Please help me on 6,7and8

After solving the equation, the solution if the equation is -2 and -11/5.

To solve the rational equation we first express the given statement in the form of mathematical equation. After that we solve the equation.

As the statement is 5 over X + 2. It can be written as 5/(x + 2)

Then the second statement is -11 over X to the 2nd + 2X which is written as -11/(x² + 2x).

There have equal sign between both expression. So the expression is

5/(x + 2) = -11/(x² + 2x)

Now solve it.

Multiply by (x² + 2x) on both side, we get

5(x² + 2x)/(x + 2) = -11

Multiply by (x + 2) on both side, we get

5(x² + 2x) = -11(x + 2)

Now simplify using the distributive property

5x² + 10x = -11x - 22

Add 11x on both side, we get

5x² + 21x = - 22

Add 22 on both side, we get

5x² + 21x + 22 = 0

Now we factor the equation

5x² + (11 + 10)x + 22 = 0

5x² + 11x + 10x + 22 = 0

x(5x + 11) + 2(5x + 11) = 0

(5x + 11)(x + 2) = 0

Now equating equal to 0.

5x + 11 = 0                     x + 2 = 0

5x = -11                          x = -2

x = -11/5

The solution if the equation is -2 and -11/5.

To learn more about distributive property link is here

brainly.com/question/5637942

#SPJ4

The complete question is:

Solve the rational equation 5 over X + 2 equals -11 over X to the 2nd + 2X.

Answer:

18/40

or

9/20

Step-by-step explanation:

13 marbles are initially removed.

40 - 13 = 27

1/3 of that is removed.

27 - 9 = 18

We take whatever is left over (18 marbles), and put it in a fraction to represent what fraction is left over from 40.

18/40

or

9/20

Answer:

To find the total area of the figure, we need to find the area of each of the individual triangles and rectangles and then add them up.

The rectangle on the left has a length of 6 and a width of 3, so its area is 6 x 3 = 18 square units.

The triangle on the left has a base of 6 and a height of 5, so its area is 1/2 x 6 x 5 = 15 square units.

The triangle on the right has a base of 6 and a height of 3, so its area is 1/2 x 6 x 3 = 9 square units.

The rectangle on the right has a length of 3 and a width of 6, so its area is 3 x 6 = 18 square units.

Adding up the areas of each shape, we get:

18 + 15 + 9 + 18 = 60 square units

Therefore, the total area of the figure is 60 square units. Answer: (d) 60 units squared.

The constant of proportionality (k) for the data points on this graph is 7.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7/1 = 14/2 = 21/3 = 28/4 = 35/5

Constant of proportionality, k = 7.

Read more on proportional relationship here: brainly.com/question/28350476

#SPJ1

25. The scale factor is 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 115 degrees

25. The scale factor of JKLM and EFGH is calculated using corresponding sides

side EF * scale factor = side JK

8 * scale factor = 20

scale factor = 20 / 8

scale factor = 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 360 - 90 - 90 - 65 = 115 degrees

27.  the ratios of the corresponding side lengths

JK / EF is proportional to KL / FG is proportional to LM / GH is proportional to MJ / EH

28. the values of x, y, and z

x = 2.5 * FG = 2.5 * 11 = 27.5

y = 30 / 2.5 = 12

z = 65 degrees

29. the perimeter of each polygon

the smaller polygon EFGH = 8 + 11 + 3 + 12 = 34

the bigger polygon JKLM = 20 + 27.5 + (3 * 2.5) + 30 = 85

30. the ratio of the perimeters of JKLM to EFGH

= 85 / 34 = 2.5

31. the area of each polygon

the smaller polygon EFGH = 0.5(3 + 8) * 11 = 60.5

the bigger polygon JKLM = 0.5(20 + 7.5) * 27.5 = 378.125

32. the ratio of the areas of JKLM to EFGH​

= 378.125 / 60.5 = 6.25

Learn more about similar polygons at:

https://brainly.com/question/1493409

#SPJ1

When A U B = C & A ∩ B = φ, then A = C - B. The solution has been obtained by using properties of sets.

What is a set?

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Curly brackets are typically used to represent sets.

We know that

A - B = (A ∪ B) - B

On substituting A U B = C in this, we get

A - B = C - B       ...(1)

Similarly,

A - B = A - (A ∩ B)

On substituting  A ∩ B = φ in this, we get

A - B = A        ...(2)

From (1) and (2), we get

A = C - B

Hence, when A U B = C & A ∩ B = φ, then A = C - B.

