we can write equations from the statements
a washer and dryer cost 1001 combined
[tex]w+d=1001[/tex]where w is the price of the washer and d the price of the dryer
the washer costs 51 more the than the dryer
[tex]w=51+d[/tex]then we can replace the value of w from the second equation to the first equation
[tex]\begin{gathered} (51+d)+d=1001 \\ 51+d+d=1001 \\ 51+2d=1001 \end{gathered}[/tex]and solve for d
[tex]\begin{gathered} 2d=1001-51 \\ 2d=950 \\ d=\frac{950}{2} \\ \\ d=475 \end{gathered}[/tex]the cost of the dryer was $475
Michael annual salary is 39,110 and has a budget of 26%of annual salary for housing what is the most that Michael may spend on monthly rent
Since each year has 12 months, divide the annual salary by 12 to find the monthly salary. Then, multiply it by 26/100 to find the amount of money that Michael may spend.
[tex]\frac{39,110}{12}\times\frac{26}{100}=847.38333\ldots[/tex]Therefore, the most that Michael ay spend on monthly rent, is approximately:
[tex]847.38[/tex]You want to put a 4 inch thick layer of topsoil for a new 23 ft by 31 ft garden. The dirt store sells by the cubicyards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Remember that
1 ft=12 in
1 yd =36 in
so
The garden is 23 ft by 31 ft
Convert to inches
23 ft=23*12=276 in
31 ft=31*12=372 in
Find out the volume
V=(276)*(372)*(4)
V=410,688 in3
Convert to cubic yards
410,688 in3=410,688*(1/36)^3=8.80 cubic yards
Remember that
The store only sells in increments of 1/4 cubic yards
so
The volume is 9 cubic yardsQuestionFind the equation of a line that contains the points (-6, 3) and (5,-8). Write the equation in slope-intercept form.
ANSWER
y = -x - 3
STEP BY STEP EXPLANATION
Step 1: The given points are:
(-6, 3) and (5, -8)
Step 2: The slope-intercept form is
[tex]y\text{ = mx + c}[/tex]where m is the slope and c is the intercept
Step 3: Find the slope m
[tex]\begin{gathered} \text{slope (m) = }\frac{y_2-y_1}{x_2-x_1} \\ \text{m = }\frac{-8_{}-\text{ 3}}{5\text{ - (-6)}} \\ m\text{ = }\frac{-11}{11}\text{ = -1} \end{gathered}[/tex]Step 4: Solve for intercept c using either of the points
[tex]\begin{gathered} y\text{ = mx + c} \\ c\text{ = y - mx} \\ c\text{ = 3 - (-1)(-6)} \\ c\text{ = 3 - 6} \\ c\text{ = -3} \end{gathered}[/tex]Step 5: Re-writing the slope-intercept form to include the values of m and c
[tex]\begin{gathered} y\text{ = mx + c} \\ y\text{ = -x - 3} \end{gathered}[/tex]Hence, the equation of the line in slope-intercept form is y = -x - 3
E is the midpoint of DF, DE = 2x + 4 and EF = 3x - 1 how do I find the value of x, DE, EF and DF
We know that
E is midpoint of DF, that means DE is equal to EF, so we can form the following equation
[tex]DE=EF[/tex]Replacing the given equations, we have
[tex]\begin{gathered} 2x+4=3x-1 \\ 4+1=3x-2x \\ x=5 \end{gathered}[/tex]Now, we replace this value in each equation to find each part of the segment.
[tex]\begin{gathered} DE=2x+4=2(5)+4=10+4=14 \\ EF=3x-1=3(5)-1=15-1=14 \end{gathered}[/tex]Therefore, each part of the segment is 14 units, and DF is 28.Find the cube roots of 4−6i4−6iShow all your work.Include an explanation and diagram showing how DeMoivre's Theorem helps to solve this problem.
Given the following complex number
[tex]z=4-6i[/tex]We will find the cube root of the complex number using the following formula:
[tex]^3\sqrt{z}=\sqrt[3]{|z|}*(cos\text{ }\frac{\theta+2\pi k}{3}+i*sin\text{ }\frac{\theta+2\pi k}{3})[/tex]The formula is called De Moivre's theorem of the nth root
We have substituted n = 3
So, first, we will convert the given number from the rectangular form to the polar form
[tex]\begin{gathered} |z|=\sqrt{4^2+6^2}\approx7.211 \\ \theta=tan^{-1}\frac{-6}{4}=303.7\degree \end{gathered}[/tex]Substitute the magnitude and the angle and k = 0, 1, 2
So, there are 3 cubic roots of the given number as follows:
[tex]\begin{gathered} k=0\rightarrow z_1=\sqrt[3]{7.211}(cos\frac{303.7}{3}+i*sin\frac{303.7}{3})=1.932(cos101.23+i*sin101.23) \\ \\ k=1\rightarrow z_2=\sqrt[3]{7.211}(cos\frac{303.7+2\pi}{3}+i*sin\frac{303.7+2\pi}{3})=1.932(cos221.23+i*sin221.23) \\ \\ k=2\rightarrow z_3=\sqrt[3]{7.211}(cos\frac{303.7+4\pi}{3}+i*sin\frac{303.7+4\pi}{3})=1.932(cos341.23+i*sin341.23) \end{gathered}[/tex]Which angles are adjacent to each other? Select all that apply.
Answer:
I think it's all the options but I cant confirm.
Step-by-step explanation:
adjacent angles are angles that:
- have the same vertex
- share one side
The illustration below shows the graph of y as afunction of xComplete the following sentences based on thegraph of the function.(Enter the x-intercepts from least to greatest.)* This is the graph of a (nonlinear, linear orconstant) function.* The y-intercept of the graph is the function value y = ___.The x-intercepts of the graph (in order from leastto greatest) are located at x = ___ and x = ___.* The greatest value of y is y = ___ and it occurswhen x = ___.* For x between x = 2 and x = 6, the function value y (<, 2, or =) 0.
* This is the graph of a (nonlinear, linear or constant) function.
Answer:
This is the graph of a nonlinear function (In this case it is a quadratic function).
--------------------------------------------------------------------------------------
The y-intercept of the graph is the function value y =
Answer:
From the graph we can conclude that, the y-intercept is:
[tex]y=-6[/tex]----------------------------------------------------------------------------
The x-intercepts of the graph (in order from least to greatest) are located at x = ___ and x = ___.
Answer:
From the graph, we can conclude that the x-intercepts are located at:
[tex]\begin{gathered} x=2 \\ and \\ x=6 \end{gathered}[/tex]----------------------------------------------------------------------
The greatest value of y is y = ___ and it occurs
Answer:
From the graph, we can see that the vertex of the function is:
[tex]\begin{gathered} y=2 \\ when \\ x=4 \end{gathered}[/tex]----------------------------------------------------------------
For x between x = 2 and x = 6, the function value y is.
Answer:
For those values, y is always greater than or equal to 0, so:
[tex]2\le x\le6\to y\ge0[/tex]Company operates stores under multiple banners in 13 states in the United States
Given:
Banners in 13 states in united states:
Total states in united state is 50.
(A)
Do not have store is:
[tex]\begin{gathered} =50-13 \\ =37 \end{gathered}[/tex]So in 37 states Company not operates any store.
(B)
Fraction do not have a store operates :
[tex]\begin{gathered} =\frac{37}{50} \\ =0.75 \end{gathered}[/tex]Which of the following could be an example of a function with a domain (-0,) and a range (-0,2)? Check all that apply. A. V= - (0.25)* - 2 - B. v= -(3)*-2 O c. v= -(3)*+2 1 v= - (0.25)*+2 D.
It is desired that the domain and range of the function should, respectively, be
[tex]\begin{gathered} \text{Domain}=(-\infty,\infty) \\ \text{Range}=(-\infty,2) \end{gathered}[/tex]Observe the given choices of function.
It is evident that all the functions are exponential functions, so their domain must be the set of all real numbers,
[tex](-\infty,\infty)[/tex]Now, we have to check the range of each of the 4 given functions.
Option A:
The function is given as,
[tex]y=-(0.25)^x-2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(0.25)^x\rightarrow0\Rightarrow-(0.25)^x-2\rightarrow-2\Rightarrow y\rightarrow-2 \\ x\rightarrow-\infty\Rightarrow-(0.25)^x\rightarrow-\infty\Rightarrow-(0.25)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,-2)[/tex]Since this does not match with the desired range. This is not a correct choice.
Option B:
The function is given as,
[tex]y=-(3)^x-2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(3)^x\rightarrow-\infty\Rightarrow-(3)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \\ x\rightarrow-\infty\Rightarrow-(3)^x\rightarrow0\Rightarrow-(3)^x-2\rightarrow-2\Rightarrow y\rightarrow-2 \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,-2)[/tex]Since this does not match with the desired range. This is not a correct choice.
