please help me with this

Answer:

[tex](C) \dfrac{x+3}{x}[/tex]

Step-by-step explanation:

We want to determine an  equivalent expression to:

[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]

Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.

[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]

Step 2: Change the division sign to multiplication

[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]

Step 3: Cancel out common terms and simplify

[tex]= \dfrac{x+3}{x}[/tex]

The correct option is C.

The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Given expression is,

                        [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]

Use factorization,   [tex]x^{2} -9=(x-3)(x+3)[/tex]

Now simplify the given expression.

                       [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]

Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Learn more:

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Answer:

she is paying back 9112.5 R.O

Interest paid back is 2,403.95

Step-by-step explanation:

To find the amount, we use the compound interest formula.

This is given as;

A = I( 1 + r/n)^nt

where A is the amount we are trying to calculate

I is money borrowed = 6709

r is the interest rate = 12 1/3% = 37/3 = 12.33% which is same as 12.33/100 = 0.1233

n is the number of times interest is compounded. We have 15 2 months in 2 and a half years

t is the number of years = 2.5

Plugging these values, we have;

A = 6709(1 + 0.1233/15)^(15)(2.5)

A = 6709(1.0082)^(37.5)

A = 9112.95 R.O

Interest is amount - principal( money borrowed)

9112.95 - 6709 = 2403.95

Answer:

radius x radius x pi = area of circle

6 x 6 = 36

36 x 3.14 = 113.04

113.04

Hope this helps

Step-by-step explanation:

Answer:

3.98 cm

Step-by-step explanation:

V= πr²h

V= 200 cm³, r= 4 cm, h=?

h= V/(πr²)= 200/(3.14*4²)= 3.98 cm

Answer:

Step-by-step explanation:

The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.

For us,

p = ??,

r = .05,

t = 18, and

I = 225.

Filling in:

p(.05)(18) = 225 and

.9p = 225 so

p = 250

Answer:

The answer is $250.

Step-by-step explanation:

First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.

Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.

Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.

Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.

Hey there! :)

Answer:

x = -24.

Step-by-step explanation:

Plug in the values to find the value of 'k':

-3 = k(6)

Divide both sides by 6 to solve for 'k':

-3/6 = k

k = -1/2

Plug this into the equation to solve for the value of x when y= 12:

12 = -1/2(x)

Divide both sides by -1/2:

-24 = x

x = -24.

Answer:

x would be -24

Step-by-step explanation:

since k is a constant, we have to find out what k is from the equation

. -3=6(k) divide both sides by 6 to get that k is -0.5/-1/2.

then, solve for what x is when y is 12 by setting up the equation 12=(-0.5)x. this would result in x being -24

Answer:  The sum of the numbers is 3x + 12

Step-by-step explanation: A brief explanation of an arithmetic progression would be useful for a start.

An arithmetic progression (also known as arithmetic sequence) is series of consecutive numbers in which every term in the entire series is determined by adding a common difference to the previous term. In other words, if x and y are two successive numbers in an arithmetic term, y can be determined by adding the common difference to x. Similarly, the term that comes after y is determined by adding the same common difference to y.

As stated in the question, the numbers x, y and z are successive terms of an arithmetic progression, and the common difference is given as 4. This simply means;

y = x + 4

z = y + 4

z = (x + 4) + 4

z = x + 8

The terms x, y and z can now be re-written as follows,

x, x + 4, and x + 8

The sum of these numbers therefore is derived as,

Sum = x + x + 4 + x + 8

Sum = 3x + 12

Answer:

Please see the attached picture...

Hope it helps...

Good luck on your assignment....

Answer:

The number Alexis thinks of first is 6.7.

Step-by-step explanation:

Let the number Alexis thinks of be x and the first answer he got be y.

Since he multiplies the number by x and divides the answer by 100, the equation is

10x = y

10x = [tex]\frac{y}{100}[/tex]

Then, he multiplies this answer, [tex]\frac{y}{100}[/tex], by 1000 and gets a final answer of 67. The equation is

[tex]\frac{y}{100}[/tex] × 1000 = 67

To find y, you divide 1000y by 100 which gives 10y.

i.e. [tex]\frac{1000y}{1000} = 67[/tex]

10y = 67

Divide both sides of the equation by the coefficient of y (which is 10)

[tex]\frac{10y}{10} = \frac{67}{10}[/tex]

y = 6.7

Substituting 6.7 for y in 10x = y

10x = 6.7

Divide both sides of the equation by the coefficient of x (which is 10)

[tex]\frac{10x}{10} = \frac{6.7}{10}[/tex]

x = 0.67

∴ The number Alexis thinks of first is 0.67.

Hope this helps!!! :))

Answer:

0.67

Step-by-step explanation:

Solution 1

We can work out the initial number by going backwards from the end:

67/1000= 0.067

0.067*100= 6.7

6.7/10= 0.67

Solution 2

(x*10/100)*1000= 67

x/10*1000= 67

100x= 67

x=67/100

x=0.67

Answer:

14 [tex]u^2[/tex]

Step-by-step explanation:

The attached image shows the diagram of the triangle drawn on the Cartesian plane.

