Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at x = 4.

Answer:

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x -----> the amount invested at 5.5%

(64,000-x) -----> the amount invested at 9%

in this problem we have

[tex]t=1\ years\\I=\$4,500\\ P=\$64,000\\r1=0.055\\P1=\$x\\P2=\$64,000-\$x\\r2=0.09[/tex]

so

[tex]I=P1(r1t)+P2(r2t)[/tex]

substitute the given values

[tex]4,500=x(0.055*1)+(64,000-x)(0.09*1)[/tex]

[tex]4,500=0.055x+5,760-0.09x[/tex]

[tex]0.09x-0.055x=5760-4,500[/tex]

[tex]0.035x=1,260[/tex]

[tex]x=\$36,000[/tex]

[tex]64,000-x=64,000-36,000=\$28,000[/tex]

therefore

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Answer:

could it be letter H? please lmk

[tex]\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)sin(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad -\quad cos(\alpha+\beta)]\qquad \leftarrow \textit{we'll use this one} \\\\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)] \\\\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)][/tex]

[tex]\bf cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5x)sin(3x)\implies \cfrac{cos(5x-3x)-cos(5x+3x)}{2}\implies \cfrac{cos(2x)-cos(8x)}{2}[/tex]

Answer:[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right )[/tex]

Step-by-step explanation:

Solution

[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )[/tex]

We know

[tex] 2sin\left ( a\right )sin\left ( b\right )=cos\left ( a-b\right )-cos\left ( a+b\right ) [/tex]

Applying formula

[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )=\frac{1}{2}\left ( cos\left ( 5x-3x\right )-cos\left ( 5x+3x\right )\right )[/tex]

=[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right ) [/tex]

Answer: 70

Step-by-step explanation:

Solve the equation in the innermost parentheses first that means solving 4+1 =5

The next step would be subtracting 9 from five which gives you 4

Next multiply 3 to 4 which gives you 12

Then multiply 5 with 12 which equals 60

Now you have the equation 60+20/4*2

Solve the division and multiplication part of the equation first because of the rule pemdas which shows multiplication comes before addition

First divide 20/4 which gives you 5 then multiply with 2 which gives you ten

After dividing and multiplying you are left with the equation 60+10

The answer is 70

Answer:

the number 6 is in the tenths place.

Hope this helps!

Answer:

First problem: Solving for g.

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]x=3.5[/tex]

Step-by-step explanation:

First problem: Solving for g.

[tex]g^{x-2}=27[/tex]

Raise both sides by 1/(x-2).

[tex](g^{x-2})^{\frac{1}{x-2}}=27^{\frac{1}{x-2}}[/tex]

[tex]g^{1}=27^{\frac{1}{x-2}}[/tex]

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]g^{x-2}=27[/tex]

x is in the exponent so we have to convert to logarithm form since we desire to solve for it:

[tex]\log_g(27)=x-2[/tex]

Add 2 on both sides:

[tex]\log_g(27)+2=x[/tex]

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]9^{x-2}=27[/tex]

I'm going to solve this in a different way than I did above but you could solve it exactly the way I did for x when 9 was g.

I'm going to write both 9 and 27 as 3 to some power.

9=3^2 while 27=3^3.

[tex](3^2)^{x-2}=3^3[/tex]

[tex]3^{2x-4}=3^3[/tex]

Since both bases are the same on both sides, we need the exponents to be the same:

[tex]2x-4=3[/tex]

Add 4 on both sides:

[tex]2x=7[/tex]

Divide both sides by 2:

[tex]x=\frac{7}{2}[/tex]

[tex]x=3.5[/tex]

Now earlier for x in terms of g we got:

[tex]x=\log_g(27)+2[/tex]

I we input 9 in place of g and put it into our calculator or use some tricks without the calculator to compute we should get 3.5 as the answer like we did above when g was 9.

