Use the net as an aid to compute the surface area (rounded to the nearest integer) ofvthe triangular pyramid with an equilateral triangle base. A) 106 ft^2 B) 114ft ^2 C) 122ft^2 D) 130ft^2
Answers
Answer:
106 ft²
Step-by-step explanation:
The surface area of a triangular pyramid is calculated with the following formula:
[tex]SA = \frac{H B}{2} + \frac{3 B S}{2}[/tex]
Where:
H is the height of the triangle base,
B is the side of the base triangle
S is the length of the slant.
so, if we plug in our numbers, we have:
[tex]SA = \frac{5.2 * 6}{2} + \frac{3 * 6 * 10}{2} = 15.6 + 90 = 105.6[/tex]
105.6 sq ft, which we round up to 106 square feet.
Related Questions
The function y=3.75 + 1.5(x-1) can be used to determine cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?
Answers
Answer:
1.5 dollars/miles
Step-by-step explanation:
Given function [tex]y=3.75 + 1.5(x-1)[/tex] can be used to determine cost in dollars for a taxi ride of x miles.
Now we need to find about what is the rate of change of the cost in dollars with respect to the number of miles.
First we need to rewrite [tex]y=3.75 + 1.5(x-1)[/tex] in y=mx+b form
[tex]y=3.75 + 1.5(x-1)[/tex]
[tex]y=3.75 + 1.5x-1.5[/tex]
[tex]y=2.25 + 1.5x[/tex]
[tex]y=1.5x + 2.25[/tex]
comparing with y=mx+b, we get m=1.5
Hence rate of change of the cost in dollars with respect to the number of miles is 1.5.
Write the phrase "twelve more than the product of seventeen and a number" as a mathematical expression.
A. 12 – 17x
B. 12 + 17x
C. 12 > 17x
D. 17 + 12x
Answers
Answer:
The answer is B. 12+17x
Step-by-step explanation:
Twelve more stands for +12 and the product of seventeen and a number is equal to 17*x or 17x.
Answer: OPTION B.
Step-by-step explanation:
You need to remember that a product is the result of a multiplication.
Let be the number mentioned in the problem "x", "the product of seventeen and a number" means that:
[tex](17)(x)=17x[/tex]
Now "twelve more than the product of seventeen and a number" indicates that you need to add 12 to [tex]17x[/tex].
Therefore, you can write the phrase in the following mathematical expression:
[tex]17x+12[/tex] or [tex]12+17x[/tex]
This matches with the option B.
(17 points)
Determine if line AB is tangent to the circle
Answers
1. If AB is tangent to the circle, then
[tex]18^2=(2\cdot7.2)^2+10.8^2[/tex]
We have
[tex]18^2=324[/tex]
[tex](2\cdot7.2)^2+10.8^2=324[/tex]
so AB is indeed tangent to the circle.
2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,
[tex](10+8)^2=8^2+15^2[/tex]
but we have
[tex](10+8)^2=324[/tex]
[tex]8^2+15^2=289[/tex]
so that cannot be a right triangle and AB is not tangent to the circle.
In a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
Answers
Answer:
123480
Step-by-step explanation:
We have to choose:
2 cellists from 8 cellists;4 violonists from 7 violonists;4 cellists or violonists from 9 remaining musicians (8-2=6 - cellists left, 7-4=3 - violonists left, 6+3=9 - left musicians in total)1. 2 cellists from 8 can be chosen in
[tex]C_8^2=\dfrac{8!}{2!(8-2)!}=\dfrac{8!}{2!6!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=28[/tex]
different ways.
2. 4 violonists from 7 can be chosen in
[tex]C_7^4=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!3!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{4!\cdot 2\cdot 3}=35[/tex]
different ways.
3. 4 musicians from 9 can be chosen in
[tex]C_9^4=\dfrac{9!}{4!(9-4)!}=\dfrac{9!}{4!5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!\cdot 2\cdot 3\cdot 4}=126[/tex]
different ways.
