A triangular prism and two nets are shown:
Which is the correct net of the prism and what is the surface area of the prism?
Answers
surface area of the prism is
Surface area = Area of two triangular faces + Area of bottom rectangle + Area of two side rectangles
View attachment
Hope this helps
The correct net of the prism is net A and the surface area of the prism is 510 square inches
How to determine the surface areaTo calculate the area of the triangular prism, we make use of the net A
Start by calculating the area of the rectangle.
The dimension of the rectangle is (5 + 12 + 13) by 15
So, the area of the rectangle is:
[tex]Area = (5 + 12 + 13) * 15[/tex]
[tex]Area = 450[/tex]
Next, calculate the area of the two congruent triangles of base 5 and height 12
[tex]Area = 2 * 0.5 * (5 * 12)[/tex]
[tex]Area = 60[/tex]
Sum both areas
[tex]Total = 450 + 60[/tex]
[tex]Total = 510[/tex]
Hence, the surface area of the prism is 510 square inches
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Related Questions
how can you tell before dividing that the first digit of the quotient 2,874/3 is in the hundreds place?
Answers
Final answer:
You can tell that the first digit of the quotient of 2,874 divided by 3 is in the hundreds place by using estimation and recognizing that 287 (the first three digits) is greater than 3 multiplied by 100, thus ensuring the quotient reaches the hundreds place.
Explanation:
To determine if the first digit of the quotient of 2,874 divided by 3 is in the hundreds place before actually dividing, we can use an estimation technique. Estimation helps us to predict the placement of the quotient's digits without doing the full calculation. For the divisor 3 to produce a number in the hundreds place, it must be able to go into the first three digits of the dividend (here, 2,874).
We look at the thousands and hundreds places of the dividend. Since the number 2,874 has a 2 in the thousands place, we know 3 cannot be divided into 2 to give us a number in the hundreds place. But when we include the next digit in the hundreds place, we have 287, which is greater than 3 imes 100. Therefore, we can say that 3 will go into 287 at least 100 times, making the first digit of the quotient in the hundreds place.
This estimation is further validated by the recognition that the number in the hundreds place of 2,874 (which is 8) is more than twice 3, and therefore, dividing it by 3 will definitely yield a number greater than 100 but less than 1,000.
To join a fitness club there is a $30 joiner fee and a $12 monthly fee. Write an equation in slope intercept form that models this situation.
Answers
I think this is correct. But please don't hold me to it:) Hope I helped!
the jacksons went camping in a state park.One of the tents they took is shown . What is the volume of the tent.
Answers
The volume of the Jacksons' camping tent is 94.5 cubic feet. To calculate the volume, you multiply the dimensions: height (3.5 ft) by length (6 ft) by width (4.5 ft).
Explanation:The formula for calculating the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
The length (l) of the tent is 6 feet, the width (w) is 4.5 feet, and the height (h) is 3.5 feet.Substitute these values into the formula: V = 6 ft * 4.5 ft * 3.5 ft.Multiply the values together: V = 94.5 cubic feet.The volume of the tent is determined by multiplying its length, width, and height. In this instance, the Jacksons' tent has a volume of 94.5 cubic feet, providing ample space for their camping needs. Understanding the volume of a three-dimensional object is essential for assessing its capacity and ensuring it meets the requirements of its intended use.
Complete Question:
The Jacksons went camping in a state park. One of the tents they took is shown, tent size in the attached picture 3.5 ft high, 6 ft long and 4.5 ft wide. What is the volume of the tent?
An 8-foot piece of pipe is cut into 1/3 foot sections. How many sections of pipe are there?
A) 20
B) 24
C) 30
D) 36
Answers
wo equations are given below: a − 3b = 9 a = b − 3 What is the solution to the set of equations in the form (a, b)? (−9, −6) (−4, −3) (−6, −3) (−9, −7)
Answers
a = b - 3
With our set of equations, we should substitute our variables with their values, and whichever answer equals (or cancels) out is the correct one.
(-9, -6);
-9 - 3(-6) = 9
-9 + 18 = 9
18 = 18
This is correct so far.
(-9, -6);
-9 = -6 - 3
-9 = -9
This is also correct!
From the work above, we can conclude that the set of equations (-9, -6) is the correct answer.
I hope this helps!
You are having a discussion about sequences with your classmate. She insists the the sequence 2,3,5,8,12 must be either arithmatic or geometric. Is she correct or incorrect? Explain.
Answers
.. a[n] = (n*(n -1))/2 +2
First differences are increasing, so the sequence will not be arithmetic. An arithmetic sequence has constant first differences.
