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Applying the vertical angles theorem and other properties, the value of x is 20. The reason for each statement has been explained below.
What are Vertical Angles?A pair of vertical angles are formed when two straight lines intersect each other at a common point. The angles that face each other directly are vertical angles and they are congruent or equal to each other.
Given the diagram below, to find the value of x, the following are the each reason that justifies each of the statements in each step:
Statement Reasons
1. m∠DOB = m∠DOE + m∠BOE 1. Angle Addition Postulate
2. m∠DOB = 90 + x 2. Substitution
3. m∠AOC = m∠DOB 3. Vertical Angels Theorem
4. 110 = 90 + x 4. Substitution
5. x = 20 5. Algebra
To solve using algebra, step 4 is solved as explained below:
110 - 90 = 90 + x - 90
20 = x
x = 20.
Therefore, applying the above steps and reasons that includes the use of vertical angles theorem, the value of x is determined to be: x = 20.
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Related Questions
Hello! I need some help with this homework question, please? The question is posted in the image below. Q4
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a) f(0) = -1
b) f(1) = 1
c) f(4) = 7
d) f(5) = 121
Explanation:
. Since for every value between -2 (excluded) and 4 (included)
~ 0 , 1 and 4
You have to use the first equation
=> f(0) = 2 * 0 - 1 = -1
=> f(1) = 2 * 1 - 1 = 1
=> f(4) = 2 * 4 - 1 = 7
. For values between 4 (exclude) and 5(included)
~ 5
You have to use the second equation
=> f(5) = 5^3 - 4 = 121
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $30 for covered pavilion seats and $20 for lawn seats. Total receipts were $32,000. Howmany tickets of each type were sold?How many pavilion seats were sold?
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Let p be the number of pavilion seats and l be the number of lawn seats. Since there were sold 1400 tickets, we can write
[tex]p+l=1400[/tex]and since the total money was $32000, we can write
[tex]30p+20l=32000[/tex]Then,we have the following system of equations
[tex]\begin{gathered} p+l=1400 \\ 30p+20l=32000 \end{gathered}[/tex]Solving by elimination method.
By multiplying the first equation by -30, we have an equivalent system of equation
[tex]\begin{gathered} -30p-30l=-42000 \\ 30p+20l=32000 \end{gathered}[/tex]By adding these equations, we get
[tex]-10l=-10000[/tex]then, l is given by
[tex]\begin{gathered} l=\frac{-10000}{-10} \\ l=1000 \end{gathered}[/tex]Now, we can substitute this result into the equation p+l=1400 and obtain
[tex]p+1000=1400[/tex]which gives
[tex]\begin{gathered} p=1400-1000 \\ p=400 \end{gathered}[/tex]Then, How many tickets of each type were sold? 400 for pavilion seats and 1000 for lawn seats
How many pavilion seats were sold? 400 tickets
State which pairs of lines are:(a) Parallel to each other.(b) Perpendicular to each other.
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So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.
So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:
[tex]\begin{gathered} 8y+4=-2x \\ 8y+4-4=-2x-4 \\ 8y=-2x-4 \end{gathered}[/tex]Then we can divide both sides by 8:
[tex]\begin{gathered} \frac{8y}{8}=\frac{-2x-4}{8} \\ y=-\frac{2}{8}x-\frac{4}{8} \\ y=-\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]So its slope is -1/4 and its y-intercept is -1/2.
For equation (iii) we can add 8x at both sides:
[tex]\begin{gathered} 2y-8x=-2 \\ 2y-8x+8x=-2+8x \\ 2y=8x-2 \end{gathered}[/tex]Then we can divide both sides by 2:
[tex]\begin{gathered} \frac{2y}{2}=\frac{8x-2}{2} \\ y=\frac{8}{2}x-\frac{2}{2} \\ y=4x-1 \end{gathered}[/tex]Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).
In summary, the three equations in slope-intercept form are:
[tex]\begin{gathered} (i)\text{ }y=4x-1 \\ (ii)\text{ }y=-\frac{1}{4}x-\frac{1}{2} \\ (iii)\text{ }y=4x-1 \end{gathered}[/tex]It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:
- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).
- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:
[tex]-\frac{1}{m}[/tex]Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.
So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.
For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:
[tex]-\frac{1}{m}=-\frac{1}{4}[/tex]Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).
Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
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Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
Please help! I think this is a simple question but I'm overthinking.
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We have the following:
We can solve this question by means of the Pythagorean theorem since it is a right triangle, in the following way:
[tex]c^2=a^2+b^2[/tex]a = 2.3
b = 3.4
replacing
[tex]\begin{gathered} c^2=2.3^2+3.4^2 \\ c^2=5.29+11.56 \\ c=\sqrt[]{16.85} \\ c=4.1 \end{gathered}[/tex]Therefore, the answer is 4.1
Which angles are adjacent and do NOT form a linear pair?
