2(x + 4) = 4x + 3 - 2x + 5
In the answer space below, provide one of the two positive integers whose product is 196 and whose sum is a minimum.
Answer:
14
Step-by-step explanation:
The value of two positive integers are 14 and 14.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Product of two positive integers are 196.
Sum of two positive integers are minimum.
Now,
Let two positive integers are x and y.
Since, Product of two positive integers are 196.
So, we can formulate;
xy = 196 ... (i)
And, Sum of two positive integers are minimum.
So, we can formulate;
s = x + y
From equation (i);
y = 196/x
Substitute in above equation, we get;
s = x + y
s = x + 196/x
Differentiate with respect to x as;
d/dx (s) = d/dx(x + 196/x)
ds/dx = 1 - 196/x² ... (ii)
Substitute ds/dx = 0, we get;
ds/dx = 1 - 196/x² = 0
1 - 196/x² = 0
1 = 196/x²
x² = 196
x = ± 14
Differentiate equation (ii) again;
d²s/dx² = 0 - (-2 × 196)/x³
d²s/dx² = 392/x³
At point x = 14,
d²s/dx² = 392/8³ > 0
Hence, At x = 14, the value is minimum.
So, we get;
xy = 196
at x = 14
y = 196/14
y = 14
Hence, The value of two positive integers are 14 and 14.
Learn more about the product visit:
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divide 0.12 by 0.04. That means we want to find out how many times 0.04, or four-hundredths, goes into 0.12, or twelve-hundredths.
Answer:
3
Step-by-step explanation:
0.12 ÷ 0.04
if we want to calculate without calculator ,
multiply both nenominator and denominator by 100;
Then,
(0.12×100)÷(0.04 ×100)
= 12÷4
= 3
what is a two variable linear equation
Answer: Linear equations in two variables. If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax+by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r.
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
It's an equation that has two variables
that's to say it has x and y (generally)
it is linear when you graph it, it forms a line and that only happens when the mayor exponent is one
so
[tex](something_1)x^{1}+(something_2)y^{1} =(something_3)[/tex]
notice all the something are completely different
or you could find it as
[tex]y=mx+b[/tex]
where m is the slope
and b some number
so that's it
4 - 3x = 8 - 4x Plz answer this question
Answer:x=4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4−3x=8−4x
4+−3x=8+−4x
−3x+4=−4x+8
Step 2: Add 4x to both sides.
−3x+4+4x=−4x+8+4x
x+4=8
Step 3: Subtract 4 from both sides.
x+4−4=8−4
x=4
Answer:
x=4
Step-by-step explanation:
4-3×=8-4x
4-8=-4x+3x
-4=-×
x=4
(both side have negative so you just cancel out the negative sign)
3(x−2)=9 :solve for x?
Answer:
x=5
Step-by-step explanation:
3(x−2)=9
Divide both sides by 3.
x-2=9/3
Divide 9 by 3 to get 3.
x−2=3
Add 2 to both sides.
x=3+2
Add 3 and 2 to get 5.
x=5
Answer:
5
Step-by-step explanation:
S=Ut + 1\2 at^2
U=10 a=-2 t=1\2
Work out the value of S
Hope u guys get this!
Central Park in New York City is shaped like a rectangle. On a map of the park
in the coordinate plane, three of the vertices are located at (-1.25, -0.25),
(-1.25, 0.25), and (1.25, 0.25). Distances on the map are in miles. What is the
perimeter of Central Park? Show your work,
Answer:
6
Step-by-step explanation:
Given that the coordinate plane, three of the vertices of the rectangle are located at (-1.25, -0.25),
(-1.25, 0.25), and (1.25, 0.25)
The length L of the shape will be:
L = 0.25 - ( - 0.25 )
L = 0.25 + 0.25
L = 0.5
The width of the shape will be:
W = 1.25 - ( - 1.25)
W = 1.25 + 1.25
W = 2.5
Perimeter P = 2L + 2W
Substitute the Length and the width into the formula
P = 2(0.5) + 2(2.5)
P = 1 + 5
P = 6 metres
Therefore, the perimeter of the shape is 6 metres
What are the next 3 numbers in the pattern: 10, 11, 13, 16, 20 ... *
Answer:
25, 31, 38
Step-by-step explanation:
The first differences are increasing by 1 each time. The next differences will be 5, 6, 7, so the next numbers will be 25, 31, 38.
