The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies k^2+2k-3>0
Step-by-step explanation:
For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,
b^2 - 4ac must be positive.
b^2 - 4ac > 0
(k - 3)^2 - 4(3 - 2k) > 0
k^2 - 6k + 9 - 12 + 8k > 0
k^2 + 2k - 3 > 0
To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
How to prove the expressionTo have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;
Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.
In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0
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How many 10-bit strings have weight 1?
How many 10-bit strings have weight 5?
How many 10-bit strings have weight 9?
Answer:
ok so it will be 16-bit
Step-by-step explanation:
Complete the table of values for y=x2-x-5.
Answer:
when -2 , y = 1
when 0, y = -5
when 2, y = -3
when 3, y = 1
when 4, y = 7
Trong 300 người bệnh chỉ dùng thuốc A có 55% người khỏi; trong 240 người bệnh chỉ dùng thuốc B có 50% người khỏi. Với mức ý nghĩa 5% có thể nói thuốc A hiệu quả hơn thuốc B không?
vâng vì phụ nữ là những người tán gẫu
Helppppppppppppp please
Answer:
1.45 x 10^2
Step-by-step explanation:
In scientific notation, you get the number down to 1 digit before the decimal place and all the rest after it, then multiply by 10 raised to a power in order to get it back to the original. An easy way to do it is to count the number of times you moved the decimal and remember which direction you did it. The number is the power (in this case 2) and the direction tells you if it's positive or negative (in this case it was to the left, so it's positive two.)
In simpler terms, slide the decimal to the right two places and make it 1.45, then multiply it by 10^2 (which is 100) to make it equal to 145. This leaves you with 1.45 x 10^2.
Someone help me plzz-
Answer:
ㅛ해 주는 것이 좋다 나쁘다 라고 말하는 것은 아니다 싶으면 이 때 가장 중요한 역할을 하는 것 같다 ㅛ요톸 매매 ㅑ져뎌 재료 본연의 맛과 향을 느낄 수도 있다 보니
Show all work to multiply quantity 6 plus the square root of negative 64 end quantity times quantity 3 minus the square root of negative 16 end quantity
Answer: 50
Step-by-step explanation:
[6+√-64] × 3-√-16
(6+8i)(3-4i)
6(3-4i)+8i(3-4i)
18-24i+24i+32
18+32=50
the answer is 50Answer:
fifty
Step-by-step explanation:
fifty
what is the value of 17-2(5-3)
Answer:
13
Step-by-step explanation:
17-10+6
7+6=13
hope it helps
The question is in the screenshot!!
-3-(-5)What is the answer to this equation
Answer:
2Step-by-step explanation:
[tex] - 3 - ( - 5) \\ - 3 + 5 \\ 2 \\ [/tex]
without using a calculator or mathematical table sove 187²-87²
In the month of September, all of the Kroger grocery stores in Nashville sold 429,382 eggs. In that same month, all of the Kroger grocery stores in Memphis sold 283,054 eggs. How many eggs did the Nashville and Memphis Kroger grocery stores sell all together in the month of September? Use 2 strategies to show how you found out how many eggs Kroger sold in September.
Answer:
712436 eggs were sold together
Step-by-step explanation:
429,382 + 283,054 = 712436
what is 4/5 divided by 2/3 simplest
Answer:
1 1/5
Step-by-step explanation:
4/5 ÷ 2/3
4/5 × 3/2
12/10
6/5
1 1/5
What do you add to 3 7/8 to make 5
Step-by-step explanation:
we will add 3+37=40
40/8=5
mark me brainlist plz
Answer:
You have to add a certain amount of a number to 3 7/8 to make five. Or the easy way, 5 - 3 7/8 = 1 1/8
Step-by-step explanation:
If you want can you make me brainlyist?
Also, I hope this helped!
