Step-by-step explanation:
These aren't a perfect square bec. 1 st and 3rd terms must be perfect square
A(X) = X^2+6X +13 be perfect square if 13 Changed to 9
= X ^2+6X +9
A(x)= 2X^2+8X +14 be perfect square
= 4X ^2+ 8X + 16
Consider points A(1, 6) and B(8, 8). Find point C on the x-axis so AC +BC is a minimum.
The point that minimizes AC +BC is C (_ , _)
Answer:
The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)
Step-by-step explanation:
The given coordinates of the points A and B are A(1, 6) and B(8, 8)
The location of the point C = The x-axis
Therefore;
The coordinates of the point C = (x, 0)
The length of the segment AC = √((1 - x)² + (6 - 0)²) = √((1 - x)² + 6²)
The length of the segment BC = √((8 - x)² + (8 - 0)²) = √((8 - x)² + 8²)
At minimum distance of AC + BC, we have;
d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = (1 - x) × 2 × (0.5 - 1)× (√((1 - x)² + 6²)^(0.5 - 1) + (8 - x) × 2 × (0.5 - 1)× √((8 - x)² + 8²)^(0.5 - 1)
∴ d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = -(1 - x)/√((1 - x)² + 6²) - (8 - x)/√((8 - x)² + 8²)
-(1 - x)/√((1 - x)² + 6²) = (8 - x)/√((8 - x)² + 8²)
(8 - x)·√((1 - x)² + 6²) = -(1 - x)·√((8 - x)² + 8²)
Squaring both sides gives;
(8 - x)²·((1 - x)² + 6²) = (1 - x)²·((8 - x)² + 8²)
Expanding, using an online tool, we get;
x⁴ - 18·x³ + 133·x² -720·x + 2368 = x⁴ - 18·x³ + 161·x² - 272·x + 128
Which gives;
(161 - 133)·x² - (272 - 720)·x + 128 - 2368 = 28·x² + 448·x - 2240 = 0
Dividing by 28 gives;
x² + 16·x - 80 = 0
(x + 20)·(x - 4) = 0
Therefore, x = -20 or x = 4
The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)
The coordinates of a point is the position of the point, on the coordinate plane.
The point C that minimizes AC + BC are (-20, 0) and (4, 0)
The given parameters are:
[tex]\mathbf{A = (1,6)}[/tex]
[tex]\mathbf{B = (8,8)}[/tex]
From the question, we understand that point C is on the x-axis.
This means that:
[tex]\mathbf{C = (x,0)}[/tex]
Calculate segments AC and BC using the following distance formula
[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AC = \sqrt{(1 - x)^2 + (6 - 0)^2}}[/tex]
[tex]\mathbf{AC = \sqrt{(1 - x)^2 + 6^2}}[/tex]
[tex]\mathbf{BC = \sqrt{(8 - x)^2 + (8 -0)^2}}[/tex]
[tex]\mathbf{BC = \sqrt{(8 - x)^2 + 8 ^2}}[/tex]
Add both distance
[tex]\mathbf{AB + BC = \sqrt{(1 - x)^2 + 6^2} + \sqrt{(8 - x)^2 + 8^2}}[/tex]
Differentiate, to calculate the minimum distance
[tex]\mathbf{d' = (1 - x) \times 2 \times (0.5 - 1) \times ((1 - x)^2 + 6^2)^({0.5 - 1}) + (8 - x) \times 2 \times (0.5 - 1) \times ((8 - x)^2} + 8^2))}^{(0.5 - 1)} }[/tex]
Simplify
[tex]\mathbf{d' = -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}}- \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}}}[/tex]
Set to 0
[tex]\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} - \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} = 0}[/tex]
Rewrite as:
[tex]\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} = \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} }[/tex]
Cross multiply
[tex]\mathbf{(8 - x) \times\sqrt{(1 - x)\² + 6\²} = -(1 - x) \times\sqrt{(8 - x)\² + 8\²}}[/tex]
Square both sides
[tex]\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (-(1 - x))^2 \times (8 - x)\² + 8\²}[/tex]
[tex]\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (1 - x)^2 \times (8 - x)\² + 8\²}[/tex]
Expand
[tex]\mathbf{x^4 - 18x^3 + 133x^2 -720x + 2368 = x^4 - 18x^3 + 161x^2 - 272x + 128}[/tex]
Evaluate like terms
[tex]\mathbf{133x^2 -720x + 2368 = 161x^2 - 272x + 128}[/tex]
Collect like terms
[tex]\mahbf{161x^2 - 133x^2 - 272x + 720x + 128 - 2368 = 0}[/tex]
[tex]\mathbf{28x^2 + 448x - 2240 = 0}[/tex]
Factor out 28
[tex]\mathbf{28(x^2 + 16x - 80) = 0}[/tex]
Divide through by 28
[tex]\mathbf{x^2 + 16x - 80 = 0}[/tex]
Expand
[tex]\mathbf{x^2 + 20x - 4x - 80 = 0}[/tex]
Factorize
[tex]\mathbf{x(x + 20) + 4(x + 20) = 0}[/tex]
Factor out x + 20
[tex]\mathbf{(x + 20)(x - 4) = 0}[/tex]
Solve for x
[tex]\mathbf{x =- 20\ or\ x = 4}[/tex]
Hence, the point C that minimizes AC + BC are (-20, 0) and (4, 0)
Read more about coordinate points a:
https://brainly.com/question/18154638
Is the following a function ?
