Dan and Matt's ages add up to 56. Dan is 13 times older than Matt. How old are they?

The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-2 - (-11)]/[0 - (-3)]

(-2 + 11)/(0 + 3)

9/3

3

So, the slope point is obtained as m = 3.

The equation becomes - y =3x + b

To find the value of b substitute the values of x and y in the equation -

-11 = 3(-3) + b

-11 = -9 + b

b = -11 + 9

b = -2

So, the value for b is -2.

Now, the equation becomes -

y = 3x - 2

The graph is plotted for the function.

Therefore, the equation is y = y = 3x - 2.

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Answer:

in order from top row to bottom row

Step-by-step explanation:

There are five possibilities for whole numbers such that radical expression 4 ≤ √3 + √x ≤ 5: {6, 7, 8, 9, 10}

In this problem we have the case of a radical expression, from which we need to determine at least a whole number such that following inequality is fulfilled:

4 ≤ √3 + √x ≤ 5

This can be done by algebra properties. First, determine the limits of the inequality:

4 ≤ √3 + √x

4 - √3 ≤ √x

(4 - √3)² ≤ x

x ≥ (4 - √3)²

x ≥ 16 - 8√3 + 3

x ≥ 19 - 8√3

√3 + √x ≤ 5

√x ≤ 5 - √3

x ≤ (5 - √3)²

x ≤ 25 - 10√3 + 3

x ≤ 28 - 10√3

There are five possibilities for five whole numbers: 6, 7, 8, 9, 10

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The details which describe the free African American who lived in the South is that they were counted as part of population statistics which is denoted as option D.

This is referred to an an entire set of items from which you draw data for a statistical study while on the other hand, population refers to the people who live in a particular area at a specific time.

From the passage we were told that there was about 225,964 free African americans of which only 6 percent were free black people which made them less than those found in the North. They were counted during census which means that they were part of the population statistics.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with this problem. (see explanation)

Step-by-step explanation:

1. Repeating Decimal

2. Rational Number

This is all I can think of at the moment.

Answer: AAS → Makes the most sense

- They give two angles and a side for both triangles

Step-by-step explanation:

2:1 is the  new ratio of the number of Mimi’s Eminem cd’s to Rita’s.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

let Rita has X CDs.

Then Mimi has x-18 CDs.

x-18/x=5/8

8(x-18)=5x

Apply distributive property

8x-144=5x

Subtract 5x+144 on both sides

3x=144

Divide both sides by 3

x=48

Now Rita has 48-22= 26 CDs .

Mimi has 30+22= 52 CDs.

Required Ratio = 52:26 = 2:1

Hence, 2:1 is the  new ratio of the number of Mimi’s Eminem cd’s to Rita’s.

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The variables are x = 1/2 and y = 5/3

From the figure, we have been told 21x = 5x + 8. So let's solve for x.

21x = 5x + 8

21x - 5x = 8

16x = 8

x = 8/16

x = 1/2 = 0.5

Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:

(20y-2)/(17y + 3) = (5x+8)/(21x)

Substitute x = 0.5 and solve for y:

(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))

(20y-2)/(17y + 3) = (10.5)/(10.5)

(20y-2)/(17y + 3) = 1

20y-2 = 17y + 3

20y - 17y = 3 + 2

3y = 5

y = 5/3

Thus, the variables are x = 1/2 and y = 5/3

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The number of sides of a regular polygon with an interior angle that measures 150° is equal to 12 sides.

In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.

In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Where:

n represents the number of sides of a regular polygon.

Similarly, the number of sides of a regular polygon with a given interior angle can be calculated by using this mathematical expression:

Interior angles = 180 × (n - 2)/n

150° = 180(n - 2)/n

150n = 180n - 360

180n - 150n = 360

30n = 360

n = 360/30

n = 12 sides.

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The total number of visitors to the zoo that day=3980.

Given:

cost of each ticket for an adult=$25

cost of each ticket for an adult=$10

Total ticket sales one day=$47,750.

