Find the equation of the tangent line to the curve x^2 + xy + y^2 = 3 at the point (1,1)

Answer:Options 'A' and 'C' are correct.

Step-by-step explanation:

Let the number of sheep be 's'.

Let the number of goats be 'g'.

According to question, we have given that

the number of sheep and goats are not more than 43.

The number of goats are fewer than 22.

So, the inequalities would be

[tex]g<22\\\\and\\\\s+g<43[/tex]

Hence, Options 'A' and 'C' are correct.

The two inequalities for Harold's sheep and goats situation are A. g < 22 and C. s + g ≤ 43.

To represent the situation described about Harold's sheep and goats, we need to set up two inequalities based on the given information:

Using these inequalities, we can help Harold determine how to distribute his sheep and goats in the new field.

The domain is the set of all point where you can evaluate the function.

As you can see, the first piece is defined from -infinity to 2 (included).

The second piece is defined from 2 to 6 (excluded).

The third piece is defined from 6 (excluded) to +infinity.

So, the domain of the function is composed by all the real numbers which are not 6:

[tex](-\infty,6)\cup(6,\infty) = \mathbb{R}\setminus\{6\} = \{x \in \mathbb{R}\ :\ x\neq 6\}[/tex]

As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.

The second piece is constantly equal to 2, so it adds nothing.

The third piece spans the y axis from -2 to -infinity, so the range is

[tex](-\infty,-2)\cup[0,\infty) = \mathbb{R}\setminus [2,0) = \{x \in \mathbb{R}\ :\ x\geq 0\ \lor\ x<-2\}[/tex]

The domain is the set of all point where you can evaluate the function.

As you can see, the first piece is defined from -infinity to 2 (included).

The second piece is defined from 2 to 6 (excluded).

The third piece is defined from 6 (excluded) to +infinity.

So, the domain of the function is composed by all the real numbers which are not 6:

As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.

The second piece is constantly equal to 2, so it adds nothing.

The third piece spans the y axis from -2 to -infinity, so the range is

Answer:

Price per foot of skydive is 31.11 repeated, or 31 1/9

Step-by-step explanation:

Jesse is going on 2 jumps, which is 14000*2=28000.

Each Skydive is $400, and two jumps would be $800. Plus a $100 training fee, it would cost $900 for 2 jumps.

28000/900=31.1111 repeated.

Answer:

The right answer is 3a - 11 ≤ 7 ⇒ 4th answer

Step-by-step explanation:

* Lets study the problem

- From the figure

# The blue line started from 6 and the point is bold that means

   the inequality sign is ≤ or ≥

# The blue line started from 6 and moved to the negative numbers

   that means the inequality is less than or equal

∴ a ≤ 6

* Now lets look to the answers

- There is only one answer has the sign ≤ , the last answer

* Now lets solve it to be sure

∵ 3a - 11 ≤ 7 ⇒ add 11 to the both sides

∴ 3a ≤ 18 ⇒ divide the both sides by 3

∴ a ≤ 6

* The right answer is 3a - 11 ≤ 7

Answer:

[tex]\$32,526.28[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ A=\$50,000\\ r=0.043\\n=365[/tex]  

substitute in the formula above  

[tex]\$50,000=P(1+\frac{0.043}{365})^{365*10}[/tex]  

[tex]P=\$50,000/[(1+\frac{0.043}{365})^{3,650}]=\$32,526.28[/tex]  

Answer:

The fourth graph (last graph)

Step-by-step explanation:

Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:

[tex]f(x)=(x-1)(x+4)[/tex]

[tex](x-1)(x+4)=0[/tex]

[tex]x-1=0,x+4=0[/tex]

[tex]x=1,x=-4[/tex]

Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.

Since both x values inside the parenthesis are positive, our parabola is opening upwards.

The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.

We can conclude that the graph of [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.

ANSWER

See attachment.

EXPLANATION

The given function is

f(x) = (x – 1)(x + 4).

This parabola will open upwards because the leading coefficient is positive.

The x-intercepts can be found by equating the function to zero.

[tex](x - 1)(x + 4) = 0[/tex]

By the zero product property;

[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]

This implies that,

[tex]x = 1 \: or \: x = - 4[/tex]

The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.

The correct choice is D.

Answer:

5 · a³ · b³ · √5b

Step-by-step explanation:

Start with √(50a^6b^7).  Rewrite 50 as the product of the largest possible perfect square and a multiplier:  50 = 25 · 2.  Then √50 = 5√2.

a^6 is already a perfect square, so find its square root:  √a^6 = a^3.

b^7 = b · b^6, so √b^7 = b^3√b

Now rewrite (50(a^6) (b^7)) as √(50a^6b^7).

Then rewrite √(50a^6b^7) as 5√2 · a³ · b³ · √b.

This latter result can be simplified to 5 · a³ · b³ · √5b

This matches possible answer #1.

Answer:

86.19°

Step-by-step explanation:

Let x represent the missing value.

