie needs 8 pupils and 8 staff members for each team to have an equal number of staff members.

The major issue is that there are 40 pupils in total, depending on common variables.

The biggest positive integer that divided each of the figures is the greatest common divisor of two or more numbers that are not all equal to zero. This phrase is used in arithmetic. The process which enables the largest common factor of the two numbers x and y.

The number of workers is 24, thus there are 24 workers.

Since she wants each squad to have the same amount of students and staff members, Flossie needs GCF.

GCF has 24 staff members and 40 students.

GCF for 40 and 24 equals 8.

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The final expression of the algebraic expression is; (30√2)/2

The algebraic expression is expressed as;

(18/√2) - 12/√32

Now, we know that √32 can be expressed as;

√(16 * 2) = √16 * √2

= 4√2

Thus, the expression is now;

(18/√2) - 12/4√2

= (18/√2) - (3/√2)

Factorizing common factor gives;

(1/√2)(18 - 3)

= 15/√2

Rationalizing the denominator gives;

(30√2)/2

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12a2b = 2  2  3 a a b b; 15ab2 = 3  5 a b b b. The factors 3, a, and b are shared by the two terms. This demonstrates that the given expression's factors are a, b, and (4a + 5b).

We can deduce from the problem's options that (4a-5) is not a factor of the given expression.

12 is the highest-common factor between 12 and 36. However, neither the 12x nor the 36 given monomials contain any common literal. 12 is the most common factor.

In mathematics, factorization or factoring is defined as the breakdown or decomposition of an entity—such as a number, matrice, or polynomial—into another product or common factors that yield the original number or matrix when repeated together, among other things.

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The table representing a proportional relationship is given as follows:

x −3 0 3

y −2 0 2

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the definition, we get that a proportional relationship is a linear function with an intercept of zero, meaning that when x = 0, y = 0.

This means that the correct table is given by the last table, as for the other tables, y has values different of zero when x = 0.

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Answer: The answer is the last one D.

Step-by-step explanation:

The cost if a client earns $1500 the first month is;  $36875

The formula for the equation of a straight line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

We are told that a job hotline service charges $25 plus a 4% commission, c, on the first month of earnings.

First month total charge;

T = $25 + 0.04c

We are told that the client earns $1500. Thus;

1500 = 25 + 0.04c

c = (1500 - 25)/0.04

c = $36875

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The account will be worth $215,958.88 after 3 years.

The account will be worth $215,958.88 after 3 years. This can be calculated by using the formula: A = P(1 + r/n)^(nt) where A is the final amount, P is the initial principal (or balance) of $165,000, r is the annual interest rate of 8%, n is the number of times that interest is compounded per year (annually in this case, so n = 1), and t is the number of years the money is invested for (3 in this case).

Plugging these values into the formula: A = 165,000(1 + .08/1)^(1*3) = 215,958.88.

The subject you are asking about is called compound interest. Compound interest is a concept related to finance and economics. It is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is often used in personal finance, such as in savings and retirement accounts, as well as in business and investment contexts.

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The probability that the player will be a boy is 0.52.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

The team has a total of 25 players. 12 of the players are girls.

Now, Number of boys in a team = 25 - 12

                                                  = 13

Hence, The probability that the player will be a boy is,

⇒ 13 /25

⇒ 0.52

Thus, The probability that the player will be a boy is 0.52.

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The process to sketch the graph of y =  absolute value x is explained below .

What is Absolute Value ?

The absolute value of a number is the distance of the number from origin of a number line. It is denoted as |a|, which defines the magnitude of any integer "a". Absolute Value is represented by two vertical lines "|a|" , which is called as modulus of a .

we have to sketch the graph of the absolute function given as ; y = |x| ;

put x = -2 , we get ⇒ y = 2 ;

put x = 2 , we get ⇒ y = 2 ;

we see that if we put any value of "x" , positive or negative , the result "y" will always be positive .

Therefore , the graph of the function will be a V shaped graph facing upwards .

The given question is incomplete , the complete question is

How do you graph y =  absolute value x ?

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The slope of the line 3x - 4y = -12 is 3/4, obtained by dividing -3 by -4 after isolating y.

What is slope ?

Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.

The slope of a line can be found by rearranging the equation to the slope-intercept form y = mx + b. To find the slope of the equation 3x - 4y = -12, you can divide both sides by -4 and then divide by 3.

3x - 4y = -12

-4y = -3x -12

y = (3/4)x +3

So , The slope of the line 3x - 4y = -12 is 3/4, obtained by dividing -3 by -4 after isolating y.

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Answer:

  The square of x, or x times x.

Step-by-step explanation:

You want to know the meaning of x2.

As often seen on Brainly, and in poorly-edited math curriculum materials, the expression x2 is a badly-formatted version of x². It is often the result of a copy/paste operation in which the superscript text formatting is lost.

