f(x)=3x-7 and g(x)=2x-4 find (f+g)(x) and (f-g)(x)

Answer:

Polygon ABCDE = 50 units

Polygon FGHIJ = 23.4 units

Polygon KLMNO = 19.24 units

Polygon UVWXY = 38 units

Step-by-step explanation:

In order to find the perimeter, we have to find lengths of all sides of given points

The distance formula will be used to find the lengths

[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]

where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)

So,

For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)

AB = 13 units

BC = 2 units

CD = 17 units

DE = 15 units

EA = 3 units

Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units

For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)

FG = 2 units

GH = 5 units

HI = 6.40 units

IJ = 5 units

JF = 5 units

Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units

For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)

KL = 4 units

LM = 5 units

MN = 6 units

NO = 2.24 units

OK = 2 units

Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units

For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)

PQ= 5 units

QR= 4 units

RS=6.40 units

ST= 5 units

TP = 5 units

Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units

For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)

UV = 8 units

VW = 10 units

WX = 12 units

XY = 5 units

YU = 3 units

Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units

Answer:

The total  number of votes was [tex]7,007[/tex]

Step-by-step explanation:

Let

x -----> the number of yes votes

y -----> the number of no votes

we know that

[tex]\frac{x}{y} =\frac{6}{5}[/tex]

isolate variable y

[tex]y=\frac{5}{6}x[/tex] -----> equation A

[tex]x=3,822[/tex] -----> equation B

Substitute equation B in equation A and solve for y

[tex]y=\frac{5}{6}(3,822)=3,185[/tex]

therefore

To find out the total number of votes sum the number of yes votes plus the number of no votes

[tex]3,822+3,185=7,007[/tex]

Answer: 7,007 votes :)

Step-by-step explanation:

Hope that helps

Answer:

x=2

Step-by-step explanation:

Vertical lines have the same x value all the time.  It is of the form x=

Their slope is undefined

The line passes through the point (2,4) and the x value is 2

x=2

Answer:

[tex]\sin(x)=\frac{\sqrt{95}}{12}=0.8122[/tex]

[tex]\cos(x)=\frac{7}{12} \approx .5833[/tex]  

[tex]\tan(x)=\frac{\sqrt{95}}{7} \approx 1.3924[/tex]  

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12}) \approx 54.3147[/tex] degrees.

I don't know what you want to round to but I can tell you are rounding...

Step-by-step explanation:

Soh Cah Toa is the acronym we will use to help us solve this.

This says sine is opposite over hypotenuse.

It also says cosine is adjacent over hypotenuse.

And finally tangent is opposite over adjacent.

Note:  Opposite and adjacent can change depending on how you are looking at the triangle, like which angle you are referring to.

Let's look at x:

The side that is opposite, not touching, the angle whose measurement is x, is the side that has measurement [tex]\sqrt{95} \approx 9.7[/tex].

I see you already found this measurement. This is really good.  I might use the exact value for now and round at the end.

The side that is the hypotenuse no matter the angle you are referencing is always going to be opposite the angle whose measurement is 90 degrees. It is also the longest side (since it is opposite the largest angle).  This side has measurement 12.

The hypotenuse will be one of the sides touching your angle you are referencing.  The other side that is touching your angle is the adjacent side.  This side has measurement 7.

Anyways let's plug into the definitions we had above:

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]  (O/H)

[tex]\cos(x)=\frac{7}{12}[/tex]   (A/H)

[tex]\tan(x)=\frac{\sqrt{95}}{7}[/tex]   (O/A)

Now we can solve anyone of these for x.

Take your pick.

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12})[/tex]

[tex]x=54.3147[/tex] degrees.  

Answer:

48

Let me know if this was right :)                                                

a) 600340

b) 600300

c) 600000

Answer:

range=u ± 3.09 sd

Step-by-step explanation:

Given:

mean, u= 26.8 mpg

standard deviation, sd=72 mpg

% contained in interval = 99.8%

the interval for 99.8% of the values of a normal distribution is given by

mean ± 3.09 standard deviation= u ± 3.09 sd

                                                      =26.8  ± 3.09(72)

                                                      =26.8 ± 222.48

                                                      = 249.28 , -195.68

range=u ± 3.09 sd = 249.28 , -195.68 !

