Answers
Answer:
1008 [tex]cm^2[/tex]
Step-by-step explanation:
Given:
Triangular prism with
Base of triangle = 5 + 9 = 14 cm
Height of triangle = 12 cm
Here, we have 3 faces of the prism as a rectangle, all have width = 20 cm
Lengths of faces = 13cm ,14cm and 15 cm respectively
To find:
Total surface area = ?
Solution:
3 faces are rectangular shape and 2 faces are triangular shape.
[tex]Area\ of\ rectangle = Length \times Width[/tex]
The formula for Total Surface Area of a triangular prism is given as:
[tex]TSA = 2 \times \text{Area of triangular base}+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 2 \times \dfrac{1}{2}\times Base \times Height+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 14 \times 12 + 15 \times 20+ 13 \times 20+ 14 \times 20\\\Rightarrow TSA = 168 + 840\\\Rightarrow TSA = 1008\ cm^2[/tex]
So, the total surface area of the given triangular prism is 1008 [tex]cm^2[/tex].
Related Questions
6
5
WEM
-8-8-54-2-10
2
-2
3
c
B
-5
Which of the four images was formed by a reflection of the letter M?
А
Answers
Answer:
The answer is option A.
Hope this helps you
(04.03 LC
Given the following system of equations:
3x + 5y = 30
X + 3y = 10
Which action creates an equivalent system that will eliminate one variable when they are combined?
Answers
Answer:
multiply second equation by (-3)
new system of equations:
3x + 5y = 30
-3x - 9y = -30
Step-by-step explanation:
x + 3y = 10
multiplied by (-3):
-3x - 9y = -30
combinig:
3x+5y + (-3x-9y) = 3x - 3x + 5y - 9y = -4y
10 + (-30) = -20
so: -4y = -20
Answer:
Multiply the second equation by −3 to get −3x − 9y = −30.
Step-by-step explanation:
Figure ABCD is a rectangle find the value of x
Answers
Answer:
8
Step-by-step explanation:
BD is 32 units.
BE is half of BD
3x - 8 = 32/2
3x - 8 = 16
3x = 16 + 8
3x = 24
3/3x = 24/3
x = 8
Answer:
8Solution,
Diagonals of rectangle bisects each other.so,
2 BE = BD
2( 3x - 8 ) = 32
6x - 16 = 32
Add 16 on both sides
6x - 16 + 16 = 32 + 16
Simplify
6x = 48
divide both sides of equation by 6
6x/6 = 48/6
calculate
X = 8
Hope this helps...
Good luck on your assignment..
Work out the size of angle x: 38° is at the top of the triangle, 101° is at the bottom right of the triangle, work out the size of angle x which is at the bottom left of the triangle.
Answers
Answer: x = 41°
Step-by-step explanation:
The sum of the angles in a triangle equals 180°.
To find the missing angle, subtract the sum of the two given angles from 180.
101 + 38 = 139
180 - 139 = 41
x = 41°
The size of the angle at the bottom left of the triangle is 41°.
What is a triangle?A triangle is a geometric figure which has three edges and three vertices. The sum of a triangle's three angles is 180°.
How to solve this problem?Given that the two angles of the triangle are 38° and 101°. We have to find the size of the other angle which is at the bottom left of the triangle. Let the size of the angle be x°.
We have to solve the equation:
x + 38 + 101 = 180
i.e. x = 180 - (38 + 101) = 180 - 139 = 41°
Therefore, the size of the angle at the bottom left of the triangle is 41°.
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Which graph represents this system? y = one-half x + 3. y = three-halves x minus 1 On a coordinate plane, a line goes through (0, 3) and (4, 5) and another goes through (0, negative 1) and (2, 2). On a coordinate plane, a line goes through (0, 3) and (1, negative 3) and another goes through (0, negative 1) and (3, 1). On a coordinate plane, a line goes through (negative 1, negative 2) and (1, 4) and another goes through (0, 1.5) and (1.5, 0). On a coordinate plane, a line goes through (negative 3, negative 3) and (0, 3) and another goes through (0, negative 1) and (3, 1).
