(a) what is the degree of vertex A?(b) list all the even vertices and all the odd vertices.(c) list all vertices that are adjacent to vertex E.
Answers
SOLUTION
(a) All the vertices have 3 lines emanating from them with the exception of C which has 2 lines. That is points A, B, D, and E have 3 lines emanating from them. So their degree is 3.
Therefore, the degree of vertex A is 3
(b) The even vertex is the one that has 2 lines emanating from it. So, the even vertex is C, and the odd vertices are A, B, D, and E. Because they have 3 lines.
(c) All the vertices that are adjacent to E are all the lines drawn to touch all the other vertices. So, A, B, and D are connected to E.
Therefore the vertices adjacent to E are A, B, and D
Related Questions
Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as improper fractions, if necessary.
passes through (−2, 2), perpendicular to y=−5x−8
Answers
Equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to y= -5x-8 is equal to y = 5x+12.
As given in the question,
Line passes through the point ( -2, 2)
Required line is perpendicular to the given line y = -5x -8.
Let the point by ( x₁ , y₁) = ( -2, 2)
Standard equation of line is
y =mx +c
Slope = m
Slope of given line is -5
Lines are perpendicular
Slope of required line is 5
Required equation in slope-intercept form is:
y -2 =5(x-(-2))
⇒ y -2 = 5x +10
⇒ y= 5x +12
Therefore, equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to y= -5x-8 is equal to
y = 5x+12.
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completed the chart for ordered pairs .Using the equation12x-8y=16x tea chart : __,0,2,__y tea chart: 0,__,__,3fil in the blanks
Answers
Given
Equation
[tex]12x-8y=16[/tex]x tea chart __, 0, 2, __
y tea chart 0,__, __, 3
Procedure
y = 0
12x = 16
x = 16/12
x = 4/3
x = 0
-8y = 16
y = 16/-8
y = -2
x = 2
12(2) - 8y = 16
24 - 8y = 16
-8y = 16-24
-8y = -8
y = 1
y = 3
12x - 8(3) = 16
12x - 24 = 16
12x = 16+24
12x = 40
x = 40/12
x = 20/6
x tea chart 4/3, 0, 2, 20/6
y tea chart 0, -2, 1, 3
PLEASE OMG I CANT DO THIS PLEASE JUST HELP OMG!!!!
Answers
Then use vertical angle theorem to make it adjacent to (9x+19)
Use supplementary angle theorem to make them equal to 180
Solve for x
62+9x+19=180
9x+19=118
9x=99
X=11
For each equation determines whether y is a funcation of x
Answers
All linear relations are functions
The quadratic equations can be a function if we restrict the domain of it
The given relations are
[tex]x=-9y[/tex]This is a linear relation, then it is a function, we can put it in the form
[tex]y=-\frac{1}{9}x[/tex][tex]y=8x[/tex]This is a linear relation, then it is a function
[tex]x+3y=6[/tex]This is a linear relation, then it is a function, we can put it in the form
[tex]y=\frac{6-x}{3}[/tex][tex]x=2y^2-3[/tex]We will put it in the form of y as a subject
[tex]y^2=\frac{x+3}{2}[/tex]To find y we will take square root for both sides
[tex]\begin{gathered} \sqrt[]{y^2}=\pm\sqrt[]{\frac{x+3}{2}} \\ y=\pm\sqrt[]{\frac{x+3}{2}} \end{gathered}[/tex]That means each value of x has 2 values of y, then
This can not be a function
How to make 16 using the numbers 4,3,3,1
Answers
Answer:
[tex](4*3)+3+1[/tex]
[tex]4*3=12[/tex]
[tex]12+3+1=16[/tex]
In the similar triangles below, what is the measure of the angle C
Answers
Step 1:
Similar triangles are triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion. Corresponding angle are angles in two different triangles that are “relatively” in the same position.
Step 2
Angle A is congruent to angle D
Angle B is congruent to angle E
Angle C is congruent to angle F.
Final answer
The measure of the angle C = 63
use long or synthetic division to find the following quotients (w^3-2w^2-2w+1)÷(w-1)
Answers
The given polynimial exression is
(w^3-2w^2-2w+1)÷(w-1)
We wuld apply the long division method as shown below
The first step is todivide w^3 by w to give us w^2. w^2 is used to multiply w + 1 to give us w^3 + w^2 and this is subtracted from w^3 - 2w^2. The process continues until we cannot divide further. Thus, from the daigram above, the solution is
w^2 - 3w + 1
Please help me with this pls.The question is:“Choose a phrase that describes the slope of each graph”
Answers
The Solution:
The slope of the graph is undefined.
