The lateral surface area of prism is 240cm2, total surface area is 250cm2 of prism , the volume of prism is 100cm2.
What is lateral surface of prism?
The lateral surface area of the right triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h, where a, b and c are the bases of the rectangular faces and h is the common height or the total height of the prism. Also, (a + b + c) is the perimeter of the base (triangle).
What is total surface area of prism?
The total surface area of a right prism is T. S. A. = PH+2A, where P is the base perimeter, A is the base area, and H is the height of the prism.
What is volume of prism?
The formula for the volume of a prism is given by the product of the base and height of the prism. Thus, the volume of a prism can be given as V = B × H where V is the volume, B base area, and H height of the prism.
Given that,
The sides of prism are a=3cm, b= 4cm, c= 5cm
Also given that the height of the prism is h=20cm.
The lateral surface area of prism (LSA) = ah + bh + ch
Lateral surface area of prism = (3)(20)+(4)(20) +(5)(20)
Lateral surface area of prism = 60 + 80 + 100
Lateral surface area of prism = 240 cm2
The Total surface area of prism (TSA) = ph+2a
Total surface area = (LSA) + area of 2 bases
Total surface area = 240 + 2(5)
Total surface area = 250cm2
The volume of prism = base x height
Volume of prism = 5 x 20
Volume of prism = 100cm2.
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The common difference of an arithmetic series is 5 and its tenth term is 98,find its first term
Answer:
First term = 53,
Step-by-step explanation:
a10 = a1 + (10 - 1)d so:
98 = a1 + 9*5
a1 = 98 - 45
= 53,
What is 8-6= for the sum
The value and the summation expression are 2 and -6 + 8
How to determine the value and the summation expression?The expression is given as:
8 - 6
When expressed as a sum, the expression can be rewritten as
-6 + 8
When the expression is evaluated, we have
-6 + 8 = 2
Hence, the value and the summation expression are 2 and -6 + 8
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What's the product of 8 and the sum of a number and 5?
Answer:
8(n+5)=5-n
Step-by-step explanation:
First it says "the product of". A product is formed when you multiply two numbers or expressions. The word "and" is used to divide the two items being multiplied. So "The product of 8 and ---" means that you are multiplying 8 and what ever follows the "and" in the problem, in this case it is "the sum of a number and 5". Since what follows the "and" is another expression, it would be written in parentheses. To this point we have: 8 * ( ?? ), where the ?? replaces the expression.
The words "the sum" means that we are adding two numbers or expressions. As with multiplication, "and" separates the two addends. The first addend in the sum is "a number" - thus we know it isn't another expression and that we need to use a variable, because we aren't told the number. You can choose any letter or figure for your variable name, so lets call it "n". The part following the "and" is the number 5. Putting it together results in (n + 5), which will now be combined with the 8 * in the product, resulting in 8 * (n + 5).
The next thing that comes in your problem is "results in". This means "is equal to" and may also be written "is". Mathematical replacement is "=". Following the "=" is another expression: "the difference between 5 and the number". A difference is subtraction and, again, the "and" represents the break between the two values. The first number is 5 the second number is "the number" meaning the same number as before, so we use the same variable. The "difference between 5 and the number" is written: 5 - n
Putting it all together: "The product of 8 and the sum of a number and 5results in the difference of 5 and the number." Translates into math as:
is this false, i think maybe because you cant factor the right side. am i right
Answer:
its true
Step-by-step explanation:
a3 = 125 solve (Type integers or simplified fractions.)
Answer:
41.666 =~41.67
Step-by-step explanation:
3a=125
a=125÷3
a=41.67
Answer:
41.667
Step-by-step explanation:
3a=125
a= 125/3
a=41.667
NEED NOW what is (-3, 0) (0, -3) in slope-intercept form
Answer:
y=-x-3
Step-by-step explanation:
Write in slope-intercept form, the equation is y=mx+b .
y=−x−3
Simplify completely:
(c^-6 d^4)^1/2
Answer:
d^2/c^3
Step-by-step explanation:
write problem with negative exponent rule
(1/c^6 d^4)^1/2
combine 1/c^6 & d^4
(d^4/c^6)^1/2
use exponent rules to finish simplifying
d^2/c^3
Which graph represents the equation 12 = 3x + 4y? Explain how you know.
Answer:
Graph A
Step-by-step explanation:
First, isolate the y variable and simplify
12 = 3x + 4y
-3x+12=4y
-(3/4)x+3=y
From here, you can tell that your graph has a negative slope and a y-intercept at 3.
