the sum of numerator and denominator of the fraction is 12 and the denominator is 2 more than numerator.find the fraction

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The inequality boils down to

|y| > y

By definition of absolute value, we have

• |y| = y if y ≥ 0

• |y| = -y if y < 0

So if y ≥ 0, we have

y > y

but this is a contradiction.

On the other hand, if y < 0, we have

-y > y   ==>   2y < 0   ==>   y < 0

and no contradiction.

Now replace y with (x + 1)/(x - 1) + 1. Then you're left with solving

(x + 1)/(x - 1) + 1 < 0

(x + 1 + x - 1)/(x - 1) < 0

2x/(x - 1) < 0

The left side is negative if either 2x > 0 and x - 1 < 0, or 2x < 0 and x - 1 > 0. The first case reduces to x > 0 and x < 1, or 0 < x < 1. In the second case, we get x < 0 and x > 1, but x cannot satisfy both conditions, so we throw this case out.

Answer:

D(0 , 4)

Step-by-step explanation:

Point D is on the y axis. So, x-coordinate  = 0

y- coordinate is the vertical length from origin which is 4

Answer:

D(0 , 4)

Step-by-step explanation:

Answer:772

Step-by-step explanation:

5404/7 = 772

Answer:

772 buttons

Step-by-step explanation:

as is stated 5404 buttons are produced in a week

a week contains 7 days, so in order to find out how many buttons are produced in a day we have to divide 5404/7

this gives us 772

meaning, 772 buttons are produced in a day

hope this helped :)

Answer:

length = 48 feet , width = 32 feet

Step-by-step explanation:

Using

2W + 2L = 160 with W = L - 16 , then

2(L - 16) + 2L = 160 ← distribute and simplify left side

2L - 32 + 2L = 160

4L - 32 = 160 ( add 32 to both sides )

4L = 192 ( divide both sides by 4 )

L = 48

Substitute L = 48 into W = L - 16

W = 48 - 16 = 32

Thus length = 48 feet and width = 32 feet

Answer:

l = 48 cm

w =  32 cm

Step-by-step explanation:

length = l

Width w= l - 16

Perimeter = 160 ft

2*(l + w) = 160

2*(l + l -16) = 160

2*(2l - 16) = 160

Use distributive property

2*2l - 2*16 = 160

4l - 32 = 160  {add 32 to both sides}

4l = 160 + 32

4l = 192            {Divide both sides by 4}

l = 192/4

l = 48 cm

W = 48 - 16 = 32 cm

Answer:

Answer:

384 cm^2

Step-by-step explanation:

Start with the prism (I multiply by 2 because some of the surfaces are more of):

The Triangular Prism (I divide by 2 because it is a triangle shape on the sides):

The Last Step (adding everything):

120+180+24+12+18+30=384

Answer:

sqrt 51

Step-by-step explanation:

You should use the pythagorean theorem, which states a^2+b^2=c^2. So the missing side length for the smaller triangle is sqrt{2^2+3^2}=sqrt{4+9}=sqrt{13}. And the side length x is sqrt{8^2-sqrt{13}^2}=sqrt{64-13}=sqrt{51}

Using a system of equations, it is found that:

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

This question is solved using a system of equations. I am going to say that:

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

Thus:

[tex]x + y = 24 \rightarrow y = 24 - x[/tex]

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

Thus:

[tex]2x + 4y = 80[/tex]

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Number of chicken:

Since [tex]y = 24 - x[/tex]

[tex]2x + 4y = 80[/tex]

[tex]2x + 4(24 - x) = 80[/tex]

[tex]2x + 96 - 4x = 80[/tex]

[tex]2x = 16[/tex]

[tex]x = \frac{16}{2}[/tex]

[tex]x = 8[/tex]

There are 8 chickens in the yard.

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

Number of pigs:

[tex]y = 24 - x = 24 - 8 = 16[/tex]

There are 16 pigs in the yard.

A similar problem is given at https://brainly.com/question/24104709

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

1071.79 yd³

Step-by-step explanation:

radius r = 16/2 = 8 yd

height = 16 yd

volume = (1/3)×πr²h

= (1/3)×3.14×8²×16

= 1071.79 yd³ (rounded to the nearest tenth)

Answer:

$290

Step-by-step explanation:

We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.

Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.

