Answer:
I would say you're right, 2 + 2
Step-by-step explanation:
Final answer:
The mathematics optimization problem involves finding the maximum sum of the square of one non-negative number and the cube of the other, with their total being 4. Calculus is applied by taking the derivative of the function representing the sum, setting it to zero to find critical points, and checking the second derivative to ensure a maximum is found. The optimized numbers are x and 4-x, based on the critical point found.
Explanation:
To solve the optimization problem, we need to use calculus to find the maximum value of the sum of the square of one number and the cube of the other, given that the sum of the two numbers is 4. Let's call these numbers x and y, with x + y = 4. We want to maximize S = x^2 + y^3.
Since x + y = 4, we can express y as y = 4 - x. Substituting this into S, we have S = x^2 + (4-x)^3. This becomes a function of one variable.
To find the maximum value, we differentiate S with respect to x, set the derivative equal to zero, and solve for x. We can check the second derivative to ensure it is a maximum. The function S' will have a maximum when the first derivative is zero (S'(x) = 0) and the second derivative is negative (S''(x) < 0).
Therefore, the two non-negative numbers that maximize S are x and 4-x, with x being the value at which S' equals zero with S'' negative.
Determine m angle F by using the figure
Answer:
The measure of angle F is m∠F=130°
Step-by-step explanation:
step 1
Find the measure of angle E
we know that
An isosceles triangle has two equal sides and two equal interior angles
In this problem
DF=EF ----> given problem
so
Triangle DEF is an isosceles triangle
m∠D=m∠E
we have
m∠D=25°
substitute
m∠E=25°
step 2
Find the measure of angle F
we know that
The sum of the measures of the interior angles in a triangle must be equal to 180 degrees
so
m∠D+m∠E+m∠F=180°
substitute the values
25°+25°+m∠F=180°
50°+m∠F=180°
m∠F=180°-50°
m∠F=130°
Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the rest . What is the area planted in corn
Answer:
Corn was planted in 24 sq.ft. of the vegetable garden.
Step-by-step explanation:
Length of garden = 9 ft
width of garden = 8 ft
Hence we will first find the total area of garden.
Total area of garden = length × width = [tex]8 \times 9 = 72ft^2[/tex]
He planted 1/2 of the garden with vegetables.
Hence.
Area of Vegetables garden = [tex]\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2[/tex]
He planted tomatoes in 1/3 of the vegetable garden and corn in the rest
Area in which tomatoes was planted = [tex]\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2[/tex]
Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = [tex]36ft^2-12ft^2=24ft^2[/tex]
Hence Area of vegetable garden in which corn was planted is 24 sq.ft.
County fair charges 1.25 per ticket for rides. Tom bought 25 ride tickets and spent a total of $43.75 total for rides and admission. The price of admission is the same for everyone. Use y to represent total cost and x for the number of tickets.
Define variables
Write linear equation to determine the cost for rides tickets and admission
Answer:
The linear equation is 1.25x + 0.5x = y
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Price of ride ticket at country fair = US$ 1.25
Total spent by Tom for rides and admission= US$ 43.75
Number of ride tickets bought by Tom = 25
Price of admission is the same for everyone
Total cost = y
Number of tickets = x
2. Let's find out the cost of the admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Replacing with real values:
1.25 * 25 + Cost of admission * 25 = 43.75
31.25 + 25 * Cost of admission = 43.75
25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)
25 * Cost of admission = 12.50
Cost of admission = 12.50/25 (Dividing by 25 at both sides)
Cost of admission = 0.50
3. Let's write a linear equation to determine the cost for rides tickets and admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Total cost = y
Number of tickets = x
1.25x + 0.5x = y
if 25% of next month's rent is $174.25 what is the total next month's rent
Answer:
$697
Step-by-step explanation:
25% × 4 = 100%
174.25 × 4 = 697
Answer:
174.25
Step-by-step explanation:
174.25 × 4 = 697
697 × 0.25 = 174.25
Answer: 174.25
Please help I gave extra points please it’s super simple to some of you I just don’t know how to do it :(
Answer:
1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]
2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]
3. The x-intercept of the linear model is [tex]d = x = 12[/tex]
Step-by-step explanation:
Given:
[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]
Where,
[tex]P_{2}[/tex] is the number of phones.
d is the number of days he has worked that week.
This is a linear model type equation.
Can be represented in the slope intercept form which is equal to
[tex]y = mx + c[/tex]
Where,
m = Slope of the line.
c = y-intercept.
