which is the rationalized form of the expression the square root of x divided by the square root of x +the square root of 7

Answer:

75

Step-by-step explanation:

Geometric means you should think common ratio (words like multiplication or division).

First term=3

Second term=15

What can you multiply to first to give you second term? Please say 5! Yes 5! Why? Because 3*5=15.

So 5 is called the common ratio.  5 is the number that you will multiply to a term to find the very next term.

So the third term would be 15*5=75

The next value in the geometric sequence is 75.

A geometric sequence is a sequence of numbers in which each term can be found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, to find the next value in the sequence, we need to determine the common ratio. We can divide the second term (15) by the first term (3) to find the common ratio:

Common ratio = 15/3 = 5

Now that we know the common ratio is 5, we can find the third term in the sequence:

Third term = Second term × Common ratio = 15 × 5 = 75

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So, the event "rolling an even number on the die and drawing an even-numbered card" corresponds to exactly one outcome of the experiment.

In this experiment, there are six possible outcomes from rolling the die (1, 2, 3, 4, 5, or 6) and ten possible outcomes from drawing a card (1, 2, 3, 4, 5, 6, 7, 8, 9, or 10).

To find the total number of outcomes, we multiply the number of outcomes from rolling the die by the number of outcomes from drawing a card: [tex]6 (outcomes from the die) * 10 (outcomes from the card) = 60 possible outcomes.[/tex]

An event corresponds to a specific combination of rolling the die and drawing a card. For example, rolling a 1 on the die and drawing a card numbered 1 is one possible outcome.

Now, let's consider the definition of an event that corresponds to exactly one outcome of the experiment:

An event where the die shows an even number (2, 4, or 6) and the card drawn is also even (2, 4, 6, 8, or 10) would correspond to exactly one outcome of the experiment.

For example, if the die rolls a 2 and the card drawn is a 4, this combination uniquely identifies one outcome of the experiment.

Answer:

The correct answer is third option 3 : 4

Step-by-step explanation:

It is given that,Jamaal has 20 models of planes and cars

Also he has  three times as many cars as planes

Let 'x' be the number planes.

Then number of cars = 3x

Total number of models = x + 3x = 4x

To find the ratio of his cars to total models

cars : total models = 3x : 4x

 = 3 : 4

Therefore the correct answer is third option 3 : 4

Answer:

3:4 is the answer and give the guy above me brainliest

Step-by-step explanation:

[tex]a_1=-3\\r=7\\a_n=a_{n-1}\cdot r\\\\ \boxed{a_n=7a_{n-1}}[/tex]

[tex]a_{n+1} =7a_{n}[/tex].

If we know the term [tex]n^{th}[/tex] and the common relation, r, of a geometric sequence, you can find the term [tex](n+1)^{th}[/tex] using the recursive formula [tex]a_{n+1} =a_{n}.r[/tex].

The first term of the geometric sequence is a₁ = -3.

The common relation we have to find the relationship between a term and the term that precedes it.

[tex]r=\frac{-21}{-3} = 7[/tex]

The recursive formula is:

[tex]a_{1} =-3[/tex]

[tex]a_{n+1} =7a_{n}[/tex]

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of line

Answer:

x + 2y = 4

Step-by-step explanation:

The y intercept (where it crosses the y axis) is (0,2)

Another point on the line is (4,0)

We can find the slope from these two points

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

   = (0-2)/(4-0)

   =-2/4 = -1/2

We have the slope and the y intercept

y = mx+b  where m is the slope and b is the y intercept

y = -1/2x +2

We want the equation of the line in standard form

Ax +By =C

Add -1/2x to each side

1/2x +y =  -1/2x +1/2x +2

1/2x +y =   2

Multiply by 2 because we do not want fractions

2(1/2x +y) = 2* 2

x + 2y = 4

Answer:

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

Step-by-step explanation:

g(x) = -3(1/2)^x

Putting values of x

x     g(x)

-2    -3(1/2)^-2 = -12

-1     -3(1/2)^-1 = -6

0     -3(1/2)^0 = -3

1      -3(1/2)^1 = -3/2

Now, making the graph we will plot

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

The graph is shown in figure below.