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Adjacent angles share a common side and a common vertex but do not overlap each other.
A linear pair is two adjacent angles that creat a straight line, thus adjacent angles which do not form a linear pair could be:
[tex]\angle2\text{ and }\angle3[/tex]Graph the system below. What is the x-coordinate of the solution to the system of linear equations?y= -4/5x + 2y= 2/3x + 2A. -4B. 2C. 3D. 0
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The solution is (x,y) = (0,2)
The functions s and t are defined as follows.Find the value of t(s(- 4)) .t(x) = 2x ^ 2 + 1s(x) = - 2x + 1
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EXPLANATION
Since we have the functions:
[tex]s(x)=-2x+1[/tex][tex]t(x)=2x^2+1[/tex]Composing the functions:
[tex]t(s(-4))=2(-2(-4)+1)^2+1[/tex]Multiplying numbers:
[tex]t(s(-4))=2(8+1)^2+1[/tex]Adding numbers:
[tex]t(s(-4))=2(9)^2+1[/tex]Computing the powers:
[tex]t(s(-4))=2*81+1[/tex]Multiplying numbers:
[tex]t(s(-4))=162+1[/tex]Adding numbers:
[tex]t(s(-4))=163[/tex]In conclusion, the solution is 163
Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-3y=9
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Answer:
y=4/3x+3
Step-by-step explanation:
we know that slope intercept form is y=mx+b, where m is the slope and b is the y intercept
for 4x-3y=9, we have to isolate y
we subtract 4x to both sides to get
-3y=-4x+9
to get y alone, we divide both sides by -3
y=4/3x+3
Answer:
Y=4/3x-3
Step-by-step explanation:
Y=4/3x-3
the other guy had the right idea but the two negatives make a positive!
in this problem you will use a ruler to estimate the length of AC. afterwards you will be able to see the lengths of the other two sides and you will use the pythagorean theorem to check your answer
Answers
Answer:
5.124
Explanation:
Given the following sides
AB = 6.5cm
BC = 4.0cm
Required
AC
Using the pythagoras theorem;
AB^2 = AC^2 + BC^2
6.5^2 = AC^2 + 4^2
42.25 = AC^2 + 16
AC^2 = 42.25 - 16
AC^2 = 26.25
AC = \sqrt{26.25}
AC = 5.124
Hence the actual length of AC to 3dp is 5.124
Use a system of equations to solve the following problem.The sum of three integers is380. The sum of the first and second integers exceeds the third by74. The third integer is62 less than the first. Find the three integers.
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the three integers are 215, 12 and 153
Explanation:
Let the three integers = x, y, and z
x + y + z = 380 ....equation 1
The sum of the first and second integers exceeds the third by 74:
x + y - 74 = z
x + y - z = 74 ....equation 2
The third integer is 62 less than the first:
x - 62 = z ...equation 3
subtract equation 2 from 1:
x -x + y - y + z - (-z) = 380 - 74
0 + 0 + z+ z = 306
2z = 306
z = 306/2
z = 153
Insert the value of z in equation 3:
x - 62 = 153
x = 153 + 62
x = 215
Insert the value of x and z in equation 1:
215 + y + 153 = 380
368 + y = 380
y = 380 - 368
y = 12
Hence, the three integers are 215, 12 and 153
what is 0.09 as a percentage?
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Use the graph to evaluate the function for the given input value. 20 f(-1) = 10 f(1) = х 2 -10 -20 Activity
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we have that
[tex]f(-1)=-8,f(1)=-12[/tex]Hello! Need a little help on parts a,b, and c. The rubric is attached, Thank you!
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In this situation, The number of lionfish every year grows by 69%. This means that to the number of lionfish in a year, we need to add the 69% to get the number of fish in the next year.
This is a geometric sequence because the next term of the sequence is obtained by multiplying the previous term by a number.
The explicit formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We know that a₁ = 9000 (the number of fish after 1 year)
And the growth rate is 69%, to get the number of lionfish in the next year, we need to multiply by the rate og growth (in decimal) and add to the number of fish. First, let's find the growth rate in decimal, we need to divide by 100:
[tex]\frac{69}{100}=0.69[/tex]Then, if a₁ is the number of lionfish in the year 1, to find the number in the next year:
[tex]a_2=a_1+a_1\cdot0.69[/tex]We can rewrite:
[tex]a_2=a_1(1+0.69)=a_1(1.69)[/tex]With this, we have found the number r = 1.69. And now we can write the equation asked in A:
The answer to A is:
[tex]f(n)=9000\cdot1.69^{n-1}[/tex]Now, to solve B, we need to find the number of lionfish in the bay after 6 years. Then, we can use the equation of item A and evaluate for n = 6:
[tex]f(6)=9000\cdot1.69^{6-1}=9000\cdot1.69^5\approx124072.6427[/tex]To the nearest whole, the number of lionfish after 6 years is 124,072.