Explanation:
The slope of the grap
What is the measure of z?zХГУ49Z =z = [?]VGive your answer in simplest form.Enter
Answers
In order to find the value of z, proceed as follow:
By using the Pythagorean theorem for the bigger triangle, you obtain:
[tex]\begin{gathered} z^2=(4+9)^2-x^2 \\ z^2=13^2-x^2 \end{gathered}[/tex]Now, if you consider the second bigger triangle:
[tex]y^2=z^2-9^2[/tex]And in the smaller triangle:
[tex]x^2=y^2+4^2[/tex]Next, replace the second equation for y^2 into the previous one:
[tex]\begin{gathered} x^2=(z^2-9)+4^2^{} \\ x^2=z^2-9+4^2 \\ x^2=z^2-9+16=z^2+7 \end{gathered}[/tex]Now, replace the previous expression for x^2 into the first equation for z^2 and simplify:
[tex]\begin{gathered} z^2=13^2-(z^2+7) \\ z^2+z^2=13^2+7 \\ 2z^2=169+7 \\ z^2=\frac{176}{2} \\ z^2=88 \\ z=\sqrt[]{88}=\sqrt[]{4\cdot22}=2\sqrt[]{22} \end{gathered}[/tex]Hence, the value of z is 2√22
[tex]3x + 2 = 3[/tex]please help, thanks!
Answers
Solve
[tex]\begin{gathered} 3x+2=3 \\ \text{Subtract 2 from both sides of the equation} \\ 3x+2-2=3-2 \\ 3x=1 \\ \text{Next step, you divide both sides by 3} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]The answer is x = 1/3
A canoe rental service charges per hour. The price can be represented by the following relationship: P(h) = 8.5h + 30Complete the following statements. Let P^-1 be the inverse function of P.a) Write a statement that describes P^-1(x)b)Find an equation for P^-1(x)c)Determine P^-1(72.5)
Answers
Given:
The function is,
[tex]g(x)=-\frac{3}{4x}[/tex]The objective is to find g(g(x)).
The value of g(g(x)) can be calculated as,
[tex]\begin{gathered} g(g(x))=-\frac{3}{4(-\frac{3}{4})} \\ =-\frac{3}{4}(-\frac{4}{3}) \\ =1 \end{gathered}[/tex]Hence, the value of g(g(x)) is 1.
What are the coordinates of A, B, C after a rotation of 90 degrees clockwise around the 1,1. Plot the points and label them A’B’C’
Answers
Answer:
A'(5, 8)
B'(2, -1)
C'(-1, 2)
Explanation:
We need to rotate each point A, B, and C 90 degrees clockwise around point (1, 1). So, the angles formed in the following diagram are 90 degrees.
Therefore, the coordinates of points A', B' and C' are:
A'(5, 8)
B'(2, -1)
C'(-1, 2)
considering the changes in the bank account balance whose account balance change the most
Answers
Let's begin by listing out the information given to us:
Customer A = -$95.00
Customer B = -$75.00
Customer C = -$40.00
Customer D = -$92.00
Observing the figures above, we will observe that the greatest or biggest change is observed with Customer A. The account of Customer A decreased the most decreasing by $95; this was $3 more than Customer
Which of the following are correct statements? Check all that apply.A. A ray has only one endpoint.O B. A ray continues forever.C. A ray can have more than one endpoint.D. A ray can be named in more than one way.O E. A ray can only be named one way.
Answers
A ray is a piece of a line with one endpoint and continues forever in the other direction. Then, the correct statements are: A, B, E
ABCD is a quadrilateral
Work out the length of CD
Give your answwer in 3 significant figures
Answers
The length of CD is 20.48 cm
In this question, we have been given a quadrilateral ABCD.
We need to find the length of CD.
From given figure, consider right triangle ABD
We find the value of sine of angle ADB
sin(∠ADB) = AB/DB
sin(38°) = 10 / DB
0.61587 = 10/DB
DB = 10/0.6157
DB = 16.24 cm
Applying sine rule to triangle BCD,
sin(B)/CD = sin(C)/DB
sin(105°) / CD = sin(50°) / 16.24
0.9659 / CD = 0.766 / 16.24
CD = (0.9659 * 16.24) / 0.766
CD = 20.48 cm
Therefore, the length of CD is 20.48 cm
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What is the volume of a figure with that is 5 inches wide, 10 inches tall and 5 inches long
Answers
The volume of a box is:
[tex]\begin{gathered} V=W\cdot T\cdot L \\ \end{gathered}[/tex]So for our problem will be:
[tex]V=5\cdot10\cdot5=250[/tex]Write an equation of a quadratic function that has x-intercepts -2 and -5.
Answers
We have to write an equation of a quadratic function that has x-intercepts -2 and -5. This is, a function that has two roots: -2, and -5.