Now if we compare the given model by slope intercept formula we get
[tex]m = \frac{-25}{3}\\\\c = 100[/tex]
So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].
and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]
For finding x-intercept put y = 0
Here,[tex]P_{2}(d) = 0[/tex]
[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]
So, the x intercept of the linear model is [tex]d = x = 12[/tex]
Samantha cut 6 3/4 yd of yarn into
3 equal pieces. Explain how she could use mental
math to find the length of each piece.
Answer:
27/12
Step-by-step explanation:
6 3/4=27/4
(27/4)/3
(27/4)(1/3)=27/12
Which of the following is equivalent to 18 -sqrt -25?
[tex]\bf 18-\sqrt{-25}\implies 18-\sqrt{-1\cdot 25}\implies 18-\sqrt{-1}\cdot \sqrt{25}\implies 18-5i[/tex]
Answer: 18-5i
Step-by-step explanation:
Complete the solution of the equation. Find
the value of y when x equals -8.
7x - 2y = -52
Enter the correct answer,
Answer:
y = -2
Step-by-step explanation:
to do this, you have to plug in -8 for x
7(-8) - 2y = -52
-56 - 2y = -52
+56 +56
-2y = 4
/-2 /-2
y = -2
The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .
What is the equation of the circle in standard form?
The equation of the circle in standard form is: (x + 2)² + (y - 1)² = 1
What is the equation of the circle?
The general form of the equation of a circle is:
(x - h)² + (y - k)² = r²
Where;
(h, K) is the coordinate of the center of the circle.
r is radius.
To find the equation of the circle in standard form, we need to determine the center and radius of the circle.
Since the center of the circle lies on the line y = 3x + 1 and is tangent to the x-axis at (-2,0), we can determine that the center of the circle is (-2,1) and the radius is 1.
Therefore, the equation of the circle in standard form is:
(x + 2)² + (y - 1)² = 1
find the answer to this problem 15/16 - -3 / 16
Answer:
The answer would be 18/16 or 1 1/8.
You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
Answer:
The segment area [tex]= 113.09\ unit^2[/tex]
Step-by-step explanation:
Area of the segment = [tex]\frac{(\theta)}{360} \times \pi r^2[/tex],where [tex]\theta[/tex] is the angle.
We can also say that [tex]90\ degrees[/tex] is covered with one segment and we have total [tex]4[/tex] segments (quadrants),so area of the circle divided by [tex]4[/tex] will give us the segement area of the arc.
So area [tex]\frac{\pi r^2 }{4} =\frac{\pi(12)^2}{4} = 113.09\ units^2[/tex]
So the area of the segment [tex]= 113.09 \ units^2[/tex]
The royal fruit company produces two type of fruit drinks. The first type is 70% pure fruit juice , and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 80% pure fruit juice
Answer:
66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.
Step-by-step explanation:
Let
x ----> pints of pure fruit juice at 70%
y ----> pints of pure fruit juice at 95%
we know that
[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation A
Remember that
[tex]70\%=70/100=0.70[/tex]
[tex]95\%=95/100=0.95[/tex]
[tex]80\%=80/100=0.80[/tex]
so
[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.70(110-y)+0.95y=0.80(110)[/tex]
solve for y
[tex]77-0.70y+0.95y=88[/tex]
[tex]0.25y=88-77[/tex]
[tex]0.25y=11[/tex]
[tex]y=44[/tex]
Find the value of x
[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]
therefore
66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.
For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH.
Answer:
Option 4 : 19
Step-by-step explanation:
For trapezoid ABCD : AB = 16 and CD = 28
E and F are midpoints of the legs
So, EF = (AB + CD)/2 = (16+28)/2 = 44/2 = 22
GH be the median of ABFE
So, GH = (AB + EF)/2 = (16+22)/2 = 38/2 = 19
The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters, as shown. What is the area of
the top of the lid?
6 cm
Use the formula for the area of a square, A - 52, where A represents the area and s represents the side length.
12 cm²
24 cm²
36 cm²
72 cm²
Answer:
c.)36
Step-by-step explanation:
Answer:
36 cm
Step-by-step explanation:
The area of a square is length times width. Since it is a square all sides are equal so you multiply 6×6.
Formula: A=s^2 or A=s×s
Quick question what’s 2ab+3b+7b+3a•3a•b+4b-8ab•8ab+5a•5a•b-12ab?