The given trigonometric equation becomes:

[tex]\tan x=15[/tex]

We take the inverse tangent of both sides to obtain:

[tex]\tan^{-1}(\tan x)=\tan^{-1}(15)[/tex]

This implies that;

[tex]x=\tan^{-1}(15)[/tex]

We use at least a scientific calculator to evaluate this and obtain:

[tex]x=86.18592517\degree[/tex]

To the nearest hundredth, the missing value is [tex]x=86.19\degree[/tex]

Answer:

He will pay 916

Step-by-step explanation:

Answer:

the correct choice is marked

Step-by-step explanation:

The red line has intercept -3 and slope 1/3, so is ...

y = 1/3x -3

The blue line has intercept +1 and slope -1, so is ...

y = -x +1

The graph solves this system of equations, which can also be written as the single equation ...

y = y

1/3x -3 = -x +1

The total surface area for the figures aee;

1) 128 m²

2) 714 in²

1) To find the surface area, we need to find the area of each surface that makes up the object and add together.

Thus:

T.S.A = 4(4 * 4) + (4 * 4) + 4(½ * 4 * 6)

T.S.A = 128 m²

2) The total surface area here is;

T.S.A = 2(15 * 10) + 2(10 * 7) + 2(15 * 7) + 4(4 * 4)

T.S.A = 714 in²

Read more about surface area at: https://brainly.com/question/30794567

#SPJ3

Without more information, we cannot give a specific numerical answer for the total interest on a 20-year loan. As a rule, total interest paid will be less on a shorter loan, despite higher monthly payments.

The question is asking how much total interest would Misty pay on a 20-year loan, given she knows the total interest paid on a 25-year loan to be $57,810. We're not given enough information to provide a specific numerical answer for this - the loan interest for a 20-year loan and a 25-year loan involve different payment schedules and amounts - so we can't directly compare or convert the total interest paid.

However, generally speaking, the total interest paid over a shorter loan term (i.e. 20 years) is expected to be less than that of a longer term (i.e. 25 years), assuming all else (loan amount, interest rate) remains equal - this is because the principal balance is being paid down more rapidly, leaving less time for interest to accrue. The trade-off is that monthly payments would be higher on the shorter term loan.

https://brainly.com/question/29011216

#SPJ12

Answer:

x^2 + y^2 + 6x - 8y + 21= 0.

Step-by-step explanation:

The center of this circle is (-3, 4) and the radius id 2.

So in Standard form, the equation is:

(x + 3)^2 + ( y - 4)^2 = 2^2

Converting to General form we have:

x^2 + 6x + 9  + y^2 - 8y + 16 = 4

x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0

x^2 + y^2 + 6x - 8y + 21= 0.

I believe the answer is d. 156,029

I think the answer is D

Answer: 5/6

Step-by-step explanation:

Add both of the fractions.

1/6+ 2/3

Need to make the denominator the same for both fractions.

Denominator would be 6. Multiply by 2 up and down for 2/3

1/6+4/6

5/6

Answer:

$1615.00

Step-by-step explanation:

First Place Vote: 4x867= 3468

Second Place Vote: 2x301= 602

Third Place Vote: 1x432= 432

3468+602+432= 4502.

Your answer is therefore D.

I hope this helps! :)

Answer:

D) 4502

Step-by-step explanation:

It is given that,

Points for first place = 4 points

Second place = 2 points

Third place = 1 point

Thus, First Place Vote : 4 × 867 = 3468

Second Place Vote: 2 × 301= 602

Third Place Vote: 1 × 432= 432

Thus, Total Points = 3468 + 602 + 432 = 4502.

Hence, last option is correct.

Answer:

Min: 76

Q1: 82

Med: 89

Q2: 95

Max: 100

Step-by-step explanation:

First arrange the data set 76, 100, 88, 83, 97, 94, 90, 99, 82, 86, 95, 81, 79, 95 in ascending order:

76, 79, 81, 82, 83, 86, 88, 90, 94, 95, 95, 97, 99, 100

The minimum number is 76 and the maximum number is 100. There are 14 numbers, the median is the average of two middle terms:

[tex]Med=\dfrac{88+90}{2}=89[/tex]

The middle term of first 7 numbers is 82 and the middle term of the second seven numbers is 95, so the five-number summary is

Min: 76

Q1: 82

Med: 89

Q2: 95

Max: 100

Answer: FIRST OPTION

Step-by-step explanation:

You need the formula for calculate the arc lenght:

[tex]arc\ length=2\pi r(\frac{C}{360})[/tex]

Where  "r" is the radius and and "C" is the central angle in degrees.

You know that the radius is:

[tex]r=7.5[/tex]

And the central angle ∠CAT is:

[tex]C=\angle CAT=125\°[/tex]

Then, you need to substitute these values into the formula  [tex]arc\ length=2\pi r(\frac{C}{360})[/tex] to calculate the length of CT.

