2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.Let each side of he square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
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I need help with this question please
Answer:
x=-4.5 x=-0.5
y=-1
vertex=-2
The concession stand are the football games are 288 customers. Those customers, about 77% bought a hot dog. About how many customers buy a hotdog?
The length of a base of a rectangular prism is 12 dm and the width is 5 dm. What should be the height of the rectangular prism be so that it's volume is smaller than the volume of a cube with a side of 9 dm? (for 30 points) will give you brainlyiest or smthing title
Answer:
Must be less than 12.15 dm
Step-by-step explanation:
How do you proof that sqrt(2) is irrational?
I tried this,
p/q = sqrt(2)
p^2/q^2=2
p^2=2q^2
let p = q * sqrt(2) , (equation from top one)
(q*sqrt(2))^2=2q^2
2q^2=2q^2,
q=q
Is anything wrong or does this also prove that sqrt(2) is irrational, if so how?
Assume √2 is rational, so
√2 = p/q
for some relatively prime integers p,q - meaning we can't reduce p/q any further - and q ≠ 0.
Then
p = √2 q
and squaring both sides gives
p² = 2q²
This tells us that p² is even, so 2 divides p². But if 2 divides p², it must also divide p, since p is a square number. So p = 2r for some integer r, and we have
(2r)² = 2q²
4r² = 2q²
2r² = q²
We're in the same situation as before - 2 divides q², so 2 divides q. Both p and q are thus divisible by 2, but this contradicts our assumption that p and q are relatively prime, which means √2 cannot be expressed as a rational number p/q. Therefore √2 is irrational.
What you've written in your proof is technically correct, but it doesn't help in the irrationality proof.
is 15 feet above sea level negative or positive or a zero
Answer:
Positive
Step-by-step explanation:
Below sea level would be negative and at sea level would be zero.
PLEASE HELP IM BEGGING
Answer:
y= 3/2 x + -4
Step-by-step explanation:
-4 Is the y intercept (the vertical axis)
the 3/2 is the rise over run of the line (how many up over how many across). It's positive because of the slope up to the right.
Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are ✔ –1, 1, 2 . Determine the end behavior of f(x).
Answer:
1, -1 and 2
Step-by-step explanation:
The zeros of the given polynomial function are 1, -1 and 2
Given the polynomial function
First, we need to assume a value of x to check if it will give us zero after substituting:
Assuming x = 1
Since f(1) =0, hence x - 1 is a factor
Dividing x - 1 by the given polynomial function, we will have:
Equating the result to zero
x + 1 = 0 and x - 2 = 0
x = -1 and 2
Hence the zeros of the given polynomial function are 1, -1 and 2
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the first one please help!!
The y-intercept of f(x) is equal to the y-intercept of g(x).
Y-intercept explained ?the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.
How can I find the y-intercept?Finding the value of y at x=0 will help you locate the y-intercept on a graph. The graph's intersection with the y-axis occurs here.
What is the slope's y-intercept?When the slope of the line being studied is known, and the provided point is also the y - intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B is used in the equation to indicate the y value of the y intercept point.
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3. Sandra signed up for Workout Jazz during the
spring special. Which equation represents
the proportional relationship?
The proportional relationship that models this situation is given by:
y = 16.99x, 0 ≤ x ≤ 12.
What is a direct proportional relationship?In a direct proportional relationship, the output variable y is found as the multiplication as the multiplication of the constant k by the input variable x, according to the following rule:
y = kx
In the context of this problem, the input variable and the output variable are given as follows:
x: number of months.y: total cost of the plan during x months.The monthly cost for the first 12 months is of $16.99, hence the constant is given as follows:
k = 16.99.
Considering the given domain, the relationship is modeled by the following equation:
y = 16.99x, 0 ≤ x ≤ 12.
What is the missing information?The missing information is that for the first 12 months, the monthly cost of the plan is of $16.99.
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Which function produces a range of {−11,−5,1,4,10} given a domain of {−2,0,1,3,5}?
theres a pic to help u understand more
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Plug domain into each function and see if it matches any values in the range.
Solve this problem!!! PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1.264×10^-5
Step-by-step explanation:
If you are allowed to use a calculator, it will totally do this question for you. Check mode for Sci Not or use the ^ or EE button.
If no calculator allowed, factor out the 10^-6 and add the numbers. Change back to Scientific Notation and fix the first number. It has to have one digit to the left of the decimal. Adjust the exponent to account for changing 12.64 to 1.264 See image.
For a project in her Geometry class, Mila uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.45 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.2 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The goalpost is 15.13 meters tall which is labeled as X in the figure which has been attached below.
She walks 13.45 meters away from the goalpost, then places a mirror flat on the ground with an X in the center. She next walks 1.2 meters to the opposite side of the mirror, where she can easily see the top of the goalpost depicted in the X. Her partner determines that the distance between her eyes and the ground is 1.35 meters.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
As per the given information, the figure has been attached below.
