Answer:
She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume
Step-by-step explanation:
Length = L = 10 inches
Width = W = 6 inches
Suppose x is cut from the 4 corners to make a box.
Dimensions of the Box:
L= 10 - 2x
W = 6 - 2x
H = x
Volume of the Box:
V = (L)(W)(H)
V = (10-2x)(6-2x)(x)
V = 4x³ - 32x² + 60x
For Maximum value:
[tex]\frac{dV}{dx}=0[/tex]
[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]
The values of x found are:
x= 4.12 , x = 1.21
If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.
We discard 4.12. Now x=1.21
So,
If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V
Write in slope-intercept form an equation of the line that passes through the given points.
Answer:
y = x+5
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
m = (7-3)/(2 - -2)
=(7-3)/(2+2)
= 4/4
= 1
The slope intercept form is
y = mx+b
y = x+b
Substitute a point in
7 = 2+b
Subtract 2 from each side
5 =b
y = x+5
Answer:
y = x + 5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (7 - 3) / (2 - (-2))
= 4/4
= 1
Since y = mx + b and m = 1,
y = (1) * x + b
y = x + b
7 = 2 + b
b = 5
Putting b = 5 in y = x + b, we get:
y = x + 5
Hope this helps!
Give me the answers to thissss plssss rnnnn asapppp!!!!
[tex]\\ 1. (3x ^{2} + 2xy + 7) - (6x ^{2} - 4xy + 3) \\ = 3x ^{2} + 2xy + 7 - 6x ^{2} + 4xy - 3 \\ = 3x ^{2} - {6x}^{2} + 2xy + 4xy + 7 - 3 \\ = { - 3x}^{2} + 6xy + 4 \\ 2. \: {9x}^{2} - 2x + 3 - ( {4x}^{2} + 7x - 5) \\ = 9x ^{2} - 2x + 3 - 4x ^{2} - 7x + 5 \\ = {9x}^{2} - {4x}^{2} - 2x - 7x + 3 + 5 \\ = {5x}^{2} - 9x + 8 \\ 3. \: {x}^{2} - 5x + 6 \\ = {x}^{2} - (3 + 2)x + 6 \\ = {x}^{2} - 3x - 2x + 6 \\ = x(x - 3) - 2(x - 3) \\ = (x - 3)(x - 2) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer with step by step explanation
[tex](1)(3 {x}^{2} + 2xy + 7) - (6 {x}^{2} - 4xy + 3) \\ 3 {x}^{2} + 2xy + 7 - 6 {x}^{2} + 4xy - 3 \\ = - 3 {x}^{2} + 6xy + 4[/tex]
[tex](2)9 {x}^{2} - 2x + 3 - (4 {x}^{2} + 7x - 5) \\ 9 {x}^{2} - 2x + 3 - 4 {x}^{2} - 7x + 5 \\ = 5 {x}^{2} - 9x + 8[/tex]
[tex](3) {x}^{2} - 5x + 6 \\ {x}^{2} - 3x - 2x + 6 \\ x(x - 3) - 2(x - 3) \\ (x - 2)(x - 3)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
URGENT!!LAST 3 QUESTION!!!! PLS JUST TAKE A LOOK! EASY BUT I AM DUMB!!!!!! WILL GIVE BRANLIEST!!
1. If a triangle has two angles that measure 57 and 94 degrees, what is the measure of the third angle?
A) 29°
B) 37°
C) 57°
D) 33°
FIND X ( FIRST IMAGE) A) 21.125 B) 7 C) 22.5 What is the measure of angle EGH? SECOND IMAGE A) 26° B) 102° C) 38°
Answer:
1. A
2. B
3. B
Step-by-step explanation:
1. 180+57-94= 29
2. 4x + 7 + 97 + 180 - 17x - 13 = 180
-13x = -91
x = 7
3. 180 - 64-38 = 78
180-78 =. 102
Answer:
A) 29°
B) 7°
B) 102°
Step-by-step explanation:
1. ------------------------
sum of angles= 180°missing angle= 180°-57°-94°= 29°2. ------------------------
4x+7°+97°=17x+13°13x=91°x=7°B) 7°3. ------------------------
EGH=GEH+EFGEGH=64°+38°=102°B) 102°This table gives a few (2, y) pairs of a line in the coordinate plane.
y
-21
-64
- 15
-48
-9
-32
What is the x-intercept of the line?