In total, there are [tex]28\cdot 35\cdot 126=123480[/tex] differnt ways to fill all vacancies.
Identify the following as exponential or linear and growth or decay
Answers
This would be linear growth because the y values are increasing, but not at an exponential rate.
Find the surface area of the regular hexagonal prism. Round your answer to the nearest hundredth.
Answers
Answer:
860.55 mm²
Step-by-step explanation:
The surface area of an hexagonal prism, also known as an octahedron, is given by the following formula (since we have the apothem):
S= 6*b*(a+h)
where b = is the side of the base, a is the apothem length, and h = the height
S = 6 * 8 * (4√3 + 11) = 48 * 17.92812 = 860.55 sq mm
Could have also have used another formula without the apothem:
S =3 * √3 * b² + 6 * b * h
S = 3 * √3 * 8² + 6 * 8 * 11 = 3√3 * 64 + 528 = 332.55 + 528 = 860.55 sq mm
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c + 20s ≤ 4,000, where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
Answers
Answer:
Option B is the correct answer.
Step-by-step explanation:
Find the length of the missing side. The triangle is not drawn to scale. Show your work. (Will give brainliest)
Answers
A^2 + b^2 = c^2
C is your hypotenuse or the longest side of the triangle; you plug in your values and solve for the missing side:
15^2 + b^2 = 17^2
225 + b^2 = 289
*-225 on both sides to get b by itself*
B^2 = 64
*to get rid of the ^2; you take the square root*
B = sqrt 64
B= 8 <— final answer
We can use the Pythagorean Theorem to solve for the missing side length (a).
Pythagorean Theorem:
a² + b² = c²
a and b are the legs (shorter sides) of the triangle and c is the hypotenuse (the longer side of the triangle).
1. Substitute in the known values.
a = ?
b = 15
c = 17
a² + 15² = 17²
2. Solve for a.
a² + 15² = 17²
a² + 225 = 289
a² + 225 - 225 = 289 - 225
a² = 64
√a² = √64
a = 8
Hope this helps!
Which statistical question could the data below answer ? Cost of toys
Answers
The statistical question that could be answered by the data is "maximum cost of toys".
The graph shown is a line graph which is a type of chart that displays data points connected by a line. It's a common way to visualize how a particular quantity changes over time or across different categories.
Line graphs makes it easy to determine statistical measures including minimum and maximum values of a category or data.
Here, the maximum cost of toys is 10 and the minimum is 5.
Find the lateral area and surface area of cone
Answers
Answer:
[tex]\large\boxed{L.A.=168\pi\ in^2}\\\boxed{S.A.=232\pi\ in^2}[/tex]
Step-by-step explanation:
The formula of a lateral area of a cone:
[tex]L.A.=\pi rl[/tex]
r - radius
l - slant height
The formula of a surface area of a cone:
[tex]S.A.=\pi r^2+\pi rl[/tex]
We have r= 8in and l = 21in. Substitute:
[tex]L.A.=\pi(8)(21)=168\pi\ in^2[/tex]
[tex]S.A.=\pi(8^2)+168\pi=232\pi\ in^2[/tex]
This table shows the length, in inches, of several nails.
Length (in.)
1
2
1
8
3
8
5
16
5
16
5
16
1
2
5
16
3
16
1
8
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Answers
A construction of the line plot for the length, in inches, of several nails is shown in the image attached below.
In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given length (in yards) of several nails on a line plot as shown in the image attached below;
Length Frequency
1/2 2
5/16 4
1/8 2
3/8 1
3/16 1
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5/16 because it has the highest frequency of 4.
Complete Question;
This table shows the length, in inches, of several nails.
Length (in) 1/2, 5/16, 1/8, 1/2, 3/8, 5/16, 5/16, 3/16, 5/16, 1/8.