Graph A is the only graph with a negative slope.
The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?
The water level after the rainfall is 3.05m
How to calculate the measurement of the water level after the rainfall ?
The water level in colorado river is 2.55m below average
A larger rainfall happened and the water level rose by 0.8m
Therefore the water level after the rainfall can be calculated by adding the previous water level which is 2.55 by the new increase which is 0.8
= 2.55 + 0.8
= 3.05
Hence the water level after the rainfall is 3.05 m
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If (m-1÷m)=3 , find the value of m^3 - 1÷m^3
The value of given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
Given a equation i.e.[tex]\frac{m-1}{m}[/tex]=3 and asked to calculate the value of the equation [tex]m^{3} -\frac{1}{m^{3} }[/tex]
To calculate the value of [tex]m^{3} -\frac{1}{m^{3} }[/tex] , Need to use various operations like subtraction and division)
Given .[tex]\frac{m-1}{m}[/tex]=3
⇒m-1=3m ( cross multiplies 3 and m)
⇒2m=-1( subtraction is used)
⇒m=-[tex]\frac{1}{2}[/tex]( division is used)
Thefore the value of m in the given equation i.e.[tex]\frac{m-1}{m}[/tex]=3 is -[tex]\frac{1}{2}[/tex]
⇒ [tex]m^{3} -\frac{1}{m^{3} }[/tex]
Here the value of m =-[tex]\frac{1}{2}[/tex]
Substituting the value of m in the given equation
⇒[tex](\frac{-1}{2} )^{3}[/tex]-[tex](-2)^{3}[/tex]
⇒[tex]\frac{-1}{8}[/tex]+8(addition is used)
⇒[tex]\frac{64-1}{8}[/tex]
⇒[tex]\frac{63}{8}[/tex]
Therefore, the value of the given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
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Find the derivative of the function using the definition of derivative. g(t) = 3 t
The derivative of the function using the definition of derivative is 3.
The given function is g(t) = 3t.
We have to find the derivative of the function using the definition of derivative.
We know that,
Definition of derivative:-
The derivative of a function is the rate of change of the function's output relative to its input value.
Here,
Input value = t
Output value = g(t)
Given y = g(t), the derivative of g(t), denoted g'(t) (or dg(t)/dt), is defined by the following limit:
[tex]g'(t)= \lim_{h \to 0} \frac{g(t+h)-g(t)}{h}[/tex]
We have the function:-
g(t) = 3t
Hence, according to the data given in the question, we can write,
g'(t) =
[tex]\lim_{h \to 0} \frac{g(t+h)-g(t)}{h} \\\\ \lim_{h \to 0} \frac{3(t+h)-3(t)}{h}\\\\ \lim_{h \to 0} \frac{3t+3h-3t}{h}\\\\ \lim_{h \to 0} \frac{3h}{h}\\\\\lim_{h \to 0} 3[/tex]
g'(t) = 3
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19.6 is 24.5% of what number?
- For 11 points
Answer:
80
Step-by-step explanation:
[tex]\frac{24.5}{100} *x = 19.6\\x = 19.6 *\frac{100}{24.5} \\x = 80[/tex]
19.6 is 24.5% of 80
Answer:
24.5% of 80= 19.6
Step-by-step explanation:
24.5% of what number is equal to 19.6
24.5
____ x = 19.6
100 100
x = 19.6 x ____
24.5
= x =80
HOPE IT HELPS
What does the pair of equations y = 1, z = 8 represent? in other words, describe the set of points (x, y, z) such that y = 1 and z = 8. a plane
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis in the plane.
What is the equation of a line in a plane?The equation of a plane in R has the generic form: ax + by + cz + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.
Given: Equations of the lines:
y = 1z = 8To find: description of the points (x, y, z) in the plane.
Finding:
According to the given conditions, the lines y = 1 and z = 8 describe two lines with constant values of y and z coordinates respectively in the plane.
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis and can have infinitely many values of x in the plane.
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5x - 8x - 7=-3x+5-7 won’t pull an answer to check my answer
Calculus Derivative Question
(a) Differentiate [tex]s(t)[/tex] to get the velocity.
[tex]s(t) = \cos(t^2 - 1)[/tex]
Use the chain rule.
