The diagonal of a square is x units. What is the area of the square in terms of x? square units square units 2x square units square units

Answers

Answer 1

For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:

[tex]l ^ 2 + l ^ 2 = x ^ 2[/tex]

Where:

l: It's the side of the square.

[tex]2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}[/tex]

We know that the area of a square is given by:

[tex]A = l ^ 2[/tex]

So, the area is:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer 2

Answer:

Option A: 1/2 x^2

Step-by-step explanation:

The Diagonal Of A Square Is X Units. What Is The Area Of The Square In Terms Of X? Square Units Square

Related Questions

Which statement accurately explains whether a reflection over the Y axis and a 270° counterclockwise rotation would map figure ACB onto itself?

Answers

C is the answer. It’s really long to explain I used some points to do it.

When you reflect point C over (3,4) -> (-3,4) rotate 270 counter clockwise (-3,4) -> (4,3)
Final answer:

Neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.

Explanation:

To determine whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure ACB onto itself, we need to analyze the effects of these transformations.

A reflection over the y-axis would change the x-coordinates of the points, but not the y-coordinates. So, figure ACB would not be mapped onto itself after a reflection over the y-axis.A 270° counterclockwise rotation would change the position of the points by rotating them around the origin. After a 270° counterclockwise rotation, figure ACB would not be mapped onto itself as the shape and position of the points would change.

Therefore, neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.

The quotient of 4 and 2, decreased by a number, equals that number multiplied by 3

Answers

Answer:

.5

Step-by-step explanation:

4/2   -n=3n

2      -n=3n

2          =4n

2/4      =n

.5        =n

What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
36%
26%
45%
50%

Answers

Answer: 26%

Step-by-step explanation:

See attached photo. - my answer got deleted lol

Final answer:

Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.

Explanation:

To find the percentage of students age 15 and above who travel to school by bus, we need to compare the number of students who travel by bus to the total number of students in that age group. However, we don't have that information in the given question.

We need more data to calculate the percentage. Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.

What is the first step needed to solve 2/5x-6=-16?

Answers

Answer:

Add 6 to both sides.

Step-by-step explanation:

You are trying to solve for x in this type of question. In this case, note that there is a equal sign, and that what you do to one side you do to the other. Also note that to isolate the x (your goal), you must do the opposite of PEMDAS. (Note that PEMDAS = Parenthesis, Exponent (& Roots), Multiplication, Division, Addition, Subtraction).

So your first step is to add 6 to both sides.

2/5x - 6 (+6) = -16 (+6)

Simplify. Solve:

2/5x + (-6 + 6) = -16 + 6

2/5x = -10

_________________________________________________________

Finish finding for x.

Multiply the recipricol of the fraction to both sides to isolate the x. Multiply 5/2 to both sides:

(5/2)(2/5)x = (-10)(5/2)

x = (-10)(5/2)

x = (-50)/2

x = -25

x = -25 is your answer.

~

Suppose f(x)=x^2.What is the graph of g(x)=f(5x)?

Answers

Answer:

D

Step-by-step explanation:

g(x)=f(5x)

this means plugging in 5x for x in f(x):

g(x)=f(5x)=(5x)^2

which can be further simplified:

5^2x^2=25x^2

Since the coefficient of x being larger means a vertical stretch, the answer is D

example:

g(2)=f(5*2)=f(10)=f(10^2)=100

so for g(x), it has the coordinates (2,100), which is most definitely not C

Final answer:

The graph of g(x) = f(5x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5, with the vertex remaining the same.

Explanation:

The graph of g(x) = f(5x) can be obtained by substituting 5x for x in the function f(x) = x^2. So, g(x) = f(5x) = (5x)^2 = 25x^2. This means that the graph of g(x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5. The vertex of the parabola remains the same, but the x-values and the y-values are scaled.

A local public library decides to track the number of hours that a certain computer is being used. The table represents the number of hours, y, which is dependent on the number of days, x.

What is the linear equation that represents this situation?

Answers

Answer:

Second option: y = 8x-3

Step-by-step explanation:

The equation tha satisfies the given values will be the required linear equation

So,

y = 8x + 45

For x=3 and y=21

21 = 8(3) +45

21 = 24+45

21≠69

As this equation is not satisfied by the values, it is not the correct option..

For y = 8x-3

x=3,y=21

21 = 8(3)-3

21 = 24-3

21=21

x=5, y=37

37 = 8(5)-3

37=40-3

37=37

x=7, y=53

53 = 8(7)-3

53 = 56-3

53 = 53

As the equation is true for all values of x and y. This is this correct option..

