Part A:
By Angle-Angle Theorem,
Triangle BCA is similar with triangle BDC (∠B ≅ ∠B, and ∠C ≅ ∠D)
Triangle CDA is similar with triangle BCA (∠CBA ≅ ∠DCA, and ∠BCA ≅ ∠CDA)
By transitive property
ΔBCA ~ ΔCDA ~ BDC
Part B:
[tex]\begin{gathered} \text{By properties of similar triangle} \\ \frac{b}{c}=\frac{d}{b} \end{gathered}[/tex]Part C:
Cross multiplying the proportions we have
[tex]\begin{gathered} \frac{b}{c}=\frac{d}{b} \\ b\cdot b=cd \\ b^2=cd \end{gathered}[/tex]A 6 inch by 10 inch rectangle is dilated by afactor of 3. What is the area of the dilatedrectangle?
Given;
There are given that the 6 inches by 10-inch rectangle.
Explanation:
dilated by a factor of three means that the two dimensions needed for the area are multiplied by 3.
So,
The width of the rectangular is:
[tex]width=6\times3=18[/tex]And,
The length of the rectangular is:
[tex]10\times3=30[/tex]Then,
The area of dilated rectangular is:
[tex]\begin{gathered} Area\text{ of dilated rectanular=}width\times\text{length} \\ =18\times30 \\ =540inch^2 \end{gathered}[/tex]Final answer:
Hence, the area of the dilated rectangle is 540 inch^2.
Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 10 hours longer to clearthe land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to thenearest tenth.)
To answer this question we will set and solve a system of equations.
Let A be the time (in hours) that it would take Company A to clear the parcel of land alone, and B be the time (in hours) that it would take Company B to clear the parcel of land alone.
Since working together, the two companies can clear the parcel of land in 8 hours, and wirking alone, it would take Company A 10 hours longer than Company B, then we can set the following system of equations:
[tex]\begin{gathered} \frac{1}{A}*8+\frac{1}{B}*8=1, \\ A=B+10. \end{gathered}[/tex]Substituting the second equation in the first one we get:
[tex]\frac{8}{B+10}+\frac{8}{B}=1.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} \frac{8B}{(B+10)B}+\frac{8(B+10)}{(B+10)B}=1, \\ \frac{16B+80}{(B+10)B}=1. \end{gathered}[/tex]Multiplying the above result by (B+10)B we get:
[tex]\begin{gathered} \frac{16B+80}{(B+10)B}*(B+10)B=1*(B+10)B, \\ 16B+80=(B+10)B. \end{gathered}[/tex]Simplifying the above result we get:
[tex]16B+80=B^2+10B.[/tex]Subtracting 16B+80 from the above result we get:
[tex]\begin{gathered} 16B+80-(16B+80)=B^2+10B-(16B+80), \\ 0=B^2-6B-80. \end{gathered}[/tex]Using the quadratic formula we get:
[tex]\begin{gathered} B=\frac{6\pm\sqrt{(-6)^2-4*1(-80)}}{2*1}=\frac{6\pm\sqrt{36+320}}{2} \\ =\frac{6\pm\sqrt{4*89}}{2}=3\pm\sqrt{89}. \end{gathered}[/tex]Since a negative value of B has no real meaning, we get that:
[tex]B=3+\sqrt{89}\approx12.4.[/tex]Answer: 12.4 hours.
in the diagram below angle E congruent angle H enter the segments in tye blanks provided that would result in a true equation
ANSWER
DF/GF or DE/GH
EXPLANATION
We know that angle H and angle E are congruent. We also know that angles HFG and EFD are congruent too because they are vertical angles. Thus, by the AA postulate, triangles HGF and EDF are similar.
If two figures are similar, the ratio between corresponding sides must be constant. Of these two triangles, the corresponding sides are
• EF and HF
,• DF and GF
,• DE and GH
So the ratio between corresponding sides is,
[tex]\frac{EF}{HF}=\frac{DF}{GF}=\frac{DE}{GH}[/tex]The answers could be DF/GF or DE/GH
helpful please math
Given data:
The given graph.
The range is the value of y, for which the given function is defined.
[tex]R=\lbrack0,\text{ }\infty)[/tex]Thus, the range of the given graph is [0, ∞).