The superscript 2 is an "exponent." It tells you how many times x is a factor in the product:

  x² means x·x . . . . . a product in which x is a factor 2 times.

When superscript characters are not available, an exponent is usually signified in plain text using a caret (^) symbol:

  x² ⇔ x^2

Please note that superscript text acts to group expressions that are part of an exponent:

  [tex]x^{a+b}[/tex]

If you write this as x^a+b, it looks like b is added to the value of x^a. The expression above would be correctly written in plain text as x^(a+b), using parentheses to do the grouping that would otherwise be provided by the superscript font.

The value of  x is -7 in the set of solutions to the equation 4x-12≤16+8x.

Given the equation:

4x-12≤16+8x

By demonstrating any of the following, an inequality can be used to compare two (2) variables or integers in a mathematical equation:

Fewer than ()

More than (>)

Equal to or less than the other ()

Equal to or greater than the other ()

Group like terms:

4x-12≤16+8x

Simplify the like terms:

-4x≤28

Solve for x by dividing both sides by -4

x≤-28/4

Simplify further, we get:

x≤-7

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Truth serum has 91% accuracy when guilty, 94% accuracy when innocent, 6% false positive, 9% false negative.

What is percentange ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%" (percent sign) and it's used to express a proportion or ratio. For example, if a student scored 80 out of 100 in an exam, the percentage score would be 80%, which means the student answered 80 out of 100 questions correctly.

A truth serum given to a subject is known to have a 91% reliability rate when the person is guilty and a 94% reliability rate when the person is innocent. This means that when the person is guilty, there is a 91% chance that the truth serum will indicate that the person is guilty, and a 9% chance of a false negative (indicating the person is innocent when they are guilty). Similarly, when the person is innocent, there is a 94% chance that the truth serum will indicate that the person is innocent, and a 6% chance of a false positive (indicating the person is guilty when they are innocent).

Truth serum has 91% accuracy when guilty, 94% accuracy when innocent, 6% false positive, 9% false negative.

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Calculating the total number of factors for a given number is done by using the formula total number of Factors for N=(a+1)(b+1)(c+1). A prime factor is any non-zero natural integer that can be divided only by itself and by 1.

Actually, some of the first prime numbers are 2, 3, 5, 7, 11, and so forth. a sum that has been multiplied to yield a new sum. By dividing 15 by 3 and 5, for instance, we obtain 3 5=15. major components: All prime but non-composite components are referred to as prime factors. 2, 3, and 5 are a handful of the prime factors of 30. The only prime factors of 12 are 2 and 3, therefore listing 2 twice as in mathematics.

Particularly in statistics, there are many different mean types.Each mean is used to summarise a particular set of data, typically in order to assess the overall importance of that data set. A statistic known as the standard deviation describes the degree of variance or dispersion in a group of values. A low standard deviation indicates that the values often tend to be close to the set mean, whereas a large standard deviation denotes that the values are distributed over a wider range.

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A polygon with 6 angles is called hexagon

The regular hexagon is a convex polygon with six equal sides and six equal angles, always divided into symmetric or asymmetric triangles. It is closely related to equilateral triangles: By joining each vertex with its opposite, the regular hexagon is divided into six equilateral triangles.

The sum of the interior angles of a hexagon is 720°

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (6-2) x 180°

Sum of Interior Angles = 4 x 180°

Sum of Interior Angles = 720°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

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Since there are two complex conjugates as the roots of the quadratic equation 5x2 4x 3 0 there is no way to describe them in terms of real integers.

The roots can only be roughly calculated because they are irrational numbers.

Two complex conjugates, which are unable to be expressed in terms of real numbers, make up the roots of the quadratic equation 5x2 4x 3 0. Using the quadratic formula, the roots can be discovered. The coefficients of the equation are necessary for the formula, and in this example, they are a=5, b=4, and c=3. When the quadratic formula is used, two complex roots are produced, denoted by the expressions x1 = -1/5 + (16)/5i and x2 = -1/5 - (16)/5i. Since their roots are irrational integers, they can only be roughly calculated. When b2-4ac, the discriminant, is negative, complex roots are frequently discovered. The discriminant in this situation is -64, which is negative and shows that the equation has complex roots.

Inequality = b2-4ac = 42-4(5)(3) = -64.

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Full Question = What is the nature of the roots of the quadratic equation  5x2 – 4x + 1 = 0?

Radical expressions are numbers which have root values in them. The root can be an nth root, a square root, or a cube root. To simplify the radical expressions we can use the product property.

We first locate the radicand's greatest factor which is also a perfect power of the index.

Then we use that factor to rewrite the radicand as the product of two factors. Rewrite the radical as the result of two radicals by applying the product rule and then reduce the perfect power to its most basic form.