Option C:
The function is given as,
[tex]y=-(3)^x+2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(3)^x\rightarrow-\infty\Rightarrow-(3)^x+2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \\ x\rightarrow-\infty\Rightarrow-(3)^x\rightarrow0\Rightarrow-(3)^x+2\rightarrow2\Rightarrow y\rightarrow2 \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,2)[/tex]Since this exactly matches with the desired range. This is a correct choice.
Option D:
The function is given as,
[tex]y=-(0.25)^x+2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(0.25)^x\rightarrow0\Rightarrow-(0.25)^x+2\rightarrow2\Rightarrow y\rightarrow2 \\ x\rightarrow-\infty\Rightarrow-(0.25)^x\rightarrow-\infty\Rightarrow-(0.25)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,2)[/tex]Since this exactly matches with the desired range. This is also a correct choice.
Thus, the we see that the functions in option C and D possess the desired domain and range.
Therefore, option C and option D are t
What are the coordinates of M', the image of M (2,4), after a counterclockwiserotation of 90° about the origin?
If M(h,k) is rotated 90° counterclockwise about the origin, the new position would be M'(k, -h)
M(2, 4)-> M'(4, -2)
Which number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
An electronics store sends an email survey to all customers who bought tablets. The previous month, 570 people bought tablets. Surveys were sent to 300 of these people, chosen at random, and 138 people responded to the survey. Identify the population and the sample. (4 points)The population is 570. The sample is 138.The population is 570. The sample is 300.The population is 300. The sample is 138.The population is 138. The sample is 570.The population is 138. The sample is 300.
Answer:
The population is 300. The sample is 138.
Explanation:
In statistics, population refers to the entire group of persons or things that a study is to be carried out on. Looking at the given question, we can see that, even though there were 570 people that bought tablets, the surveys were only sent to 300 people chosen at random. It shows that only 300 of the 570 people are to be surveyed, therefore, the population is 300.
A sample is the particular/specific group of persons or things that data is to be received from.
Looking at the given question, we can see that, out of the 300 people that the surveys were sent to, only 138 people responded to the survey. So the sample is 138.
Rapheal is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is -20t + 45, where t is the number of hours he has been traveling. What is his speed in miles per hour?
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
A and B are the two points of a straight line.Distance between two points is given as :d₀ = -20t + 45 miles
t = the number of hours of travelling.The starting time = 0
i.e. the initial position = 0
Then
we put t=0
At t=0
d₀ = -20(0) + 45
= 0 + 45
= 45 miles
the distance travel after starting first hour is :
T= d₁ & d₀
than we put t = 1
At t = 1;
d₁ = -20(1) + 45
= -20 + 45
= 25 miles
now
Difference between d₁ & d₀ is
d = d₁ - d₀
45 - 25 = 20 miles
Total distance covered = 20 miles
To find the speed we use formula:
Speed = distance/time
Speed=20/1
Speed = 20 miles/hour
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
To know more about speed
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I need help A. -3 B. 3 C. -2D. -10
The average rate of change can be calculated as the division of the output of the function on the interest interval by the size of the interval. To do that we have to find the value of "y" at the end of the interval and subtract it by the value of "y" at the beggining. This is shown as an expression below:
[tex]\text{average rate of change=}\frac{y_{\text{ final}}-y_{\text{ initial}}}{x_{\text{ final}}-x_{\text{ initial}}}[/tex]For this function the values of x are:
[tex]\begin{gathered} x_{\text{ initial}}=0 \\ x_{\text{ initial}}=3 \end{gathered}[/tex]The values for y are:
[tex]\begin{gathered} y_{\text{ initial}}=10 \\ y_{\text{ final}}=1 \end{gathered}[/tex]Using these values we can calculate the average rate of change:
[tex]\text{average rate of change=}\frac{1-10}{3-0}=\frac{-9}{3}=-3[/tex]The average rate of change for this function is approximately -3 for the given interval. The correct answer is A.
For f(x) = 2x+1 and g(x) = x² − 7, find (f+ g)(x).
