Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q?
[p and q are integers]


Step 1 x2 + 10x + 24 − 1 = 0 − 1
Step 2 x2 + 10x + 23 = −1
Step 3 (x + 5)2 = −1

Step 1 x2 + 10x + 24 − 2 = 0 − 2
Step 2 x2 + 10x + 22 = −2
Step 3 (x + 5)2 = −2

Step 1 x2 + 10x + 24 + 2 = 0 + 2
Step 2 x2 + 10x + 26 = 2
Step 3 (x + 5)2 = 2

Step 1 x2 + 10x + 24 + 1 = 0 + 1
Step 2 x2 + 10x + 25 = 1
Step 3 (x + 5)2 = 1

Answer:

-4

Step-by-step explanation:

4/6 - 3/6p=16/6

Multiply each side by 6

4 - 3p = 16

Subtract 4 from both sides

-3p = 12

Divide both sides by -3

p = -4

Answer:

-4

Step-by-step explanation:

   [tex]\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}[/tex]

To find the value of 'p', isolate 'p',

         [tex]\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\[/tex]

                 [tex]\sf = \dfrac{12}{6}[/tex]

                  = 2

             [tex]\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4[/tex]

Answer:

685200 is ten and hundred 685000 thousand 690000 ten thousand 700000 hundred thousand

n(A) is 6 when A = {14, 16, 18, 20, 22, 24}

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things. Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given Data

A = {14, 16, 18, 20, 22, 24}

We are aware that the cardinality, which is represented by the letter n, is the number of items in any set A.

n(A) = number of elements in set

n(A) = 6

n(A) is 6

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Answer:

Lmafo

Step-by-step explanation:

The function that has the greater slope is the function g(x) that is represented by the graph.

The slope (m) of a function using two points on a graph can be calculated as:

Slope of the line (m) = change in y/change in x

If we are given the equation of the line using function notation as .f(x) = mx + b, the slope of the function is represented in the equation as "m". The value of "m" is the slope of the function given.

Given the function, .f(x) = 3x + 1, the value that represents "m" which is 3. Therefore, the slope of the function .f(x) = 3x + 1 is: 3.

Find the slope of the function of the graph using two points on the line, say (2, 3) and (3, 7):

Slope of the function (m) = change in y / change in x = (7 - 3)/(3 - 2)

Slope of the function (m) = 4/1

Slope of the function (m) = 4

The larger the value of the slope, the greater the slope of the function.

Therefore, the function g(x) that is represented by the graph has a greater slope.

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Answer: B

Step-by-step explanation:

Simple

The correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” is "StartFraction n cubed Over 16 EndFraction minus 2 + 8"

The correct answer option is option a

The value of the expression when n = 4 is 10. option D

quotient of a number cubed and sixteen

= n³ / 16

two less than the quotient of a number cubed and sixteen

= (n³ / 16 - 2)

two less than the quotient of a number cubed and sixteen, increased by eight”

= (n³ / 16 - 2) + 8

If n = 4

(n³ / 16 - 2) + 8

= (4³ / 16 - 2) + 8

= (64/16 - 2) + 8

= (4 - 2) + 8

= 2 + 8

= 10

In conclusion, the expression can be written as "StartFraction n cubed Over 16 EndFraction minus 2 + 8"

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Answer: 10) √85 units    12) 4 units

Step-by-step explanation:

          [tex]\boxed {l=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}[/tex]

10) (8,5)   (-1,3)

[tex]x_1=8\ \ \ \ x_2=-1\ \ \ \ y_1=5\ \ \ \ \ y_2=3\\\\l=\sqrt{(-1-8)^2+(3-5)^2} \\\\l=\sqrt{(-9)^2+(-2)^2} \\\\l=\sqrt{81+4}\\\\l=\sqrt{85}\ units[/tex]

12) (-6,-10)   (-2,-10)

[tex]x_1=-6\ \ \ \ \ x_2=-2\ \ \ \ \ y_1=-10\ \ \ \ y_2=-10\\\\l=\sqrt{(-2-(-6)^2+(-10-(-10))^2} \\\\l=\sqrt{(-2+6)^2+(-10+10)^2}\\\\l=\sqrt{4^2+0^2} \\\\l=\sqrt{4^2} \\\\l=4\ units[/tex]

Answer:

i got

Step-by-step explanation:

seventy-nine

Answer:

[tex]\frac{5}{1+5}[/tex]

Step-by-step explanation:

Hope this helps :))

ANSWER

EXPLANATION

We want to find the volume of the sphere.