Which of the following is a factor
Answer:
(3x-8)
Step-by-step explanation:
6x^2-13x-8=(3x-8)(2x+1)
Thus, (3x-8) is one of the factors of the formula.
Determine if the expression -c2 + 2c4 is a polynomial or not.
Answer:
5
Step-by-step explanation:
Which best represents the law of conservation of mass? mass of reactants > mass of products mass of reactants < mass of products mass of reactants = mass of products mass of reactants → mass of products
Answer:
C. mass of reactants = mass of products
Step-by-step explanation:
The mass of products = mass of reactants
This question asks us about the law of conservation of mass
What is law of Conservation of MassThe law of conservation of mass states that matter can neither be created nor destroyed but can be transformed form one state or form to another. This is the basics of science which implies that whatever matter we have, it was created from something before it was converted into what we have at the moment.
However, this law does not hold nuclear reactions because they undergo changes in the core of the matter which can change the proton of that same matter or neutron from one element to another. This is to say that in nuclear reactions, matter can be created and it can also be destroyed.
The answer to this problem is mass of products = mass of reactants.
Learn more on conservation of matter here;
https://brainly.com/question/18434745
6) Which is an equation of the line with a slope of -4 and a y-intercept of -2?
x - 4y = 8 x + 4y = -8
4x + y = -2
4x - y = 2
Answer:
its 4x+y-2 I think but I am not totally sure
Step-by-step explanation:
Triangles XYZ and RST are similar. XY
is 24 inches, YZ is 16 inches, XZ is
12 inches, RS is 18 inches, and RT is
9 inches. Find the length of ST.
Answer:
g
Step-by-step explanation:
What is the value of X? What is the measure of angle ABC?
Answer:
x=14
Step-by-step explanation:
create an equation out of it. 4x+2x-6=90. Or 6x=84
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpppppppppppppppp
-3 1/5 ÷2 1/5
Answer:
−16×5 / 5×11
= -16/11
I need the answers bad
Answer:
Im not 100% sure but i think these are the right answers
Step-by-step explanation:
∠2 = 82°
∠3 = 98°
∠4 = 82°
Solve for x in the picture below
Answer:
X = 4
Step-by-step explanation:
Given : Both the triangles are congruent.
And, LM = QR ;
Therefore,
=>. 2x + 11 = 3x - 9
By interchanging.....
=> 11 + 9 = 3x + 2x
=>. 20 = 5x
=> 4 = x
Or,
=> x = 4
Hope it's help you.... ^_^A performer expects to sell 5000 tickets for an upcoming concert. They plan to make a total of 311000 in sales from these tickets. Assume that all tickets have the same price. How much money will they make if they sell 7000 tickets?
Linear or Not?
10y = 4x
Is it linear or not yes or no
Answer:
no
\
Step-by-step explanation:
Desmond has already jarred 4 liters of jam and will jar an additional 3 liters of jam every day. Write an equation that shows the relationship between the days d and the jam made j. Write your answer as an equation with j first, followed by an equals sign.
Answer: j = 3d + 4
======================================================
Explanation:
Referring to the answer above, the "+4" at the end represents the amount Desmond already has. He started off with 4 liters.
The 3d represents the 3 liters he gets per day, where d is the number of days.
So we combine the two elements getting 3d+4 representing the number of liters at any given day. That's why the answer is j = 3d+4
If we plug in d = 0, then j = 3d+4 = 3*0+4 = 4 liters is what he starts with.
If we plug in d = 1, then j = 3d+4 = 3*1+4 = 7 liters is what he has the following day. This shows Desmond gained 3 more liters.
If you plug in d = 2, you'll find that 3d+4 becomes 10, showing yet another 3 liters is added on. This process can go on for as long as you want.
Tyra has 1223 cups of sugar. If r is the amount of sugar called for in one batch of cookies,
the expression 1223 ÷ r can be used to find how many batches Tyra can make with the sugar she has.
If r is 23 cup, how many batches of cookies can Tyra make?
Enter your answer in the box.
Answer:
1223 ÷ 23 = 53.1739130435
Randolph is creating rectangle WXYZ so that WX has equation of y = 1/4x + 4. Segment XY must pass through the point (-2,6). Which of the following is the equation for XY?
Answer:
A. y - 6 = ¼(x - (-2))
Step-by-step explanation:
Equation of a line can be represented in the point-slope form, y - b = m(x - a),
Where, (a, b) is a point that the line passes through, and m is the slope of the line.
The equation of line WX, is given in the slope-intercept form, y = mx + b. Which is y = ¼x + 4.
Thus, the slope (m) = ¼.
