a) The following is a graph with four nodes and eight edges.
b) A planar graph's faces are regions in the plane that are bordered by the edges of the graph.
Since we know that this graph is planar, we can utilize Euler's Formula, which states that V - E + F = 2, where V, E, and F are the number of vertices, edges, and faces, respectively.
There are four vertices and eight edges in this graph. Let's say there are F faces.
V - E + F = 2 is Euler's equation, which we may utilize to find F.
4 - 8 + F = 2F = 6 There are six faces.
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MULTIPLE CHOICE
Question 10
Liam wants to treat some friends to lunch. He has $50 and knows that lunch will cost $8 per person. For how many people can Liam buy lunch?
A
Liam can buy lunch for 7 or fewer people, including himself.
B
Liam can buy lunch for 7 or more people, including himself.
C
Liam can buy lunch for 6 or fewer people, including himself.
D
Liam can buy lunch for 6 or more people, including himself.
Answer:
C
Step-by-step explanation:
8 x 6 would equal 48, which results in not having enough money to buy lunch for more people.
Answer:
the answer should be c
Step-by-step explanation:
let's do a equation for this problem.
8x = 50
/8 /8
x = 6.25
x represents the amount of friends. we divide 8 by both sides to isolate x by itself.
since the final result gives us a decimal, we have to round it to the nearest whole number. it's not possible to have a decimal amount of friends. it should be 6. it cannot be 7 if you are wondering because 7 is bigger than 6.25. there's no way there can be 7 friends when there is a limit amount of 6. therefore, the answer is c.
Find (a) the perimeter and (b) the area of the figure. Use 3.14 or 22/7 for Pi. Round your answer to the nearest hundredth, if
necessary.
a. Total perimeter = 89.12 ft
b. Total area = 174. 24 ft²
How to determine the valuesTo determine the perimeter, we have;
Perimeter of triangle = a + b + c = 8 + 6 + 10 = 24ft
Circumference of a circle is expressed a;s
= 2πr
Circumference = 2× 3.14 × 4
Multiply the values
Circumference = 25. 12 ft
Perimeter of a square = 4a)
Perimeter = 40 ft
Total perimeter = 40 + 25.12 + 24 = 89.12 ft
For area;
Triangle = 1/2bh = 1/2 (48) =24 ft²
Square = a² = 100ft²
Circle = 3.14 × 4² = 50.24ft²
Total area = 174. 24 ft²
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Find an expression for c that will make 9x2 + 12xy +c aperfect square trinomial
Answer: To find the value , divide the coefficient of by and square the result.
Step-by-step explanation:Use the formula ( b 2 ) 2 in order to create a new term in order to find the perfect square trinomial.
9 x 2 − 12 x + c + 4
(3.6 X 102)(1.9 x 10-4)
Multiply write the answer in scientific notation
Question 2
(4.7. x 10)(2.0 x 10
Answer:
1.)5508 2.)5600 x^2
Step-by-step explanation:
The first step in solving 7 + 3(x - 2) = 2x + 10 is to
Answer:
x=9
Step-by-step explanation:
Simplify 7+3x−67+3x−6 to 3x+13x+1.
Subtract 11 from both sides
Simplify 2x+10−12x+10−1 to 2x+92x+9.
Subtract 2x2x from both sides.
Simplify 3x−2x3x−2x to xx.
Answer: x=9
Step-by-step explanation:
7+3(x-2)=2x+10
7+3x-6=2x+10
1+3x=2x+10
1+3x-2x=2x-2x+10
1+1x=10
1x=9
x=9
Why can’t we use the rules for exponents when the bases are not common?
Answer:
Ok, the rules of the exponent come from a logic construction.
If we have x^n
this means that n is multiplied by itself n times.
If we decompose n into a + b, we have:
x by itself a times, and then x by itself b times, and for how the product works, this is equivalent:
if n = 5, a= 2 and b = 3
x^5 = (x*x*x*x*x) 5 times-
x^5 = x^(2 + 3) = (x^2)*(x^3) = (x*x*)*(x*x*x) = x*x*x*x*x = x^5
And the same for the other rules:
(x^n)^b = x^n*b and such.
Obviusly, this only works when we have a common base.
So the correct answer is that we constructed the exponential rules in a way that only can be used when we have a common base, and this happens because to construct them, we started with common bases.
I’ll give brainliest if someone can explain that answer
Answer:
no
Step-by-step explanation:
Answer:
No
Because 5 and 1 have the same output as 1.
A jar holds 2 cups of water. How much is this in fluid ounces?
Answer:
16 fluid ounces
Step-by-step explanation:
how many different three-letter words (including nonsense words) are there in which successive letters are different?
16250 many different three-letter words—including nonsense words—have different letters in the next position.
Given that,
We have to find how many different three-letter words—including nonsense words—have different letters in the next position.
We know that,
The number of alphabets are 26
First letter has 26 choices.
Second letter can not be same has first letter so 25 choices.
Third letter can not be same has second letter so 25 choices.
So,
Total words = 26×25×25=16250
Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.
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The triangle on the left is a scale drawing of the real object on the right. The scale drawing was made using a scale factor of 2.
