Find point
on the x-axis so that AC + BC is a minimum.
A(4,-5), B(12,3)
Answer:-3
Step-by-step explanation:
The minimum value of a function can be obtained from its derivative
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
Reason:
Let (d, 0) represent the coordinate of the point, on the x-axis, we have;
[tex]\overline{AC}[/tex]² = (4 - d)² + (-5)²
[tex]\overline{AC}[/tex] = √((4 - d)² + (-5)²)
[tex]\overline{BC}[/tex]² = (12 - d)² + 3²
[tex]\overline{BC}[/tex] = √((12 - d)² + 3²)
[tex]\overline{AC}[/tex]² + [tex]\overline{BC}[/tex]² = L = 4² + (-5 - d)² + 12² + (3 - d)²
When [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] is minimum, we have;
[tex]\lim_{n \to \infty} a_n \dfrac{d}{dd} (\overline{AC} + \overline{BC}) = \dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = 0[/tex]
Which gives;
[tex]\dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = \dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8\cdot d + 41} }[/tex]
Therefore;
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} } = 0[/tex]
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } =- \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} }[/tex]
Squaring both sides and cross multiplying gives;
16·d² - 528·d + 3456 = 0
Which gives;
16·(d - 24)·(d - 9) = 0
Therefore, d = 24, and d = 9
The point (9, 0), is closer to the given points than the point (24, 0), therefore;
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
Learn more here:
https://brainly.com/question/17117378
Question 2
The cell membrane controls what enters and exits the cell to maintain
A.energy
B. Photosynthesis
C.respiration
D.homeostasis
Solve the system using a method of your choice
Answer:
(4, 1)
Step-by-step explanation:
Method elimination would be good for this system
2x - y = 7 ........ (1)
x + y = 5 ......... (2)
(1) + (2)
3x = 12 ⇒ x = 4
4 + y = 5 ⇒ y = 1
(4, 1)
choose all that apply
Answer:
C and D
Step-by-step explanation:
The function R(x) = -0.0065x² +0.23x + 8.47 models the American marriage rate R (the
number of marriages per 100 population) x years after 1960. Based on this function, in what
year was the marriage rate the highest? (Hint: The vertex of a parabola is the maximum or
minimum.)
please help
Given:
The American marriage rate R, x years after 1960 is defined by the function
[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]
To find:
The year in which the marriage rate is the highest.
Solution:
We have,
[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]
It is a quadratic function with negative leading coefficient. So, it is a downward parabola and vertex of downward parabola is maximum.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then
[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]
In the given function,
[tex]a=-0.0065,b=0.23,c=8.47[/tex]
Now, x-coordinate of vertex is
[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{2(-0.0065)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{-0.013}[/tex]
[tex]-\dfrac{b}{2a}\approx 17.69[/tex]
It means the marriage rate is highest after 17 years of 1960.
[tex]1960+17=1977[/tex]
Therefore, the marriage rate is highest in year 1977.
Geneva already has $3.00 and earns $2.50 for each chore she completes. She wants to download an album on Apple Music which is at least $17. Write an inequality in terms of c (chores) that represents this situation.
Answer:
c ≤ 6
Step-by-step explanation:
Lets make our equation!
2.5 per chore thats our slope
+3 she starts with 3 dollars
y = 2.50x +3
Substitute y for 17!
17 = 2.5x +3
Subtract 3!
14 = 2.5x
Divide both sides by 2.5!
x = 5.6
5.6 --> 6
x = 6
Turn it into an inequality!
c ≤ 6
Consider Brainliest! Hope I helped!
Question is attached!
Answer:
what are the answer
Step-by-step explanation:
What is the equation of a line that passes through the points (3, 6) and (8, 4)?
Answer:
2x + 5y = 36 in standard form
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~
(3, 6)
(8, 4)
m = [tex]-\frac{2}{5}[/tex]
y - 6 = [tex]-\frac{2}{5}[/tex] ( x - 3 )
y = [tex]-\frac{2}{5}[/tex] x + [tex]\frac{36}{5}[/tex] in slope-intercept form
2x + 5y = 36 in standard form
Answer:
D.
Step-by-step explanation:
right on edge 2022
A person invests 5500 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars?