Answers
Answer:
it is A or the first one
Step-by-step explanation:
The graph represents the system y = 1/2x + 3 and y = 3/2x - 1 is the lines and passes by (0, 3) and (4, 5), Option A.
Two equation of lines is given y = 1/2x + 3 and y = 3/2x - 1.
A graph to be identified showing the coordinate.
A line can be defined by a shortest distance between two points is called as a line.
Here, slope of equations of lines y = 1/2x + 3 and y = 3/2x - 1 are 1/2 and 3/2 and intercept is 3 and -1 now matching this with option we identified option A contains both the lines and passes by (0, 3) and (4, 5).
Thus, The graph represents the system y = 1/2x + 3 and y = 3/2x - 1 is the lines and passes by (0, 3) and (4, 5) ,Option A.
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write 26/39 simplest form
Answers
Answer:
2/3
Step-by-step explanation:
26/39
26 and 39 are multiples of 13.
Simplify the fraction.
26 ÷ 13 / 39 ÷ 13
⇒ 2/3
The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was per hour. The water output rate for the Perry family's sprinkler was per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of . How long was each sprinkler used
Answers
The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 15 L per hour. The water output rate for the Perry family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850 L . How long was each sprinkler used
Answer:
Hours of use of sprinkler by Lewis family is 30 hours.
Hours of use of sprinkler by Perry family is 35 hours.
Step-by-step explanation:
Let W = hours of use by Lewis family
65 - W = hours of use by Perry family
Then;
15W + 40*(65 - W) = 1850
15W + 2600 - 40W = 1850
(15 - 40)W = 1850 - 2600
-25W = −750
W = 750/25 = 30
Therefore;
W = 30
65 - W = 65 - 30 = 35
Hence,
Hours of use by Lewis family is 30 hours.
Hours of use by Perry family is 35 hours.
Here's a graph of a linear function. Write the
equation that describes that function. Express it in slope-intercept form.
Answers
Answer:
y = -2x -5
Step-by-step explanation:
The line crosses the y-axis at -5. So, b = -5.
It goes down 2 units for each 1 unit to the right, so has a slope of ...
m = rise/run = -2/1 = -2
__
The slope-intercept form of the equation of a line is ...
y = mx +b where m is the slope and b is the y-intercept
For the slope and y-intercept shown, the equation is ...
y = -2x -5
Find the solution set. 8x^2-2x-3=0 separate the two values with with a comma.
Answers
Answer:
x = -1/2, 3/4
Step-by-step explanation:
Step 1: Factor
(2x + 1)(4x - 3) = 0
Step 2: Find roots
2x + 1 = 0
2x = -1
x = -1/2
4x - 3 = 0
4x = 3
x = 3/4
I don’t quite understand what to do or how to solve it. Can someone explain please ?
Answers
Answer:
True.
Step-by-step explanation:
Remember the vertical line test. Anywhere on that graph, you can draw a vertical line, and it will not touch the function two times. Because of this, it is true.
Which equation has the steepest graph?
A. y = 10x-5
B. y=3/4x-9
c. y = -14x+1
D. y = 2x + 8
Answers
The equation that has the steepest slope is y = -14x + 1
What is a slope?A slope is the ratio of the change in the y-coordinates to the change in the x-coordinates of a line segment.
Analysis:
A line is said to be the steepest if it has the highest absolute value of the gradient or slope.
From the equations, the coefficient of x in the equations is taken as the slope. y = -14x+ 1 is the equation with the highest absolute value 14. The absolute value means ignoring the minus sign, since it indicates a negative slope.
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Answer:
Y=-14x+1
Step-by-step explanation:
Fiona's school is in the shape of a triangle, with three hallways connecting the corners. Fiona enters the building and walks 90 yards through the first hallway to the first corner. Then, she walks 60 yards through the second hallway to the second corner. A triangle is shown. The side lengths are 60 yards, 90 yards, and question mark. The top point is labeled exit and the bottom right point is labeled entrance. The distance between exit and entrance is question mark. What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answers
Answer:
bettween 30 and 150 yards
Step-by-step explanation:
test
Answer:
Between 30 yds and 150 yds.
