Are these two equal ?
Can we make -x/x+1 to x/-(x+1) and becomes x/-x-1​

Step-by-step explanation:

Let the consecutive positive integer be x , x+1

now, we know that there product is less then 10000

so, x(x+1) = 10000

x² + x - 10000 = 0

On solving the quadractic equation,

we get the roots = (-100.50124999219 ), (99.501249992188)

since we are asked for less then 10000 we can approximate the answer to x = 99.5

Answer:

99.5

Step-by-step explanation:

Let the consecutive positive integer be n , n+1

now, we know that there product is less then 10000

so, n(n+1) = 10000

So, the question asked " Less than 10,000 " so, we get the roots = (-100.50124999219 ), (99.501249992188)

n² + n - 10000 = 0

Let's solve this equation together!

n approximate number is 99.5.

[tex]x=57^{\circ}[/tex] (alternate segment theorem)

[tex]y=67^{\circ}[/tex] (alternate segment theorem)

The sum of the first ten prime numbers is 129.

The prime numbers are those numbers that have only one factor namely 1 and the number itself.

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Their sum is

2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

= 129

Hence, the sum of the first ten prime numbers is 129.

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Answer:

$1150 will be the weekly wage

Step-by-step explanation:

184 = 16%*x

184 = 0.16*x

184/0.16 = x

x = $1150

Here, "x" is her weekly wage.

Answer:

Step-by-step explanation:

Comment

Find the number of square yards

Area = L * w

L = 2

w = 1

Area = 2 * 1

Area = 2

Now for the counter top

1 sq yard costs 204.63

2 sq yards cost 2 * 204.63

2 sq yards cost 409.26

Answer: 409.26

Answer:

in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D . We know that the sum of the angles of a quadrilateral is 360o. Hence, ABCD is a parallelogram.

Answer:

arc TBU = 268°

Step-by-step explanation:

the measure of the tangent- chord angle TUV is half the measure of its intercepted arc UT , then

UT = 2 × 46° = 92°

the sum of the arcs in a circle = 360° , that is

TBU + UT = 360°

TBU + 92° = 360° ( subtract 92° from both sides )

TBU = 268°

The pattern in the values as the exponents increase is multiply the previous value by 2.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

Powers of 2      Values

[tex]2^{-5}[/tex]                         1/32

[tex]2^{-4}[/tex]                           1/16

[tex]2^{-3}[/tex]                           1/8

[tex]2^{-2}[/tex]                           1/4

[tex]2^{-1}[/tex]                           1/2

As, from the given data we can see that negative powers of 2 reducing by 1.

as, 2^-5 * 2= 2^-4

Hence, multiply the previous value by 2 to obtain the next value.

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Answer:

The runner in first place is 16 meters ahead of the runner in last place

Step-by-step explanation:

There are 4 boys racing - Pete, Nick, Manny, and Oliver.

Pete is 11 meters ahead of Nick, Oliver is 10 meters ahead of Manny, and Oliver is ahead of Pete by 5 meters.

This means Oliver is ahead of the other three racers, putting him in first place, and Manny is between Nick and Pete.

So in order to find out the distance between the racer in first place (Oliver) and the racer in last place (Nick), add the distance between Oliver and Pete and the distance between Pete and Nick.

Add the distances: 5 + 11

Therefore, the runner in first place (Oliver) is 16 meters ahead of the runner in last place (Nick).

Answer:

3

Step-by-step explanation:

Answer:

table A

Step-by-step explanation:

A direct variation can be expressed as: [tex]\frac{y}{x}=k[/tex]. The y/x is equal to a constant value k. Multiply both sides by x you get: [tex]y=kx[/tex]. So as x increases by 1, y increases by some constant value. So to find which one will create a direct variation, see which of the tables has a constant y/x

Table A:
   7/2 = 3.5

   14/4 =3.5

   17.5/5=3.5

   21/6 = 3.5

   this has a constant y/x so it is a direct variation

Table B:

   7/2 = 3.5

   14/4 = 3.5

   21 / 5 = 4.2

   this is not a direct variation, it doesn't have a constant y/x

table C:

   7 / 2 = 3.5

   14 / 4 = 3.5

   15/5 = 3

   This is not a direct variation, it doesn't have a constant y/x

table d:
   7/2 = 3.5

   14/4 =3.5

   17/5=3.4

   This is not a direction variation, it doesn't have a constant y/x

Answer:

a.

Step-by-step explanation:

a= y-k/ (x-h)^2

Since intersection means the element in set A that are also in set B, hence (A ∩ B) = {3, 7}

Sets are arrangements of elements in a specific order. Given the following sets.

A = {1, 3, 7, 8, 11}

B = {2, 3, 6, 7, 12}

Determine the intersection of A and B

Since intersection means the element in set A that are also in set B, hence;

(A ∩ B) = {3, 7}

Hence the elements of (A ∩ B) is {3, 7}

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Answer:

D) (3,7)

Step-by-step explanation:

P(AnB) mean intersection, which is (3,7)

P(AUB) mean Union

However. if the question was asking this "What are the elements of P(AUB) then the answer would be A) {1, 2, 3, 6, 7, 8, 11, 12}.

