Answer:
Step-by-step explanation:
The discriminant must be zero.
Discriminant = (-48)^2 - 4*9k = 2304 - 36K
36k = 2304
k = 64
Using the square of a subtraction, it is found that k = 64.
What is a square of a subtraction?It is a notable product, given by:
[tex](ax - b)^2 = a^2x^2 - 2abx + b^2[/tex]
In this problem, the expression is:
[tex]9x^2 - 48x + k[/tex]
We want it to be the square of a binomial, hence:
[tex]a^2x^2 - 2abx + b^2 = 9x^2 - 48x + k[/tex]
Then, comparing both sides, first the value of a is found:
[tex]a^2 = 9[/tex]
[tex]a = \sqrt{9}[/tex]
[tex]a = 3[/tex]
Then, with the second term, the value of b is found.
[tex]2ab = 48[/tex]
[tex]6b = 48[/tex]
[tex]b = \frac{48}{6}[/tex]
[tex]b = 8[/tex]
Finally, the value of k is found.
[tex]k = b^2 = 8^2 = 64[/tex]
You can learn more about the square of a subtraction at https://brainly.com/question/9239489
write a real world problem for the following inequality X < 17 brainly
Answer:
i want to drive alone but i am 15 and need to be 17
Step-by-step explanation:
5. The value of an investement increased by 10%. The original amount of the
investment was $40.00. What is the current value of the investment?
Show your work
Please help me on this I need help
Answer:I Dont know about this one soryy
Step-by-step explanation:
) Express each of these statements using mathematical and logical operators, predicates, and quantifiers, where the domain consists of all integers. a) The sum of two negative integers is negative. b) The difference of two positive integers is not necessarily positive. c) The sum of the squares of two integers is greater than or equal to the square of their sum. d) The absolute value of the product of two integers is the product of their absolute values.
Answer:
a. ∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0
b. ∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0
c. ∀ a, b ∈ Z, a² + b² ≥ (a + b)
d. ∀ a, b ∈ Z, |ab| = |a||b|
Step-by-step explanation:
a. The sum of two negative integers is negative.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if a and b are negative, we write if a < 0 ∧ b < 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, if a < 0 ∧ b < 0. Then finally, we use the logical operator ⇒ to imply the summation of the two integers as ⇒ a + b. And since we are to show that their sum is less than zero, we write ⇒ a + b < 0.
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0
b. The difference of two positive integers is not necessarily positive.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if there exists a and b that are positive, we write if a > 0 ∧ b > 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, a > 0 ∧ b > 0. Then finally, we use the logical operator ⇒ to imply the difference of the two integers as ⇒ a - b. And since we are to show that their difference is either less than zero or greater than zero, we write ⇒ a - b < 0 ∨ a - b > 0 where ∨ implies the logical operator "or".
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0
c. The sum of the squares of two integers is greater than or equal to the square of their sum.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are dealing with the sum of the squares of each integer, we write a² + b². And, we are to show that this sum is greater than the sum of the individual integers, we write their sum as a + b, and we show the previous sum to be greater than or equal to this as a² + b² ≥ (a + b).
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, a² + b² ≥ (a + b)
d. The absolute value of the product of two integers is the product of their absolute values.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are to show that absolute value of the product of the integers equals the product of the absolute value of the individual integers, we write the that absolute value of the product of the integers as |ab| and the product of the absolute value of the individual integers as |a||b|.
Since we are to show that this expression and the previous expression are equal, we write |ab| = |a||b|.
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, |ab| = |a||b|
HELP PLEASE I NEED ANSWERS NOT JUST EXPLANATION
Answer:
x f(x) + 1
-4 6
-2 8
2 2
4 -1
Step-by-step explanation:
5 + 1 = 6
7 + 1 = 8
1 + 1 = 2
-2 + 1 = -1
Can someone please answer this question
Giving brainleist!
Answer:
a) 9000
b) 40
c) 630
d) 125
plz help right now plz
Please help I don't get this
Answer:
18n+9
Step-by-step explanation:
9(2n+1)
multiply the 9 with the numbers in the parenthesis18n+9
I need to multiply 10,170 by 0.775
Answer:
7881.75
Step-by-step explanation:
10,170x0.775
Answer:
7881.75
Step-by-step explanation:
pls help with both the equations
Answer:
what is the question send it in the comment fast
What is MA and ABC ifMB = 35° and MC equals 92°
Simplify the expression by combining like terms:
-3m-8(m+1)
Answer: -11m-8
Step-by-step explanation: first you would distribute (m+1) into -8 causing it to be -3m-8m-8 you then combine like terms getting you -11m-8
Answer:
16m
Step-by-step explanation:
-3m -8 (m+1) any variable has 1.
-8 (-2m)
16m
Which figures are polygons?
Select each correct answer.
Figure A
Figure B
Figure C
Figure D
Find the equation of the line parallel to y=6 that contains the point (-1,1). Write the equation in slope intercept form
Given:
The equation of parallel line is [tex]y=6[/tex].
The line contains the point (-1,1).
To find:
The equation of the line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
The equation of parallel line is
[tex]y=6[/tex]
It can be written as
[tex]y=(0)x+6[/tex]
The slope of this line is 0.
