The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?

Answer:

Step-by-step explanation:

You want the steps to finding the equation of the hyperbola with center (1, 4), vertices (-7, 4) and (9, 4) and that includes the point (-11, -6).

The standard-form equation of a hyperbola with center (h, k) and semi-axes 'a' and 'b' is ...

  [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

The "linear eccentricity" 'c' is the distance from the center to a focus, and satisfies the equation ...

  c² = a² +b²

The vertices are (h±a, k) and the foci are (h±c, k).

The center of the hyperbola is given as (1, 4). The distance from the right vertex to the center is ...

  a = 9-1 = 8

The equation thus far is ...

  (x -1)/8² -(y -4)/b² = 1

The value of 'b' can be determined from the given point:

  (-11 -1)²/8² -(-6 -4)²/b² = 1

  9/4 -100/b² = 1

  5/4 = 100/b²

  b² = 100/(5/4) = 80

The linear eccentricity is ...

  c² = a² +b²

  c² = 64 +80 = 144

  c = √144 = 12

The foci are (1±12, 4) = (-11, 4) and (13, 4).

The equation is ...

  (x -1)²/64 -(y -4)²/80 = 1

Answer:

[tex]\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1[/tex]

Step-by-step explanation:

Standard equation of a horizontal hyperbola (opening left and right):

[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

Given:

Therefore:

Find the value of a using the x-values of the vertices:

[tex]\begin{aligned}\implies h-a &= -7\\1-a &= -7\\a &= 8\end{aligned}[/tex]

[tex]\begin{aligned}\implies h+a &= 9\\1+a &= 9\\a &= 8\end{aligned}[/tex]

Therefore, a = 8.

Substitute the values of h, k and a into the formula:

[tex]\implies \dfrac{(x-1)^2}{8^2}-\dfrac{(y-4)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{b^2}=1[/tex]

Substitute the given point on the hyperbola (-11, -6) into the equation and solve for b²:

[tex]\implies \dfrac{(-11-1)^2}{64}-\dfrac{(-6-4)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{(-12)^2}{64}-\dfrac{(-10)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{144}{64}-\dfrac{100}{b^2}=1[/tex]

[tex]\implies \dfrac{144}{64}-1=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{144}{64}-\dfrac{64}{64}=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{80}{64}=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{5}{4}=\dfrac{100}{b^2}[/tex]

[tex]\implies b^2=\dfrac{4 \cdot 100}{5}[/tex]

[tex]\implies b^2=\dfrac{400}{5}[/tex]

[tex]\implies b^2=80[/tex]

Therefore, the equation of the hyperbola is:

[tex]\boxed{\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1}[/tex]

To find the foci, first find c where c² = a² + b²:

[tex]\implies c=\sqrt{a^2+b^2}[/tex]

[tex]\implies c=\sqrt{64+80}[/tex]

[tex]\implies c=\sqrt{144}[/tex]

[tex]\implies c=12[/tex]

Substitute the found value of c, along with the values of h and k into the foci formula:

[tex]\implies (h+c, k)=(1+12, 4)=(13,4)[/tex]

[tex]\implies (h-c,k)=(1-12,4)=(-11,4)[/tex]

Therefore, the foci are (-11, 4) and (13, 4).

Answer: 48

Step-by-step explanation:  

         first you divide 25/2 and you get 12.5 and that is irrelevant but what is relevant is that you divide 96 by 2 and you get 48 thus giving you the answer to that question. :)

The number of ladies in the club = 18

and the number of gentlemen in the club = 2

Let x be the number of gentlemen.

So, the number of ladies would be 3x + 12

Total number of people in garden = x + (3x + 12)

                                                         = 4x + 12

In a garden club, 90% is ladies.

This means, (3x + 12) is 90 percent of (4x + 12)

We get an equation,

(3x + 12) = 90/100 * (4x + 12)

We solve above equation to find the value of x.

30x + 120 = 36x + 108

6x = 12

x = 2 (number of gentlemen)

So, the number of lades would be:

3x + 12 = 3(2) + 12

            = 18

Therefore, the number of ladies in the club = 18 and the number of gentlemen in the club = 2

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Answer:

ASA

Step-by-step explanation:

As you can see in the picture it is giving us 2 angles, in between those 2 angles are aside. Therefore it is ASA.

We can also eliminate SSS because 2 angles and shown and SAS can also be eliminated because there are 2 angles, not sides.

