Which of the following tables shows the correct steps to transform x^2 + 10x + 24 = 0 into the form (x - p)^2 = q? [p and q are integers]
Answers
Answer: D
Step-by-step explanation:
The correct transformation of the equation is achieved by completing the square to obtain the form (x + 5)^2 = 1, which gives the values of p = -5 and q = 1.
The transformation of the quadratic equation x^2 + 10x + 24 = 0 into the form (x - p)^2 = q involves completing the square. To complete the square, one must find a number that, when added to x^2 + 10x, completes a perfect square trinomial. This number is calculated by taking half of the x-coefficient (b/2), squaring it, and adding it to both sides of the equation. In this case, (10/2)^2 = 25. We then have x^2 + 10x + 25 on the left and 25 - 24 on the right, which simplifies to (x + 5)^2 = 1. The values of p and q are thus -5 and 1, respectively.
Related Questions
SO CONFUSED PLEASE HELP
Which situations can be represented by an exponential function? Select each correct answer.
On the highway, Kareem's car gets 38 mpg.
Shu Fang has $25.75 deducted from her checking account every month.
A toad population is increasing by about 7.5% each year.
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
Answers
Answer: A toad population is increasing by about 7.5% each year.
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
Step-by-step explanation:
On the highway, Kareem's car gets 38 mpg.
This can be modeled with a linear relationship between the miles and the gallons of fuel needed.
Shu Fang has $25.75 deducted from her checking account every month.
Here we know that each month a constant amount is deducted from her, this is not an exponential relation.
A toad population is increasing by about 7.5% each year.
If the population initially was an amount P, after one year the population is P*1.075, after two years the population is P*(1.075)^2 and so on, this can be modeled with an exponential function where the years variable, the function will have the general form:
Population(y) = P*(1.075)^y
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
If the first year the population is X, the year after the attendance will be (4/5)X, and the year after this process applies again, so you have a 4/5 of the previous attendance, the attendance now is (4/5)^2*X
This also can be modeled with an exponential function, of the shape:
Attendance (y) = X*(4/5)^y, where again, y means years.
The thing you may notice is that in this case the model only works for the lapse of 5 years that the event organizer said.
Find the vertex of a function f(x)=-3x^2+9x-15 by completing the square
Answers
Which of the following represents the graph of f(x) = 2x + 2? i will give a medal if you help cooperatively
Answers
f(x) = 2^x + 2
To find which graph represents this function we should find at least 2 points. We take some value of x we want and calculate y for it. And do that at least 2 times (can be done 1 time but its likely that some graph match in some points)
for x = 0 we get
f(x) = 3
for x = 1
f(x) = 4
we can also note that f(x) cannot be less than 2 because 2^x is always greater than 0, and that as x increments f(x) increments. With all of this in mind answer is last graph.
Answer is graph D
What is the surface area of a piece of pipe that is open at both ends, has a radius of 6 inches, and a height of 18 inches? (Use 3.14 for π.)
Answers
2π(6)(18)
you can imagine it like this:
imagine you take a sheet of paper and roll it into a tube
the lateral aera=circumference times height because if yo open the paper, the area is legnth times width, and when you roll it up, width turns into circumference
so
LA=h(circumference0
LA=h2pir
LA=18*2*pi*6
LA=216pi
pi=3.14 for this question
LA=678.24
SA=678.24 in²
Evaluate 7 + (-3x2) for x = 0.
-2
0
4
7
Answers
7+(-3.0^2)
7+0
7
Answer:7+(-3.0^2)
7+0
7
Step-by-step explanation:
How to put 0.258 0.4 0.52 1.25 0,04 from least to greatest?
Answers
125 + .375=?
0.654 + 0.389 - 0.293=?
Answers
and for the second it's 0.75
0.654+0.389-0.293 equals0.75
the total amount of degrees in the center is 360 degrees if all five vertex angles meeting the center are congrent what is the measure of a base angle of one of the triangles
A) 54 degrees
B) 72 degrees
C) 108 degrees
D) 144 degrees
Answers
Answer:
(B) 72°
Step-by-step explanation:
A prime number is always greater than 1 false or truth and why
Answers
hope this helps you
A prime number must be greater than 1 because by definition, a prime number has exactly two distinct positive divisors: 1 and the number itself. If a number is less than or equal to 1, it cannot be prime.