Create a line plot to display this data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
answer this fast
will mark brainlist for sure
answer the question whichever u know
:)
Answers
Answer:
[tex]\large\boxed{1.\ 38\ and\ 22}\\\boxed{1'.\ 42\ and\ 30}[/tex]
Step-by-step explanation:
[tex]1.\\x,\ y-the\ numbers\ (x>y)\\\\\text{We have the system of equations:}\\\\\underline{\left\{\begin{array}{ccc}x-y=16\\x+y=60\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=76\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=38}\\\\\text{Put the value of x to the second equation.}\\\\38+y=60\qquad\text{subtract 38 from both sides}\\\boxed{y=22}[/tex]
[tex]1'.\\x-larger\ part\\x-12-smaller\ page\\\\x+(x-12)=72\\x+x-12=72\qquad\text{add 12 to both sides}\\2x=84\qquad\text{divide both sides by 2}\\\boxed{x=42}\\\boxed{x-12=30}[/tex]
Need help with b and c
Answers
Answer:
Step-by-step explanation:
the formula is:
[tex]a_n = \frac{n+1}{n+2}[/tex]
[tex]a_100 = \frac{101}{103}[\tex]
Answer:
see explanation
Step-by-step explanation:
We note that for each term, the numerator increases by 1 and the denominator increases by 1 from the previous term, that is
term 1 = [tex]\frac{1+1}{1+2}[/tex] = [tex]\frac{2}{3}[/tex]
term 2 = [tex]\frac{2+1}{2+2}[/tex] = [tex]\frac{3}{4}[/tex]
term 3 = [tex]\frac{3+1}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]
-----------------------------------------------------------------------------
term 100 = [tex]\frac{100+1}{100+2}[/tex] = [tex]\frac{101}{102}[/tex]
If we let n be the term value, then the n th term is
[tex]a_{n}[/tex] = [tex]\frac{n+1}{n+2}[/tex]
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus two.
Answers
Answer:
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
Step-by-step explanation:
We have the following limit
[tex]\lim_{x \to 0}\ x^2 -2[/tex]
To solve this limit using direct substitution to substitute the value that tends x into f(x) and simplify.
In this case x tends to zero, then we substitute x = 0 in the function and simplify
[tex]\lim_{x \to 0}\ x^2 -2= (0)^2 -2= -2[/tex]
Therefore
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
When x approaches 0 then f(x) it tends to -2
suppose that F(x)=x^3 and G(x)=-2x^3
Answers
Answer:
A
Step-by-step explanation:
Given a function f(x) = x^2, we can say:
g(x) = -(x^2) is the reflection of f(x) in the x-axish(x) = ax^2 is a vertical stretch if a > 1 and a vertical compression if 0 < a < 1The negative sign in front says that G(x) is flipped over the x-axis with respect to F(x). Also, the 2 in front tells us that it is a vertical stretch of the function F(x), since a > 1.
Hence, answer choice A is right.
Answer:
it is answer A
Step-by-step explanation:
Ap*x
Use the elimination method to solve the system of equations
Answers
Answer:
D- (3, 1).
Step-by-step explanation: Add the first equation so you can figure out what x equals. Then, plug the value into your next equation in order to find y. Hope this helps. :)
For this case we have the following system of equations:
[tex]2x + 4y = 10\\3x-4y = 5[/tex]
We solve by the method of elimination, then:
We add both equations:
[tex]2x + 3x = 10 + 5\\5x = 15\\x = \frac {15} {5}\\x = 3[/tex]
We find the value of y:
[tex]3 (3) -4y = 5\\9-4y = 5\\9-5 = 4y\\4 = 4y\\y = \frac {4} {4}\\y = 1[/tex]
Answer:
(3,1)
Option D
A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is the sale price?
Answers
First you divide 45/7 to find out what 10% of 45 is since 70% is $45
45/7= 6.42, so now you multiply 6.42 by 3 to fin out what the 30% is
6.42(3)= $19.28
Now you add $19.28+45 to add the 30% and the 70%, which is $64.28
100 - 70% = 30
0.30 × p (p=45)
0.30 × 45 = 13.5
the sale price is $13.50
Which of the following is an outlier in the set of data below? I think it’s 12 but I’m not so sure.
