Ingat rumus determinan fungsi kuadrat yaitu :
[tex]\longmapsto\boxed{\sf{D = b^2 - 4ac}}[/tex]
Maka, Kita kembali jawab soalnya.
⏩Nomor (1) :
»8x² + 7x + 10 = 0
Didapatkan nilai² a, b, dan c yaitu :
a = 8 | b = 7 | c = 10Maka, nilai determinannya adalah
D = b² - 4ac D = 7² - 4(8)(10) D = 49 - 4(80) D = 49 - 320 D = -271✅[tex]\:[/tex]
⏩Nomor (2) ;
»2x² + 10x + 10 = 5
»2x² + 10x + 10 - 5 = 0
»2x² + 10x + 5 = 0
Didapatkan nilai² a, b, dan c yaitu :
a = 2 | b = 10 | c = 5Maka, nilai determinannya adalah
D = b² - 4ac D = 10² - 4(2)(5) D = 100 - 4(10) D = 100 - 40 D = 60✅[tex]\\ \rm\hookrightarrow 8x^2+7x+10=0[/tex]
Determinant be D
[tex]\\ \rm\hookrightarrow D=b^2-4ac[/tex]
[tex]\\ \rm\hookrightarrow D=7^2-320[/tex]
[tex]\\ \rm\hookrightarrow D=49-320[/tex]
[tex]\\ \rm\hookrightarrow D=-271[/tex]
#2
[tex]\\ \rm\hookrightarrow 2x^2+10x+10=5[/tex]
[tex]\\ \rm\hookrightarrow 2x^2+10x+5=0[/tex]
[tex]\\ \rm\hookrightarrow D=10^2-40[/tex]
[tex]\\ \rm\hookrightarrow D=100-40[/tex]
[tex]\\ \rm\hookrightarrow D=60[/tex]
Complete each statement using <, >, or =. Use your number line to explain your reasoning
Answer:
<
Step-by-step explanation:
Huilan is 8 years older than Thomas. The sum of their ages is 70. What is Thomas's age?
Answer:
T = 31
Step-by-step explanation:
(T + 8) + T = 70
subtract 8 from both sides
T+T = 62
Rewrite
2T = 62
divide both sides by 2
T = 31
50 POINTS // This graph represents a proportional relationship.
What is the constant of proportionality for this relationship?
•1/3
•1/2
•2
•I don't know
We need slope
(3,1)(6,2)[tex]\\ \rm\Rrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{2-1}{6-3}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{1}{3}[/tex]
This can be solved using two methods:
Method #1:
Rise/Run = Slope=> 1/3 = SlopeThe slope is 1/3.
Method #2:
y₂ - y₁/x₂ - x₁ = Slope=> 2 - 1/6 - 3 = Slope=> 1/3 = SlopeThe slope is 1/3.
Looking at the two methods, we can conclude that:
The slope of the line is 1/3.
Zach worked 1,040 hours this year and made $9 per hour. How much money did he earn over the course of the year?
$9,060
$9,360
$10,360
$12,660
Answer:
$9,360
Explanation:
$9 per hour, rewrite: 1 hour he earned $9so for 1040 hours, he earned:
$9 * 1,040
$9,360
Problem 0: Compute the inverse Laplace Transforms of:
[tex]F(s) = \frac{s + 1}{s(s - 1)(s - 3)} [/tex]
[tex]F(s) = \frac{1}{(s - 1)(s - 2)(s - 3)} [/tex]
Decompose each given F(s) into partial fractions.
[tex]F(s) = \dfrac{s+1}{s(s-1)(s-3)}[/tex]
has partial fraction decomposition
[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac as + \dfrac b{s-1} + \dfrac c{s-3}[/tex]
Combine the rational terms on the right and solve for the coefficients:
[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac{a(s-1)(s-3) + b s(s-3) + c s(s-1)}{s (s-1) (s-3)}[/tex]
[tex]1 = a(s-1)(s-3) + bs(s-3) + c s(s-1)[/tex]
[tex]1 = 3 a + (-4 a - 3 b - c) s + (a + b + c) s^2[/tex]
[tex]\begin{cases}3a=1 \\ -4a-3b-c = 0 \\ a+b+c=0 \end{cases} \implies a=\dfrac13, b=-\dfrac12, c=\dfrac16[/tex]
Then
[tex]F(s) = \dfrac13 \times \dfrac1s - \dfrac12 \times \dfrac1{s-1} + \dfrac16 \times \dfrac1{s-3}[/tex]
Using the frequency-shifting property, the inverse transform is
[tex]\boxed{f(t) = \dfrac13 - \dfrac{e^t}2 + \dfrac{e^{3t}}6}[/tex]
The other transform can be dealt with in the same manner.