Answer:
It’s 17.6
Step-by-step explanation:
8. If b(x) = -2(x-50), what is the value of
b(20)? Request
Which of the following ordered pairs is a possible solution to the equation y = 3x - 2?
Answer:
D) (1,1)
Step-by-step explanation:
You can find the solution by plugging the x-value of each coordinate into the equation. It will be a solution if the y-value of the equation equals the y-value of the coordinate.
For example:
y = 3x -2
y = 3(1) - 2
y = 3-2
y = 1
1 = 1
(1, 1) are the coordinates that are on the given line.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given a equation y = 3x -2
To find which coordinates will satisfy the equation:
For coordinates (2, 0)
at x = 2, y should be zero
y = 3 * 2 -2
y = 4
Not satisfied
For coordinates(-3, 0)
at x = -3, y should be 0
y = 3 * -3 - 2
y = -9 -2
y = -11
Not satisfied
For coordinates(0, 2 )
at x = 0, y should be 2
y = 3*0 -2
y = -2
Not satisfied
For coordinates(1, 1)
at x = 1, y should be 1
Y = 3*1 - 2
y = 3 - 2
y = 1
satisfied
Therefore, (1, 1) are the coordinates that are on the given line.
Learn more about coordinates here:
https://brainly.com/question/20282507
#SPJ6
A grocery store clerk can scan 1 product every
1/2
of a second. At what rate can she scan products?
1. If mPCV = 42, then mZVCN =
Answer:
Easy lol mzvcn=48
Step-by-step explanation:
Answer for brainliest and 15 points
Answer:
1) C
2) O
3) P
4) T
5) I
6) C
7) P
8) S
9) A
10) L
11) T
12) E
13) L
Step-by-step explanation:
identify the type of represented f(x)=3/8(4)^x
Answer:
Exponetial Growth
i need help with this ASAP
Answer:
There are sixteen 15-cent stamps and eight 20-cent stamps.
Step-by-step explanation:
Stamp collector has:
15c stamps
20c stamps
Total value is $4
x($0.15) + y($0.20) = $4.00
The # of 15c stamps is 8 - than 3 * the # of 20c stamps; 15c = 8 - 3c
x = 3y - 8
(3y-8)(0.15)+y(0.20) = $4.00
0.45)y-1.20+(0.20)y = 4.00
(0.65)y-1.20 = 4.00
(0.65)y = 5.20
y = 8
x = 3(8)-8 = 16
There are sixteen 15-cent stamps and eight 20-cent stamps.
Check:
16($0.15)+8($0.20) = $2.40+$1.60 = $4.00
Give triangle abc is congruent to triangle def find x
Answer:
x=9
Step-by-step explanation:
FE is 3x-7
since ΔABC≅ΔDEF the equivalent of FE is CB, or BC...which is 20
3x-7=20
3x=27
x=9
I’ll mark brainliest please help!
Answer:
4x + 2 = 30
Step-by-step explanation:
To find the perimeter of a triangle, add up the length of all three sides of the triangle.
Here, the sides of the triangle are "x+6", "x+6", and "2x-10". When you add up all three sides of the triangle, it should be equal to the perimeter, 30. So:
(x+6) + (x+6) + (2x-10) = 30
We can simplify this equation:
(2 * (x+6)) + (2x-10) = 30
2x + 12 + 2x - 10 = 30
4x + 2 = 30
Answer D: 4x + 2 = 30
A student has some $1 bills and $5 bills in his wallet. He has a total of 13 bills that are worth $45. How many of each type of bill does he have?
Answer:
8 $5 bills and 5 $1 bills
Step-by-step explanation:
5x8=40, which would be $40
1x5=5, which would be $5
$40+$5=$45
hope this helps! :)
Answer:
it's not possible. I've tried every way, r these the right amounts?
Tristán wants to build a square garden in his backyard if the garden is going to be 64 ft2 how many feet of material will he need for the perimeter of the garden
Answer:
Tristan will need 32 feet of material for the perimeter of the garden.
Step-by-step explanation:
Given that
Area of square garden = A = 64 square feet
Perimeter = P = ?
We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.
So,
[tex]Area = A = s^2[/tex]
s is for side
Putting the value of area
[tex]64 = a^2[/tex]
Taking square root on both sides
[tex]\sqrt{s^2} = \sqrt{64}\\s = 8\ feet[/tex]
The length of side is 8 feet.