Given the functions:
[tex]\begin{gathered} f(x)=2x+1 \\ \\ g(x)=x^2-7 \end{gathered}[/tex]By definition, (f+g)(x) is equivalent to:
[tex](f+g)(x)=f(x)+g(x)[/tex]Finally, using the expressions for f and g:
[tex]\begin{gathered} f(x)+g(x)=2x+1+x^2-7 \\ \\ \therefore(f+g)(x)=x^2+2x-6 \end{gathered}[/tex]I thought this answer was the sixth root, cubed, value of 16. But I am not sure so I need help with the question
In order to find the correct options, we need to know the following property:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]So, rewriting the expression 243^(3/5), we have:
[tex]243^{\frac{3}{5}}=\sqrt[5]{243^3}[/tex]That is, 243^(3/5) is the 5th root of 243 cubed. Its value is:
[tex]\sqrt[5]{243^3}=\sqrt[5]{14348907}=27[/tex]6. Line 1 passes through the points (1,4) and (-2,5). Line 2 passes through the points (1,0) and (0,3). What is true about Line 1 and Line 2? (2 points) (A) (B) They are perpendicular. They are parallel. They both decrease. They both increase. (C) (D)
First, calculate the slope (m) of both lines.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Line 1:
Point 1 = (x1,y1) = (1,4)
Point 2 = (x2,y2) = (-2,5)
Replacing:
[tex]m=\frac{5-4}{-2-1}=\frac{1}{-3}=-\frac{1}{3}[/tex]Line 2:
Point 1 = (x1,y1) = (1,0)
Point 2 = (x2,y2) = (0,3)
[tex]m=\frac{3-0}{0-1}=\frac{3}{-1}=-3[/tex]Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.
None of the slopes are equal or negative reciprocal. SO, A and B are false-
Now, for the increase/ decrease
We can see that both lines have a negative slope, so they both decrease.
Correct option: C
how many shirts can Jeanette sew at most of and still have 1. spool of thread left
Answer:
The number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Explanation:
Given a graph that relates the number of spools of thread left to the number of shirts sewn.
We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.
To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.
Tracing the line down we can observe that it is at shirt sewn equals 5.
So, the number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]-87, -70, -27, -36,...a(n)= 17n - 10432nd term
We have the arithmetic progression given by
[tex]a_n=17n-104[/tex]if n = 1 we have the first term, n = 2 the second one and, so on, to find the 32nd term we just do n = 32, therefore
[tex]\begin{gathered} a_{32}=17\cdot32-104 \\ \\ a_{32}=544-104 \\ \\ a_{32}=440 \end{gathered}[/tex]The 32nd term is 440.
49x^2 + 16y^2 - 392x +160y + 400 = 01. give the coordinates of the upper vertex2. give the coordinates of the lower vertex3. give the coordinates of the upper focus(round to the nearest hundredths)4. give the coordinates of the lower focus(round to the nearest hundredths)5. give the eccentricity
we have
49x^2 + 16y^2 - 392x +160y + 400 = 0
Complete the square
Group terms
[tex](49x^2-392x)+(16y^2+160y)=-400[/tex]Factor 49 and 16
[tex]49(x^2-8x)+16(y^2+10y)=-400[/tex][tex]49(x^2-8x+16)+16(y^2+10y+25)=-400+16(49)+25(16)[/tex][tex]\begin{gathered} 49(x^2-8x+16)+16(y^2+10y+25)=784 \\ 49(x^{}-4)^2+16(y+5)^2=784 \end{gathered}[/tex]Divide by 784 both sides
[tex]\begin{gathered} 49(x^{}-4)^2+16(y+5)^2=784 \\ \frac{49(x^{}-4)^2}{784}+\frac{16(y+5)^2}{784}=1 \end{gathered}[/tex]simplify
[tex]\frac{(x^{}-4)^2}{16}+\frac{(y+5)^2}{49}=1[/tex]we have a vertical elipse
the center is the point (4,-5)
major semi axis is 7
we have
a^2=16 --------> a=4
b^2=49 ------> b=7
Find the value of c
[tex]\begin{gathered} c=\sqrt[]{b^2-a^2} \\ c=\sqrt[]{33} \end{gathered}[/tex]see the attached figure to better understand the problem
Find the distance between the points (4,1) and (2,4) using distance formula
Given:-
[tex](4,1)(2,4)[/tex]To find the distance.
So the distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting we get,
[tex]\begin{gathered} d=\sqrt{(2-4)^2+(4-1)^2} \\ d=\sqrt{-2^2+3^2} \\ d=\sqrt{4+9} \\ d=\sqrt{13} \end{gathered}[/tex]So the required distance is root 13.
Find the missing side of this righttriangle.x816x= V[?]=Enter the number that belongs in the green box.Enter
As gien by the question
There are given that the right angle triangle.
Now,
To find the value of x, use Pythagoras theorem:
So,
From the Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=16^2 \\ x^2+64=256 \\ x^2=256-64 \\ x=\sqrt[]{192} \end{gathered}[/tex]Hence, the value of x is shown below:
[tex]x=\sqrt[]{192}[/tex]At a party 15 handshakes took place. Each person shook hands exactly once with each of the other present. How many people were at the party?