[tex]x=\log_9(27)+2[/tex]

[tex]x=\frac{3}{2}+2[/tex]

[tex]x=1.5+2[/tex]

[tex]x=3.5[/tex]

Answer:

$132,612.50

Step-by-step explanation:

We will use the present value - future value formula. WHich is:

[tex]FV=PV(1+r)^t[/tex]

Where

FV is the future value (amount)

PV is the present value (amount)

r is the rate of interest (per year)

t is the number of years

In the problem given, the present amount (PV) is 125,000. The rate of interest (r) is 3%, or 0.03. And the time frame is 2 years, or t = 2.

Plugging these info in the equation, we can get the future value as shown:

[tex]FV=PV(1+r)^t\\FV=125,000(1+0.03)^2\\FV=125,000(1.03)^2\\FV=132,612.5[/tex]

This is the future vallue of $125,000 3% in 2 years.

The circumference of a circle with an area of 50.3 m² is 25.12 m.

For example;

For example;

In this case;

The Area of a circle = 50.3 m²

π = 3.14

But; Area of a circle = πr²

Therefore;

3.14r²= 50.3 m²

r² = 50.3/3.14

   =16.019

r = √16.019

 = 4.0023

 ≈ 4.00

But;

Circumference of a circle is given by 2πr

Thus;

Circumference = 2 × 3.14 × 4.00

                          = 25.12 m

Keywords; Perimeter, Area, Area of a circle, Circumference of a circle

Level: Middle school

Subject; Mathematics

Topic: Area and Perimeter

Sub-topic: Area and circumference of a circle

Answer:

See attachment

Step-by-step explanation:

The mapping for a dilation with a scale factor k, about the origin is given by:

[tex](x,y) \to \: (kx,ky)[/tex]

From the graph, the coordinates of B are (1,1) and the scale factor is k=4.

We substitute into the rule to get

[tex]B(1,1) \to \: B'(4,4)[/tex]

The image of point B is plotted on the graph in the attachment.

To find the image of point B under a dilation with a scale factor of 4 about the origin (0,0), multiply the coordinates of point B by 4.

To plot the image of point B under a dilation with a scale factor of 4 about the origin (0,0), we need to multiply the coordinates of point B by the scale factor. If point B is represented as (x,y), then the image of B would be (4x, 4y).

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[tex]\bf \textit{volume of a square pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{4\times 4}{16}\\ V=37.3 \end{cases}\implies 37.3=\cfrac{1}{3}(16)h\implies 111.9=16h \\\\\\ \cfrac{111.9}{16}=h\implies 6.99375=h[/tex]

Answer:

6.99

Step-by-step explanation:

To find the height use the formula 3*V/b squared

So plug the numbers you have which is the base and volume

3*37.3/4 squared

Now solve:

4 squared = 16

3*37.3 = 111.9

111.9/16 = 6.99375

6.99375 can be rounded down to 6.99

Answer:

a) negative

Step-by-step explanation:

When you multiply a given negative number by a positive number, the result becomes smaller than the original.

For instance let [tex]-100[/tex] be the original number.

Multiply by 2.

The result is -200

We know [tex]-200\:<\:-100[/tex]

The correct answer is A.

Answer: a) negative

Step-by-step explanation:

-100x2=-200

-200 is negative.

Answer:

Area = [tex]\frac{75}{4} \sqrt{15} sq mm[/tex]

Step-by-step explanation:

Here we are given with all the sides of the triangle , and we are asked to find the area of it. we will use Heron's Formula to find the area. The formula is as under

Area [tex]= \sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]

Where [tex]s= \frac{a+b+c}{2}[/tex]

Where a , b and c are the three sides of the triangle

a=15 , b=10 and c=20

Substituting those values in the two formula one by one we get

[tex]s=\frac{15+10+20}{2}[/tex]

[tex]s=\frac{45}{2}[/tex]

now putting this value of s in main formula we get

Area= [tex]\sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45}{2}-15) \times (\frac{45}{2}-10) \times (\frac{45}{2}-20)}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45-30}{2}) \times (\frac{45-20}{2}-) \times (\frac{45-40}{2})}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{25}{2}) \times (\frac{5}{2})}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{20}{2}-) \times (\frac{5}{2})}[/tex]

Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]

Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]

Area = [tex]\frac{1}{4} \sqrt{9 \times 5 \times 5 \times 3 \times 25 \times 5}[/tex]

Area = [tex]\frac{3\times 5 \times 5}{4} \sqrt{3 \times5}[/tex]

Area = [tex]\frac{75}{4} \sqrt{15}[/tex]

The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]

For example;

                    =  1/2 x base x height

For example;

In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm

Therefore, we use the Heron's formula;

Area= [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

 [tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

       = [tex]22.5\sqrt{12.5(12.5-15)(22.5-10)(22.5-20)}[/tex]

       =[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]

[tex]= 72.618 mm^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle

The question revolves around understanding the concepts of fixed costs, marginal costs, and economies of scale in the context of a computer manufacturing company. The company's ability to make substantial profits over a period of four years marks an effective management of these costs and leveraging economies of scale.

The computer company's scenario primarily involves understanding the concept of fixed costs and marginal costs in a business context. The fixed cost noted here is $250, which remains constant irrespective of the number of computers produced. The marginal cost, on the other hand, is variable depending on the volume of production.

For example, the company's marginal cost for producing computers is $700 for the first one, $250 for the second, and so on. The total cost is obtained by adding the fixed cost and the total variable (marginal) costs. Understanding these costs is critically important for the company to make decisions about pricing its products to achieve desired profit margins.

It means that if the company managed to make profits of $80 million after 4 years, they have effectively managed their fixed and variable costs and priced their computers profitably. In this example, by leveraging the economies of scale, that is, an advantage that companies gain when production becomes efficient with the increasing scale of output, the company has managed to reduce the average cost of production and increase profits.

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Answer: 120 cm.

Step-by-step explanation: Each triangle has 3 sides, and each side is 1 cm. Multiply the number of sides for one triangle by the total number of triangles. 3 x 40=120. The perimeter is 120 cm.

For a standard normal distribution, the standard deviation is always equals 1

Z score is used to determine by how many standard deviations the raw score is above or below the mean.

It is given by:

z = (raw score - mean) / standard deviation

For a standard normal distribution, the standard deviation is always equals 1

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Answer:

2

Step-by-step explanation:

To find the slope of a line given two points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] you could use the formula: [tex]\frac{y_2-y_1}{x_2-x_1} \text{ or even } \frac{y_1-y_2}{x_1-x_2}[/tex].

However, what I'm fixing to do is equivalent to that except I think easier to remember.

You line up the points vertically and subtract, then put 2nd difference over 1st difference.

Like this:

 ( 3  ,   4)

- ( 5  ,   8)

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

-2        -4

So the slope is -4/-2=4/2=2.

The slope is 2.

Hey there!

Isolate the y variable by subtracting 12x in both sides:

-4y = -12x - 8

To solve for y divide -4 in both sides

y = 3x + 2

Our answer would be y = 3x + 2

Answer:

y = 3x + 2

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 )

Rearrange 12x - 4y = - 8 into this form

Subtract 12x from both sides

- 4y = - 12x - 8 ( divide all terms by - 4 )

y = 3x + 2 ← in slope- intercept form

Answer:

x = 2.

Step-by-step explanation:

9(x + 1) = 25 + x

9x + 9 = 25 + x

Subtract x from both sides:

9x - x + 9 = 25

Subtract 9 from both sides:

9x - x = 25 - 9

8x = 16

x = 16/8 = 2.

