The lateral area of the triangular prism is 21 square inches and the total surface area is 35 square inches.
Explanation:
To find the lateral area of the triangular prism, we need to calculate the area of all three sides excluding the bases. Since the bases are equilateral triangles with side lengths of 4 inches, the area of each base is ½ × base length × height = ½ × 4 × 3.5 = 7 square inches. The lateral area is the sum of the areas of the three sides, which is 3 × 7 = 21 square inches.
The total surface area of the prism includes the bases as well. So we need to calculate the area of the two triangular bases and add it to the lateral area. The total surface area is 2 (area of base) + lateral area = 2 × 7 + 21 = 35 square inches.
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The lateral area of the triangular prism is 60 square inches, and the total surface area is 74 square inches.
To find the lateral area and total surface area of a triangular prism:
Step 1: Calculate the Area of One Triangular Base
The base is an equilateral triangle with sides of 4 inches and a height of 3.5 inches. The area of an equilateral triangle is calculated using the formula:[tex]Area = \frac{1}{2}*base*height[/tex]
So the area is:[tex]Area = \frac{1}{2} *4\ in*3.5\ in = 7\ square\ inches[/tex]
Step 2: Calculate the Perimeter of the Base
The perimeter of the base is:Perimeter = 3 * side length = 3 * 4 in = 12 inches
Step 3: Calculate the Lateral Area
The lateral area of a prism is given by:Lateral Area = Perimeter * height of the prism
Therefore, the lateral area is:Lateral Area = 12 in * 5 in = 60 square inches
Step 4: Calculate the Total Surface Area
The total surface area is the sum of the lateral area and the areas of the two triangular bases:Total Surface Area = Lateral Area + 2 * Area of one baseTotal Surface Area = 60 square inches + 2 * 7 square inches = 74 square inchesThus, the lateral area and total surface area are 60 square inches and 74 square inches.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead and so on. Write the numbers for the first eight beads that are white. What is a rule for the pattern?
In Barb's necklace pattern, white beads occur at position numbers 1, 5, 9, 13, 17, 21, 25, and 29. The rule for the pattern is that any white bead will appear at a position that is 4n + 1, where n is any non-negative integer.
Explanation:The student's question involves determining the position numbers of the first eight white beads in a pattern and identifying a rule for this pattern. The pattern established by Barb is one white bead followed by three blue beads, which then repeats. To find the positions of the first eight white beads, let's enumerate the pattern until we have identified eight white beads.
WhiteBlueBlueBlueWhiteBlueBlueBlueWhite...As we can see, the white beads appear in a consistent pattern at every fourth position in the sequence. Thus, by listing out the pattern, we can identify the first eight white beads' position numbers as follows:
1591317212529The rule for the pattern can be described as follows: any white bead will be at a position number that is 1 more than a multiple of 4 (i.e., 4n + 1, where n is a non-negative integer).
The first eight white beads in Barb's necklace pattern are in positions 1, 5, 9, 13, 17, 21, 25, and 29. The rule for the pattern is 4n - 3 for the nth white bead.
Explanation:Barb is making a bead necklace with a repeating pattern: 1 white bead, followed by 3 blue beads, and then the pattern repeats. To determine the numbers for the first eight beads that are white, we can examine the pattern more closely. Since the pattern begins with a white bead and every white bead is followed by three blue beads, we can deduce that it takes 4 beads in total to complete one cycle of the pattern (1 white + 3 blue).
The positions of the first eight white beads are as follows: 1st, 5th, 9th, 13th, 17th, 21st, 25th, and 29th. The rule for this pattern can be expressed as follows: To find the position of any white bead in the sequence, you can use the formula 4n - 3, where n represents the nth white bead in the sequence.
For example, to find the position of the third white bead, we substitute n with 3 into our formula: 4 * 3 - 3, which equals 9. Therefore, the third white bead is the 9th bead in the overall pattern.
A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a 2 inch overhang around the base of the water heater? (Round to the nearest tenth.) square inches.
If you add the extra 2 inches in each side and give the base a diameter of 24. The area comes out to 452.39. The answer is 452.39.
Area of the metal base of the water heater is equals to 452.6 square inches.
What is area of a circle?
"Area of a circle is the region enclosed by the circle in two dimensional plane."
Formula used
Area of a circle = πr²
Value of π = 22 /7
According to the question,
Given diameter = 20 inches
2 inches extended around the base of the water heater
New diameter = 24 inches
Therefore, radius = 12inches
Substitute the value of radius and π in the formula we get ,
Area of the base of the water heater = ( 22/ 7) ×(12)²
= 452.57 square inches
= 452.6 square inches (nearest tenth)
Hence, area of the metal base of the water heater is equals to 452.6 square inches.
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Divide £24.50 in the ratio 3:4
Final answer:
24.50 divided in the ratio 3:4 gives £10.50 and £14.00.
