Find the sum:
1
6
+ √6 =

[tex]f(x) = \sqrt{x}[/tex] could be transformed to [tex]g(x) = \sqrt{x + 7}[/tex] responses horizontal shift of 7 units left.

What if graph transformation?

Graph transformation, often known as graph rewriting, is the process of algorithmically constructing a new graph from an original graph. It has several uses, including software engineering, layout algorithms, and image production.

Consider, the given equation of graph

[tex]f(x) = \sqrt{x}[/tex]

The graph becomes,  [tex]g(x) = \sqrt{x + 7}[/tex].

The constant value remains unchanged. As a result, the graph will not move vertically. The graph shifts in the horizontal direction as a unit's variable changes.

Therefore, the transformation of graph is, horizontal shift of 7 units left.

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On a given map each unit represnts= 100 miles

Given that the airports are located at coordinates p(1,17) and q(12,10) in this puzzle, the distance between them is given by: Since 100 miles are represented by each unit, the distance in miles is calculated as follows: D = 13.03 x 100 = 1303 miles.

Therefore the distance to the nearest whole mile between the two airports= 1303 miles.

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a) An equation to describe the relationship between time and the number of restaurants in the United States, with 2012 as the base, is Y = 980 + 16.5x.

b) Using this equation, we can predict that the number of restaurants in 2018 will be 1,079 thousand.

An equation is a mathematical statement or function claiming that two mathematical expressions that may combine numbers, variables, and constants are equal or equivalent.

Equations are depicted with the equation symbol (=) to establish the equality of expressions.

The number of thousands of restaurants in the United States:

2012 = 980

2016 = 1,046

4 years (2016 - 2012) = 66 more restaurants (1,046 - 980)

In 1 year = 16.5 more restaurants (66/4)

(0, 980) and (4, 1,046)

Y = 980 + 16.5x

Where Y = the number of thousands of restaurants in the year

x = the number of years past.

In 2018, the number of restaurants, Y = 980 + 16.5x

The number of years between 2018 and 2012 = 6 years

The expected number of restaurants Y = 980 + 16.5(6)

= 1,079.

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Answer:

20

Step-by-step explanation:

Let x = number of members.

Let y = number of chairs.

75% of x = 5/6 of y

3x/4 = 5y/6

x/y = 5/6 × 4/3

x/y = 20/18

x/y = 10/9

The ratio of members to chairs is 10/9.

We need the smallest numbers in the ratio of 10/9 for which 75% of the first number and 5/6 of the second number are whole numbers.

Try 10:9; 75% of 10 = 7.5; not a whole number

Try 20/18; 75% of 20 = 15; 5/6 of 18 =  15 both whole number. This is the answer.

Answer: 20

The smallest possible number of people in the club is 20

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x = number of members.

Let y = number of chairs.

Therefore,

75% of x = 5/6 of y

3x/4 = 5y/6

x/y = 5/6 × 4/3

x/y = 20/18

x/y = 10/9

The ratio of members to chairs is; 10/9.

We want the smallest numbers in the ratio of 10/9 for which 75% of the first number and 5/6 of the second number are whole numbers.

10:9;

75% of 10 = 7.5; not a whole number

20/18;

75% of 20 = 15;

5/6 of 18 =  15 both whole number.

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The volume of the entire shape, given that the figure is a solid shape, and the unit cubes, is d. 32 cubic units.

The volume for the shape can be found by the formula:

= Length  Width x Height

Each small cube is a unit cube which means that the measurements of the dimensions are:

Length = 4 units because there are 4 unit cubs along the length

Width = 4 units for the same reason

Height = 2 units because there are 2 unit cubes needed to get the height

The volume would therefore be:

= 4 x 4 x 2

= 32 cube units

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The interval notation of the inequality 6<x<7 is:

(6,7)

Given the inequality is:

6<x<7

the interval notation is:

(6,7)

The leftmost number of the set, a comma, and the rightmost number of the set are written using interval notation. Depending on whether those two integers are part of the set, we either place parentheses around the pair or square brackets around it (sometimes we use one parenthesis and one bracket!).

Hence we get the required interval notation.

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Answer:

proportional, unite rate = 3

Step-by-step explanation:

15 : 5 = 3

24 : 8 = 3

The cost function, C(x) = x² - 20·x + 340, where x is the units sold, indicates;

The person should sell 10 units of tacos to minimize the costs. The minimum cost is $240

A function is the definition of the relationship between the input and output variables of an ordered pair, such that each input has one output.

The daily cost function for the sale of Tacos is, C(x) = x² - 20·x + 340

Where;

C(x) = The cost of selling x tacos

x = The number of units of tacos sold

The function in the question is a quadratic function and the positive coefficient of x² indicates that the graph of the function which is a parabola, is concave upwards.

