A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?

y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x

Answer:

  $385.50

Step-by-step explanation:

The amount of commission is found by multiplying the commission rate by the value of the sale.

  1.5% × $25,700 = $385.50

A commission of $385.50 is made on an average car sold.

Answer:

Step-by-step explanation:

Solution,

We use the slope formula, setting x=a :

[tex] \displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }[/tex]

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.

Answer:

No. (-1/2) is not an integer

Integers involve all the no. +ve and -ve. which can be written without fraction. ie whole no. are counted as integers.

(-1/2) is a fraction

Answer:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Step-by-step explanation:

To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:

[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]

Evaluate the expression and finally, we have:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

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should i create the world problem with 12 3 and 9?

The remaining elements if Venn diagram is  S= { 4, 9}

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

Given:

E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

S = square numbers

E = even numbers

Element in set S= { 4, 9}

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Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.

Assuming this rate was x, the following formula would apply:

Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount

Solving gives:

x/365 x 32 x 8,000 = 140

701.369863x = 140

x = 140 / 701.369863

= 19.96%

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Step-by-step explanation:

1. True

2. False

3. True

5. Falsw

6.True

7.True

8.False

10.True

15. always

17. always

I'm assuming you meant to write y = 3x-4

We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).

The slope is

[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]

So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]

Answer:

212

Step-by-step explanation:

Simple addition and subtraction is to be used here.

5, 3 = 28

5-3 = 2 , 5+3 = 8

9 , 1 = 810

9-1 = 8 , 9+1 = 10

8 , 7 = 115

8-7= 1 , 8+7 = 15

6 , 2 = 48

6-2 = 4 , 6+2 = 8

7 , 5 = 212

7-5 = 2 , 7+5 = 12

Answer:

212

Step-by-step explanation:

Rule

5 - 3 = 2

5 + 3 = 8

Therefore: 28

9 - 1 = 8

9 + 1 = 10

Therefore: 810

8 - 7 = 1

8 + 7 = 15

Therefore: 115

6 - 2 = 4

6 + 2 = 8

Therefore: 48

7 - 5 = 2

7 + 5 = 12

Therefore: 212

Answer:

which p? there isn't any p in above equation

Answer:

  y ≈ 15272.9(1.06306^x) . . . . from regression tool

  y = 15300(1.0624^x) . . . . calculated "by hand"

Step-by-step explanation:

An exponential model is one that uses the exponential function ...

  f(x) = a·b^x

to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.

__

An exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...

  y ≈ 15272.9(1.06306^x)

__

We can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...

  average rate of growth =

  ((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624

Using the first table value as the initial value, the model formed this way is ...

  y = 15300(1.0624^x)

__

For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:

  average rate of growth = (220/153)^(1/6) ≈ 1.0624

This gives the same growth factor as above, hence the same model.

The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.

The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.

__

The values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:

Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.

The expression of base area of box will be 4x + x²

The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.

Given,

Length = 4+x

width = x

height = x²+1

We have to find the expression of base area of box

Given the length, width, and height

The formula for area of rectangle is as follow:

Area of rectangle = length x width

Area of rectangle = (4+x) x (x)

Area of rectangle = 4x + x²

Hence the expression of base area of box will be 4x + x²

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Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]

[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]

Question 1

[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]

[tex]\implies x=55^{\circ}[/tex]

Question 2

[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]

[tex]\implies x=11^{\circ}[/tex]

Question 3

[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]

Answer:

Vertical angles are angles opposite of each other. hope it helps

Answer:

(0, 7/12)

Step-by-step explanation:

to find the y intercept we equate x to 0.

hence,

f(0) = 7/12

the coordinate is (0, 7/12)

Answer:

[tex](0,\frac{7}{12})[/tex]

Step-by-step explanation:

In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.

[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]

Simplify:

[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]

Therefore, the y-intercept for the equation is:

[tex]\frac{7}{14}[/tex]

Part 1

[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]

Multiplying the numerator and denominator by x,

[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]

Part 2

The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).

The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]

Answer:

whats the question? please explain

The balance in Yolanda's saving plan after 14 years is; $9,455.36

We want to find the balance in Yolanda's saving plan after 14 years.

For Yolanda;

PV = 0

PMT = 250

i% = 4%/12 = 0.33%

N = 14 yrs * 12 = 168

FV = ?

For Zach:

PV = 0

PMT = $3300

i% = 4%

N = 14 yrs

FV = ?

From online future value calculator, we have;

Yolanda FV = $9,455.36

Zach FV = $47,204.19

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Answer:

A = 5, B = 9, C = 6

Step-by-step explanation:

let me know if you want an explanation :))

Answer:

p^2/r

Step-by-step explanation:

so I have shown every work in the picture attached

please let me know if this doesn't help

The ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

The ordered pairs will be calculated as:-

y = x² − 4

At  x = -2

y = ( -2)² - 4 = 4 - 4 = 0

At x = -1

y = (-1)² - 4 = -3

At x = 0

Y = 0² - 4 = -4

At x = 1

Y = 1 ² - 4 = -3

At x = 2

Y = (2)² - 4 = 0

Therefore ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

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Answer:

x/ 3x + 2

x approach 1

1/3 (1) + 2

1/ 5.

Last option: (50, 30); 50 adult tickets and 30 child tickets

A linear equation is an equation in which the highest power of the variable is always 1.

We have the system of equations:

x + y = 80

6x + 4y = 420

We will use elimination method to solve it:  

Multiply the first equation by -6 and then add the equations:

- 6x - 6y = -480

6x + 4y = 420  

We get:

-2y = -60

After dividing both sides by -2 we get:

y = 30

then plugging 30 in place of y into the original first equation we get:

x+30=80

Then subtracting 30 from both sides we get:

x = 50

The solution to the system is (50, 30)

Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.

Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.

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Answer:

( 50, 30)

Step-by-step explanation:

Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.

Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.

In general, the temperature equation for Portland, Maine is stated mathematically as

PoT=-PhT

As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,

PoT=-PhT

PhT =+PoT

Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.

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the end behavior is:

If we have a polynomial of even degree, then the end behavior in both ends is the same one.

Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.

In this case, the polynomial is:

y = 9x⁴ + 8x - 2

Notice that the degree is 4, even, and the leading coefficient is 9 (positive).

Then the end behavior is:

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Answer:

No solution

Step-by-step explanation: