Simplify the following exponent (x¹⁰ ÷ x²) x x³

To find the slope of the line that passes through (9, 10) and (6, 12)

We will use the formula;

From the points given;

x₁ = 9 y₁=10

x₂ = 6 y₂=12

Substitute the values into the formula;

Evaluate;

Answer: 80

Step-by-step explanation:

You do 2 times= 8 and multiply 8 to the 5 white and black tiles which equals 40+40=80.

The total area for the parallelogram shaped tiles Felix needs to buy is 80cm² at the price of $40.

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

Given that, the base of one parallelogram shaped tile is 4cm with height as 2cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix needs to buy a total of 80cm² of 10 parallelogram shaped tiles.

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The equation of the line that passes through the points ( -3,18 ) and ( 2,-7 ) is f(x) = -5x + 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point 1( -3,18 )

Point 2( 2, -7 )

First, we find the slope of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -7 - 18 ) / ( 2 - (-3) )

m = ( -25 ) / ( 2 + 3 )

m = ( -25 ) / ( 5 )

m = -5

Next, next we find the y-intercept

y = mx + b

18 = (-5)(-3) + b

18 = 15 + b

b = 18 - 15

b = 3

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-5)x + 3

y = -5x + 3

Therefore, the equation of the line is y = -5x + 3

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After simplification the answer is 31.418 or 31.42

Define Radicals

The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

The given expression is,

2√6(√2 + 5)

First, open the brackets

2√6 * √2 + 5 * 2√6

we know, √6 = √3 * 2 = √3 * √2

so, 2√3 * √2  * √2 + 10√6

We didn't open the both √6 values it's because we want to remove  root from √2 so as we know √2 * √2 = 2

2√3 * 2 + 10 * √6

=> 4√3 + 10 * √6

Now, put the values of √3 = 1.732 and √6 = 2.449

=> 4 *  1.732 + 10 * 2.449

=> 6.928 + 24.49

=> 31.418 or 31.42

Therefore, the answer is 31.418 or 31.42

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Let

x -----> the number of milliliters of the 3.5% solution

y ----> the number of milliliters of the 6% solution

we have that

3.5%=3.5/100=0.035

6%=6/100=0.06

5%=5/100=0.05

so

0.035x+0.06y=0.05(500) -------> equation A

and

x+y=500 -----> x=500-y ------> equation B

solve the system of equations

substitute equation B in equation A

0.035(500-y)+0.06y=0.05(500)

solve for y

17.5-0.035y+0.06y=25

0.025y=25-17.5

0.025y=7.5

y=300

Find out the value of x

x=500-300=200

therefore

Given the regular price is $43.

S.P= 35% off on regular price i.e.

Hence, after 35% off, the price is $27.95

Basketball 12 votes; Soccer 24 votes; Football 24 votes

Here, we want to select the options that could represent the percentage

From what we have, soccer and football are same value and basketball is half of these

So the option where we have the given outline is the correct answer

Looking at the options, the only place we have the outline is;

Basketball 12 votes; Soccer 24 votes; Football 24 votes

The number of bookshelves needed if each bookshelves contain 5 books is 10.

She has 47 books. . She wants to put them all on bookshelves.

Therefore, the number of bookshelves she will need if each shelf holds 5 books can be calculated as follows:

The total number of books she has in her possession is 47 books.

All the books must have a place in the bookshelves.

Each bookshelves can only contain 5 books.

Hence,

let

x = number of bookshelves

Therefore,  the equation to find the number of bookshelves is as follows:

5x = 47

divide both sides by 5

x = 47 / 5

x = 9.4

Therefore, Shiloh will require 10 book shelves.

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We have here that Roberto has a total of $3300 in two savings account.

Then, if y represents the amount in one account, we have that the sum of both accounts is up to $3300.

We can suppose that the other account is x. Then, we have:

If we subtract y from both sides of the equation, we have:

Therefore, the algebraic expression for the amount in Roberto's other account is (since x is not mentioned, we have):

In summary, the amount in Roberto's other account is $3300 - y.

The mid-point of LP is 1.5.

Here we have to find the mid-point of the line LP

L is on -2 on the line and P is on 5.

To find the mid-point we have a formula:

mid-point = (b - a)/2

where a and b are two points between which we have to find the mid-point.