⇒$25+$10=47,750

⇒25+10=47,750-----(1)

Also,

c=6a+270

6a-c=-270------(2)

multiplying eq(2) with 10 we get:

60a-10c=-2700----(3)

Adding eq(1) and eq(3) we get

25a+10c=47,750

60a-10c=-2700

--------------------------

85a=45050

--------------------

To calculate a value just divide 45050 by 85 we get

a=45050/85

a=530

Now to get the value of c substitutes a value.

c=60(530)+270

c=3450

Number of Adult visitors=530

Number of children visitors=3450

Total Number of visitors=3980.

Therefore, the total number of visitors to the zoo that day=3980.

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The probability of drawing a king then getting an 1 is P = 0.006

First we need to find the probability of randomly drawing a king from the deck, that is equal to the quotient between the number of kings on a deck and the total number of cards on the deck.

There are 4 kings and 52 cards, thus the probability is:

p = 4/52

Then we want to get a 1, the probability is computed in the same way, notice that now there are 51 cards on the deck because we already drawn one.

q = 4/51

The joint probability (first drawing a king and then a 1) is equal to the product between the individual ones.

P = (4/52)*(4/51) = 0.006

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Answer: The answer is 7

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

Subtract 7 on each side to isolate X

7 + x = 14

-7         -7

x = 7

Aaron would make $73000 salary after 6 years. His salary after t years will be 52000 + 3500t. The solution has been obtained by using the linear expression.

What is a linear expression?

The expression with the highest degree of one is a linear expression. This demonstrates that there are no variables in a linear expression with an exponent bigger than one. Such an equation yields a straight line on the graph.

We are given that Aaron has just accepted a job at a new company where he will make an annual salary of $52000.

Also, for each year he stays with the company, he will be given a salary raise of $3500.

So, let's formulate a linear expression for the given situation.

The expression comes out to be

52000 + 3500t, where t denotes the number of years

Salary after 6 years will be

⇒52000 + 3500(6)

⇒52000 + 21000

⇒$73000

Hence, Aaron would make $73000 salary after 6 years and his salary after t years will be 52000 + 3500t.

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To evaluate the expression 1+(-2/3)-(-m) where m = 9/2, we need to substitute the value of m into the expression and simplify it.

What is a mathematical expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

1+(-2/3)-(-m)

1+(-2/3)-(-9/2)

Here, we have to simplify the inner expressions first,

-9/2 can be simplified to -4.5

1+(-2/3)-(-4.5)

Next, we add and subtract the terms:

1-2/3+4.5

Now, we simplify -2/3 by multiplying both numerator and denominator by -1:

1+4/3+4.5

Now, we add the fractions,

1+4/3+4.5

7/3+4.5

Finally, we get the value of the expression as

7/3+4.5 = 4.5 + 7/3 = 25/3.

So the final value of the expression 1+(-2/3)-(-m) where m=9/2 is 25/3.

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The range of h include the following: A. -4 ≤ h(x) ≤ 6.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Generally speaking, 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.

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

Range = [-4, 6]

In mathematical notation, the range of this graph can be rewritten as -4 ≤ h(x) ≤ 6.

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Answer:

  9.  reduction, 1/2

  10.  enlargement, 3/2

  11.  enlargement, 3

  12.  reduction, 1/3

Step-by-step explanation:

You want to know whether the dilations shown are reduction or enlargement.

Dilation

If the image (figure B) is larger, the dilation is an enlargement. (10, 11)

If the image (figure B) is smaller, the dilation is a reduction. (9, 12)

The scale factor is the ratio of a length on the image to the corresponding length on the original figure. It will also be the ratio of distances from the center of dilation (the origin) of corresponding points.

The ratio of line lengths B/A is 3/6, a reduction by a factor of 1/2.

The ratio of distances from the origin on the x-axis is 3/2, an enlargement by a factor of 3/2.

