please please answer these five questions !!!!!!!!!

Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...

1. [tex]x=1[/tex]

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

3. [tex]x=1[/tex]

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

Step-by-step explanation:

1.

[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]

To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.

Let's add [tex]\frac{x-2}{3x}[/tex]

[tex]\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}[/tex]

Add the numerators and keep the same denominator.

[tex]\frac{1}{x}=\frac{4+x-2}{3x}[/tex]

[tex]\frac{1}{x}=\frac{2+x}{3x}[/tex]

To get rid of the denominator x on the left side, we can multiply by x.

[tex](x)\frac{1}{x}=\frac{2+x}{3x}(x)[/tex]

[tex]1=\frac{2+x}{3}[/tex]

Now multiply by 3.

[tex](3)1=\frac{2+x}{3}(3)[/tex]

[tex]3=2+x[/tex]

Subtract 2.

[tex]3-2=x\\1=x[/tex]

The value of x is 1.

Proof.

[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]

[tex]\frac{1}{1}-\frac{1-2}{3(1)}=\frac{4}{3(1)}[/tex]

[tex]1-\frac{-1}{3}=\frac{4}{3}[/tex]

[tex]1+\frac{1}{3}=\frac{4}{3}[/tex]

[tex]\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}[/tex]

I can't show the proof to the following problems because I have a 5000 character limit.

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2.

[tex]\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}[/tex]

Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.

[tex]\frac{5x-5-5}{x^2-4x}=\frac{1}{x}[/tex]

[tex]\frac{5x-10}{x^2-4x}=\frac{1}{x}[/tex]

Again, we can multiply by x to get rid of the x in the denominator.

[tex](x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)[/tex]

Do not distribute the x in the numerator yet because we're gonna eliminate it later.

[tex]\frac{(x)(5x-10)}{x^2-4x}=1[/tex]

Factor the denominator.

[tex]\frac{(x)(5x-10)}{(x)(x-4)}=1[/tex]

Simplify x's.

[tex]\frac{5x-10}{x-4} =1[/tex]

Multiply by x-4 to get rid of the denominator.

[tex](x-4)\frac{5x-10}{x-4} =1(x-4)[/tex]

[tex]5x-10=x-4[/tex]

Add 10

[tex]5x=x-4+10[/tex]

Subtract x

[tex]5x-x=-4+10[/tex]

Combine like terms;

[tex]4x=6[/tex]

Divide by 4.

[tex]\frac{4x}{4}=\frac{6}{4}[/tex]

[tex]x=\frac{6}{4}[/tex]

Simplify by 2.

6/2 = 3

4/2 = 2

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

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3.

[tex]\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4[/tex]

Same denominator, add numerators.

[tex]\frac{x^2-7x+10+1}{x}=x+4[/tex]

[tex]\frac{x^2-7x+11}{x}=x+4[/tex]

Multiply by x to get rid of the x.

[tex](x)\frac{x^2-7x+11}{x}=(x+4)(x)[/tex]

[tex]x^2-7x+11=x^2+4x[/tex]

Subtract [tex]-x^2-4x[/tex]

[tex]x^2-7x+11-x^2-4x=0[/tex]

Combine like terms;

[tex]-11x+11=0[/tex]

Subtract 11.

[tex]-11x=-11[/tex]

Divide by -11

[tex]x=\frac{-11}{-11} \\x=1[/tex]

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4.

[tex]\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}[/tex]

It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.

[tex]\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}[/tex]

Now, since we have the same denominators, we can simply subtract numerators.

[tex]\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}[/tex]

Distribute the negative sign.

[tex]\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}[/tex]

Combine like terms;

[tex]\frac{20x-30}{5x-30}=-\frac{x}{x-6}[/tex]

Factor.

I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.

[tex]\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}[/tex]

Simplify.

[tex]\frac{4x-6}{x-6}=-\frac{x}{x-6}[/tex]

Multiply by x-6

[tex](x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)[/tex]

This will simplify the denominators.

[tex]4x-6=-x[/tex]

Add x and 6.

[tex]4x+x=6\\[/tex]

Combine like terms;

[tex]5x=6[/tex]

Divide by 5.

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

Answer:

number : number

Step-by-step explanation:

for example, 1:3

this means 1 to 3

so for every 1 banana there are 3 apples

Answer:

Step-by-step explanation:

The given table is

Days     Bees

  0        10,000

 10        7,500

 20       5,600

 30       4,200

 40       3,200

 50       2,400

Where [tex]x[/tex] represents days and [tex]y[/tex] represents bees.

The exponential function that models this problem must be like

[tex]y=a(1-r)^{x}[/tex], which represenst an exponential decary, because in this case, the number of bees decays.

We nned to use one points, to find the rate of decay. We know that [tex]a=10,000[/tex], because it starts with 10,000 bees.

