The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
Learn more about the Area:
https://brainly.com/question/1631786
#SPJ1
How much will 1,000.00 amount to in 2 years at 13%2% simple interest
ments
nts
ns
Mai says, "I know how to find the area of a sector or the length of an arc for central angles like 180
degrees or 90 degrees. But I don't know how to do it for central angles that make up more complicated
fractions of the circle."
1. In the diagram, the sector's central angle measures 8 degrees and the circle's radius is r units. Use
the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and
radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded
sector, and the length of the arc defined by the sector.
160%
5 in
The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
How to find a sector area, and arc length?For a sector that has a central angle of θ, and a radius of r;
The sector area, and the arc length are:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] --- sector area
[tex]L = \frac{\theta}{360} * 2\pi r[/tex] ---- arc length
How to find the given sector area, and arc length?Here, the given parameters are:
Central angle, θ = 160
Radius, r = 5 inches
The sector area is
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{160}{360} * \frac{22}{7} * 5^2[/tex]
Evaluate
A = 34.92
The arc length is:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{160}{360} * 2 * \frac{22}{7} * 5[/tex]
L = 13.97
Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
Read more about sector area and arc length at:
https://brainly.com/question/2005046
#SPJ1
Huilan is years 15 younger than Thomas. The sum of their ages is 73 . What is Thomas's age?
thomas age:44
huilan age: 29
Step-by-step explanation:
h = t + 15
t + t + 15 = 73
2t = 73 - 15
2t = 58
t = 29
Another day, another math problem 3
If f(x)=x²+2 and g(x)=x²+5 then the domain of the (fog) (x) is (-∞,∞).
Given the f(x)=x²+2 and g(x)=x²+5
We have to find the domain of the (fog) (x)
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
then,(fog) (x)= (x²+5)²+ 2
=x⁴+25+10x²+2
= x⁴+27+10x²
Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.
So domain (fog) (x)= (-∞,∞).
Learn more about the domain here: https://brainly.com/question/26098895
#SPJ10
What are the zeros of the quadratic function f(x)=6x^2+12x-7?
The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.
What is a quadratic function ?The quadratic function is given as ax² + bx + c = f(x).
For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0
The given function is f(x) = 6x² + 12x – 7
Then the zeroes of the quadratic function will be
[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]
Here a =6 , b = 12 ,c = -7
Therefore the zeroes are
[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]
[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]
Therefore the correct option is A.
To know more about Quadratic Function
brainly.com/question/17376136
#SPJ1
Pls ,see the attachment
How does understanding of 5 x 12 = 60 help to solve for the product of 5
x 120? Explain in words
Answer:
c6
Step-by-step explanation:
justjustcancacanjustadda0totheproduct of5cxwewtogetthesameresultasx1totoandtimes
3) Number: 640,700
the value of 4 in this number is 40,000
Number: 64,070
the value of 4 in this number is 4,000
So, times greater: 40,000 ÷ 4,000 = 10 times greater.
4)
The multiplication, 5 × 12 = 60. So, 5 × 120 = 600.
There is an extra zero at the very last of the result as '120' was multiplied with 5 instead of '12' which does not have zero at last which changes the result.
Similar cases with: 5 × 10 = 50. So, 5 × 100 = 500.
A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in^2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
2x^2 + 36x = 20
2x^2 + 72 = 20
4x^2 + 36x = 20
4x^2 + 72x = 20
a) Write VW as a column vector.
b) Write WV as a column vector.
c) Write a sentence to explain what you notice about
your answers.
W
V
Answer:
vector VW= w - v
vector WV= v - w
Step-by-step explanation:
there are no figures to solve the question so i'll just write the formula..
vector VW= w - v
vector WV= v - w
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s^2. How much time does it take to travel 95.1 m?
The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
From the second equation of motion:
[tex]\rm s = u + \dfrac{1}{2}at^2[/tex]
We have given:
s = 95.1 m
u = 26.8 m/s
a = 4.73 m/s²
[tex]\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2[/tex]
The above equation is a quadratic equation:
After simplification:
[tex]\rm \dfrac{4.73}{2}t^2=68.3[/tex]
[tex]\rm t^2=28.879[/tex]
t = 5.373 seconds ≈ 5.34 seconds
Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
Learn more about quadratic equations here:
brainly.com/question/2263981
#SPJ1
Find the area of the shaded region
O100 m²
O 105 m²
O 75 m²
O 50 m²
5m
10 m.
5m
15 m
How do I solve this problem?
Answer:
y≤x²+4x-1.
