The base of a triangular prism is an isosceles right triangle with a hypotenuse of
√50 centimeters. The height of the prism is 8 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.
Answers
Lateral area = perimeter of base x height
An isosceles triangle has two congruent base segments. The hypotenuse of an isosceles right triangle is (length of base segment) x (the square root of 2). I did the math for you (shown above) to get 5 as a base.
So 5 + 5 + square root of 50 is your perimeter
Multiply the perimeter times your height (8) and you get the lateral area.
Add your lateral area to the base area (triangle = 1/2 bh)
LA = 136.568...
Area of Triangle base = 12.5
Surface area = 149.068... square cm
Related Questions
Help I don’t understand this
Answers
- 4x - 8 = 24
Add 8 to each side
- 4x = 32
Divide each side by - 4
x = - 8
So your ordered pair is (- 8, 8).
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
Answers
The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
Explanation:To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:
x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)
y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)
Substituting the given coordinates into the formula, we have:
x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8
y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6
Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
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what are the factors of 2n^2 -5n- 42
Answers
The factors of the quadratic expression 2n^2 - 5n - 42 are found by looking for two numbers that multiply to -84n^2 and add up to -5n. The correct pair is 7n and -12n, leading to the factors (2n + 7) and (n - 6).
Explanation:The factors of 2n^2 - 5n - 42 need to be determined by finding two numbers that multiply to 2n^2 times -42 (which is -84n^2) and add up to -5n. To factor this quadratic expression, we should look for a pair of numbers that meet these criteria.
Upon inspecting possible pairs, we find that 7n and -12n are the numbers that work since (7n) * (-12n) = -84n^2 and 7n + (-12n) = -5n. The quadratic trinomial can be expressed as:
2n^2 - 5n - 42 = (2n + 7)(n - 6)
By factoring this way, we have broken down the expression into its factors, which are (2n + 7) and (n - 6).
The factors of the quadratic expression [tex]\(2n^2 - 5n - 42\)[/tex] are [tex]\(2n + 7\)[/tex] and [tex]\(n - 6\)[/tex].
To find the factors of the quadratic expression \(2n^2 - 5n - 42\), we can use the factoring method. This involves finding two numbers that multiply to give the product of the coefficient of \(n^2\) (which is 2) and the constant term (which is -42), and also add up to the coefficient of \(n\) (which is -5).
The product of the coefficient of [tex]\(n^2\)[/tex] and the constant term is:
[tex]\(2 \times -42 = -84\)[/tex]
Now we need two numbers that multiply to -84 and add up to -5. These numbers are -12 and 7 because:
[tex]\(-12 \times 7 = -84\)[/tex]
[tex]\(-12 + 7 = -5\)[/tex]
Now we can rewrite the middle term of the quadratic expression using -12 and 7:
[tex]\(2n^2 - 12n + 7n - 42\)[/tex]
Next, we can factor by grouping. Group the first two terms and the last two terms:
[tex]\(2n(n - 6) + 7(n - 6)\)[/tex]
Notice that [tex]\(n - 6\)[/tex] is a common factor. We can factor this out:
[tex]\((2n + 7)(n - 6)\)[/tex].
Find the greatest common factor for the list of terms 110x3, 30x4,60x8
Answers
30×4 = 3×5×2×2×2
60×8 = 3×2×2×5×2×2×2
Greatest common factor = 2×3×5
= 30
Hope this helps!
30x⁴ = 10x³(3x)
60x⁸ = 10x³(6x⁵)
Answer: GCF = 10x³
one month charlie rented 2 movies 3 video games for a total of $21. The next month he rented 4 movies and 8 video games for a total of $53. Find the rental cost of each movies and each video game.
Answers
y= cost per video game
EQUATION 1:
2x + 3y= $21
EQUATION 2:
4x + 8y= $53
STEP 1:
multiply equation 1 by -2.