The volume of a sphere is given as:

where r = radius of the sphere.

Therefore, we have that the volume of the sphere is:

That is the volume of the sphere.

The volume of the tank is 15315.35

Volume is a measurement of three-dimensional space that is occupied. [1] Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.

Given that,

Top Outlet Tank

Height (h): 2550 mm

Diameter (d): 2100mm

radius (r) : 2.1/2

Mass: 650kg

The volume, in cubic metres, of the tank is

volume of tank = 2π + π[tex]r^{2} h[/tex]

= 2π(1100) + π(2.1/2)(2550)

= 2(3.14)1100+ (3.14)(2.1/2)(2550)

= 6908+ 8407.35

= 15315.35

Therefore, the volume of the tank is 15315.35

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Answer:

420 mark Brainliest

Step-by-step explanation:

distance is going up by 60 and the points are moving 2 for time so at 12 it will be 360 then 14 will be 420 so the answer is 420

The area of the triangle formed by his path is mathematically given as

Area = 29284.886 ft^2

This is further explained below.

Generally, the equation for the defining cosine rule  is mathematically given as

[tex]b^2 = a^2 + c^2 - 2ac cos B[/tex]

where

b = side B of the triangle

a = side A of the triangle

c = side C of the triangle

Therefore

[tex]b^2 = 180^2 + 329^2 - 2(180 * 329)cos 81.5[/tex]

b^2  = 32400 + 108241 - 17506.55

b = 350.91 ft

We calculate the area of the triangle using heron's formula.

Area = [tex]\sqrt{(p(p - a)(p - b)(p - c))}[/tex]

b = side B of the triangle

a = side A of the triangle

c = side C of the triangle

p = path

Where

p = (a + b + c)/2

p= (180 + 350.91 + 329)/2

p= 429.955 ft

Area = [tex]\sqrt{(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)}[/tex]

Area = 29284.886 ft^2

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Answer:

x=4.4

Step-by-step explanation:

To get from 4 to 10 what happens?

Well, we multiply 4 by 2.5.

That should be the same for x.

Thus, 2.5x=11

x=4.4

The value of the greatest integers will be 5.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' An integer is subtracted from 5 times the next consecutive odd integer, the difference is 22''.

Now,

Write the mathematical expression for an algebraic expression as;

Let an integer = 2x + 1

Then, The next consecutive odd integer = 2x + 3

So, We can formulate;

5 (2x + 3) - (2x + 1) = 22

Solve for x as;

5 (2x + 3) - (2x + 1) = 22

10x + 15 - 2x - 1 = 22

8x + 14 = 22

Subtract 14 both sides, we get;

8x + 14 - 14 = 22 - 14

8x = 8

Divide by 8,

x = 8/8

x = 1

Since, The greatest integers = 2x + 3

Substitute x = 1, we get;

The greatest integers = 2x + 3

The greatest integers = 2 × 1 + 3

The greatest integers = 2 + 3

The greatest integers = 5

Therefore, The value of the greatest integers will be 5.

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On solving the given statement, the length of AC equals 37.

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

According to the given statement,

AC = 2x + 21

AB = x + 9

BC = 3x - 4

As B is the mid point of the segment AC,

⇒ AB + BC = AC

⇒ x + 9 + 3x - 4 = 2x + 21

⇒ 4x + 5 = 2x + 21

⇒ 2x = 16

⇒ x = 8

Length of AC = 2 (8) + 21

= 16 + 21

= 37

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The equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.

A straight line is made up of an infinite number of points connected at their ends.

Any straight line's slope, "m," is determined by:

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

The slope of the line y = -6x + 8

m = -6

The slope of the line passing point P (-1,-4)

M = -6

y - (-4) = -6(x - (-1))

y + 4 = -6(x + 1)

y = -6x - 10

Thus, the equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.

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Answer:

thw answer is 67.910

Step-by-step explanation:

the second one

Answer:

#2

Step-by-step explanation:

the four answers start with 67. So if you focus on the digits that come after the decimal, which ever digits are higher than the original decimal will be your answer

Answer:

$367

Step-by-step explanation:

738-550+189-10=367

If Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, then he will have $0 remaining, as plotted on the number line in the reference attachment hereby.

