Use the equation below and the indicated value to find an ordered pair that is a solution.
y=2x-1 Let x = 4.
The ordered pair is 4.

Based on the division of polynomials and logical inference, the missing factor is 10x².

Note that the result of:

[15x³ - 22x² + (?)] / (5x-4) = 3x²

This means that
3x² *  (5x-4) = [15x³ - 22x² + (?)]  .............................1

But

3x² *  (5x-4)  = 15x³ - 12x²

By reverse calculation, therefore,

We state:

-22x² + (?) = - 12x² [Assume for a moment that x² is eliminated]

-22 + (?) = -12
(?) = -12 +22, Hence

(?) = 10x²

Thus,
[15x³ - 22x² + 10X²) ] / (5x-4) = 3x² .........................................2

Proof:

15x³ - 22x² + 10x² ...................................................................3
= 15x³ - 12x²

Taking common factors:
15x³ - 12x² ⇒ 3(5x³-4x²)

Find one factor

3x² (5x-4) .....................................................................................4

Recall that the problem states that equation 3 /  (5x-4) = 3x²

If 15x³ - 22x² + 10x² when simplified  =
3x² (5x-4)

Then

15x³ - 22x² + 10x²/ (5x-4)  = 3x² (5x-4)/(5x-4)

= 3x²

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Answer:

Explanation:

Let x represent the length of segment ST.

Given that the lines QT and RS are parallel, the, then the triangles QPT and RPS are similar.

So, the ratio of their sides will be equal;

Given;

substituting;

Therefore;

Answer:

Explanation:

We are told that the grocery bill b is a function of n (the number of bags of chips). This means that the grocery bill can be represented as b(n).

Furthermore, we know that each bag of chips costs 2.42, meaning n bags of chips will cost 2.42n - which is the grocery bill b(n); therefore,

which is the equation the gives the grocery bill (as a function of n, the number of chips bags bought).

Let's divide 5/6, we just place each part as an extended division

When the dividend is less than the divisor, we have a decimal point

Answer:

  (c)  five raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

The given expression can be simplified as follows:

  [tex](5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}[/tex]

__

Additional comment

We find math expressions easier to understand when they are written using math notation, instead of words.

Answer:

10

Step-by-step explanation:

1234 / 34 = 1224

1234 - 1224 = 10

The remainder = 10

Answer:

we can now graph the function as;

Explanation:

Given the equation;

Firstly, to derive the period, Amphitude and midline, let us compare to the general form;

From the given equation;

With the above characteristics we can now graph the function as;

Please, give me some minutes to take over your question

_________________________________

I'm working on it

__________________________

a probability model has some features

Events (This part is ok, the probabilities are between 0 - 1 )

1) p1 = 0.2

2) p2 = 0.5

3) p3 = 0.1

____________________

The sample space is not 1 because p1+p2+p3 = 0.8

______________________________________

Answer

FALSE. No, this is not a valid probability model

ANSWER

3/7 is less than 0.516

EXPLANATION

Wwe want to compare the two numbers 3/7 and 0.516.

Let us convert 3/7 to decimal so we can compare properly:

3/7 = 0.429

As we can see:

0.429 is less than 0.516

So, 3/7 is less than 0.516

In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°

the equation to find x is

we need to isolate the x

the answer is c x=90°

Given:Three dice are tossed.

To find: Probability of rolling 3 different numbers.

Let E be the event of getting same number on three dice.

So,the favorable cases for E will be

(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).

So, the number of favorable cases=6

Now,the total number of cases for E will be

Since each dice has 6 numbers so three dice will have these number of cases.

Now, the probability to have a same number on 3 dice will be

Now, probability of rolling 3 different numbers is

Hence, the probability of rolling three different numbers is

Given:

KM=12 cm.

KO=1+KL

Since KM=12 cm, we can write

Therefore, KL can be calculated as,

Now, KO can be calculated as,

Now, using geometric property,

Putting the values in the above equation, KN can be calculated as,

Now, ON can be calculated as,

Since LM=9 is a chord longer than MN in the given circle, the length of MN is less than 9.

Therefore, the segments with length 9 are LM and KN.

The sum of the expression will be given as 26. Thus, option B is correct.

An expression may be defined as the collection of numbers and variables related to one another by arithmetic operations. A number x is said to be a perfect square of a certain number y if the number y is multiplied to itself again. The square root of the number y will be equal to x. For example, 25 is the perfect square of 5 and 9 is the perfect square of 3. Square root of a number may be defined as the number to the power of half. The square root of √121 = 11 as 121 is perfect square of 11 and square root of √225 = 15 as 225 is perfect square of 15.

Now, √121 + √225 =?

As, √121 = 11 and √225 = 15

=> 11 + 15 = 26 which is the required answer.

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The functions and its domain are a representation of their dependance on one another.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.

[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]

The domain of the function is given as

[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]

In the second composition of the function,

[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]

The third composition of function

[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]

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Answer: 7

Step-by-step explanation:

1) Set up an equation. Let x be the number of hours he works.

[tex]400\leq 64x[/tex]

2) Solve the equation

(<= mean less or equal to)

400/64 <= x

6.25 <= x

3) Solve the problem

We need to round up 6.25 as 6.25 is not on the list. Since the number has to be greater than 6.25, the next option is 7.

Answer:

Choice A. 0.7

Explanation:

The place value of the numbers is given below

T

Step 1

Given;

Step 2

Match each of the following expressions to its meaning in the context of this situation.



Answer:

Graphing the points we have;

Above is the graph of the given equation showing the derived points.

Explanation:

Given the equation;

To plot the graph we need to calculate the corresponding values of x and y at each point.

Let us calculate the values of y for x = -4,-2,0,2, and 4;

Therefore, Graphing the points we have;

Above is the graph of the given equation showing the derived points.