Explanation:
To divide £24.50 in the ratio 3:4, you first need to add the parts of the ratio together, which gives you 3 + 4 = 7 parts in total.
Then, you should divide the total amount of money by the total number of parts to find the value of one part.
In this case, £24.50 ÷ 7 = £3.50 per part.
Since the ratio is 3:4, you multiply the value per part by the number of parts for each portion of the ratio.
For the first part of the ratio, you multiply £3.50 by 3, giving £10.50. For the second part, you multiply £3.50 by 4, giving £14.00.
Hence, £24.50 divided in the ratio 3:4 gives £10.50 and £14.00.
the measure of two supplementary angles have a ratio of 5:4. What is the measure of the larger angles?
Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smaller circles with a diameter one-half that of the large circle. Which statements about the areas are true? Check all that apply.
1.The radius of the large circle is 4.
2.The radii of the small circles are each 2.
3.The radii of the small circles are each 4.
4.The area of one small circle will be one-half of the area of the large circle.
5.The total area of the two small circles will equal that of the large circle.
6.The total area of the two small circles will be one-half of the area of the large circle.
Answer:
The answer is: 1, 2, and 6
Step-by-step explanation:
Answer with Step-by-step explanation:
Diameter of larger circle=8
Diameter of smaller circles=4
We know that radius is half times the diamketer
and Area=πr² where r is the radius
Radius of larger circle=4
Radius of smaller circles=2
Area of larger circle=π×4²
=16π
Area of two smaller circles=2×π×2²
= 8π=one-half the area of larger circle
Area of one small circle=π×2²
=4π=one fourth the area of larger circle
Hence, the correct options are:
1.The radius of the large circle is 4.
2.The radii of the small circles are each 2.
6.The total area of the two small circles will be one-half of the area of the large circle.
A line with a slope of 1/4 passes through the points (9, -8) and (5, d). what is the value for?
The value of the digit in the hundreds place in the number 653841 is 1/10 the value of the digit in the thousands place in which number?
A) 748917
B) 749817
C) 784917
D) 797481
A=LW;for L. Solve for the indicated variable. Include all work in the answer.
Solving for L , we get A/W= L
What are linear equations ?
Equations of degree 1 are called Linear Equation
To solve the above equation for the variable L . We need to isolate the variable on one side of the equation with the other terms on the other side
Given liner equation :
A= LW
In order to get L , need to isolate L and need to divide whole equation by W
A/W = LW/W
A/W= L
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Monica purchased adult and youth tickets for the fair. She bought x adult tickets for $28 each and y youth tickets for $15. Write an expression that can be used to show the total cost, C, of all tickets
simplify the expression 3 b 7 3b 21
Write an equation of the line that is perpendicular to y = −4x + 8 and passes through the point (5, 1)
Can someone please help me answer theses questions
Thank u so much
The graph show is
A)fails the vertical line test at (2,3) and (2,-2)
B) fails the vertical line test at (2,3) and (-1,3)
C) passes the vertical line test
So the line is
A) a function
B) not a function
a used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars?
Answer:
a
Step-by-step explanation:
m,n
The required expression for the sales price is 0.85p.
Given that,
A used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Cost price is the price the buyer pays to the seller for an object or product.
Here,
The original sales price of the card is p dollars,
There is a 15% discount on the sale of cars,
15 % discount,
= p 15/100
= 0.15p
Now, price after discount,
= p - 0.15p
= 0.85p
Thus, the required expression for the sales price is 0.85p.
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Caitlin says that AC is the longest segment of fencing
i really need help with this question
Which figure can be formed from the net?
Ms Hendricks is buying a rectangular piece of land that is 2/5 mile on one side and 5/6 mile on an adjacent side. What is the area of the piece of land. help me please I don't get this
Final answer:
To find the area of Ms. Hendricks' rectangular land, multiply the lengths of the sides (2/5 mile and 5/6 mile), resulting in an area of 1/3 square mile.
Explanation:
The area of a rectangular piece of land is calculated by multiplying the length by the width. For Ms. Hendricks' piece of land, which measures 2/5 mile on one side (length) and 5/6 mile on an adjacent side (width), you would calculate the area by multiplying these two dimensions together:
Convert the fractions to have a common denominator if needed.Multiply the numerators of the fractions to find the numerator of the area.Multiply the denominators of the fractions to find the denominator of the area.Simplify the fraction if possible to find the final area in square miles.So, the calculation for the area would be:
(2/5) mile * (5/6) mile = (2*5)/(5*6) square miles = 10/30 square miles = 1/3 square mile.
Therefore, the area is 1/3 square mile.
how do I do identify calculate the area and perimeter for quadrilaterals
To calculate the area and perimeter of a quadrilateral, you need to know the shape of the quadrilateral and the lengths of its sides. The area can be calculated using different formulas depending on the shape, such as trapezoid, rectangle, parallelogram, or square. The perimeter is calculated by adding the lengths of all the sides.