Answer:
14b - 10ab + 34a²b - 64a²b²
Step-by-step explanation:
We have to simplify the expression
2ab + 3b + 7b + 3a × 3a × b + 4b - 8ab × 8ab + 5a × 5a × b - 12ab
= 2ab + 3b + 7b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
{Since (3a × 3a × b) = 9a²b, (8ab × 8ab) = 64a²b² and (5a × 5a × b) = 25a²b}
= 2ab + 10b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
= 14b - 10ab + 34a²b - 64a²b² (Answer)
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply f(x)=1/(x+1)(x+2)
Answer:
x=-1 and x=-2
Step-by-step explanation:
Given
[tex]f(x)=\dfrac{1}{(x+1)(x+2)}[/tex]
This function is undefined when the denominator becomes 0. Find values of x for which the denominator is 0:
[tex](x+1)(x+2)=0\\ \\x+1=0\ \text{or}\ x+2=0\\ \\x=-1\ \text{or}\ x=-2[/tex]
Thus, the lines with equations [tex]x=-1[/tex] and [tex]x=-2[/tex] represent vertical asymptotes (see attached graph)
Answer: -1 and -2
Step-by-step explanation:
Could someone help me please:(
Answer:
Domain: -∞ < x < +∞
Range : 2 ≤ f(x) < +∞
Step-by-step explanation:
See the graph attached to this question.
The two arrow shows the graph of a function y = f(x).
Now, the value of x varies from +∞ to -∞.
So, the domain of the function is -∞ < x < +∞
Again from the graph the range of the function i.e. values of y varies from 2 to +∞ and including 2.
Therefore, the range of the function is 2 ≤ f(x) < +∞ (Answer)
a group of adults plus a child attend a movie tickets cost $9 for adults and $6 for children the total for the movie is $78 write an equation to find the number of adults in the group
How many roots can a quadratic equation have
Answer:
2 roots, 1 root, or no roots
Step-by-step explanation:
There is a maximum of two roots
If the maximum or minimum is on the x-axis there is 1 repeated root
The roots are imaginary if it does not touch the x-axis
Step-by-step explanation:
It all depends on the discriminants sign.
The quadratic equation:
[tex]ax^2+bx+c=0[/tex]
The discriminant:
[tex]\Delta=b^2-4ac[/tex]
If Δ < 0, then the equation has no real solution
If Δ = 0, then the equation has one solution [tex]x=\dfrac{-b}{2a}[/tex]
If Δ > 0, then the equation has two different solution
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
gets brainilist!!!!!!!what is the absoulute value of -4.5 and what is the absoulute value of 1
Answer:
The absolute value of a number is its distance from zero on the number line. For example, -7 is 7 units away from zero, so its absolute value would be 7
|-4|=4
|1|=1
Step-by-step explanation:
the absolute value of - 4.5 = | - 4.5 | = + 4.5
the absolute value of 1 = | 1 | = + 1
Which expression shows 56x+40y−48z written as a product of the greatest common factor and one other factor?
A
8(7x+5y−6z)
B
8(7x+5y+6z)
C
8x(7+5y−6z)
D
4(14x+10y−12z)
The expression 56x+40y−48z can be rewritten as a product of the greatest common factor and one other factor, which is 8(7x+5y−6z). Therefore, the correct answer is A.
Explanation:The expression 56x+40y−48z can be factored by identifying the greatest common factor (GCF). In this case, the GCF of 56, 40, and 48 is 8. Therefore, you divide each term in the expression by the GCF which will give you 7x+5y-6z. Hence, the expression can be rewritten as a product of the GCF and one other factor, which is 8(7x+5y−6z). So, the correct answer is A - 8(7x+5y−6z).
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Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)
y^2 = -12x
y^2 = -3x
y = negative x^2 divided by 12
y = negative x^2 divided by 3
Answer:
From given option , the equation of parabola is y = negative x² divided by 12
Step-by-step explanation:
Given as for parabola :
The focus is at (0 , - 3)
The directrix equation is y = 3
Now, equation of parabola parallel to y-axis is
( x - h )² = 4 p ( y - k )
where focus is ( h , k+p ) and directrix equation is y = k - p
So, from equation
h = 0 and k + p = - 3
And y = k - p i.e k - p = 3
Now solving ( k + p ) + ( k - p ) = - 3 + 3
or, 2 k = 0 ∴ k = 0
Put the value of k , k + p = - 3
So, 0 + p = - 3 ∴ p = - 3
Now equation of parabola with h = 0 , k = 0 , p = - 3
( x - h )² = 4 p ( y - k )
I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )
Or, x² = - 12 y is the equation of parabola
Hence From given option , the equation of parabola is y = negative x² divided by 12 Answer
A computer and printer cost a total of $1028. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
Printer: $257, Computer: $771
Step-by-step explanation:
First you want to make a part to part diagram. It sounds stupid at first but trust me it works, We assume the both have the same amount. Now we draw 3 boxes for printer because it is 3 times as much. Now we have 4 boxes. divide 1028 by 4 and get 257. That is the amount for each box. You now know the printer is 257 dollars. Now multiply that by 3 to find cost of printer. 257x3=771.