Perimeter will be:
[tex]P = 4*s\\P = 4*8\\P = 32\ feet[/tex]
Hence,
Tristan will need 32 feet of material for the perimeter of the garden.
I have no idea how to do this, any clues?
Answer:
(2x-5)+(x+25)+x
4x+20
Step-by-step explanation:
Simplify the expression.
16/21 decimal rounded to the nearest hundreth
Answer:
0.76
Step-by-step explanation:
Hundredth is just the 2nd decimal point
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Answer:
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
Step-by-step explanation:
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Let x be the number of liters of the 45% acid solution
The number of liters of the 70% acid solution is y
x + y = 50
x = 50 - y
Also
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?
We have:
45% × x + 70% × y = 65% × 50
0.45x + 0.70y = 0.65 × 50
0.45x + 0.70y = 32.5
We substitute x = 50 - y in the equation
0.45(50 - y) + 0.70y = 32.5
= 22.5 - 0.45y + 0.70y = 32.5
= - 0.45y + 0.70y = 32.5 - 22.5
= 0.25y = 10
Divide both sides by 0.25
= y = 10/0.25
y = 40 liters
x = 50 - y
x = 50 - 40
x = 10 liters
Hence,
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
HELP ME OUT IM DUMB
Answer:
around 15.3
Step-by-step explanation:
3^2 + 15^2=c^2
Answer:
Step-by-step explanation:
Formula:
a^2 + b^2 + c^2
3^2 + 15^2 + c^2 = To find hypotenuse
3 • 3 + 15 • 15 = -c^2
9 + 225 = -c^2
234 = c^2
square root of 234 = 15.2970585408
c = 15.2970585408
The roof is 15.2970585408
You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
Army in Sevilla in the year 1842. Outside your barracks window is a stack of
cannonballs, as shown in the illustration. On an idle afternoon you decide to
calculate the number of cannonballs in the stack. What is the number of
cannonballs?
Answer: The correct answer would be 164(c)
Step-by-step explanation:
You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
Army in Sevilla in the year 1842. Outside your barracks window is a stack of
cannonballs, as shown in the illustration. On an idle afternoon you decide to
calculate the number of cannonballs in the stack. What is the number of
cannonballs?
650 is the number of cannonballs. It typically fires a projectile propelled by an explosive chemical.
What is cannonballs?A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.
Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.
By utilizing the formula of a square pyramid,
n(n+1)(2n+1)/6
12(12+1)(2(12)+1)/6
12(13)(25)/6
2*13*25
=650
Therefore, 650 is the number of cannonballs.
To know more about cannonballs, here:
https://brainly.com/question/14330897
#SPJ7
f(x)=2x+3 g(x)=x-4 Find (f+g)(2)
Please help asappp
Answer:
(f+g)(2)=5
Step-by-step explanation:
Subsitute 2 in for x in both functions. Then add the answers of the functions together.
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy?
Help please!!!! thank you sm!!
Answer:
64 cups
Step-by-step explanation:
Help this is confusing
Answer:
A, 21
Step-by-step explanation:
84 divided by 3 = 28
28 per hour
3/4 of 28 is 21
The answer would be A. 21.
whats the slope for (-2,4) and (10, -2)
Answer:
-1/2
Step-by-step explanation:
y2-y1 over x2-x1
-2-4 over 10+2
which equals -6/12
which simplifies to -1/2
Answer:
-1/2
Step-by-step explanation:
Slope formula- m = y2 - y1
x2 - x1
x1,y1
-2, 4
x2,y2
10,-2 -2 - 4
10 - (-2) = -6/12 = -1/2
Simplify completely:
Answer:
(3)¼×¾
Step-by-step explanation:
3⁴/⁴
hope its write
Answer:
[tex]\frac{13}{4}[/tex] · [tex]\frac{15}{4}[/tex]
Step-by-step explanation:
Focusing on the first fraction, in order to simplify it, you have to multiply the denominator by the whole number; 4 x 3 is 12. You add the product to the numerator, so 12 + 1 would be 13. Therefore, the first fraction simplified would be [tex]\frac{13}{4}[/tex].
We can apply the same procedure to the next fraction, so 3 x 4 is 12, and 12 + 3 is 15. [tex]\frac{15}{4}[/tex] would be your answer.
Hope this helps! :)