The statement that a prime number is always greater than 1 is indeed true. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. If a number is less than or equal to 1, it cannot be prime because the prime numbers must be greater than 1 to have at least two distinct positive divisors (1 and the number itself).
For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. Each of these numbers is greater than 1 and cannot be divided evenly by any number other than 1 and itself. By contrast, the number 1 is not considered a prime because it has only one positive divisor, which is 1 itself. Since primes must have exactly two distinct divisors, 1 does not meet this criterion.
HELP ASAP!!!
The markup on appliances at Tom’s store is 50%. If the wholesale price of a dishwasher is $380, what price will Tom list when selling the dishwasher?
A. $570
B. $665
C. $760
D. $950
Answers
1/2 x = 20 solve for x
Answers
2/2x=40
1x=40
x=40
the way i got that was i times .5 to 20 and got my answer because .5 is 1/2
Hopes this helps if you have more question just hmu and ask :)
Given the function f(x) = x3 + 2x2 − 3x − 5, what is resulting function when f(x) is shifted to the right 1 unit?
Answers
f(x - 1) = (x - 1)^3 + 2(x - 1)^2 - 3(x - 1) - 5
= (x^3 - 3x^2 + 3x - 1) + 2(x^2 - 2x + 1) - 3(x - 1) - 5
= x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5
= x^3 - x^2 - 4x - 1
I hope this helps
60 minutes is 20% of ? minute s
Answers
What is 830% written as a decimal?
8300
83
0.0083
8.3
8.3 i think
Answers
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, AB and CD , which of these conditions needs to be met to prove that AB is perpendicular to CD?
see attachment for choices
Answers
it is c)
[y4-y3/x4-x3][y2-y1/x2-x1]= -1
proof
two lines are perpendicular if the product of their slope equals -1
Answer:
[tex]\frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Step-by-step explanation:
We know that,
If two line segments are perpendicular then the product of their slope is equal to -1,
Also, the slope of a line segment having the end points [tex](x_n,y_n)[/tex] and [tex](x_m,y_m)[/tex] is,
[tex]m=\frac{y_m-y_n}{x_m-x_n}[/tex]
So, the slope of line segment AB having end points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is,
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
Similarly, the slope of line segment CD having end points [tex]C(x_3,y_3)[/tex] and [tex](x_4,y_4)[/tex] is,
[tex]m_2=\frac{y_4-y_3}{x_4-x_3}[/tex]
Hence, by the above property of perpendicular line segments ,
If AB and CD are perpendicular then,
[tex]m_1\times m_2=-1[/tex]
[tex]\implies \frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Third option is correct.
The only part of the United States explored by Russia was the:
A : Hudson River
B : Southwest and Mexico
C : Mississippi River
D : Northwest coastline
Answers
Answer:
d
Step-by-step explanation:
d
The maximum speed of the Tupolev Tu -144 airliner is 694 m/s. What is this speed in kilometers per hour?
Answers
The speed is [tex]694m/s = \frac{694m}{1s} [/tex]
1 m = 0.001 km ⇒ 694 m = 694 * 0.001 km = 0.694 km
1 h = 60 min = 60 * 60 s = 3600 s
Therefore:
[tex] \frac{694m}{1s}= \frac{3600*0.694km}{3600s} = \frac{2498.4km}{1h} =2498.4km/h[/tex]
Answer: the correct answer would be 2498.4 km/h
*i got this question correct*
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3770. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x ...?
Answers
The hourly profit of an airline operating a plane can be calculated by subtracting the operating cost from the revenue earned from passengers.
Explanation:The hourly profit of an airline operating a plane can be expressed as the difference between the revenue earned from passengers and the operating cost of the plane.
The revenue earned from passengers can be calculated by multiplying the fare per passenger by the number of passengers. In this case, the fare is $100 per hour of flight, and the number of passengers is represented by x.
