Multiply corresponding components, then add the products:
[tex]v\cdot w=3(-4)+(-8)(-2)+(-3)(-6)=22[/tex]
The resultant of the dot product of two vectors is:
[tex]v\cdot w=22[/tex]
Step-by-step explanation:We are asked to find the dot product of the two vectors v and w.
The vectors are given by:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
This means that in the vector form they could be written as follows:
[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]
Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.
i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.
Hence, the dot product of v and w is calculated as:
[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]
Pls help!!!
The volume of a triangular pyramid is 1800 cubic inches. If the base of the solid has a height of 18 inches and a base of 12 inches, what is the height of the pyramid?
Answer:
The height of the pyramid is [tex]50\ in[/tex]
Step-by-step explanation:
we know that
The volume of a triangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
we have
[tex]V=1,800\ in^{3}[/tex]
The area of the base B is equal to
[tex]B=\frac{1}{2}(12)(18)=108\ in^{2}[/tex]
substitute and solve for H
[tex]1,800=\frac{1}{3}(108)H[/tex]
[tex]5,400=(108)H[/tex]
[tex]H=5,400/(108)=50\ in[/tex]
In ideal conditions 200 colony forming units (cfu) of e. Coli can grow to 400 cfu in 20 minutes to 800 cfu in 40 minutes and to 1600 cfu in an hour. Write an equation that models the function
Answer:
Step-by-step explanation:
The population doubles every 20 minutes, so:
x = 200 (2)^(t / 20)
A wheel with a dot on its edge rolls on the ground. The radius of the wheel is 15 inches. When the dot is at the position shown below, at an angle of 112°, what is the distance of the dot above the ground, to the nearest tenth of an inch?
Answer:
The distance of the dot above the ground is 28.9 in
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle ABC is an isosceles triangle
CA=CB=15 in ------> is the radius of the circle
∠ACD+112°=180° ---> because the diameter divide the circle into two equal parts
∠ACD=180° -112°=68°
In the right triangle ACD
Find AD we have sin(68°)=AD/AC AD=AC*sin(68°) substitute the value AD=15*sin(68°)=13.9 in
Find the distance AB
AB=2*AD AB=2*13.9=27.8 in
The diameter is equal to
2*15=30 in
The distance of the dot above the ground is equal to
AB+(30-27.8)/2
27.8+1.1=28.9 in
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
1 ≥ 2x
6x ≥ 3 + 8x – 4
Answer:
6x ≥ 3 + 4(2x - 1)
⇔ 6x ≥ 3 + 8x - 4 => remove the parentheses
⇔ 6x - 8x ≥ 3 - 4
⇔ -2x ≥ -1
⇔ 2x ≤ 1 (or 1 ≥ 2x)
⇔ x ≤ 1/2
⇔ x ≤ 0.5
The answer for the question should be:
1 ≥ 2x
6x ≥ 3 + 8x – 4
and the first graph.
Answer:
1 ≥ 2x
6x ≥ 3 + 8x - 4
and the first line graph.
Step-by-step explanation:
6x ≥ 3 + 4(2x – 1)
6x ≥ 3 + 8x - 4
6x - 8x ≥ -1
-2x ≥ -1
x ≤ 1/2
or 1 ≥ 2x.
Which of the following is a solution to the system of linear equations below ? 2x+y=2 x-3y=-27
Answer:
(-3, 8)
Step-by-step explanation:
We are given two equations and we have to find the solution to the given equations. We can do this by using substitution method as shown below:
[tex]2x+y=2[/tex] Equation 1
[tex]x-3y=-27[/tex] Equation 2
From Equation 1, we can get the value of y as:
[tex]y=2-2x[/tex] Equation 3
Using this value of y in equation 2, we get:
[tex]x-3(2-2x)=-27\\\\ x-6+6x=-27\\\\ 7x=-21\\\\ x=-3[/tex]
Thus value of x is -3. Using this value in Equation 3, we get:
[tex]y=2-2(-3)\\\\ y=2+6\\\\ y=8[/tex]
Thus the solution to the given equations is (-3, 8)
How are symbols useful in math?
Answer:
They are clearly written to be able to find a clear solution, it clearly tells you what to do, and how, you just have to find out the way to be able to use the hints in a simple word problem, so it finds its way to be solved
Step-by-step explanation:
the difference between 100,000,000 and -100,000,000 is greater than a hyphen. Mathematical sentences without symbols would be as nonsensical as regular sentences without verbs: they tell you what to do
Which answer describes this type of series 240+144+86.4+51.84
Well this series is neither arithmetic or geometric as said in the other solution but since there are addition signs I will find the sum
The sum is 522.24
Which of the following equations can be used to find the length of BC in the triangle below??? Help :)
Answer:
D
Step-by-step explanation:
Using Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence
(BC)² = 10² + 30² → D
The equation that is needed to find the length of BC is [tex]BC^2 = 10^2 + 30^2[/tex].
The correct option is D.
To find the length of side BC in the triangle ABC, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, triangle ABC has a right angle at angle BAC.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can use this theorem to find the length of BC.
Let BC be denoted as x. According to the Pythagorean theorem, we have:
[tex]BC^2 = AB^2 + AC^2[/tex]
Substituting the given values, we get:
[tex]BC^2 = 10^2 + 30^2[/tex]
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If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ? (1 point)
[tex]\sin\theta=\dfrac13>0[/tex], so
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}<0\implies\cos\theta<0[/tex]
Recall that
[tex]\cos^2\theta+\sin^2\theta=1[/tex]
for all [tex]\theta[/tex], and knowing that [tex]\cos\theta<0[/tex] we have
[tex]\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt2}3[/tex]
It takes 20 minutes for 5 people to paint 5 walls. How many minutes does it take 9 people to paint 9 walls
5 people , 1 wall ~ 20/5 = 4 minutes
1 person, 1 wall ~ 4/5 minutes
9 people, 1 wall ~ (4/5) x 9 = (36/5) minutes
Therefore 9 people, 9 walls ~ (36/5) x 9
= 64.8 minutes
= 1h 4 min 48 s
Answer:
It takes 20 minutes :)
Step-by-step explanation:
On a trip to Griffith Observatory, Dave rode his bicycle six more than twice as many miles in the afternoon as in the morning. If the entire trip was 57 miles long, then how far did he ride in the morning and in the afternoon?
Answer:
Dave rode his bicycle 17 miles in the morning
Dave rode his bicycle 40 miles in the afternoon
Step-by-step explanation:
* Lets study the information to solve the question
- Dave rod his bicycle in the morning and again in the afternoon
- Six more than twice as many miles in the afternoon as in the morning
means the distance in the afternoon is 6 more than twice the distance
in the morning
- The entire trip was 57 miles means the total distance in the morning
and in the afternoon was 75
* To solve the question let the distance in the morning is x miles
∵ The distance in the morning = x miles
∵ The distance in the afternoon is 6 more than twice the distance
in the morning
∴ The distance in the afternoon = 2x + 6 miles
∵ The distance in entire trip = 57 miles
- The distance in the morning and the distance in the afternoon = 57 miles
∴ x + (2x + 6) = 57 ⇒ simplify
∴ 3x + 6 = 57 ⇒ subtract 6 from both sides
∴ 3x = 51 ⇒ divide both sides by 3
∴ x = 17 miles
∵ The distance in the morning is x miles
∴ Dave rode his bicycle 17 miles in the morning
∵ The distance in the afternoon = 2x + 6 miles
- Substitute the value of x
∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles
∴ Dave rode his bicycle 40 miles in the afternoon
Help, please Jake has $100 of birthday money in his wallet. He spends $15 at Twistee Treat and $10 at Wawa. While walking home he finds a $20 bill on the ground. His friend borrows $40 from Jake. At home, Jake mows the lawn and earns $35. Evaluate an expression to determine how much money Jake has in his wallet.
Answer:
The expression is [tex]x=100-15-10+20-40+35[/tex]
Jake has in his wallet [tex]\$90[/tex]
Step-by-step explanation:
Let
x-----> the money that Jake has in his wallet
we know that
The expression that represent the situation is equal to
1) Jake has $100 of birthday money in his wallet
so
[tex]x=100[/tex]
2) He spends $15 at Twistee Treat and $10 at Wawa
so
[tex]x=100-15-10[/tex]
3) He finds a $20 bill on the ground
so
[tex]x=100-15-10+20[/tex]
3) His friend borrows $40 from Jake
so
[tex]x=100-15-10+20-40[/tex]
4) At home, Jake mows the lawn and earns $35
so
[tex]x=100-15-10+20-40+35[/tex]
[tex]x=\$90[/tex]
Jake has $90 in his wallet after accounting for all his expenses, earnings, and the money borrowed by his friend. This calculation includes his birthday money, spending, found money, and earnings from mowing the lawn.