Answer:
(3,0)
Step-by-step explanation:
I need help I keep getting it wrong
Find the area of the triangle and multiply by the length of the prism.
Area = 1/2 x 8x3 = 12 square yds.
Volume = 12 x 6 = 72 cubic yards.
Plzz give an example
how do you round to the nearest cubic
Answer:
I'm assuming that you mean "Cubic Unit". I will use inches in this example, but this will work with other units as well.
Let's say that the volume of a figure was 124.86 cubic inches.
Rounding to the nearest cubic inch is the same thing as rounding to the nearest whole number.
Locate the 'ones' place:
124.86
Check next door:
124.86
If the next door number is greater than or equal to 5, then we round up. If it's less than 5, we round down.
8 is greater then 5. Therefore, we would round up.
So, 124.86 cubic inches to the nearest cubic inch is 125 in³.
124.86in³ ≈ 125in³
What is (n^2)(n^3)^-2?
simplify the expression (3+8i) - (4+2i) pls show work!
Subtract like terms:
3 -4 = -1
8i - 2i = 6i
The answer is -1+6i
Wyatt wants to study the relationship between the number of siblings that a student has and the student's grade-point
average using a scatterplot. He believes that if the points form a straight line, then there is a relationship between the two
variables. Which scatterplot proves that Wyatt's statement is not always true?
Number of Siblings vs. Grade-Point Average
Answer:
the answer is D
Step-by-step explanation:
Because of how the students grade ar goung not down but up were the y or x
The scatterplot that shows that Wyatt is not always right to say that a straight line shows a relationship between two variables is the graph attached.
When does a straight line show a relationship between variables?The only time a straight line can be said to be proof that two variables are related is when this straight line is diagonal as it shows correlational change.
If the straight line is vertical or horizontal as shown attached, it means that there is no relationship because one variable is not changing when the other one does.
Find out more on straight-line relationships between variables at https://brainly.com/question/1078661.
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(14)+(-11) plz help idk what it is
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
(14)+(-11)=3
Solve 3 (3 - 3x) +4= -5.
Answer:
x=2
Step-by-step explanation:
3 (3 - 3x) +4= -5
Subtract 4 from each side
3 (3 - 3x) +4-4= -5-4
3 (3 - 3x)= -9
Divide by 3
3/3 (3 - 3x) = -9/3
3-3x = -3
Subtract 3 from each side
3-3x-3 = -3-3
-3x = -6
Divide by -3
-3x/-3 = -6/-3
x = 2
Please help me and explain your answer
Thank you!
Answer:
The bottom right
Step-by-step explanation:
switch the x and y and solve for y again
Dymin had a lot of boxes ready for moving. She went out and
bought seven more boxes. A week later her little brother
destroyed half of them. There are now only 22 boxes left.
How many did she start with?
Answer:
37 boxes
Step-by-step explanation:
At first, Dymin had some boxes. Let x be the starting number of boxes.
Then, she bought 7 more boxes. Let y be the new number of boxes that she had.
y = x + 7
Next, her little brother destroyed half of them. It means half of y. So, the number of boxes left is
Number of boxes = y/2
The number of the boxes left is 22 boxes. Then, we can use the equation above.
Number of boxes = 22
y/2 = 22
Substitute y = x + 7 into the equation.
(x + 7)/2 = 22
x + 7 = 44
x = 44 - 7
x = 37
Thus, Dymin has 37 boxes at first.
What figure can be made using the net shown?