So, mid-point of LP = 5 - (-2) / 2

                                = 7/ 2

                               = 3.5

Now we have to find the value so we will subtract -2 with 3.5.

So the mid-point is 3.5 - 2= 1.5.

Therefore the mid-point of the line LP is 1.5.

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We will investigate how to graph a straight line on cartesian coordinate plane.

All equations of straight line are expressed in a general slope-intercept form as follows:

Where,

To graph any straight line we need the equation of the straight line or atleast two points that must lie on the line.

We are given the slope ( m ) and one of the points that lie on the line as follows:

We need one another point that lies on the line to plot the graph of a straight line. To find another point we must completely express the equation of the straight line ( general form given above ).

We see that an equation of a straight line is defined by two parameters i.e ( m and c ). We are given the value of the slope ( m ). We will go ahead and plug it into the general slope-intercept form given above:

Now to determine the value of parameter ( c ) we must have atleast one point that lies on the line. We will use the point given to us and plug in the respective coordinates in the equation developed above and solve for ( c ) as follows:

We will go ahead and update the equation of the straight line as follows:

Now to get one more point to graph the plot we will assume any value of the for either variable ( x or y ) and then determine the value of the other variable as follows:

Therefore, we have the two points to plot the graph as follows:

We can go ahead and select the above points on the given grid to construct the straight line!

⇒First step is to find the gradient

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} } \\m=\frac{8-(-3)}{-5-2} \\m=\frac{8+3}{-7} \\m=-\frac{11}{7}[/tex]

In the general equation y=mx+c let us find the value of c by plugging in the known values

I will use the point (-5,8) Note you can use any .You will get the same value of c.

[tex]8=-\frac{11}{7} (-5)+c\\8=\frac{55}{7} +c\\c=8-\frac{55}{7} \\c=\frac{1}{7}[/tex]

The equation now is:

[tex]y=-\frac{11}{7} x+\frac{1}{7}[/tex]

ANSWER

A. x ≥ -5 and x < 4

EXPLANATION

We have the two inequalities:

- 4x + 1 ≤ 21 and 5x + 2 < 22

Let us solve them separately:

FIRST ONE

-4x + 1 ≤ 21

Collect like terms:

-4x ≤ 21 - 1

-4x ≤ 20

Divide through by -4, the sign changes:

SECOND ONE

5x + 2 < 22

Collect like terms:

5x < 22 - 2

5x < 20

Divide through by 5:

x < 20 / 5

x < 4

The answer is Option A.

Answer: C. 8

When we have two chords intersecting inside a circle, the products of the lengths of the segments are equal to one another. This means that for the given circle, we have the following:

10 * 4 = 5 * x

We can solve for x by multiplying 10 by 4, which is 40, and then dividing by 5, to isolate x, which is 8.

The room is a rectangle with dimensions 25 and x + 10. The area of a rectangle is the product of its dimensions, so the area will be:

We have to add the parenthesis because we first need to add 10 and x and then multiply. Distributing the 25, we have:

As we can see, this matches what Ron thinks the area will be, so he is correct. Thus, the answer is "Yes". The why can be both because the area is the sum of 25*10 and 25x and because the area is the product of 25 and 10 + x.

So, the correct alternatives are A and D.

Answer:

y = 3x + 3 :D

Step-by-step explanation:

Equation of line: y = mx + b :)

b: Y intercept

m: Slope

Now lets solve :)

Lets find M first :)

We need 2 points so lets use (0,3) and (1,6) :)

We fist need to subtract :)

6 - 3 = 3

1 - 0 = 1

Now we divide :)

3/1 = 3

Lets put that into our equation :)

y = 3x + b

Now lets find B :)

To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!

The y intercept will be 3 :)

The final equation will be y = 3x + 3 :)

Have an amazing day!!

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The conclusion from the factor table of 18 is that, 18 is not a prime number i.e. it is composite

From the question, the number is given as

Number = 18

The factors of 18 are represented as

Factors of 18 = 1, 2, 3, 6, 9 and 18

When these factors are picked in pairs, we have the following  representations

Factors pairs of 18 = (1, 18), (2, 9), (3, 6)

Next, we represent the factors on a factor table

So, we have

Factors      Factor pairs        Prime factorization

1, 2, 3,           (1, 18)                       2 x 3²

6, 9 and        (2, 9)

18                   (3, 6)  

Because the number 18 has factors other than 1 and 18, then the number 18 is a composite number

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Answer:

5/3

Step-by-step explanation:

rise over run

(8-3)/(3-0)

We have the function f(t) defined as:

We have to find f'(x).