-2(2x + 3y)= -2($21)
-4x - 6y= -42
STEP 2:
solve linear equations by elimination. use equation 2 and equation answer from step 1. add the two equations together. the x terms will cancel out. solve for y.
4x + 8y= 53
-4x - 6y= -42
2y= 11
divide both sides by 2
y= 11/2
divide
y= $5.5 per video game
STEP 3:
substitute y answer from step 2 into either original equation to solve for x.
2x + 3y= $21
2x + 3(5.50)= 21
2x + 16.50= 21
subtract 16.50 from both sides
2x= 4.50
divide both sides by 2
x= $2.25 per movie
CHECK:
4x + 8y= $53
4(2.25) + 8(5.50)= 53
9 + 44= 53
53= 53
ANSWER: The cost per movie is $2.25 and the cost per video game is $5.50.
Hope this helps! :)
The cost to rent a movie is $2.25 and to rent a video game is $5.50, which was determined by solving a system of linear equations derived from the problem statement.
Explanation:This problem is a classic example of a system of linear equations, and we can solve it using either substitution or elimination method. Let's denote the cost of renting a movie as 'm' and the cost of a video game as 'v'. From the problem statement, we know:
2m + 3v = $214m + 8v = $53We can multiply the first equation by 2, giving us 4m + 6v = $42. Now if we subtract the second equation from this, we can solve for 'v':
(4m + 6v) - (4m + 8v) = $42 - $532v = $11v = $5.50Substitute 'v' back into the first equation to solve for 'm':
2m + 3($5.50) = $212m + $16.50 = $212m = $4.50m = $2.25Therefore, the cost to rent a movie is $2.25 and to rent a video game is $5.50.
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which one is equivalent?
Answers
I hope this answers your question!
-T
The table below shows the deliveries for Floral World for the week. What is the mean, or average, number of deliveries per day?
Answers
13+15+17+19+16=80
80 divided by 5 is 16. The answer is 16
Can I have Brainliest?
Thanks!!
Answer:
The average number of deliveries per day is 16 deliveries.
Step-by-step explanation:
The mean of a data set is the average value within it. Means are used as a way of describing data and finding the central tendency. To calculate the mean of a data set, add all values of all data points, then divide the resulting number by the amount of data points.
13 + 15 + 17 + 19 + 16 = 80
80 / 5 = 16
So, the average number of deliveries made per day by Floral World is 16 deliveries.
Math Help PLEASE! ASAP
Answers
5,000 x 0.50 = 2,500
Answer is $2,500
2. a full circle = 360 degrees
40% = 0.4
360 * 0.4 =144 degrees
3. third one shows the correct circle graph
A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.
(PICTURE IS BELOW)
Which of the following inferences can be drawn about the buying pattern of the online customers versus that of the walk-in customers?
A.Online customers buy an average of four packs compared with walk-in customers, who buy an average of one pack.
B.Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
C.Online customers buy an average of four packs compared with walk-in customers, who buy an average of two packs.
D.Online customers buy an average of five packs compared with walk-in customers, who buy an average of one pack.
Answers
The random Sample can be drawn the buying pattern on the online customers versus that of the walk in interview, the correct option is B.
What is sample?Sample is "a small and manageable version of a larger group".
According to the question,
The number of packs ordered by random samples through the online customers = 100
The number of packs ordered by random samples through the walk-in-interview =100
To find the inferences,
Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
Hence, the Option B.
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A number m minus 3 is more than -4
Answers
> = more than/greater than
Expression:
m - 3 > -4
If you have to also solve:
m - 3 > -4
add 3 to both sides
m > -1
ANSWER: expression is m - 3 > -4;
expression solved for m is m > -1
Hope this helps! :)
Jason is covering an ottoman with fabric. The ottoman is in the shape of a rectangular prism that is 37 cm long, 21 wide, and 30 cm high. How much fabric is needed to cover the sides and top of the ottoman? Explain your strategy.