How does the scale factor affect the angle measures in the scale drawing?
Answer:
It doesn't
Step-by-step explanation:
When a shape is scaled up or down, the angles don't change.
It's easier to picture using a square. Like no matter how long the sides are, the angles are all 90 degrees. Its the same with every shape though- as long as it's evenly resized.
I need help
Solving this problem
The required value of x is 22 degrees for the given figure.
Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.
As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:
According to the given figure, it can be written as follows:
2x + 24 + 6x - 20 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176/8
x = 22
Therefore, the required value of x is 22 degrees for the given figure.
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The complete question is as follows:
Find the value of x for the below figure.
2 examples of a commutative property?
Answer:
hope this helps :)
Step-by-step explanation:
Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.
Answer: Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.
if this makes sense
John earns $8.35 an hour. Last week he worked 21 hours.This week he worked 33 hours.
What is his straight time pay for the two weeks?
A. $460.90
B. $450.90
C. $175.35
D. $275.55
E. $409.15
WILL GIVE BRAINLIEST!! IF YOU JUST TAKE THE POINTS ILL REPORT
The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods.
Answer:
In the context of the situation, Nicholas started with 825 canned goods and sold (or lost in some way, I'm assuming sold) 63 a day.
what does it mean when a radical does not have an index? is the expression equal to the radicand? explain.
The expression is not equal to the radicand.
What is Radical Index?
The root symbol nx. is known as a radical, and it is thus read "x radical n," or "the nth root of x." The horizontal line in the radical sign is known as the vinculum, the quantity under the vinculum is known as the radicand, and the quantity n written to the left is known as the index.
The radical is defined by the expression
\(\sqrt[n]{a}\)
where a is radicand and n is index.
The index value of square roots is two. When there is no index provided for a radical, it is presumed to be an index of two, or a square root.
\(a^{1/2}\) =\(\sqrt{a}\)
Thus, the expression is not equal to the radicand.
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The expression is not equal to the radicand.
What is Radical Index?
The root symbol nx. is known as a radical, and it is thus read "x radical n," or "the nth root of x." The horizontal line in the radical sign is known as the vinculum, the quantity under the vinculum is known as the radicand, and the quantity n written to the left is known as the index.
The radical is defined by the expression
where a is radicand and n is an index.
The index value of square roots is two. When there is no index provided for a radical, it is presumed to be an index of two or a square root.
= a^(1/2)
Thus, the expression is not equal to the radicand.
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CJ=6x−6C, J, equals, 6, x, minus, 6 and
\qquad JT = 7x - 8JT=7x−8J, T, equals, 7, x, minus, 8
Find CTCTC, T.
What is the sum of (x ^ 2 - 3x + 2) and (5x ^ 2 - 3x - 8)
Answer:
6x^2-6x-6
Step-by-step explanation:
(x^2-3x+2)+(5x^2-3x-8)
x^2+5x^2-3x+(-3x)+2+(-8)
6x^2-3x-3x+2-8
6x^2-6x+2-8
6x^2-6x-6
Marina needs to replace a broken window at her house. The window is shaped like a triangle with dimensions shown below. If glass cost 18.75 per square foot how much for the square replacement window cost?
The cost for the replacement for the window as required to be determined in the task content is; $1826.77.
What is the cost of replacing the window?It follows from the task content that the cost of replacing the window is required to be determined.
Since the triangular window mimics an equilateral triangle, it's area, A given side length, a is;
A = √3/4 • a².
Ultimately, the area of the window is;
A = √3/4 • 15²
A = 97.42785793 ft².
Since glass costs; 18.75 per square foot; it follows that the cost of replacing the window is; 97.42785793 ft² × 18.75 = $1826.77.
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Find the missing numbers in these equations.
A.) ? x 4 = 32
B.) -49 x 3 = ?
Answer:
A.) 8 B.) -147
Step-by-step explanation:
A.) Divide 32 by 4. 32/4 = 8
B.) Multiply -49 by 3. -49 x 3 = -147
-10a-5=135
thank you
Answer:
-10a-5=135
-10a = 140 add 5 to both sides
a=-14 divide both sides by -10
Step-by-step explanation:
Answer:
a= -14
Step-by-step explanation:
-10a-5=135
-10a=140
a= -14**
Four friends are playing a "Guess my Age" game. The come up with the following
clues. Dave's age is 15% of Sabrina. Luca's age is 75% of Sabrina and Rhianna is 300%
of Dave. The sum of their ages is 141. How old is Rhianna?
Show your work!
Answer:
27 years old
Step-by-step explanation:
What I know
Let D = Dave, S = Sabrina, etc. Then:
(1) \(D=0.15S\)
(2) \(L=0.75S\)
(3) \(R=3.00D\)
(4) \(D+S+L+R=141\)
Want to find R. Taking equation 3 and rewriting equation 4, we get
\(R=3.00D\)
\(R=141-D-S-L\)
So if \(R=R\), then
\(3D=141-D-S-L-R\)
\(4D=141-S-L\) by adding \(D\) to both sides.