Answers
I think the answer might be 2
because
in the data given above all the numbers are between 12-19 they are all bigger than 10
and then there's 2 which is very far from 12 or any other numbers there and it is also less than 10
which makes more sense for it to be an outlier.
Hope this helps
Answer #6 and tell the steps of how u did it
Answers
Answer:
3131x+1
Step-by-step explanation:
Make equation simple
5x times 5x times 5x times 5x times 5x +x+1
Solve
5 times 5 times 5 times 5 times 5 = 3125
x times x times x times x times x times x = 5x
3125+5x=3130x
Now you might be thinking you cant add x but here your can because it is just broken apart
now add x+1
3131x+1
Type the correct answer in the box. Round your answer to the nearest hundredth.
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º.
Scarlett's height is 1.65 meters, so the height of the dam is meters.
Answers
Answer:
top question is not correct
Step-by-step explanation:
Answer:
what
Step-by-step explanation:
kate has 2/3 yards of fabric to make small flags each flag requires 1/6 yards of fabric how many flags cane kate make
Answers
Answer:
THE ANSWER IS 7
Step-by-step explanation:
CAUSE UR MOM IS A TRASHIE i'm sorry i meant YO MAMA
Final answer:
Kate can make 4 small flags from 2/3 yards of fabric since each flag requires 1/6 yards of fabric.
Explanation:
Kate has 2/3 yards of fabric and each small flag requires 1/6 yards of fabric. To find out how many flags Kate can make, you divide the total amount of fabric by the amount needed for one flag:
2/3 yards \/ 1/6 yards = 4 flags.
Here's the step-by-step calculation:
First, recall that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/6 is 6/1.
So, multiply 2/3 by the reciprocal of 1/6:
2/3 × 6/1 = 12/3 = 4.
Thus, Kate can make 4 small flags from the fabric she has.
___ cosb =1/2 sin(a+b)+sin(a-b)?
Answers
Answer:
That would be sina.
Step-by-step explanation:
sin(a+b) = sinacosb + cosasinb
sin(a-b) = sinacosb - cosasinb
Adding we get sin(a+b) + sin(a-b) = 2sinaccosb
so sinacosb = 1/2sin(a+b) + sin(a-b)
Answer:
sina
Step-by-step explanation:
We have
sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1
sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2
eqn 1 + eqn 2
sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb
sin(a+b) + sin(a-b) = 2sina cosb
[tex]sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))[/tex]
So answer is sina
x^2+y^2-16x-161=0 factor it
Answers
(x-8)^2+y^2=225 I'm not able to factor it
Please expla your answer as well. THX!!!
Answers
Answer:
[-7,5]
Step-by-step explanation:
The range is all the permitted values of y in the function. The lowest to the highest.
Looking at the function, the lowest y value is -7
and
the highest y value is 5
So we can say the range is [-7,5], the last choice
Which statement about these rectangles is true ?
Answers
the answer for this question is the dilation is reduction
The statement which is true about these rectangles is:
The dilation is an enlargement.
Step-by-step explanation:Dilation Transformation--
It is the translation which changes the size of the original figure.The shape of the figure is conserved.Also, in dilation either the size increases (i.e. the figure enlarges) or it decreases( i.e. the figure reduces).Also, in a polygon if there is a dilation then there is a scalar multiplication in each of the sides of the polygon.If the scalar multiple is greater than 1 then there is a enlargement.and if the scalar multiple is less than 1 but greater than 0 then there is a reduction.Here we see that each of the sides of the original figure is multiplied by "1.5" to obtain a larger rectangle.
This means that the dilation is a enlargement.
( since the scalar is strictly greater than one )
you find a triangle that has an area of 10 sq ft. the height of the triangle is 10 feet. what is the length of the base of the triangle?
Answers
Solution:
Given :
Area of triangle = 10 ft² Height of triangle = 10 ftSo, We have to find the Base of Triangle .