Since we know the value of m = ¼, and we have a point that the line runs through, (a, b) = (-2, 6), let's write the equation in point-slope form by substituting m = ¼, a = -2, and b = 6 into y - b = m(x - a).
We have:
y - 6 = ¼(x - (-2))
The answer is A
Answer:
Answer:y - 6 = - 4(x - (-2))
Step-by-step explanation:
Kylie lives 4/5 kilometer from her friend's house. She has walked
5/8
of the distance. How many kilometers has Kylie walked so far?
Answer:
she has walked half of the journey
can i have brainliest please
Sally is selling two types of seashells by the seashore. She is selling large and small shells. She sells small shells for 2 dollars each and large shells for 5 dollars each. She sold a combined 15 shells for total of 60 dollars. How many of each type of shell did she sell? Show your work.
A - 5 small shells and 10 large shells
B - 10 small shells and 5 large shells
C - 7 small shells and 8 large shells
D - 8 small shells and 7 large shells
Answer:
The answer is A
Step-by-step explanation:
If you plug in the numbers it looks like this:
(A) 5(2) + 10(5) = 60
(B) 10(2) + 5(5) = 45
(C) 7(2) + 8(5) = 54
(D) 8(2) + 7(5)
so a is the only one that equals 60
She will sell 5 small shells and 10 large shells. The answer is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Sally is selling two types of seashells by the seashore. She is selling large and small shells. She sells small shells for 2 dollars each and large shells for 5 dollars each. She sold a combined 15 shells for a total of 60 dollars.
The numbers will be calculated as
(A) 5(2) + 10(5) = 60
(B) 10(2) + 5(5) = 45
(C) 7(2) + 8(5) = 54
(D) 8(2) + 7(5)
Here, option A is giving the correct sum. Therefore, she will sell 5 small shells and 10 large shells.
To know more about an expression follow
https://brainly.com/question/3310061
#SPJ2
*please be serious *
*Solve for y*
Answer:
y = + 4
Step-by-step explanation:
I used an online algebra calculator to check my answer, so you can trust that this is correct.
Answer:
y=x+4
Step-by-step explanation:
2y=2x+8
Divide everything by 2y
y=x+4
What is the slope of a line that is perpendicular to the line
whose equation is y = 4x + 1?
Answer:
-4x-1
Step-by-step explanation:
Perpendicular means opposite i think
Answer:
The slope would be -4 since perpendicular lines are lines that meet at a right angle
30 points!!! I think. Anyways, what’s your favorite thing to do with your mom.
Answer: My favorite thing to do with my mom is either go shopping with her or cooking yummy desserts, like cookies, brownies, Etc...
The downside is that my mom get's really annoyed with me so i don't really go shopping especially with all this Coronavirus stuff going on.... And also what's your favorite thing to do with your mom???
Thank you so much!!! :D Stay safe and have a great day/night!!! :D
A boat took 2 hours to travel 24km down a river. And 3 hours to travel back upstream. Find the spread of the boat in still water at the speed of the current.
What is the answer please hurry
Answer:
I dunno
Step-by-step explanation:
A botanist is collecting data from a particular species of plant. The scientist found that the data is normally distributed with a mean value of =147 μ = 147 cm and standard deviation of =30 σ = 30 cm. If the sample size is =4000 N = 4000 how many specimens have a height greater than 73 73 cm
Answer:
3972.72 specimens
Step-by-step explanation:
We solve using the z score formula:
z = (x-μ)/σ where
x is the raw score = 73 cm
μ is the population mean = 147 cm
σ is the population standard deviation = 30 cm
N is the number of samples = 4000
For x > 73
z = 73 - 147/30
z = -2.46667
Probability value from Z-Table:
P(x<73) = 0.0068189
P(x>73) = 1 - P(x<73) = 0.99318
The probability of having a height greater than 73cm is: 0.99318
The number of specimens that have a height greater than 73cm is calculated as: 0.99318 × 4000
= 3972.72 specimens
Hellpppppp i need help
Answer:
4 pounds of turkey
Step-by-step explanation:
Each person eats 2/6 pound of turkey
Multiply 2/6 by 12 because you have 12 people
Will give brainlist.. thanks!
Which equation is represented by this graph?
A. Y=3/2x + 3
B. Y=2/3x + 3
C. Y=3/2x - 2
D. Y= -2/3x - 2
C. Y= 2/3x - 2
Answer:
Step-by-step explanation:
C) Y=2\3x-2
- 3/4f = 5/4
f = ??
find f
Answer:
the answer to that, f= -5/3
I think of a number q, multiply it by 2 and add 5. I get the same answer as when I minus 2 from q. Find the value
Answer:
Q is -7
Step-by-step explanation:
Q×2+5=x
Q-2=x
Q=-7
Type the correct answer in each box. If necessary, use / for the fraction bar.
Find the solution to this system of equations.
Answer:
I is 1/2 Y is 1/2 in Z is a half
f(x)=4x+2 and g(x)=4(x−9)+2.
What transformation occurs from function f to function g?
Answer:
horizontal translation of 9 units right and 2 units up
Step-by-step explanation:
I think this is right.