Thus;

P(x) for expensive sofa = 1/5

P(x) for sofa in sale advertisement = 4/5

Thus, expected value is;

E(X) = (1/5)450 + (4/5)250

E(x) = 90 + 200

E(x) = $290

Answer:

Step-by-step explanation:

Cost of advertised sofa = [tex]\$250[/tex]

Cost of more expensive sofa = [tex]\$450[/tex]

So, the average cost of sofa,

[tex]E(x) = (450*\frac{1}{5})+ (250*\frac{4}{5})\\\\E(x) = 90 + 200\\\\E(x) = 290[/tex]

Hence,

The average cost of a sofa = [tex]\$290[/tex]

For more information, visit

https://www.bartleby.com/questions-and-answers/question-13-a-furniture-store-is-having-a-sale-on-sofas-and-youre-going-to-buy-one.-the-advertisers-/61410cf1-5b19-4491-9893-42336374e48e

Answer:

3.465 %

Step-by-step explanation:

10000 = 5000 [tex]e^{20r}[/tex]

2= [tex]e^{20r}[/tex]

ln(2) = 20r ln(e)

r = ln(2)/20

r = 0.03465

Answer:

2/5

Step-by-step explanation:

The fraction that play basketball is the number that play basketball over the total

14/35

Divide the top and bottom by 7

2/5

Answer:

I think the perimeter is 50cm the solids is 600cm³

Step-by-step explanation:

Perimeter: (5×10)=50cm

Solids: divided with 2box(A box & B box)

Abox: 5cm x 5cm x 12cm

=300cm³

Bbox: 5cm x 12cm x 5cm

=300cm³

Solids:(Abox +Bbox) 300cm³ + 300cm³

=600cm³

I think, I'm sorry if it's wrong

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\sqrt{2} } } =\\\\\\ 5\cdot \sqrt{\frac{3}{2\sqrt{3-\sqrt{2} } } \cdot \frac{2\sqrt{3+\sqrt{2} } }{2\sqrt{3+\sqrt{2} } } } = \\\\\\5\cdot \sqrt{\frac{6\sqrt{3+\sqrt{2} } }{4\cdot \sqrt{9-2} } } =5\sqrt{\frac{6\sqrt{3+\sqrt{2} } }{2\sqrt{7} } }[/tex]

But if the condition would be like this

[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\boldsymbol2\sqrt{2} } } =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot \sqrt{\underbrace{2+1-2\sqrt{2} \cdot \sqrt{1} }_{(\sqrt{2} -1)^2} } }} =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot (\sqrt{2}-1) } } } = \\\\\\ 5\cdot \sqrt{\frac{3}{2(\sqrt{2}-1 )} \cdot \frac{\sqrt{2} +1}{\sqrt{2}+1 }} =5 \sqrt{\frac{3}{2(2-1)} } =\boxed{5\sqrt{1,5} }[/tex]

Answer:

(1/21)(21×5^(x+2)-4×5^2x)

Step-by-step explanation:

5^(x+2)-4×5^x÷21×5^x

= 5^(x+2)-4×5^2x/21

= 1/21(21×5^(x+2)-4×5^2x)

Answer:

x^5/y^7

Step-by-step explanation:

x^8 y^2 / x^3 y^9

We know that a^b/ a^c = a^(b-c)

Simplify the x terms

x^8 / x^3 = x^(8-3) = x^5

Simplify the y terms

y^2 / y^9 = y^(2-9) = y^-7

We know a^-b = 1/a^b

y^-7 = 1/y^7

Put the terms back together

x^5/y^7

Answer:

D

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to pre image

scale factor = [tex]\frac{18}{14}[/tex] = [tex]\frac{9}{7}[/tex] → D

Answer:

3/8

Step-by-step explanation:

first year's work is 1/6

second year's work is 1/8

third year's work is 1/12

combining all 3 gives us

1/6 + 1/8 + 1/12

which simplifies to 3/8

Answer:

3

Step-by-step explanation:

2k-1=5

>2k=5+1=6

>k=3

Answer:

1)

An onto function is a function where it's range is the term in that function.

[tex]{ \sf{if \: function \: is \: x \: to \: y}} \\ { \sf{then \: range \: of \: function \: is \: y}} \\ i.e \: \: f(x) = y[/tex]

It is given by formula:

[tex]{ \boxed{ \sf{ {x}^{y} - {}^{x} c _{1}(n - 1) {}^{y} + {}^{x} c _{2} (x - 2) {}^{y} + ..... {x}^{n} }}}[/tex]

2).