Second differences are constant, so the sequence will not be geometric. A geometric sequence will have first-, second-, third-differences, and those to any level, that have the same constant ratio as the terms of the original sequence.
all my points to person who has best answer plz make it simpule
Solve 8 x^2 + 5 = 35 Round to the nearest hundredth.Enter your answers in the boxes.The solutions are approximately and .
Answers
this is the answer because you subtract the 5 on both sides then divide by 8 which would be x^2=3.75, finally take the square root of both sides to get x=1.94 after rounding
8x² = 35 - 5
8x² = 30
x² = 30/8
x² = 3.75
x = ±1.94 to the nearest hundredth
So x₁ = -1.94 and x₂ = 1.94
Without calculating, explain how many decimal places are in the product 0.6 X0.4 X 1.9. Rewrite the expression as the product of two decimals to support your answer.
Answers
Looking at the problem, you see both .6 and .4 are placed to the right of the decimal, otherwise known as the tenths place (1/10).
Looking at 1.9, you see you have one number (1) placed to the left of the decimal, the ones place, and another number placed to the right of the decimal (9), in the tenths place.
Well, this is simple. You can look and see that your multiplying fractions against a whole number, which will of course make this whole number even smaller. By how much though??
Well, you can really tell this by looking at how MANY numbers are behind the decimal. You have .9, .4, and .6
That's 3 numbers behind the decimal place. This may not help you solve the problem itself, but this tells you here (ignoring the 1, that will be taken out immediately while solving and turned into a 0) that you will have 3 numbers placed from the tenths place all the way to the thousandths place.
Basically, this tells you that you'll have three decimal places to the right of the decimal.
As for rewriting your problem to better show this, that's simple too.
All you have to do is simple multiplication, just in the tenths place. How? You know that 6*4 (referring to .6 and .4) is 24, that means that .6*.4 will be .24
How does this support your answer before? .24 has TWO numbers to the right of the decimal. That's TWO decimal places. With the .9 in 1.9, that's still THREE decimal places to the right of the decimal, and your answer would be the same.
So, here's it re-written.
1.9*.24=X
~Hope this helps!
The product 0.6 x 0.4 x 1.9 has three decimal places.
Explanation:To determine the number of decimal places in the product 0.6 x 0.4 x 1.9, we can rewrite each decimal as the product of two decimals and count the total number of decimal places.
0.6 can be written as 0.6 x 1.0, which has one decimal place.
0.4 can be written as 0.4 x 1.0, which also has one decimal place.
1.9 can be written as 1.9 x 1.0, which has one decimal place.
Since each decimal has one decimal place, the product 0.6 x 0.4 x 1.9 has a total of three decimal places.
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At the malt shop a large chocolate shake takes 0.2 of a pint of milk. If a medium shake takes 0.7 the amount of a large, how much does the medium shake take?
Answers
1.
A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B', has the coordinates (2, –3). What is the scale factor of the dilation?
110
15
5
10
2.
A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A' has coordinates of (–0.25, 0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply.
The coordinates of C' are (0.75, 0.5).
The coordinates of C' are (1.5, 1).
The scale factor is 18
.
The scale factor is 8.
The scale factor is 14
.
The scale factor is 4.
The coordinates of B' are (-0.25, 1).
The coordinates of B' are (-0.5, 2).
3.
What is the scale factor of a triangle with a vertex of A(–6, 4) that has been dilated with a center of dilation at the origin so the vertex of its image is A'(–24, 16)?
4.
Three transformations will be performed on triangle ABC. Which set of transformations will always produce a congruent triangle?
Dilation, rotation, translation
Reflection, dilation, translation
Rotation, reflection, dilation
Rotation, translation, reflection
Answers
The scale factor is [tex] \frac{1}{5} [/tex]
Question (2):
scale factor = [tex] \frac{1}{8} [/tex]
coordinates of C' are (0.75 , 0.5)
coordinates of B' are (-0.25,1)
Question (3):
The scale factor is 4
Question (4):
Rotation, translation, reflection
Exact steps and explanation for each question are shown in the attached images.
Hope this helps :)
Answer:The scale factor is \frac{1}{5}
Step-by-step explanation:
If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?
Answers
The function that describes a cell population of 100 cells tripling every hour is stated by the formula p(t) = 100(3)^t, which represents exponential growth.
Explanation:This problem describes a phenomenon where the initial population experiences exponential growth in a way that it triples every hour. Exponential growth is typically represented by the function p(t) = p⁰×r^t, where:
- p(t) represents the final amount of entities (in this case, population) after time t,
- p0 is the initial amount of entities (in this case, initial population),
- r is the growth factor,
- and t is time.
In these types of problems, the base number of the exponent (in this case 3) represents the growth factor. This is based on the fact that every time period (in this case, every hour), the population triples, or in other words, gets multiplied by 3.
The initial population given is 100 cells. This is represented by p0 in our formula and is also the coefficient in our function.
By considering both the initial population and the rate at which it triples, we can construct the function as p(t) = 100 × 3^t.
Therefore, according to our built function, the correct choice is b. p(t) = 100 × 3^t.
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Question:If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?
a. p(t)=3(100)^t
b. p(t)=100(3)^t
c. p(t)=3t+100
d. p(t)=100t+3
The graph of a function in the form f(x) a(x - h)2 +k is shown. Use the graph to find an equation for f(x).
Answers
(h; k) are the coordinates of the vertex.
On the graph are (3; 4), therefore we have:
[tex]f(x)=a(x-3)^2+4[/tex]
We have the x-intercept (1; 0) → x = 1; y = 0.
Substitute them in the equation:
[tex]0=a(1-3)^2+4\\\\0=a(-2)^2+4\\\\4a+4=0\ \ \ |-4\\\\4a=-4\ \ \ \ |:4\\\\a=-1[/tex]
so. We have the answer:
[tex]\boxed{f(x)=-(x-3)^2+4}[/tex]
Which is NOT a Correct name for the line shown
Answers
———————————————-
Ahcienzue cod
nR is not a correct name for the line shown.
What is Line?A line is a straight geometrical figure in one dimension. It is extended to both sides to infinity.
A line only has length and has no width, thus it is a one dimensional figure.
Given is a line where both sides extended to infinity.
The line is given a name n.
So we can denote the given line as n.
There are points marked on the line like R, S and T.
So we can denote the line also has the lines RT, ST and RS.
But we cannot denote the line with names like n R, n S and n T, all of which are incorrect notation.
Hence the incorrect notation for the given line is the second option n R.
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sum of 5 z and 4 divided by two is 7
Answers
[tex]Sum: + (add) \\ \\ 5:5 \\ \\ z:z \\ \\ 4:4 \\ \\ divided by: division \\ \\ 2:2 \\ \\ is: = \\ \\ 7:7 [/tex]
Answer: [tex] \frac{5z +4}{2} = 7 [/tex]
_______________________________________________________________
[tex] \frac{5(2)+4}{2} [/tex]
[tex]5(2) = 10 [/tex]
[tex]10 + 4 = 14 [/tex]
[tex] \frac{14}{2} = 7 [/tex]
Answer: [tex]z = 2[/tex]
__________________________________________________________________
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
uppose you send about 12 text messages a day, and your older sister sends more text messages than you do. Together, you send a total of about 26 messages per day. About how many text messages does she send a day? Write an equation and solve for the unknown value
Answers
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(7.5, 4.5) , B′(4.5, 10.5) , and C′(1.5, 6) . The center of dilation is the origin.
What is the scale factor of the dilation?
Answers
To find the scale factor, we have to look at what's going on in the problem.
In point A, we are converting from (5, 3) to (7.5, 4.5).
We can write and solve equation to find the change (scale factor)
5x = 7.5 and 3x = 4.5
If you solve either equation, you will find the scale factor is 1.5.
Good luck,
MrEQ
Answer:
3/2
Step-by-step explanation
What is the volume of the right rectangular prism?
17 in³
68 in³
108 in³
168 in³
Answers
In this problem, you multiply all the measurements:
2 × 9 × 6 = 108
The answer is 108 in squared, or the third option.
Hope this helped!
Wolfgang wants to enlarge a picture he developed. Which factor listed below would scale up (enlarge) his picture the most if he used it to multiply its current dimensions? 7/8 14/14 1 4/9 3/2
Answers
Final answer:
The factor that would scale up Wolfgang's picture the most is 1 4/9.
Explanation:
The factor that would scale up Wolfgang's picture the most is 1 4/9.
To find the scale factor, we compare the given factors: 7/8, 14/14, 1 4/9, and 3/2.
Out of these options, 1 4/9 would enlarge the picture the most when used to multiply its current dimensions.
Juan has a box that is filled with toys. The box is 3 1/2 feet long,6 feet wide ,and 3 feet high. What is the volume and surface area of a box.
Answers
Volume = 3.5 x 6 x 3 = 63 ft^3
Surface Area (if we're talking about a closed box and only talking about the outside area) = ∑Areas of the sides
Surface Area = 3.5 x 6 + 3.5 x 6 + 6 x 3 + 6 x 3 + 3.5 x 3 + 3.5 x 3 = 99 ft^2
Leta is making strawberry-almond salad for a party. For every head of lettuce that she uses, she adds 5 ounces of almonds and 10 strawberries. If she uses 75 ounces of almonds, how many heads of lettuce, how many strawberries does Leta use?