As per the question statement, Steven had $5 that his mom gave him to buy lunch at school and he spent all of the $5 on his lunch.

We are required to plot a point on the number line to depict how many dollars Steven has left with himself after spending on his lunch.

To solve this question, we simply need to subtract the amount Steven spent for his lunch, from the amount, his mother gave him to spend on lunch, and then plot the result of the said subtraction on the number line to obtain our desired answer.

Since, Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, he has $(5 - 5) = $0 left with himself after spending on his lunch.

That is, we will have to plot 0 on the number line, which is shown in the reference attachment hereby.

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It is true but incomplete, a percent is found by dividing the percentage by the base and multiplying it with 100.

What is percentage?

Percentage is a relative value that represents hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Divide the percentage by the quantity to get the percent of a number, then multiply the result by 100. Put the word "percent" (%) after the finished item.

Example of calculation of percentage:

What percent of 10 is 7?

here, 7 is percentage and 10 is quantity, On dividing we get,

7/10 = 0.7

Now multiplying by 100, we get

70 %

This is the answer

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Answer:

c/2-3+6/d

=

14/2-3+6/3

= (Order of Operations)

7-3+2

=

6

Step-by-step explanation:

See explanation above

In scientific notation, it should be written as 1 × 10⁶

In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 ×10⁸ in scientific notation.

Given Data

Sergio Is asked to write one million in scientific notation. He writes 106 and gets it wrong.

He should have written as 1 × 10⁶

A power of 10 and a number in the range of 1 to 10 are required for standard form.

In scientific notation, it should be written as 1 × 10⁶

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Answer:

g(-9)+h(-9)=59

the answer is B

The constraints of a linear programming issue must all be concurrently satisfied for a solution to be viable. We are aware that the ideal solution must maximize the value of the goal function and be located at one of the corners of the feasible region.

All of the constraints on the problem are met by a feasible solution. A feasible answer that, when maximized, yields the highest possible value for the objective function is known as an optimum solution (or smallest when minimizing). A linear program with two variables can be solved using a visual solution method.

A fundamental feasible solution (BFS), according to the theory of linear programming, is a solution with a small number of non-zero variables. Each viable solution polyhedron's corner correlates geometrically to a BFS. There must be an optimal BFS if there is an optimal solution. Therefore, taking into account the BFS-s is adequate to arrive at an ideal solution. The simplex algorithm, which effectively moves from one BFS to another until one is found that is optimal, makes use of this property.

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Answer:

  (a) -48

Step-by-step explanation:

You want the solution to the equation 1/6(x +18) = -5.

The first step to solving this can be to multiply both sides by 6, eliminating the fraction:

  x +18 = -30

The second step can be to isolate the variable by subtracting 18 from both sides.

  x = -48

The solution is x = -48.

__

Additional comment

Sometimes you may want to simplify the equation before you start the solution process. Here, you can also start by eliminating parentheses:

  1/6x +3 = -5

Now, subtracting 3 gives ...

  1/6x = -8

Finally, multiplying by 6, we have ...

  x = -48

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Answer:

Step-by-step explanation:

interval notation is (-∞,∞)

set-builder notation is {x|x ∈ R}

Answer:

Step-by-step explanation:

Given,

The marked price of a jacket at dealer shop is Rs. 2400

The dealer allows a discount of 15% to the retailer.

The marked price of the retailer should be same as the dealer's marked price.

To find,

1. SP the retailer should fix for the jacket

2. Its final price if 10% VAT is imposed

3. The actual gain of the retailer if 10% discount is allowed

Solution,

The SP rate for the jacket without VAT 2400

Let 10% VAT on jacket price 2400 be x

x= 2400÷10

x= 240

So, the final price including 10% VAT = 2640 (2400+240)

As the dealer allowed discount of 15% to the retailer, the retailer gain profit is 15% on the jacket price i.e., 2400

Let y be the gain of the retailer

y= 15/100 × 2400

y= 360

Therefore,

SP the retailer should fix for the jacket is 2400

final price if 10% VAT is imposed is 2640

the actual gain of the retailer is 360