To determine how much money Jake has in his wallet, we need to account for all his spending, earnings, and borrowings.
Start with Jake's initial amount: $100Subtract his spending at Twistee Treat: $100 - $15 = $85Subtract his spending at Wawa: $85 - $10 = $75Add the $20 bill he found: $75 + $20 = $95Subtract the $40 borrowed by his friend: $95 - $40 = $55Add the earnings from mowing the lawn: $55 + $35 = $90Therefore, Jake has $90 in his wallet.
Convert 6cis (5pi)/6 to rectangular form.
A. 3 Square root of 3 + 3i
B. -3 Square root of 3 +3i
C. 3 Square root of 3 - 3i
D. -3 Square root of 3 - 3i
E. 3 - 3 Square root of 3 i
Answer:
B
Step-by-step explanation:
I love these! Ok, the expanded formula you need for this is
[tex]6(cos\frac{5\pi }{6}+sin\frac{5\pi }{6}i)[/tex]
From the unit circle we get the cos and sin of that angle and fill them in:
[tex]6(-\frac{\sqrt{3} }{2}+\frac{1}{2}i)[/tex]
Distributing through the parenthesis gives you
[tex]-\frac{6\sqrt{3} }{2}+\frac{6}{2}i[/tex]
which simplifies to
[tex]-3\sqrt{3}+3i[/tex]
To convert 6cis (5pi)/6 from polar form to rectangular form, use the formula r*cos(theta) + r*sin(theta)*i. The magnitude (r) is 6 and the angle (theta) is 5pi/6. The rectangular form results to be B. -3 Square root of 3 +3i.
Explanation:The student is asked to convert the complex number 6cis (5pi)/6 from polar form to rectangle form. In polar form, a complex number can be represented as rcis(theta), where r is the magnitude and theta is the angle. To convert this to rectangular form, we use the formula r*cos(theta) + r*sin(theta)*i. In this case, r=6 and theta=5pi/6. Therefore, the rectangular form of the given number is (6*cos(5pi/6)) + (6*sin(5pi/6))*i which equals -3 +
3 square root
of 3*i. Hence, the correct answer is B. -3 Square root of 3 +3i.
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the time to complete a project, T, varies inversely with the number of employees, E, if 6 employees can complete the project in 7 days, hoy long will it take 12 employees?o
Answer:Add T with e and thats your answer.
Step-by-step explanation:
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 5x+7=2y and y-9x=23
A) {}
B) 1 solution
C) Infinite
Answer:
The correct option is option B. It has one solution, and it's x=-3
Step-by-step explanation:
We have the following system of equations:
5x+7 = 2y (1)
y-9x=23 (2)
Step 1: Solve for 'y' in equation (2):
y-9x = 23
y = 9x + 23
Step 2: Substitute in equation (1):
5x + 7 = 2y
5x + 7 = 2(9x + 23)
5x + 7 = 18x + 46
Step 3: Solve for x:
7 - 46 = 18x - 5x
-39 = 13x
x= -3
So the correct option is option B. It has one solution, and it's x=-3
Answer: Option B
The system has 1 solution
Step-by-step explanation:
We must solve the following system of equations
[tex]5x+7=2y\\\\y-9x=23[/tex]
To solve it, clear y from the second equation and then substitute in the first equation
[tex]y=23 + 9x[/tex]
Now substitute in the first equation
[tex]5x+7=2(23 + 9x)\\\\5x +7 = 46 + 18x\\\\5x -18x = 46-7\\\\-13x = 39\\\\x = -\frac{39}{13}\\\\x=-3[/tex]
A triangle has side lengths:
5,13,12 Is this triangle a right triangle, an acute triangle of an obtuse triangle?
Answer
5^2 + 12^2 = 25 + 144 = 169 = 13^2
Therefore, it is a right triangle.
Step-by-step explanation:
Answer:
5² + 12² = 25 + 144 = 169 = 13²
Therefore, it is a right triangle.
Step-by-step explanation:
A washer and a dryer cost $696 combined. The washer costs $46 more than the dryer. What is the cost of the dryer?