******Please help me please help me help please help*****
9514 1404 393
Answer:
(c) y = 36·5
Step-by-step explanation:
If x represents the number of chocolates, the given formula ...
y = kx
with the values k = 36 and x = 5 inputted will look like ...
y = 36·5
find reason and statements
Answer:
Missing reason/statements:
R1, R2, R3 - GivenS4. ∠1 ≅ ∠3R4. Transitive propertyR5. Definition of congruenceS6. m∠1 = 120°R6. SubstitutionWhich equation matches the graph?
Answer:
Option C): f(x) = 3x - 4.
Step-by-step Explanation:
What is a Linear Function in Slope-intercept Form?A linear function in slope-intercept form is given by f(x) = mx + b where:
"m" represents the slope, which is the measure of steepness and orientation of a nonvertical line. "b" represents the y-coordinate of the y-intercept, (0, b). The y-intercept is the point on the graph where the line intersects the y-axis. It is also the point where the x-coordinate equals to zero.How to solve for the slope?We can solve for the slope by using the following formula:
[tex]\displaystyle\mathsf{Slope\:(m)\:=\:\frac{Rise}{Run}\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)}[/tex]
Choose two points from the graph and substitute their values into the slope formula.
(x₁, y₁) = (2, 2)(x₂, y₂) = (0,-4)[tex]\displaystyle\mathsf{Slope\:(m)\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)\:=\:\Bigg(\frac{2-(-4)}{2-0}\Bigg)\:=\:\Bigg(\frac{2+4}{2}\Bigg)\:=\:\frac{6}{2}\:\:=\:3}[/tex]
Therefore, the slope of the line is 3.
How to find the y-intercept (b)?As defined in the previous section of this post, the y-intercept (0, b) is the point on the graph where it crosses the y-axis. We can see that the line intersects the y-axis at point (0, -4). This means that the value of our y-intercept, b, is -4.
Finding the y-intercept algebraically.Alternatively, we can solve for the y-intercept (b) by choosing a point on the graph and substitute its values into the slope-intercept form.
We will use and substitute the values of (x₁, y₁) and the slope into the function to solve for b.
(x₁, y₁) = (2, 2)Slope (m ) = 3f(x) = mx + b
⇒ 2 = 3(2) + b
⇒ 2 = 6 + b
⇒ 2 - 6 = 6 - 6 + b
⇒ -4 = 0 + b
⇒ - 4 = b
Hence, the value of the y-intercept is: b = 4.
Final Answer:Based from our calculations, we can infer that the linear function that matches the graph is Option C: f(x) = 3x - 4.
__________________________Keywords:Linear functions
Linear equations
Slope-intercept form
_______________________________
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Answer:
f(x)=3x-4
Step-by-step explanation:
(7x)(2xy) how do I rewrite that as a sum
g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025
Answer:
a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000
b) $83,421.88
c) s[n] = 70000·1.05^n -20000
Step-by-step explanation:
a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...
s[0] = 50000 . . . . the recursion relation initial condition
The next year, the salary is multiplied by 1.05 and 1000 is added:
s[1] = 1.05·s[0] +1000
This pattern repeats, so the recursion relation is ...
s[n] = 1.05·s[n-1] +1000
__
c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).
The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...
base salary after n years = 50,000·1.05^n
The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:
sum = a1(r^n -1)/(r -1) . . . . . (see note below)
sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)
So, the total salary after n years is ...
s[n] = 50000·1.05^n + 20000(1.05^n -1)
The exponential terms can be combined, so we have the explicit formula ...
s[n] = 70000·1.05^n -20000
__
b) The year 2025 is 8 years after 2017, so we want to find s[8].
s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000
= 103,421.88 -20000 = 83,421.88
In 2025, the employee's salary will be $83,421.88.
_____
Note on the sum of the add-ons
A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....
The sum of such a geometric sequence has the formula
Sn = a1·(r^n -1)/(r -1)
Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as
Sn = 20000·(1.05^n -1).
solve pls brainliest
Answer:
28.5
Step-by-step explanation:
1/2 is 0.5 as a decimal.
