2. Solve by using the quadratic formula 3x2 - 6x - 4 = 0 round to the nearest hundredth.
Answer:
[tex]let \: \alpha \: and \: \beta \: be \: two \: roots \: of \: above \: [/tex]
[tex]equation \: .[/tex]
[tex] \alpha = 2.52 \: and \: \beta = -0.52[/tex]
Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,) and (3,0) and minimize it.]
Question:
Find the point (,) on the curve [tex]y = \sqrt x[/tex] that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:
[tex](x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})[/tex]
Step-by-step explanation:
[tex]y = \sqrt x[/tex] can be represented as: [tex](x,y)[/tex]
Substitute [tex]\sqrt x[/tex] for [tex]y[/tex]
[tex](x,y) = (x,\sqrt x)[/tex]
So, next:
Calculate the distance between [tex](x,\sqrt x)[/tex] and [tex](3,0)[/tex]
Distance is calculated as:
[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]
So:
[tex]d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}[/tex]
[tex]d = \sqrt{(x-3)^2 + (\sqrt x)^2}[/tex]
Evaluate all exponents
[tex]d = \sqrt{x^2 - 6x +9 + x}[/tex]
Rewrite as:
[tex]d = \sqrt{x^2 + x- 6x +9 }[/tex]
[tex]d = \sqrt{x^2 - 5x +9 }[/tex]
Differentiate using chain rule:
Let
[tex]u = x^2 - 5x +9[/tex]
[tex]\frac{du}{dx} = 2x - 5[/tex]
So:
[tex]d = \sqrt u[/tex]
[tex]d = u^\frac{1}{2}[/tex]
[tex]\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}[/tex]
Chain Rule:
[tex]d' = \frac{du}{dx} * \frac{dd}{du}[/tex]
[tex]d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}[/tex]
[tex]d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}[/tex]
[tex]d' = \frac{2x - 5}{2\sqrt u}[/tex]
Substitute: [tex]u = x^2 - 5x +9[/tex]
[tex]d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}[/tex]
Next, is to minimize (by equating d' to 0)
[tex]\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0[/tex]
Cross Multiply
[tex]2x - 5 = 0[/tex]
Solve for x
[tex]2x =5[/tex]
[tex]x = \frac{5}{2}[/tex]
Substitute [tex]x = \frac{5}{2}[/tex] in [tex]y = \sqrt x[/tex]
[tex]y = \sqrt{\frac{5}{2}}[/tex]
Split
[tex]y = \frac{\sqrt 5}{\sqrt 2}[/tex]
Rationalize
[tex]y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]y = \frac{\sqrt {10}}{\sqrt 4}[/tex]
[tex]y = \frac{\sqrt {10}}{2}[/tex]
Hence:
[tex](x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})[/tex]
What are the zeros of the quadratic function shown in the graph?
a) –2 and –10
b) –2 and 10
c) 6
d) 2 and 10
Answer:
D
Step-by-step explanation:
Look at where the graph intercepts on the x-axis
If u can't see it's 2 and 10
Answer:
the answer is D
Step-by-step explanation:The answer is 2 and 10 because its directly on the line.
Hope I helped
The probability of spinning a 9 on Luke's game spinner is 2/9. The probability of rolling a 6 on a fair die is 1/6. Which shows the probability of spinning a 9 and then rolling a number that is not 6
Answer:
5/27
Step-by-step explanation:
P(9) = 2/9
P(not 6) = 5/6
2/9 x 5/6 = 10/54 or 5/27
HELP YALL HELP PLEASE
Answer:
66 ur welcome
Please help me if you know!! Thank you!!!!
Answer:
Triangle GHI is the right angled triangle.
Step-by-step explanation:
A right angled triangle follows the pythagoras theorem where,
h² = p² + b²
h is the longest side.
So,
15² = 12² + 9²
225 = 144 + 81
225 = 225
Hence this follow the pythagoras theorem and is a right angled triangle.
A rhombus has an angle measure of 120, and it’s longer diagonal has a length of 10 inches. What is the area?
Answer:
1200INCHES²
Step-by-step explanation:
the formula for the area of rectangle and rhombus is same so l*b will work....120*10=1200
I have a test I don’t know what to do. Can someone please help me?
area of rectangular figures
Answer:
531 in^2
Step-by-step explanation:
21 x 18 = 378 in^2
17 x 9 = 153 in^2
378 + 153 = 531 in^2
pls try itt brainliiestttt
Answer:
$25,377.11 or
$25,759.92
Step-by-step explanation:
hope that helps
PLEASE HURRY
I need help with EDGE2021
Answer:
D
Step-by-step explanation:
i really need help with this
The number 720 can be expressed as
24 x 36 x 5. Work out the values of a and b.
Answer:
24×36×5=4,320
4,320÷6=720
Answer:
I don't understand your question.
Select the correct answer.
A school supervisor wants to determine the percentage of students that bring their lunch to school.
Which of the following methods would assure random selection of a sample population?
ITS NOT "A" please help ill mark you the brainlyest!!!!