Learn more about set from the given link

https://brainly.com/question/30096133

#SPJ1

11. The area of the floor is 24. 62 m²

12. The area of the enclosed string is 3, 853. 09cm²

13. The circumference of the circular mat is  4.39m

The formula for the area of a circle is expressed with the equation;

A = πr²

Where;

Also, circumference of a circle is 2πr

For a circumference of 17. 6m, we have

17. 6 = 2×3.14r

r = 2. 80

Substitute the value

Area = 3.14 × (2. 80)²

Area = 24. 62 m²

For the string, circumference = 220cm

220 = 2× 31.4r

r = 35. 03 cm

Area of the enclosed string = 3.14 × (35. 03)²

Area = 3, 853. 09cm²

For the circular mat

1.54 = 3.14r²

r² = 0. 49

Take the square root

r = 0. 7m

Circumference = 2× 3.14 × 0. 7 = 4.39m

Learn about circles at: https://brainly.com/question/14283575

#SPJ1

The value of kˣ for the exponential function is [tex]27^{(1/x)}.[/tex]

We can use the properties of exponents to solve this problem and determine the value of kˣ.

To find the value of h(3x), we can use the property that [tex](a^b)^c = a^{bc}[/tex] for any real numbers a, b, and c. This is shown in the solution below.

h(3x) = 3³ˣ    (since h(x) = 3ˣ)

= (3³)ˣ

= 27ˣ

Therefore, we have:

kˣ = 27ˣ

To find the value of kˣ, we can take the x-th root of both sides:

[tex]k = 27^{(1/x)}[/tex]

So, the value of kˣ is [tex]27^{(1/x)}[/tex].

Learn more about exponential functions here: https://brainly.com/question/30127596

#SPJ1

The amount of centiliters in a picoliter is A = 1 x 10⁻¹⁰ cL

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.

A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.

Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.

Given data ,

Let the first unit of measurement be represented as A

where A = centiliters

Now , the amount of Liters in a centiliter is

From the unit conversion ,

1 L = 100 cL

And , 1 cL = 10⁻² L

Now , the amount of Liters in a picoliter is

1 L = 10¹² picoliters

And , amount of centiliters in a picoliter is A

where A = 10⁻¹⁰ cL

So , the 1 pL = 10⁻¹⁰ cL

Hence , the unit conversion of liters is solved

To learn more about unit conversion click :

https://brainly.com/question/19420601

#SPJ9

The ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The given inequality is y > 3x + 4. To check which ordered pair is not a solution of this inequality, we need to substitute the values of x and y from each ordered pair into the inequality and check whether the inequality holds or not.

Checking the ordered pairs one by one, we have:

(2, 12): y = 12 and x = 2, so 12 > 3(2) + 4 is true. Therefore, (2, 12) is a solution of the inequality.

(0, 5): y = 5 and x = 0, so 5 > 3(0) + 4 is true. Therefore, (0, 5) is a solution of the inequality.

(-2, 1): y = 1 and x = -2, so 1 > 3(-2) + 4 is false. Therefore, (-2, 1) is not a solution of the inequality.

(1, 7): y = 7 and x = 1, so 7 > 3(1) + 4 is true. Therefore, (1, 7) is a solution of the inequality.

Therefore, the ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

To learn more about inequality visit:

https://brainly.com/question/30933467

#SPJ1

We need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

To make container A and B equal in volume, we need to pour some liquid from container B into container A. Let's call the amount of liquid that we need to pour from container B to container A as "x" ml.

After pouring x ml of liquid from container B to container A, the total volume of liquid in container A will be (750 + x) ml, and the total volume of liquid in container B will be (1250 - x) ml.

Since we want the volumes of both containers to be equal, we can set up the equation:

750 + x = 1250 - x

Solving for x:

2x = 500

x = 250

Therefore, we need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

To learn more about Equation

https://brainly.com/question/29657988

#SPJ4

Answer:

h(-2) = 13, h(0) = 9, and h(5) = -1.

Step-by-step explanation:

To evaluate h(x) = -2x + 9 for the given values of x, we can substitute each value of x into the expression and simplify:

h(-2) = -2(-2) + 9 = 13

h(0) = -2(0) + 9 = 9

h(5) = -2(5) + 9 = -1

Therefore, h(-2) = 13, h(0) = 9, and h(5) = -1.

Answer:

187

Step-by-step explanation:

how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.

Answer:

187

Step-by-step explanation:

I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.

150 x 3 = 450. So know it narrows it down to between 150 and 200.

175 x 3 = 525

180 x 3 = 540

185 x 3 = 555

190 x 3 =570

So now it's between 185 and 190.

Now I just need to do the following.

186 x 3 = 558

187 x 3 = 561

And there we have the answer.

Answer:

(24 divided by 3) + x

Step-by-step explanation:

i did it

The number 100-x has a decreasing worth as x rises.