Which statement could describe the dog’s movement 5 seconds after the command was given?

Answers

Final answer:

The dog’s movement 5 seconds after the command, considering different frames of reference for speed, can be described by the distance it would have traveled: either 25 meters on the sidewalk (at 5 m/s) or 10 meters from the student's perspective (at 2 m/s).

Explanation:

The student's question pertains to describing the dog’s movement 5 seconds after the command was given, considering the dog's speed. Since we have learned that the dog has different speeds in different frames of reference—5 m/s on the sidewalk and 2 m/s in the student’s frame—we can describe the dog’s movement based on these speeds. If the dog started moving at the moment the command was given and continued to move for 5 seconds, we can calculate the distance it would have covered in that time.

For the sidewalk's frame, where the dog's speed is 5 m/s, the dog would have covered a distance of:

Distance = Speed × Time

Distance = 5 m/s × 5 s = 25 meters

In the student’s frame, where the dog's speed is 2 m/s, it would have moved:

Distance = 2 m/s × 5 s = 10 meters

The statement that could describe the dog’s movement 5 seconds after the command was given is that the dog could have traveled either 25 meters from its starting point on the sidewalk or 10 meters from the student's perspective, depending on the frame of reference being considered.

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
4. Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer. Provide your conclusion.

Answers

Answer:

a) Equation: 9x+9 = 72

b) x =7

Step-by-step explanation:

The total cost of 9 bracelets = $72

Shipping charge = $9

a) Define your variable and write an equation that models the cost of each bracelet.

Let x be the cost of one bracelet, the equation will be

9x + 9 = 72

As 9 bracelets were there and the shipping cost was 9 and total cost was 72.

b) Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer.

Now solving the equation to find the value of x that represent cost of each bracelet

9x + 9 = 72

Adding -9 on both sides

9x +9 -9 = 72 -9

9x = 63

Dividing both sides by 9

9x/9 = 63/9

x = 7

The value of x=7 so, the cost of each bracelet is $7

c) Provide your conclusion.

So, each bracelet was of cost $7 and $9 was the shipping charge. so, the total cost is $72.

We would check whether our equation is satisfied.

9x+ 9 = 72

9(7) + 9 = 72

63 + 9 = 72

72 = 72

The equation is satisfied.

Answer:

The cost of each bracelet is: $7

Step-by-step explanation:

Let's call x the cost of each bracelet.

Then the cost of the 9 bracelets is:

9x

If we know that the cost of the bracelets plus the shipping was $ 72 and the cost of shipping is $ 9.

So

The total cost was:

[tex]9x + 9 = 72[/tex]

Now we solve the equation for the variable x.

[tex]9x + 9 = 72[/tex]

Subtract 9 on both sides of equality

[tex]9x + 9-9 = 72-9[/tex]

[tex]9x = 72-9[/tex]

[tex]9x = 63[/tex]

Divide by 9 on both sides of equality

[tex]\frac{9}{9}x = \frac{63}{9}[/tex]

[tex]x = \frac{63}{9}[/tex]

[tex]x = \$7[/tex]

What is the sign of -567.45 + 567.45?
Choose 1 answer:
A
Positive
B
Negative
(C) Neither positive nor negative-the sum is zero.​

Answers

The answer is c they cancel out and the answer would be 0

Answer:

C

Step-by-step explanation:

-567.45 + 567.45 = 0

The system of equations is solved using the linear combination method. What does 0= -12 mean regarding the solution to the system?
Answers:
There are no solutions to the system because the equations represent parallel lines.

There are no solutions to the system because the equation represent the same line.

There are infinitely many solutions to the system because the equations represent parallel lines.

There are infinitely many solutions to the system because the equations represent the same line.

Answers

Answer:

There are no solutions to the system because the equation represents parallel lines

Answer:

There are no solutions to the system because the equations represent parallel lines.

Step-by-step explanation:

We know by given that the system result is 0 = -12.

This results means that there are no solutions in the system, because the statment 0 = -12 is false, also lines are parallels, that's the real reason why there's no solution.

Remember that parallel lines won't intercept, and a solution of a linear system means that those lines intercept. So, if they don't, then, there's no solution.

Therefore, the right answer is the first choice.

What is y-5=3(x+1) in slope intercept form

Answers

Answer:

y=3x+8, :m=3, b=8

Hope this helps!