But the question was asking for P(AnB) which is D) (3,7)

The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .

The formula for the volume of the cylinder v = [tex]\pi[/tex][tex]r^{2}[/tex]h, To find the maximum volume of the cylinder we apply the condition of maxima  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]

                                                        [tex]5000[/tex] = [tex]2\pi r^{2} +2\pi rh[/tex]

                                                             [tex]h[/tex] =   [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex] .............(1)

Volume of the cylinder v = [tex]\pi r^{2} h[/tex]

Substitute the value of [tex]h[/tex] in the above equation

[tex]\Rightarrow[/tex]                                       = [tex]\pi r^{2}[/tex] × [tex]\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ][/tex]

[tex]\Rightarrow[/tex]                                      = [tex]\frac{r}{2}[/tex] ×  [tex](5000-2\pi r^{2} )[/tex]

[tex]\Rightarrow[/tex]                                    v = [tex]2500r-\pi r^{3}[/tex] ..............(2)

Now, for the maximum volume of the cylinder  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0

[tex]\Rightarrow[/tex]                                                            [tex]\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0[/tex]

[tex]\Rightarrow[/tex]                                                                      [tex]3\pi r^{2} = 2500[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r^{2} = \frac{2500}{3\pi }[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]

Volume is maximum for  [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]  

Then, v = [tex]2500r-\pi r^{3}[/tex]

[tex]\Rightarrow[/tex]              =  [tex]2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}[/tex]                              

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } }[/tex]×[tex]\frac{2}{3}[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{250000}{3\sqrt{3\pi } }[/tex]                                                              

[tex]\Rightarrow[/tex]          v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .                                                

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4 and 8 will equal the same since they are corresponding angles

So since 8 and 7 make a line they equal 180

180= 132+"7

Subtract both sides by 132

48=angle 7.



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Answer:

[tex]\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }[/tex]

Step-by-step explanation:

We can break the problem into three parts,

tan45 = sin(45)/cos(45)=[tex]\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1[/tex]

[tex]tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2[/tex]

[tex]tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}[/tex]

Then, [tex]tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3[/tex]

Therefore, the solution is sqrt(3)/3

The price of flowers in September exists $1.25.

Total money released in October = $420.

The class gained more money in September and they gained $30 better than in October.

Part A

Let the cost of flowers in September be x, then

(100 + 20)/100 [tex]*[/tex] x = $1.50

120/100 [tex]*[/tex] x = $1.50

1.2x = $1.50

x = $1.50/1.2 = $1.25

The price of flowers in September exists $1.25

Part B

Total money released in September = $1.25 [tex]*[/tex] 900 = $1,125

40% earned = 0.4 [tex]*[/tex] $1,125 = $450

Total money released in October = $1.50 [tex]*[/tex] 700 = $1,050

40% earned = 0.4 [tex]*[/tex] $1,050 = $420

The class gained more money in September and they gained $30 better than in October.

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The percentages for each acid are:

Here we just need to use the given formula:

[tex]percent\ disolved = \frac{initial\ mass - \ final \ mass}{initial \ mass}*100 \%[/tex]

For the 0% acid, the initial and final mass are the same:

initial mass = final mass = 10.3g

Then the percent dissolved is:

[tex]percent\ disolved = \frac{10.3g - 10.3g}{10.3g}*100 \% = 0 \%[/tex]

For the 33% acid we have:

Then:

[tex]percent\ disolved = \frac{10.1g - 10g}{10.1g}*100 \% = 1 \%[/tex]

For the 66% acid:

[tex]percent\ disolved = \frac{10g - 9.8g}{10g}*100 \% = 2 \%[/tex]

for the 100% acid:

[tex]percent\ disolved = \frac{9.9g - 9.5g}{9.9g}*100 \% = 4.2 \%[/tex]

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The data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We have data:

6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7

Intervals   Frequency

 0 - 3     6

 3 - 6     11

 6 - 9     3

 9 - 12     0

The histogram is shown in the attached picture.

Thus, the data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

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Answer:

D

21√2/2

C

C

C

Step-by-step explanation:

For all problems, the ratios of the lengths of the sides are:

30-60-90 triangle 1 : √3 : 2

45-45-90 triangle 1 : √2 : √2

Problem 3:

30-60-90 triangle at left

Hypotenuse = 11

Short leg = 11/2

Long leg = 11/2 × √3

45-45-90 triangle at right

x = 11/2 × √3 × √2 = 11√6/2

Answer: D

Problem 4:

30-60-90 triangle at top

Hypotenuse = 7√3

Short leg = 7√3/2

Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2

45-45-90 triangle at right

x = 21/2 × √2 = 21√2/2

Answer: 21√2/2

Problem 7:

30-60-90 triangle

Long leg = 4√3

Short leg = y = 4√2/2 = 2√2

Answer: C.

Problem 6:

30-60-90 triangle at left

Hypotenuse = 12√6

Short leg = 12√6/2 = 6√6

Long leg = 6√6 × √3 = 6√2√3√3 = 18√2

45-45-90 triangle at right

x = 18√2/√2 = 18

Answer: C.