A mathematical statement is referred to as an expression or an algebraic expression if it contains numbers, factors, and a numerical operation between them..For example, the arithmetic sign + separates the terms 4m and 5 from of the variable m in the expression 4m + 5..

The number 100-x has a decreasing worth as x rises. This is due to the fact that the phrase 100-x denotes a linear equation with a -1 slope. This indicates that the expression's value drops by one for each unit rise in x. As a result, the expression's value decreases as x increases. For instance, if x is 50, the expression's value is 50; however, if x is 70, the expression's value is 30. The meaning of the equation decreases in proportion to how much x increases.

To know more about Expression visit:

https://brainly.com/question/1859113

#SPJ1

Answer:30

Step-by-step explanation:

Answer:

The median is the middle value when a set of data is arranged in order from smallest to largest.

First, let's arrange the given shoe sizes in order:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5

The median of this data set is 6.5 because it is the middle value.

Now, let's add a shoe size of 9 to the data set:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9

The new median of this data set is 7, which is greater than the previous median of 6.5.

Therefore, the answer is: The median increases to 7.

Answer: The median increases to 7.

Step-by-step explanation: I took the test and got a 100%

The statement that 35 percent of 150 is about 50  is completely false and hence unreasonable as 35 percent of 150 is exactly equal to 52.50.

In the given problem which is related to percentage of some specific number, the value is obtained by direct multiplication of percentage with the given number to get the answer. Percentage is defined as the ratio which is given with respect to number 100 or 100 units as a whole. Its symbol is %. It is a dimensionless quantity and hence has no units as ratios does not have units.

The given equation can be represented as follows to obtain the answer:

(35/100) × 150 = 52.50

Since 52.50 cannot be considered close to 50, hence the statement is u reasonable. Though 52.5 can be considered as about 52 or 53.

Learn more about percentage at:

brainly.com/question/24877689

#SPJ4

A. The equation given can be expressed in polar form using the Pythagoras theorem.
Let the polar coordinate of a point be (r, θ).
Let r = √(x^2 + y^2)
=> r^2 = x^2 + y^2
=> r^2 = 2x^2 - 6xy - 2x
Let θ = tan^-1 (y/x)
Now, the equation in polar form is:

r^2 = 2x^2 - 6xy - 2x

tan^-1 (y/x) = θ


To find the exact values, solve the equation for the given values of x and y:


For x = 0 and y = 2:

r^2 = 0 - 6*2 - 0

=> r^2 = -12

=> r = √12

=> r = 2√3

tan^-1 (2/0) = θ

=> θ = 90°

Hence, the point (x, y) = (0, 2) has polar coordinates (2√3, 90°).

B. The given cycle has a period of 12 hours. This means that the time between each high and low tide is 12 hours. The height of high tide is 6 feet and the height of low tide is 2 feet. This means that the amplitude of the cycle is 4 feet (6 feet - 2 feet).

Hence, the equation for the tide cycle can be expressed as:

Height = 4sin (π/6 * t) + 4

Where t is time in hours.

Know more about polar form here:

https://brainly.com/question/11741181

#SPJ11

The answer to 0.03 as a fraction is 1/300. But as a percentage, it is 3%.

Fractions and percentages are both ways of expressing parts of a whole. A fraction represents a part of a whole, which is divided into equal parts, while a percentage is a fraction expressed as a number out of 100.

The main difference between fractions and percentages is their format. Fractions are typically written as a ratio of two numbers, with the numerator representing the part and the denominator representing the whole. Percentages, on the other hand, are typically written as a number followed by the symbol "%", which represents the part out of 100.

Full question "What is 0.03 as a fraction?"

Read more about Decimal

brainly.com/question/28393353

#SPJ1

a. The general exponential growth equation is given by: y = abˣ

b. The general exponential decay equation is given by: [tex]y = a (1 - r)^x[/tex]

Exponential growth is a type of growth pattern in which a quantity grows at an increasing rate proportional to its current value. This means that the larger the quantity, the faster it grows.

a. The general exponential growth equation is given by:

 y = abˣ

Where y is the final value, 'a' is the initial value, b is the growth factor or base, and x is the time or number of periods.

Exponential decay is a type of decay pattern in which a quantity decreases at a decreasing rate proportional to its current value. This means that the larger the quantity, the slower it decays.

b. The general exponential decay equation is given by:

[tex]y = a (1 - r)^x[/tex]

Where y is the final value, a is the initial value, r is the decay rate, and x is the time or number of periods

Learn more about Exponential growth at

https://brainly.com/question/17161065

#SPJ1

Reflect point A over the line to get point A', -1,2 is A'.

What is a graph?

A graph is a structure that fundamentally consists of a set of items where some pairs of the objects are "connected" in some way. This definition comes from discrete mathematics, more especially graph theory. The items are represented by mathematical abstractions called vertices, and each pair of connected vertices is known as an edge.