To find g(x) values, substitute the x-values into the function equation. Calculate the result which gives you the y-value (g(x)) for each x-value. Plot these pairs of values on a graph to show the function's behavior.

To find the corresponding values of the function g(x), you need to substitute the x-values given into the function equation of g. For instance, if g(x) is a linear function given by y=3x+9, when x=1 the value of g(x) is 3*1+9=12, and this is the y-coordinate of the point plotted on the graph. Repeat this process with all the given x-values to get the corresponding y-values. Afterwards, plot all the (x, g(x)) pairs on the coordinate grid. The points are found at the intersection of the x and y (g(x)) values on the grid. After plotting, you can connect the points to give a graphical representation of the dependence of y on x.

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Answer:

28.27 mm squares.

Step-by-step explanation:

Total Surface area of the cone is given by the circular base and the curved part of the cone. This means that there are a total of 2 parts of the shape. The following 2 expressions have to be added in order to gain the total surface area:

1) Surface Area of Cone (without base) = π*r*s.

2) Area of Circle = π*r^2.

It is given that r = 2 mm and s = 2.5 mm. Plugging in the values gives:

Total Surface Area of the Diamond Ring = π*2*2.5 + π*2^2.

Total Surface Area of the Diamond Ring = 5π + 4π = 9π = 28.27 mm squares.

This means that the total surface area is 28.27 mm square (correct to 2 decimal places)!!!

Answer:

The angle of descent of Artemis' plane is 6°

Step-by-step explanation:

Let

x -----> the angle of descent of Artemis' plane

we know that

The tangent of angle x is equal to divide the opposite side to angle x (altitude) by the adjacent side to angle x (horizontal distance)

see the attached figure to better understand the problem

so

tan(x)=2.2/22

x=arctan(2.2/22)=5.71°

Round to the nearest degree

x=6°

Answer:

The angle of descent of Artemis' plane is 6°

Step-by-step explanation:

[tex]\bf y = \stackrel{\stackrel{monthly~fee}{\downarrow} }{10}~~\stackrel{\stackrel{month}{\downarrow }}{x}+\underset{y-intercept}{\stackrel{\stackrel{registration~fee}{\downarrow }}{30}}~\hfill \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer: a. The y-intercept is 30. This is the cost of registration.

Step-by-step explanation:

The standard equation of line in intercept form is given by  :-

[tex]y=mx+c\ \ \ \ \ \ \ (i)[/tex], where m is the slope of the line and c is the y-intercept.

Given : Sara plotted the data and determined that the average gym costs consist of a one-time registration fee and a monthly fee modeled by the equation :-

[tex]y = 10x + 30[/tex]

By comparing it to the equation (i), we have

c=30 and m=10

i.e. The y-intercept is 30.

Also, y-intercept of any function shows the starting value of the function when x=0.

Thus, This is the cost of registration ( starting fee).

A graph is a function if it passes the vertical line test. The vertical line test is where you take a vertical (up and down) line and test all spots of the graph. If the graph intersects the vertical line more then once then it is not a function, it is a relation. If the vertical line only crosses the graph once then it is a function.

Look at the image below to see the vertical line test for this graph:

The vertical line crosses the graph twice, therefore this is not a function. It is a relation.

Hope this helped!

~Just a girl in love with Shawn Mendes

1/6 is smaller than 1/2

4/7 is greater than 1/2

1/6 is smaller than 4/7

b) 5/9 is greater than 3/8

have a great day!

Answer:

Hi!

a)

b)

Step-by-step explanation:

If you are having problems doing the comparision, the best form to check if a number is greater or smaller than another, you can divide the fraction and obtain the decimal form.

Example:

1/6 ≅ 0.16.

4/7 ≅ 0.57.

1/2 = 0.50.

3/8 ≅ 0.37.

5/9 ≅ 0.55.

Now, you can replace the numbers and check again:

b)

Answer:

Option B is correct.

Step-by-step explanation:

(x+2<5) U (x-7>-6)

Solving and finding the value of x and then taking Union of both answers

x+2 < 5

x < 5-2

x < 3

x-7 > -6

x > -6 + 7

x > 1

So, x < 3 or x > 1

{x|x<3 or x > 1}

Option B is correct.