Step-by-step explanation:
1) to define the equation of the given graph; it is y=x²+4x-1 (its vertex is (-2;-5));
2) to define inequation accorging to the given graph (the area outside of the parabola means ≤).
How to find x and y
he value of x and y from the given figure are 49/5 and 49/15
Similarity theorem of trianglesFrom the given similar triangles, the following expression is true
21/30 = 7/15 = k
Also, x/21 = y/7 = 7/15
Equate
x/21 = 7/15
15x = 7 * 21
5x = 7 * 7
x = 49/5
Similarly
y/7 = 7/15
15y = 49
y = 49/15
Hence the value of x and y from the given figure are 49/5 and 49/15
Learn more on similar triangle here; https://brainly.com/question/14285697
#SPJ1
Which of the following is the balance for a single $2.520 deposit in an account with an APR of 1.16% that compounds interest monthly and is invested for 37 years? Which of the following is the balance for a single $ 2.520 deposit in an account with an APR of 1.16 % that compounds interest monthly and is invested for 37 years ?
Answer:
The balance after 37 years is $3869.99
Step-by-step explanation:
Given:
Principal (P) = $2,520Rate of Interest (R) = 1.16%Time (t) = 37 yearsCompounds Interest Monthly (n) = 12The Amount (A),
A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex] if compound n times per year
Amount (A) at 37 years,
A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]
A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]
A = ($2,520) (1.00096667 [tex])^{444}[/tex]
A = ($2,520) (1.5357)
A = $3869.9944
Learn more about Compounds Interest here: https://brainly.com/question/12325365
Use the grouping method to factor this polynomial completely.
4x³ + 8x²+3x+6
O A. (4x2 + 2)(x+3)
OB. (4x2+2)(x+2)
O C. (4x²+3)(x+3)
D. (4x² + 3)(x + 2)
Answer:
D. [tex](4x^2 + 3)(x + 2)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms and factor each group.
Factor by Grouping[tex]4x^3 + 8x^2 + 3x + 6[/tex][tex](4x^3 + 8x^2) + (3x + 6)[/tex][tex]4x^2(x + 2) + 3(x + 2)[/tex]Now we can combine the like factors:
[tex](4x^2 + 3)(x + 2)[/tex]The answer is Option D.
Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
3
Answer:
74 mStep-by-step explanation:
Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
to find the side, having the area, you need to use the inverse formula Area = W * L
so
L = A: W
L = 37 : 5 = 7.4 m
If the area of the shed is 37 m²,width of the shed is 5 m as a result the length of the shed will be 7.4 m.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that, the area of the shed is 37 m². The width of the shed is 5 m.
Since the shed is rectangular. The length of width is found as,
Area = length × width
A = l × w
l=A/w
l=37/5
l=7.4 m
Thus, if the area of the shed is 37 m², the width of the shed is 5 m as a result the length of the shed will be 7.4 m.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ2
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Answer: 2.7545
The question was a little off, but I can understand enough
Step-by-step explanation:
Grade Grade Point(x) Course Credit(y) Product(xy)
A 4 3 12
B 3 4 12
B 3 4 12
B 3 4 12
C 2 2 4
D 1 3 3
Total 20 55
This means, the GPA of the student is :
[tex]GPA=\frac{55}{20}[/tex]
[tex]2.75[/tex]
Prove that the function
Answer:
See proof below
Step-by-step explanation:
Important points
understanding what it means to be "onto"the nature of a quadratic functionfinding a value that isn't in the rangeOnto
For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.
However, the co-domain here is suggested to be [tex]\mathbb R[/tex], whereas the range of f is not [tex]\mathbb R[/tex] (proof below).
Proof (contradiction)
Suppose that f is onto [tex]\mathbb R[/tex].
Consider the output 7 (a specific element of [tex]\mathbb R[/tex]).
Since f is onto [tex]\mathbb R[/tex], there must exist some input from the domain [tex]\mathbb R[/tex], "p", such that f(p) = 7.
Substitute and solve to find values for "p".
[tex]f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2[/tex]
Next, apply the square root property:
[tex]\pm \sqrt{-1} =\sqrt{p^2}[/tex]
By definition, [tex]\sqrt{-1} =i[/tex], so
[tex]i=p \text{ or } -i =p[/tex]
By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots. Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.
However, neither [tex]i[/tex] nor [tex]-i[/tex] are in [tex]\mathbb R[/tex], so there are zero values of p in [tex]\mathbb R[/tex] for which f(p)= 7, which is a contradiction.