To simplify the radical expressions we can use the quotient property. Make the fraction in the radical simpler then rewrite the radical as the quotient of two radicals by using the Quotient Property. Radicals in the numerator and denominator should be made simpler.

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The congruency postulates for each question is;

1) SSS

2) Not enough information

3) Not enough information

4) SAS

5) ASA

6) Not enough information

In mathematics, when it comes to triangles, there are different postulates or theorems that are used to prove congruency and they include;

SAS which stands for Side- Angle - Side Congruency

SSS which stands for Side- Side - Side Congruency

ASA which stands for Angle- Side - Angle Congruency

AAS which stands for Angle - Angle - Side Congruency

HL which stands for Hypotenuse Leg Congruency

1) We see that we are given three congruent sides to the other triangle and as such the congruence postulate is SSS.

2) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

3) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

4) We are given two congruent sides and the included angle and this is SAS congruency.

5) We are given two congruent angles and the included angle and this is ASA congruency.

6) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

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It will take 36 months for the populations of Rock Hill and Greenville to be the same.

What is the Division?

Division is a mathematical operation used to find the number of times one number, known as the dividend, is contained within another number, known as the divisor. It is represented by the symbol "/" or the word "divided by". It is the inverse operation of multiplication.

To determine when the populations of Rock Hill and Greenville will be the same, we need to find the difference in population growth between the two cities and divide it by the difference in population growth rate. We can use the following formula:

(Population of Rock Hill - Population of Greenville) / (Population growth rate of Rock Hill - Population growth rate of Greenville) = Number of months until populations are equal

First, we will calculate the population growth rate of Rock Hill and Greenville:

Population growth rate of Rock Hill = (100 people move in) - (150 people move out) = -50 people/month

Population growth rate of Greenville = 200 people move in/month

Now we can use this information to calculate the number of months until the populations are equal:

(70,000 - 61,000) / (-50 - 200) = (9,000) / (-250) = 36

It will take 36 months for the populations of Rock Hill and Greenville to be the same.

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The value of x = 10 and y = 8.

The method of elimination is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

Equation 1
-2y = 2 - 3x
-2y + 3x = 2
3x - 2y = 2 .....(1)


Equation 2
-5y = 10 - 5x
-5y + 5x = 10
5x - 5y = 10
Taking 5 common we get,
5(x - y) = 5(2)
x - y = 2 .....(2)

On multiplying equation (2) by 3, we get

3x - 3y = 6 .....(3)

Adding equation (1) and (3),
 
       3x - 2y = 2
       3x - 3y = 6
     _____________
                y = 8
       
Putting the value of y in equation (2) we get,
x - 8 = 2
x = 2 + 8
x = 10

So, the value of x = 10 and y = 8.

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As per the concept of line the vertex formula is used to find the vertex of a parabola is D = b² - 4ac.

The term line in math  a one-dimensional figure which has length but no width and it is made of a set of points which is extended in opposite directions infinitely here we have also know that it is determined by two points in a two-dimensional plane.

Here we need to identify the formula that can be used for vertex.

Here we know that the vertex formula helps to find the vertex coordinates of a parabola.

Here we have write the  standard form of a parabola is written as,

=> y = ax² + bx + c.

And the vertex form of the parabola is written as,

=> y = a(x - h)² + k.

And here we also know that there are two ways in which we can determine the vertex(h, k) is written as,

=> (h, k) = (-b/2a, -D/4a),

Here the  D refers discriminant

And the formula for D is written,

=> b² - 4ac

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If the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle.

Sidewalks must be at least 6.0 feet wide at the curb face or 5.0 feet wide if set back from the curb. The basic standards for people with impairments are not met by any width that is smaller. The social activity of walking.

500 feet must separate any two people in order for them to be able to stroll side by side. If the hypotenuse and one of the right triangle's sides equals the hypotenuse and the corresponding side of the second right-angled triangle, the two triangles are said to be congruent to one another.

The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. 

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The range is the set of possible outcome values, which are shown on the y-axis.

The range of a function directs to all the possible values y could be. The formula for finding the range of a function is y = f(x). It is a function of every x value that corresponds to only one y value.

To find the range of a function on a graph, draw (or plot) the domain (x) and range (y) coordinates on a piece of graph paper using small dots. This can assist you to see the shape of the function. You will notice a straight line, a curved line shaped like a "u" or "n", or something that looks like waves.

When making a graph, move left or right on the x-axis, depending on whether the x-coordinate is negative or positive. Then, move up or down on the y-axis, depending on whether the y-coordinate is positive or negative.

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The Gardener's rate per hour if he charged $450 for 9 hours is $50 per hour.

Number of days the Gardener worked = 5 days

Amount charged for 9 hours = $450

Fixed amount charged by the Gardener = $325

The gardener's rate per hour = Total amount charged for hours worked / Number of hours worked

= $450 / 9

= $50 per hour

Therefore, the Gardener charges $50 per hour

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A and D have the same rate of change, which is 0.5.

