Simplify f+g / f-g when f(x)= x-6 / x+7 and g(x)= x-7 / x+6

Answer:

-24-36x-5x

-24-41x

or -41x-24

Step-by-step explanation:

Answer:

C) 1.4

Step-by-step explanation:

The probability of choosing 2 good ones is 7/10·6/9 = 42/90.

The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.

The probability of choosing 0 good ones is 3/10·2/9 = 6/90

The expected value is the sum of the product of number of good ones and their probability:

... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4

Answer:

Correct choice is D

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..[/tex]

Fro mthe first equation

[tex]y=8-4x.[/tex]

Substitute into the second equation [tex]8-4x[/tex] instead of y:

[tex]6x-9(8-4x)=12.[/tex]

Note that [tex]8-4x=-4x+8,[/tex] then the second equation will take look

[tex]6x-9(-4x+8)=12.[/tex]

Answer:

x = 22 tan 31

x is approximately equal to 13.22

Step-by-step explanation:

We know from trigonometric functions that

tan A = opposite side/ adjacent side

tan 31 = x / 22

Multiply each side by 22

22 tan 31 = x

13.2189332

x is approximately equal to 13.22

Answer:

The answer is C)

Step-by-step explanation:

In order to fully solve a system of equations, you need both variables, x And y. Therefore he has to go back and solve for x

The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex]     multiply both sides by 3

[tex]a=\dfrac{3}{2}=4.5[/tex]

[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex]    multiply both sides by 4

[tex]b=\dfrac{3}{2}\cdot4=6[/tex]

[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex]     multiply both sides by 6

[tex]c=\dfrac{3}{2}\cdot6=9[/tex]

[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex]    multiply both sides by 7

[tex]d=\dfrac{21}{2}=10.5[/tex]

The perimeter:

[tex]P=4.5+6+9+10.5=30[/tex]

Answer:

36

Step-by-step explanation:

The previous answerer forgot to add the two 3's to the sum so the correct answer it 36

[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1[/tex]

Answer:

D

Step-by-step explanation:

The domain is the set of all x-values. We know the domain by finding the start and stop point of the function on the x-axis. The domain is all the values in between if the function is continuous without any breaks.

Here the function begins at x=-5 and ends at x=6.

We write the domain as [tex]-5\leq x\leq 6[/tex].

Answer is D.

Hey there!

"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"

In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator

So,  

[tex]80\frac{1}{4}[/tex]

[tex]80(4) = 320[/tex]

[tex]320 +1 = 321[/tex]

[tex]4[/tex] stays the same

[tex]\boxed{Answer: \frac{321}{4}}[/tex]

If you want the decimal form, simplify the  the mixed  to a improper then you should get a outcome of: [tex]80.25[/tex]

For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.

The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex].  To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Answer:

D. it does not converge

Let's do the usual thing and make t the years since 1950.   We'll just abbreviate a billion B.

f(1950-1950)=39.4 B

f(2000-1950) =2025.2 B

Our exponential form for f will be

[tex]f = a e^{kt}[/tex]

[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]

[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]

Dividing

[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]

[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]

[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]

Our function is

[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]

Since [tex]e^{0.0787932} \approx 1.08198[/tex]

[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]

around 8.2 % annualized growth.

Final answer:

An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Explanation:

We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.

From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:

f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.

f(50) = 2025.2 = 39.4 × b^50.

To find the value of 'b', we solve the second equation:

2025.2 = 39.4 ×  [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]

Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:

[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.

Answer:

(–6, –4)

Step-by-step explanation:

After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)

Answer:

(–6, –4)

Step-by-step explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.

It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.

Using the substitution method, make y the subject in the first equation

y = 5x + 26

substitute into the second equation

2x -7(5x + 26) = 16

-33x - 182 = 16

-33x = 16 + 182

-33x = 198

x = 198/-33

x = -6

since y = 5x + 26

y = 5(-6) + 26

= -30 + 26

= -4

hence (x,y) = (-6,-4)

Final answer:

To create a rectangular field with the same perimeter but a smaller area than the original 115 yards by 75 yards field, one could have a field that is 130 yards long and 60 yards wide.

Explanation:

To find the length and width of another rectangular field that has the same perimeter as a 115 yards by 75 yards field but a smaller area, we first calculate the perimeter of the original field:

Perimeter = 2(length + width) = 2(115 yd + 75 yd) = 2(190 yd) = 380 yd

To have a smaller area, the new field cannot be a square (which would maximize the area) and the sides need to have a greater difference in their measurements while still adding up to half of the original perimeter:

Let's assume the new length is 130 yards, to find the new width: 380 yd / 2 - 130 yd = 60 yd

Therefore, a new rectangular field could be 130 yards long and 60 yards wide.

Let us Represent the Line A in the Standard form : y = mx + c

where : m is the Slope of the Line and c is the y-intercept

Given : Equation of Line A is 2x + 3y = 10

[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]

Comparing with the Standard form, We can notice that :

Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]

We know that : Parallel lines have Same Slope

Given : Line A and Line B are Parallel

⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]

Given : Line B passes through the Point (-6 , 8)

We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)

Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]

Equation of Line B is :

[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]

⇒ 3y - 24 = -2x - 12

⇒ 2x + 3y = 12

Answer:

a. -1, odd; 2, even

b. [tex](x+1)(x-2)^2[/tex]

c. odd likely 3

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -1,2

We can write them in intercept or factored form as (x+1) and (x-2).  

Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.

The graph is ends up and is a sideways s so is positive with an odd degree.

This means the function has a degree of 3 or higher with the degree being odd.

