What is the solution to the inequality 14y−14≥14?

Answer:

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Step-by-step explanation:

The equation of the line through the point [tex](x_o,y_o)[/tex] & [tex](x_1,y_1)[/tex] can be represented by:

[tex]y-y_o = m(x - x_o)[/tex]

Making m the subject;

[tex]m = \dfrac{y_1 - y_0}{x_1-x_0}[/tex]

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

[tex]m= \dfrac{2-1}{1-0}[/tex]

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

[tex]m = \dfrac{1-2}{4-1}[/tex]

[tex]m = \dfrac{-1}{3}[/tex]

∴

[tex]y-2 = -\dfrac{1}{3}(x-1)[/tex]

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

[tex]\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Answer:

Equation: y = 0.4x

y = 2.4

Step-by-step explanation:

Use the direct variation equation, y = kx, where k is a constant

Plug in x and y:

y = kx

10 = k(25)

Solve for k:

0.4 = k

So, the equation is y = 0.4x

Then, use this equation to find y when x = 6:

y = 0.4x

y = 0.4(6)

y = 2.4

A direct proportion is a proportion such that the ratio between both variables remains constant thus the given proportion will be y = 04x and the value of y at x = 6 will be 2.4.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

a)

Let's say the direct proportion as,

y = kx

Given that y = 10 when x = 25.

10 = k(25)

Solve for k,

0.4 = k

Therefore, the equation will be y = 0.4x

y = 0.4x

b)

The value of y when x = 6

y = 0.4(6)

y = 2.4

For more information about ratios and proportions,

brainly.com/question/26974513

#SPJ2

y-1= ±3/10(x-2)

Im not sure how to get this answer but my teacher gave it to me so i hope this helps!

The equation of the asymptote of the given hyperbola is; y - 1 = ±(3/10)(x - 2)

We are given the equation of the hyperbola as;

[(y - 1)²/9] - [(x - 2)²/100] = 1

We can rewrite this equation as;

[(y - 1)²/3²] - [(x - 2)²/10²] = 1

The general equation form of hyperbola is;

[(y - k)²/a²] - [(x - h)²/b²] = 1

Comparing this general form to our given equation we can see that;

k = 1

h = 2

a = 3

b = 10

Now the equation of the asymptote of a hyperbola follows the general formula;

y = ±[a(x - h)/b] + k

Plugging in the relevant values gives us;

y = ±(3/10)(x - 2) + 1

y - 1 = ±(3/10)(x - 2)

Read more about hyperbola asymptotes at;https://brainly.com/question/12919612

Answer:

Each student will get 1/6 liters of soda.

Step-by-step explanation:

In order to do this, we need to divide 1/2 by 3.

All we had to do is multiply 2 by 3.

1/6 is smaller than 1/2, and because 6 is 2 x 3, it's 3 times smaller, or less.

Therefore, each student will get 1/6 liters of soda.

Hope this helps! :D

Answer:

Carly is wrong. The correct answer is 4:3

Step-by-step explanation:

40/10=4

30/10=3

Answer:

Carlie is wrong

Step-by-step explanation:

The correct answer is 4:3

Answer:

2.5

Step-by-step explanation:

Answer:

y= 4/3x -1/3

Step-by-step explanation:

Find slope: y2-y1/x2-x1 = 5-(-3)/4-(-2) = 8/6 = 4/3

Use point slope to find the equation:

y - y1 = m ( x - x1 )

y - (-3) = 4/3 ( x - (-2))

y = 4/3x + 8/3 + (-3)

y = 4/3x + 8/3 - 9/3

y= 4/3x -1/3

654 over 3 = divide the both 654 and 3 by 3.

It will give you 218 over 1.

So the answer is 218.

Answer:

$51.75

Step-by-step explanation:

The meal cost $45. $45 is 100% of the cost. She wants to leave a 15% tip, so add 15% to 100%.

15% + 100% = 115%

She will pay 115% of $45.