Hube
a hexagonal prism
an octagonal prism
a hexagonal pyramid
an octagonal pyramid
Answer:
Correct option: First one -> Hexagonal prism
Step-by-step explanation:
In the figure we have two hexagons and six rectangles. If we fold each part correctly, we can use the two hexagons as horizontal bases of a prism, and the six rectangles would be the sides of the prism (each rectangle connected to one side of lower hexagon and one side of upper hexagon).
So the figure created would be a hexagonal prism.
Correct option: First one.
Answer:
First one
Step-by-step explanation:
Find Sn for the given arithmetic series.
Q1 = -40, d =-7, n=22
Answer:
[tex]S_n =[/tex] -2497
Step-by-step explanation:
We are given an arithmetic series with the following terms:
First term, [tex]Q_1[/tex] = -40
Common difference, d = -7
Number of terms, n = 22
To find out: Sum of n terms, where n is 22
We know that Sum of n terms in an arithmetic series is given as:
[tex]S_n =\dfrac{n}{2} (2Q_1+(n-1)d)[/tex]
Putting the values in the formula:
[tex]S_{22} = \dfrac{22}{2} (2 \times -40+(22-1)\times (-7))\\\Rightarrow S_{22} = 11 \times (-80-147)\\\Rightarrow S_{22} = 11 \times (-227)\\\Rightarrow S_{22} = -2497[/tex]
So, the sum of 22 terms is -2497.
If paint cost $24 and their is a sale for the next month, and the discount is 25% off paint, how much will the paint be after if you buy it during the sale?
4 Student is 20% of ____ students
I need the answer please help me I don't want to fail my math class
Answer:
4 Student is 20% of 20 students
Step-by-step explanation:
if 4 = 20% then 1 = 5% to get a hundred percent then you need to multiply by 20
so 20
4 Student is 20% of 20 students
Answer:
4 Student is 20% of _20___ students
Step-by-step explanation:
20% of x = 4
20% = 0.20
of means multiplication so
0.2 * x = 4
x = 4 / 0.2 = 40 /2 =20
two consecutive negative integers have a product of 110 . what are the integers?
Is 1/2x-4 a function?
Answer:
Yes it is
Step-by-step explanation:
Each x value is represented by exactly one y value.
63 as a product of prime factors
Answer:
3*3 *7
Step-by-step explanation:
63 = 9*7
7 is prime but 9 is not
Break 9 into its factors
= 3*3 *7
All of these are prime
Answer:3x3x7
Step-by-step explanation:
A movie producer held a preview screening of her new movie to find out how the film would be received by viewers of different age groups. The table shows the number of viewers of different age groups who rated the movie as excellent, average, or poor. Note: A rating of "excellent" means the audience liked the movie, while a rating of "poor" means the audience disliked the movie.
Age Excellent Average Poor Marginal Total
16-30 78 33 43 154
30-44 33 41 37 111
45+ 38 23 20 81
MT: 149 97 100 346
Out of the total number of respondents, the percentage of respondents in the 30-44 age group who rated the film as excellent rounded to the nearest hundredth of
Answer:
120%
Step-by-step explanation:
Because the answer is 1 1/5 that converted to a percentage(%) is 120%.
9.53% people between the age 30 to 44 rated the movie as excellent.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
According to the given question.
We have a data of people of different ages who rated the movie as excellent, Average, and poor.
Now,
Total number of people between the age 30 to 44 who rated the movie excellent is 33
And, the total number number of people who watched the movie is 346.
Therefore, the percentage of people who are in between 30 to 44 and rated the movie as excellent is given by
[tex]percentage = \frac{total\ number\ of\ people\ between\ 30\ to\ 44\ and\ rated\ movie\ as\ excellent\ }{total\ number\ of\ people\ who\ watched\ the\ movie}[/tex]
[tex]\implies percentage = \frac{33}{346} =9.53\%[/tex]
Hence, 9.53% people between the age 30 to 44 rated the movie as excellent.