Answers
Final answer:
Jason needs 4,257 square centimeters of fabric to cover the sides and top of his rectangular prism shaped ottoman, calculated by finding the area of each side and adding them together.
Explanation:
To calculate the amount of fabric needed to cover the sides and top of a rectangular prism shaped ottoman with dimensions 37 cm in length, 21 cm in width, and 30 cm in height, we start by determining the surface area of the ottoman that needs covering. We ignore the bottom surface, assuming the ottoman sits directly on the floor.
First, calculate the area of each side:
Top/bottom surface (only top applies here) = length × width = 37 cm × 21 cm = 777 cm²
Front/back surface = length × height = 37 cm × 30 cm = 1,110 cm² (two sides, so × 2)
Left/right side = width × height = 21 cm × 30 cm = 630 cm² (two sides, so × 2)
Next, add all the calculated areas together:
777 cm² (top) + 2,220 cm² (front/back) + 1,260 cm² (left/right) = 4,257 cm²
Therefore, Jason needs 4,257 square centimeters of fabric to cover the sides and top of the ottoman.
PLEASE someone do this math EASY picture attached
Answers
5/8 ÷ 3/2 = (5/8 × 2/3) = 10/24 = 5/12
5/12 × 2/3 = 10/36 = 5/18
Your answer is 5/18
Hope this helps :)
Answer:
5/18
Step-by-step explanation:
5/8 ÷ 3/2
switch 3/2 to 2/3
5/12 × 2/3
10/36 divide each 2 5/18
plz help me asap!!!!
Answers
distance=√((x₂-x₁)²+(y₂-y₁)²), Pythagorean Theorem c²=a²+b²
a) (-5,6), (-5,-6), (4,-6)
d= √((-6-6)²+(-5+5)²)
d=12
d=√((-6+6)²+(4+5)²)= 9
d=√((-6-6)²+(4+5)²)= 15
A is correct
Mary and Jerry are exercising on a track
-Mary is walking at a rate of 3 miles per hour
-Jerry starts jogging at a rate of 4 miles per hour after Mary has been walking for 15 minutes
-Jerry jogs 2 miles as Mary continues walking and they both stop at the same time
Enter the total distance, in miles, that Mary walks around the track
Answers
With Mary's rate of walk, 3 miles per hour, we can just convert it to minutes and find the distance she has covered after 30 minutes.
3 miles/ 60 minutes, multiplying both numerator and denominator by 1/2, we will have 1.5 miles/30 minutes. Therefore, Mary has covered a distance of 1.5 miles around the track after the walk.
Answer:
2.25
Step-by-step explanation:
Mary walks for 15 mins which is 0.75 mi. Jerry then starts jogging for 2 miles which is 30 minutes because he is jogging at 4 mph. This means Mary walked for 30 minutes which is 1.5 mi.
0.75+1.5=2.25
what is 15% of "x"
PLEASE HELP
Answers
Answer:
0.15x
Step-by-step explanation:
15% of anything is 15/100 or 0.15 of it. You find that value by multiplying the "anything" by 0.15.
Since we don't know the value of x, the best we can do is show that the number of interest is x multiplied by 0.15.
Paul wrote a check to the dentist for $345.69. He’ll use the check register to record his transaction. What will be his new balance?
Answers
Answer:
The answer is $704.73
Step-by-step explanation:
Answer:
The answer is A. $704.73
Step-by-step explanation:
could rectangle a be a scale drawing of rectangle b? explain.
Answers
Please help choose the best answer x/-4 >6
A: x <-24
B: x >-24
C: x < 10
D: x > 2
Answers
x/-4 * -4 > 6 * -4
(when you multiply by a negative number, the sides will switch:)
x < -24
The answer is option A
If a recipe requires 3/4 cup of water and Lisa wants to make only 1/3 of the recipe.how many cups of water should she use?