Therefore, the contradiction supposition must be false, proving that f is not onto [tex]\mathbb R[/tex]
A woman bought some large frames for $10 each and some small frames for $4 each at a closeout sale. If she bought 22 frames for $106, find how many of each type she bought.
Answer:
19 small frames and 3 large frames
Step-by-step explanation:
follows the steps in the attached
Megan bought 3 tickets to the ballet for $57.50. How much would it cost for her to buy 15 tickets?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
The scatter plot shows a correlation between the years and the rainfall in centimeters in Tennessee.
The line of regression models that correlation.
Enter a number to complete each statement.
please help
Answer:
7
4
Step-by-step explanation:
The actual values are shown on the given graph as blue points.
The line of regression is shown on the given graph as the red line.
From inspection of the graph, in the year 2000 the actual rainfall was 43 cm, shown by point (2000, 43). It appears that the regression line is at y = 50 when x is the year 2000.
⇒ Difference = 50 - 43 = 7 cm
In 2000, the actual rainfall was 7 centimeters below what the model predicts.
From inspection of the graph, in the year 2003 the actual rainfall was 44 cm, shown by point (2003, 40). It appears that the regression line is at y = 40 when x is the year 2003.
⇒ Difference = 44 - 40 = 4 cm
In 2003, the actual rainfall was 4 centimeters above what the model predicts.
(a) Solve the following formula for b.
1
A = Zab
6
(b) Evaluate b when A= 18 and a = 5
1
(a) The formula A = ab solved for b is b =
6
(b) Evaluate b when A= 18 and a =
5
b = (Type an integer or a simplified fraction.)
Answer:
J Trump has to be a great day of school and I have a great
Step-by-step explanation:
you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you for your loss of school and I have a great day of school ii
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answer:
the answer is c. the row is chili, the column is no cheese
If you bought a stock last year for a price of $66, and it has gone down 13.9% since then, how much is the stock worth now, to the nearest cent?
The stock worth now, to the nearest cent, is $58.14.
How to find the current worth of stock?The current worth of stock = initial price of stock+increase in the price of stocks
If you bought stock last year for a price of $66, and it has gone down 13.9% since then,
Let X be the worth of stock;
66 × 100 = (13.5% + 100%) × X
6600 = 113.5X
X = 6600/113.5
X = 58.14458
X = $58.14
Hence, The stock worth now, to the nearest cent is $58.14.
Learn more about the stock;
brainly.com/question/16553868
#SPJ1
please help with this question
The two triangles are similar What is the value of x? Enter your answer in the box x =
Answ x=59
Step-by-step explanation:
Review the graph.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, negative 2), B is (1, negative 6), C is (9, negative 2), D is (9, negative 6), z 1 is (3, negative 4), and z 2 is (negative 4, 1).
Which expression is the result of subtracting (z2 – 3i) from (z1 + 2)?
A
B
C
D
[tex]z_{2}-3i=(-4+i)-3i=-4-2i\\\\z_{1}+2=(3-4i)+2=5-4i\\\\(z_{1}+2)-(z_{2}-3i)=(5-4i)-(-4-2i)=9-4i+4+2i=9-2i[/tex]
which corresponds with point C
The expression which is the result of subtracting (z2-3i) from (z1+2) is 9-2i.
Given On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, -2), B is (1, -6), C is (9,- 2), D is (9, - 6), z 1 is (3, - 4), and z 2 is (- 4, 1).
Coordinate plane is a two dimensional plane formed by the intersection of two number lines. One is horizontal line and one is vertical. On horizontal line x values are denoted and on vertical line y values are written. There can be three dimensional plane also.
z2-3i=(-4+i)-3i=-4-2i
z1+2=(3-4i)+2=5-4i
(z1+2)-(z2-3i)=(5-4i)-(-4-2i)
=9-4i+4+2i
=9-2i
Hence for the expression (z1+2)-(z2-3i)=9-2i
Learn more about coordinate plane at https://brainly.com/question/13854649
#SPJ10
Which of these could be the graph of F(x) = log₂ x?
A
A. Graph A
B. Graph B
C. Graph C
D. Graph D
The graph of the function is shown in the attached image.
find the value of x ( fast fast fast)
The value of x is calculated with the help of a similar triangle is 24.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.
Then we have
x / 12 = 32 / 16
x = 24
Then the value of x is 24.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
What is −7.6 − 2(2.2)
Answer:
-12
Step-by-step explanation:
Order of operations:
PEMDAS
First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12