[tex]2(n-5)\geq2n+10\\2n-10\geq2n+10\\-10\geq 10\\n\in\emptyset[/tex]

The key  property of the absolute value parent function is:

        C. It’s vertex is at the origin.

The absolute value parent function is given by:

                  [tex]f(x)=|x|[/tex]

i.e. the graph of the function lie in the first and second quadrant.

Answer: P(red): 1/2

P(red or black):3/4

Step-by-step explanation: Count the total number of marbles. There are 8. Since there are 4 red marbles out of the 8, put this into a fraction. It will be 4/8, but simplify to 1/2. The P(red) is 1/2.

Since there are 4 red marbles and 2 black marbles, add them. There are 6 out of the 8 marbles. The fraction is 6/8 simplify to 3/4. The P(red or black) is 3/4.

The probability of choosing a red marble from the box is 0.5 and the probability for choosing either a red or black marble is 0.75.

The subject of this question refers to calculating probabilities which is a concept in Mathematics, specifically in the scope of Statistics. To calculate the probability of an event, we need to know the total amount of outcomes and the amount of favorable outcomes. In the context of the question, these outcomes are represented by marbles.

First, we need to add the total number of marbles, which is 4 red + 2 black + 2 green = 8 marbles in total.

To find the probability of picking a red marble, we divide the number of red marbles by the total number of marbles. Hence, P(red) = 4/8 or 0.5.

To find the probability of picking a red or black marble, we add the number of red and black marbles and divide by the total number of marbles. Hence, P (red or black) = (4 red + 2 black) / 8 total = 6/8 or 0.75.

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[tex]xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18[/tex]

Answer:

The product of x and y is 8.

Step-by-step explanation:

It is given that

[tex]x=\log_{5\sqrt{5}}\left(125\right)[/tex]

[tex]y=\log_{2\sqrt{2}}\left(64\right)[/tex]

We need to find the product of x and y.

[tex]x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)[/tex]

It can be written as

[tex]xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4[/tex]

Using the properties of logarithm, we get

[tex]xy=2\cdot 4[/tex]                    [tex][\because log_aa^x=x][/tex]

[tex]xy=8[/tex]

Therefore the product of x and y is 8.

Answer:

Increasing

Step-by-step explanation:

Let's see what happens if we choose a value for b greater than 1.

Let's try b=2.

[tex]f(x)=2^x[/tex].

I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.

Let's start with x=1.

[tex]y=2^1=2[/tex]

Now x=2.

[tex]y=2^2=4[/tex]

The y's got higher as you increased x so the function is increasing.

The function keep increasing for the varying value of x, hence the exponential function is increasing

Given the exponential function f(x) = [tex]b^x[/tex]

We are to check if the function is increasing or decreasing if b is greater than 1

Let b = 2 and x = 1

[tex]f(1) = 2^1\\f(1) = 2[/tex]

Let b = 2 when x = 2

[tex]f(2)=2^2\\f(2)=4[/tex]

Let b = 2 when x = 3

[tex]f(3)=2^3\\f(3)=8[/tex]

You can see that the function keep increasing for the varying value of x, hence the exponential function is increasing

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Answer:

C

Step-by-step explanation:

MEAN:4+7+11+11+16+17=66÷6=11

MEDIAN:11+11=22÷2=11

MODE=11

Answer:

The correct answer is option C

4,7,11,11,16,17

mean = mode = median = 11

Step-by-step explanation:

Check option A

10,10,12,12,13,13

Mean = 12, mode = 12,13 , 14 and median = 12

Check option B

2,3,4,4,5,7

Mean = 4.15, mode = 4 and median = 4

Check option C

4,7,11,11,16,17

Mean = 11, mode = 11 and median = 11

Check option D

1,2,3,3,5,6

Mean = 3.33, mode =3 and median = 3

The correct answer is option C

4,7,11,11,16,17

mean = median = mode = 11

Answer:

15/56

Step-by-step explanation:

You just multiply 3/7 by 5/8 to get 15/56. Since you cannot simplify it more, that is the fraction of boys in mrs.jones class compared to the whole sixth grade class

Answer:

15/56

Step-by-step explanation:

Let the total number of students be x

Number of boys=[tex]\frac{3}{7}[/tex] of x

Number of boys in Mrs jones' class= [tex]\frac{3}{7}[/tex]of[tex]\frac{5}{8}[/tex]

Fraction of number of boys of Mrs jones' class to total class strength=[tex]\frac{15x/56}{x}[/tex]

Hence, the fraction is[tex]\frac{15}{56}[/tex]

Answer:

lol i need help with the same question

Step-by-step explanation:

Roger, with a batting average of 0.250, recorded 60 successful hits from a total of 240 attempts. Therefore, he failed to get a hit 180 times.