I got the answer 1/4 but I just want to make sure it’s right
Answers
1/3 of the recipe = 1/3 x 3/4 = 1/4 cup
Answer: 1/4 cup
Use a 10-square model to solve. What percent of 80 is 40?
Answers
Hope this is right!
:)
a $1,400 loan has a simple annual interest rate 4%. how much simple interest is paid on the loan for 1 year?
Answers
The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.
Explanation:The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:
Convert the interest rate of 4% to a decimal by dividing by 100. So, 4/100 = 0.04.The time is 1 year, so you don't need to convert it.Substitute the values into the simple interest formula. Therefore, the simple interest is: $1,400 x 0.04 x 1 = $56.So, the simple interest paid on the loan for 1 year is $56.
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This table shows the size, in acres, of four large water parks. What is the median of the sizes of the four water parks? 60 acres 63 acres 64 acres 65 acres Park Size (in Acres) A 66 B 70 C 60 D 60
Answers
The median size of the four water parks, given as 66, 70, 60, 60 acres, is 63 acres.
Explanation:To find the median of the sizes of the four water parks, we first need to list the sizes in ascending order. Given the sizes are 66, 70, 60, 60, the arranged list becomes 60, 60, 66, 70.
As there are four numbers, the median is the average of the middle two numbers. So by adding 60 and 66 and then dividing by 2, we find that the median size of the water parks is 63 acres.
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((cosx)/(1+sinx))+((1+sinx)/(cosx)=2secx
Answers
A rectangle field is five times as long as it is wide. If the perimeter of the field is 288 yards, what are the field's dimensions?
Answers
[tex]x + x + 5x + 5x = 288 \\ 12x = 288 \\ x = 24[/tex]
Width = 24 yards
Length = 24 x 5 = 120 yards
Area =
[tex]24 \times 120 = 2880 \: sq. \: yrds[/tex]
Hope this helps. - M
d=1/2at^2 ; for a
solve for a
Answers
Answer:
a = 2d/t²
Step-by-step explanation:
1- Divide by 1/2 on both sides:
(d ÷ 1/2 = d × 2/1 = 2d)
2d = at²
2- Divide by t² on both sides:
2d/t² = a
a = 2d/t²
You can do those two steps in one but I made it in two so it's easier to understand.
log base 6 (2x+1) = log base 6 (x-3) + log base 6 (x+5)
Answers
Use the rules of logarithms to rewrite as a single log. Then take the antilog and solve the resulting quadratic.
[tex]\log_{6}(2x+1)=\log_{6}(x-3)+\log_{6}(x+5)=\log_{6}((x-3)(x+5))\\\\2x+1=(x-3)(x+5)=x^{2}+2x-15\\\\0=x^{2}-16=(x-4)(x+4)[/tex]
The term [tex]\log_{6}(x-3)[/tex] is only defined for x > 3, so the only solution to this equation is x = 4.
What does this equation equal to? 2010=0.507x+5.543
Answers
or in fraction form
x=154189/39
In 2/3 of a hour, workers had installed 2/5 of a foor. At the rate,what fraction of the flooring is finished after 1 hour?
Answers
2/3 hour is 40 minutes, so 1/3 is 20 minutes.
40 minutes have passed and 2/5 of the progress on the floor is complete. In 20 minutes, 1/5 of the work is complete. Add 20 minutes to 40 minutes to get 60 minutes, or an hour.
Because of this, we need to add the progress of 20 minutes and 40 minutes. 1/5+2/5=3/5.
a bonsai tree grows 0.056 cm per year. If the tree is currently 10 cm tall, how tall will it be 5 years from now?
Answers
0.056 * 5 = 0.28 + 10 = 10.28 cm. Hope this helps!
what is the slope of the line through (-2,3) and (1,1)?
Answers
This is found by using the equation y2 - y1/x2 - x1. Filling in for each factor, you would have 1-3/1+2 (since subtracting a negative makes it positive). This will give you a final answer of -2/3.
Here is a graph of the full equation of the line.
I hope this helps!