a pieace of cheese is in the shape of a triangular prism.the dimensions of the cheese are shown below
what is the surface area of the piece of cheese
a)14.5
b)20.5
c)29
d)32
Answers
1) Two triangular faces
2) Three rectangular faces.
Surface area is the SUM of the areas of all of the faces.
Let us find these faces one by one:
1.
As you know, the area of the triangle is:
[tex] \frac{1}{2} * base * height [/tex]
Since, the base = 6 inches, and height = 4 inches;
Therefore, The area of ONE triangle = (1/2) * 6 * 4 = 12 inches squared.
In triangular prism, there are two triangles, therefore,
Two triangular faces = 2 * 12 inches = 24 inches squared --- (A)
2.
Now let us find the areas of three rectangular faces...
Since, two of the three rectangular faces are the same, therefore, we would find the area of one rectangular face, and multiple the result with two to get the total area of two rectangular faces.
Area of one rectangular face = base * height.
Since, base = 0.5 inches, height = 5 inches, therefore,
Area of one rectangular face = 0.5 * 5 = 2.5 inches squared.
Now that we have one rectangular face, therefore,
Area of two rectangular faces = 2 * 2.5 = 5 inches squared.
The area of the third rectangular base = 6 * 0.5 = 3 inches squared
Therefore,
The area of the three rectangular faces = 5 + 3 = 8 inches squared --- (B)
Now add both "area of two triangular faces(A)" and "area of three rectangular faces(B)" to get the final surface area of the triangular prism.
Surface Area of the triangular prism = Area of Two Triangular faces + Area of Three Rectangular faces
Surface Area = 24 + 8 = 32 inches squared
The surface area of the triangular prism = 32 inches squared.
The correct option is: d
-i
Answer:
Answer is d
Step-by-step explanation:
sorry that im 4 years late
Related Questions
How many outcomes are there in the sample space for rolling 1 die?
Answers
Answer:
6
Step-by-step explanation:
a puppy pen is 4 square feet wide and 5 feet long. is 21 square feet of fabric large enough to make a mat for the pen? Explain
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Michael will be travelling out of town for business. During his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. His employer will pay him for these meals at the following rate: $ 22.65 for dinner, $ 10.95 for lunch, and $ 6.53 for breakfast.
Answers
4 dinners = 22.65 x 4 = $90.60
one lunch = 10.95
5 lunches = 10.95 x 5 = $54.75
one breakfast = 6.53
3 breakfasts = 6.53 x 3 = 19.59
Total = $90.60 + $54.75 + $19.59 = $164.94
10 points!!!
Todd Gunderson went into a partnership with two of his friends. Manny and Jose, to share a route delivering newspapers. Manny owns 1/4 of the partnership, while Jose has a 1/5 interest. If the partnership's monthly revenue amounts to $765, how much of that is Todd's? Round to the nearest cent.
Answers
Todd + Manny + Jose = 1
X + 1/4 + 1/5 = 1
Change fractions to decimals for easier solving
x +.25 +.20 = 1
combine like terms
x+ .45 = 1
Subtract .45 from both sides
x=.55
todd has 55% of the shares
Revinue * Todd's Percent = Todd's Shares
765*.55 = 420.75
what is 0.080 as a fraction
Answers
Answer:
To write 0.080 as a fraction you have to write 0.080 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.080 = 0.080/1 = 0.8/10 = 8/100
So your final answer is: 0.080 as a fraction equals 8/100
Step-by-step explanation:
The decimal number 0.080 as a fraction is A = 2/25
Given data:
The decimal number is represented as 0.080
Step 1: Count the number of decimal places in the given decimal. So, there are three decimal places.
Step 2: Write the decimal as the numerator of the fraction. The decimal 0.080 becomes the numerator 80.
Step 3: Determine the denominator of the fraction. Since there are three decimal places, the denominator should be 10 raised to the power of the number of decimal places. So, the denominator is 10³ = 1000.
Putting it all together, 0.080 as a fraction is 80/1000.
Dividing both the numerator and denominator by 40:
80 ÷ 40 / 1000 ÷ 40 = 2/25
Hence, 0.080 as a simplified fraction is 2/25.
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Janice makes 4 pizzas for dinner. There are 5 people to eat dinner. How much will each person get to eat?