Step-by-step explanation:
Got it right Edge 2021
They can leave tonight by bus, or they can save two hours by leaving tomorrow morning and using the express train which travels 20 km/h faster than the bus. If the distance between South Central High and Calgary is 800 km, determine how long it will take to travel by bus, rounded to the nearest hour.
Answers
Answer:
The bus will take 10 hours to travel from South Central High to Calgary.
Step-by-step explanation:
Let suppose that both bus and express train travels at constant speed, whose kinematic formula is now described:
[tex]v = \frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]v[/tex] - Speed, measured in kilometers per hour.
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
The transportation time is cleared afterwards:
[tex]\Delta t = \frac{\Delta s}{v}[/tex]
The kinematic expressions for the bus and the express bus are, respectively: ([tex]\Delta s = 800\,km[/tex])
Bus
[tex]\Delta t = \frac{800\,km}{v}[/tex]
Express train
[tex]\Delta t - 2\,h = \frac{800\,km}{v + 20\,\frac{km}{h} }[/tex]
By eliminating [tex]\Delta t[/tex]:
[tex]\frac{800\,km}{v} -2\,h = \frac{800\,km}{v+20\,\frac{km}{h} }[/tex]
[tex]\frac{800\,km}{v} - \frac{800\,km}{v+20\,\frac{km}{h} } = 2\,h[/tex]
[tex]800\cdot (v+20)-800\cdot v = 2\cdot v\cdot (v+20)[/tex]
[tex]16000 = 2\cdot v^{2}+40\cdot v[/tex]
[tex]2\cdot v^{2}+40\cdot v -16000 = 0[/tex]
Which is a second-order polynomial and whose roots are:
[tex]v_{1} = 80\,\frac{km}{h}[/tex] and [tex]v_{2} = -100\,\frac{km}{h}[/tex]
Only first root is physically reasonable, as speed is a scalar, that is, a number that is represented only by magnitude. Then, the time taken by the bus to travel from Central High to Calgary is: ([tex]v = 80\,\frac{km}{h}[/tex])
[tex]\Delta t = \frac{800\,km}{80\,\frac{km}{h} }[/tex]
[tex]\Delta t = 10\,h[/tex]
The bus will take 10 hours to travel from South Central High to Calgary.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
c.) x-2
Step-by-step explanation:
Answer:
X-2
Step-by-step explanation:
Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5
Answers
Answer:
[tex]g(x) = 8\cdot (x-3)^{2}-5[/tex]
Step-by-step explanation:
Given that parent function represents a parabola, the standard form with a vertex at (h,k) is now described:
[tex]y-k = C\cdot (x-h)^{2}[/tex]
[tex]y = C \cdot (x-h)^{2} + k[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Independent and dependent variables, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical component of the vertex, dimensionless.
[tex]C[/tex] - Vertex factor, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, there is an absolute maximum).
After reading the statement of the problem, the following conclusion are found:
1) New function must have an absolute minimum: [tex]C > 0[/tex]
2) Transformation to the right: [tex]h > 0[/tex].
3) Transformation downwards: [tex]k < 0[/tex]
Hence, the right choice must be [tex]g(x) = 8\cdot (x-3)^{2}-5[/tex].
Answer:
Choice D
Step-by-step explanation:
Took the test
Select the correct answer.
A particular strain of a common bacteria replicates itself every 14 minutes. Which of the following does this situation represent
Answers
Answer:
c
Step-by-step explanation:
Answer:
Both a relation and a function
Step-by-step explanation:
Replicates itself every 14 minutes, which is exponential function
Kite E F G H is inscribed within a rectangle. Points F and H are midpoints of the sides of the rectangle. Points E and G are parallel to the side of the rectangle.
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
Which statement describes how the location of segment EG affects the area of EFGH?
The area of EFGH is One-fourth of the area of the rectangle if E and G are not midpoints.
The area of EFGH is One-half of the area of the rectangle only if E and G are midpoints.
The area of EFGH is always One-half of the area of the rectangle.
The area of EFGH is always One-fourth of the area of the rectangle.