Using equation 1 and equation 2, I can rewrite everything in terms of \(S\) and get:
\(4(0.15S)=141-S-0.75S\)
\(0.6S=141-1.75S\)
\(2.35S=141\) by adding \(1.75S\) to both sides.
\(S=60\) by dividing 2.35 both sides.
Now that I know Sabrina's age, I'll work towards getting Rhianna's using equation 1 and equation 3:
\(D=0.15(60)=9\)
\(R=3.00(9)=27\)
Checking my work:
Dave: 9
Sabrina: 60
Luca: 45 (since 9+60+45+27=141)
Rhianna: 27
9 is 15% of 60
45 is 75% of 60
27 is 300% of 9
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
three to the one third power all over three to the one sixth power
A. the square root of three to the one sixth power
B. the ninth root of three squared
C. the square root of three to the sixth power
D. the sixth root of three
Answer:
D. The sixth root of three
Step-by-step explanation:
Translate from words to math symbols:
three to the one third power all over three to the one sixth power
\(\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\\)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
\(\frac{\sqrt[3]{3} }{\sqrt[6]{3} }\)
Simplify:
\(\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}\)
Answer:
\(\sqrt[6]{3}\)
D. the sixth root of three
. The price of a new TV is £540, which includes 20% VAT.
Find the cost of the TV excluding VAT.
Answer:
450
Step-by-step explanation:
Based on the given conditions, formulate:
Calculate the sum or difference:
Convert decimal to fraction:
Divide a fraction by multiplying its reciprocal:
Cross out the common factor:
Calculate the product or quotient:
Answer:
Rita plans to make a call using a calling card. For each call, rita has two options: 1. Pay $0. 49, plus an additional $0. 019 per minute. 2. Pay $0. 059 per minute. She predicts that her call will be x minutes long. Which inequality represents the statement, "rita would save money using the second option"?.
The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x
"Information available from the question"
In the question:
1. Pay $0. 49, plus an additional $0. 019 per minute.
2. Pay $0. 059 per minute.
Now, According to the question:
How to determine the inequality that represents the statement?
We have the following parameters that can be used in our computation:
1. Pay $0.49, plus an additional $0.019 per minute.
2. Pay $0.059 per minute.
These statements can be represented as
Option 1: y = 0.49 + 0.019x
Option 2: y = 0.059x
Where y is the total amount and x is the number of minutes
When she saves money, we have
Option 2 < Option 1
Substitute the known values in the above equation, so, we have the following representation
0.059x < 0.49 + 0.019x.
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3√+5√? i need help asap!!
It is true that the expression √3 + 5 cannot be simplified
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine if the expression can be simplified?The expression is given as
√3 + 5
The above expression is a combination of a radical expression and an integer
The radical expression √3 cannot be simplified
This means that the expression √3 + 5 cannot be simplified
Hence, the expression √3 + 5 cannot be simplified
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Complete question
Can √3 + 5 be simplified?
Yes or no
What are the digits that repeat in the smallest sequence of repeating digits in the decimal equivalent of 2411?
Answer:
18
Step-by-step explanation:
A 1-pound bag of sunflower seeds provides 96 grams of protein, There
are 58.5 grams of protein in a 6.5-ounce bag of pumpkin seeds. Which
type of seed has more grams of protein per ounce? How many more
grams of protein are there in 24 ounces of the higher-protein seeds?
Answer:
Pumpkin seed has more grams of protein per ounce
216 grams of protein
Step-by-step explanation:
1 pound = 16 ounce
16 ounce of sunflower seeds = 96 grams of protein
6.5 ounce of pumpkin seeds = 58.5 grams of protein
Which type of seed has more grams of protein per ounce?
Sunflower seeds:
Protein per ounce = 96 grams / 16 ounce
= 6 grams of protein per ounce
Pumpkin seeds:
Protein per ounce = 58.5 grams / 6.5 ounce
= 9 grams of protein per ounce
Therefore,
Pumpkin seed has more grams of protein per ounce
How many more grams of protein are there in 24 ounces of the higher-protein seeds?
Quantity of protein = 24 ounces ×
9 grams of protein per ounce
= 216 grams of protein
3[7x - 4(x - 3)] + 1
Answer:
9x+37
Step-by-step explanation:
Answer:
9x + 37
Step-by-step explanation:
3[7x - 4(x - 3)] + 1
3[7x-4x+12] + 1
3[3x +12] +1
9x + 36 +1
9x + 37
You can buy 5 cans of beans at the Village Market for $3.20. You can buy 10 of the same cans of beans at Sam’s Club for $7.30. Which place is the better buy?
Answer:
Village Market
Step-by-step explanation:
3.20÷5=.64
7.30÷10=.73
Exercise 10
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. What is the probability of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth.
The probability of choosing a 5 and then a 6 is 1/49
Finding the probability of the compound eventFrom the question, we have the following parameters that can be used in our computation:
The tiles
Where we have
Total = 7
The probability of choosing a 5 and then a 6 is
P = P(5) * P(6)
So, we have
P = 1/7 * 1/7
Evaluate
P = 1/49
Hence, the probability of choosing a 5 and then a 6 is 1/49
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Question
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6