The given rational expression when added gives

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

Given:

[tex] \frac{5}{(x + 3)(x - 4)} + \frac{7}{(x + 2)(x - 4)} [/tex]

=

[tex] \frac{5(x + 2) + 7(x + 3)}{(x + 3)(x - 4)(x + 2)} [/tex]

=

[tex] \frac{5x + 10 + 7x + 21}{(x + 3)(x - 4)(x + 2)} [/tex]

=

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

So therefore, the addition of the rational expression is

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

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Answer:

84

Step-by-step explanation:

80 x 0.05 = 4

80 + 4 =84

Answer:

X - 111

Y - 104

Z - 76

Step-by-step explanation:

X - Just add 45 and 66

Y - 180 minus 76

Z - 119 minus 43

Answer:

Step-by-step explanation:

M is slope

B is y intercept

X and y are given

using the equation for the y intercept

b=y1-mx1

B=1−(1/2)⋅(−6)=4

Write in y=Mx+b

=12+4

The general equation of the line is −2+8=0

The values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.

Given that; the equation F=9/5C+32 and ordered pairs are (25, F1), (−30, F2)

To convert the values to degrees Fahrenheit, we have to substitute the given values into the equation to get F1 and F2 respectively:

For (25, F1);

F = 9/5 C+32      

Now put C= 25 in the equation;

F1 = 9/5(25) + 32

F1 = 45 +22

F1 = 77 degrees Fahrenheit

For (−30, F2);

F = 9/5 C+32      

Now put C= -30 in the equation;

F2 = 9/5(-30) + 32

F2 = -54 + 32

F2 = -22 degrees Fahrenheit

Hence, the values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.

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The derivative function f' for the function f is f'(x) = -10 / (5x+3)^2 and Equation of the line tangent to the graph of f  is 5x+2y+7=0.

Given function:

f(x) = 2/5x+3

a.

f'(x) = d/dx(2/5x+3)

According to power rules:

1/u = -1/u^2

= 2(1/(5x+3)^2) d/dx(5x+3)

= 2*5 / (5x+3)^2

= -10/(5x+3)^2

Hence derivative function f' for the function f is f'(x) = -10 / (5x+3)^2.

b.

(a,f(a)) and a = -1

f(-1) = 2/5(-1)+3

= 2/-5+3

= 2/-2

= -1

point (-1,-1)

slope f'(x) = -10/(5x+3)^2

f'(-1) = -10/(5(-1)+3)^2

= -10/(-2)^2

= -10/4

m = -5/2

Equation of the line is  y - y1 = m(x-x1)

y - (-1) = -5/2(x-(-1)

2(y + 1) = -5x - 5

5x + 2y + 2 + 5 = 0

5x+2y+7=0.

Equation of the line tangent to the graph of f  is 5x+2y+7=0.

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Answer:

y = -2/5 x + 1

Step-by-step explanation:

slope = -2/5

y-3 = -2/5 (x -(-5)

y-3 = -2/5 (x+5)

y - 3 = -2/5 x - 2

y = -2/5 x - 2 + 3

y = -2/5 x + 1

Answer:

2 people watch tv 3 hours a day, 3 people watch tv 0 hours a day, 2 people watch tv 1 hour a day, 2 people watch tv 2 hours a day, and 1 person watches tv 4 hours a day

Step-by-step explanation:

hope it helped :)

From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

As given in the question,

Given pair of lines,

Condition given that two angles are congruent ,

∠5 ≅ ∠7

Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.

Opposite angle and Angle 7 are pair of corresponding angles.

Line l should be parallel to the line m to satisfied the condition of

∠5 ≅ ∠7.

Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

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Answer:

It is positive and increasing

Step-by-step explanation:

After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"

Answer:

The Question is not Correct but answer is f 3 and g 3

The volume or the upper limit of the jellybean jar is 2,208.83cm³.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Volume and mass are the two fundamental characteristics of matter.

Volume is only the amount of space that a thing occupies.

There are a few methods for determining an object's volume depending on its physical state.

So, the volume of the Jellybean jar:

Formula: πr²h

Now, insert values and calculate as follows:

πr²h

π(6.2)²18.3

π38.44(18.3)

π703.452

2,208.83

Therefore, the volume or the upper limit of the jellybean jar is 2,208.83cm³.

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Answer:

y = - 3x - 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (- 4, - 2 ) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = - 3x - 14 ← equation of line

The angle B is 66°

Given,

In the question:

If angle A is (2x) and angle B is (3x+11)°

and, the sum of angle A and angle B is 66°

To find the angle of B.