Set up the proportional and solve for x
1.2 : 13.45 = 1.35 : x
⇒ 1.2 / 13.45 = 1.35 / x
Cross multiplication, and we get
⇒ 1.2x = 1.35 × 13.45
Divided by 1.2 into both sides of the above equation,
⇒ x = (1.35 × 13.45) / 1.2
⇒ x = 15.13
Therefore, the goalpost is 15.13 meters tall.
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Simple Interest Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?
Given Data:
The initial investment is: P=$100
The total period of investment is: t=3
The annual interest is: 6%.
For the simple interest, the expression to calculate the interest in t years is,
[tex]I=(P\times\frac{r}{100})\times t[/tex]Here r is in percentage.
Substitute known values in the above expression.
[tex]\begin{gathered} I=(100\times\frac{6}{100})\times3 \\ =(6)\times3 \\ =18 \end{gathered}[/tex]Thus, the total intrest for 3 years will be $18.
Please Help me turn vertex form to standard form!!
Answer:
See below
Step-by-step explanation:
y = -(x-1)^2 +4 Expand R side
y = - ( x^2 -2x+1) + 4
y = -x^2 +2x -1 + 4
y = -x^2 + 2x + 3 a = -1 b = 2 c = 3
Surface Area from a Net
He used 647.75 square meters of wrapping paper to wrap the gift.
According to the question,
We have the following information:
We have a figure made of 2 same triangles and 3 rectangles with different measurements.
Area of triangle = 1/2 * base*height
Area of triangle = (1*7*14)/2
Area of triangle = 49 [tex]m^{2}[/tex]
Now, the area of another same triangle will also be 49 [tex]m^{2}[/tex].
Now, we have:
Area of upper rectangle = length*breadth
Area of upper rectangle = 15*14
Area of upper rectangle = 210 [tex]m^{2}[/tex]
Area of middle rectangle = length*breadth
Area of middle rectangle = 15*7
Area of middle rectangle = 105 [tex]m^{2}[/tex]
Area of lower rectangle = length*breadth
Area of lower rectangle = 15.65*15
Area of lower rectangle = 234.75 [tex]m^{2}[/tex]
Now, the area of the wrapping paper will be the sum of all of these areas.
Area of paper = Area of 2 triangles + area of upper rectangle + area of middle rectangle + area of lower rectangle
Area of paper = 49+49+210+105+234.75
Area of paper = 647.75 [tex]m^{2}[/tex]
Hence, the area of wrapping paper is 647.75 [tex]m^{2}[/tex].
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PLEASE HELP. Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. 1. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. 2. Describe how you would graph this line using the slope-intercept method. Be sure to show all your work. 3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to show all your work. 4. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. 5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
They are similar because they have the same slope the equation is
y = -2/3x + 531
What is in slope-intercept form?
Given a line's slope and the intercept it makes with the y-axis, one of the mathematical forms used to determine a straight line's equation is called the slope intercept form. The slope intercept form is expressed as y = mx + b, where m is the slope of the straight line and b is the y-intercept.changing 2x+3y=1470 to slope intercept form is solving for y
minus 2x both sides and divide by 3
y = -2/3x + 490
the slope is -2/3
the y intercept is y=490 or the point (0,490)
to graph it, I would start at the origin and go up 490 units on the y axis and put a point there
then go -2 units up (2 down) and 3 to the right and put a point there
then connect the 2 points with a line
in function notation, replace y with f(x) to get
y = -2/3x + 490
graph below
intercepts labeled
2x+3y=1593
they are similar because they have the same slope
the equation is y = -2/3x + 531
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graph this function f(x) = 1/4(x) - 7
Answer:
This is your graph to the following equation f(x) = 1/4(x) - 7
A rectangle is 32ft by 8ft. Stephanie dilated the rectangle and the dimensions of the image were 24ft by 6ft. What was the scale factor used?
Answer:4
Step-by-step explanation:
image dimension = 24 by 6 feet
preimage dimension = 32 by 8 feet
so 24/6 = 32/8 = 4
scale factor = 4
A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where
K is a
non-zero
Constant
1)Find the Set
the value of k
for which the
curve and line have no common point.
(1) state the value for which the line is a
tangent to the Curve and for this case, find the coordinates
of the point where the line
touches the curves
The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).
The value for which the line is a tangent is k = 4.
The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).
What is tangent?
Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.
Given equations in the question:
y = kx² + 1
y = kx
Equating y
kx² + 1 = kx
kx² -kx + 1 = 0
This is Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
D = b²-4ac is called discriminant.
and we know that,
D >0 roots are real and distinct
D =0 roots are real and equal
D < 0 roots are imaginary ( not real ) and different
For no common solution D < 0
For tangent D = 0
so,
kx² -kx + 1 = 0
D = (-k)² - 4k = k² - 4k = k(k - 4)
k(k - 4) < 0
if 0 < k < 4
Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).
for tangent
k(k - 4) = 0
k is non zero
Hence k = 4
After putting the value of k, given equations are:
y = 4x² + 1
y = 4x
solving these equations to get value of x and y:
4x² + 1 = 4x
4x² - 4x + 1 = 0
(2x - 1)² = 0
x = 1/2
y = 2
Point of tangency = ( 1/2 , 2)
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A floor plan of an apartment has a rectangular living room. Its length is 10 centimeters and its width is 4 centimeters. The scale of the floor plan diagram is 2 centimeters for every 1 meter. What is the actual area of the apartment's living room?