[tex]u = t^2 - 1 \implies \dfrac{du}{dt} = 2t[/tex]
[tex]s(u) = \cos(u) \implies \dfrac{ds}{du} = -\sin(u)[/tex]
[tex]\implies \dfrac{ds}{dt} = \dfrac{ds}{du} \dfrac{du}{dt} = \boxed{-2t\sin(t^2-1)}[/tex]
(b) Evaluate the derivative from (a) at [tex]t=0[/tex].
[tex]\dfrac{ds}{dt}\bigg|_{t=0} = -2\cdot0\cdot\sin(0^2-1) = \boxed{0}[/tex]
(c) The object is stationary when the derivative is zero. This happens for
[tex]-2t \sin(t^2 - 1) = 0[/tex]
[tex]-2t = 0 \text{ or } \sin(t^2 - 1) = 0[/tex]
[tex]t = 0 \text{ or } t^2 - 1 = n\pi[/tex]
(where [tex]n[/tex] is any integer)
[tex]t = 0 \text{ or } t = \pm\sqrt{n\pi + 1}[/tex]
We omit the first case. In the second case, we must have [tex]n\ge0[/tex] for the square root to be defined. Then in the given interval, we have two solutions when [tex]n=\in\{0,1\}[/tex], so the times are
[tex]t_1 = \sqrt{1} = \boxed{1}[/tex]
[tex]t_2 = \boxed{\sqrt{\pi + 1}} \approx 2.035[/tex]
(d) A picture is worth a thousand words. See the attached plot. If you're looking for a verbal description, you can list as many features of the plot as are relevant, such as
• intercepts (solve [tex]s(t)=0[/tex] to find [tex]t[/tex]-intercepts and evaluate [tex]s(0)[/tex] to find the [tex]s[/tex]-intercept)
• intervals where [tex]s(t)[/tex] is increasing or decreasing (first derivative test)
• intervals where [tex]s(t)[/tex] is concave upward or concave downward (second derivative test; at the same time you can determine any local extrema of [tex]s(t)[/tex], which you can see in the plot agrees with the critical points found in (c))
A farmer uses five bushels of strawberries to make a large batch of jam. the jam is poured into 20-ounce jars. to transport the jam to the market for sale, the farmer uses crates that hold 16 jars. if a bushel is equivalent to 64 pints, how many crates will the farmer need for this batch of jam?
Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set? 26, 29, 27, 28, 29, 27, 27, 53, 25, 29
The mean of the data is 30 and the median of the data is 27.5.
What are the mean and median?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. The mean of the data will be calculated by adding all the numbers and dividing it by the quantity of the numbers.
The median of the data generally refers to the middle most value of the series. The median of the data is calculated by arranging the numbers in increasing order and getting the middle value of the numbers.
Given data is 26, 29, 27, 28, 29, 27, 27, 53, 25, 29 arrange all the numbers in increasing order.
25,26,27,27,27,28,29,29,29,53
Mean = Sum of all the numbers / Total numbers
Mean = (25 + 26 + 27 + 27 + 27 + 28 + 29 + 29 + 29 + 53 ) / 10
Mean = 300 / 10
Mean = 30
Median = ( 27 + 28 ) / 2 = 27.5
Therefore, the mean of the data is 30 and the median of the data is 27.5.
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Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because 4+8=12 and 1+8=9 is kareem correct? explain how you know.
No, Kareem is not correct because the ratio of 4:1 can never be equal to the ratio of 12:9.
Here,
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.
Because 4+8=12 and 1+8=9.
We have to find that Kareem is correct or not.
What is a ratio?
Ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Now,
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.
Calculate the ratio as;
12 / 9 = ( 3 x 4 ) / ( 3 x 3 ) = 4/3
So,
12 / 9 = 4 / 3
Hence, Kareem is incorrect because the ratio of 4:1 can never be equal to the ratio of 12:9.
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Write the name of the metric system prefix associated with each mathematical factor. Do not use any hyphens in your answers and do not abbreviate the prefixes. Spelling counts.
The name of the metric system prefix are : 10^-6: micro , 1/100: centi , 0.001: milli, 1000: kilo
In mathematical exponents, prefixes are referred to as the alphabetic names related to the mathematical factors, such as 10⁻⁹: it nano ,10⁻¹²: Pico and so on.In order to identify the prefixes of the metric system, we first convert from factor to exponent form.
such :
10^-6 is micro
1/100 = 0.01x 10^2: centi
0.001 = 1x 10 ^-3 : milli
1000 = 1x 10^3 : kilo
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Write the name of the metric system prefix associated with each mathematical factor. Do not use any hyphens in your answers and do not abbreviate the prefixes. Spelling counts.
