Which could be the missing first term

Using square process method, we can get the values of x to be 12 and 6.

The formula a (x + m)2 + n = a (x + m)2 + n is the simplest to remember while learning how to complete the square technique.

The following formulas can be used to compute m and n in this situation: m = b/2a and n = c - (b2/4a).

From the question,

x² - 18x + 72= 0

⇒ x² - 18x = -72

Complete the square by adding the half of the square of the coefficient of x to both sides of the expression as shown:

⇒ x² - 18x + (18/2) ² = -72 + (18/2) ²

⇒ x² - 18x + 9² = -72 + 81

⇒ (x-9) ² = 9

⇒ x-9 = ± 3

So, values of x are:

x = 3 + 9

= 12

x = -3 + 9

= 6

Therefore, the values of x are 12 and 6.

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Using algebraic expressions, x = 7/2 and y = -21/2.

An algebraic expression might be made up of a single word or a group of words.

An algebraic expression can be any number, variable, or set of operations, whereas an equation is two different algebraic expressions connected together with an equal sign.

x = 7/2 and y = -21/2

Let x and y be those numbers.

In response to your query

x + y = -7

x - y =14

both equations added

2x = 7

or x = 7/2

the equivalent x value in either equation

y = -21/2

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Complete question -

What are the two numbers if their sum is −7 and their difference is 14?

Answer:

Step-by-step explanation:

-3(2x-1)

Using the concept of percentage, we can deduce that Kareem does not have enough money with him

To solve the questions given, we need to apply the concept of percentage on some.

a) Rounding the price of the guitar to a convenient amount, we get $180.

b) 10% of the rounded price is: 0.1 x $180 = $18.

c) 1% of the rounded price is: 0.01 x $180 = $1.80.

d) To get the estimated tax, we need to multiply the rounded price by the HST rate: 0.13 x $180 = $23.40. Dividing this by $1.80, we get approximately 13.

e) The estimated tax is $23.40.

f) Adding the estimated tax to the rounded price, we get $180 + $23.40 = $203.40.

Since Kareem has $200 cash with him, he does not have enough money to buy the guitar at the estimated price of $203.40. Therefore, the answer is NO.

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Is sin (θ) = - 2/ 3, the options that are possible include:

Since sec(θ) is negative, cos(θ) is also negative (sec(θ) = 1/cos(θ)). This means θ is in the second or third quadrant, but since sin(θ) is negative, θ must be in the third quadrant. Now let's check if the given tan(θ) value is correct:

tan(θ) = sin(θ)/cos(θ)

Since we already know that cos(θ) is negative, we have cos(θ) = -(√5)/3.

Now calculate tan(θ):

tan(θ) = (-2/3) / (-(√5)/3) = 2/√5

The given values in option A are correct.

cos(θ) = -(√5)/3 and tan(θ) = 2/√5

These are the same as in option A. So, this option is also possible.

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Answer:

Step-by-step explanation:

In quadrilateral ABCD, we have:

AB is parallel to DC

AD is parallel to BC

AC = 40 in (given)

BD = 50 in (given)

AB = 25 in (given)

We can use the fact that opposite sides of a parallelogram are equal in length to find the length of CD:

CD = AB = 25 in

Next, we can use the fact that the diagonals of a quadrilateral bisect each other to find the length of AO and OC:

AO = BO = BD/2 = 50/2 = 25 in

OC = OD = AC/2 = 40/2 = 20 in

Now we can use the triangle inequality to find the perimeter of triangle COD:

CO + OD + CD > OC

CO + 20 + 25 > 20

CO + 45 > 20

CO > -25

CO + OC > CO

CO + 20 > 0

CO > -20

CO + CD > OD

CO + 25 > 20

CO > -5

Therefore, the possible range of values for CO is:

-20 < CO < -5

However, since lengths cannot be negative, we can take the absolute value of CO to get:

5 < CO < 20

So the perimeter of triangle COD is:

CO + OD + CD = CO + 20 + 25 = CO + 45

Substituting the possible range of values for CO, we get:

5 + 45 < CO + 45 < 20 + 45

50 < CO + 45 < 65

So the perimeter of triangle COD is between 50 in and 65 in.

Therefore, the perimeter of triangle COD is between 50 in and 65 in, but the exact value depends on the length of CO, which is between 5 in and 20 in.

The inverse function of f(x) = (x + 5)² on the domain x >= -5 is given as follows:

[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]

The domain of the inverse function is given as follows:

x >= 0.

The function for this problem is defined as follows:

f(x) = (x + 5)² on the domain x >= -5.

