Solve the following system of linear equations by graphing:
-x+y = -7
4x + 4y = 20

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:

total population of school = 1000

1000 - 450 males = 550 female students

550 - 200 females not in extra curriculars = 350 females in extra curriculars

350 + 90 males in extra curriculars = 440 total in extra curriculars

Circle A = 440

Circle B - overlap = 200 females not in extra curriculars

440 + 200 = 640

1000 - 640 = 370 students represented by the portion of the Venn diagram not in either circle

Step-by-step explanation:

Answer:

Its a

Step-by-step explanation:

Answer:

true i think

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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:

The probability is 406/625

Step-by-step explanation:

If they are of different materials, we have the following combinations of selection;

(gold and silver) or ( silver and titanium) or (gold and titanium )

The number of earrings present is 13 + 10 + 12 = 25

Probability of selecting a gold earring is 13/25

Probability of a silver is 10/25

Probability of a titanium is 12/25

Substituting these into the probabilities, we have;

(13/25 * 10/25) + (10/25 * 12/25) + (13/25 * 12/25)

= 130/625 + 120/625 + 156/625 = 406/625

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:

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

Step-by-step explanation:

Answer:

(1,1)

Step-by-step explanation:

sub to pewdiepie

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:

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:

Calloway Peak is 6,464 Feet. And Flat Rock is 4061.5 Feet

Step-by-step explanation:

For Calloway Peak Started at 0 so 4646.4+1817.6=6,464

Zen then descends which means he walked back down 2402.5 feet.

To find Flat Rock you subtract the height of Calloway Peak by 2402.5 the amount that he walked back down to get how tall Flat Rock is in Feet

6464-2402.5=4061.5 Feet

So Flat Rock is 4061.5 Feet tall.

Answer:

2.5

Step-by-step explanation:

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:

28

Step-by-step explanation: This should be 28. 42 divided by 3 is 14. Why would you divide it by 3? Because the full ratio is 2:3. So 42 divided by 3 is 14. Then you add fourteen twice, for the two in the ratio. Fourteen plus fourteen is 28.

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:

:)))

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:

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:

-0.96p - 1.82

Step-by-step explanation:

All of them produce an angle of 90 degrees, therefore

90 degrees x 4 = 360 degrees

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

Answer:

62.5% decrease

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:

A. y = arcsinx and y = arccosx

Step-by-step explanation:

edge

The trigonometric functions have a domain of [–1, 1] is sine and cosine function.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

From the given identity, the following things can be interpreted:

cos²x = 1- sin² x

cos x = √(1- sin2x)

Since the cosine function is known to be defined for real numbers, the value contained within the root is always positive. Therefore,

1- sin²x ≥ 0

sin²x ≤ 1

sin x ∈ [-1, 1]

Similarly,

1- cos²x ≥ 0

cos²x ≤1

cos x ∈ [-1,1]

Learn more about Domain here:

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Answer:25

Step-by-step explanation:

Answer:

with i cant see the problem so i dont lnow

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

It will give you 218 over 1.

So the answer is 218.

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,

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