The property use to solve the equation is as follows:

The equation can be solved as follows:

−2a = 10 − 3(2a + 6)

Using distributive property,

−2a = 10 − 3(2a + 6)

- 2a = 10 - 6a - 18

According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

Combine like terms

- 2a = 10 - 6a - 18

- 2a = -6a - 8

Using additive property of equality, we will add 6a to both sides of the equation.

The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.

- 2a = -6a - 8

- 2a + 6a = -6a + 6a - 8

4a = - 8

using division property of equality, we will divide both sides of the equation by 4.

The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.

4a = - 8

4a / 4 = -8 / 4

a = - 2

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Assuming that the question is as follows:

If we represented this angle as a right triangle (in fact, a right-angled isosceles triangle) with sides (legs) equal to one, then, we have that (for this case, the triangle has two angles that equal 45 degrees):

We need to multiply both, the numerator and the denominator by the square root of 2 to have no irrational number in the denominator.

Therefore, the value of the inverse cosine of sqrt(2)/2 is the angle 45 (the correct answer is option D).

An isosceles triangle is a triangle which has two of its sides with the same length

Answer: t =  4

Isolating a variable: rearranging an equation so that the variable is on its own

Calculations:

[tex]\frac{\frac{t}{4} }{16} = \frac{1}{16}[/tex]

[tex]\frac{t}{4}= 16/16[/tex]   - calculated by multiplying 1/16 by 16

[tex]t= 16/16[/tex] × [tex]4[/tex]  

[tex]t= \frac{64}{16}[/tex]

[tex]t=4[/tex] - simplified answer

Answer:

$809.455

Step-by-step explanation:

How to find the new cost:

890/100*15

= 133.5

So: 890-133.5

= 756.5

next we find 7% of it (tax):

Which we will find the 7% of it and plus it in

so the new answer is: 809.455

Let's first identify at least two points that pass through the given line.

Let's use the following points:

Point A: x1, y1 = 0, -7

Point B: x2, y2 = 6, 2

a.) Let's determine the slope of the original line:

Therefore, the slope of the given line is 3/2.

b.) Let's determine the slope of the line perpendicular to the given line:

Therefore, the slope of the line perpendicular to the given line is -2/3.

c.) Let's plot the graph of the perpendicular line.

Let's first determine the equation of the given line.

m = 3/2

x,y = 0, -7

y = mx + b

-7 = (3/2)(0) + b

-7 = b

y = mx + b

y = 3/2x - 7

Let's determine the equation of the perpendicular line.

m = -2/3

x,y = 0, -7 ; let's use this as the point of intersection.

y = mx + b

-7 = -2/3(0) + b

-7 = b

y = mx + b

y = -2/3x - 7

Let's now plot the graph.

We need to know about quadratic equation to solve the problem. The year when the number of cases will be 50,000 is 2017.

Quadratic equation is an equation that has a maximum degree of two. Quadratic equations always have two roots, it can be solved by factorization method. In this question we have been given a function that we can simplify to get a quadratic equation. We need to find the year when the identity theft cases reach 50,000, we need to equate the equation to 50,000 and then solve the quadratic equation to get x.

f(x)=0.058x+2.175x+340.2[tex]x^{2}[/tex]-1500x+20000 =340.2[tex]x^{2}[/tex]-1497.767x+20000

50000=340.2[tex]x^{2}[/tex]-1497.767x+20000

340.2[tex]x^{2}[/tex]-1497.767-30000=0

Using Sridharacharya's method,

x=1497.767±[tex]\sqrt{2243305.99+40824000}[/tex]/680.4=1497.767±6562.56855/680.4

x=11.85 or x=-7.44

Here x cannot be negative, so the right value of x is approximately 12,

year when cases is 50000= 2005+12=2017

Therefore the year when identity theft cases reach 50000 is 2017.

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Given:

$10 price = 1000 customers per week.

$6 price = 2950 customers per week.

Let's write a linear equation for the attendance in terms of the price, p.

Apply the slope-intercept form:

y = mx + b

In this case, let's use the form:

A = mp + b

Where m is the average rate of change(slope) and b is the y-intercept.

To find the slope, m, apply the slope formula:

Where:

(x1, y1) ==> (10, 1000)

(x2, y2) ==> (6, 2950)

Hence, we have:

The average rate of change is -$487.5

To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.

Let's take the first point: (10, 1000)

A = mp + b

1000 = -487.5(10) + b

1000 = -4875 + b

Add 4875 to both sides:

1000 + 4875 = -4875 + 4875 + b

5875 = b

b = 5875

Therefore, the lineart equation for the attendance in terms of the price, p is:

A = -487.5p + 5875

ANSWER:

The answer is 11.

Using system of equations:

Length of each Plan A workout is: 0.5 hour

Length of each Plan B workout is: 1.25 hours

The number of hours that each of the workout plans last can be represented as a system of linear equations. The explanation below shows how to solve this problem using the elimination method.

Let,

x = number of hours for each plan A workout.

y = number of hours for each plan B workout.

Create the system of equations below:

Equation for Friday would be:

3x + 2y = 4 --> equation 1

Equation for Saturday would be:

8x + 4y = 9 --> equation 2

Multiply equation 1 by 4 and equation 2 by 2:

12x + 8y = 16 --> eqn. 3

16x + 8y = 18 --> eqn. 4

Substract eqn. 4 from eqn. 3:

-4x = -2

x = 1/2 = 0.5 [0.5 hours or 1/2 an hour for Plan A]

Substitute x = 0.5 into eqn.1:

3(0.5) + 2y = 4

1.5 + 2y = 4

2y = 4 - 1.5

2y = 2.5

y = 2.5/2

y = 1.25 [1.25 hours for Plan B]

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