Problem 8:

45-45-90 triangle

Hypotenuse = 2

Leg = y = 2/√2 = 2√2/(√2√2) = √2

Answer: C.

Answer:

2/5

Step-by-step explanation:

To find the slope of a line segment, find the difference in y and divide by the difference in x (delta y / delta x)

Delta y: -7 - (-13) = 6

Delta x: 15 - 0 = 15

Slope = delta y / delta x

Slope = 6/15 = 2/5

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Answer:

60 in²

Step-by-step explanation:

Area of a Regular Polygon

  [tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

From inspection of the diagram:

Substitute the values into the formula and solve for A:

[tex]\implies \sf A = \dfrac{5 \times 6 \times 4}{2}[/tex]

[tex]\implies \sf A = \dfrac{120}{2}[/tex]

[tex]\implies \sf A = 60\:in^2[/tex]

Therefore, the area of the given regular pentagon IJKLM is 60 in².

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{First thing, let's get the formula for}\\\huge\textbf{the regular pentagon/polygon.}[/tex]

[tex]\mathbf{\dfrac{1}{2}\times \boxed{a}pothem\times\boxed{p}erimeter = {\boxed{a}rea}}[/tex]

[tex]\huge\textbf{Or we could simply say....}[/tex]

[tex]\mathbf{\dfrac{\boxed{n}umber\ of\ sides\ you\ have \times \boxed{s}ide \ length\ on\ one\ side\times \boxed{a}pothem}{2} = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Let's plug the pieces to the equation,}\\\huge\textbf{since we have that information out the}\\\huge\textbf{way.}[/tex]

[tex]\bullet\mathbf{\ Number\ of\ sides \rightarrow \boxed{\bf 5}}[/tex]

[tex]\bullet\mathbf{\ Side\ length\ of\ one\ side \rightarrow \boxed{\bf 6\ inches}}[/tex]

[tex]\bullet\mathbf{\ Apothem \rightarrow \boxed{\bf 4\ inches}}[/tex]

[tex]\huge\textbf{Making the equation for you:}[/tex]

[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Solving for the result:}[/tex]

[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{30\times 4}{2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{120}{2} =\boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{120\div2}{2\div2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{60}{1} = \boxed{a}rea}[/tex]

[tex]\mathbf{60\div1 = \boxed{a}rea}[/tex]

[tex]\mathbf{60 = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Met the result....}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{60\ in^2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assingment \& enjoy your day!}[/tex]

The values of a and b of the given sequence are; a = 6 and b = -15

We are given the formula for nth term of a sequence as;

an² + bn

We are given that;

Third term = 9

Sixth term = 126

Thus;

a₃ = 9 = a(3)² + b(3)

9a + 3b = 9    ------(1)

Similarly for the 6th term;

a(6)² + b(6) = 126

36a + 6b = 126    ------(2)

Multiply eq 1 by 2 to get;

18a + 6b = 18    ------(3)

Subtract eq 3 from eq 2 to get;

18a = 108

a = 6

18(6) + 6b = 18

6b = 18 - 108

6b = -90

b = -90/6

b = -15

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The inequality equation of the lines are given as 4x – y ≤ 4 and 2x – 2y ≤ 3. Then the correct option is A.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The graph is given below.

From the graph, equation of the lines are given as

4x - y = 4 and 2x - 2y = 3

But for the inequality is shown in graph. Then the inequality equation of the lines are given as

4x – y ≤ 4 and 2x – 2y ≤ 3

Then the correct option is A.

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Answer:

80 - 30

Step-by-step explanation:

I'm just guessing

Answer:

3rd option : 5

Step-by-step explanation:

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its a slope question

f(x) is y

y2-y1/x2-x1

-10+25/-1+4

15/3

5

Since we know that the equation of a line in slope-intercept form is: , where, m= Slope and b= y-intercept.

Upon substituting m = 5 in slope-intercept form of equation we will get,

Now let us find y-intercept by substituting coordinates of one point in our given line.

So the equation of given line will be,

Now let us find value of n by substituting x = n and y = 20 in our equation.

Therefore, the value of n is 5.

$ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame. This can be obtained by finding the perimeter of the painting and multiplying with the cost of wood per meter.

Given that,

length of the painting (l) = b meters

width of the painting (b) = 4 meters

Perimeter of the painting = 2(l+b)

                                          = 2(b+4)

                                          = 2b + 8

Cost of the frame = (2b + 8)× $10 per meter

                             = $ (20b + 80)

Hence $ (20b + 80) is the cost to buy a frame for the panting given that measures b meters by 4 meters and charges $10 per meter for a wooden frame.

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Answer:

Step-by-step explanation:

Horizontal translation of the graph of a function is accomplished by replacing x with (x-h) for translation h units to the right. Vertical translation of the graph is accomplished by adding the amount of translation to the function value: f(x)+k translates the graph k units upward.

Reflection of a function over the x-axis is accomplished by changing the sign of every function value: -f(x).

We observe that f(x) has been transformed by ...

The effect of these transformations is (correspondingly) ...

__

The attached graph shows a function f(x) (red) and the transformed function (blue).