For part C, we need to use the recursive form of a geometric sequence:
[tex]a_n=r(a_{n-1})[/tex]We know that the first term of the sequence is 9000. After the first year, the scientists remove 1400 lionfish. We can write this as:
[tex]\begin{gathered} a_1=9000 \\ a_n=r\cdot(a_{n-1}-1400) \end{gathered}[/tex]Because to the number of lionfish in the previous year, we need to subtract the 1400 fish removed by the scientists.
The answer to B is:
[tex][/tex]Given: B is the midpoint of AC. Complete the statementIf AB = 28, Then BC =and AC =
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If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,
[tex]AB=BC[/tex]Answer A
Thus, if AB = 28, BC = 28 too.
Answer B: Therefore, AC = 56
A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(red, then blue).
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5 + 6 + 4 = 15
red is 6/15 then taken out
then blue is 5/14
6/15 * 5/14 = 1/7
1/7 or about 0.143
Solve the triangle for the missing sides and angles. Round all side lengths to the nearest hundredth. (Triangle not to scale.)
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The Law of Cosines
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:
[tex]c^2=4^2+5^2-2\cdot4\cdot5\cos 100^o[/tex]Calculating:
[tex]c^2=16+25-40\cdot(-0.17365)[/tex][tex]\begin{gathered} c^2=47.946 \\ c=\sqrt[]{47.946}=6.92 \end{gathered}[/tex]Now we can apply the law of the sines:
[tex]\frac{4}{\sin A}=\frac{5}{\sin B}=\frac{c}{\sin 100^o}[/tex]Combining the first and the last part of the expression above:
[tex]\begin{gathered} \frac{4}{\sin A}=\frac{c}{\sin100^o} \\ \text{Solving for sin A:} \\ \sin A=\frac{4\sin100^o}{c} \end{gathered}[/tex]Substituting the known values:
[tex]\begin{gathered} \sin A=0.57 \\ A=\arcsin 0.57=34.7^o \end{gathered}[/tex]The last angle can be ob
How do I do this ? I need to find the solution for it
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]11. Suppose that y varies inversely with x. Write a function that models the inverse function.x = 1 when y = 12- 12xOy-y = 12x
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We need to remember that when two variables are in an inverse relationship, we have that, for example:
[tex]y=\frac{1}{x}[/tex]In this case, we have an inverse relationship, and we have that when x = 1, y = 12.
Therefore, we have that the correct relationship is:
[tex]y=\frac{12}{x}[/tex]In this relationship, if we have that x = 1, then, we have that y = 12:
[tex]x=1\Rightarrow y=\frac{12}{1}\Rightarrow y=12[/tex]Therefore, the correct option is the second option: y = 12/x.
Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
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Two liters of soda cost $2.50 how much soda do you get per dollar? round your answer to the nearest hundredth, if necessary.
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If two litters of soda cost $2.50;
Then, a dollar would buy;
[tex]\begin{gathered} =\frac{2}{2.5}\text{litres of soda} \\ =0.80\text{ litres of soda} \end{gathered}[/tex]Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?
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Answer
• Exponential model
[tex]A(t)=13.60(1+0.25)^{t}[/tex][tex]A(8)\approx81.06[/tex]Explanation
The exponential model equation can be given by:
[tex]A(t)=C(1+r)^t[/tex]where C is the initial value, r is the rate of growth and t is the time.
We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:
[tex]A(t)=13.60(1+r)^t[/tex]Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:
[tex]26.56=13.60(1+r)^3[/tex][tex]\frac{26.56}{13.60}=(1+r)^3[/tex][tex](1+r)^3=\frac{26.56}{13.60}[/tex][tex]\sqrt[3]{(1+r)^3}=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]1+r=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]r=\sqrt[3]{\frac{26.56}{13.60}}-1\approx0.2500[/tex]Thus, our rate is 0.25, and we can add it to our equation:
[tex]A(t)=13.60(1+0.25)^t[/tex]Finally, we evaluate t = 8:
[tex]A(8)=13.60(1+0.25)^8=81.06[/tex]Need some help thanks
Answers
In the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25What exactly are equations?When two expressions are equal in a mathematical equation, the equals sign is used to show it.A mathematical statement is called an equation if it uses the word "equal to" in between two expressions with the same value.Using the example of 3x + 5, the result is 15.There are many different types of equations, such as cubic, quadratic, and linear.The three primary categories of linear equations are point-slope, standard, and slope-intercept equations.So, solving for variables:
(A) 1/5a = -2:
1/5a = -2a = -2 × 5a = -10(B) 8 + b = 7.8:
8 + b = 7.8b = 7.8 - 8b = -0.2(C) -0.5 = -2c:
-0.5 = -2cc = -0.5/-2c = 0.25Therefore, in the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25Know more about equations here:
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What is the probability that a meal will include a hamburger
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ANSWER:
The probability that a meal will include a hamburger is 25%
SOLUTION:
The total combination of one entree and one drink is 4* 2 = 8
The total combination of one hamburger meal is 1*2 = 2
The probability is 2/8 or 1/4 or 25%
Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
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EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
2/___=4/18What is the answer to the problem
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Explanation:
These are equivalent fractions, we have to find the missing denominator from the fraction on the left. Since the numerator of the fraction on the right is 4 and the numerator of the fraction on the left is 2, we can see that we have to divide by 2. Therefore 18 divided by 2 is 9. This is the numerat
Answer:
Suppose A is true, B is true, and C is true. Find the truth values of the indicated statement.