To calculate the area and perimeter of a quadrilateral, we need to know the shape of the quadrilateral and the lengths of its sides.
1. Area:
Trapezoid: The area of a trapezoid can be calculated using the formula A = (base1 + base2) × height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the distance between the parallel sides.Rectangle: The area of a rectangle is calculated by multiplying its length by its width, so A = length × width.Parallelogram: The area of a parallelogram is calculated using the formula A = base × height, where base is the length of one side and height is the perpendicular distance between the base and the opposite side.Square: The area of a square is calculated by multiplying the length of any side by itself, so A = side × side.2. Perimeter:
Trapezoid: The perimeter of a trapezoid is calculated by adding the lengths of all its sides.Rectangle: The perimeter of a rectangle is calculated by adding the lengths of its four sides, so P = 2 × length + 2 × width.Parallelogram: The perimeter of a parallelogram is calculated by adding the lengths of its four sides.Square: The perimeter of a square is calculated by multiplying the length of one side by 4, so P = 4 × side.Jeannie ate 1/4 of an apple.kelly ate 2/4 of the apple.how much did they eat together
Answer:
3/4
Step-by-step explanation:
fill in the blank with a symbol that makes this statement true 5/12 and 1/3
Which answer shows a correct order to solve this story problem? Victor bought 3 sandwiches for $3.25 each, 3 bags of chips for $1.10 each, and a bottle of water for $1.99. He left the waiter a $2.25 tip. How much did Victor spend?
A. Step 1: Add the price of a sandwich to the price of the bottle of water. Step 2: Multiply that total by 3. Step 3: Add the total price of 3 bags of chips to that total. Step 4: Add the tip to the final total for all the items.
B. Step 1: Calculate the total price of the 3 sandwiches. Step 2: Calculate the total price of the 3 bags of chips. Step 3: Add $1.99 to total cost for the sandwiches and chips. Step 4: Add the tip to the final total for all the items.
C. Step 1: Add the price of a sandwich and a bag of chips. Step 2: Add $1.99 to total for the sandwiches and chips. Step 3: Multiply that total by 3. Step 4: Add the tip to the final total for all the items.
How do you tell a triangle is not a right triangle
if a=37 degrees and b=6, find a.
A. 3.4
B. 4.5
C. 6.1
D. 2.5
To find the value of 'a' when a = 37 degrees and b = 6, trigonometry principles are used to calculate 'a' as approximately 34.08 degrees.
Given: a = 37 degrees and b = 6. To find a.
Using trigonometry: We can use the trigonometric ratio tangent to find a. tan(a) = b/c, where c is the hypotenuse. So, tan(37) = 6/c. Therefore, c = 6/tan(37) = 8.37. Hence, a = tan-1(b/c) = tan-1(6/8.37) ≈ 34.08 degrees.
Answer: Therefore, a = 34.08 degrees.
help please 40 points per question
different varieties of field daisies have numbers of petals that follow a fibonacci sequence.Three varieties have 13,21, and 347 petals.
How many petals do the next two varieties of field daisy have?
a. 42, 55
b. 47,60
c. 42,50
d. 55,89
Answer: D
55,89
I just did it and I got it right
Step-by-step explanation:
The table shows summary statistics for the dollar amounts spent by customers at two store locations over a period of 2 weeks.
Location Mean amount spent ($) Range ($)
A 84 15
B 97 25
Which conclusion is true?
Answer:
A.
Step-by-step explanation:
Curtis build a dog house with base shaped like a cube and a roof shaped like a pyramid. The cube has an edge lenght of 3 1/2 feet. The height of the pyramid is 5 feet. Find the volume of the doghouse rounded to the nearest tenth.
what does these equation equal to [x+x]+[x+x+x]=blank and [x+x+x]+[x+x+x]=
Answer:
[x+x] + [x+x+x] = [2x] + [3x] = 5x
[x+x+x] + [x+x+x] = [3x] + [3x] = 6x
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Chris is twice as old as Don, and next year the sum of their ages will be four times as much as Don’s age last year. Find their present ages.
Answer:
Chris is 12 years old and Don is 6 years old.
Step-by-step explanation:
;)
The present age of Don is 6 years old and Chris age is 12 years.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's denote Don's current age as x.
As Chris is twice as old as Don, Then, Chris's current age is 2x.
Next year, their ages will be x+1 and 2x+1 respectively.
The sum of their ages will be four times as much as Don’s age last year.
(x+1) + (2x + 1) = 4(x-1).
Expanding and solving for x:
3x + 2 = 4x - 4
x = 6
So, Don is 6 years old and Chris is 2×6 = 12 years old.
Hence, the present age of Don is 6 years old and Chris age is 12 years.
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