Generally, The term "rate of change" (ROC) refers to the rate at which something varies over a period of time.

Therefore, the size of individual changes is not as important as the pace at which they are occurring or the rate at which they are accelerating or decelerating.

When it comes to financing, understanding price returns and recognizing momentum in trends may both be accomplished via the usage of rate of change.

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A region in the first quadrant defined by the x-axis, the graph of x=y2+2, and the line x=4 is called R then the area of R be [tex]$-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$[/tex]

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. A parabola is a U-shaped curve that represents the graph of a quadratic function.

Students are able to fill in the gap between the mathematics they learn in class and the things they see in real life by drawing a comparison between the equation of a parabola and a shape found in the real world (the parabaloid). They can conceive difficult ideas that they might otherwise find repugnant by doing this.

Sketch the graph of [tex]$x=y^2+2$[/tex] by sketching the sideways parabola [tex]$x=y^2$[/tex] then adding 2 to the x coordinates (translate 2 to the right).

Add the x axis and the vertical line x = 4.

The area can be found by either

[tex]$\int_2^4 \sqrt{x-2} d x$$[/tex] or [tex]$\int_0^{\sqrt{2}}\left(4-\left(y^2+2\right)\right) d x$$[/tex]

[tex]$=\int_0^{\sqrt{2}}-x^2+2 d x$$[/tex]

Apply the Sum Rule: [tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]

[tex]$=-\int_0^{\sqrt{2}} x^2 d x+\int_0^{\sqrt{2}} 2 d x$$[/tex]

simplifying the equation, we get

[tex]$\int_0^{\sqrt{2}} x^2 d x=\frac{2 \sqrt{2}}{3}$$[/tex]

[tex]$\int_0^{\sqrt{2}} 2 d x=2 \sqrt{2}$$[/tex]

[tex]$=-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$[/tex]

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If UV = x and TW = x+99 ,using triangle proportional theorem, then the value of x is 99

Triangle proportion theorem states that if a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

since TU = TS and S W = VW. This show that triangle SUV is an isosceles triangle

then TW / UV = 1/2

therefore x/-x+99 = 1/2

2x = -x+99

Collect like terms

2x- x = 99

x= 99

therefore the value of x is 99

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Answer: 10.5 or 21/2

Step-by-step explanation:

I take it that thats division? well if so then that would be 63 divided by x (6) which is 10.5 or in fraction terms 21/2

RS = 80. The two legs of the trapezoid, SU and RV, have lengths of 80 each. This can be found by adding the lengths of UV (35) and QT (55).

Two of a trapezoid's four sides are parallel to one another.

Four angles, two non-parallel sides, and two sets of parallel sides make up this shape. It has two dimensions, four vertices, and four sides.

The bases of the trapezoid are the two parallel sides, while the other two sides are referred to as the legs.

Every time, the two bases are different lengths, and the same is true of the two legs. Rectangles, squares, and circles are just a few of the shapes that can have their areas calculated using trapezoids in geometry.

They are also employed to figure out the areas of various shapes, such as arcs and triangles.

To design structural elements like walls and foundations, trapezoids are also employed in engineering, architecture, and construction.

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Answer:

  82°

Step-by-step explanation:

You want the unmarked remote interior angle of a triangle, given that one of them is 61°, and the exterior angle opposite is 143°.

The exterior angle is the sum of the remote interior angles:

  143° = 61° +∠B

  ∠B = 143° -61° . . . . subtract 61°

  ∠B = 82°

__

Additional comment

In case you don't remember the remote interior angles theorem, you can get the same result using angle relations you do remember:

The interior angle at A is the supplement of the exterior angle:

  ∠A = 180° -143°

When ∠A is added to the other two interior angles, the total is 180°:

  ∠A +∠B +61° = 180°

  (180° -143°) +∠B +61° = 180° . . . . . . use the above expression for ∠A

Rearranging this to give the value of angle B, we have ...

  ∠B = 180° -180° +143° -61°

  ∠B = 143° -61° = 82° . . . . . . as above

Another way to get there is to consider ...

  The sum of ∠B and 61° is supplementary to interior angle A (their total is 180°). The exterior angle 143° is supplementary to interior angle A. Two angles supplementary to the same angle are equal, so the sum of ∠B and 61° is equal to the exterior angle 143°.

Before any taxes, deductions, and other adjustments, she earns $98.40 per week.

To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

You've provided that information:

Talia works 6 hours per day on Fridays and Saturdays each week.

Her pay rate is $8.20 per hour.

First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.

Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:

$8.20/hour x 12 hours/week = $98.40/week

So, Talia's gross pay for a week is $98.40.

Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.

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