You're buying two items, we can represent them as X. First you set one of the X's to be the dryer, and since we know that the washer costs 46 more than the dryer, that can be represented as X + 46. The equation can be written as follows:
x + (x + 46) = 696
2x + 46 = 696
2x = 650
x = 325
Therefore, the dryer costs $325, and the washer costs $371
The cost of the dryer is found by setting up an equation where x represents the dryer's cost and solving for x. The calculation steps reveal that the dryer costs $325.
The student is asking how to find the cost of a dryer when given the combined cost of a washer and dryer, and that the washer costs $46 more than the dryer. To solve this, we first let the cost of the dryer be x dollars. Therefore, the cost of the washer would be x + $46. We are told that combined they cost $696.
Setting up the equation: x + (x + $46) = $696.
Combine like terms: 2x + $46 = $696.
Subtract $46 from both sides: 2x = $696 - $46.
Calculate the remaining balance: 2x = $650.
Divide both sides by 2 to find the cost of the dryer: x = $325.
Therefore, the cost of the dryer is $325.
1. Find the area of the regular polygon to the nearest tenth.
square with a radius of 13 m
A) 344 m²
B) 676 m²
C) 169 m²
D) 338 m²
2. Find the area of the triangle give the answer to the nearest tenth. The drawing may not be to scale.
(see picture attached)
A) 47.4 cm²
B) 94.8 cm²
C) 7.5 cm²
D) 303.1 cm²
Answer:
D) 338 m² A) 47.4 cm²Step-by-step explanation:
You can use the same formula in each case. The area of a triangle with sides "a" and "b" separated by angle α is ...
A = (1/2)ab·sin(α)
1. The area of the square is 4 times the area of the right triangle whose legs are radii of the square:
square area = 4·(1/2)·(13 m)(13 m)sin(90°) = 2·(13 m)² = 338 m²
__
2. The area is ...
A = (1/2)(8 cm)(12 cm)sin(81°) ≈ 47.4 cm²
For this one, you don't need to work out the answer in detail. You know it will be less than, but nearly, 48 cm², which is half the product of the side lengths.
What is the surface area of the regular pyramid below
[tex]
S=14\times14+4(\frac{14}{2}\times18) \\
S=196+4(7\times18) \\
S=196+4\times126 \\
S=196+504 \\
S=\boxed{700}
[/tex]
Answer:
B. [tex]700\text{ inches}^2[/tex].
Step-by-step explanation:
We have been given an image of a pyramid. We are asked to find the total surface area of the given pyramid.
[tex]\text{Surface area of pyramid}=A+\frac{1}{2}*ps[/tex], where,
A = Area of base of pyramid.
p = Perimeter of base,
s = Slant height,
Upon substituting our given values, we will get:
[tex]\text{Surface area of pyramid}=14^2+\frac{1}{2}*4*14*18[/tex]
[tex]\text{Surface area of pyramid}=196+2*14*18[/tex]
[tex]\text{Surface area of pyramid}=196+504[/tex]
[tex]\text{Surface area of pyramid}=700[/tex]
Therefore, the total surface area of given pyramid is 700 square inches and option B is the correct choice.
please help ASAP.. Question below
Answer:
option B and option D
0 and 2
Step-by-step explanation:
Given in the question two functions
f(x) = x² - 4x + 3
g(x) = -x² + 3
f(x) = g(x)
x² - 4x + 3 = - x² + 3
Rearrange the like terms, x terms to the left and constant term to the right.
x²+ x² - 4x = 3 - 3
2x² - 4x = 0
Divide by two
2x²/2 - 4x/2 = 0/2
x² - 2x = 0
Take x as a common term
x(x-2) = 0
so
x = 0
or
(x-2) = 0
x = 2
Answer:
0
3
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2-4x+3[/tex]
We can rewrite this function in the vertex form to obtain;
[tex]f(x)=(x-2)^2-1[/tex]
This is the graph of the parent function [tex]h(x)=x^2[/tex] shifted, 2 units to the right and 1 unit down.
The second function is
[tex]g(x)=-x^2+3[/tex]
This is the graph of the parent function [tex]h(x)=x^2[/tex] reflected in the x-axis and shifted up 3 units.
The graph of the two functions are shown in the attachment.
The solution to f(x)=g(x) is where the two graphs meet.