In this question, we are dealing with Roger's batting average and his performance. A batting average of 0.250 means that for every 4 at-bats, Roger gets a hit on average 1 time. So, if he has been at bat a total of 240 times, we can expect that he got hits 0.250 times out of these at-bats. So to calculate the number of successful hits, we multiple 240 by 0.250 which equals 60. Therefore, Roger has hit the ball 60 times. To find out how many times he failed to get hits, we subtract his hits from his total tries. So, 240 - 60 = 180. Therefore, Roger failed to get a hit 180 times.

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Answer:

A

Step-by-step explanation:

equivalent because each are 1:2

Final answer:

After simplifying each pair of ratios, only 12: 24, and 50:100 (Pair A) are equivalent ratios, as both simplify to 1:2. The other pairs are not equivalent since their simplified forms are different.

Explanation:

To determine which of the pairs of ratios are equivalent, we can simplify each ratio or convert them to fractions and simplify to see if they have the same value. Let's look at each pair:

From the above, only the pair A) 12: 24, 50:100 are equivalent ratios.

Answer:

[tex]\3.11\ ounces[/tex]

Step-by-step explanation:

we know that

To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles

so

[tex]\frac{84}{27}=3.11\ ounces[/tex]

Answer: 3.1

Step-by-step explanation: which is 3.1 with the line on top!

To prove that two functions are inverse, we need to show that applying one function and then the other will result in the original input. By evaluating f(g(x)) and g(f(x)), we can confirm that f(x) = x + 3/2 and g(x) = 2x - 3 are inverse functions.

To prove that two functions f(x) and g(x) are inverse, we need to show that applying one function and then the other will result in the original input. In other words, f(g(x)) = x and g(f(x)) = x. Let's check if this holds true for the functions given:

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f(x) = x + \frac {3}{2} and g(x) = 2x - 3 are indeed inverses of each other.

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f(x) and g(x) are inverse functions.

To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses, find their compositions and show they equal x, establishing them as inverse functions.

To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses:

Answer:

3x -5

Step-by-step explanation:

(4x – 12) + (–x + 7)

= 4x – 12 –x + 7

= 3x -5 (answer)

Answer:

3x-5

Step-by-step explanation:

(4x – 12) + (–x + 7)

Open the parenthesis

=4x-12-x+7

Solve the like terms:

=3x-5

The answer is 3x-5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]

[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]

[tex]\huge\text{Eliminate option B and D}[/tex]

→ [tex]\huge\text{Find the absolute value of the problem}[/tex]

→ [tex]\huge\text{You can now know that  it could be:}[/tex]  

[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]

→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]

→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]  

[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

option B

Step-by-step explanation:

Given:

per day late costs= 1.50

Purchase price= 9.99

A round trip cab ride to the video store will cost = 10

5 day late cost= 5(1.50)

                       = 7.50

Payment after 5 day late= 5 day late cost + Purchase price

                                       = 7.50 + 9.99

                                       = 17.49

If she gets a cab, then total payment= 10 + 7.50

                                                             = 17.50

Hence both costs almost the same, option B is true

b.

It would cost about the same to keep or return the movie. Susan should keep it!

[tex]x^2=40^2+9^2\\x^2=1600+81\\x^2=1681\\x=\sqrt{1681}=41[/tex]

To solve this you must use Pythagorean theorem:

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

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 9

b = 40

c = x

^^^Plug these numbers into the theorem

[tex]9^{2} +40^{2} =x^{2}[/tex]

simplify

81 + 1600 = [tex]x^{2}[/tex]

1681 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

41 = x  

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

f || m

Step-by-step explanation:

If f is parallel to k and k is parallel to m

then f must be parallel to m

Answer:

They must mix

37 pounds of the House Blend

3 pounds of the Kenya Blend.