Answer:
The answer is 25 and 31. The pattern is adding the numbers 1, 2, 3 every time it goes up. For example. 10+ 1 = 11, 11 + 2 = 13, 13 + 3= 16, 16+ 4 = 20... and so on. Thus you would add 20 + 5 and get the answer 25. THEN you would add 25 + 6 and get 31.
Answers: 25, 31
Hope that helps
What is the slope between the points (3,1) and (4,-1)
Answer:
Step-by-step explanation:
(-1 - 1)/(4 - 3)= -2/1= -2
y - 1 = -2(x - 3)
y - 1 = -2x + 6
y = -2x + 7
Answer:
-2
Step-by-step explanation:
-1 -1
4-3
-2/1= -2
Help plzzzz I need help ASAP thank you
Answer:
D
Step-by-step explanation:
Martin decided to buy 2 bags of grapes weighing 5 and two-thirds pounds each, instead of the 3 bags weighing 4 and one-fifth pounds each, because the bigger bags were on sale. Did he end up with more grapes or less grapes by buying the bigger bags?
Answer:
Martin ended up buying less grapes by buying the bigger bag.
Step-by-step explanation:
5 ⅔ + 5 ⅔ = 10 4/6
4 ⅕ + 4 ⅕ + 4 ⅕ = 12 3/15
Answer:D
Step-by-step explanation: hope this helps
1. Simplity the following into lowest term
3x - 2 - 2x
Answer:
x-2
best of luck!
2/m-5=3/m+5 solve for m
Answer:
-1/10
Step-by-step explanation:
Answer: m= −1 /10
Step-by-step explanation:
2 m −5= 3 m +5
2 m +−5= 3 m +5
Multiply all terms by m and cancel:
2+−5m=3+5m
−5m+2=5m+3(Simplify both sides of the equation)
−5m+2−5m=5m+3−5m(Subtract 5m from both sides)
−10m+2=3
−10m+2−2=3−2(Subtract 2 from both sides)
−10m=1
−10m
−10
=
1 −10
(Divide both sides by -10)
m= −1 /10
Check answers. (Plug them in to make sure they work.)
m=
−1 /10
(Works in original equation)
m= −1 /10
True or False: If your expression contains more than one set of parentheses, you should evaluate all of them before doing anything else.
absolute value of -3 |xy|
Answer:
|-3| = 3
Step-by-step explanation:
You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $34.95 plus 8 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans (Round your answer to one decimal place). C1= C2= If you talk for minutes the two plans will have the same cost.
Answer:
249.64285714 minutes
Step-by-step explanation:
Let
The number of minutes you talk = t
C1 = Cost in dollars of the first plan
C2 = Cost in dollars of the second plan
First plan
The first plan charges a rate of 22 cents per minute
Converting cents to dollars
100 cents = 1 dollars
22 cents =
22/100 cents
=$ 0.22
C1 = $0.22 × t
C1 = 0.22t
Second Plan
The second plan charges a monthly fee of $34.95 plus 8 cents per minute.
Converting cents to dollars
100 cents = 1 dollars
8 cents =
8/100 cents
=$ 0.08
C2 = $34.95 + 0.08t
Find the number of talk minutes that would produce the same cost for both plans
We would Equate C1 to C2
C1 = C2
0.22t = $34.95 + 0.08t
Collect like terms
0.22t - 0.08t = $34.95
= 0.14t = $34.95
Divide both sides by 0.14
= t = $34.95/0.14
t = 249.64285714
Therefore, the number of talk minutes that would produce the same cost for both plans is 249.64285714 minutes.
How I can solve this quadratic equation using the quadratic formula? x2 + 4x = 5.
Answer:
Step-by-step explanation:
x^2 + 4x - 5 = 0
-4/2 + (sqrt(16 - 4(1)(-5)))/2
-2 + (sqrt(16+20)/2
-2 + (sqrt(36)/2
-2 + 6/2
-2 + 3
-2 + 3 = 1
-2 - 3 = -5
HELLPPPPPPP ASAPPPP PLEASEEEE
Answer:
2. f(-7)= -3(-7)-2
21-2
=19
10. h(1)= | 1-7(1) |
|-6|
=6
11. h(-7) =|1-7(-7)|
|1-49|
|-48|
=48
12. [23-h(9) =|1-7(-9)|]
h(9) =|1-7(9)|
|-62|
23-62
=39
Step-by-step explanation:
What is the following expression when simplified 5x + 8(5 + 2x)?
Answer:
5x+56
Step-by-step explanation:
5x+8(5+2)
5x+8(7)
Find the surface area of the
triangular prism.
138 because take 6×8×.5×2 + 7×10×.5+ 7×8×.5 + 6×7×.5 to get 138 square neters
Admission to the fair costs $5. Each ticket for a ride costs $1.50. You have $20 to spend at the fair on admissions and rides. Express the number of tickets you can buy as an inequality.
Lani’s father is paying for a $20 meal. He has a 15%-off coupon for the meal. After the discount, a 7% sales tax is applied to the discounted price. What does Lani’s father pay for the meal? $_________
Answer:
18.19
Step-by-step explanation: hope this helps
Tickets to the movies are $7 for adults and $4 for children. If 272 tickets
sold $1694, then how many of each type were sold?
Answer:
202 tickets for adults were sold and 70 tickets for children are sold.
Step-by-step explanation:
Solve this question using simultaneous linear equation.
•Let the number of tickets sold for adults be a
•Let the number of tickets sold for children be b
The question stated that 272 tickets were sold altogether. So:
[tex]a + b = 272[/tex]
Now, make sure that only one of the unknown values remain on the left hand side. For example:
[tex]a = 272 - b[/tex]
I will refer to the above equation as equation 1.
Now, the question also stated that the tickets sold $1694. This means that:
[tex]7a + 4b = 1694[/tex]
I will refer to this equation as equation 2.
Now, substitute equation 1 into equation 2 by replacing the a in equation 2 with the values on the right hand side in equation 1. For example:
[tex]7(272 - b) + 4b = 1694[/tex]
Then just solve the equation by finding the value of b.
[tex]7(272 - b) + 4b = 1694 \\ 1904 - 7b + 4b = 1694 \\ 1904 - 3b = 1694 \\ 1904 - 1694 = 3b \\ 210 = 3b \\ b = 210 \div 3 \\ = 70[/tex]
Lastly, find the value of a. Just take the value of b and then substitute into equation 1.
[tex]a = 272 - b \\ = 272 - 70 \\ a = 202[/tex]
How would you go about simplifying 5,759 over 999?
Answer:
it can't be simplified.
Step-by-step explanation:
The size of a playground is 160 feet by 360 feet. A model is created that measures 4 inches by 9 inches. Is it a rate, ratio only or a proportion?
Answer:
The model is made in a 1:40 ratio
Step-by-step explanation:
How many times is 4 multiplied to be equal to 160?
4(x) = 160
X = 160 / 4
X = 40
The proportion, rate, and ratio are almost the same.
They represent the correspondence between the parts and the whole since they all express a binary relationship between the quantities, that is, objects, people, tablespoons.
If the ratio is 1: 2 it could be read that for every 1 there are 2.
For example 1: 2 cups; For every cup of something there are 2 cups of something else.
In this case, 1:40; For every inch of the model, there are 40 feet in the playground.
Must show all work for 15 points
Answer:
Hey there!
a)
10x-1=4x+2
6x-1=2
6x=3
x=1/2 cm.
10x-1=4 cm.
So the width of the rectangle is 10/4, or 2.5 cm.
b)
l=3w
2l+2w=24
2(3w)+2w=24
6w+2w=24
8w=24
w=3
l=9
The are is 27 units squared.
Let me know if this helps :)
can someone please simply teach me what mean, median, and mode is pls pls pls
Mean is when you sum up all the numbers in a data set and divide that sum with the total amount of numbers in the data set.
Median is the middle number of a data set.
Mode is the number that shows up the most in a data set.
Best of Luck!
Answer:
The mean is the average of a data set. The mode is the most common number in a data set. The median is the middle of the set of numbers.
Step-by-step explanation:
i hope you get it.
Which of the following statements is true
regarding the solutions to the quadratic
equation 5x2 + 6x + 2 = 0?
Answer:
c. This quadratic equation has two complex solutions.
Step-by-step explanation:
Of the choices ...
a. This quadratic equation has exactly one real solution.
b. This quadratic equation has two real solutions.
c. This quadratic equation has two complex solutions.
d. This quadratic equation has no solutions.
The one that is true is c: two complex solutions.
__
The discriminant of quadratic ax^2 +bx +c = 0 is ...
d = b^2 -4ac
For this quadratic, the value is 6^2 -4·5·2 = -4.
When the discriminant is positive, there are two distinct real solutions.
When the discriminant is zero, there is one real solution.
When the discriminant is negative, there are two complex solutions. The discriminant of this quadratic is negative, so there are two complex solutions.
what is 3 3/4 as a decimal
Answer:
3.75
Step-by-step explanation:
Answer: 3.75
Step-by-step explanation: 3/4=.75 so add 3 and you get 3.73