Area of triangle = 1/2*b×h, Where represents
B represent Base H represent HeightStep : Substitute those value in Formula;
Area of triangle = 1/2 × b × h
10 = 1/2 × b × 11
20 = 11 × b
b = 20/11
b = 1.81 ft
Therefore, Base of Triangle is 1.81 ft
Final answer:
To find the base of a triangle with an area of 10 sq ft and a height of 10 ft, use the formula 1/2 × base × height. By rearranging the formula and substituting the known values, the base is calculated to be 2 feet.
Explanation:
The question is asking to find the length of the base of a triangle when the area is 10 square feet and the height is 10 feet. The formula for the area of a triangle is 1/2 × base × height. In this case, we know the area (10 sq ft) and the height (10 ft), and we need to solve for the base.
Inserting the known values into the formula gives us:
Area = 1/2 × base × height
10 = 1/2 × base × 10
To solve for the base, we rearrange the formula:
base = 2 × Area / height
base = 2 × 10 / 10
base = 2 feet
Therefore, the length of the base of the triangle is 2 feet.
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product?
Answers
Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.
Explanation:To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.
Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.
Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).
Next, we can simplify the expression by combining like terms and further distributing where necessary:
3x2 – 36x2 + 3x2 – 2x2 + 8x – 8Combine like terms:
– 35x2 + 8x – 8Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.
Find the area of the following polygon
Answers
Answer:
84 m^2
Step-by-step explanation:
We can break the polygon into a rectangle and a triangle
The rectangle at the bottom is 12 by 4
A = 12*4 = 48
The triangle at the top has a base of 12 and a height of (10-4) = 6
A = 1/2 (12) *6 = 36
The total is the sum of the two areas
A = 48+36 =84 m^2
Match the description to the best example so that all terms have a matching example.
1. A set of decimal fractions
2. A set of whole numbers
3. A set of integers
4. A set of natural numbers
5. A set of rational numbers
here are the options
{3,4,5}
{¼,½, ¾ }
{0.1, 0.2, 0.3}
{0,1,2,3 }
{-2, -1, 0, +1}
Answers
Answer: 1. A- (0.1 0.2 0.3)
2.a-(3,4,5)
3.A-(-2,-1,0,+1)
4.a-(0123)
5.a-( 1/4 1/2 3/4
Step-by-step explanation:
I'm sorry you had to wait a whole year to get your answer :)
The exercise involves matching the terms decimal fractions, whole numbers, integers, natural numbers, and rational numbers to their respective sets of numbers. The correct matches are: decimal fractions {0.1, 0.2, 0.3}, whole numbers {0,1,2,3}, integers {-2, -1, 0, +1}, natural numbers {3,4,5}, and rational numbers {1/4,1/2, 3/4}.
Explanation:The goal here is to
match
the given
description
or term to the given sets of numbers according to their properties. Let's start.
A set of decimal fractions would be {0.1, 0.2, 0.3} as these are fractions written in decimal format. A set of whole numbers would be {0,1,2,3}. Whole numbers include all natural numbers and zero. A set of integers would be {-2, -1, 0, +1}. Integers are numbers that do not have fractional or decimal parts and they include both positive and negative numbers, and the number zero. A set of natural numbers would be {3,4,5} as these are numbers naturally counted starting from 1. Finally, a set of rational numbers would be {1/4,1/2, 3/4}. Rational numbers are numbers that can be expressed as fractions or ratios.So, we have successfully made a
matching
for each description.
Learn more about matching here:https://brainly.com/question/36757679
#SPJ2
The volume of a cube is 85.184 cubic inches. What is the length of each side of the cube?
Answers
Answer:
4.4 inches
Step-by-step explanation:
To work out the length of each side of the cube you would need to cube root of the volume as seen below:
[tex] \sqrt[3]{85.184} [/tex]
And this gives the answer 4.4 inches.
Answer:
Volume = Length * Width * Height
A cube has equal length, width, and height values.
[tex]\sqrt[3]{85.184}[/tex] is 4.4
So the length of each side is 4.4 units