Step-by-step explanation:

Let 'x' be House coffe and 'y' be Kenya Coffee. Then:

10.50x + 12.80y = 10.67(40)

Also, we knw that:

x + y = 40

Solving the system of equations above, we have that:

x ≈37.0435 ≈ 37 pounds

y ≈2.95652 ≈ 3 pounds

They must mix

37 pounds of the House Blend

3 pounds of the Kenya Blend.

Answer:

Step-by-step explanation:

-3*j = -3j

(-3)(-1) = 3

Answer

-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.

20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.

Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base)  imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.

First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.

Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.

Answer:

C.) percent= 20%, Amount=unknown, Base =50

Step-by-step explanation:

20% is the percent

50 is the amount

20% of 50 is the unknown. This is the amount.

20% of 50 = 0.2 × 50 = 10

Answer:

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Step-by-step explanation:

System #1: x=4

[tex]2x+y=10\\x-3y=-2[/tex]

To solve, start by isolating your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Now, plug this value of y into your second equation.

[tex]x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4[/tex]

System #2: x=1

[tex]x+2y=5\\2x+y=4[/tex]

Isolate your second equation for y.

[tex]2x+y=4\\y=-2x+4[/tex]

Plug this value of y into your first equation.

[tex]x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1[/tex]

System #3: x=6

[tex]5x+y=33\\x=18-4y[/tex]

Isolate your first equation for y.

[tex]5x+y=33\\y=-5x+33[/tex]

Plug this value of y into your second equation.

[tex]x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6[/tex]

System #4: all real numbers (not included in your diagram)

[tex]y=13-2x\\8x+4y=52[/tex]

Plug your value of y into your second equation.

[tex]8x+4(13-2x)=52\\8x+52-8x=52\\0=0[/tex]

all real numbers are solutions

System #5: x=2

[tex]x+3y=5\\6x-y=11[/tex]

Isolate your second equation for y.

[tex]6x-y=11\\-y=-6x+11\\y=6x-11[/tex]

Plug in your value of y to your first equation.

[tex]x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2[/tex]

System #6: no solution (not included in your diagram)

[tex]2x+y=10\\-6x-3y=-2[/tex]

Isolate your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Plug your value of y into your second equation.

[tex]-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2[/tex]

no solution

System #7: x=3

[tex]y=10+x\\2x+3y=45[/tex]

Plug your value of y into your second equation.

[tex]2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3[/tex]

Answer:

Mary = 24

Chau = 15

David = 48

Step-by-step explanation:

The formula is

Mary + Chau + David = 87

And we know that

Chau = Mary - 9

David = Mary * 2

So when we fill this in

Mary + Mary - 9 + Mary * 2 = 87

4Mary - 9 = 87

4Mary = 96

Mary = 24

Chau = Mary - 9 = 15

David = Mary * 2 = 48

Final answer:

The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.

Explanation:

The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.

Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.

Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.

Answer:

17.167 rounded

Step-by-step explanation:

17+(1/6)

17+0,166

17.167

well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.

[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]

Answer: A) 1.7 Years

Step-by-step explanation:

Answer:

A. 1.7 years

Step-by-step explanation:

Let [tex]P_1[/tex] be the original value of first car,

Since, the car depreciates at an annual rate of  10%,

Let after [tex]t_1[/tex] years the value of car is depreciated to 60%,

That is,

[tex]P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1[/tex]

[tex]P_1(1-0.1)^{t_1}=0.6P_1[/tex]

[tex]0.9^{t_1}=0.6[/tex]

Taking ln on both sides,

[tex]t_1ln(0.9) = ln(0.6)[/tex]

[tex]\implies t_1=\frac{ln(0.6)}{ln(0.9)}[/tex]

Now, let [tex]P_2[/tex] is the original value of second car,

Since, the car depreciates at an annual rate of 15%

Suppose after [tex]t_2[/tex] years it is depreciated to 60%,

[tex]P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2[/tex]

[tex]P_2(1-0.15)^{t_2}=0.6P_2[/tex]

[tex]0.85^{t_2}=0.6[/tex]

Taking ln on both sides,

[tex]t_2ln(0.85) = ln(0.6)[/tex]

[tex]\implies t_2=\frac{ln(0.6)}{ln(0.85)}[/tex]

[tex]\because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}[/tex]

[tex]=1.70518303046[/tex]

[tex]\approx 1.7[/tex]

Hence, the approximate difference in the ages of the two cars is 1.7 years,

Option 'A' is correct.