The operating cost of the plane is given as $3770 per hour.
Therefore, the hourly profit P can be expressed as:
P = (fare per passenger) * x - (operating cost of the plane)
Substituting the given values:
P = $100 * x - $3770
How many times can 57 go into 413?
Answers
The sum of the perimeters or two different squares is 32 centimeters , and the difference between there perimeters is 8 centimeters. if x represents the side length of the larger square and y represents the side length of the smaller square , Which of the following systems of equations could be used to find the dimensions of the squares?
A. x+y=32
x-y=8
B. 4x+4y=32
4x-4y=8
C. 2x+2y=32
2y-2x=8
D. 2x+2y=32
4x-2y=8
Answers
The correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
Explanation:To find the dimensions of the squares, we can set up a system of equations. Let x represent the side length of the larger square and y represent the side length of the smaller square.
The sum of the perimeters is given as x + y = 32. The difference between the perimeters is given as x - y = 8.
So, the correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
The correct system of equations to find the dimensions of the squares is x + y = 32 and x - y = 8. Solving this system using the method of elimination gives us the dimensions of the squares: 20 cm for the larger square and 12 cm for the smaller square.
Explanation:The correct system of equations to find the dimensions of the squares is:
x + y = 32
x - y = 8
To solve this system, we can use the method of elimination. Adding the two equations will eliminate the y terms, allowing us to solve for x.
Adding the equations:
x + y + x - y = 32 + 8
2x = 40
x = 20
Substituting the value of x back into one of the original equations, we can solve for y.
Using the equation x + y = 32:
20 + y = 32
y = 12
Therefore, the dimensions of the larger square are 20 cm, and the dimensions of the smaller square are 12 cm.
Simplify.
1/4+4(1/2−3/4)^2
Answers
Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.
2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
Answers
1) 2x + y + z = –7
2) x – 3y + 4z = –14
3) x – 2y – 3z = –11
elimination of x
2) - 3) -y + 7z = - 3
1) - 2.3) 5y +7z = 15
now we solve the simple system
-y + 7z = - 3 a)
5y +7z = 15 b)
elimination of y
5. a) + b) implies 42 z=12 and z= 2/7
-y +7 . 2/7= -3 implies y = 5
y=5, z =2/7, so 2x + 5 + 2/7 = –7 implies x= - 43/7
final solution
x= - 43/7, y=5 and z =2/7
proof
2.(- 43/7) + 5 + 2/7 = -7, (true)
Write two (2) scenarios that describe two different real-world functions. Think of your own variables that are not included in the above list. As you did for the other functions, identify the independent and dependent variables and assign the letters x and y to represent each variable quantity. Then create a set of at least five ordered pairs in (x, y) form with values that make sense for your function.
Answers
2. Lexy has 456$ she gave it to four friends. Let M represent how much she gave each friend if she was left with 50$ What does X equal?
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralf, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
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a(x+b)=c solve for x
Answers
x+b = c / A
x = c/A - b
Hope this helps!
What is the area of a regular octagon with 12 as each side. Round to nearest hundredth.
Answers
The sum of two numbers is 10. if one number is subtracted from the other the result is -2. find two numbers
Answers
Form an equation to describe the situation
x+y=10
Then use the other information they gave you and form another equation
x-y=2
You can add the two equations together, and you see that the y variables cancel out(elimination)
2x=12
Solve for one variable and then plug it back into the original equation
x=6
6+y=10
y=4
Tomorrow, 567 people will want tickets to concert. only 417 tickets are available. how many people will be able to get tickets?
Answers
Intersecting chords form a pair of congruent, vertical angles.
A. True
B. False
Answers
Answer:
True!
Step-by-step explanation:
280 divided by 30 what is it
Answers
The division yields to quotient is 9, and there is 10 as remainder
We have to divide 280 by 30.
So, the division performed as
30 | 280 | 9
270
-______
10
So, the quotient is 9, and there is 10 as remainder.
So, 280 divided by 30 is equal to 9.33 (rounded to two decimal places) or simply 9.
Learn more about Division here:
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