Line u has a slope of -2/9. Line v is perpendicular to u. What is the slope of line v?
Answer: Say you have a line with a slope of -4. What is the slope of the line perpendicular to it? First, take the negative of the slope of your line -(-4) = 4 Second, take the inverse of that number. 4 is a whole number so its denominator is 1. The inverse of 4/1 is 1/4.
Step-by-step explanation:
Rectangle A measures 20 cm by 4 cm. Rectangle B is a scaled copy of Rectangle A. Select ALL of the measurement pairs that could be the
dimensions of Rectangle B.
100 cm by 20 cm
15 cm by 5 cm
12.5 cm by 2.5 cm
20 cm by 5 cm
5 cm by 1 cm
The measurement pairs that could be the dimensions of rectangle B are 100 cm by 20 cm, 12.5 cm by 2.5 cm, and 5 cm by 1 cm.
The rectangle A measures 20 cm by 4 cm.
The ratio of the dimensions of rectangle A is 20:4 = 5.
Rectangle B is a scaled copy of rectangle A.
The dimensions of rectangle B must be in the same ratio as those of rectangle A.
The first set of dimensions is 100 cm by 20 cm.
The ratio of dimensions is 100:20 = 5.
Thus, these could be the dimensions of the rectangle B.
The second set of dimensions is 15 cm by 5 cm.
The ratio of dimensions is 15:5 = 3.
Thus, these cannot be the dimensions of the rectangle B.
The third set of dimensions is 12.5 cm by 2.5 cm.
The ratio of dimensions is 12.5:2.5 = 5.
Thus, these could be the dimensions of the rectangle B.
The fourth set of dimensions is 20 cm by 5 cm.
The ratio of dimensions is 20:5 = 4.
Thus, these cannot be the dimensions of the rectangle B.
The fifth set of dimensions is 5 cm by 1 cm.
The ratio of dimensions is 5:1 = 5.
Thus, these could be the dimensions of the rectangle B.
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Which expression equals 15.51
Let x is the number multiplied by 2.2 gives 15.51
So:
[tex]\begin{gathered} x\times2.2=15.51 \\ x=\frac{15.51}{2.2} \\ x=7.05 \end{gathered}[/tex]Hence option D is correct.
Rule: y = 2xx|y9| |101|
you have the equation:
y = 2x
in order to complete the table, proceed as follow:
for x=9
y = 2(9) = 18
for y=10, solve the equation for x and replace y:
x=y/2
x=10/2=5
for x=1
y = 2(1) = 2
Then, you have:
x | y
9 18
5 10
look at this diagram. if TV and WY are parallel lines and m
The measure of the angle ∠YXU is 138°.
We are given that the lines TV and WY are parallel to each other. Parallel lines in geometry are two lines in the same plane that are at an equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. We are given two angles in the diagram. The measure of the angle ∠VUS is 138°. We can see that the angles ∠VUS and ∠YXU are corresponding angles. Corresponding angles are any pair of angles that are both on the same side of a transversal. So, the angles must be equal to each other.
∠YXU = ∠VUS = 138°
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A homeowner
has a budget of $135 for
the installation of a light fixture. An
electrician charges $60 per hour plus a
one-time trip charge of $45. What is the
greatest amount of time, in hours, the
electrician can work on the installation
while staying within the homeowner's
budget? Write your answer as a decimal.
The greatest amount of time that the electrician can work is 1.5 hours.
What is the greatest amount of time that the electrician?The first step is to form a linear equation using the information provided in the question. A linear equation is an equation that increases at a constant term.
Total cost = cost of the one-time trip + (cost per hour x number of hours)
$135 = $45 + ($60 x h)
$135 = $45 + $60h
$135 - $45 = $60h
$90 = $60h
h = $90 / $60
h = 1.5 hours
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0.7 mg of a medication has been ordered. The recommended maximum dosage of the drug is 0.35 mg, and the minimum recommended dosage is 0.175 mg is the dosage ordered within the allowable limits?
The ordered quantity, 0.7 mg, is outside the recommended dosage permissible range.
What is the range?
The range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest. The range in a piece of data is the distinction between the highest and lowest value.
It is given the maximum, and minimum dosage of medicine is 0.35 and 0.175 mg, respectively.