Let's use the points (10, 7500)

[tex]y=a(1-r)^{x}\\7500=10000(1-r)^{10}[/tex]

Solving for [tex]r[/tex], we have

[tex]\frac{7500}{10000}=(1-r)^{10} \\(1-r)^{10} =0.75[/tex]

Using logarithms, we have

[tex]ln((1-r)^{10}) =ln(0.75)\\10 \times ln(1-r)=ln(0.75)\\ln(1-r)=\frac{ln(0.75)}{10} \approx -0.03\\e^{ln(1-r)}=e^{-0.03}\\1-r =e^{-0.03}\\r=-e^{-0.03}+1 \approx 1.97[/tex]

Replacing all values in the model, we have

[tex]y=10000(1-1.97)^{x}\\y=10000(0.97)^{x}[/tex]

Therefore, the right answer is the first choice, that's the best approximation to this situation.

Answer:

A. y = 9,958(0.972)x

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

259 + 279 = 538

Rounded to nearest 10

= 540

Answer:

6 apples and 5 bananas

Step-by-step explanation:

x + y = 11

x = 11 - y

1.75x + 0.70y = 14

1.75(11 - y) + 0.7y = 14

19.25 - 1.75y + 0.7y = 14

5.25 = 1.05y

y = 5

x = 11 - 5 = 6

Answer:

3 apples and 7 bananas

Step-by-step explanation:

sry thats 1

Answer:Height:  

15.8  meters

Explanation: For a rectangular prism:  XXX  Volume  =  height  ×  width  ×  depth  and  XXX  Area (of base)  =  width  ×  depth  ⇒  height  =  Volume  Area  =  306.52

19.4  =  15.

Answer:  100 CUBIC METERS

Step-by-step explanation:

Answer: There isnt enough information to asnwer

Step-by-step explanation:

Answer:

36⁄12

Step-by-step explanation:

Answer:

An inequality, such as x>2 can be graphed on the number line.

Step-by-step explanation:

An inequality, such as x>2 can be graphed on the number line. An open circle as a stating point, indicates the number is NOT included in the solution. Where as a closed circle or "dot" indicates the number IS included in the solution.

Answer:

An inequality, such as x>2 can be graphed on the number line.

Step-by-step explanation:

Answer:

8(a+2c)

Step-by-step explanation:

Answer:

C. 8(a + 2c)

Step-by-step explanation:

Answer:

A,C,D are triangles, B is not.

Step-by-step explanation:

Let 3 sides of a triangle be a,b,c.

A triangle have the sum of 3 angles = 180 degree

and

a-b<c<a+b (similar for a and b)

a. three sides measuring 6 cm, 8 cm, and 10 cm

Satisfied the a-b<c<a+b property -> triangle

b. three angles measuring 40 degrees, 70 degrees, and 65 degrees

Total of 3 angles = 40+70+65 = 175 > 180

-> not triangle

c. three angles measuring 10 degrees, 25 degrees, and 145 degrees

Total of 3 angles = 10+25+145 = 180

-> triangle

d. three sides measuring 9 m, 15 m, and 9 m

Satisfied the a-b<c<a+b property -> triangle

Answer:

C

All triangle must equal 180, 40 + 70 + 65 = 175

Answer:

50x5

Step-by-step explanation:

The question is an illustration of a distance-time graph.

From the question, we have the following highlights

The graphs are not given, so I will attach the graph that represents the scenario.

See attachment for the graph that answers the question.

Read more about distance-time graphs at:

https://brainly.com/question/19836052

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The min is 4 as this is the smallest value and it is visually shown as the left-most point on the boxplot. This is the tip of the left whisker.

The value of the first quartile (Q1) is the left edge of the box and that is 7. The left whisker goes from 4 to 7. The left whisker represents 25% of the data, which is another way of saying "25% of the data is below Q1". So 25% of the distribution has between 4 and 7 teams.

Answer:

b

Step-by-step explanation:

Answer:

the normal heart rate of the grizzley bear = 12.5 beats per minute

Step-by-step explanation:

let the normal heart rate = x

hibernating heart rate = 20% of normal value = x - 10

20% of x = x - 10

20/100 of x = x - 10

0.2 × x = x - 10

0.2x = x - 10

x - 0.2x = 10

0.8x = 10

x = 10 ÷ 0.8 = 12.5 beats per minute

Answer:

15 1/4

Step-by-step explanation:

16-3/4

64/4-3/4

61/4

15 1/4

Answer:

pounds - ½, 2, 5

ounces - 8, 32, 80

Step-by-step explanation:

Answer:

A =70 ft^2

Step-by-step explanation:

The area of the triangle is equal to

A = 1/2 bh where b is the base and h is the height

A = 1/2 (20) *7

A =70 ft^2

Answer:

(x - 10)(x + 9)

Step-by-step explanation:

[tex] {x}^{2} - x - 90 \\ = {x}^{2} - 10x + 9x - 90 \\ = x(x - 10) + 9(x - 10) \\ = \red{ \boxed{ \bold{ (x - 10)(x + 9) }}}\\ [/tex]

Answer:

V = 703.36 in³   (This matches answer option A.)