Answers
Divide the number of pizzas Janice makes by the number of people who will eat dinner.
4 ÷ 5 = 0.8
Each person will get to eat 0.8 of the pizza.
Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground
Answers
tan 65°=y/25------------> y=tan 65°*25 ( distance of the washer at the eye level)
[the window washer high above the ground]=[(tan 65°)*25+5.5]
[the window washer high above the ground]=[53.61+5.5]=59.11 ft
the answer is 59.11 ft
A stained glass window is shaped like a semicircle the bottom edge of the window is 36 inches long what is the area of the stained glass window
Answers
so, if the semi-circle has a diameter of 36, then the radius is half that, or 18
[tex]\bf \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2}\quad \begin{cases} r=radius\\ -----\\ r=18 \end{cases}\implies A=\cfrac{\pi 18^2}{2}\implies A=\cfrac{324\pi }{2} \\\\\\ A=162\pi [/tex]
A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions of the first garden. What is the percent of change in perimeter from the first garden to the second garden? The perimeter increases % from the first garden to the second garden.
Answers
Answer:
100%
Step-by-step explanation:
When the dimensions double, the perimeter doubles.
The percent change can be found from ...
percent change = ((new value)/(old value) -1) × 100%
Filling in your values, you have ...
percent change = ((2×(old perimeter))/(old perimeter) -1) × 100%
= (2 - 1) × 100%
= 100%
The perimeter increases by 100% from the first garden to the second.
Help!!!!!!!!!!!!!!!!!!!!!!!
please ty
c:
Answers
.. A = (1/2)*b*h
.. 36 in^2 = (1/2)*b*(9 in)
.. (72 in^2)/(9 in) = b . . . . . . . . multiply by 2, divide by 9 in
.. 8 in = b
The base is "none of the above", 8 inches.
_____
This question has a couple of problems:
.. 1) area is not measured in "inches"; it is measured in "square inches."
.. 2) ALL of the offered answer choices are INCORRECT.
Please help me out with #8 surface area and please explain
Answers
angle symbol is meant to connect to the vertical line closest to us.
What's all the writing to the left and right. What does it say?
Finally what do you know? Can you find area using Heron's Formula for area. I'm going to hold off saying much. You can put a remark somewhere. The magic editor will pick it up and tell me you've done it.
Andy and alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid 20$ for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large sized prints cost
Answers
Final answer:
To find the cost of small and large prints, we create two equations based on Andy's and Alex's orders and solve for the two variables. The small 4x6 inch prints cost $0.50 each, and the large 8x10 inch prints cost $1.25 each.
Explanation:
To solve how much small and large sized prints cost, we can set up a system of linear equations based on the information given:
Andy's order: 40 small prints and 10 large prints for $32.50Alex's order: 20 small prints and 8 large prints for $20.00Let s represent the cost of a small 4x6 inch print, and let l represent the cost of a large 8x10 inch print. We can then form the equations:
40s + 10l = 32.5020s + 8l = 20.00By dividing the first equation by 2, we get:
20s + 5l = 16.25Subtracting the second equation from this result gives:
(20s + 5l) - (20s + 8l) = (16.25 - 20)-3l = -3.75l = 1.25With the cost of a large print found, we can plug this back into the second equation to find the cost of a small print:
20s + 8(1.25) = 2020s + 10 = 2020s = 10s = 0.50Therefore, the cost of a small 4x6 inch print is $0.50 and a large 8x10 inch print is $1.25.