So, permissible range=[0.175,0.35]
0.7 mg of medicine is ordered.
Note that 0.7>0.175.
Also, 0.7>0.35
That means 0.7 does not lie in the permissible range.
So, the ordered quantity, 0.7 mg, is outside the recommended dosage range.
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9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer10. Refer to problem 9. If each woman filled the order for 30 dresses by herself, how manymore days would it take Alberta Emery?AnswerSteung can
We know rate and time are inverses of each other.
Let's take the inverse of each time to find their rates.
Alberta Emery
It takes her 3 days to sew a dress. So, her rate is 1/3
Allison Taylor
It takes her 2 days to sew a dress. So, her rate is 1/2
Their combined rate (when working together) is '1/3 + 1/2'
We know
rate x time = job completed
We can use the combined rate (just found) and jobs = 30 dress, to find the time it will take both of them working together to sew 30 dresses.
The equation is,
[tex](\frac{1}{3}+\frac{1}{2}_{})t=30[/tex]Solving for "t", we get,
[tex]\begin{gathered} (\frac{1}{3}+\frac{1}{2}_{})t=30 \\ (\frac{2}{6}+\frac{3}{6})t=30 \\ \frac{5}{6}t=30 \\ t=\frac{30}{\frac{5}{6}} \\ t=30\times\frac{6}{5} \\ t=\frac{180}{5} \\ t=36 \end{gathered}[/tex]So, it will take them 36 days to sew 30 dresses if they work together.
which has the larger 15th term when comparing the arithmetric and geometric sequences below? show evidence that support your answer Arithmetic sequence: 150, 650, 1150, 1650Geometric sequence:4,12, 36, 108
Answer
For the arithmetic sequence,
15th term = 7,500
For the geometric sequence,
15th term = 19,131,876
We can see that the geometric sequence has the larger 15th term.
Explanation
The general formula for an arithmetic progression is
f(n) = a + (n - 1)d
where
a = first term = 150
n = number of terms
d = common difference
= (Second term) - (First term)
= (Third term) - (Second term)
= Difference between consecutive terms
= 650 - 150
= 500
f(n) = 150 + (n - 1)500
f(n) = 150 + 500n - 500
f(n) = -350 + 500n
For the 15th term, n = 15
f(n) = -350 + 500n
f(15) = -350 + 500(15)
f(15) = -350 + 7500
f(15) = 7,150
For the geometric sequence,
[tex]f(n)=ar^{n-1}[/tex]where
a = first term = 4
n = number of terms
r = common ratio
= (Second term)/(First term)
= (Third term)/(Second term)
= Ratio of consecutive terms
= (12/4)
= 3
For the 15th term, n = 15
[tex]\begin{gathered} f(n)=ar^{n-1} \\ f(15)=4\times3^{15-1} \\ f(15)=4\times3^{14} \\ f(15)=19,131,876 \end{gathered}[/tex]Hope this Helps!!!
Find the value of h(0). include proper units. what does this output represent?
Answer:
you will suffer inpain with hell
1+1 pls help me im 4
Answer:
2
Step-by-step explanation:
because i say so and i am older
A gardener plants three different sapling at East Green Central Park. The number of magnolia saplings he planted was 3 less than crab apples saplings. The Kwanzan cherry sapling planted amounted to twice the number of magnolia. Is 35 saplings were planned in all, how many Kwanzan cherry sapling he planted?
16 number of Kwanzan cherry saplings he planted.
Let the gardener plant the no of Crab apple saplings was x
Since the no of magnolia in saplings he planted was 3 less than crab apple saplings.
Therefore, the no. of magnolia Saplings planted was x-3
Also, the Kwanzan Cherry sapling planted amounted to twice the number of magnolia.
Therefore, the Kwanzan Cherry sapling was. planted by him 2(x-3)
Conditionally,
x+(x-3)+2(x-3) = 35
= x+x-3 +2x-6 = 35
4x = 44
x = 11
Hence the no. of kwanzan Cherry sapling. he planted was
=2(11-3).