We can solve this integral as:

If we derive this expression for f(x) we obtain:

NOTE: This expression could have been derived from the function inside the integral.

We can now find f'(3) as:

Answer:

f'(x) = x^4

f'(3) = 81

There are two disccount applied to this computer, the first one is 30%. To calculate its value, we need to multiply the original price by the fraction that represents 30%

The first discount was 16,800. To determine the price after this, we need to subtract the listed price by the discount 1, this is done below:

Then we need to calculate the second discount, which was equal to 20%.

The final price is the subtraction between the price 2 and the discount 2, we have:

The final price is 31,360.

Answer:

1/2

Step-by-step explanation:

Do divide fractions, multiply the first number by the reciprocal (the numbers flipped) of the second number.

So, 1/3 * 3/2

1/3 * 3/2 = 3/6

3/6 = 1/2

The return trip takes 0.7 hrs more than the delivery.

Let the time  taken while going be x  therefore the time taken while returning will be 10 - x.

Given :

The truck driver averages 60 miles per hour while delivering freight

The speed is 45 mph on the return trip.

Therefore according to the question,

60x = 45 ( 10 - x)  [ As the distance is same]

=> 4x = 3 ( 10 - x)

=> 4x = 30 - 3x

=> 7x = 30

=> x = 30 / 7

=> x = 4.3

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Answer:

9

Step-by-step explanation:

The answer you divide 65 by 7 which would get you 9.2857142857143. The remainder is 2.

MATHEMATICALLY WE WRITE THE PROBLEM AS

[tex] = \frac{65}{7} \\ [/tex]

SOLVING FURTHER

[tex]65 \div 7 \\ = 9.285714286[/tex]

BUT 7 GOES 9 TIMES IN 65 NOT CONSIDERING THE REMINDER.

HOPE THIS HELPS

The value of g(x) will be expressed as g(x) = (x + 5)

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called as independent variable and output variable is called dependent variable. Composite functions are the functions which are written as combination of two functions. A function f(x) may be defined as composite function of another function g(x) when it can be written as either f(g(x)) or g(f(x)). We know that f(x) = x⁹ and the composite function H(x) = f(g(x)) = (x + 5)⁹. So, from this we can say that the function g(x) will be given as (x + 50 as we put (x + 5) as x in the function H(x).

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To reflect the figure, we have to draw the new vertex at the same distance from the line x = -4, the image below shows this reflection.

Notice that the new figure has the same distance from x = -4 as the pre-image.

We have

1. The timing shown in the morning is from 8:15 to 12:15, this is the number of hours worked in the morning is 4 hours.

The pay is $13.50 per hour

Therefore, the pay earned in the morning is:

then, the pay earned in the morning is $54

2. The timing shown in the afternoon is from 13:00 to 17:30, this is the number of hours worked in the afternoon is 4 hours and 30 minutes. Therefore, the pay in the afternoon is:

then, the pay earned in the afternoon is $60.75

The pay per 1 day is:

pay in the morning + pay in the afternoon

Answer: pay for a day is $114.75

a. Greg can eat 8 breakfasts from 1 box.

b. The cost of 1 breakfast from a regular-sized box is $34.32.

c. Greg will enjoy 4 breakfast more.

a. A regular-sized box contains 12 servings. If Greg eats 1 1/2 servings for breakfast every day, the number of breakfasts that Greg can eat from 1 box will be:

= 12 ÷ 1 1/2

= 12 ÷ 1.5

= 8

b. Since the regular-sized box of cereal costs $4.29. The cost of 1 breakfast from a regular-sized box of cereal cost Greg will be:

= 8 × $4.29

= $34.32

c. If Greg purchased the family-sized box of cereal that contains 18 servings, the number of breakfasts will be:

= 18 ÷ 1.5

= 12 breakfast

The difference will be:

= 12 - 8

= 4 breakfast more.

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Answer:

No

Step-by-step explanation:

In order to solve this, we plug in the values for x and y. Remember that x = -1 and y = -9

-9 = 7 - 2(-1)

-9 = 7 + 2

-9 ≠ 9