[tex]F(s) = \dfrac1{(s-1)(s-2)(s-3)} = \dfrac a{s-1} + \dfrac b{s-2} + \dfrac c{s-3}[/tex]
[tex]\implies 1 = a(s-2)(s-3) + b(s-1)(s-3) + c(s-1)(s-2)[/tex]
[tex]\implies 1 = 6 a + 3 b + 2 c + (-5 a - 4 b - 3 c) s + (a + b + c) s^2[/tex]
[tex]\implies \begin{cases}6 a + 3 b + 2 c=1 \\ -5a-4b-3c = 0 \\ a+b+c=0\end{cases} \implies a=\dfrac12, b=-1, c=\dfrac12[/tex]
[tex]\implies F(s) = \dfrac12 \times \dfrac1{s-1} - \dfrac1{s-2} + \dfrac12 \times \dfrac1{s-3}[/tex]
[tex]\implies \boxed{f(t) = \dfrac{e^t}2 - e^{2t} + \dfrac{e^{3t}}2}[/tex]
Please answer the question in the picture
Answer:
Option A
Step-by-step explanation:
Both fractions have common denominators (x - 4). So, we can add the numerators.
[tex]\dfrac{x-9}{x-4}+\dfrac{x^{2}-x+5}{x-4}=\dfrac{x-9 +x^{2}-x +5}{x-4}\\\\\\=\dfrac{x -x +x^{2}-9+5}{x-4}\\\\\\=\dfrac{x^{2}-4}{x-4}[/tex]
The y- intercept is when x= ?
Answer:
The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero. To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.
Step-by-step explanation:
hope it helps
Let f(x)=cos(x)x^-2
F’(x)=
[tex]f(x)=cos(x)x^{-2}\implies f(x)=\cfrac{cos(x)}{x^2}\implies \cfrac{df}{dx}=\stackrel{\textit{quotient rule}}{\cfrac{-sin(x)\cdot x^2-cos(x)\cdot 2x}{(x^2)^2}} \\\\\\ \cfrac{df}{dx}=\cfrac{-x[x\cdot sin(x)+2cos(x)]}{x^4}\implies \cfrac{df}{dx}=\cfrac{-[xsin(x)+2cos(x)]}{x^3}[/tex]
Triangle ABC is isosceles. It is reflected across the y- axis and then translated up 1 unit to form triangle ABC.
Answer:
Step-by-step explanation:
Answered here: https://brainly.com/question/26774005
what is the area of a square and a right triangle combined?
Answer:
you would have to separate the shapes and find out what the area of them both and add them together
Step-by-step explanation:
hexadecimal numbers to decimal (base-10) numbers. 51) 4D 53.) BC2
In hexadecimal/base-16, we have B₁₆ = 11, C₁₆ = 12, and D₁₆ = 13, so
4D₁₆ = 4 × 16¹ + 13 × 16⁰ = 77
and
BC2₁₆ = 11 × 16² + 12 × 16¹ + 2 × 16⁰ = 3010
Three students, Carson, Andrew, and London, line up one behind the other. How
many different ways can they stand in line?
What is the range of U.S. property tax rates?
What is the range?
5 2 4 6 0 0
Answer:
You find the range by subtracting the smallest value from the highest in the set. So in this case, it would be 5-0=0
Step-by-step explanation:
Hope This Helps
Have A Great Day
~Zero~
Select proportional or not proportional to correctly classify the pair of ratios 1.8/7.2 and 0.4/1.6
Answer: proportional
Step-by-step explanation: just took the quiz
Y'all I don't understand this
Answer:
Step-by-step explanation:
x-axis and y-axis meet at (0, 0), that is the origin
the tangent decimal of a 25-degree angle is .4463. what can be determined about the length of the angles opposite sides compared to the length of the angles adjacent sides?
heres a link hope it help you
https://www.journaldespalaces.com/carriere/offre-118597-Officier-de-restauration-Cafetier.html
Stephen rolls a fair dice 78 times.
How many times would Stephen expect to roll an odd number?
Answer:
Step-by-step explanation:
1 3 5 are all odd numbers.
There are 6 numbers all together on a die. 1 2 3 4 5 6
That means that 3/6 times, he should roll an odd number
3/6 * 78 = 39
He should get 39 rolls which are an odd number.
Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andres
notebooks contain?
Find the solution
Answer:
300
Step-by-step explanation:
60 * 5 = 300
What is the factored form for the quadratic function?
Answer:
Step-by-step explanation:
The factored form of a quadratic function is f (x) = a (x - p) (x - q) where p and q are the zeros of f (x).
This table contains x and y values in equivalent ratios fil in the missing value in the table
Answer:
where is the table?
Step-by-step explanation:
._.
What is 1 2/3 divided by 1 5/6
Answer:
10/11
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
The answer is B 80.00 hope this helps
have a nice day
Step-by-step explanation:
HELP ME OUT PLS!!!!
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is equal to the area of the largest square. Which three squares are an example of this relationship?
Hugh and his brothers are on a road trip. His brother makes a table comparing how long they have traveled in hours ( x ) with the number of miles they have traveled ( y ). Which equation can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven?
The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x
Equation of a graph and tableGiven the following variables
Time taken to travel is x
Mils traveled is y
Using the coordinate points (2, 130) and (4, 260)
The standard linear equation is y = mx + b
slope m = 260-130/4-2
m = 130/2
m = 65
For the intercept
130 = 65(2) + b
b = 0
The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x
Learn more on linear functions here; https://brainly.com/question/14323743
HELP THIS IS URGENT NEED TODAY!!!!!!!!!!!!!
Marvin earns $7.75 per hour at his summer job. He wants to buy a video game system that costs $193.75.
Enter an equation to model the relationship between the number of hours worked h and the amount earned e.
Answer:
If he earns (e) $7.75 per hour, this implies e = 7.75h.
Step-by-step explanation:
If you wanted to solve that-
e = 7.75h
193.75 = 7.75h
Divide both sides by 7.25
h = 25
What is the area of a rectangle with a length of 214 inches and a width of 234 inches?
714 in²
6316 in²
4316 in²
3332 in²
Given :
The length of a rectangle is 214 inches and the width is 234 inches.⠀
To Find :
The area of the rectangle.⠀
Solution :
We know that,
[tex]\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:[/tex]
⠀
Now substituting the values :
[tex]\qquad {\dashrightarrow{ \sf{214 \: in\times 234 \: in = Area_{(rectangle)}}}}\:[/tex]
[tex]\qquad {\dashrightarrow \: { { \sf{50,076 \: {in}^{2} = Area_{(rectangle)}}}}\:}
[/tex]
⠀
Hence, The area of the rectangle is 50,076 in² .
The area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.
How to find the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle.
The rectangle given in the problem has,
A length of 2 1/4 inches. A width of 2 3/4 inches.Thus, the area of the rectangle is,
[tex]A=2\dfrac{1}{4}\times2\dfrac{3}{4}\\A=\dfrac{8+1}{4}\times\dfrac{8+3}{4}\\A=\dfrac{9}{4}\times\dfrac{11}{4}\\A=\dfrac{99}{16}\\\A=\dfrac{96+3}{16}\\A=6\dfrac{3}{16}[/tex]
Thus, the area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.
Learn more about the area of rectangle here;
https://brainly.com/question/11202023
Which function represents a parabola that is translated 2 units to the left and 6 units down from the parent function, f(x)=x^2
Translation involves moving a function along its coordinates
The image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]
How to determine the new functionThe parent function is given as:
[tex]f(x) = x^2[/tex]
When the function is translated 2 units left, we have:
[tex]f'(x) = (x + 2)^2[/tex]
When the function is translated 6 units down, we have:
[tex]f"(x) = (x + 2)^2 - 6[/tex]
Rewrite as:
[tex]g(x) = (x + 2)^2 - 6[/tex]
Hence, the image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]
Read more about translation at:
https://brainly.com/question/11468584
HELPPPP IF YOU CAN pls?
Answer:
i'm not sure but here's some encouragement- YOU CAN DO IT
Step-by-step explanation:
A line crosses the y-axis at (0,55). What is the y-intercept of this line?
Answer:
[tex]\huge\boxed{\sf{b=55\:(b=y-intercept\:;)}}[/tex]
Step-by-step explanation:
Hello.
The y-intercept of a line is a point where the graph touches the y-axis.
Y-intercepts always have an x-coordinate of 0.
Now, what is the y-intercept?
If we have a point (0, b) then b is the y-intercept.
This is just a formula, so don't think that the y-intercept is b, okay?
The y-intercept is b, but only in formulae. :)
Using the formula, we can deduce that
the y-intercept is 55.
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]