Answers
Heads of lettuce=15
Tymere says that 7/10 × 7/10 equals 49/10. Which of the statements below is true?
Answers
I need help with question 7, don't really get it?
Answers
then:
x+ y will always be irrational
x - y will always be irrational
xy will always be irrational
Therefore the answer is (3)
The volume of a cone is 471.24 cubic inches and the height is 8 inches. What is the diameter
Answers
h = 8
pi = 3.14
V =471.24
r = ???
d = ???
471.24 = 3.14 * 8 * r^2
471.24 = 25.12 * r^2
471.24 / 25.12 = r^2
18.76 = r^2
r = sqrt(18.76)
r = 4.312
The diameter is 2*4.312 = 4.624 in. <<<<<==== answer.
Choose a number from 101 to 110 write it draw a picture to show it as 10 tens and more.
Answers
Choose a number from 101 to 110, we selected 106. To represent it with tens and ones, draw ten groups of ten for 'ten tens' which equals 100, and then draw 6 individual objects depicting 'and more' to visually show that 106 is 100 plus 6.
To choose a number from 101 to 110 and represent it as ten tens and more, let's select the number 106. The number 106 can be broken down into ten tens (which is 100) and an additional 6 to make up the full number.
A visual representation of this could be:
For the ten tens, you can draw ten groups of ten sticks or circles together, which would represent 100.
For the additional 6, draw six more sticks or circles away from the groups of tens.
So the drawing will show ten sets of ten objects, such as sticks or dots for the tens, and then six individual objects for the ones, clearly indicating that 106 consists of 100 (ten tens) plus 6 more.
Taxicabs downtown charge a flat fee of $2.50, plus a state tax of $0.50, plus $0.50 for each 1/5 mile they travel with a passenger.
Explain how you would write 1/5 mile as a fraction with 10 in the denominator, a fraction with 100 in the denominator, and as a decimal.
Answers
Final answer:
To convert 1/5 mile to other forms, it can be represented as 2/10 when the denominator is 10, 20/100 when the denominator is 100, and 0.2 as a decimal.
Explanation:
To convert 1/5 mile into a fraction with 10 in the denominator, multiply both the numerator and the denominator by 2 to get 2/10. To get a fraction with 100 in the denominator, multiply both the numerator and the denominator of 1/5 by 20 to get 20/100. As a decimal, 1/5 is equivalent to 0.2 because 1 divided by 5 equals 0.2.
A rectangular quilt is 5 feet wide and 7 feet long. How many feet of lace are needed to cover the edges of the quilt?
Answers
L = 7
W = 5
P= ???
P = 2*7 + 2*5
P = 14 + 10
P = 24 feet of lace.
The rectangular quilt has length 7 feet and width as 5 feet.
In order to find the perimeter, we have this formula:
[tex] P = 2(l+w) [/tex]
Plugging these values in the formula:
[tex] P = 2(7+5) [/tex]
Perimeter = 24 feet.
So 24 feet of lace are needed to cover the edges of the quilt.
Rewrite 3x + 4y = 10 using function notation.
Answers
[tex]3x+4y=10 \\ 4y=-3x+10 \\ y = \frac{-3}{4}x+ \frac{5}{2} \\ \\ f(x) = \frac{-3}{4}x+ \frac{5}{2} [/tex]
Chick fil a prints out a free sandwich coupon receipt every 7 receipts. What is the probability of not getting a coupon receipt
Answers
Hope this helps!
How does the volume of the cylinder compare to the volume of the cone
Answers
Vcone = (1/3)*π*r^2*h
Vcylinder = π*r^2*h
Dennis is thinking of two number. The only common factors of the number are 1 and 3.Thier first common multiple is 18.One of the number is 9. What is the other number?
Answers
Final answer:
Dennis's other number, considering the conditions of only having 1 and 3 as common factors and 18 as the least common multiple with 9, is 6.
Explanation:
To solve the problem regarding Dennis's numbers, it's crucial to understand the conditions provided: the numbers only share common factors of 1 and 3, one of the numbers is 9, and their first common multiple is 18. To find the other number, knowing one of the numbers allows us to apply the rule of least common multiples (LCM). Since 9's factors are 1, 3, and 9, and the LCM with the other number is 18, this other number must be divisible by itself and 3 but not be a multiple of 9 to maintain the unique common factors condition. The only number that satisfies the condition in which 18 is the LCM and shares only 1 and 3 as common factors with 9, would be 6, since 18 is the smallest number that both 9 and 6 can divide into without other common multiples.