Answer:

- Hope 18.92

- Casey 19.25

- Daniela 20.2

Explanation:

divide the points/basketball games

Answer:

Hope, Casey, Daniela

Step-by-step explanation:

Since,

[tex]\text{Points per game}=\frac{\text{total scores}}{\text{Total number of games}}[/tex]

Given,

Daniela scored 101 points in 5 basketball games,

Daniela's His points per game = [tex]\frac{101}{5}=20.20[/tex]

Casey scored 154 points in 8 games,

Casey's points per game = [tex]\frac{154}{8}=19.25[/tex]

Hope scored 227 points  in 12 games.

Hope's points per game = [tex]\frac{227}{12}\approx 18.92[/tex]

∵ 18.92 < 19.25 < 20.20

Hence, the order of the players by their points per game from least to greatest,

Hope, Casey, Daniela

Answer:

4th option

Step-by-step explanation:

i have answered ur question

Answer:

y=2

Step-by-step explanation:

If I interpreted what you wrote correctly, the equations were 5x-4y=7 and x=5-y. Given these equations, we can substitute the x=5-y into the other equation due to it quite literally being equal to x. When you substitute the x-equation in, it reads 5(5-y)-4y=7. Distribute the 5 into the (5-y) to get 25-5y-4y=7. Combine like terms to get 25-9y=7. Next, subtract the 25 from each side to isolate the -9y. This leaves yoy with -9y= -18. Divide by -9 on each side to isolate and find y. This leaves you with y=2. You can check your work by substituting the y=2 into the second equation to find x and then use the x and y to check your solution in the first equation. :)

Answer:

36/23

Step-by-step explanation:

Answer:

The average power use is 806 watts....

Step-by-step explanation:

We all know that there are 31 days in May.

To find the total number of hours in 31 days, multiply the hours of one day by 31.

31*24 = 744 hours

Now we have given 600.kilowatt

To find average power, simply divide the given kilowatt by the total number of hours in 31 days.

= 600/744

Average power = 0.806 kilowatt

Since they have asked for the answer in watts we will convert kilowatt into watts.

We know that 1000 watts = 1 kilowatt, so we will multiply 0.806 by 1000 to convert it into watts

= 0.806*1000

= 806 watts.

Therefore the average power use is 806 watts....

Answer:

Part 1) The price of a USB memory, stick selling at a 21% discount of its market price (m) ------> 0.79m

Part 2) The price or a CD that sells for 21% more than the amount (m) needed to manufacture the CD -----> 1.21m

Part 3) The final value of a painting after its initial value m, increases by 2/5 -----> [tex]\frac{7}{5}m[/tex]

Part 4) The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy ----->  [tex]\frac{3}{5}m[/tex]

Step-by-step explanation:

Part 1) The price of a USB memory, stick selling at a 21% discount of its market price (m)

we know that

100% is the market price m

100%-21%=79%

79%=79/100=0.79

so

The price of a USB memory with a 21% discount of its market price is equal to multiply m by 0.79

(0.79)*m=0.79m

Part 2) The price or a CD that sells for 21% more than the amount (m) needed to manufacture the CD

we know that

100% is the amount m

100%+21%=121%

121%=121/100=1.21

so

The price or a CD that sells for 21% more than the amount (m) is equal to multiply m by 1.21

(1.21)*(m)=1.21m

Part 3) The final value of a painting after its initial value m, increases by 2/5

we know that

100% is the initial value m

2/5=0.40=40%

100%+40%=140%

140%=140/100=1.4

Convert to fraction

1.4=14/10=7/5

so

The final value is equal to m multiplied by 7/5  

[tex]\frac{7}{5}m[/tex]

Part 4) The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy

we know that

100% is the number of makers m

2/5=0.40=40%

100%-40%=60%

60%=60/100=0.6

Convert to fraction

0.6=6/10=3/5

The total number of markers that Nancy has is equal to multiply m by 3/5

so

[tex]\frac{3}{5}m[/tex]

Answer:

[tex] 2x + 3 [/tex]

the sum of twice the number x and the number 3

[tex] x ^ 2 + y ^ 2 [/tex]

the sum of squares of the number x and the number y

[tex] 5x-2y [/tex]

the difference between five times more than the number x and twice the number y

[tex] x + 3x [/tex]

the sum of the number x and the number of triple x

[tex] \dfrac {ab} {3} [/tex]

the quotient of the product of the number a and the number b by the number 3

[tex] \dfrac {4x} {3y} [/tex]

the quotient of the product of the number 4 and the number x by the triple number y

[tex] \dfrac {m ^ 2} {n} +5 [/tex]

the sum of the quotient of the square of the number m by the number n and the number 5

[tex] 4-x [/tex]

the difference between the number 4 and the number x

[tex] p + 8q [/tex]

the sum of the number p and the product of the number 8 by the number q

[tex] n-6 [/tex]

the difference between the number n and the number 6

For this case we must evaluate the following expression:

14 + (- 8) ÷ 2 * -3

According to the method of algebraic resolution, called PEMDAS, the divisions and multiplications must be made from left to right, before the addition and subtraction, then:

14 + (- 4) * - 3 =

We eliminate the parenthesis keeping in mind that [tex]- * - = +[/tex]

[tex]14 + 12 =[/tex]

Equal signs are added and the same sign is placed:

[tex]14 + 12 = 26[/tex]

Answer:

26

Answer:

x = 13/k

Step-by-step explanation:

kx - 4 = 9

Add 4 to each side

kx - 4+4 = 9+4

kx = 13

Divide each side by k

kx/k = 13/k

x = 13/k

Answer:

x = 13/k

Step-by-step explanation:

1) Combine the constants, obtaining:

kx = 13

2) Divide both sides by k to isolate x:

x = 13/k

Answer:

The answer is a translation of 2 units to the left and 7 units up

Step-by-step explanation:

we know that

In the rule for the translation of a rectangle

(x, y) → (x – 2, y + 7).

the term (x-2) means a translation of 2 units to the left  

the term (y+7) means a translation of 7 units up

Therefore,

The answer is a translation of 2 units to the left and 7 units up....

Answer:

16 -> 15/20 -> 0.65 -> -7/25

Step-by-step explanation:

Why?

Most of the numbers in the set are rational where there is only ONE nature number which is 16 and it's the greatest. Comes after is 15/20 which equals .75 and it's obviously larger than 0.65 which will come after. The negative number is the smallest so it goes last :)

Answer:

1/8

Step-by-step explanation:

i added and combined like terms and got 1/8

Answer:   [tex]x[/tex] ≈ [tex]\±0.782[/tex]

Step-by-step explanation:

You need to solve for "x" in order to find its value.

 First, you need to apply the Negative exponent rule. This is:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

 Then:

[tex]3x^{- 4}= 8[/tex]

[tex]\frac{3}{x^4}=8[/tex]

Now you can solve for "x":

 [tex]3=8x^4[/tex]

[tex]\frac{3}{8}=x^4[/tex]

Remember that:

[tex]\±\sqrt[n]{a^n}=\±a[/tex]

Then, you get:

[tex]\±\sqrt[4]{\frac{3}{8}}=x[/tex]

 [tex]x[/tex] ≈ [tex]\±0.782[/tex]

Answer:

Always

Step-by-step explanation:

The Parallel Postulate:

When a line is already given, let's say the line is a, and the point be called A. If there is a point outside the line, only one line can be drawn through the point which doesn't intersect the line i.e. which is parallel to the given line. Hence, this statement is always true ..

Answer:

Always

Step-by-step explanation:

Given statement: Through a point not on a line, one and only one line can be drawn parallel to the given line.

Draw a line l.

Let point P not on the line l.

Slope of two parallel lines are same.

We need to draw a line which is passes through the point P and parallel to the line l.

Infinite number of lines having different slopes can pass through a single point.

That is two lines don't have same slope.

Hence only one line is possible, which is parallel to l and passes through the point P.

Therefore the given statement is always true.