Answer:

sin = √2/2, cos = -√2/2, tan = cot = -1

csc = √2, sec = -√2

Step-by-step explanation:

Angle runs around unit circle (where x^2+y^2=1)

from (1,0) to (-√2/2,√2/2)

A value which x represent in the function when determining the population after 6 years is 6.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

In this context, we can reasonably infer and logically deduce that the variable x in the standard form of the equation of an exponential function represent time, which can either be measure in years, months, days, hours, minutes, or seconds.

In conclusion, x represents 6 in the exponential function when determining the population after 6 years.

Complete Question:

An initial population of 8 wolves increases by 9% each year. The function [tex]f(x) = ab^x[/tex] models this situation. Which value does x represent in the function when determining the population after 6 years?

Final answer:

Ali's fish weighs 25/6 lb more than Lisa's fish.

Explanation:

To find out how much more Ali's fish weighs compared to Lisa's fish, we need to subtract the weight of Lisa's fish from the weight of Ali's fish.

Ali's fish weighs 9 and 1/2 lb, which can be rewritten as 19/2 lb. Lisa's fish weighs 5 and 1/3 lb, which can be rewritten as 16/3 lb.

Now, subtracting the weight of Lisa's fish from Ali's fish, we have:

Ali's fish weight - Lisa's fish weight = (19/2) lb - (16/3) lb = (57/6) lb - (32/6) lb = 25/6 lb.

Therefore, Ali's fish weighs 25/6 lb more than Lisa's fish.

Answer: choice A only

(1,-2) is the only solution (from the list of choices)

====================================

Explanation:

Let's go through each answer choice. We'll plug the coordinates in one at a time.

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

Choice A has the point (1,-2) so x = 1 and y = -2 pair up together

y < -|x|

-2 < -|1|

-2 < -1

This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.

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

Choice B) plug in (x,y) = (1,-1)

y < -|x|

-1 < -|1|

-1 < -1

False. A number is not smaller than itself. So we can cross B off the list.

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

Choice C) plug in (x,y) = (1,0)

y < -|x|

0 < -|1|

0 < -1

This is false because -1 is smaller than 0. Cross choice C off the list.

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

Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.

The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.

After evaluating each point against the inequality y < -|x|, only point A (1, -2) satisfies the condition, making it the correct answer.

To determine which point is a solution for the inequality y < -|x|, we need to check if the y-value of each point is less than the negative absolute value of its corresponding x-value.

Therefore, the correct answer is point A (1, -2), as it is the only point where the y-value is less than the negative absolute value of the x-value.

Answer: P = 4w + 4

Step-by-step explanation:

width (w) = w

length (L) = w + 2  (2 more than its width)

Perimeter (P) = 2L + 2w

P = 2L + 2w

  = 2(w + 2) + 2(w)

  = 2w + 4   +  2w

  = 4w + 4

Answer:

11x+8 cm = Perimeter

Step-by-step explanation:

A triangle has 3 sides.  We add up all three sides to get the perimeter.

s1+s2+s3 = Perimeter

(x+4) +( 3x+1) + (7x+3) = Perimeter

Combine like terms

11x+8 = Perimeter

Answer:

P = 11x + 8 cm

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of the three sides.

... P = s1 + s2 + s3

... P = (x +4 cm) +(3x +1 cm) +(7x +3 cm) . . . . substitute for s1, s2, s3

... P = x(1 +3 +7) + cm(4 + 1 + 3) . . . . . . collect terms

... P = 11x + 8 cm

Answer:

SSS can be used to prove that the given triangles are congruent.

Step-by-step explanation:

In the given two triangles ΔADC and ΔABC,

Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.

SSS congruence-

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Greetings!

Answer:

2370 miles can be travelled

Step-by-step explanation:

If 474 miles can be travelled in 1 hour, this means that to find the total amount in 5 hours we can simply multiply this value by 474:

474 * 5 = 2370

So it can travel 2370 miles!

Answer:

66

Step-by-step explanation:

divide 264/4=66

Answer:

C) 66 jumps

Step-by-step explanation:

Dana can jump 264 times in 4 minutes

Divide 364 by 4 to see how many times she can jump in one minute

264/4 = 66

Answer:

After 33 weeks.

Step-by-step explanation:

Let w be number of weeks.

We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.

To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.

[tex]20w+40=700[/tex]

Let us subtract 40 from both sides of equation.

[tex]20w+40-40=700-40[/tex]

[tex]20w=660[/tex]

Upon Dividing both sides of our equation by 20 we will get,

[tex]\frac{20w}{20}=\frac{660}{20}[/tex]

[tex]w=\frac{660}{20}[/tex]

[tex]w=33[/tex]

Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.

Answer:

$573

Step-by-step explanation:

955* 0.60=573

or

10% of 955= 95.5

50% of 955=477.5

477.5=95.5=573

The sale price of the computer is given by the equation A = $ 573

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the sale price of the computer after the price reduction be A

Now , the equation will be

The initial sale price of the computer = $ 955

The price reduction percentage on computer = 40 %

So , the sale price after reduction A = initial sale price of the computer - ( price reduction percentage x initial sale price of the computer )

Substituting the values in the equation , we get

The sale price after reduction A = 955 - ( 40/100 ) x 955

On simplifying the equation , we get

The sale price after reduction A = 955 - 382

The sale price after reduction A = $ 573

Therefore , the value of A is $ 573

Hence , the price of the computer is $ 573

To learn more about equations click :

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Answer:

You will want to set up the ratio for each and set them equal to each other. Then you can cross multiply to verify if you get the same answer. Another strategy is to set up each ratio and then reduce to lowest terms to see if you get the same fraction.

Step-by-step explanation: