Answers
Answer:
Surface area = 850 cm²
Volume = 1000 cm³
Step-by-step explanation:
Applying,
A = h(a+b+c+d)................ Equation 1
Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.
From the diagram in the question,
Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm
Substitute these values into equation 1
A = 25(6+14+7+7)
A = 25(34)
A = 850 cm²
From the volume,
V = A'h...................... Equation 2
Where A' = Area of the base.
From the diagram,
A' = 1/2(6+14)4
A' = 40 cm²
Therefore,
V = 40×25
V = 1000 cm³
Related Questions
Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0
The answer is 32/3. But how do I get to that answer?
Answers
Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
7. You are mixing some concrete for a home project, and you've calculated according to the
directions that you need six gallons of water for your mix. But your bucket isn't calibrated, so you
don't know how much it holds. On the other hand, you just finished a two-liter bottle of soda. If you
use the bottle to measure your water, how many times will you need to fill it?
Answers
Answer:
11.4 bottles for US gal.
13.6 bottles for Imperial gal.
Step-by-step explanation:
1 US gallon = 3.8 L
6 US Gallons = 6*3.8 L = 22.8 L = 11.4 bottles
1 Imperial gallon = 4.54 L
6 Imperial gallons = 6*4.54 L = 27.24 L = 13.6 bottles.
How do you get total cost from price of $2.75 and qty demanded of 1250
Answers
Answer:
$3437.5
Step-by-step explanation:
Given data
Unit cost= $2.75
qty demanded= 1250
To get to the total, we have to multiply the quantity by the unity cost
=2.75*1250
=$3437.5
Hence the total cost is
$3437.5
what is 72 Times 27 equal
Answers
Answer:
1,944
Step-by-step explanation:
72x27=1,944
Have a wonderful day or night
Answer
1944
Step-by-step explanation:
72*27 = 1944
the image above should clarify how you're actually supposed to do it! couldn't submit this without 20 characters :,)
A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.
Answers
Answer:
The current value of the stamp collection is of $2,191.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A stamp collection is purchased for $1,000.
This means that [tex]P = 1000[/tex]
The rate of return on the stamp collection is 4% per year
This means that [tex]n = 1, r = 0.04[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]
[tex]A(t) = 1000(1.04)^{t}[/tex]
What is the current value of the stamp collection?
This is A(20). So
[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]
The current value of the stamp collection is of $2,191.
Answer:
Step-by-step explanation:
y = 1000(1+0.04)^20
y = 1000(1.04)^20
Rounded to the nearest hundredth
y = 1000(2.19)
y = $2190
This is for my brother’s test
What are the measures of L1 and L2? Show your work or explain your answers.
Answers
Answer:
angle 2 is 75°osjdiajsjoasnndosnsnd
76 is what percent of 79
Answers
Answer:
79
100
0.79%
76
100
0.76%
PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!
Answers
Answer:
2, 3, 4, 7, 8, 10 I hope
Answers
Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent=================================================
Explanations:
As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).---------------
Acronyms
SSS = side side side
SAS = side angle side
ASA = angle side angle
AAS = angle angle side
If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?
Answers
Answer:
The correct answer is - 178.
Step-by-step explanation:
The standard deviation is a measure of the amount of dispersion in a set of values.
Given:
Mean of a normal distribution (m) = 154
Standard deviation (s) = 15
z-score = 1.6
Solution:
To find: value (x) that has a z-score of 1.6
z-score is given by = x-u/15
1.6*15 = x-154
=> 154+24 = x
x = 178
If you know two corresponding sides of two triangles and you know that the corresponding angles are equal, how can you find out if they are similar triangles? a. the other angles are proportional c. ratios of the sides will be equal b. the vertical angles will be congruent d. ratio of the sides will not be equal Please select the best answer from the choices provided A
Answers
Answer:
I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using
-SSS (side-side-side) which would tell you if all three corresponding sides are congruent
-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent
-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent
-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles
Jill calls a plumber to her house to fix the leaking faucets . The plumber charges a one-time fee of $50 plus an additional $35 per hour of labor. What are the independent and dependent variables
Answers
Answer:
independent=$50
dependent=$35X
Step-by-step explanation:
50 is the independent variable because it doesn't change.
35X is the dependent variable because it does change.
In this scenario, the independent variable is the number of hours of labor and dependent variable is the total cost.
The independent variable is the number of hours. It is the variable that we can control or change.
The dependent variable is the total cost charged by the plumber.
It depends on the number of hours of labor and is determined by the plumber's fee structure, which includes a one-time fee of $50 plus $35 per hour of labor.
The total cost is calculated based on the number of hours of labor, making it the dependent variable in this situation.
Learn more about Independent variable here:
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the points -6/5 and -5/6 will line in which quadrant
Answers
A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.
Answer: 3rd quadrant
solve the following function 3x^{2x-7}=9.
Answers
Answer:
3x-2x+7=-9
We simplify the equation to the form, which is simple to understand
3x-2x+7=-9
We move all terms containing x to the left and all other terms to the right.
+3x-2x=-9-7
We simplify left and right side of the equation.
+1x=-16
We divide both sides of the equation by 1 to get x.
x=-16
I hope this helps you
100° - y А (x+2) units Match the values based on parallelogram ABCD, shown in the figure. length of BC value of y mZDAB value of I 56 4 44 2
Answers
Answer:
BC = 4 units
Value fo y = 44
∠DAB = 56°
Value of x = 2
Step-by-step explanation:
100 - y = 12 + y (opposite angles of parallelogram are equal)
2y = 88
y = 44
Similarly,
6-x = x+2 (opposite sides of parallelogram are equal)
2x = 4
x = 2
Which shows the following expression after the negative exponents have been eliminated?
Answers
Step-by-step explanation:
The given expression is :
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}[/tex]
We need to simplify the above expression.
a³ is in numerator and a is in denominator. It gts cancelled.
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}=\dfrac{a\times a\times a\times b\times b\times b\times b}{a\times b \times b}\\\\=\dfrac{a^2\times b^{-2}\times b^4}{1}\\\\=\dfrac{a^2}{b^{-2}}[/tex]
Hence, this is the required solution.
What is the period of the graph of y = 5 sin (πx) + 4?
Answers
Answer:
I think it’s 2 hope my answer was good have a nice day as well
Step-by-step explanation:
The period of the given function y = 5 sin (πx) + 4 is π.
We have given that,
y = 5 sin (πx) + 4
We have to determine the period
What is the period?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π.
Therefore the period of the given function is π.
To learn more about the period visit:
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If a product normal retails for $40, and a customer has a coupon for 15% off, what will the discounted price of the product be?
Answers
Answer:
$34
Step-by-step explanation:
price of the product = $40
coupon = 15% off
discount price = 15% of price of a product
=15/100 * $40
=$600/100
=$6
New price of the product = original price - discount
=$40 - $6
=$34
Look at the illustration.
What is WX?
Answers
Answer:
O 0.5 units
Step-by-step explanation:
so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W'X' is:
W'X' = 3 units *(1/6) = 0.5 units
show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1
Answers
Answer:
y³ + x³ = 1
First, differentiate the first time, term by term:
[tex]{3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}[/tex]
↑ we'll substitute this later (4th step onwards)
Differentiate the second time:
[tex]3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\[/tex]
[tex]3y^{2}.\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x}{y^{5}}[/tex]
if marvin bought 490 soda cans and candy bars, where the ratio is 3:4, respectively, how many of each did marvin buy?
Answers
9514 1404 393
Answer:
210 soda cans280 candy barsStep-by-step explanation:
The 3+4 = 7 ratio units represent the total of 490 snacks, so each ratio unit represents 490/7 = 70 snacks.
The number of soda cans is 3·70 = 210.
The number of candy bars is 4·70 = 280.
Marvin bought 210 soda cans and 280 candy bars.
what number must you add to complete the square? x^2+24x=50
Answers
Answer:
144
Step-by-step explanation:
Divide the b term which is 24 by 2
Gives you 12, then square it.
that's 144
formula for completing squares is [tex](b/2)^{2}[/tex]
I got 7 to go :( help plz
Answers
Answer:
I think the second one is the answer ; 2√b
Find the value of x and show work
Answers
Answer:
20
Step-by-step explanation:
Differentiate the function. y = (2x - 5)^2 (5 - x)?
Answers
Answer:
[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x)
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor: [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4: [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative: [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x): [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms: [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor: [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
WILL MARK YOU IF YOU ANSWER SO PLEASE HELP
Answers
Answer:
x= 83
first take vertical opposite angle then take corresponding angles then you're done
Answer:
x value is 83 degree
because they both are alternate exterior angle
What are the coordinates of the vertices of the triangle under the translation (x, y) -> (x + 2, y + 3)?
(−4, 5), (3, 4), (0, 0)
(6, −5), (5, 2), (1, −1)
(5, −4). (4, 3), (−1, 2)
(−5, 6), (2, 5), (−1, 1)
Answers
9514 1404 393
Answer:
(d) (−5, 6), (2, 5), (−1, 1)
Step-by-step explanation:
No answer choices have any points in common, so we only need to find one translated point to determine the correct answer choice.
For the point on the y-axis, (0, 2), the translation is ...
(x, y) ⇒ (x +2, y+3)
(0, 2) ⇒ (0 +2, 2 +3) = (2, 5) . . . . matches choice D
The volume of a cone with a diameter of 9 and a height of 120
Answers
Answer: 15268.1403 unit^3 (unit: cm,m,mm)
Step-by-step explanation:
volume of a cone= 1/2*pi*r^2*h
r= radius (unit: cm,m,mm)
h= perpendicular height (unit: cm,m,mm)
volume= 1/2*pi* (9)^2* 120 = 15268.1403 unit^3
You deposit $10,000 in an account that pays 4.5% interest compounded quarterly. Find the future value after one year.
Answers
Answer:
11800
Step-by-step explanation:
4.5%=0.045
0.045x10,000=450
450x4(quarterly)=1800
10,000+1800= 11800
Answer:
After 1 year, $10,457.65
Step-by-step explanation:
P = $ 10, 000
r = 4.5% = 0.045
T = 1 year
n = 4 ( compounded quarterly )
[tex]A = P( 1 + \frac{r}{n})^{nt}[/tex]
[tex]= 10000( 1 + \frac{0.045}{4})^{4 \times 1}\\\\=10000 \times 1.01125^{4}\\\\= 10000 \times 1.04576508633\\\\= 10457.6508633\\\\= \$ 10, 457.65[/tex]
Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answers
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
What is 5^-3?
Please I really need someone to explain to me what do you do when there is a negative sign in the exponent. Thank you :)
Answers
You take out the negative and do the regular equation but turn it into the fraction with one as the numerator and the solution of the exponent as the denominator.
Answer: 1/125 or 0.008 (simplify 1.125 or should I do it?)
Step-by-step explanation:
Well, when there is a negative sign in the exponent you only move the negative exponents. Moving only negative exponents is recommended because using this rule, you multiply two exponents with the same base and add their powers.