10^-6 ______________
1/100 ______________
0.001 _____________
1000 ______________
Find the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4)
The midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinate is expressed as;
M(x, y) = (x₁+x₂/2, y₁+y₋/2 )
Given the coordinate points( -3, 8) and (2, -4)
Substitute
M(x, y) = (-3+2/2, 8-4/2)
M(x, y)= (-1/2, 4/2)
M(x, y) =(-0.5, 2)
Hence the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
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The students in art class have blue cloth that's 60 inches long, glod cloth that is 48 inches long, and white cloth that is 72 inches long. They want to cut all the cloth into pieces of equal lenght for a project.
What is the greatest lenght of the pieces without having any cloth leftover? explain your reasoning.
Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches are greatest lenght of the pieces by greatest common factor.
What does "largest common factor" mean?
A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the largest, we refer to the GCF of 12, 20, and 24 as four.a. As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find GCF(greatest common factor) of 60, 48 and 72.
First we will factor out all three numbers completely
60 = 2 × 2 × 3 × 5
48 = 2 × 2 × 2 × 2 ×3
72 = 2 × 2 × 2 × 3 × 3
The common factors are: 2, 2 and 3
Thus the GCF = 2 × 2 × 3 = 12
So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.
b. For finding the number of pieces for each color cloth, we will just divide the length of each cloth by 12. So
Number of pieces for blue cloth = 60/12 = 5
Number of pieces for gold cloth = 48/12 = 3
Number of pieces for white cloth = 72/12= 6
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what is 3-5b=-32 in algebra
Answer:
b=7
Step-by-step explanation:
3-5b=-32
-5b=-32-3
-5b=-35
Divide both sides by -5
b=7
( I also had trouble with these kind of expressions)
Is the sum of –8 + 3 negative? How do you know?
Answer:
The sum is negative because the number with the greatest value is negative.
Step-by-step explanation:
If the it's the same sign add, if not subtract.
8-3=5
keep the sign of the bigger number.
-5
Hope It Helps
Sorry If I'm Wrong
Answer: Yes
Step-by-step explanation:
The answer is negative. That is because you are adding three to negative 8.
Think about it. 8 is greater than three, right?
-8 + 3 = -5
You are bringing -8 closer to 0:
-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...
Bring -8 three spaces closer to 0. You get -5.
Hope this helps.
Please help! Need answers fast
It took 5 hours to drive to Durham to Birmingham. The average speed was 48mph. What was the distance from Durham to Birmingham?
I need the explanation
Answer:
240 miles
Step-by-step explanation:
Because it took 5 hours going 48 miles per hour, therefore 5 x 48 =240
solve 12n + 7p - 6n = 25p for n
Answer:
n = 3p
Step-by-step explanation:
12n + 7p - 6n = 25p
12n - 6n +7p = 25p
12n - 6n = 25p - 7p
6n = 18p
[tex]n=\frac{18p}{6}[/tex]
n = 3p
A car can be rented for $95 per week plus $0.20 per mile. How many miles can be driven if you have at most $370 to spend for weekly transportation?
Answer:
1375 miles
Step-by-step explanation:
0.20x+95=370
0.20x=275
x=1375
Find all the zeros of the quadratic function.
y=x^2+ 8x + 12
If there is more than one zero, separate them with commas.
If there are no zeros, click on "None".
Answer:
x=-2, -6
Step-by-step explanation:
factor the expression
y=x^2+ 8x + 12
y= (x+2)(x+6)
set the equation equal to 0, since you are finding zeros, or solutions
0=(x+2)(x+6)
split the equation into two parts
0=(x+2) and 0=(x+6)
solve the equations
you should get 2 zeros
x=-2, -6
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
Answer:
Diagonals linse
Step-by-step explanation:
Find the indicated measure(part 3)
I will give brainliest to the right answer with solution
Answer:
VU = 120° , WX = 100°
Step-by-step explanation:
(7)
An inscribed angle is half the measure of its intercepted arc , or
the intercepted arc is twice its inscribed angle, then
arc TV = 2 × 30° = 60°
the diameter is TU then arc TU = 180°
the sum of the arcs in the circle = 360° , so
VU + TV + TU = 360°
VU + 60° + 180° = 360°
VU + 240° = 360° ( subtract 240° from both sides )
VU = 120°
(8)
WY = 2 × 75° = 150°
WX + WY + YX = 360°
WX + 150° + 110° = 360°
WX + 260° = 360° ( subtract 260° from both sides )
WX = 100°