Now, According to the question:

Based on the given condition:

Angle A = 2x

Angle B = (3x + 11)°

The sum of angle A and B is 66°

2x +  (3x + 11)° =  66°

5x + 11 =  66°

Calculate the sum or difference

5x = 66 - 11

3x = 55

x = 55/3

The angle B is = 3x + 11

Plug the value of x in angle B

3 × 55/3 + 11

= 66

Hence, The angle B is 66°

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Answer: [tex]6\\[/tex]

Step-by-step explanation:

[tex]\frac{(3+9) * 2}{4}[/tex]

Add 3 and 9 to get 12.

[tex]\frac{12 * 2}{4}[/tex]

Multiply 12 and 2 to get 24.

[tex]\frac{24}{4}[/tex]

Divide 24 by 4 to get 6.

[tex]6[/tex]

Answer:

(7,-4)

Step-by-step explanation:

y +  4 = -5(x-7)  Substitute in 7 for x and -4 for y

-4 + 4 = -5 (7-7)

0 = 5(0)

0 = 0  This is a true statement.

The distance travelled before their first gas stop is 76.68 miles.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Consider that the distance covered before their first stop for gas be 'x'

The Total distance travelled is 372 miles

WE have given that after stopping for gas they travelled  65 1/4 miles and then tripled their distance. The equation is;

x + 261/4 + 3x = 372

4x + 261/4 = 372

16x + 261 = 1488

16x = 1227

x = 76.68 miles

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It would take 11.1 hours to decay from 500 grams to 299 grams.

We know that for an element with an half-life T has a decay equation that can be written as:

f(t) = A*e^(-t*ln(2)/T)

Where A is the initial amount, and f(t) is the amount of the element t hours after.

Here we know that:

A = 500g

T = 15h

Then the function is:

f(t) = 500g*e^(-t*ln(2)/15h)

And we want to find the value of t such that f(t) = 299g, then:

299g =  500g*e^(-t*ln(2)/15h)

299/500 = e^(-t*ln(2)/15h)

ln(299/500) = -t*ln(2)/15h

-ln(299/500)*15h/ln(2) = t

11.1h = t

It will take 11.1 hours.

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Answer:

96

Step-by-step explanation:

Area of a triangle

A = (1/2) × base × height

A = (1/2) × 12 × 16

A = (1/2) × 192

A = 96 units²

I hope this helps!

The value of the investment at the end of 5 years be $ 15,281.012.

Given, 10400 dollars are invested at an interest rate of 8%.

We have to find the value of the investment at the end of 5 years.

Now, on using the compound interest formula, we get

Amount = P(1 + r/100)^t

Amount = 10400(1 + 8/100)^5

Amount = 10400(1.08)^5

Amount = 10400(1.469)

Amount = 15,281.012

Hence, the value of the investment at the end of 5 years be $ 15,281.012.

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The airplane is 359.12 feet high.

Given,

The distance between the observers = 1050 feet

When an aero plane crosses the line connecting them, each observer measures the plane's elevation angle.

Angle A = 40 degrees

Angle B = 30 degrees

We have to find the height of the airplane.

Here,

C = 180 - (40 + 30) = 110°

According to the sine rule :

Sin110 / 1050 = Sin40 / b = Sin 30 / a

1050 sin40 / sin 110 = b = 718.24 ft

1050 sin 30 / sin 110 = a = 558.69 ft

Sin 40 = h / 558.69

h = 558.69 × sin 40

h = 359.12 feet

That is,

The airplane is 359.12 feet high.

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Answer:

$48.5

Step-by-step explanation:

From the question, we know that Jen and Kevin are definitely adults and the fee for adults

= $22.50

Jon is 14, and any number from 12 to 17 is classified as a youth, so his fee is

= $16.25

Beth is 8, classified as a child, her fee is

= $9.25

Joshua's age which is below 5 is granted free entry without a fee

Hence, the total cost of admission for the family is

$22.50 + $16.25 + $9.75

= $48.5

Considering the situation described, it is found that:

At the null hypothesis, it is tested if the mean is of 6 minutes, that is:

[tex]H_0: \mu = 6[/tex]

At the alternative hypothesis, it is tested if the mean is less than 6, hence:

[tex]H_1: \mu < 6[/tex]

The test statistic is obtained as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters of the equation are:

Using a calculator from the sample, the values of the parameters are:

[tex]\overline{x} = 5.39, \mu = 6, s = 1.22, n = 15[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{5.39 - 6}{\frac{1.22}{\sqrt{15}}}[/tex]

t = -1.94.

The p-value is obtained with a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.94 and 15 - 1 = 14 df, hence it is of 0.0364.

Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected and there is not enough evidence that the mean is less than 6 days.

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Answer:

At this price, i would say the demand is: Unitary Inelastic Elastic Based on this, to increase revenue we should: Lower Prices Raise Prices Keep Prices