Answer:

 m    = (-9-3)/(1+7)

Step-by-step explanation:

To find the slope given two points we use

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

m    = (-9-3)/(1--7)

 m    = (-9-3)/(1+7)

m = -12/8

   = -3/2

Slope m has a form of,

[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Your points say A and B have a form of,

[tex]A(x_1,y_1),B(x_2,y_2)\longrightarrow A(-7,3),B(1,-9)[/tex]

We can populate our slope formula to,

[tex]m=\dfrac{-9-3}{1-(-7)}=\dfrac{-12}{8}=\boxed{-\dfrac{3}{2}}[/tex]

The slope of the line that passes through point A and B is m = -3/2

Hope this helps.

r3t40

Answer:

B - 0.18B

0.82B

Step-by-step explanation:

If B is the price of the board game, then the discount will be:

B * 18/100

= B * 0.18

= 0.18B

The expression for the cost Bo will pay for the game is:

B - 0.18B => Original price - discount

The expression can also be written as: (after solving)

0.82B ..

Answer:

A=0.82B

E=B−0.18B

hope this helps

Answer:

The given equation is NOT linear.

Step-by-step explanation:

5x^4+5y = 9

The given equation is NOT linear.

Reason:

A linear equation is defined as the equation for the straight line, where the degree of variables involved is always equal to 1.

But in the given equation :

Degree if x = 4

and degree of y = 1

As degree of x≠ 1 so, the given equation is not linear,

Final answer:

To solve the equation (3x-9)+x+(x+28)=184, you combine like terms to get 5x + 19 = 184, subtract 19 from both sides to get 5x = 165, and then divide both sides by 5 to find that x = 33.

Explanation:

To solve the equation (3x-9)+x+(x+28)=184, we begin by combining like terms. This involves adding together the x terms and combining the constant numbers. The x terms (3x, x, and x) add up to 5x, and the constants (-9 and +28) add up to 19. Therefore, the equation simplifies to 5x + 19 = 184.

Next, we isolate the variable x. We do this by subtracting 19 from both sides of the equation, getting 5x = 165. Then, we divide both sides by 5 to find x. Dividing 165 by 5, we find that x = 33.

Thus, the solution to the equation is x = 33.

Answer:

A) The Length Of Diagonal PS And Diagonal P'S' Are In The Ratio 1:3

Step-by-step explanation:

when a polygon is multiplied or scaled by k, a constant scalar number to form another polygon then these two polygons are similar. And similar polygons have proportional lengths of corresponding sides. Ratios within the polygons sides will be equal to the corresponding sides ratios of the other polygons.  The corresponding sides of image are scalar multiple of preimage

x'=kx

where x' is side in image

x is side in preimage

and k is scalar number

so the ratio between these two corresponding side will be 1:3

In given case as the scalar factor k is 3 so the ratio between corresponding sides will be 1:3.

Hence option A is correct:The Length Of Diagonal PS And Diagonal P'S' Are In The Ratio 1:3!

A statement about polygon PQRST and its image after dilation, polygon P'Q'R'S'T', that is correct include the following: A) The Length Of Diagonal PS And Diagonal P'S' Are In The Ratio 1:3.

In Mathematics and Geometry, the formula for calculating the scale factor of any geometric object or figure is represented by the following:

Scale factor = side length of image/side length of pre-image

Based on the graph, the length of diagonal P'S' is 5 units while the length of diagonal PS is 15 units. In this context, the length of segment A'B' can be calculated as follows;

Scale factor = P'S'/PS

Scale factor = 5/15

Scale factor = 1/3 ⇒ Ratio = 1 : 3.

In conclusion, we can logically deduce that the length of diagonal PS and diagonal P'S' are in the ratio 1 : 3, which implies that diagonal PS is three times as long as diagonal P'S'.

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Answer:

c.  (5,-2), (3, 1), (4,2).

Step-by-step explanation:

The solutions are in the dark red area, with some on the continuous blue line but none on the red dotted line.

The only option that has only solutions for the system is option C.

Each inequality has a region of solutions defined by the shaded areas, such that the double shaded area represents the region of points that are solutions for both inequalities at the same time.

So we just need to see from the options, which ones belong to the double shaded area.

We can see that the only option that has all the points belonging to the double shaded area is option C, with the points:

(5, - 2), (3, 1), (4, 2)

While in the other 3 options we can find at least one point that is not a solution for the system, these are:

If you want to learn more about systems of inequalities, you can read:

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