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Solution:
If A is true, B is true, and C is true, then:
[tex]A\lor(B\wedge C)=\text{ T }\lor(T\wedge T)\text{ = T}\lor(T)\text{ = T }\lor\text{ T = T}[/tex]we can conclude that the correct answer is:
TRUE
To find the length of a side, a, of a square divide the perimeter, P by 4. Use the above verbal representation to express the function s, symbolically, graphically, and numerically.
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Solution
- We are told to find the numerical, graphical, and symbolic expression for the side of a square, s, given its perimeter, P
Symbolic Representation:
- The symbolic representation simply means the formula we can use to represent the side of a square given its perimeter, P.
- The side of a square is simply the perimeter P divided by 4.
- Symbolically, we have:
[tex]\begin{gathered} s=\frac{P}{4} \\ \text{where,} \\ s=\text{side of the square} \\ P=\text{Perimeter of the square} \end{gathered}[/tex]Numerical Representation:
- We are given a set of numbers to create a table given some numbers for P.
- We are given a set of values for P: 4, 8, 10, 12.
- We can use the formula in the symbolic representation to find the corresponding values of s.
[tex]\begin{gathered} \text{When P = 4:} \\ s=\frac{4}{4}=1 \\ s=1 \\ \\ \text{When P=8:} \\ s=\frac{8}{4}=2 \\ s=2 \\ \\ \text{When P=10:} \\ s=\frac{10}{4}=2.5 \\ s=2.5 \\ \\ \text{When P=12:} \\ s=\frac{12}{4}=3 \\ s=3 \end{gathered}[/tex]- Now that we have the values of P and the corresponding values of s, we can proceed to create a table of values as the question asked of us.
Determine the system of inequalities that represents the shaded area .
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For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]57-92=17 -2c-ust +1 8x1322-1) = 677343 (x + 55-22-20 K 54+32--1 5x+363) = -1 5x+aen -6 8+2=6 2:6-8 -44)-5)-(2) 16-3942=12 18-y-18 -x-57-3222 - (-1)-sy-5633=2 2-35-17 = 2 2.3.3 -Byzo yo TARE 3) -x - 5y + z = 17 -5x - 5y +56=5 2x + 5y - 3z=-10 4) 4x + 4y + 2x - 4y+ 5x - 4y
Answers
ANSWER:
[tex]\begin{gathered} x=4 \\ y=2 \\ z=0 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x+4y+z=24\text{ (1)} \\ 2x-4y+z=0\text{ (2)} \\ 5x-4y-5z=12\text{ (3)} \end{gathered}[/tex]We solve by elimination:
[tex]\begin{gathered} \text{ We add (1) and (2)} \\ 4x+4y+z+2x-4y+z=24+0 \\ 6x+2z=24\text{ }\rightarrow x=\frac{24-2z}{6}\text{ (4)} \\ \text{ We add (1) and (3)} \\ 4x+4y+z+5x-4y-5z=24+12 \\ 9x-4z=36\text{ (5)} \\ \text{ replacing (4) in (5)} \\ 9\cdot(\frac{24-2z}{6})-4z=36 \\ 36-3z-4z=36 \\ -7z=36-36 \\ z=\frac{0}{-7} \\ z=0 \end{gathered}[/tex]Now, replacing z in (4):
[tex]\begin{gathered} x=\frac{24-2\cdot0}{6} \\ x=\frac{24}{6} \\ x=4 \end{gathered}[/tex]Then, replacing z and x in (1):
[tex]\begin{gathered} 4\cdot4+4y+0=24 \\ 16+4y=24 \\ 4y=24-16 \\ y=\frac{8}{4} \\ y=2 \end{gathered}[/tex]