The slopes of two parallel lines are always equal. So, the slope of the required line is also 0. It passes through the point (-1,1) so the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-1=0(x-(-1))[/tex]
[tex]y-1=0[/tex]
[tex]y=1[/tex]
Therefore, the equation of the required line is 1.
What is the area of the shaded sector of the circle?
O 201 units?
O 40tt units?
O 180 units?
O 400 units?
Answer: 180 pie units^2
Step-by-step explanation:
Got it right on edg
The area of the shaded sector subtending 162° at the center is 180π units².
The option (3) is the correct answer.
What is the sector of a circle?A sector is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is the major sector.
In the diagram, we are given a circle with a shaded sector:
The radius of the circle (r) = 20 units
The angle subtended by the shaded sector = 162°
To find the area of the shaded sector, we can use the formula:
= [tex]\frac12 \theta r^2[/tex]
Where θ is the angle subtended in radians and r is the radius.
162° = 162° × (π/180°) rad
= 0.9 π rad
area of the shaded sector = (1/2) × 0.9 π × 20² = 180π units²
Hence, the area of the shaded sector subtending 162° at the center is 180π units².
To learn more about sector of a circle, click:
https://brainly.com/question/25305793
#SPJ7
How can you use standard deviations to compare the spread of each data set?
Sample A: 2,5,1,2,3,3,4,3
Sample b: 10,5,1,2,3,7,4,3
Calculate the standard deviation for each data set:
Sample A = 1.246
Sample B = 2.924
The smaller the deviation the closer the data set is, the larger the deviation the more widespread the data set is.
Sample B has a larger deviation so the spread of the data is wider.
Find the value of y if the mean is 22 and 18 ( 2y+1), 10 and 20 is 15
Answer:
2
Step-by-step explanation:
Mean = sum of data/sample size
Sum of data = 22 + 18 + 2y+1 + 10 + 20
Sample size = 5
Mean = 15
Substitute
15 = 22 + 18 + 2y+1 + 10 + 20/5
15*5 = 22 + 18 + 2y+1 + 10 + 20
75 = 70+2y+1
2y = 75-71
2y = 4
y = 4/2
y = 2
Hence the value of y is 2
Which statements are true??
They boost the economy
Answer:
I think the question is incorrect
Step-by-step explanation:
they boost the economy why is this in mathematics
♀️♀️
what fraction is 15 minutes of 1 hour
Answer:
1/4
Step-by-step explanation:
Convert 1 hour to minutes
1 hour = 60 minutes
Then you can find the fraction
15/60
simplifies to 1/4
15 minutes is 1/4 of 60 minutes/1 hour
Answer part C. I want step by step on this problem.
Answer:
[tex]Rate = 58007956.5217[/tex]
Step-by-step explanation:
Solving (c): The rate of change:
In this concept, the formula to use is:
[tex]Rate = \frac{V2 - V1}{t2 - t1}[/tex]
Where
[tex](t1,v1) = (0,62817000)[/tex] ----- In 2004
[tex](t2,v2) = (23,1397000000)[/tex] ------ In 2026
So, we have:
[tex]Rate = \frac{1397000000 - 62817000}{23 - 0}[/tex]
[tex]Rate = \frac{1334183000}{23}[/tex]
[tex]Rate = 58007956.5217[/tex]
PLEASEEEE HELP THIS IS DUE TODAY!!!
Answer: $200
Step-by-step explanation:
On the X axis, it shows the kilograms. Since the problem asks for how much money she makes for 60 kg, go to the point on the X axis that represents 60 kg and then go up to the corresponding y or dollar value, which is 200.
sofia and two of her friends are going to share one-fourth of a pizza. How much will each person get? I need some help
Answer:
83/100
Step-by-step explanation:
Convert 20 miles to km
Answer:
32.1869
Step-by-step explanation:
You can use an online converter!
You can look up Miles to KM
Tims piggy bank contains nickels and quarters worth $6.70. He has 62 coins in all. How many of each coin does Tim have?
Answer:
well you see it really
Step-by-step explanation:
Using two or more complete sentences, describe and correct the error in the solution.
Solve the system of equations.
3x - 2y = 2
9x - 6y = 6
3x - 2y = 2 → 9x - 2y = 6
9x - 6y = 6 → 9x - 6y = 6
-8y = 12
y = 1.5
3x - 2y = 2 → 3x - 2(1.5) = 6
3x - 3 = 6
3x = 9
x = 3
Answer:
In the very first step, when they multiply both sides by 3 the -2y should become -6y but instead it stays as -2y. The correct solution would be:
9x - 6y =6
9x - 6y = 6
0 = 0
This means there are infinite solutions.
What is the value of x?
Answer:x=31
not sure
Step-by-step explanation:
A $7.00 item is marked down by 10%.
What is the new cost of the item?
Round to two decimals if needed.
$
Answer:
6.3
Step-by-step explanation:
Write an equation to represent the total cost y for x days of renting a mid-size car from each of these companies. *
Answer:
Step-by-step explanation:
Hindi ko alm hehe
How many solutions ?
Answer:
one solution
the solution is x=0
Answer:
1
Step-by-step explanation:
You can figure this out using a simple trick. The highest number to the power that a variable goes to is the number of answers for that question. Meaning if There was an x cubed in that problem, there would be 3 answers.
Could someone help me with this
Answer:
try to do this formula
XYZ
= X times Y times Z