We can see that it has the following measures:

base: [tex]b=7u[/tex]

height: [tex]h=4u[/tex]

the area of a triangle is given by the formula:

[tex]A=\frac{b*h}{2}[/tex]

substituting the values:

[tex]A=\frac{(7u)(4u)}{2}\\ \\A=\frac{28u^2}{2} \\\\A=14u^2[/tex]

the area, in square units, of the triangle is 14

Answer:

believe its 2x cause 1 was wrong

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

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Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

The correct option is;

A. a shaded region below a solid boundary line

Step-by-step explanation:

The parameters given are;

The equation, y ≤ 2x - 1

We compare the above equation with the equation for a straight line, y = m·x + c to get

The slope m = 2

The y-intercept c = -1

Therefore, we have;

The graph of an inequality of a y value which is less than or equal to a function is represented by a solid line having the shaded region, which shows the area that satisfies the inequality, shaded below the line

Which gives the correct option as A. A shaded region below a solid boundary line.

Answer:

f(-7)=224

Step-by-step explanation:

[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]

If you know the angle in radians, then the length of the arc is

(measure of the angle in radians) x (radius of the circle) .

In this circle, we know the angle and we know the radius.

Arc AB = ( π/4) x (16")

Arc AB = 4π inches

Arc AB =  about 12.566... inches

Answer:

6 pie correct on edge

Step-by-step explanation:

Answer:

1) 38

2) 160

3) 40

Step-by-step explanation:

Answer:

23, 42, 12

Step-by-step explanation:

Step-by-step explanation:

I hope you understand what I did

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

m<EAD=29°

m<CAB=119°

Solution,

< CAE+<EAD+90°=180°( angles on a straight line)

61+<EAD+90°=180°

<EAD=180-(90+61)

=180-151

=29°

<CAB+<FAB=180°( Linear pair)

<CAB+61°=180°

<CAB=180°-61°

<CAB=119°

hope this helps ..

Good luck on your assignment..

Answer:

That is already at its simplest form.

Step-by-step explanation:

(y + 1)(y + 1) or (y + 1)² is the factored form of y² + 2y + 1. You cannot break it down any further after you reached binomials after you factor unless you are solving for x.

Answer:

3, 12, 27 and 300

Step-by-step explanation:

Plug n as 1, 2, 3 and 10.

3(1)² = 3

3(2)² = 12

3(3)² = 27

3(10)² = 300

Answer:

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled [tex]\triangle OBT[/tex])

with [tex]\angle B =90^\circ[/tex]

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

[tex]\angle O = 55^\circ[/tex]

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]

So, height of building is 57.12 m.

Answer:

y = -3x + 4

Step-by-step explanation:

Slope intercept form:

y = mx + b

Slope = y2 - y1/x2 - x1

-2 - 4/2-0 = slope

slope = -6/2  or  -3

Equation:

y = -3x + 4

Answer:

[tex]y = 4x-3[/tex]

Step-by-step explanation:

y-intercept = b = 4 (because x becomes zero here)

Now, Finding the slope:

Slope = m = [tex]\frac{rise}{run}[/tex]

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

Slope = [tex]\frac{-6}{2}[/tex]

Slope = -3

Now putting m and b in the slope intercept equation to get the required form:

=> [tex]y = mx+b[/tex]

=> [tex]y = 4x-3[/tex]

Answer:

  C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

Answer:

c and something is not d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Katie gets 32/8 = 4 lots of sweets

Pavel gets 4 lots x 3 = 12 sweets

Answer:

The answer is A B C and E

Step-by-step explanation:

I just took it

The statements are true A, B, C, and E.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

The given data in the problem is;

No of the  students from Midland High = 5

No of the students from Leasburg High= 3

No the students from Cassville High = 6

The statements that are true will be;

A.Order matters in this scenario.

B.There are 2,184 ways to select a first-place,second-place, and third-place winner.

C.The probability that all three winners are from Midland High is 0.0275.

E.The probability that all three winners are from Cassville High is 0.0549

Hence the statements are true A, B, C, and E.

To learn more about the probability refer to the link;

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Answer:

[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Step-by-step explanation:

We are given that in 1995, the USPS approximated that they handled  [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex]  pieces.

To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.

Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]

Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]  

As it is clear that more pieces of mail were handled in 1995.

So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]

=  [tex]10^{11} \times (1.8 -1.7)[/tex]

=  [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]

Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Answer:

x = 8

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.

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Answer:

$2466.55

Step-by-step explanation:

We use the formula for Compound Amount, the amount gotten after a particular time, to find the balance:

[tex]A = P(1 + r)^t[/tex]

where P = Principal = $700

r = rate = 6.5% = 0.065

t = time elapsed 20 years

Therefore:

[tex]A = 700(1 + 0.065)^{20}\\\\A = 700(1.065)^{20}\\[/tex]

A = $2466.55

The balance of the account will be $2466.55