Now you know the computer cost 771 dollars. You can check your work by adding them up. Hope this helped!!!!
Printer | []
Computer| [] [] []
write the first five terms of the sequence using the recursive formula shown:
a1=6 an=4/3a n-1
The first five terms of the sequence are:
6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]
Step-by-step explanation:
The recursive formula of the sequence is
[tex]a_{1}=6[/tex] and [tex]a_{n}=\frac{4}{3}*a_{n-1}[/tex]
To find the first five terms do that:
[tex]a_{1}=6[/tex][tex]a_{2}=\frac{4}{3}*a_{1}[/tex][tex]a_{3}=\frac{4}{3}*a_{2}[/tex][tex]a_{4}=\frac{4}{3}*a_{3}[/tex][tex]a_{5}=\frac{4}{3}*a_{4}[/tex]∵ [tex]a_{1}=6[/tex]
∴ [tex]a_{2}=\frac{4}{3}*6[/tex]
∴ [tex]a_{2}=8[/tex]
∵ [tex]a_{2}=8[/tex]
∴ [tex]a_{3}=\frac{4}{3}*8[/tex]
∴ [tex]a_{3}=\frac{32}{3}[/tex]
∵ [tex]a_{3}=\frac{32}{3}[/tex]
∴ [tex]a_{4}=\frac{4}{3}*\frac{32}{3}[/tex]
∴ [tex]a_{4}=\frac{128}{9}[/tex]
∵ [tex]a_{4}=\frac{128}{9}[/tex]
∴ [tex]a_{5}=\frac{4}{3}*\frac{128}{9}[/tex]
∴ [tex]a_{5}=\frac{512}{27}[/tex]
The first five terms of the sequence are:
6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]
Learn more:
You can learn more about sequences in brainly.com/question/1522572
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Using data for the population in the state of Alabama calculate the percent change in population growth to the nearest thousandth place from 2004 to 2005
Answer:Can You please like this I want to rank up
Step-by-step explanation:
Press the Heart
P.S. Please
PLEASE HELP ASAP with questions 12 and 13
Answer:
12. x = 50
13. m∠M = 34°
Step-by-step explanation:
12.
Since the triangles are congruent, the sides' lengths are proportional. We can set up a ratio and solve for x.
Side JG corresponds to Side KM
Side HG corresponds to Side LM
Now, we can set up a ratio, cross multiply, and solve for x. Shown below:
[tex]\frac{35}{70}=\frac{25}{x}\\35x=70*25\\35x=1750\\x=\frac{1750}{35}\\x=50[/tex]
Thus, the value of x is 50
13.
The triangles are similar, so sides are proportional and angles are not related in the same way. Angles are same for both.
We want the value of Angle M, that angle corresponds to Angle G of the left triangle.
It is given that Angle G = 34, so Angle M would be the same degree measure as well.
Hence,
m∠M = 34°
what the range set of blank means
Answer:
The range of a set of data is the difference between the highest and lowest values in the set
Step-by-step explanation:
Answer:
point blank range is the range at which you don’t need to aim high or low to hit your aiming point. Maximum Point Blank Range (MPBR) is simply the farthest end of that distance.
Step-by-step explanation:
Leila writes 6 pages per day starting on Sunday. She wants to know how many pages she will write by the end of the day on Saturday. Write a multiplication equation to represent the problem.
Answer: 42 pages
Step-by-step explanation: 6 pages x 7 days= 42 pages
At a local fitness center, members pay a $12 membership fee and $2 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Final answer:
The costs for members and nonmembers of a local fitness center will be the same after attending 6 aerobics classes. Members have an initial $12 membership fee plus $2 per class, while nonmembers pay $4 per class.
Explanation:
To find the number of aerobics classes for which the cost for members and nonmembers will be the same, we need to set up an equation that compares the two cost structures. For members, the cost is a $12 membership fee plus $2 per class, which we can express as Cm = 12 + 2n, where Cm is the cost for members and n is the number of classes. For nonmembers, the cost is $4 per class, so we can express that as Cnm = 4n, where Cnm is the cost for nonmembers.To find the number of classes where costs are the same, we set Cm equal to Cnm:
Subtract 2n from both sides: 12 = 2n
Divide both sides by 2: n = 6
Therefore, the costs for members and nonmembers will be the same when they attend 6 aerobics classes.
The quotient of 5 times a number and 2
Answer:
Let x be the number
5 times a number:
5x
The quotient of the number and 2.
5x / 2
Final answer:
The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.
Explanation:
The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.