The line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line:

y - 5 = 3(x + 1)

In slope intercept form:

y = 3x + 3 + 5

y = 3x + 8

Thus, the line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

Learn more about the straight line here:

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What is the measure of DG?
Enter your answer in the box.

Answers

Minor arc DG is 110 degrees because we double the inscribed angle (DHG) to get 2 *55 ... Central angle GDC is

Need help finding the length of Ac

Answers

Answer:

We need to know angle C which is (180 -123 -34) = 23°

We'll use the Law of Sines

Sine (A) / side a = Sine (B) / side b

Sine (34) / 10 = Sine (123) / side b

0.55919 / 10 = 0.83867 / side b

10 * .83867 / .55919 = side b

side b (or line AC) = 14.998

Step-by-step explanation:

Julie needs to cut 4 pieces of yarn, each with the same length and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut what is the equation that can be used to determine the total length of all of the yarn that she ends up, cutting,y? Is the graph of the equation continuous or discrete

Answers

Answer:

Total length of the x inches long pieces = 4x inches

She has to cut another piece = 7.75 inches

Total length = 4x + 7.75

This is what y represent, so

y = 4x + 7.75

The graph of the equation is continuous

Answer:

The required equation is [tex]y=4x+7.75[/tex] and the graph of the equation is continuous.

Step-by-step explanation:

Consider the provided information.

Julie needs to cut 4 pieces of yarn,

Let x  represent the length of each yarn.

Then the length of 4 pieces will be: 4x

y represents the total length of all of the yarn that Julie decides to cut

Therefore the required equation that can be used to determine the total length of all of the yarn is:

[tex]y=4x+7.75[/tex]

Here, the graph is continuous, because the length of yarn can be any number.

What is the equation of the line in point-slope form?
y+ 4 = 1/2(x+4)
y-4 = 1/2(x + 4)
y-0 = 2(x - 4)
y-4 = 2(8-0)

Answers

Answer: y=-2x+2/4

Step-by-step explanation:

Answer:

y + 4 =1/2 (x + 4)

Step-by-step explanation:

Your welcome uwu

Thank you so much for thisb

Answers

Answer:

Choice B

Step-by-step explanation:

Formula for slope:

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y_2 = 1\\y_1 = -10\frac{2}{3} \\\\x_2 = -3\\x_1 = 4[/tex]

[tex]1 - (-10\frac{2}{3}) = 11\frac{2}{3} \\-3 - 4 = -7[/tex]

[tex]\frac{-11\frac{2}{3} }{-7} = \frac{5}{3} = 1\frac{2}{3}[/tex]

What’s the common ratio of this sequence?
3, 21, 147

Answers

Answer:

r = 7

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex], that is

r = [tex]\frac{21}{3}[/tex] = [tex]\frac{147}{21}[/tex] = 7

The common ratio of the sequence 3, 21, 147 is 7.

Start with the first and second terms:
21 ÷ 3

= 7

Confirm with the second and third terms:
147 ÷ 21

= 7

Thus, the common ratio (r) is 7.

Samantha works in a bakery. The profit of cupcakes in dollars, after t weeks, is given by the function, C(t) = 0.1t3. The profit of cookies in dollars, after t weeks, is given by the function, K(t) = 5(1.07)t - 5. Which function describes the total profit, M(t), at the bakery after t weeks?

Answers

Answer:

M(t) = 0.1t3 + 5(1.07)t - 5

Step-by-step explanation:

Answer:

[tex]M(t) = 0.1t^{3}[/tex] [tex]+ 5(1.07)^{t}[/tex]- 5

Step-by-step explanation:

(on attachment with step by step explanation)

Please someone help me thank you

Answers

Answer:

D. 9/4 ÷ 3/4

Step-by-step explanation:

In the question, the number line represents 9/4 divided into 3 equal units.

The size of each unit is 3/4 as shown.

Showing that 3/4 divides 9/4 into 3 divisions:

9/4 ÷ 3/4

= 9/4 x 4/3

= 9/3 x 4/4

= 9/3 x 1

= 3 x 1

= 3

Hence, the number line represents three divisions given by 9/4 ÷ 3/4.

What is the product of the polynomials shown below?

Answers

Answer:

B. 14x^3+39x^2+18x+20

Step-by-step explanation:

Given polynomials are:

[tex](7x^2+2x+4)(2x+5)\\For\ product\\(2x+5)(7x^2+2x+4)\\= 2x(7x^2+2x+4)+5(7x^2+2x+4)\\= 14x^3+4x^2+8x+35x^2+10x+20\\Combining\ alike\ terms\\= 14x^3+4x^2+35x^2+8x+10x+20\\=14x^3+39x^2+18x+20[/tex]

The product of given polynomials is:

14x^3+39x^2+18x+20

Hence, Option B is correct ..