Answers
Answer:
The area of EFGH is always One-half of the area of the rectangle.Step-by-step explanation:
If F and H are midpoints of sides of rectangle then FH is parallel to the other side of rectangle so FH is perpendicular to the EG. That means the lenght of FH is equal to lenght of rectangle, and the lenght of EG is equal to width of rectangle.
So the area of the rectangle: [tex]A_{rectangle}=EG\cdot FH[/tex]
FH ⊥ EG so the area of quadrangle EFGH:
[tex]A_{_{EFGH}}=\frac12EG\cdot FH=\frac12A_{rectangle}[/tex]
no matter the location of segment EG
The area of EFGH is always One-half of the area of the rectangle.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have given that;
the kite EFGH is inscribed in a triangle and F and H are midpoints and EG is parallel to the side of rectangle.
The kite consists of 2 triangle that are EFG and EHG.
Now,
In a triangle EFG is,
= 1/2 x EG x h......(1)
where h is the height from F to EG
Also the area of EHG:
= 1/2 x EG x h₁
where is the height from H to EG
We also know that h₁ + h is the width of the rectangle and EG is the length of the rectangles.
Area of Kite = = 1/2 x EG x h + 1/2 x EG x h₁
Also, The area of a rectangle is rectangle length × rectangle width.
Thus, The Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
Hence, The statement describes how the location of segment EG affects the area of EFGH is the area of EFGH is always One-half of the area of the rectangle.
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PLEASE HELP ASAP THIS IS TIMED. If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)? On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2) On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5). On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Answers
Answer:
4th Graph
Step-by-step explanation:
Step 1: Find (f + g)(x)
-x² + 3x + 5 + x² + 2x
3x + 5 + 2x
5x + 5
Step 2: Graph
Answer:
option d on edge trash
Step-by-step explanation:
The avarage monthly salary of m male employees and f female employees of a company is 2000 if the avarage monthly salary of the male employees is (b+200) find the avarage monthly salary of the female employees
Answers
Answer:
[tex]Average = \frac{2000(m+f) - (b + 200)m}{f}[/tex]
Step-by-step explanation:
Given
Number of male = m
Number of female = f
Average salary = 2000
Average Salary of male = b + 200
Required
Average salary of female
Average is calculated as follows;
[tex]Average = \frac{Total\ Salary}{Staffs}[/tex]
For the whole company;
The formula becomes
[tex]2000 = \frac{Total\ Salary}{m + f}[/tex]
Multiply both sides by m + f
[tex]2000(m+f) = Total\ Salary[/tex]
The total salary is the sum of the male salary and female salary;
In other words;
Total Salary = Male Salary + Female Salary;
The above expression becomes
[tex]2000(m+f) = Male\ Salary + Female\ Salary[/tex] --------- equation 1
For the male staffs;
[tex]Average = \frac{Male\ Salary}{Male\ Staffs}[/tex]
[tex]b + 200 = \frac{Male\ Salary}{m}[/tex]
Multiply both sides by m
[tex](b+200)m = Male\ Salary[/tex]
Substitute (b + 200)m for Male Salary in equation 1
[tex]2000(m+f) = Male\ Salary + Female\ Salary[/tex]
[tex]2000(m+f) = (b + 200)m + Female\ Salary[/tex]
Subtract both sides by (b + 200)m
[tex]2000(m+f) - (b + 200)m = (b + 200)m -(b + 200)m + Female\ Salary[/tex]
[tex]2000(m+f) - (b + 200)m = Female\ Salary[/tex]
At this point, the average monthly salary of female staffs can be calculated;
[tex]Average = \frac{Female\ Salary}{Female\ Staffs}[/tex]
[tex]Average = \frac{2000(m+f) - (b + 200)m}{f}[/tex]
help quick plz must get this correct I will make u a brainllest
Answers
Answer:
CPCTC
Step-by-step explanation:
You already proved that triangle BAD is congruent to CAD, this means that all of the corresponding angles and sides with be congruent (CPCTC). That means BD is congruent to CD. Hope this helps!