The vertex of the parabola, of the equation, f(x) = a·x² + b·x + c,  is at the point where, x = b²/(2·a)

Comparison with the equation, C(x) = x² - 20·x + 340, indicates that we have;

a = 1

b = -20

c = 340

The x-coordinate of the vertex, which is the minimum point of a concave up parabola is; x = (20)/(2×1) = 10

The number of units sold that yields minimum cost is; x = 10

The number of units the person should sell to minimize the cost is 10.

The minimum cost is therefore;

C(10) = 10² - 20 × 10 + 340 = 240

The minimum cost is $240

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Answer:

Federalism

Step-by-step explanation:

refers to the division and sharing of power between the national and state governments.

17.16 is the estimated 22% of 78.

What is estimation?

To make calculations simpler and more realistic, estimation of a number refers to a plausible assumption of the actual value.

Estimation is the process of approximating a quantity with the necessary accuracy.

The result is quickly and roughly determined by rounding off the numbers used in the calculation.

Assumedly, 22% of 78.

78 comes out to 80.

Therefore, cut 22% to 1/5.

78 through 80 is increased.

80/5 = 16( close to 17.16) ( approximate to 17.16)

Or

22% = 22/100

22% of 78 = 22 × 78 /100 = 1716/100

= 17.16.

As a result, 17.16 is the estimated 22% of 78.

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The average, the median, and the range of the given data are 75, 75.7, and 25.3, respectively.

We are given the weights of five people that go to the gymnasium to exercise. The weights are 58 kg, 75 kg, 83.3 kg, 83 kg, and 75.7 kg. The average is found by dividing the sum of all the weights by the number of persons.

A = (58 + 75 + 83.3 + 83 + 75.7)/5 = 375/5 = 75

Hence, the average weight is 75 kg. The median weight is the center value when all the weights are arranged in ascending or descending order. The weights arranged in the ascending order are 58 < 75 < 75.7 < 83 < 83.3. The third weight lies in the center. Hence, the median weight is 75.7 kg. The range of the data is the difference between the maximum and the minimum weight. The maximum and minimum weights are 83.3 kg and 58 kg, respectively.

R = 83.3 - 58 = 25.3

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The point-slope form of the equation is y - 2 = -(x + 2)

From the graph, we have the following points

(-2, 2) and (2, -2)

Start by calculating the slope of the points

This is calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

This can be rewritten as

m = (y₂ - y₁)/(x₂ - x₁)

Where

slope = m

(x, y) = (-2, 2) and (2, -2)

So, we have

m = (-2 - 2)/(2 + 2)

Evaluate the expression

m = -1

From the question, we understand that:

(x₁, y₁) = (-2, 2)

The equation of the line is then calculated as

y - y₁ = m(x - x₁)

Substitute the known values in the above equation, so, we have the following representation

y - 2 = -1(x + 2)

Evaluate

y - 2 = -(x + 2)

Hence, the equation of the line is y - 2 = -(x + 2)

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The cost for each pound of chocolate chips and each pound of walnuts is: $1.25 and $9.75

Given,A store is having a sale on chocolate chips and walnuts.

For 3 pounds of chocolate chips and 5 pounds of walnuts, the total cost is 18.00 .

For 12 pounds of chocolate chips and 2 pounds of walnuts, the total cost is 45.

we are asked to determine the cost for each pound of chocolate chips and each pound of walnuts.

let x=cost/lb of walnuts

let y=cost/lb of chocolate chips

we frame the equations as:

3x+5y=16

6x+2y=22

Multiply eq 1 by 2.

we get:

6x+10y=32

6x+2y  = 22

subtract now,

8y = 10

y = 10/8

y=1.25

x = x=16-5y=9.75

cost/lb of walnuts=$1.25

cost/lb of chocolate chips=$9.75

Hence we get the required cost.

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The function [tex]24x^{3}[/tex] + [tex]Ax^{2}[/tex] -3x + B results to the equation A + 4B = 114 hen f(x) is divided by (2x - 1) and with a remainder 30.

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

For example, 10 is not exactly divided by 3. Since the closest value, we can get 3 x 3 = 9.

Hence, 10 ÷ 3 → 3 R 1, where 3 is the quotient and 1 is the remainder.

if ( 2x - 1) divides  [tex]24x^{3}[/tex] + [tex]Ax^{2}[/tex] -3x + B with a remainder 30, it means if x = 1/2 when substituted should give 30.

The substitute x = 1/2 into the given function and equate it to 30

24[tex](\frac{1}{2}) ^{3}[/tex] + A[tex](\frac{1}{2}) ^{2}[/tex] - 3(1/2) + B = 30

24[tex](\frac{1}{8})[/tex] + A[tex](\frac{1}{4})[/tex] - 3/2 + B = 30

3 + A/4 -3/2 + B = 30

multiply through by 4

12 + A -6 + 4B = 120

keeping A + 4B at the left we have

A + 4B = 120 -12 + 6

A + 4B = 114

Proved

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Answer: C

Because X is less than or equal to 11 the number line can include 11 and because its less than the arrow should be decreasing or going towards negative infinity

The total cost per yard is $4

How do we calculate the total cost?