The given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y = c1e4x + c2e−x, (−∞, ∞); y'' − 3y' − 4y = 0, y(0) = 1, y'(0) = 2
Answers
Solution:
The given differential equation is,
[tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex]------(A)
Differentiating once,with respect to x,
[tex]y'=4C_{1}e^{4 x}-C_{2}e^{-x}[/tex]-------(1)
Differentiating again with respect to x,
[tex]y"=16C_{1}e^{4 x}+C_{2}e^{-x}[/tex]-------(2)
Equation (1) + Equation (2)
y' +y" [tex]=20 C_{1}e^{4 x}[/tex]
[tex]C_{1}=\frac{y'+y"}{20e^{4 x}}[/tex]
4 ×Equation (1) - Equation (2)
4 y'- y"[tex]=-5 C_{2}e^{-x}[/tex]
[tex]C_{2}=\frac{4y'-y"}{-5e^{-x}}[/tex]
Substituting the value of [tex]C_{1},C_{2}[/tex] in A,we get
[tex]y=\frac{y'+y"}{20}+\frac{4 y'-y"}{-5}\\\\ 20 y=y'+y"-16 y'+4 y"\\\\ 20 y=-15 y'+5y"\\\\ 4 y+3 y'-y"=0[/tex]
As, y(0)=1 , and y'(0)=2, gives
[tex]C_{1}+C_{2}=1\\\\ 4C_{1}-C_{2}=2[/tex]
gives , [tex]5C_{1}=3\\\\ C_{1}=\frac{3}{5}\\\\ 5 C_{2}=2\\\\ C_{2}=\frac{2}{5}[/tex]
So, member of the family that is a solution of the initial-value problem, [tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex] is
[tex]5 y=3 e^{4 x}+2 e^{-x}[/tex]
Grace has 2 cups of strawberries and plans to divide this amount into equal parts to make 3 strawberry pies. What fraction of a cup of strawberries will be used for each pie?
Answers
[tex] \frac{2}{3} [/tex]
cups for each individual pie.
Number of cups of Strawberries are there for 3 pies =2
Now we apply unitary method here to find how many strawberries are need for 1 pie.
Number of cups of Strawberries required for 1 pie = 2/3
Answer: So Grace would require 2/3 cups of Strawberries for making one pie.
The gandhara region is the home of many portrayals of ____.
Answers
What is the GCF of 14x^2 and 4xy? A. 10x B. 28x^2y C. 2x2 D. 2x
Answers
14x^2 and 4xy
answer is D. 2x
The low temperature in Leroy’s town one day was -4. The difference between the high temperature and the low temperature that day was 6. The equation h-(-4)=6 can be used to find h, the high temperature in the town that day in degrees Fahrenheit. What was the high temperature in the town that day, in degrees Fahrenheit?
Answers
Solve and plot your answer on the number line below: 7.08 + 2x=15.96
Answers
-7.08. -7.08
-------------------------
2x=8.88 divide each by 2
X=4.44
You would plot it in between 4 and 5 but on one of the line marks depending on what there value are
Which undefined term is needed to define an angle????
Answers
POINT WASNT AN OPTION ON MY TEST. THE ANSWER WAS PLANE. THE ANSWER CAN BE POINT, LINE, OR PLANE.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
Christian got a haircut yesterday afternoon if the hair stylist charged $18 and christian gave 20% tip how much dod he pay for the haircut
Answers
Answer:
He paid $ 21.6 for the haircut.
Step-by-step explanation:
Given,
The amount charged by hair stylist = $ 18,
The percentage of tip = 20 %,
So, the amount of the tip = 20 % of 18
= 0.2 × 18
= $ 3.6,
Hence, the total amount paid by him for haircut = The amount charged by hair stylist + Tip
= $ 18 + $ 3.6
= $ 21.6
A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p? 0.07p 0.93p 1.07p 7.00p
Answers
If you have an item that costs 10 dollars and a sales tax of 7% you could do it this way
10 * 7/100 = 0.70 dollars.
The total cost is 10.70 dollars. or 10 dollars and 70 cents.
The best way to do the total however is to multiply the cost by 1.07. You will get the number the customer has to pay.
10 * 1.07 = 10.70
So for any price (p) it would be 1.07*p
Answer:
1.07p
Step-by-step explanation:
The tax equals the price times the tax rate
We know the price p and the tax rate 7%
tax = p*7%
Changing this to decimal form
tax = .07p
The final price of the item is the sales tax plus the price
final price = tax + price
.07p +p
1.07p
Zakai cuts a piece of birthday cake as shown below.
What is the volume of the piece of cake?
Answers
A=10*18/2
A=90
V=A*H
V=90*6
V=540
ASAP Select the statement that correctly describes the expression below.
(2x+5)^2
a) the sum of the square of 2 times x and 5
b)the square of the sum of 2 times x and 5
c)the square of 2 times the addition of x and 5
d)the sum of 2 times x and the square of 5
Answers
Answer:
Option B
Step-by-step explanation:
The given expression is ( 2x + 5)²
We have to form a statement to describe the expression given.