The ratio of distances from the origin on the x-axis is 6/2, an enlargement by a factor of 3.

The ratio of distances from the origin on the x-axis is 2/6, a reduction by a factor of 1/3.

The figures in the triangle represent the coefficients of the terms on the right side of a binomial equation.

Binomial Theorem: The expansion grows complex and time-consuming to calculate as the power rises. The Binomial Theorem can be used to quickly calculate a binomial statement that has been raised to a very high power. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.

An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem.

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the total FBT liability for this benefit is $329 ($700 x 47% = $329).

Fringe Benefits Tax (FBT) is imposed by the Australian Taxation Office (ATO) on certain non-cash benefits provided to employees. If a company provides a weekend stay in Sydney valued at $1,000 as a Christmas gift in December 2022, the FBT liability is calculated as follows:

The taxable value of the benefit is calculated by deducting the expenses that are not subject to FBT, i.e. $300 (flight) from the total value of the gift, i.e. $1,000. This leaves a taxable value of $700 ($1,000 - $300 = $700).

The FBT liability is then calculated by multiplying the taxable value, i.e. $700, by the FBT rate which is currently 47% (as of 2021). This results in an FBT liability of $329.

Therefore, the total FBT liability for this benefit is $329 ($700 x 47% = $329).

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After setting f (x) = 0, solve for to determine the intercept(s) of. Set y = f(0) and then find to determine the intercept of. Choose test points to establish the sign of each interval on the axis after using the intercept(s) to divide it into intervals. Determine the test points.

The Use of Zeros When Graphing Polynomials

You may graph a polynomial function using the steps below.

To assess how the graph will behave at its finish, use the leading-term test.

Choose the x− capture(s) of f(x) by putting f(x)=0 and then figuring up a solution for x .

Choose the y− a snare in f(x) by putting y=f(0) and discovering y.

Use the x− dividing intercept(s) x−

Divide the axis into intervals and then select test points to ascertain the sign of f(x) per interval.

the test points on a map.

To identify the general form of the graph, locate additional points as necessary.

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The Area of the circle, A is 530.66 inch.

An area of a circle is the amount of two-dimensional space within the boundaries of the circle. It is the region enclosed by a circle's circumference. The area of a circle can be found by using the formula A = πr2, where A denotes the area of the circle, r represents its radius, and π is equal to 3.1416. The radius of a circle is the distance from its center to its circumference. It can also be found by dividing the circumference by 2π.

Given,

Diameter, d = 26 inch

Radius, r = d/2 = 26/2 = 13 inch

π = 3.14 or 22/7

We apply all these above values in the formula, we get area of circle:

A = πr²

A = 3.14 x (13)²

A = 530.66 inch

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The solution for the system of inequalities is (-0.43,4.15).

What is an inequality?

An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions. A symbol of inequality has non-equal expressions on both sides.

We are given a graph on which two inequalities are plotted

First, we need to frame the equations from the points.

For the blue line, we have points (0,2) and (-1,7)

So, using slope-intercept form, we get the equation as

y+5x>2

For the red line, we have points (0,4) and (3,3)

So, using slope-intercept form, we get the equation as

y+0.33x >4

Now, in order to find the solution, we will subtract both the equations

On subtracting, we get

⇒(y+5x) - (y+0.33x) = 2 - 4

⇒y+5x - y-0.33x = -2

⇒4.67x = -2

⇒x = -0.43

Substituting this value in the equation, we get

⇒y+5(-0.43) = 2

⇒y-2.15 = 2

⇒y = 4.15

Hence, the solution for the system of inequalities is (-0.43,4.15).

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Time in GMT is 5:14:20 P.M (GMT)

Eastern Daylight Saving Time is four hours behind GMT (Greenwich Mean Time).

The time on the Earth's meridian, or zero-degree line of longitude, is known as Greenwich Mean Time (GMT). This passes via the Old Royal Observatory in the London district of Greenwich on its way from the North Pole to the South Pole.