For doing so, we remember that if a function has n roots, it can be written as:
[tex]f(x)=(x-x_1)(x-x_2)_{}\ldots(x-x_n_{})[/tex]In this case, replacing the roots we have, we obtain that a quadratic function that has x-intercepts -2 and -5 is:
[tex]\begin{gathered} f(x)=(x-(-2))(x-(-5)) \\ f(x)=(x+2)(x+5) \end{gathered}[/tex]Given the function f(x)=x^2-5x-2, determine the average rate of change of the function over the interval -1≤x≤5
Answers
ANSWER
[tex]-1[/tex]EXPLANATION
Given;
[tex]\begin{gathered} f(x)=x^2-5x-2 \\ (-1,5) \end{gathered}[/tex][tex]\begin{gathered} f(-1)=(-1)^2-5(-1)-2 \\ =1+5-2 \\ =4 \end{gathered}[/tex]For x = 5;
[tex]\begin{gathered} f(5)=(5)^2-5(5)-2 \\ =25-25-2 \\ =-2 \end{gathered}[/tex]The average is calculated using;
[tex]\begin{gathered} \frac{f(-1)-f(5)}{-1-5} \\ =\frac{4-(-2)}{-1-5} \\ =\frac{6}{-6} \\ =-1 \end{gathered}[/tex]A
f(x) = 4x2 + 5.0 - 3g(x) = 4.3 - 3x2 + 5Find (f +9)(x).O A. (f +g)(x) = 4x3 + x2 + 5x + 2O B. (f +g)(x) = 4x3 + 4x2 + 2x + 2O c. (f+g)(x) = 8x3 + 2x + 2O D. (f +g)(x) = -4x3 + 7x2 + 53 - 8SUBMIT
Answers
ANSWER
A. (f + g)(x) = 4x³ + x² + 5x + 2
EXPLANATION
To add this functions we have to combine and add like terms:
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=4x^2+5x-3+4x^3-3x^2+5 \\ (f+g)(x)=(4-3)x^2+5x+4x^3+(5-3) \\ (f+g)(x)=x^2+5x+4x^3+2 \\ \text{ordering the terms} \\ (f+g)(x)=4x^3+x^2+5x+2 \end{gathered}[/tex]Determine the number of significant figures in the following masses.
Answers
From the question;
We are to determine the number of significant figures in
a) 0.00040230g
b) 405,000g
a) For 0.00040230g
Trailling zeros to the right of the decimal point are significant
The digits zeros before 4 are not significant
Therefore, the mass has 5 significant figures
b) For 405,000g
Trailling zeros in a whole number with no decimal point are not significant
Therefore
The mass has 3 significant figures
Thomas is saving money for a few montain bike. the amount(a) Thomas needs to save is more than $50.45. which inequality models the amount Thomas needs to save A.$50.45=a. B.$60.45$50.45. D.a
Answers
From the information given in the statement you know that:
*a is the amount of money Thomas needs to save
*Thomas needs to save more than $ 50.45.
Then, the inequality that models the amount Thomas needs to save is
[tex]a>\text{ \$}50.45[/tex]Charles asked his teammates how many hours they practiced swimming during the week. He recorded his data in thetable below and used the shaded columns to calculate three sample means. What is the range of the values for thesample means?463Hours of Swim Practice53352447u ooo53234.6123.754.75
Answers
gAnswer
Range of the sample means = 3.34
Explanation
The range is defined as the difference between the highest and the lowest number. Mathematically,
Range = Highest number - Lowest number
So, the range of the sample means is the difference between the highest and the lowest sample means.
Range of the sample means =
(Sample mean with the highest value) - (Sample mean with the lowest value)
From the table, we can calculate the sample means. The sample mean is given as the sum of the variables divided by the number of variables.
Note that we are told that Charles used only the shaded columns to calculate three sample means. The shaded columns, grouped include
4, 3, 3. Mean = 3.33
8, 5, 7. Mean = 6.67
6, 4, 3. Mean = 4.33
5, 3, 6. Mean = 4.67
Sample mean with the highest value = 6.67
Sample mean with the lowest value = 3.33
Range of the sample means = 6.67 - 3.33 = 3.34
Hope this Helps!!!
10% of a water tank fills every 5 minutes. If you are filling a 40 gallon tank, how many gallons will there be in 30 minutes?
Answers
After 30 minutes, there are 24 gallons within the water tank due to cross multiplication.
How to Use Cross Multiplication to Estimate the Filling Time of a Water Tank?
The water tank is filling at a constant rate of 10% tank capacity every 5 minutes, according to the statement. The tank holds 40 gallons of water.The gained capacity is calculated by multiplying the following cross multiplication by the water capacity, which is directly proportional to the filling time:
x ∝ tx = (n / 100) · V × (T / t) (1)Where:
n - The initial capacity percentage of the water tank, expressed as a percentage.V - Total water tank capacity in gallons.T - Time remaining in minutes.t - The starting time in minutes.By substituting the values:
x = [0.1 (40 gal)] x (30 minutes / 5 minutes)x = 24 gallonsTherefore, after 30 minutes, there are 24 gallons within the water tank due to cross multiplication.