That would mean that 28 1/2 is the same as 28.5.
Hope this helps! Brainliest would be really appreciated!
Choose the number sentence that illustrates the distributive property of multiplication over addition.
A. 2 × (6 + 9) = (2 × 6) + 9
B. 2 × (6 + 9) = (2 × 6) + (2 × 9)
C. 2 × (6 + 9) = (2 + 6) × (2 + 9)
The answer is B It basically just expressing the 2×(6+9)
The expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example we can write a(c+b) in the form of (ac+bc).
We have an expression:
= 2 × (6 + 9)
After applying the distributive property:
= (2 × 6) + (2 × 9)
= (12) + (18)
= 30
Thus, the expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.
Learn more about the distributive property here:
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Hhhhhhhhhhhhhhhhjjjjjj
Answer:
8.75 per hour
Step-by-step explanation:
Since it is a linear function we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 370-20)/(40-0)
=350/40
= 8.75
5
6
✓
Question 19 (5 points)
Simplify by using long division:
x+2x-6
8
9
x-2
.
A) x + 4 - 22
4
x-
11
12
>
B) x +4 +
14
15
C) x + 2 +
17
18
D) x + 2 -
2-42
✓
20
Question 20 (5 points)
Answer:
1. 2/5
2. 3/20
3. 6 1/9
4. 1/5
5. 11
6. 1
7. 3/13
8. 1 5/11
9. 2
10. 6 1/2
11. 20/27
12. 2 3/16
13. 4 13/18
14. 1 45/98
Hope this helps!
Step-by-step explanation:
Given the relation shown in the table below :
Answer:
domain: -7, -1, 0, 1
Range: -1, 0, 1, 2, 7
Step-by-step explanation:
I don't know the drop-down menu choices so I can't answer that one for you sorry :(
But I hope this helps :)
solve pls brainliest
Divide 47 by 14:
Answer 3.357
Rounded to nearest hundredth: 3.36
Find all triples of natural numbers (a, b, c) satisfying the system of equations
9514 1404 393
Answer:
(±7, ±1, ±4)(±13, ±11, ±16)Step-by-step explanation:
Solution of the system by the usual means yields the parametric equations ...
(a², b², c²) = (41 +t, t -7, 2t)
Since we want t-7 to be a perfect square, we can let ...
t -7 = n²
t = n² +7
Then the solutions are ...
(a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))
The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...
(±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination
PLS PLS PLS HELP ME ILL GIVE 20 points.
Answer:
if you want to know the x is.
Step-by-step explanation:
(180°－4x)+(180°－6x)+2x=180°
x=22.5°
Angles 4 & 8 are an example of which type of angle? *
O Alternate Exterior
O Alternate Interior
O Corresponding
O Vertical
Answer:
Corresponding
Step-by-step explanation:
They are on the same side which makes them corresponding angles
(5x+5)-2x
No scam.....
Answer:
=3x+5
Step-by-step explanation:
Let's simplify step-by-step.
5x+5−2x
=5x+5+−2x
Combine Like Terms:
=5x+5+−2x
=(5x+−2x)+(5)
=3x+5
Answer:
=3x+5
Answer:
[tex]\boxed{\boxed{\sf 3x+5 }}[/tex]
Step-by-step explanation:
[tex]\sf (5x+5)-2x[/tex]
[tex]\sf \left(a\right)=a[/tex]
⇒ First step is to get rid of expression parentheses:
[tex]\longmapsto[/tex] [tex]\sf 5x+5-2x[/tex]
⇒ Now, we need to combine like terms:
[tex]\longmapsto[/tex] [tex]\sf (5x-2x)[/tex] [tex](5)[/tex]
[tex]\longmapsto[/tex] [tex]\sf 3x+5[/tex]
__________________________________
help and i ill give brainliest
Answer:
11
Step-by-step explanation:
f(16) = 7 + 16/4
= 7 + 4
= 11