This is,

Eastern Standard Time is equal to Greenwich Mean Time plus four.

Therefore,

1:14:20 p.m. EDT (Eastern Daylight) will be equivalent to;

1:14:20 p.m + 4 hours (GMT)

5:14:20 P.M (GMT)

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Answer: 59

Step-by-step explanation:

(13 + 9) + 37

13 + 9 = 22

22 + 37

59

The domain of the function graphed in this problem is given as follows:

{x | x ≥  -4}.

The domain of a function is the set composed by all the input values that the function accepts.

On the graph, the domain of the function is given by the values of x.

From the graph of the function, the function has a closed interval at x = -4, and is defined for all the values for the right of that, that is, greater than -4, hence the notation for the domain is given as follows:

{x | x ≥  -4}.

Meaning that the correct option is given by the second option.

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The value of the variable, h is 60 degrees

The properties of a trapezium are expressed as;

If the size of the angles of the trapezium are 2h, 2h, h and h

Then, it is represented as;

Add all the angles

2h + 2h + h + h

Equate the angles to the sum of the interior angles of a trapezium, we get

2h + 2h + h + h  = 360

Now, add the like terms

6h = 260

Divide both sides by the coefficient of h, we get;

6h/6 = 630/6

h = 60 degrees

Hence, the value is 60 degrees

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The length of a  rectangular rug is 84 yards and the width is 36 yards

Let 'l' represents the length of the  rectangular rug and 'w' represents the width of a  rectangular rug.

The length of the rug is 12 yards more than two times the width.

So, we get an equation,

l = 12 + 2w

Also, a  perimeter of  a rectangular rug is 240 yards

We know that the formula for the perimeter of rectangle:

P = 2(w + l)

Using this formula the  perimeter of  a rectangular rug would be,

P = 2 × [w + (12 + 2w)]

240 = 2 (12 + 3w)

120 = 12 + 3w

108 = 3w

w = 118/3

w = 36

And the length would be,

l = 2 + 2( 36)

l = 84 yards

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The complete question is:

A rectangular rug has perimeter 240 yards. The length is 12 yards more than twice the width. Find the length and width of the rug.

The volume of the solid is approximately 32π/3 cubic units.

The volume of the solid obtained by rotating the region bounded by the curves y = 4 - 1/2x, y = 0, x = 0, and x = 1 about the x-axis can be found using the method of disks/washers. The formula for the volume is given by:

V = π * ∫[a,b] (R^2 - r^2) dx

where R is the outer radius (4 - 1/2x), r is the inner radius (y = 0), a and b are the limits of x (x = 0 and x = 1), and dx represents a small slice of the solid.

Evaluating the definite integral:

V = π * ∫[0,1] (16 - x^2 - x^2) dx = π * ∫[0,1] (16 - 2x^2) dx = π * (16x - 4/3 x^3) evaluated at x = 1 - x = 0 = π * (16 - 4/3) = 32π/3 cubic units.

So the volume of the solid is approximately 32π/3 cubic units.

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In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.

It should be noted that there are two tables which give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye.

Green #1 is made by mixing blue and yellow in a ratio of 2 : 3.

Green #2 is made by mixing blue and yellow in a ratio of 1 : 2.

The first one has 2 parts of blue at 3 parts of yellow. In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2.

In grade two the blue part is half of the yellow part. This means that green #1 is bluer shade of green than Green # 2.

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If the size length of a square is 5x-7 and the perimeter is 125, then the value of x is 7.65 units.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The length of the square is given as a = (5x - 7) units

The formula for the perimeter of square is -

P = 4a

The value for perimeter of the square is 125 units.

Substitute the values in the equation -

P = 4a

125 = 4(5x - 7)

125 = 20x - 28

20x = 125 + 28

20x = 153

x = 153/20

x = 7.65

Therefore, the value of x is obtained as 7.65 units.

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