115% of $45 = 1.15 * $45 = $51.75

Answer:

62.5% decrease

Step-by-step explanation:

Answer:

When f(x) equals 17, x is equal to 8.

Step-by-step explanation:

[tex]f(x) = 3x - 7\\17 = 3x - 7\\3x = 17 + 7\\3x = 24\\x = 24/3\\x = 8[/tex]

Answer:

86

Step-by-step explanation:

180-94

Answer:

7(1+2)

Step-by-step explanation:

So find the Greatest common factor first which is7 in this case

now we divide each number by 7

1+2 now

now we put that around parthesis and multiply it by 7

7(1+2)

Thats how you factpr

Check:

using distributive property

7+14, same answer.

Answer:

7(1+2)

Step-by-step explanation:

Find the factors of each number

7 has factors of 1,7

14 has factors of 1,2,7,14

The greatest common factor is 7

7*1 + 2*7

Factor out the 7

7(1+2)

Answer:

whats the problem

Step-by-step explanation:

Answer:

yup

Step-by-step explanation:

Answer:

14.

[tex]x = 11[/tex]  [tex]m<B = 108[/tex]   [tex]m<C= 36[/tex]   [tex]m<D = 36[/tex]

15.

[tex]x = 4[/tex]     [tex]WX = 25[/tex]     [tex]XY = 17[/tex]     [tex]WY = 25[/tex]

Step-by-step explanation:

Solving (14):

[tex]BC = BD[/tex]

[tex]m<B = 13x - 35[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<D = 2x + 14[/tex]

First, we solve for x.

Since sides [tex]BC = BD[/tex], then

[tex]m<C = m<D[/tex]

This is so because the theorem of ASA (Angle-Side-Angle)

So, we have:

[tex]5x - 19 = 2x + 14[/tex]

Collect Like Terms

[tex]5x - 2x = 19 + 14[/tex]

[tex]3x = 33[/tex]

Divide both sides by 3

[tex]x = 11[/tex]

Solving for m<B, m<C and m<D.

We simply substitute 11 for x in their respective expressions.

[tex]m<B = 13x - 35[/tex]

[tex]m<B = 13*11 - 35[/tex]

[tex]m<B = 143 - 35[/tex]

[tex]m<B = 108[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<C= 5*11 - 19[/tex]

[tex]m<C= 55 - 19[/tex]

[tex]m<C= 36[/tex]

[tex]m<D = 2x + 14[/tex]

[tex]m<D = 2*11 + 14[/tex]

[tex]m<D = 22 + 14[/tex]

[tex]m<D = 36[/tex]

Solving (15):

[tex]<X = <Y[/tex]

[tex]WX = 9x - 11[/tex]

[tex]XY = 4x + 1[/tex]

[tex]WY = 7x - 3[/tex]

First, we solve for x.

Since [tex]<X = <Y[/tex], then

[tex]WX = WY[/tex]

This is so because the theorem of SAS (Side-Angle-Side)

So, we have:

[tex]9x - 11 = 7x - 3[/tex]

Collect Like Terms

[tex]9x - 7x = 11-3[/tex]

[tex]2x = 8[/tex]

Divide both sides by 2

[tex]x = 4[/tex]

Solving for WX, WY and XY

We simply substitute 4 for x in their respective expressions.

[tex]WX = 9x - 11[/tex]

[tex]WX = 9 * 4 - 11[/tex]

[tex]WX = 36 - 11[/tex]

[tex]WX = 25[/tex]

[tex]XY = 4x + 1[/tex]

[tex]XY = 4 * 4 + 1[/tex]

[tex]XY = 16 + 1[/tex]

[tex]XY = 17[/tex]

[tex]WY = 7x - 3[/tex]

[tex]WY = 7 * 4 - 3[/tex]

[tex]WY = 28 - 3[/tex]

[tex]WY = 25[/tex]

Answer:

28

Step-by-step explanation:

Multiply 35 by .8

Answer:

If he pitched 35 games then he will win 28 of his games.