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I need help identifying if this is a 90,180,270 degree transformation
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which point in the solution set of the given inequalities?
Answers
In the image, we can identify the region of the plane in which the two subregions overlap (the part of the graph which has vertical and horizontal lines). We can obtain the values of x and y in that region by means of the inequalities, in this way:
[tex]\begin{cases}x+y>2 \\ 4x+y\ge-1\end{cases}[/tex]We solve the first inequality for y
[tex]y>2-x[/tex]This gives us the first constrain for the value of y
Now, to obtain the second constrain we simply need to use the second inequality:
[tex]\begin{gathered} 4x+y\ge-1 \\ \Rightarrow y\ge-1-4x \end{gathered}[/tex]Finally, the last step is to get the constraints for the value of x.
For this, we can directly analyze the image of the region, notice how it covers any value of x. This means that there are no constraints for the value of x.
[tex]\Rightarrow x\in\mathfrak{\Re }[/tex]So, the region is given by:
[tex]x\in\mathfrak{\Re },\begin{cases}y>2-x \\ y\ge-4x-1\end{cases}[/tex]Finally, the point that is in the region is the one that satisfies the previous inequalities.
1. (2,0)
If x=2, then
[tex]\begin{gathered} ,\begin{cases}y>2-2=0 \\ y\ge-4(2)-1=-9\end{cases} \\ \Rightarrow y>0 \end{gathered}[/tex]So, (2,0) cannot be the correct option
2. (0,2)
[tex]\begin{gathered} \begin{cases}y>2-0=2 \\ y\ge-4(0)-1=-1\end{cases} \\ \Rightarrow y>2 \end{gathered}[/tex]This means that (0,2) cannot be the right option
3. (0,3) notice that the same condition (y>2) holds in this situation too (since x=0)
But y=3>2. This point indeed satisfies the conditions! (0,3) is the answer
4. (0,-1) Notice that in this case y=-1 but it should happen that y>2. So this point cannot be in the region
Rewrite the equation below so that it does not have fractions2x/3 - 2 = 3/7Do not use decimals in your answer
Answers
The given equation is expressed as
[tex]\begin{gathered} \frac{2}{3}x\text{ -2=}\frac{3}{7} \\ \text{The lowest common factor is 21. We would multiply both sides of the equation by 21. } \\ \frac{2}{3}x\times21\text{ - 2}\times21=\frac{3}{7}\times21 \\ 14x-42=9 \\ \\ \\ \end{gathered}[/tex]A bin size ofis most appropriate for this set of data:1486, 1228, 1625, 1340, 1845, 1573, 1608, 1821, 1398, 1572, 1401, 1563,1482, 1374
Answers
GIVEN:
We are given a set of data as indicated in the attached image.
Required;
Determine the appropriate bin size for the given set of data.
Step-by-step solution;
A bin size is basically a class interval in statistics. Its a way of sorting data in a histogram, more like categories.
We start by identifying the smallest and largest data points and these are;
[tex]\begin{gathered} Least=1228 \\ \\ Greatest=1845 \end{gathered}[/tex]Now we determine the range of the data set,
[tex]\begin{gathered} Range=Greatest\text{ }value-Least\text{ }value \\ \\ Range=1845-1228 \\ \\ Range=617 \end{gathered}[/tex]Let us now choose 5 bins.
Next step, we divide the range by the bin size and we have;
[tex]\frac{617}{5}=123.4[/tex]We now have a class interval of 123.4
We can round this down to 100. That means an interval of 100 between the lower limit and the upper limit of each class interval.
Therefore,
ANSWER;
Option D; 100
all you need is in the photo please show your work and answer fast
Answers
5/9 of 54 are the ones which have chocolate, so we need to multiply the fraction by 54
5/9 * 54 = 30
Since 30 pieces of candy have chocolate, then 24 don't have it. 2/3 of the last number are the ones which have gum, multiply 2/3 by 24 to get the answer:
2/3 * 24 = 16.
The answer is: 16 pieces of candy have gum
Solve for q. 4(q + 17) − 12 = 0 q =
Answers
Answer:
q = -14
Step-by-step explanation:
4(q + 17) − 12 = 0
4q + 68 - 12 = 0
4q + 56 = 0
4(q + 14) = 0
4 = 0, q + 14 = 0
q = -14
I hope this helps!
Val is going to plant y vegetable seeds in one garden and 4y +9 vegetable seeds in another. How many seeds is Val going to plant?
Answers
Given:
Val is going to plant y vegetable seeds in one garden and 4y +9 vegetable seeds in another.
So, the total seeds =
[tex]y+(4y+9)=y+4y+9=5y+9[/tex]