The average total cost formula shows the cost per unit of the quantity produced and is calculated by taking two figures where the first one is total production cost and the second one is the quantity produced in numbers and then the total cost of production is divided by the total quantity produced in numbers.

Average Total Cost = Total Cost of Production / Quantity of Units Produced

Given,

Gloria bought fabric which is = 6 3/4 yards or 27 / 4 yards

Total cost was = $27

Cost per yard is = 27 / (27/4)

                           = $4 per yard

Therefore, the total cost per yard is $4

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Answer:

y+2>y

Step-by-step explanation:

Well, first of all. Adding any sum to y makes it greater then the same variable.

Greater than sign is >. Keeping that in mind now add them. y+2>y is gonna be you’re final answer!

Answer: 40 $

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

Since the discount is 25% off the original price, and 100% - 25% = 75%, then the sale price of $30 is 75% of the original price.

75% of x = $30

0.75x = 30

x = 30/0.75 = 30/(3/4)

x = 30 × 4/3

x = 40

Answer: $40

The value of angles in triangle are ,

1) x=60°.

2) y = 15°.

3) Angle of C=45°

4) Angle of DBC=  105°.

5)Angle of CBA = 75°

What is triangle ?

 Three-sided polygons with three sides are known as triangles, however this term is not particularly common. Every triangle has three sides and three angles, some of which might be the same. Having three sides and three vertices, a triangle is a polygon. There is a 180 degree angle created inside the triangle. This indicates that a triangle's interior angles add up to 180°. Having the fewest sides of all polygons, it is that.

Here the given diagram DA is the straight line.

In straight line angle at any point is 180°. then

=>7y°+5y°=180°

=> 12y = 180

=> y = 180/12

=> y = 15°.

Then angle of DBC = 7y= 7*15 = 105°.

Now angle of CBA = 5y = 5*15 =75°.

And angle C = 3y=3*15=45°.

Now consider the triangle ABC , we know that sum of all angles in triangle is add upto 180°.

=> ∠A+∠B+∠C=180°

=> x+75+45=180

=> x= 180 - 120

=> x = 60°.

There fore the value of angles in triangle are ,

1) x=60°.

2) y = 15°.

3) Angle of C=45°

4) Angle of DBC=  105°.

5)Angle of CBA = 75°

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The answer for a measure of ∠P = 72.92° using congruence of the triangle.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

As given ∠P = ∠Q and ∠R=34.15

We know that sum of all angles in a triangle = 180 °

So 2∠P + ∠Q = 180

2∠P = 180-34.15 = 145.85

∠P = 72.92

So the measure of ∠P is 72.92°

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Answer:

9.75

Step-by-step explanation:

[tex](-2)^{4}[/tex] - [tex]2.5^{2}[/tex]  Means

(-2)(-2)(-2)(-2) - (2.5)(2.5)

16 - 6.25

9.75

Answer:

R = 4.47

Step-by-step explanation:

Simply just R = sqrt(20)

Value of n is 3 when a line that includes the points (n, -9) and (5, 7) has a slope of 8.

A line's steepness is indicated by its slope. Any line's slope is constant along its length. The direction of the line on the coordinate plane can also be determined by the slope. A line's graph can be used to determine slope, or the coordinates of any two points on a line can be used.

Given,

Slope = 8

Points = (n,-9) and (5,7)

Formula:

Slope = y₂ - y₁/ x₂ - x₁

8 = 7 -(-9)/ 5-n

Cross multiplying,

8(5 - n) = 7 +9

(5-n) = 16/8

5 -n = 2

n = 3

Value of n is 3 when a line that includes the points (n, -9) and (5, 7) has a slope of 8.

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The triangle WXY an isosceles obtuse triangle and ∠WXY is an obtuse angle

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

The three types of Isosceles Triangles are :

Given data ,

Triangle WXY with vertices

W ( -10 , 4) , X ( -3 , -1 ) and Y ( -5 , 11 )

From the coordinates , we can see that

Now ,

When two points are given P( x₁ , y₁ ) and Q( x₂ , y₂ ) , the distance between the two points is given by distance formula

D = √( x₂ - x₁)² + ( y₂ - y₁)²

So , length of WX = √( -3 - (-10) )² + ( -1 - 4 )²

WX = √( 49 + 25 )

WX = √74

WX ≈ 8.60

So , Length of WX = 8.6 units

And , Length of XY is given by

XY = √ ( -5 - (-3) )² + ( 11 - (-1) )²

XY = √ ( 4 + 144 )

XY = √ 148

XY ≈ 12.16

So , length of XY = 12.2 units

And , Length of YW is given by

YW = √( -5 - (-10) )² + ( 11 - 4 )²

YW = √( 25 + 49 )

YW = √74

YW ≈ 8.60

So , length of YW is 8.6 units

So , WX = YW

Since , the length of WX and YW are the same , we have 2 sides with equal length and therefore the triangle WXY is an isosceles triangle

And the ∠WXY can be obtuse because of the two equal sides and the base is of larger length and hence the triangle WXY is an Isosceles obtuse triangle

An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90° and 180°), and the other two acute angles are equal in measurement.