Answer:

B.  14x^3 + 39x^2 + 18x + 20.

Step-by-step explanation:

(7x^2 + 2x + 4)(2x + 5)

= 2x(7x^2 + 2x + 4) + 5(7x^2 + 2x + 4)

Distribute over the 2 parentheses:

= 14x^3 + 4x^2 + 8x + 35x^2 + 10x + 20

Add like terms:

= 14x^3 + 39x^2 + 18x + 20.

giving 50 points if you can answer this. PLEASE HELP ME ATTACHMENT BELOW

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.

Answers

Answer:

Q1: 2nd row 2nd tile

Q2: 1st row 1st tile

Q3: 1st row 3rd tile

Q4: 2nd row 3rd tile

Step-by-step explanation:

When

[tex]y = a {(x + p)}^{2} + q[/tex]

Vertex is (-p, q)

Answer:

[tex](-1,-\frac{3}{7} )-->f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\(5,\frac{2}{3} )-->f(x)=\frac{3}{5}|x-5|+\frac{2}{3}\\(0,-\frac{4}{5} )-->f(x)=\frac{1}{2}|x|-\frac{4}{5}\\(\frac{2}{5},\frac{5}{3} )-->f(x)=\frac{3}{2}|x-\frac{2}{y5}|+\frac{5}{3}[/tex]

Step-by-step explanation:

We can solve all of them by writing the equations in a general form

[tex]f(x)=a|x+b|+c[/tex]

This is a function transformation of

[tex]f(x)=|x|[/tex]

where:

a=Factor of vertical stretch

b=Horizontal shift (- shifts right, + shifts left)

c=Vertical shift (+ shifts right, - shifts left)

The original function has its vertex in [tex](0,0)[/tex] so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:

[tex]f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\b=1=HorizontalShiftof-1\\c=-\frac{3}{7}=VerticalShiftof-\frac{3}{7}\\(-1,-\frac{3}{7})\\f(x)=-\frac{3}{5}|x-5|+\frac{2}{3}\\b=-5=HorizontalShiftof5\\c=\frac{2}{3}=VerticalShiftof\frac{2}{3}\\(5,\frac{2}{3})\\f(x)=\frac{1}{2}|x|-\frac{4}{5}\\b=0=HorizontalShiftof0\\c=-\frac{4}{5}=VerticalShiftof\frac{4}{5}\\(0,-\frac{4}{5})\\f(x)=-\frac{3}{2}|x-\frac{2}{5}|+\frac{5}{3}\\b=-\frac{2}{5}=HorizontalShiftof\frac{2}{5}\\c=\frac{5}{3}=VerticalShiftof\frac{5}{3}\\(\frac{2}{5},\frac{5}{3})[/tex]

What is the distance between A (5, 8), and B(-3, 4)

Answers

Answer:

Step-by-step explanation:

4 square root 5

(4-8)^2 + (-3-5)^2

= (-4)^2 + (-8)^2

= 16+ 64

= 80

Square root of 80 is 8.94. Hope this helps!

write 7.26451 correct to 3 decimal places

Answers

726.000
This is bc you need to put the decimals to the third place:)
726.000 this would be written like this because the 4 makes everything else drop to a zero because it isn’t a 5 or above.

A line intersects the point (6,9) and (7,4). What is the slope intercept equation for this line?

Answers

Answer:

y = -5x + 39

Step-by-step explanation:

Plug either ordered pair into the Point-Slope Formula FIRST, y - y = m(x - x), then convert to Slope-Intercept Form by moving whichever term is nearest to y, over to the right side of the equivalence symbol to get the above answer.

Write two point-slope equations for the line passing through the points (6, 5) and (3, 1)

Answers

Answer:

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Step-by-step explanation:

Given two coordinate points (6, 5) and (3, 1)

Slope = (5 - 1)/(6 - 3) = 4/3

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Two point-slope equations for the line passing through the points

(6, 5) and (3, 1) are,

[tex]y-5=\frac{4}{3}(x-6)[/tex][tex]y-1=\frac{4}{3}(x-3)[/tex]Point-slope equationsPoint-slope exists in the general form y-y₁=m(x-x₁) for linear equations. It underlines the slope of the line and a point on the line (that exists not the y-intercept).The slope formula exists utilized to calculate the inclination or steepness of a line. It discovers application in choosing the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line exists defined as the change in the "y" coordinate concerning the change in the "x" coordinate of that line.

