The pair of numbers that maximizes the product and has a sum of 83 is (41.5, 41.5), which can be written as the fraction 83/2 in reduced form.
To determine the pair of numbers with a sum of 83 and maximum product, we can use the concept of quadratic equations.
Let the two numbers be x and y, where x + y = 83.
We want to maximize the product xy.
To do this, we can express one variable in terms of the other and then find the maximum value of the product using calculus.
From the equation x + y = 83, we can express y in terms of x as y = 83 - x.
The product of x and y is given by P(x) = x(83 - x).
To determine the maximum value of P(x), we can take the derivative of P(x) with respect to x and set it equal to zero:
P'(x) = 83 - 2x = 0
Solving this equation, we find x = 41.5.
Substituting this value back into the equation x + y = 83, we get y = 41.5.
This can be written in reduced form as the fraction 83/2 .
So, the answer is (83/2, 83/2).
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Given: f(x) = 2(x + 1)2 - 5
1)what direction does the graph open
2)maximum or minimum
3)name the domain and range
4) write the equation in standard form
I already graph it
vertex is 2,5
(2)_that tells it how it should run.
An/A
(1) is extra information given to an/a
Square BCDE with vertices B(-6,7),C(-2,6),D(-3,2), and E(-7,3) in the y-axis. find the reflection?
Answer:
The vertices of the square [tex]B'C'D'E'[/tex] are [tex]B'(x, y) = (6,7)[/tex], [tex]C'(x,y) = (2, 6)[/tex], [tex]D'(x,y) = (3,2)[/tex] and [tex]E'(x,y) = (7,3)[/tex]
Step-by-step explanation:
From Geometry we notice that a reflection with axis of symmetry on y-axis is represented by the following formula:
[tex](x',y') = (-x, y)[/tex], [tex]\forall \,x,y\,\in\mathbb{R}[/tex]
Thus, the vertices of the square [tex]B'C'D'E'[/tex] are [tex]B'(x, y) = (6,7)[/tex], [tex]C'(x,y) = (2, 6)[/tex], [tex]D'(x,y) = (3,2)[/tex] and [tex]E'(x,y) = (7,3)[/tex]
Coordinates of the image square B'C'D'E' after reflecting the square BCDE across y-axis will be B'(6, 7), C'(2, 6), D'(3, 2), E'(7, 2).
If a point (x, y) is reflected across y-axis, rule to be followed,
(x, y) → (-x, y)
Following this rule coordinates of image square B'C'D'E' will be,
B(-6, 7) → B'(6, 7)
C(-2, 6) → C'(2, 6)
D(-3, 2) → D'(3, 2)
E(-7, 2) → E'(7, 2)
Therefore, vertices of the image square will be B'(6, 7), C'(2, 6), D'(3, 2), E'(7, 2).
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A holiday costs £9000. work out the price after a 9% discount
Answer: 9810
Step-by-step explanation:
Help!! ASAP PLEASE!!!
What is the solution to the system of eqautions:
x[tex]x^{2} -2x +y= 8\\x-y=2[/tex]
Step-by-step explanation:
from (2)
x-y=2
y=x-2 (3)
subs (3) into (1)
x²-2x+(x-2)=8
x²-2x+X-10=0
x²+x-10=0
quadratic formula
x= (-1±√1²-4×1×(-10))/2(1)
X=( -1±√41)/2
X=(-1+√41)/2
=
x=(-1-√41)/2
=
find the length of the missing side. if necessary round to the nearest tenth
Answer:
20.5
Step-by-step explanation:
solution here
hypoteneous=c
perpendicular = 15
Base = 14
now
h^=p^+b^
H^=15^+14^
H^=225+196
H^=421
H=square root 421
H= 20.5
Simplify -62 - 12 - 2(-7).
-17
35
11
-35
Answer:
I got -60
I'm pretty good at this.. oop guess I missed a step
what is 100.552 rounded to the nearest whole number
Answer:
101
Step-by-step explanation:
We look at the tenths place if we want to round to the whole number, and since the tenths place is 5, we round up.
The answer is 101. Any number that is 5 or higher can round the number in a higher number place (by one) it up by one. In this case, we are rounding the tenths place to the ones place. 5 can be used to round the number in the ones place up by one. Therefore 100.552 -> 101.