2 people => 1 handshake (AB)
3 people => 3 handshakes (AB, BC, AC)
4 people => 6 handshakes (AB, AC, AD, BC, BD, CD)
Do you see a pattern here?
We can write a general formula for this
[tex]handshakes=\frac{n\cdot(n-1)}{2}[/tex]Since we are given that there were 15 handshakes
[tex]15=\frac{n\cdot(n-1)}{2}[/tex][tex]\begin{gathered} 2\cdot15=n\cdot(n-1) \\ 30=n\cdot(n-1) \\ 30=6\cdot(6-1) \\ 30=6\cdot(5) \\ 30=30 \end{gathered}[/tex]This means that n = 6 people were present at the party.
You can substitute n = 6 into the above formula and you will notice that it will give 15 handshakes
[tex]handshakes=\frac{n\cdot(n-1)}{2}=\frac{6\cdot(6-1)}{2}=\frac{6\cdot5}{2}=\frac{30}{2}=15[/tex]9×6 can u help me with this
You have to multiply the numbers:
9x6 =54
Multiply is the same as adding the number 6 times
9+9+9+9+9+9 =54
Describe the relationship between average velocity of a car in motion versus the instantaneous velocity of the same car in motion. Which one matters more if you get pulled over on the freeway for speeding and why?
Answer:
During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car. It shows your speed at a particular instant in time.
Step-by-step explanation:
The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as
On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour. Yet, on average, you were moving with a speed of 25 miles per hour.
hope this helps might not be the answer your looking for but a better explanation on how too figure it out :))
Consider the graph of the linear function shown.What is the approximate average rate of change of this function from = -2 to r = 2?lesleso3-Yes
The average rate of change of this function from x = -2 to x = 2 can be gotten by finding the slope of the line using both x coordintes;
From the graph, when x1 = -2, y1 = 2.5
Also when x2 = 2, y2 = 0.5
Using the formula for calculating slope expressed as;
m = y2-y1/x2-x1
Substitute the given values
m = 0.5-2.5/2-(-2)
m = -2.0/2+2
m = -2/4
m = -1/2
Hence average rate of change of this function from x = -2 to x = 2 is -1/2. Option C is correct.
Solve for y Simplify your answer as much as possible Find by linear equation.
Given the equation:
[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]We will solve the equation to find y
Multiply the equation by 4 to eliminate the denominators
[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]Combine the like terms
[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]Subtract (17) to both sides
[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]Divide both sides by (-15)
[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]So, the answer will be y = 3
Translate to an equation and solve W divided by 6 is equal to 36 w=
Answer:
[tex]w\text{ = 216}[/tex]Explanation:
Here, we want to translate it into an equation and solve
W divided by 6 equal to 36:
[tex]\begin{gathered} \frac{w}{6}\text{ = 36} \\ \\ w\text{ = 6}\times36 \\ w\text{ = 216} \end{gathered}[/tex]y - 32 = -2(x-48)what is y
y - 32 = -2( x - 48)
y - 32 = -2x + 96
y = -2x + 96 + 32
y = -2x + 128
Brainliest and 20 points please solve
Answer:
part a: x = 5
part b: no
Step-by-step explanation:
part a : 8x + 3 = 9x - 2, subtract 8x from both sides which leaves you with 1x or just x. add 2 to both sides which gives you 5. 5 is equal to 1x.
part b: a complementary angle is 2 angles whos sum equals 90 degrees. m<ABC = 43 & m<DBE = 43 & they both equal 86 not 90.
Answer/Step-by-step explanation:
A C
\ (8x + 3) /
\ /
\ /
\ /
B
/ \
/ \
/ \
/ (9x - 2) \
D E
A. Solve for x.
m∠ABC = m∠DBE
(8x + 3) = (9x - 2)
8x + 3 = 9x - 2
-9x -9x
------------------------
-x + 3 = -2
-3 -3
--------------------
-x = -5
÷-1 ÷-1
----------------
x = 5
B. Are vertical angles also complementary angles?
No, vertical angles are angles that are congruent to each other or in other words, equal. In the equation above (8x + 3) = (9x - 2). If I were to plug 5 into the equation I would get
(8(5) + 3) = (9(5) - 2)
(40 + 3) = (45 - 2)
43 = 43
Complementary angles equal to 90°. It wouldn't make sense to add these numbers together because I would end up with a fraction if I set the equation equal to 90°
I hope this helps!