(2x + 5)² square of sum of 2 times x and 5
Option B is the correct answer.
Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32?
Answers
Answer:
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
Step-by-step explanation:
First, to have the fraction to the lowest terms we will have to divide the numerator and denominator by 2, this is:
[tex]\frac{10/2}{16/2}=\frac{5}{8}[/tex]
As can be seen the expression couldn't be simplified more because there is no a common number that could divide the numerator and denominator.
Second, to have an equivalent fraction with 32 in the denominator we will have to multiply the denominator by 2 and of course the numerator, this is:
[tex]\frac{10*2}{16*2}=\frac{20}{32}[/tex]
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
To simplify 10/16 to lowest term, it becomes 5/8. An equivalent fraction of 5/8 with 32 as the denominator is 20/32.
Explanation:To simplify 10/16 to its lowest term, we have to find the greatest common divisor of 10 and 16, which is 2. Hence, when we divide both the numerator and the denominator by 2, we get 10/2 = 5 and 16/2 = 8. So, the fraction 10/16 simplified to its lowest term is 5/8.
Now, to find an equivalent fraction with 32 as the denominator, we need to multiply both the numerator and the denominator of 5/8 by the same number so as not to change the value of the fraction. Here, we multiply by 4 (since, 8*4 = 32) to get 5*4 = 20 on the numerator. Therefore, an equivalent fraction of 5/8 with 32 as the denominator is 20/32.
Learn more about Fraction Simplification here:https://brainly.com/question/15605622
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if the parent function is square root of x, describe the translation of this function square root x+7
Answers
The function [tex] y=\sqrt{x} [/tex] sits with its starting point at the origin. The function [tex] y=\sqrt{(x-h)}+k [/tex] is translated h units to the left or right and k units up or down. Since our radicand, the value under the square root sign, is x+7, putting that into our standard form it would be x-(-7) because minus a negative is a positive. So we move the parent graph to the left (-7 moves to the left) 7 units. There is no number k so our function is not moving up or down. Only to the left 7.
Use the following figure to answer the question. 1 and 4 are _____ angles. corresponding vertical supplementary adjacent
Answers
Hope this helps! Have a blessed day!
Answer:
vertical angles
Step-by-step explanation:
We need to identify ∠1 and ∠4 are which type of pair of angles .
Since we are given the options :
1, correspoding angles: Corresponding Angles
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.
2. vertical angles : The angles opposite each other when two lines cross. They are always equal.Vertical" refers to the vertex (where they cross), NOT up/down
3. supplementary angles : Two Angles are Supplementary when they add up to 180 degrees
4. adjacent angles:Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
Thus according to definitions ∠1 and ∠4 are vertical angles
Determine the x-intercept of 5x -6y =10
Answers
This is a linear equation...
A typical linear equation is written in the form
y=mx+c
Where m=gradient
And c=intercept
So all you have to do is to express y in terms of x "make y the subject of the formula"
Therefore 5x-6y=10
6y=5x-10
Divide through by 6
6y/6 = 5x/6 - 10/6
The intercept here is = - 10/6
Gradient = 5/6-----the coefficient of x....
Hope this helped.....???
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
Answers
original fraction = x/y
numerator decreased by 50% = 0.5x
denominator decreased by 25% = 0.y75
new fraction = 0.5x/0.75y = 2/3 (x/y)
new fraction is 2/3 of the original fraction. It decreased by 1/3
1/3 x 100 = 33%
Percentage decreased = 33%
Answer:
33.33% will work
Step-by-step explanation:
RSM BOI
find the surface area of the toolbox
Answers
Consider the quadratic equation x2=4x-5. How many solutions does the equation have
Answers
as you notice the term under the square root is b^2-4ac if it is postive then the equation clearly will have two real soultions if it is negative then the equation will have two imaginary soultion if it is zero then the the equation will have one soultion
so let us calculate b^2-4ac for our given equation
x^2=4x-5 so let us write it in general form which is ax^2+bx+c=0
subtracting 4x from both sides
x^2-4x=-5
adding 5 to both sides
x^2-4x+5=0
a=1,b=-4,c=5
b^2-4ac=(-4)^2-4(1)(5)=16-20=-4
which means the equation has two imaginary soultions
now, plugging in those values for the discriminant, we'd get
(-4)² - 4(1)(5).