Step-by-step explanation:

This fish tank has a cylindrical shape.  The formula for the volume of a cylinder of radius r and height h is

V = (pi)(r²)(h).

We are told that h = 14 in and r = 4 in.  Using 3.14 for pi:

V = (3.14)(4 in)²(14 in) =

V = 703.36 in³   (This matches answer option A.)

Answer:

8.a 9.acb

Step-by-step explanation:

good luck

Answer:

120 square centimeters

Step-by-step explanation:

Answer:  One solution

namely x=3.   We have a product that's zero so the solutions come from each factor being zero; here the factors are the same so we only get one solution.

Answer:

Step-by-step explanation:I hope it's only one...

plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.

To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, we can follow these steps:

1. Complete the square for the x-terms:

  Rearrange the equation to group the x-terms together:

  x^2 + 2x + y^2 + 4y = 44

  To complete the square for the x-terms, add (2/2)^2 = 1 to both sides of the equation:

  x^2 + 2x + 1 + y^2 + 4y = 44 + 1

  Simplify:

  (x + 1)^2 + y^2 + 4y = 45

2. Complete the square for the y-terms:

  To complete the square for the y-terms, add (4/2)^2 = 4 to both sides of the equation:

  (x + 1)^2 + y^2 + 4y + 4 = 45 + 4

  Simplify:

  (x + 1)^2 + (y + 2)^2 = 49

3. Identify the center and radius:

  The equation is now in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2

  Comparing this with our equation, we can see that the center of the circle is (-1, -2) and the radius is √49 = 7.

4. Plot the graph:

  The center of the circle is (-1, -2), which represents the point where the circle is centered. From this point, we can draw a circle with a radius of 7 units in all directions.

By following these steps, we can plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.

For more questions on circle .

https://brainly.com/question/28162977

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Note the full question may be:

To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, first rewrite it in standard form by completing the square for both x and y terms. Then identify the center and radius of the circle and plot the corresponding points to draw the graph.

Answer:

I want to stand on my own three feet

Step-by-step explanation:

Answer:

On the circle

Step-by-step explanation:

Because all of the points on a circle are equidistant from the center, if a circle has a radius of 10 then all of the points are 10 units from the center. Using the Pythagorean Theorem, you know that the distance from (4,0) to (-2,8) is:

[tex]\sqrt{(4-(-2))^2+(8-0)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex], meaning that it is on the circle. Hope this helps!

Correct question:

Every day Kim practice volleyball and clarinet each day she practices volleyball for 2.5 hours if after 8 days she practices both volleyball and the clarinet for a total of 36 hours how many hours per day did Kim practice clarinet.

Answer: 2 hours

Step-by-step explanation:

Everyday Kim practices volleyball and clarinet = v/ball + clarinet

Everyday volleyball practice = 2.5hours

That is clarinet(hours) + 2.5 hours of volleyball

After 8 day, total practice hours of both volleyball and clarinet equals 36 hours

The above information can be represented mathematically as thus:

Let h = hours per day of clarinet

8(h + 2.5) = 36

8h + 20 = 36

8h = 36 - 20

8h = 16

h = 16/8

h = 2

Answer:

x/2 = 12.5/5

5 · x = 12.5 · 2

5x = 25

5x / 5 = 25 / 5

x = 5

Step-by-step explanation:

Answer:

the other person is incorrect it is 3 x 3 / 2  

Step-by-step explanation:

this is my question

The volume of the given triangular prism is 31.4937 cubic inches

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

From the given triangular prism

Base side a =3 in

Base side b=3 in

Base side c=4.2

height h=7 in

The formula to find the volume of triangular prism

Volume = 1/4h√-a⁴+2(ab)²+2(ac)²-b⁴+2(bc)²-c₄

Substituting the values in the formula we get

Volume =31.4937

Hence, the volume of the given triangular prism is 31.4937 cubic inches

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

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Answer: 0.182

Step-by-step explanation:

For the first selection, the probability of picking a milk chocolate bar is equal to the number of milk chocolate bars divided the total number of bars, this is:

p1 = 5/(6 + 5) = 5/11

In the second selection we have the same equation, but now we have  4 milk chocolate bars (because one is alredy taken)

p2 = 4/(4 + 6) = 4/10

the joint probability is:

P = p1*p2 = (5/11)*(4/10) = 0.182