The actual area of the apartment's living room is 10 [tex]m^{2}[/tex]
Given
Room is in the shape of a rectangle
Length of the room (L)= 10 cm
Width of the room (W) = 4 cm
Also the scale of floor plan is 2 cm for every 1 meter
Initially the are of the living room = area of rectangle
Area of the rectangle = length × width
= 10 × 40
= 40 [tex]cm^{2}[/tex]
To find actual floor area we need to scale the dimensions
Since 2cm = 1 m
10cm = 5m and 4 cm = 2m
Now calculating the actual area
Area = length × width
= 5×2
=10 [tex]m^{2}[/tex]
Hence the actual area of the living room is 10 [tex]m^{2}[/tex]
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The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers
The number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
What is an integer ?
Integer is the collection of whole numbers and negative numbers. It does not include the fractional part.
It is given that square root of a decimal number is 9.2371 and we have to find out that the number lies between which 2 integers.
We know that the integer 9 is less than 9.2371 , so the square of 9 will be :
9² = 81
And
The square of next integer 10 is equal to 100.
The square of 9.2371 will be equal to :
= (9.2371)²
= 85.32
So , the number is 85.32 and it lies between 2 integers which are 81 and 100.
Therefore , the number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
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x³-10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working out
The value of x is approximately 5.4 when x^3 -10x = 100
How to solve the equation?
The equation is given as:
x^3 -10x = 100
Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100
After several attempts, we have:
x = 5.4 (approximately)
Substitute 5.4 for x in x^3 -10x = 100
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100This means that x is approximately 5.4 when x^3 -10x = 100
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Something's Strange about this little problem..
99 + 2 = ?
Answer:
the answer is 101 !!!
There's isn't nothing strange your just over thinking it!
MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO
The percentage of students that use other means to travel school is 24%
What is method for finding percentage?Percentage is the ratio of the number for which you want to find percentage to the total number with which you want to compare or out of and multiply this ratio with 100.
percentage = (part / whole) ×100
Given that a school has 825 total students.
Percentage of students travelling by car = 20%
Percentage of students travelling by bus = 48%
Percentage of students travelling by bicycle = 8%
Number of students travelling by car = 20% of 825 = (20/100)×825 = 165
Number of students travelling by bus = 48% of 825
= (48/100)×825 = 396
Number of students travelling by bus = 8% of 825 = (8/100)×825 = 66
Number of students travelling by other means = 825-165-396-66 = 198
Therefore, the Percentage of students travelling by other means = (198/825) ×100 = 24%
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Solve for s.
19.1 = s − –7.3
s =
what congruence short cut do I use
By ASA or SAS the triangles can be proves congruent.
What is Congruence of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.
As, from the given figure we can find some equal parts.
First we have two triangles named KOE and LOB
Now, in both triangles
EO = OB ( given)
<KOE =< LOB (Vertically opposite angle)
Now, we have one side and one angle congruent.
There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.
So, either KO = OL or
<LBO = <OKE.
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How much do 6 dresses cost if 2 dresses cost $44?
What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.
the answer in scientific notation rounding to 2 decimal places is given by 68490.98
What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.
6.849 *(10)^4=6.849* 10000=68490
2.329*(10)^-2= 0.02329
according to the question
6.849 times ten to the fourth power minus 2.329 times ten to the negative second power
therefore 68490-0.02329
=68489.9767
round to 2 decimal
the answer in scientific notation rounding to 2 decimal places is given by 68490.98
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In Barangay San Jose, it was found that the population double every 10 years. If in the year 1995, the population was 7824, what will be the population in the year 2015?
The population in the year 2015 is 31296.
In 1995 the population was 7824. It was found that the population gets double every 10 years.
We have to find the population in the year 2015.
Rate = 200% = 2
Time =( 2015 - 1995) / 10
= 20/10
= 2
The population in 2015 = population in 1995 ×[tex]rate^{time}[/tex]
= 7824 × [tex]2^{2}[/tex]
= 7824 × 4
= 31296
Therefore the population in the year 2015 is 31296.
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Help me please someone this is very confusing to me.
Answer:
7
Step-by-step explanation:
slope = rise/run = (difference in y)/(difference in x)
First, we find a difference in y.
Subtract any two values of y.
For example: 35 - 14 = 21
Now we find the corresponding difference in x.
Now subtract the x values corresponding to those y values in the same order.
-1 in x corresponds to 35 in y.
-4 in x corresponds to 14 in y.
That means your difference in x is the subtraction -1 - (-4) = -1 + 4 = 3
The difference in y is 21.
The difference in x is 3.
slope = (difference in y)/(difference in x) = 21/3 = 7
Answer: 7