Hence , The triangle WXY an isosceles obtuse triangle and ∠WXY is an obtuse angle

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Answer:

Do 2007-1979

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

The rate of change  radius of the balloon increasing  when the radius is 2 meters is 0.15  meters per minute.

A spherical balloon is being inflated with hot air at a rate

= 8 cubic meters per minute.

volume of a spherical balloon is :

[tex]volume = \frac{4}{3}\pi r^3[/tex]

rate of change of volume is given as :

dv/dt = (4/3) π 3 r² (dr/dt)

8 =  4πr²(dr/dt)

(dr/dt) = 8 / 4πr²

(dr/dt) = 8 / ( 4 x 3.14 x 2 x 2)

(dr/dt) = 0.15 Meter/mint

The rate of change  radius of the balloon increasing  when the radius is 2 meters is 0.15  meters per minute.

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The height of Liberty School  in ordinary form is 8850 m and of Festus school is 5890 m , the difference of the height values is 2960 m.

In the question ,

it is given that the height of the Liberty  school is 8.85 × 10³ m.

we have to convert this height in the ordinary form ,

8.85 × 10³ = (885/100) × 1000

= 885 × 10

= 8850 m

The height of the Festus school is 5.89 × 10³ m

in ordinary form it is

= 5.89 × 10³

= (589/100) × 1000

= 589 × 10

= 5890 m

The difference in the height of the school = height of liberty school - height of Festus school .

difference = 8850 - 5890

= 2960 m

Therefore , the height of liberty school is 8850 m and height of Festus school is 5890 m, the difference of the height values is 2960 m.

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We can cut 4 4/15 pieces from 5 1/3 inches candy bar if the length of each candy is 1 1/4 inch.

Length of candy bar is 5 1/3 which can be written as 16/3 in

Length of piece that is to be cut from long candy bar is 1 1/4 or 5/4 in

Number of pieces

= length of piece/ total length of candy bar

=  (16/3) / (5/4)

= 16/3 × 4/5

= 64/15

= 4 4/15 pieces

4 4/15 number of pieces can be cut from 5 1/3 inches long candy bar

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In the picture we can see the histogram of the data.

1 2/3, 2 and 3 1/3 lies in between [0,4] so, 3 number.

6 2/3, 7 5/6, 5 1/3, 5 1/2 and 6 1/6, lies in between [4,8] so, 5 number.

10 lies in between [8,12] so, 1 number.

Given that,

For her birthday, Teresa received a fantastic time machine. Each of the nine times she utilized the time machine is indicated by the number of years she travelled back in time.

We have to draw a histogram.

We can see in the table.

6 2/3, 7 5/6, 10, 5 1/3, 5 1/2, 6 1/6, 1 2/3, 2 and 3 1/3.

20/3, 47/6, 10, 16/3, 11/2, 37/6, 5/3, 2 and 10/3

6.6, 7.8, 10, 5.3, 5.5, 6.1, 1.6, 2 and 3.3

So,

1.6, 2 and 3.3 lies in between [0,4].

6.6, 7.8, 5.3, 5.5, 6.1 and 1.6 lies in between [4,8].

10 lies in between [8,12].

Therefore, In the picture we can see the histogram of the data.

1 2/3, 2 and 3 1/3 lies in between [0,4] so, 3 number.

6 2/3, 7 5/6, 5 1/3, 5 1/2 and 6 1/6, lies in between [4,8] so, 5 number.

10 lies in between [8,12] so, 1 number.

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The gross income of each month will be 2500/month and 30,000/year. And the net income will be 1850/month and 22,200/year.

We got 30000 a year to budget our expenses.

And the year has 12 months.

So, our monthly gross income will be 30,000/12

= 2500

Now, the tax rate is 15%

So, the tax will be,

=2500×15/100

=2500×.0.15

=375/month

And our insurance is 200 a month

Now,

we put 3% of our income for our retirement every month

so, the retirement fund will be

=2500×3/100

=2500×0.03

=75

Therefore,

The net income will be

=2500-375-200-75

=2500-650

=1850

Hence, our gross income will be 2500/month and 30000/year

And our net income will be 1850/month and 22,200/year

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