Find out more about percentage here:
https://brainly.com/question/14699403
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Students in a school are asked to pick either football, rugby or tennis to play in their lessons. the number of students who picked football and rugby are in the ratio of 4:3 the number of students who picked rugby and tennis in the ratio of 9:19 57 students picked tennis work out how many student picked football
Answer: 36 Students picked football
Step-by-step explanation: When calculating values by the use of given ratios, it is important to note that the ratio of one value as compared to the other is the same as the actual value compared to the other.
The ratio of students who picked rugby and tennis is given as ratio 9 : 19, which means for every 28 students (that was derived by 9 + 19), 9 would choose rugby and 19 would choose tennis. However, we have been given the total number of students who chose tennis as 57, hence the value 57 would now replace the ratio of 19. However the total number of those who chose rugby is not yet known, so we can write out an equation as shown below;
19/28 = t/x
Where t is the number of tennis players as represented by ratio 19 and x is the total number of both tennis and rugby players as represented by 28.
By cross multiplication we now have
19 * x = 28 * 57
x = (28 * 57)/19
x = 1596/19
x = 84
If a total of 84 students play both rugby and tennis, and 57 of them play only tennis, then the number of rugby players is derived as
r = x - t
r = 84 - 57
r = 27
Having determined that 27 students played rugby, and the ratio of football to rugby players is given as 4 : 3, the relationship can be mathematically represented as follows;
3/7 = r/y
Where r is the total number of rugby players and y is the total number of both football and rugby players
3/7 = 27/y
By cross multiplication you now have
3 * y = 7 * 27
y = (7 * 27)/3
y = 189/3
y = 63
If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;
f = y - r
f = 63 - 27
f = 36
Therefore the number of students who chose football is 36
Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple pies and 7 apple tarts, using a total of 68 apples. Nicole made 5 apple pies and 9 apple tarts, which used 76 apples. How many apples does each dessert require?
Answer:
Each apple pie requires 8 apples, and each apple tart requires 4 apples.
Step-by-step explanation:
We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.
Can anyone help me. Please
Answer:
how can I help?
Step-by-step explanation:
with what?
If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x)
A) 2x-3
B)3x-3
C)4x+1
D)2x-1
Answer:
C.
Step-by-step explanation:
How is the product of 4 and 2 shown using integer tiles? 4 positive tiles and 2 positive tiles. 4 negative tiles and 2 negative tiles. 4 sets of 2 positive tiles. 4 sets of 2 negative tiles. Plz i need help
Answer: 4 sets of 2 positive tiles.
Step-by-step explanation:
We have the product of 4 and 2.
We can represent this as:
4 is equivalent to 4 positive tiles.
if we multiplicate it by 2, then we must have 2 sets of 4 positive tiles.
Another example is using 2 positive tiles to represent the 2.
So when we multiply it by 4, we end with 4 sets of 2 positive tiles.
This is because the order of the factors does not change the product.
Then, from the given options, the correct one is:
4 sets of 2 positive tiles.
Answer:
C on edge 2021
Explanation:
4 groups of 2
[+] [+] [+] [+] [+] [+] [+] [+]
20t- (8t+ 50s + 200)
Answer:
[tex]20t- (8t+ 50s + 200)\\20t- 8t- 50s - 200\\12t-50s-200[/tex]
a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola
Answer:
Step-by-step explanation:1/2 of answer is zero
Answer:
y=1/3x^2+4/3 x -2/3
Step-by-step explanation:
y=1/3x^2+4/3 x -2/3
4x2 + 25y2
factor the following
Answer:
see explanation
Step-by-step explanation:
This polynomial is irreducible, that is cannot be factored.
4x² + 25y² ← is a prime polynomial
Answer:
1, the polynomial itself
Step-by-step explanation:
This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)
What fraction is equivalent to 5%?
A: 50/100
B: 1/20
C: 5/10
D: 1/5
Answer:
1/20
Step-by-step explanation:
5%
Percent means out of 100
5/100
Divide top and bottom by 5
1/20
Answer:
HI THERE,THE ANSWER IS
B
Step-by-step explanation:
[tex]\frac{1}{20} \\[/tex] X 100%=5%