Then, this is:

 [tex]arc\ length=CT=2\pi (7.5)(\frac{125\°}{360})[/tex]

[tex]arc\ length=CT=16.4[/tex]

Answer:

The wide would be 7.2 cm

Step-by-step explanation:

Let

x------> the wide of the proportional wall map

we know that

Using proportion

45/27=12/x

x=27*12/45

x=7.2 cm

Answer:

True

Step-by-step explanation:

The area of a regular polygon is found by multiplying 1/2 times the apothem times the perimeter.  The area for a single triangle is 1/2 times the height (which is the same as the apothem of a regular polygon) times the base (which is one of the sides of the regular polygon which you are multiplying by  to find the perimeter of the polygon).

Answer:

The given statement is true.

Step-by-step explanation:

The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas.

This is true.

Breaking down in 7 triangles and adding separately the areas of these triangles, will give the complete area of the heptagon. We can also find the area of one triangle and multiply that by 7 to get the same result.

Answer:

The answer is B

Step-by-step explanation:

just took the answer on e2020

Answer:

B:

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map  △QRS to △TUV.

Answer:

F

Step-by-step explanation:

You have to divide the the total number of yards lost (so 56) by 4 quarters. We know that lost yards are negative so therefore -56 divided by 4 is the answer

Answer:

a + b = 63

a - b = 12

So, a - b = 12 which can also be written as a = b + 12

Then use substitution and plug in (b + 12) for a in the first equation

(b+12) + b =63

-12              -12

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

2b  =  51 so b=25.5

Now, you know b which can be used to find a

63- 25.5= 37.5

So, a = 37.5 and b = 25.5

Answer:

25.5 and 37.5

Step-by-step explanation:

37.5-12=25.5

25.5+37.5=63

Answer: 530 cm^2

Step-by-step explanation:

A = 3.14 * r^2

A = 3.14 * 13 * 13

A = 3.14 * 169

A = 530 cm ^2

Answer:

Step-by-step explanation:

This is a special die.  Its six sides bear the numbers {9, 10, 11, 12, 13, 14}.

There are three possibilities for getting a multiple of two:  {10, 12, 14}, and

there is only one possibilities for getting a multiple of ten:  {10, 12, 14}

The probability here of getting a multiple of two is 3/6, and that of getting a multiple of ten is 1/6.  But one of the outcomes is found in both result sets:  10.  Getting a multiple of 10 is already included in the event that the outcome is a multiple of two.  My answer here would be 3/6, or 1/2.

the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.

The probability of rolling a multiple of two or ten on a die numbered 9 through 14 can be calculated as follows:

\

Answer:

The measure of angle EYL is [tex]45\°[/tex]

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

Let

x-----> the measure of arc EVL

y----> the measure of arc EHL

[tex]m<EYL=\frac{1}{2}(x-y)[/tex]

[tex]m<EYL=\frac{1}{3}(y)[/tex]

so

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

Multiply by 6 both sides

[tex]2y=3x-3y[/tex]

[tex]3x=5y[/tex]

[tex]x=\frac{5}{3}y[/tex] -----> equation A

[tex]x+y=360\°[/tex] -----> equation B  ( is a complete circle)

substitute equation A in equation B

[tex]\frac{5}{3}y+y=360\°[/tex]

[tex]\frac{8}{3}y=360\°[/tex]

[tex]y=(360\°)*(3)/8=135\°[/tex]

Find the value of x

[tex]x=\frac{5}{3}(135\°)=225\°[/tex]

Find the measure of angle EYL

[tex]m<EYL=\frac{1}{2}(x-y)[/tex]

substitute the values

[tex]m<EYL=\frac{1}{2}(225\°-135\°)=45\°[/tex]

Answer:

d. a=1. b=2, c=3

multiply by the Reciprocal.

Answer:

D

Step-by-step explanation:

(5/8) / (3/8)

(5/8) * (8/3)

5/3

1 ⅔

a = 1, b = 2, c = 3

Answer D.

Answer:

x = -16/7

Step-by-step explanation:

The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...

x ≈ 1.60945071137

_____

Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...

e^(x-2) = (1/e^6)^(x+3)

x -2 = -6(x +3) . . . . . . . . take the natural log of both sides

x -2 = -6x -18 . . . . . . . . . eliminate parentheses

7x -2 = -18 . . . . . . . . . . . add 6x

7x = -16 . . . . . . . . . . . . . add 2

x = -16/7

Answer:

[tex]-4[/tex]

Step-by-step explanation:

The given logarithmic equation is:

[tex]\log_7(x+1)+\log_7x=\log_712[/tex]

Recall and apply product rule of logarithms.

[tex]\log_aM+\log_aN=\log_aMN[/tex]

We apply this property to the left side of the equation to get;

[tex]\log_7x(x+1)=\log_712[/tex]

We take the antilogarithm of both sides to get:

[tex]x(x+1)=12[/tex]

We expand to obtain:

[tex]x^2+x=12[/tex]

We rewrite in the standard quadratic form:

[tex]x^2+x-12=0[/tex]

We factor to obtain:

[tex](x-3)(x+4)=0[/tex]

Either [tex](x-3)=0[/tex] or [tex](x+4)=0[/tex]

Either [tex]x=3[/tex] or [tex]x=-4[/tex]

But the domain is[tex]x\:>\:0[/tex].

Hence [tex]x=-4[/tex] is an extraneous solution.