The two graphs intersected at
(0,3) and (2,-1)
One of the steps Misaki used to solve an equation is shown below.
Which property justifies the step shown?
2q(q+4)=10 2q^(2)+8q=10
multiplicative identity property
associative property
commutative property
distributive property
inverse property
Answer:
Distributive property
Step-by-step explanation:
The given equation is:
[tex]2q(q+4)=10[/tex]
To solve this equation, we expand the left hand side using the distributive property to obtain:
[tex]2q^2+8q=10[/tex]
That was exactly what Miskai did.
Therefore the property that justifies his step shown is the distributive property.
This property says that, if a, b, and c are real numbers then,
[tex]a(b+c)=ab+bc[/tex]
If it takes 63 minutes for 4 people to paint 9 walls, how many minutes does it take for 7 people to paint 4 walls ?
Answer:
49 minutes
Step-by-step explanation:
knowing that the more people, the lower the time (divide), and the more walls, the more time (multiply)
1. find how long it takes 1 person to paint 1 wall:
63 minutes/9 walls = 7 minutes/wall with 4 people
7 minutes * 4 people = 28 minutes/wall with 1 person
2. Find for 7 people and 4 walls: 28 minutes * 7 people/4 walls = 196/4 =
49 minutes
Answer:
The correct answer is 16 minuets!
Step-by-step explanation:
You can use the formula PRT=w
(P=people) (R=rate) (T=time) (w-work)
You would start by plugging the numbers in for the given information:
(4 people)*(r)*(63min)=9walls
then solve for r
in this case r=.035714286
You can use this infromation to find what is being asked and the previously mentioned formula:
(7 people)*(.035714286)*(t) = 4 walls
Now all you have to do is solve for t to get the answer.
In this case t=16
(I also just had this question asked on an online quiz and got it correct so I know the answer is right)
Hope this helps!
WILL GIVE THE BRAINLIST !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I REALLY NEED THIS A.S.A.P !!!write 1/400 as a percent to the nearest hundredth of a percent
Answer:
0.25%
Step-by-step explanation:
To change a fraction to a percentage, we multiply the fraction by 100%.
1/400 = 1/400 x 100 = 0.25%
hope this helps
The value of the Percentage 1/400 as a percent is: 0.25%
How to calculate the percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Thus:
1/400 as a percent is calculated as:
1/400 * 100/1
= 100/400
= 0.25%
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which of the following functions is nonlinear
Answer:
D.Step-by-step explanation:
The last option, option D is not linear.
In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.
Now, specifically, in Algebra, a linear expression refers to an expression which has variables with an exponent equal to 1, like option A, B and V. As you can see option D has an expression which variable is squared, that means it's not linear, and its graph is not a line, but a parabola.
The function which is not linear equation is f(x) =x²+ 9.
Thus, option (D) is correct.
A linear equation is an equation that represents a straight line on a graph.
It is an algebraic equation in which the variables are raised to the power of 1, and there are no exponents or radicals involved.
The general form of a linear equation in two variables, x and y, is given by:
ax + by = c
a) f(x) =x have the highest degree 1.
So, it is linear equation.
b) f(x) = 10x + 100 have the highest degree 1.
So, it is linear equation.
c) f(x) = 1/5x - 2 have the highest degree 1.
So, it is linear equation.
d) f(x) =x²+ 9 have the highest degree 1.
So, it is not a linear equation.
Thus, option (D) is correct.
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If the mean of a normal distribution is 315 what is the median of the distribution? A.420
B.315
C.105
D.210
The normal distribution is symmetric about its mean. For any symmetric distribution, the mean is the same as the median. So the answer is B.
In a normal distribution, the mean and median are equal due to its symmetrical nature. Therefore, if the mean is 315, then the median is also 315.
Explanation:The question asks about the relationship between the mean and median in a normal distribution. In a normal distribution, the mean, median, and mode are all equal. This is due to the symmetrical nature of the normal distribution around its mean. So, if the mean of the normal distribution is 315, the median is also 315.
The answer to the student's question is: B.315.
An adult's dinner costs $7. A family of 2 adult's and 2 children pays $22 for their dinners. How many does a child's dinner cost?
Answer:
A child's dinner costs $4
Step-by-step explanation:
7 + 7 = 14
22 - 14 = 8
8 / 2 = 4
Choose all the examples that require measuring the area.