Answer:
B
Step-by-step explanation:
If p(x)=2x,which of the following is the graph of h(x)=p(x)-6
Answer:
the graph is the one with h(x)=2x-6
Step-by-step explanation:
it will hit the y-axis at (0,-6) and it will hit the x-axis at (3,0)
The graph of h(x)=p(x)-6 is shown below.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
p(x)=2x
Now,
To find the graph of h(x) = p(x) - 6, we need to use the concept of transformations of functions. A transformation is a change in the position, shape, or size of a function’s graph.
To graph h(x), we can start by graphing p(x) = 2x and then shifting it down by 6 units. The graph of p(x) is a straight line that passes through the origin and has a slope of 2. To shift it down by 6 units, we can subtract 6 from the y-coordinate of every point on the line. For example, the point (1, 2) on p(x) becomes (1, -4) on h(x).
The graph of h(x) is also a straight line that has the same slope as p(x), but has a y-intercept of -6. The equation of h(x) is y = 2x - 6.
Therefore, the graph of the function will be shown below.
Learn more about points lying on graph of a function here:
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Javier's speed is equivalent to
(answer) feet per second.
Answer:
please be more specific
Step-by-step explanation:
This isn't a lot of info, we don't know how fast he is, so find the speed, and divide it by feet! easy! Hope this helps enough?
Consuelo recorded the amount of time, in minutes, she spent exercising on the treadmill. 15, 25, 30, 25, 45, 20, 35, 30, 35, 30, 40 Which value best represents the mode? 10 min 10 min 30 min 30 min 35 min 35 min 25 min
Answer: 30 mins.
Step-by-step explanation:
The mode is the value that appears the most times.
In such a situation, first order the numbers in an ascending order:
15, 20, 25, 25, 30, 30, 30, 35, 35, 40, 45
As can be seen from the above, 30 is the number that appears the most so the mode is 30 mins.
Pls help me thank you
Answer:
45.4
Step-by-step explanation:
Solve for x4x=−29
fve amseer as an improper fraction on ots somplest form
Answer: x = -29/4
Step-by-step explanation: Let's solve for x.
4x = -29
4x/4 = -29/4
x = -29/4
Simplify 8x^3y^6/2xy^2
Answer:
4x^4y^8
Step-by-step explanation:
A local city collects 8% sales tax. If the total purchase was $216.09,then how much was collected for sales tax?
Answer:
$17.29
Step-by-step explanation:
8% = 0.08
216.09(0.08) = 17.29
Write a word equation for 24 = 3x
Jane made a door frame for the house but does not have a tool to measure the angles. How can she check that the corner is 90 degrees?
Answer:
She can use any square object around her. Since squares are made up of right angles, any side she chooses can be used to compare the angle of the door. If the square corner fits perfectly, the angle is 90. If the square fits with space, obtuse. If the square doesn’t fit, acute
Step-by-step explanation:
4.8-2/5(w-6)
mathematic equation
Answer:
[tex] \frac{0.56}{w - 6} [/tex]
Step-by-step explanation:
1) Simplify 4.8 - 2 to 2.8.
[tex] \frac{2.8}{5(w - 6)} [/tex]
2) Simplify.
[tex] \frac{0.56}{w - 6} [/tex]
Therefor, the answer is 0.56/w-6.
4. If y = 5x – 3 and 3x - y = -1, what is the value of y?
A 2
B -1
C 7
D -8
answers:
4.C po
Step-by-step explanation:
i hope its help
Mrs. Smith and her two sons spent a total of $53.50 at the movie theater. Together they spent $26.75 on snacks and Mrs. Smith's ticket was $11.25. How much did each son's ticket cost?
Answer:
$7.75
Step-by-step explanation:
$26.75 + $11.25=$38
$53.50 - $38=$15.5
$15.5/2= $7.75
Name and locate points in all four quadrants of the coordinate plane.
Write 9 19/20
as a decimal.
Answer:
9.95
Step-by-step explanation:
Answer:
9 19/20 = 9.95
Step-by-step explanation:
1.What is the coefficient of y in the expression -3x+5y+7?
A) -3 B) 5 C) 7 D) 5y
2.How many terms does this expression -3x+5y+7have?
-3 B) 5 C) 3 D) 2
a rectangle is 16 feet long and 8 feet wide find its area
The area of the rectangle is 128 square feet.
To find the area of a rectangle, you multiply the length by the width. In this case, the rectangle is 16 feet long and 8 feet wide.
Area = Length * Width
Substituting the given values:
Area = 16 feet * 8 feet
To perform the calculation, multiply the numbers:
Area = 128 square feet
Therefore, the area of the rectangle is 128 square feet.
The area of a rectangle represents the total amount of space enclosed within its boundaries. In this case, the rectangle measures 16 feet in length and 8 feet in width, so the area is calculated as 16 feet multiplied by 8 feet, resulting in 128 square feet.
The concept of area is fundamental in geometry and is used to measure the size of two-dimensional shapes. In the case of a rectangle, the area represents the product of its length and width, as every point within the rectangle contributes to its overall size.
Knowing the area of a rectangle can be useful in various situations. For example, if you want to determine how much flooring material is required to cover a rectangular room, you would need to know the area of the floor.
For more such questions on area visit:
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