1 meter is about how many miles? 3miles, 1 inch, 30 miles, or 3 feet
Answer ASAP!! will give brainliest hurry
Answer:The correct answer is (3. FEET)
Answer:
3 feet
Step-by-step explanation:
The second term of an arithmetic sequence is 13 and the fourth term is 7.
What is the thirteenth term?
Answer:
[tex]\bold{a_{13}=52}[/tex]Step-by-step explanation:
[tex]d=a_4-a_3=a_3-a_2\\\\a_3-a_2=a_4-a_3\\\\2a_3=a_2+a_4\\\\2a_3=13+7\\\\2a_3=20\\\\a_3=10\\\\d=10-13=-3\\\\\\a_2=a_1+d\quad\implies\quad a_1=a_2-d=13-(-3)=16\\\\a_n=a_1+d(n-1)\\\\a_{13}=16+(-3)(13-1)=16+36=52[/tex]
I need help. Thank KB
Answer:
[tex]\huge\boxed{x=20}[/tex]
[tex]\huge\boxed{H = 58, I = 71, J = 51}[/tex]
Step-by-step explanation:
In order to find the measure of our angle, we have to note angle relationships.
All angles in a triangle will add up to 180°
This means all the angles in this triangle will equal 180, or:
[tex](4x - 9) + (3x - 2) + (3x-9) = 180[/tex]
We can simplify this equation down to find the value of x.
Combine like terms:
[tex]10x - 20 = 180[/tex]
Add 20 to both sides:
[tex]10x = 200[/tex]
Divide both sides by 10:
[tex]x = 20[/tex]
Now that we know the value of x, we can substitute it into the equation for each angle to find it's value.
m∠H:
[tex]3x-2\\3(20)-2\\60-2\\\\58[/tex]
m∠I
[tex]4x-9\\4(20)-9\\80-9\\\\71[/tex]
m∠J
[tex]3x-9\\3(20)-9\\60-9\\\\51[/tex]
To further prove this is right, we would know that all the angles add up to 180°.
[tex]51+71+58=180[/tex], so we should be right.
Hope this helped!
what is the history of one world trade center please can any one inbox me
Answer:
hlo how are you
rashmi
u remember me
2+2=4
why did it not scan properly my question wasn’t that and didn’t come up with what was in the photo
Answer:
I think its 4 but i could be a fish so infinite possiblities in this pool of imagination
Step-by-step explanation:
Write an absolute value equation that has the solution x= -6 and x=10.
Answer:
[tex]/x-2/=8[/tex]
Step-by-step explanation:
[tex](-6+10)/2=2[/tex]
Midpoint= 2
Distance from midpoint =8
[tex]/x-2/=8[/tex]
Slash= Absolute Value Sign
2. The solution of linear pair of equations 19x + 17y = 55 and 17x + 19y = 53 are
(A) x = 3, y = 2 (B) x = 3, y = -2 (C) x = 2, y = 1 (D) x = 5, y = -3 mcq
Write the equation of the line parallel to the given line and passing through the given point.
a)
y=2x−8 through (3,10)
b)
y= 1/2 x+2 through (0,4)
c)
y=−2x−1 through (4,3)
Answer:
a) y = 2x +4
b) y = 1/2x +4
c) y = -2x +11
Step-by-step explanation:
The given equations are in slope-intercept for, so we can read the slope directly from the equation. It is the x-coefficient.
We can then write an equation of a parallel line using the point-slope form of the equation of a line:
y -k = m(x -h) . . . . for a line with slope m through point (h, k)
If you like, you can rearrange this to "slope-intercept" form. Add k and simplify.
y = mx +(k -mh)
__
a) m = 2, (h, k) = (3, 10)
y = 2x +(10 -2·3)
y = 2x +4
__
b) m = 1/2, (h, k) = (0, 4)
y = 1/2x +(4 -(1/2)·0)
y = 1/2x +4
__
c) m = -2, (h, k) = (4, 3)
y = -2x +(3 -(-2)(4))
y = -2x +11
Find the sum of 9x² - 6x + 7, 5-4 x
and 6-3x²
Answer:
6x² - 10x + 11
Step-by-step explanation:
Step 1: Write expression
(9x² - 6x) + (5 - 4x) + (6 - 3x²)
Step 2: Combine like terms
6x² - 10x + 11
Which of the following equations is a constant function?
x = 5
y = x
y = 5
Answer:
Y=X
Step-by-step explanation:
HELPPP PLEASE GONNA GIVE BRAINLIEST!