Answer options:
A.the space the bottom of a tent takes up
B.the distance around the outside of a tent
C.the measure from the top to the bottom of a tent
D.the measure from the top to the bottom of a flat sleeping bag
E.the space a flat sleeping bag takes up
F.the distance around the outside of a flat sleeping bag
Answer:
A and E
Explanation:
A.the space the bottom of a tent takes up- Area
B.the distance around the outside of a tent- Perimeter
C.the measure from the top to the bottom of a tent- Height
D.the measure from the top to the bottom of a flat sleeping bag-length
E.the space a flat sleeping bag takes up-area
F.the distance around the outside of a flat sleeping bag- perimeter
select the angle that correctly completes the law of cosines for this triangle
Answer:
Final answer is C. 28°.
Step-by-step explanation:
Given equation is [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex].
Now we need to find the missing value of [tex]\theta[/tex] using cosine formula. So let's compare the given equation [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex] with cosine formula [tex]b^2+c^2-2\left(b\right)\left(c\right)\cos\left(A\right)=a^2[/tex].
we get [tex]\theta =A[/tex]
which is basically the angle between given sides 15 and 17
Hence A=28°.
So the final answer is 28°.
PLEASE HELP!!
For the following questions, use Euler's Formula to find the missing number.
1. Faces: 25
Vertices: 17
Edges: ?
43
41
39
40
2. Vertices: 11
Edges: 34
Faces: ?
25
28
26
24
3. Edges: 36
Faces: 22
Vertices ?
19
15
16
17
Answer:
see explanation
Step-by-step explanation:
Using Euler's formula for Polyhedra, that is
F + V - E = 2
where F is faces, V is vertices and E is edges
1
Rearrange formula for E
F + V - E = 2 ( add E to both sides )
F + V = 2 + E ( subtract 2 from both sides )
E = F + V - 2
= 25 + 17 - 2 = 40
-------------------------------------------------
2
Rearrange formula for F
F + V - E = 2 ( add E to both sides )
F + V = 2 + E ( subtract V from both sides ) F = 2 + E - V, so
F = 2 + 34 - 11 = 25
-----------------------------------------------------
3
Rearrange formula for V
F + V - E = 2 ( add E and subtract F from both sides )
V = 2 + E - F
= 2 + 36 - 22 = 16
Answer:
1. use Euler's formula to find the missing number f=25 vertices=17 Edges=?
40
2. Mario's company makes gemstones Faces=12 vertices=? edges=20
10 vertices
3. Pierre built the model shown in the diagram for a social studies project
pentagon
4. A jewelry store buys small boxes find the surface area of the box to the nearest whole number
266 cm^2
5. Find the lateral area of the prism below Round your answer to the nearest whole number
322 m^2
6. Find the surface area of the cylinder in terms of pi
350pi cm^2
7. Allison is planning to cover the lateral surface of a large cylindrical can diameter 3 feet height 3.5 feet
33. ft^2
8. Find the surface area of the regular pyramid shown to the nearest whole number
740 m^2
9. is the figure below drawn in one point or 2 point perspective
HEY YA'LL 30 PTS FOR 1 PROBLEM!
Given: m∠EYL=1/3 the measure of arc EHL
Find: m∠EYL.
Answer:
45
Step-by-step explanation:
Two tangents drawn to a circle from an outside point form arcs and an angle, and this formula shows the relation between the angle and the two arcs.
m<EYL = (1/2)(m(arc)EVL - m(arc)EHL) Eq. 1
The sum of the angle measures of the two arcs is the angle measure of the entire circle, 360 deg.
m(arc)EVL + m(arc)EHL = 360
m(arc)EVL = 360 - m(arc)EHL Eq. 2
We are given this:
m<EYL = (1/3)m(arc)EHL Eq. 3
Substitute equations 2 and 3 into equation 1.
(1/3)m(arc)EHL = (1/2)[(360 - m(arc)EHL) - m(arc)EHL]
Now we have a single unknown, m(arc)EHL, so we solve for it.
2m(arc)EHL = 3[360 - m(arc)EHL - m(arc)EHL]
2m(arc)EHL = 1080 - 6m(arc)EHL
8m(arc)EHL = 1080
m(arc)EHL = 135
Substitute the arc measure just found in Equation 3.
m<EYL = (1/3)m(arc)EHL
m<EYL = (1/3)(135)
m<EYL = 45