Rewrte the expression with a ratational exponent as a radical expression (4^2/5)^1/4
Answers
Answer:
Step-by-step explanation:
(4^2/5)^1/4
first multiply the exponent
2/5*1/4=2/20=1/10
4^1/10= 10√4(the ten is on the top to the square root)
Amir wants to buy a $1382 Apple iPhone that is 12% off. What is 1 point
the discounted price before tax? *
Answers
Answer:
1273
Step-by-step explanation:
C) the answer on edg is C.
State if a triangle is acute ,obtuse, or right
Answers
Answer:
It is an acute angle due to the angle formed at the vertex being less than 90 degrees
Answer:
acute triangle
Step-by-step explanation: sorry no step by step explanation i am in a rush anyway have a great day bye!!! :D please give brainliest
The whole number which is not a natural number is
Answers
Answer:
All negative numbers
Step-by-step explanation:
They are not whole numbers
Answer:
0
Step-by-step explanation:
Since negative numbers are not considered whole numbers, they are not included here. All natural numbers are whole numbers but not all whole numbers are natural numbers. 0 is a whole number but it doesn't count as a natural number which makes the answer 0
NEED ANSWER ASAP What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
Answers
Answer:
(A) 1
Step-by-step explanation:
We know that the formula is x = (m/m+n) (x2-x1) + x1.
But the trick to the question which is why everyone is getting it wrong is because it asks for F to D not D to F.
The reason everyone else was getting 4 was because they were using this.
They solved the equation x = (8/8+5) (9-[-4]) -4 where it was D to F. This equation does turn out to be 4 but it is incorrect.
However, the correct equation (because it is supposed to be F to D) is
x = (8/8+5) (-4 -9) +9 which is in fact equal to 1.
I also just took the quiz and got 100%.
PRESS THAT THANKS BUTTON!!!
write the ratio 4.5: 2.25 in the form n:1
Answers
Step-by-step explanation:
you will divide both sides of the ratio I.e the 4.5 and 2.25 by 2.25
I need help on this please
Answers
Answer:
[tex]y=\frac{5}{6}x+5[/tex]
Step-by-step explanation:
Well this is actually really simple we just have to look at the line and see what attributes it has so we can make an equation.
So slope intercept form is [tex]y=mx+b[/tex].
Like to find the y intercept we know it is the point that the line touches the y axis which is 5.
Now for the slope, the slope is how far each points are from each other on a line so to find the slope we can use the following formula [tex]\frac{y^2-y^1}{x^2-x^1}[/tex].
So to do this we need two points that are on the line we can use (-6,0) and (6,10).
So y2 is 10 and y1 is 0 so 10-0 is 10 and 6 - -6 is 12 so the slope is 10/12 and we have to simplify it to 5/6 so the slope is 5/6 and now we have to put it in slope intercept -> [tex]y=\frac{5}{6}x+5[/tex]
marcus receives an inheritance of $13,000. he decides to invest this money in a 10-year certificate of deposit (CD) that pays 3.0% interest compounded monthly. how much money will marcus receive when he redeems the CD at the end of 10 years?
Answers
Answer:
Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years
Step-by-step explanation:
Principal(p)=$13,000
Rate(r)=3.0%
Period(n)=12 months
Time(t)=10 years
A=p(1+r/n)^nt
=13,000(1+0.03/12)^12*10
=13,000(1+0.0025)^120
=13,000(1.0025)^120
=13,000(1.3494)
=17,542.2
A=$17,542.2
Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years
(2*6)^3/2 in simplest form
Answers
Answer:
[tex]\sqrt{1728}[/tex]
Step-by-step explanation:
=> [tex](2*6)^{3/2}[/tex]
=> [tex](12)^{3/2}[/tex]
=> [tex]1728 ^{1/2}[/tex]
=> [tex]\sqrt{1728}[/tex]
Vincent made a sketch that measures 10 inches by 15 inches. If he creates a new drawing where each of the dimensions is tripled, what will be the perimeter of the new drawing?
Answers
Answer:
150 inches
Step-by-step explanation:
Vincent sketch is a rectangle
10 inches by 15 inches
Length=15 inches
Width=10 inches
If each dimension is tripled
Then,
Length=15*3=45
Width=10*3=30
Perimeter of the new drawing=2(length+width)
=2(45+30)
=2(75)
=150 inches