Answer: the second one
Step-by-step explanation:
Answer:
the first one
Step-by-step explanation:
bc you divided the pizza into 2 pieces and the divided it among 4 people so each person would get 1/4th of the 1/2 pizza
Brainlest plzzzz
Which of the following expressions would simplify to be the multiplicative identity?
2^ 3 • 3 ^2
2 ^1
2^ 0
2 ^3 • 2 ^3
Your answer should be B: 2^1 I'm pretty sure.
Answer:
The answer is b 2^1.
Step-by-step explanation:
1. Fully factorise the following by splitting
the middle term or 'intelligent guessing':
a. 6x2 + 5x – 4
b. 5x2 - 4x – 1
Answer:
(3x÷4 )(2x-1)
(5x÷1. )(x-1 )
3 2/5 times 2 1/3 simplified answer pls
7%of what length is 200 feet?
Step-by-step explanation:
Let the length be x
7% of x = 200ft
7/100 × x = 200
7x/100 = 200
7x = 200 × 100
7x = 20000
x = 20000/7
x = 2,857.14
Step-by-step explanation:
Basically, the question is asking what number multiplied by 0.07 is equal to 200?
2857.14286 ft (round as necessary)
the way you can do this:
x(0.07)=200
isolate x by dividing 200 by 0.07 (200/0.07=2857.14286 ft)
-9x + 6 = -x + 4
help pls ill give brainliest
Answer: x = 1/4
Step-by-step explanation:
-9x + 6 = -x + 4
+x +x
-8x + 6 = 4
-6 -6
-8x = -2
divide by -8 on both sides
x = 2/8
simplify
x = 1/4
Answer:
x = 1/4Step-by-step explanation:
-9x + 6 = -x + 4
-9x + x = 4 - 6
-8x = -2
x = 2/8
x = 1/4
Can someone also help me do these two
Answer:
Student one and student 3, and II, III, and IV
There ya go!
Answer:
1/4×100=25
7/10×100=70
13/20×100=5×13=65 TRUE(D)
Step-by-step explanation:
C IS TRUE
0.65 AND65/100 AND 13/20
What is the area of this angle
1. Which expression shows the ratio of 10 to 25?*
25:10
10:25
10-25
25 per 10
Answer:
10:25
Step-by-step explanation:
Ten to 25
Ten is first so it is first on the ratio
25 is last so 25 is last
: in between
Find x,if (18 / 23) ^4×(18 / 23) ^ −5=(18 / 23)^ 2X+1
Answer:
x=2645/5832 hope that helped
Step-by-step explanation:
What is the product of 630 and 7.2 • 10^4
Answer:
72,630
Step-by-step explanation:
630 + 7.2 x 10^4= 72,630
The value of the product of 630 & 7.2×10⁴ is 4.536 x 10⁷.
What is the scientific notation of a number?The standard form for a number is a method by which we write number in a format like b×10ˣ. The value of b should be in between 0 to 10.
To multiply two numbers in scientific notation, we can first multiply their coefficients and then add their exponents.
630 can be written as 6.3 x 10² in scientific notation.
7.2 x 10⁴ is already in scientific notation.
So, the product of 630 and 7.2 x 10⁴ can be found by multiplying the coefficients and adding the exponents:
(6.3 x 10²) x (7.2 x 10⁴)
= (6.3 x 7.2) x (10² x 10⁴) (using the distributive property of multiplication)
= 45.36 x 10⁶ (multiplying the coefficients)
= 4.536 x 10⁷ (simplifying the exponent by moving the decimal point to the left)
Therefore, the product of 630 and 7.2 x 10⁴ is 4.536 x 10⁷.
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how do you solve 68 + .765 + 2.123
Answer:
70.888
Step-by-step explanation:
here's an easier way to solve this.
so basically, re arrange the whole equation.
0.765
+ 2.123
______________
Add this up!
Then you'll end up with...
2.888
After you get 2.888
Add the whole number 68.
68.000
+ 2.888
______________
Finally you'll end up with...
70.888
It's just adding decimals !
hope this helps
sincerely
cristopherrobles
