If the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
Given that the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206.
We are required to find the time after which the rocket will splash down into the ocean and the time after which the ocean will get its peak and the height of the rocket.
The rocket will splash down when the height of the rocket is 0.
-4.9[tex]t^{2}[/tex]+106t+206=0
4.9[tex]t^{2}[/tex]-106t-206=0
t={106±[tex]\sqrt{(106)^{2} -4*4.9*(-206)}[/tex]}/2*4.9
t=(106±[tex]\sqrt{15273.6}[/tex])/9.8
We have to ignore the negative sign because the time is always shown in positive signs.
t=(106+123.59)/9.8
t=229.59/9.8
t=23.43 seconds
Rocket will be at its peak when the slope of the equation is 0.
[tex]h^{I}[/tex](t)=-9.8t+106
-9.8t+106=0
-9.8t=-106
t=-106/-9.8
t=10.82 seconds
To find the height we need to use t=10.82 in the equation.
h(10.82)=[tex]-4.9*(10.82)^{2} +106*10.82+206[/tex]
=-573.65476+1353.92
=779.26524 meters.
Hence if the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
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PLEASE HELP!!
question Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) ?
y−8=2(x+1)
y−1=2(x−8)
y−8=−2(x−1)
y−1=2(x+8)
bought for 15$ sold for 49.50, what is markup percentage?
Answer:
17.65%
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve
What is the x-intercept of the logarithmic function below?
F(x) = log3 x
OA. (3,0)
OB. (1,0)
O C. (-3,0)
O D. (-1,0)
The x-intercept of the function is (-3, 0).
What is x-intercept of a function?
A function's x-intercepts are the point(s) at which its graph crosses the x-axis. The term "x-value" is commonly used to describe the x-intercept.
Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).
The x-intercept of the given function is in option (c).
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please help with this problem if you can.
The measures of angle ACB and angle ABC are 40° and 63° respectively
How to determine the valueFrom the information given, we have that angle DAB is on a straight line
But angle D is 103°
Remember that angles on a straight line sum up to 180°
Then,
103° + Angle A = 180°
Angle A = 180 - 103
Angle A = 77°
It is important to note that sum of angles in a triangle is 180°
angle ACB + angle ABC + angle CAB = 180°
Where;
angle ACB = 3x - 14angle ABC = 3x + 9angle CAB = 77°Substitute into the formula
3x - 14 + 3x + 9 + 77 = 180
collect like terms
3x + 3x = 180 - 72
6x = 108
Make 'x' the subject
x = 108/6
x = 18
But;
Angle ACB = 3x - 14 = 3(18) - 14 = 54 - 14 = 40°
Angle ABC = 3x + 9 = 3(14) + 9 = 54 + 9 = 63°
Thus, the measures of angle ACB and angle ABC are 40° and 63° respectively.
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I really need help asap. What’s the answer?
꧁Helloo!꧂
・❥・・・❥・❥・・❥・・❥
It's a linear function because the formula of the linear function is
Y=mx+b
The h(x) is also considered the y its just another mathematical way of saying it.
the mx which is the slope is -2x
And since there is no B there it's only going to be considered zero
I hope iv been of help to you ^w^
・❥・・❥・・❥・・❥・・❥
Graph the polygon and its image after a dilation centered at C(−2,4) with scale factor k=2/3.
T(7,1), U(4,4), V(1,13), W(−2,4)
The graph of the resulting polygon is shown in the image attached below.
How to dilate a polygon set on Cartesian plane by rigid transformation
In this problem we find a polygon generated by four vertices, whose locations are shown in the picture and whose image must be found by using rigid transformation formulas.
Rigid transformations are transformations such that the form of a geometric loci is conserved, dilations are an example of rigid transformation. The general formula of a dilation is described below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factorIf we know that O(x, y) = (- 2, 4), k = 2 / 3, T(x, y) = (7, 1), U(x, y) = (4, 4), V(x, y) = (1, 13) and W(x, y) = (- 2, 4), then the coordinates of the polygon are now determined:
T'(x, y) = (- 2, 4) + (2 / 3) · [(7, 1) - (- 2, 4)]
T'(x, y) = (- 2, 4) + (2 / 3) · (9, - 3)
T'(x, y) = (- 2, 4) + (6, - 2)
T'(x, y) = (4, 2)
U'(x, y) = (- 2, 4) + (2 / 3) · [(4, 4) - (- 2, 4)]
U'(x, y) = (- 2, 4) + (2 / 3) · (6, 0)
U'(x, y) = (- 2, 4) + (4, 0)
U'(x, y) = (2, 4)
V'(x, y) = (- 2, 4) + (2 / 3) · [(1, 13) - (- 2, 4)]
V'(x, y) = (- 2, 4) + (2 / 3) · (3, 9)
V'(x, y) = (- 2, 4) + (2, 6)
V'(x, y) = (0, 10)
W'(x, y) = (- 2, 4) + (2 / 3) · [(- 2, 4) - (- 2, 4)]
W'(x, y) = (- 2, 4) + (2 / 3) · (0, 0)
W'(x, y) = (- 2, 4) + (0, 0)
W'(x, y) = (- 2, 4)
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Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances: DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600 CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260 DEBIT: Cash Dividends: 1,000 CREDITS: Fees Earned: 75,000 DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800. Total Debits = 135,260; Total Credits = 135,260 You have just determined Net Income for Adventure Travel in the previous question. Now, you must prepare the Statement of Retained Earnings. What is the Retained Earnings Balance as of the Beginning of the Year, January 1, 20XX? Specify whole number.
The Retained Earnings Balance as of the Beginning of the Year, January 1, 20XX is $10,260
What is net income?
The net income is the excess of fees earned by Adventure Travel in the year ended over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense
total expenses=32,800+16,800+3960+4000+2800
total expenses=60,360
fees earned=75,000
net income =fees earned-total expenses
net income=75,000-60,360
net income=$14,640
Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid
Retained earnings=$14,640+$ 10,260-$1,000
Retained earnings=$23,900
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15. Higher Order Thinking Describe the
transformation g of f(x) = |x| as a stretch and
as a compression. Then write two equations
to represent the function. What can you
conclude? Explain.
16
12
8
4
-4-2 0
ty
2
g
4
X
Answer: The Function of g(x) = k[f(x)] = k |x|
Following these rules we can define a vertical stretch or compression of any function.
Step-by-step explanation:
When a function of absolute values, f, is stretched or contracted vertically,
Define f(x) :
f(x) is the value of the function. m is the slope of the line. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane. x is the value of the x-coordinate.
Define g(x) :
The function g (x) is called an inner function and the function f (x) is called an outer function.
When the vertical component of a function f(x) = |x| is increased by a factor k,
g(x) = k[f(x)] = k |x|
where k > 1,
If the same function is compressed vertically by a factor k,
g(x) = k[f(x)] = k |x|
where 0 < k < 1,
Following these rules we can define a vertical stretch or compression of any function.
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I will mark brainliest!!
Answer choices are:
A. a 180 degrees clockwise rotation about the origin
B. a dilation with a scale factor of 6
C. a 90 degrees clockwise rotation about the origin
D. a reflection over the line x=6
Answer:
D
Step-by-step explanation:
My mom is a teacher lol
The graph above is a transformation of the function x^2 a
Write an equation for the function graphed above
g(x) =.
An equation for the function is y= -[tex](x-2)^{2}[/tex]+1.
A symmetry rotation around
x-axis:
(y= f(x) → y= −f(x))
So we have:
y= −[tex]x^{2}[/tex].
A translation to the right of a=2 units:
(y= f(x) a>0 , y= f(x−a))
So, we have:
y=− [tex](x-2)^{2}[/tex]
And finally, a vertical translation of one unit up of the graph of the function, c=1
(y = f(x) → c>0,y = f(x)+c)
That is:
y= -[tex](x-2)^{2}[/tex]+1.
Symmetry (from Ancient Greek: συμμετρία Symmetry "agreement in dimensions, due proportion, arrangement")in everyday language refers to a way of harmonious and beautiful proportion and balance.In mathematics, "symmetry" features a more precise definition, and is typically used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they're intricately related, and hence are discussed together during this article.
Mathematical symmetry could also be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.
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Find the unknown quantity in the following percent problem using the formula R⋅B=A. Round your answer to two decimal places, if necessary. % of 140 is 717.
The unknown quantity is 512.14 percent, that is 512.14% of 140 is 717
According to the question the formula that we have to use is
R*B = A (1)
And we have been given that
x% of 140 = 717 (2)
Thus we have to find the x percent. Comparing equation (1) and (2) we get,
R = x%
B = 140
A = 717
Therefore to find the value of R we will use the formula, R = A/B
Thus, x% = 717/140
x % = 5.12
x = 512.14
Hence the unknown quantity is 512.14 percent that is, 512.14% of 140 is 717
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How much pure acid should be mixed with 3 gallons of a 20% solution in order to get a 40% acid solution?
I know how to set up the problem but I just can't seem to get the right answer. I know the formula is:
x+%1(gallons)=%2(x+gallons)
Help Please!
One gallon of pure acid must be added to get a 40% acid solution.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
Given that
3 gallons of a 40% acid solution means you have (20%)×(3) = 0.6 gallons of acid already.
Let x of gallons of pure acid be added to get a 40% acid solution.
⇒ (0.6 +x)/(3+x) = 40%
⇒ (0.6 +x)/(3+x) = 4/10
Cross multiply, we get
⇒ 10(0.6+x) = 4(3+x)
⇒ 6 + 10x = 12 + 4x
⇒ 10x - 4x = 12 - 6
⇒ 6x = 6
⇒ x = 1
Therefore, one gallon of pure acid must be added to get a 40% acid solution.
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Background information: A worker in the United States and a worker in China can each produce 1,000 pairs of jeans per week. A worker in the United States can produce 50 cell phones in a week, and a worker in China can produce 100 cell phones in a week. Answer the following questions based on this information. Part A: If each country attempted to produce both jeans and cell phones, how many jeans and cell phones could each country produce? What would be the total number of jeans and cell phones produced by the two countries combined? (Show your work.)
The jeans and cell phones produced by US will be 500 and 25 and jeans and cell phones produces by china will be 500 and 50 and the total number of jeans and cell phones is 1000 and 75.
Given that worker in the United States and a worker in China can each produce 1,000 pairs of jeans per week and A worker in the United States can produce 50 cell phones, and a worker in China can produce 100 cell phones in given time.
US: opportunity cost of jeans = 50/1000= 0.05;
1Jeans = 0.05 cell phones
China: opportunity cost of jeans = 100/1000= 0.1
1 jeans= 0.1cell phones
US: opportunity cost of cell phones= 1000/50= 20
1 cell phone= 20 jeans
China: opportunity cost of cell phones = 1000/100= 10
1 cell phone = 10 jeans
Each country will give equal time for producing each product.
Thus, each firm will produce half of its capacity when they combined there production.
So, pair of jeans US will produce in a week 1000/2 = 500 pair jeans a week
Cell phones US will produce in a week 50/2 = 25 cell phones in a week.
Similarly, pair of jeans china will produce in a week 1000/2 = 500 pair jeans a week
& Cell phones china will produce in a week 100/2 = 50 cell phones in a week.
The total number of jeans produced by the two countries combined is
500+500=1000
The total number of cell phones produced by the two countries combined is 25+50=75.
Hence, The jeans and cell phones produced by US will be 500 and 25 and jeans and cell phones produces by china will be 500 and 50 and the total number of jeans and cell phones is 1000 and 75 when United States and a worker in China can each produce 1,000 pairs of jeans per week.
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The blueprint for the Daly's living room has a scale of 2 Inches= 3 Feet . The family wants to use a scale of 1 inch=2 feet. What is the width of the living room on the new blueprint?
The living room on the new blueprint has a width of 2m ft
In this question, we have been given the blueprint for the Daly's living room has a scale of 2 Inches= 3 Feet .
But the family wants to use a scale of 1 inch=2 feet.
We need to find the width of the living room on the new blueprint.
Given the new scale of 1 inch = 2 feet
let m denotes the width of the living room on the blueprint.
To find the width of the living room:
width of the room = blueprint dimensions × scale
so, we get an equation,
width of the room = m × 2 ft
width of the room = 2m
Therefore, the living room on the new blueprint has a width of 2m ft
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W.H. must make a decision about spending $100 to fix his old water heater. It is an electric unit and costs him $125 a year to provide his home with hot water. His other option is to buy a new gas water water for $350. The new heater will save 40% on yearly operating costs. If he sells his house 3 years from now, should he buy the new heater? use break-even point method to justify answer.
W.H. must spend $100 to fix his old water heater to reduce his overall cost
If he spends money to fix his old water heater.
Repair cost of his old water heater = $100
Electricity cost for three years as he sells his house 3 years from now = $125 * 3 = $375
Total cost If he spends money to fix his old water heater = $475
If he spends money to buy new water heater
Cost of purchasing new water heater= $ 350
Reduced yearly electricity bill = $125- 40%of $ 125 = $75
Electricity cost for three years as he sells his house 3 years from now = $75 * 3 = $225
Total cost If he spends money to buy new water heater = $575
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You invested $6000 between two accounts paying 2% and 8% annual interest, respectively. If the total interest earned for the year was $360, how much was invested at each rate?
Based on the amount invested into the two accounts and their interest rates, the amount invested at each rate is:
8% - $4,0002% - $2,000How to find the amount invested at each rate?Assuming the amount invested at 2% is x, then the formula for this amount would be:
0.02x + 0.08 (6,000 - x ) = 360
Solving for x gives:
0.02x + 0.08 (6,000 - x ) = 360
2x + 48,000 - 8x = 36,000
6x = 12,000
x = 12,000 / 6
x = $2,000
The amount invested at 8% is:
= 6,000 - 2,000
= $4,000
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Fractions that best represent 57.036
According to the question, the fraction of a decimal number can be calculated by removing the decimal from the given number and substituting the zeros in the denominator.
The expression for the fraction can be written as:
Required fraction = 57.036 = 57036/1000
Divide the calculated term by four:
Required fraction = 14259/250
Therefore, the given term can be expressed in the best form as 14259/250.
What is fraction?
Fraction is a natural numbers which can be represented as a rational number. And it is divided into two parts, first part is known as numerator and second part is denominator.
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A parallelogram has one angle that measures 18°. What are the measures of the other three angles in the parallelogram? °, °, and °
The angels of parallelogram is 162, 18, 162 and 18.
How to find the measures of the other three angles in the parallelogram?given that A parallelogram has one angle that measures 18° means one angle is 18°
we know that
A special variety of quadrilateral called a parallelogram has two sets of opposite sides that are parallel and equal.
The sum of all the angels of parallelogram is equal to 360°
so, the other means second angle of parallelogram is 18°
Let us assume the 3rd be x.
then the 4th also be x, because the opposite sides are equal.
now sum of all angles is 360°
then x + 18 + x + 18 = 360
2x + 36 = 360
2x = 360 - 36
x = 162.
so the 3rd and 4th angles are 162°.
Hence the angels of parallelogram is 162, 18, 162 and 18.
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The difference two positive integer is 3. If the smaller is added to the square of the larger the sun is 417 find the integers
Answer:
[tex]17[/tex] and [tex]20[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the larger one of the two positive integers ([tex]x > 0[/tex].) The smaller integer would be [tex](x - 3)[/tex]. The square of the larger integer would be [tex]x^{2}[/tex].
The sum of the smaller integer and the square of the larger integer is [tex](x^{2} + (x - 3))[/tex]. If this sum is equal to [tex]417[/tex], then:
[tex]x^{2} + x - 3 = 417[/tex].
[tex]x^{2} + x - 420 = 0[/tex].
Solve this quadratic equation for [tex]x[/tex] through factorization. Since [tex]420 = 21 \times 20[/tex]:
[tex]x^{2} + x - (21 \times 20) = 0[/tex].
[tex]x^{2} + 21\, x - 20\, x + (21)\, (-20) = 0[/tex].
[tex](x + 21)\, (x - 20) = 0[/tex].
Thus, either [tex]x = 20[/tex] or [tex]x = (-21)[/tex] by the Factor Theorem. However, since [tex]x > 0[/tex] (the two integers are both positive,) only [tex]x = 20[/tex] is a valid solution.
Hence, the larger one of the two integers would be [tex]20[/tex]. The smaller one of the two integers would be [tex](x - 3) = (20 - 3) = 17[/tex].
15x +15x =15x x (____+_______) = 15 x 7
Answer:
The y is the underlined slots in the parenthesis
x=1/30
y=315
12. Find the values of x and y in the diagram below.
(4y-18)
(+14)
(6x-11)
81
(x + 5)°
In the linear equation, The value of the x and y are 11/6, -5 and 18/4.
According to the statement
We have to find that the value of the x and the y.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equations are :
(4y - 18)
(6x - 11)
(x + 5)
Now take all equation equal to zero.
Then
4y - 18 = 0
y = 18/4
And then
6x - 11 = 0
x = 11/6
And then
x + 5 = 0
x = -5.
So, In the linear equation, The value of the x and y are 11/6, -5 and 18/4.
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A boy needs to grill 13 pounds of meat for a cookout . Determine the maximum cost per pound that he can afford , if he wants to spend at most $ 80 on this meat purchase ?
Answer:$6.15
Step-by-step explanation: 80 dollars divided by 13 pounds will give us a answer and we need to round down 80/13=6.15
HELP ASAP!!! PLEASE SHOW WORK
A sports equipment manufacturer makes volleyballs for indoor and outdoor play, which bring in $8 and $5 in profit, respectively. Indoor volleyballs take 20 minutes to manufacture while outdoor balls take 10 minutes to manufacture. There are up to 4800 minutes of labor available for the manufacturing process and enough supplies for up to 120 indoor volleyballs and 400 outdoor volleyballs. How many of each type of volleyball should be manufactured to maximize profit?
Suppose the midpoint of line RT is M=(3,0). If R has the coordinates (-1,-4), what are the coordinates of T?
The coordinates of Point T are (7,4)
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
The [tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
where,
([tex]x_m, y_m[/tex]) = coordinates of the midpoint
([tex]x_1, y_1[/tex]) = coordinates of the first point
([tex]x_2, y_2[/tex]) = coordinates of the second point
So, given that we have a line RT and M is the midpoint of the line RT means M divides the line in two equal segments.
Let coordinates of M be ([tex]x_m, y_m[/tex]) and coordinates of point R be ([tex]x_1, y_1[/tex]) and coordinates of point T be ([tex]x_2, y_2[/tex]).
So,
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex](3, 0) = (\frac{-1+x_2}{2}, \frac{-4+y_2}{2})[/tex]
on compairing both sides
[tex]3 = \frac{-1 + x_2}{2} \\x_2 - 1 = 6 \\ x_2 = 7[/tex]
Similarly,
[tex]0 = \frac{-4 + y_2}{2} \\y_2 - 4 = 0 \\ y_2 = 4[/tex]
So, the line RT having midpoint M has coordinates of R is (-1,-4) and
T is = (7,4).
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The coordinates of Point T are (7,4)
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
The [tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]
where,
([tex]x_m,y_m[/tex]) = coordinates of the midpoint
([tex]x_1,y_1[/tex]) = coordinates of the first point
([tex]x_2,y_2[/tex]) = coordinates of the second point
So, given that we have a line RT and M is the midpoint of the line RT means M divides the line in two equal segments.
Let coordinates of M be ([tex]x_m,y_m[/tex]) and coordinates of point R be () and coordinates of point T be ([tex]x_2,y_2[/tex]).
[tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]
[tex](3,0)=(\frac{(-1+x_2)}{2},\frac{(-4+y_2)}{2})\\[/tex]
So, on compairing both sides
[tex]3=\frac{(-4+y_2)}{2}[/tex]
[tex]x_2-1=6\\x_2=7[/tex]
Similarly,
[tex]0=\frac{-4+y_2}{2}\\ y_2-4=0\\\\y_2=4[/tex]
So, the line RT having midpoint M has coordinates of R is (-1,-4) and coordinates of T is = (7,4).
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the speed of sound is approximately 720 miles per hour at sea level. At this rate, how many feet does sound travel in 20 seconds?
Answer:
Step-by-step explanation:
[tex](\frac{720 miles}{1 hour} )(\frac{1 hour}{3600 seconds} ) (\frac{5280 feet}{1 mile} )[/tex]
Units cancel to get answer in feet per seconds.
720 x 1/3600 x 5280 = 1056 feet per seconds
1056 x 20 seconds = 21120 feet
I need an equation that equals 20 like pre algebra
The equation which equals to 20 can be x + y = 20.It can also be f(x) = 5x where x = 4 and many more.
What is a function ?A function behaves like an output or response to an input.The set of all inputs are known as independent variable and the set of all outputs are known as dependent variable.
According to the given question we need an equation that equals to 20.
As the type of equation is not defined we will construct a simple equation known as linear equation in two variables.
So, It can be formed by x + y = 20 this equation has an infinite no. of solutions.Some of them are (1,19), (2,18),.....(19,1).We can also go by negative number and a positive number.
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Mia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.30 plus $4.25 per mile. The total fare was $31.05, not including the tip. How many miles was the taxi ride?
The taxi ride was 7 miles
How to calculate the number of miles ?Mia took a taxi from her house to the airport
The taxi charged a pick up fee of $1.30
They also charged $4.25 per mile
The total fare was $31.05
The number of miles can be calculated as follows
31.05 - 1.30 = 4.25x
29.75= 4.25x
Divide both sides by the coefficient of x which is 4.25
29.75/4.25= 4.25x/4.25
x= 7
Hence the taxi ride was 7 miles
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Evaluate cross multiply
Answer:
5
Step-by-step explanation:
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Aspen has 306306306 green beads and 210210210 silver beads. For every 5\,\text{cm}5cm5, start text, c, m, end text of a belt that Aspen sews, they use 404040 green beads and 242424 silver beads.
After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?
Answer: I have no idea
Step-by-step explanation: can anyone else pls help me???
Answer:
30 cm
Step-by-step explanation:
X₁
From a 24-cm by 24-cm piece of cardboard, square
corners are cut out so that the sides can be folded up
to make a box. Complete parts a through c below.
a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square.
Answer:
V(x) = 4x³ - 96x² + 576xStep-by-step explanation:
Cut out square on each corner has side of x.
When folded up the height of the box becomes same as the side of the cut-out square.
Sides of the base of the box are:
24 - 2x cm as it is folded on both sides.The volume of the box which is the right square prism is:
V = Bh = a²h, where B- base area, a- side of the base, h- height.Substitute the values and find the volume:
V(x) = (24 - 2x)(24 - 2x)x = 4x³ - 96x² + 576x