[tex]f(k) = 2k - 1 \\ but \: f(k) = 5 \\ 2k - 1 = 5 \\ 2k = 1 + 5 \\ 2k = 6 \\ k = 3[/tex]

Answer:

-1243

Step-by-step explanation:

4.5×6-1243

27-1243

=-1216

Answer:

It is 3/2, I got it right on my exam.

Step-by-step explanation:

Dilation is a transformation that allows you to resize an object. The dilation factor of the given point is 3/2.

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.

Given the dilation of the k around the origin as K = (2,4) → (3,6), therefore, the point k is dilated 1 unit to the right and 2 units upwards.

Let the dilation factor be represented by a, then,

2 × a = 3

a = 3/2

Similarly for the y-axis,

4 × a = 6

a = 6/4 = 3/2

Hence, the dilation factor of the given point is 3/2.

Learn more about Dilation:

https://brainly.com/question/13176891

#SPJ2

Answer:

c

Step-by-step explanation:

come on ! you can literally see that in the chart.

how many parts of the gray 3/8 are covered by the gray 1/4 ?

2 parts = 2/8 are clearly covered by 1/4.

2/8 is what part of 3/8 ?

it is the same question as "2 is what part of 3" ?

is 2 a quarter (1/4) of 3 ? no, 1/4×3 = 3/4 and not 2.

is 2 one third (1/3) of 3 ? no, 1/3 of 3 = 1/3×3 = 1 and not 2.

is 2 two thirds (2/3) of 3 ? ah, 2/3 × 3 = 2. that is correct !

is 2 three quarters (3/4) of 3 ? no, 3/4×3 = 9/4 and not 2.

once you have the same denominator, you can easily compare the numerators and ignore the denominators for such problems.

Answer:

No, the above polynomials aren't similar as they don't have a constant scale factor

The following polygons given in the question are not similar .

Similar polygons are those polygon which have the similar shapes but with different size and dimensions.  Similar polygons have also the scaling factor ration equal.

There are two polygons given in the question LMNO and WXYZ .

For both of the polygons, we are checking the adjacent sides of the polygons.

The value of LM = 35 but for the other polygon , its adjacent side WX = 18.

Similar LO = 63 and WZ = 10 .

Also the adjacent angles are not equal as ∠MNO = 50° and ∠ZWX = 50° .

Therefore, the polygons given have different scaling factor.

Thus, the following polygons given in the question are not similar .

To learn more about similar polygons, refer -

https://brainly.com/question/16058229

#SPJ2

Answer:

16

Step-by-step explanation:

the quadratic equation –3 = –x2 + 2x can be changed into :

x²-2x-3= 0

a=1, b= -2 , and c = -3

so, the discriminant = (-2)²-4(1)(-3)

= 4 + 12 = 16

Answer:

[tex] P = 6E - 4M - O [/tex]

Step-by-step explanation:

[tex] E = \dfrac{O + 4M + P}{6} [/tex]

Multiply both sides by 6.

[tex] 6E = O + 4M + P [/tex]

Subtract O and 4M from both sides.

[tex] 6E - 4M - O = P [/tex]

Switch sides.

[tex] P = 6E - 4M - O [/tex]

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

Adding eq(1) and (2)

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

Put the value in eq(2)

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

put the values in eq(4)

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

Put the value in eq(3)

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

Answer:

An octagon has eight interior angles.

Interior angle total sum = (n-2) x 180, where n = number of sides.

Since an octagon has 8 sides, we have:

6 x 180 / 8, which is 135.

The answer is 135.

Let me know if this helps!

Answer:

9.4 cm^3

Step-by-step explanation:

This figure is a cylinder so the formula is V=πr^2h

r is the radius and h is the height

Here we can see the height is 3 and the radius is 1

V=π(1)^2(3)

V=π3

V=9.42 (assuming π is 3.14)

Rounded to the nearest tenth is 9.4

Answer:

9.4 cm^3

Step-by-step explanation:

This figure is a cylinder so the formula is V=πr^2h

r is the radius and h is the height

Here we can see the height is 3 and the radius is 1

V=π(1)^2(3)

V=π3

V=9.42 (assuming π is 3.14)

Rounded to the nearest tenth is 9.4