Answer:

x = 2

Step-by-step explanation:

Given

9(x + 1) = 25 + x ← distribute parenthesis on left side

9x + 9 = 25 + x ( subtract x from both sides )

8x + 9 = 25 ( subtract 9 from both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Step-by-step explanation:

let's Recall the properties of a parallelogram

1. the opposite sides of a parallelogram is congruent

AB=CD

8x-7=5x+2

8x-5x=7+2

3x=9

x=3

2. the consecutive angles are supplementary

angle A+angle D=180°

2y+50°+3y+40°=180°

5y+90°=180°

5y=90°

y=18

Answer with step-by-step explanation:

We are given that at one farmer’s market, bananas cost $0.80 per pound while at another market, bananas are sold in 5 pound bags for $4.50 per bag.

We are to explain how to find the better buy.

For the first market, the rate of bananas is given per pound but for the other market, the rate is given for a 5 pound bag so we will find the rate of bananas per pound to compare the rates of both markets.

One pound of bananas at 2nd market = 4.50/5 = $0.9

Therefore, getting bananas from the first market at $0.80 per pound is a better buy.

Answer: A

Step-by-step explanation:on My quiz I got it right

The slope of the line is the change in the Y values over the change in X values.

Using the given points (2,-5) and (-2,3)

The Y values are -5 and 3 and the X values are 2 and -2.

The slope = (3 - (-5)) / -2 - 2) = 8/-4 = -2

The slope is -2

Answer:

The answer is B) Medical Research

Step-by-step explanation:

Medical research is something typically done by private companies.

Answer: B. Medical research.

Step-by-step explanation: Public Health Programs: the types of public health programs that address STIs are: Prevention education, testing and counseling, and diagnosis and treatment.

:)

Answer:  The correct options are

(2) The coefficient is 2.

(3) The constant is 5.

(6) There are two terms.

Step-by-step explanation:  Given that Javier used the expression below to represent his score in a game of mini-golf :

[tex]E=3x+x+5-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to select the correct statements about the parts of the simplified expression if Javier simplifies the expression.

The simplification of expression (i) is as follows :

[tex]E\\\\=3x+x+5-2x\\\\=(3+1-2)x+5\\\\=2x+5.[/tex]

Therefore, we get

the constant term is 5,

the coefficient of x is 2

and

There are two terms.

Thus, options (2), (3) and (6) are correct.

Answer:

think its 2 3 and 6

Step-by-step explanation:

sorry if im late

Answer:

5i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

and [tex]\sqrt{-1}[/tex] = i

Given

[tex]\sqrt{-75}[/tex]

= [tex]\sqrt{25(3)(-1)}[/tex]

= [tex]\sqrt{25}[/tex]  × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]

= 5 × [tex]\sqrt{3}[/tex] × i

= 5i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Use (a+b)²= a²+2ab+b² formula

We can see that a²=81n² (so a=9n) and b²=100 (so b=10) and 2ab = 2*9n*10=180n.

therefore only √(81n²+180n+100) would be perfect square and this - isn't.

Answer:

4.2 meters.

Step-by-step explanation:

Area = 1/2 * base * height.

6.72 = 1/2 * 3.2 * h

h = 6.72 / 1.6

= 4.2 m.

Answer:

4.2 meters

Step-by-step explanation:

The height of a triangle with an area of 6.72 square meters and a base of 3.2 meters is 4.2 meters.

6.72 = 1/2 * 3.2 * h

Answer:

1

Step-by-step explanation:

Solve the equation for x:

3(x + 5) = -4x + 8

Distribute.

3x + 15 = -4x + 8

Combine like terms.

3x + 15 = -4x + 8

+4x         +4x

7x + 15 = 8

     -15   -15

7x = -7

Divide both sides by 7.

x = -1

The following equation has one solution, x = -1.

Answer:

1 solution,  x = -1.

Step-by-step explanation:

3(x + 5 )= −4x + 8

3x + 15 = -4x + 8

3x + 4x = 8 - 15

7x = -7

x = -1.

So,

[tex]y>1\wedge y>x[/tex]

1. Graph each inequality separately.

2. Choose a test point to determine which side of the line needs to be shaded.

3. The solution to the system will be the area where the shadings from each inequality overlap one another (purple area)

As for the system of inequalities we say it's unbounded.