The range of the function is y >= 0, as the vertex is at (-5,0) and the function is increasing over it's domain, hence the domain of the inverse function, which is the range of the original function, is given as follows:

x >= 0.

To obtain the inverse function, wee exchange x and y in the definition of the function, and then isolate y, hence:

x = (y + 5)²

[tex]y + 5 = \sqrt{x}[/tex]

[tex]y = \sqrt{x} - 5[/tex]

[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]

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Answer:

First question:

We can start by setting up the formula that relates the volume V, temperature T, and pressure P:

V = k * (T/P)

where k is a constant of proportionality. We can solve for k by plugging in the given values for V, T, and P:

70 = k * (420/18)

Simplifying the right side of the equation, we get:

70 = k * 23.3333

Dividing both sides by 23.3333, we get:

k = 3

Now we can use this value of k to find the temperature T when V is 60 cm and P is 7:

60 = 3 * (T/7)

Simplifying the equation, we get:

T/7 = 20

Multiplying both sides by 7, we get:

T = 140

Therefore, the temperature when V is 60 cm and P is 7 is 140 kelvin.

Second question: We can start by using the formula that relates the time (T), distance (D), and speed (S):

D = S * T

Since the distance between the two cities is constant, we can set the distances for the two cars to be equal:

35 * 9 = 21 * T

Simplifying the right side of the equation, we get:

315 = 21T

Dividing both sides by 21, we get:

T = 15

Therefore, the trip takes 15 hours for a car moving at 21 mph.

Hopefully this helps you! I'm sorry if it wrong. If you need more help, ask me! :]

Answer:

819/5 is the correct answer that I think

Answer:     x^2-xy-2x^2y+2xy^2+2x+2y over 2x(x - y)

Step-by-step explanation:

because im that guy

Answer:

      5x^2 - 19x + 15

Step-by-step explanation:

We must multiply the pool's length and width to determine its area. We can factor the equation f(x)=(x-3)(5x+2) to determine the length and width:

f(x) = (x-3)(5x+2)

f(x) = 5x^2 - 13x - 6

One of the parameters is the pool's length (x-3), while the other is its breadth (5x+2). We multiply these two elements to determine the area:

Area is length times width (x-3)

(5x+2)

By extending this statement using FOIL (First, Outer, Inner, Last), we may make it simpler:

Area is equal to  5x^2 - 13x - 6x + 15

Area: 5x^2 - 19x + 15

The pool at Philip and Laura's home is therefore  5x^2 - 19x + 15 square feet in size. We are unable to establish the precise square footage of the pool because we were not given a specific figure for x.

Answer:

-sqrt(2)
-sqrt(2)
1
1

Step-by-step explanation:

19/100 into decimals is 0,19

To write a fraction based on 10/100/1000... you must move the decimal point to the left the number of times equivalent to the number of zeros in the base.
In this case, base 100 has two zeros. Then move two squares to the left.

[tex]\begin{array}{l}\bf 19\\\sf {0}{,}\!\overset{\overset{2}{\curvearrowleft}}{1}\!\overset{\overset{1}{\curvearrowleft}}{9}\\\\\bf \dfrac{19}{100}=0{,}19\end{array}[/tex]

Did you see how easy the conversion was under these circumstances?

If you have any question about this solution, you can ask me in the comments :)

Answer:

this is the intersecting of lines

Answer:

gogel chrome. will answer faster than this app

Assuming that there are no other transactions or fees on the credit card, here's how to calculate the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made:

1.) Unpaid Balance: The unpaid balance is the amount of the credit card balance that remains after making the minimum monthly payment. In this case, the minimum monthly payment is $125, so the unpaid balance would be:

$5000 - $125 = $4875

2.) Interest Charge: The interest charge for unpaid balances is 18% per year. To calculate the monthly interest rate, divide the annual rate by 12:

18% / 12 = 1.5%

3.) To calculate the interest charge for the month, multiply the unpaid balance by the monthly interest rate:

$4875 x 1.5% = $73.13

So the new interest charge for the month is $73.13.

4.) Purchasing Power: Purchasing power refers to the amount of credit that is available on the credit card after making the minimum monthly payment and accounting for any interest charges. To calculate the purchasing power, subtract the unpaid balance and interest charge from the credit limit:

$5000 - $4875 - $73.13 = $51.87

So the purchasing power on the credit card after the minimum monthly payment is made is $51.87.

The height of the cylinder is approximately 42/11 inches. The answer is option C.

What is the formula for the volume of the cylinder?