Here, the line passes through the points (6,5) and (3,1).

Let,

[tex]$$(6,5)=\left(x_{1}, y_{1}\right)$$[/tex]

[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]

Substitute

Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]

Slope(m) =[tex]\frac{4}{3}[/tex]

Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]

[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]

[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)

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What is the perimeter, P, of a rectangle that has a length of x + 8 and a width of y − 1?


P = 2x + 2y + 18

P = 2x + 2y + 14

P = x + y − 9

P = x + y + 7

Answers

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

Length (L) = x + 8 units

Width (W) = y - 1 units

Perimeter (P) = 2L + 2W

P = 2(x + 8) + 2(y - 1)

P = 2x + 16 + 2y - 2

P = 2x + 2y + 16 - 2

P = 2x +2y + 14

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

The temperature in Fargo North Dakota was 6°F at noon. By 4 PM the temperature dropped to -10°F. What integer represents the change in temperature?

Answers

The change expressed as an integer is -16.

The integer that represents the change in temperature is -16°F.

How to solve for the change in temperature

To find the change in temperature, we need to calculate the difference between the final temperature and the initial temperature.

The initial temperature was 6°F, and the final temperature was -10°F. To calculate the change, we subtract the initial temperature from the final temperature:

Change in temperature

= Final temperature - Initial temperature

                             = (-10°F) - (6°F)

                             = -10°F - 6°F

                             = -16°F

Therefore, the integer that represents the change in temperature is -16°F.

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Write the point slope form of the equation of the line passing through the points (-5, 6) and (0.1).

Answers

For this case we have by definition, that the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes.

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have as data two points, replacing:

[tex]m = \frac {1-6} {0 - (- 5)}\\m = \frac {1-6} {0 + 5}\\m = \frac {-5} {5}\\m = -1[/tex]

We substitute a point, then the equation is:

[tex](y-1) = - 1 (x-0)\\(y-1) = - x[/tex]

Answer:

[tex](y-1) = - x[/tex]

Answer: [tex]y-6=-(x+5)[/tex]

Step-by-step explanation:

The Point-slope form of the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point on the line.

We know that this line passing through the points (-5,6) and (0,1), then we can find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting, we get:

 [tex]m=\frac{1-6}{0-(-5)}=-1[/tex]

Finally, we can substitute the point (-5,6) and the slope into  [tex]y-y_1=m(x-x_1)[/tex], then:

[tex]y-6=-(x-(-5))[/tex]

[tex]y-6=-(x+5)[/tex]

what is the simplified form of the following expression? assume x doesn’t = 0

Answers

For this case we must simplify the following expression:

[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]

We rewrite the expression as:

[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]

We eliminate common factors:

[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]

We multiply the numerator and denominator:

[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]

\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =

[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

Answer:

[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]

Answer:

The simplified form is [tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Step-by-step explanation:

we need to simplify the value of x in given expression:

[tex]\sqrt[5]{\frac{10x}{3x^{3}}}[/tex]

Re- write the above as,

[tex]\sqrt[5]{\frac{10}{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}}[/tex]

Multiply numerator and denominator by [tex](\sqrt[5]{3x^{2}})^{4}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}} \times \frac{(\sqrt[5]{3x^{2}})^{4}}{(\sqrt[5]{3x^{2}})^{4}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^{2}}})^4}{{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^{8}}}}{{3x^{2}}}[/tex]

[tex]\frac{x \sqrt[5]{810 x^{3}}}{3x^{2}}[/tex]

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Hence, the simplified form is

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge of 15%. The price of a book can be modeled by the equation below, where P = the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x = the number of pages: (2 points)

P = (20 + 0.5x) + 0.15(20 + 0.5x)

Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book?

Answers

Answer:

22

Step-by-step explanation:

Solve the inequality  (20 + 0.5x) + 0.15(20 + 0.5x)   ≤ $62.10 for x:

20 + .5x + 3 + 0.75x ≤ 62.10

Combining the x terms, we get:

20 + 3 + 1.25x ≤ 62.10.

Combining the constants on the left:

23 + 1.75x ≤ 62.10

Combining the constants:

1.75x = 39.10

Solving for x:  39.10/1.75 = 22.34

Thus, the max number of whole pages she can have in her book is 22.

Answer:

22

Step-by-step explanation:

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