Step-by-step explanation:

You take 35 and multiply it by the percentage. But first make the percentage a decimal by moving the decimal two places to the right making it .8

Then you multiply and you have your answer!

Answer:

4(2-2c)

Step-by-step explanation:

because you switch it around

Answer:

-1

Step-by-step explanation:

times 4 by 2c and 4 by -2

8c and -8 then you divide by each other and get -1

Answer:

:)))

Step-by-step explanation:

31/50 - .062 - 62%

17/60 - .17 - 17%

2/5 - 0.4 - 20%

6/5 - 1.2 - 120%

11/25 - .44 - 44%

13/2 - 6.5 - 650%

Answer:

Please check the explanation below.

Step-by-step explanation:

In other words, in order for relation to be a function, we must make sure there must be no repetition of 'x' coordinate values, as it would violate the fundamental definition of a function.

A) (2, 5), (5, 7), (7, 9)

Here, the x-coordinates are: 2, 5, and 7

At x = 2, y = 5

At x = 5, y = 7

At x = 7, y = 9

Thus, the coordinate pairs (2, 5), (5, 7), (7, 9) represent the function.

B) (2, 3), (1, 4), (2, 8),(0, 1)

Here, the x-coordinates are: 2, 1, 2 and 0

At x = 2, y = 3

At x = 1, y = 4

At x = 2, y = 8

At x = 0, y = 1

Please observe that the x-coordinate values i.e. x=2 are repeated.

Thus, the coordinate pairs (2, 3), (1, 4), (2, 8),(0, 1) does not represent the function.

C) (4, 8), (5, 8), (6, 8)

Here, the x-coordinates are: 4,5 and 6

At x = 4, y = 8

At x = 5, y = 8

At x = 6, y = 8

Thus, the coordinate pairs (4, 8), (5, 8), (6, 8) represent the function.

D) (-1, 4), (0, -1), (8, 3)

Here, the x-coordinates are: -1, 0, and 8

At x = -1, y = 4

At x = 0, y = -1

At x = 8, y = 3

Thus, the coordinate pairs (-1, 4), (0, -1), (8, 3) represent the function.

E) (1, 8), (8, 1), (1, 3)

Here, the x-coordinates are: 1, 8, and 1

At x = 1, y = 8

At x = 8, y = 1

At x = 1, y = 3

Please observe that the x-coordinate values i.e. x=1 are repeated.

Thus, the coordinate pairs (1, 8), (8, 1), (1, 3) does not represent the function.

F) (9, 0), (9, 1), (9, 2), (9, 3)

Here, the x-coordinates are: 9, 9,9 and 9

At x = 9, y = 0

At x = 9, y = 1

At x = 9, y = 2

At x = 9, y = 3

Please observe that the x-coordinate values i.e. x=9are repeated.

Thus, the coordinate pairs (9, 0), (9, 1), (9, 2), (9, 3) does not represent the function.

Answer:

true i think

Step-by-step explanation:

Answer:25

Step-by-step explanation:

We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]

Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.

To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:

[tex]g'(x)=-8x+4[/tex]

To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have

[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]

So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.

[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]

Therefore, the maximum point [tex]M[/tex] of the function is

[tex]\boxed{M=(0.5,-1)}[/tex]

 Glad to help! Wish you great studies.

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Answer:

with i cant see the problem so i dont lnow

All of them produce an angle of 90 degrees, therefore

90 degrees x 4 = 360 degrees

Answer:

1.14285714286 ounces per person

Step-by-step explaination:

To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate

following this rule, 8 divided by 7 is 1.14285714286

Your assignment will probably ask you to simplify

Answer:

-0.96p - 1.82

Step-by-step explanation:

Answer:

I'm pretty sure it's 1,1.

Step-by-step explanation:

Answer:

(1,1)

Step-by-step explanation:

sub to pewdiepie

Answer:

you need more than one point to find the slope of a line?

Step-by-step explanation:

Answer:

the second one, the one that is already highlighted is correct.

Step-by-step explanation:

she divided it up among them so 20 over x shows division