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:

1 and one-third = 4/3

V = π(1/3)²h = 4/3

Simplifying the equation, we get:

h = (4/3) / (π(1/3)²) = (4/3) / (π/9) = (4/3) * (9/π) = 12/π

Approximating π as 22/7, we get:

h ≈ (12/π) ≈ (12/(22/7)) = 42/11 inches

Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.

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Answer:

40,320

Step-by-step explanation:

There are 8 letters in total:

So, in the first place we can put all 8 letters

In the 2nd place we can put 7 (all except the letter in the first place and so on...)

Let's multiply the options (the order is important):

8! or 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320 (8 places for letters in total)

The inequality expression g - 17 ≥ 17 when solved has a solution of g ≥ 34

Given the inequality expression

g - 17 ≥ 17

To solve the inequality g - 17 ≥ 17, we need to isolate the variable g on one side of the inequality.

We can do this by adding 17 to both sides of the inequality:

g - 17 + 17 ≥ 17 + 17

Simplifying, we get:

g ≥ 34

So the solution to the inequality is all values of g that are greater than or equal to 34.

We can graph this solution on a number line by placing a closed circle at 34 and shading to the right, to indicate that any value greater than or equal to 34 satisfies the inequality.

The graph looks like this the attached figure

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Answer:

Answer equals 2500 according to the question

Answer:

Step-by-step explanation:

Need a z-score with all of these, which essentially makes the table needed a standard normal table with mean 0 and sd 1

z=(x-mean)/sd

a. (275-280)/20=-0.25

want the probability of z <-0.25, and that is 0.4013 or 40.13%

b.(243-280)/20=-1.85, and probability of z < -1.85 is 0.0322 or 3.22%

c. this is z of -39/20 or -1.95 and z of 21.60/20 or 1.08. This has a probability of 0.8343 or 83.43%

Use 2nd VARS 2 for normal cdf and put in the numbers, with at least -6 or +6 for minus or plus infinity. 1E99 is fine but isn't really necessary.

Answer:

1 product

Step-by-step explanation:

Given the equation that shows how the time required to complete an online shopping transaction is related to the number of products being purchased as;

t = 24p + 27

t represents the time required to complete the transaction

p is the product purchased

If it takes 51 seconds to complete a transaction, to get the amount of product purchased, we will substitute t = 51 into the expression and find p as shown;

51 = 24p + 27

Substract 27 from both sides

51-27 = 24p + 27 - 27

24 = 24p

24p= 24

p = 24/24

p = 1

Hence only 1 product is being purchased

The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.

One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.

Volume of rectangular prism = length * width * height

rectangular prism A:

length =  10 in.

Width =  3 in.

height = 6 in.

rectangular prism B:

length =  4 in.

Width =  3 in.

height = 6 in.

Thus,

volume of the solid = volume of rectangular prism A + volume of rectangular prism A

volume of the solid = 10*3*6 + 4*3*6

Thus, the correct option to determine the value of  volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.

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The correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16

What is Linear equation ?

A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power, also called a linear term.

A linear equation can be written in the form of:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope or gradient of the line, and b is the y-intercept (the point where the line crosses the y-axis).

The equations that are true for x = -2 and x = 2 are:

[tex]x^{2}[/tex] - 4 = 0, which is true for x = -2 but not for x = 2

4[tex]x^{2}[/tex] = 16, which is true for x = 2 but not for x = -2

Therefore, the correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16

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The figures to complete the table, based on the pattern, would be 6. 20, 7.00.

To complete the table, you need to find the common difference between the values in B which is :

= 4. 6 - 3. 8                                         = 5. 4 - 4. 6

= 0. 80                                                   = 0. 80

The next two values would therefore be :

= 5. 4 + 0. 80                                        = 6. 20 + 0. 80

= 6. 20                                                  = 7. 00

The complete table then is :

A -  5,    6,   7,      8,       9

B- 3.8, 4.6, 5.4, 6. 20, 7. 00

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The full question is:

Complete the table based on the pattern you see:

A- 5, 6, 7, 8, 9

B- 3.8, 4.6, 5.4, ____, ____,

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Answer:

  C'(-5, -2)

Step-by-step explanation:

You want the coordinates of point C(4, 1) after rotation 90° CW about the origin and translation by (-6, 2).

The transformation accomplished by rotation 90° clockwise is ...

  (x, y) ⇒ (y, -x)

The translation by (-6, 2) adds those values to the coordinates:

  (x, y) ⇒ (x -6, y +2)

Combined, the transformations give you ...

  (x, y) ⇒ (y -6, -x +2)

  C(4, 1) ⇒ C'(1 -6, -4 +2) = C'(-5, -2)

The coordinates of C after the transformation(s) are (-5, -2).