A graph is frequently depicted in a diagram by a collection of dots or circles for the vertices and lines or curves for the edges. Among the topics covered by discrete mathematics are graphs.

To learn more about graph from the given link

https://brainly.com/question/19040584

#SPJ1

(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.

The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).

Learn more about Average rate

brainly.com/question/12395856

#SPJ11

The equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) between two expressions, one on each side. An equation can contain variables, constants, numbers, and mathematical operations like addition, subtraction, multiplication, and division

To write an equation for the graph that passes through the points (4,-5) and (7,10), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line passing through the two points, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4,-5) and (x2, y2) = (7,10).

m = (10 - (-5)) / (7 - 4)

m = 15 / 3

m = 5

Now that we know the slope of the line, we can use either point to solve for the y-intercept, b. Let's use the point (4,-5):

y = mx + b

-5 = 5(4) + b

-5 = 20 + b

b = -25

Therefore, the equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

To learn more about Equation from given link.

https://brainly.com/question/28951575

#SPJ1

13. The reasonable domain for the function V(w) = (60-4w)w^2 is when the volume is greater than 0.

14. The graph will look like a parabola with a maximum point at w = 7.5.

15.The coordinates of the maximum point are (7.5, 506.25).
16. The width of the box that produces the maximum volume is 7.5 inches, as found in the previous question.

17. a. The expression for the height of the tube in terms of the radius is h = 60 - 2r.

This means that the values of w must be between 0 and 15, since the volume becomes negative when w is greater than 15. Therefore, the domain can be expressed as an inequality as 0 < w < 15, in interval notation as (0, 15), and in set notation as {w | 0 < w < 15}.

14. To sketch a graph of the function V(w) = (60-4w)w^2 over the domain (0, 15), we can plot points at different values of w and connect them with a smooth curve. The scale on each axis can be 1 unit per grid line.

15. Using a graphing calculator, we can find the coordinates of the maximum point of the function V(w) = (60-4w)w^2 by using the maximum function.

b. The expression for the volume of the tube in terms of the radius is V = πr^2h = πr^2(60 - 2r).

c. To find the radius that produces the maximum volume, we can take the derivative of the volume function and set it equal to 0. This gives us 2πr(60 - 4r) = 0. Solving for r, we get r = 7.5 cm.

d. The maximum volume of the tube is V = π(7.5)^2(60 - 2(7.5)) = 1265.49 cm^3.

To know more about interval notation click on below link:

https://brainly.com/question/29531272#

#SPJ11

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6800\\ P=\textit{original amount deposited}\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &16 \end{cases}[/tex]

[tex]6800 = P\left(1+\frac{0.027}{4}\right)^{4\cdot 16} \implies 6800=P(1.00675)^{64} \\\\\\ \cfrac{6800}{(1.00675)^{64}}=P\implies 4420\approx P[/tex]

The each of two individuals will get 54 and 27 sweets according to provided ratio.

Let us assume the amount of sweets each get be 2x and x. Now we know the sum is 81, so representing the information in equation form.

2x + x = 81

Performing addition on Left Hand Side of the equation

3x = 81

Rewriting the equation

x = 81/3

Performing division on Right Hand Side of the equation

x = 27

So, first person will get amount of sweets = 2×27

First person = 54

Amount of sweets for second person = 27

Thus, each will get 54 and 27 sweets.

Learn more about ratio -

https://brainly.com/question/2328454

#SPJ4

The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:

8. PT = 1

   PV = 2

9. VT = 0.76

   PV = 0.66

10. PT = 3

     PV = 6

11. PV =0.58

    PT =1.154

12. PT = 1.73

    VT = 3

13. VT = 3

     PV = 3.5

The given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.

For the first triangle whose known side is √3, the missing values can be obtained this way:

sin 60°/ √3 = sin 90/PV

PV = √3 Sin 90/ sin 60

PV = 1.732/0.866

= 2

PT = sin 60/ √3 = sin 30/ PT

PT = √3 sin 30/sin 60

PT = 1

Using this same pattern, the values for the other figures can be obtained.

Learn more about scalene triangles here:

https://brainly.com/question/30765574

#SPJ1

the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50

The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:

First equation: x + y = 72

Second equation: x - y = 50

To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:

x + y = 72

x - y = 50

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

2x = 122

Next, we can solve for x by dividing both sides of the equation by 2:

2x/2 = 122/2

x = 61

Now that we know the value of x, we can plug it back into one of the equations to find the value of y:

61 + y = 72

y = 72 - 61

y = 11

So the solution to the system of equations is x = 61 and y = 11.

Learn more about system of linear equations here. https://brainly.in/question/17239974

#SPJ11