2x8 = 16
What is sampling?Sampling means choosing a group from which you will collect data in your research. For example, if you are researching the opinions of students at your university, you can study a sample of 100 students. In statistics, sampling allows testing a hypothesis about the characteristics of a population. There are two types of sampling methods: Probability sampling involves random selection that allows strong statistical inferences to be made about the entire group.Non-probability sampling involves non-random selection based on convenience or other criteria that allow you to easily collect data.To learn more about sampling, refer;
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help me please
thank you
Answer:
Domain: A, [tex][2, \infty)[/tex]
Range: A, [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Convert the point to polar coordinates using the interval [0, 2\small \pi) for θ. Show all work.
We know that polar coordinates are defined as:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \theta=\tan ^{-1}(\frac{y}{x}) \end{gathered}[/tex]in this case we have the point (-2,-2); this means that x=-2 and y=-2. Plugging this value for the radius we have that:
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ r=\sqrt[]{4+4} \\ r=\sqrt[]{2\cdot4} \\ r=2\sqrt[]{2} \end{gathered}[/tex]Plugging the values for the angle we have:
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{-2}{-2}) \\ \theta=\tan ^{-1}(1) \\ \theta=\frac{\pi}{4} \end{gathered}[/tex]for the angle we need to be careful, we know that the point (-2,-2) in on the third quadrant, this means that the angle is greater than pi but when we use the formula we got pi/4; this comes from the fact that the formula for the angle determines the angle measure in the quadrant we are at. This means that we need to add the appropiate amount to the angle found by this formula to find the correct one. In this case, since we are on the third quadrant, we need to add pi to the angle we found, then we have:
[tex]\begin{gathered} \theta=\frac{\pi}{4}+\pi \\ \theta=\frac{\pi+4\pi}{4} \\ \theta=\frac{5\pi}{4} \end{gathered}[/tex]Hence the correct angle is 5pi/4.
Therefore the polar coordinates of the angle are:
[tex](2\sqrt[]{2},\frac{5\pi}{4})[/tex]Calculate simple interest (ordinary) and maturity valueProblem A simple interest note has a face value of 12,000, a rate of 8%, and a term of 1 year.
Solution
Given
Face value(pricipal), p = 12,000
Rate, r = 8%
Number of years, t = 1
Simple interest = prt/100
[tex]\begin{gathered} Simple\text{ interest =}\frac{12000\text{ x 8 x 1}}{100}\text{ = 960} \\ \end{gathered}[/tex]The simple interest = 960
Maturity value = Principal + interest
= 12,000 + 960
=12,960
HELP PLEASEEEEEE!!!!!!!! ILL MARK AS BRAINLIEST
A horizontal line with evenly spaced numerical increments is referred to as a number line.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
What is meant by number line?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It exists assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments exists directed to as a number line. How the number on the line can be answered depends on the numbers present. The utilize of the number exists defied by the question that it corresponds to, such as when graphing a point.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
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1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
What exactly is a number line?In basic mathematics, real numbers are represented by a number line, a representation of a graduated straight line. The presumption is that each point on a number line represents a real number, and that each real number represents a point.
There is something known as a number line, which is a horizontal line with uniformly spaced numerical increments. The numbers available determine how to respond to the number on the line. The number can be used in ways that defy the question it answers, such as when graphing a point.
1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
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(x,y) --> (x-8,y+4)
what is the image A(2,6)
Translation involves changing the position of a shape. The image of A is A' is (-6,10)
The translation rule is given as: ( x, y)--->( x-8,y+4)
The point is given as: A = (2,6)
Substitute 2 for x and 6 for y
(2,6)------>(2-8,6+4)
(2,6)------>(-6,10)
This means that: (-6,10)
Hence, the image of A is: A' = (-6,10)
What is a translated image?
Image-to-image translation is the process of transforming an image from one domain to another with the goal of learning to associate an input image with an output image.
The translation image of a form can be found using the following rule or formula. Suppose you want to translate or move point P a unit horizontally and b unit vertically. Then change the x and y values of the P coordinates. The points of the triangle are A(-3, 1), B(-, 3) and C(-2 ).
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Instructions: Find the area of the sector with the red outline. Round your answer to the nearest tenth.
HeHeThe area of a sector is given as:
[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex][tex]\begin{gathered} r\rightarrow radius,\theta\rightarrow angle\text{ at the centre} \\ r=14ft \\ \theta=210^0 \end{gathered}[/tex][tex]\begin{gathered} A=\frac{210^0}{360^0}\times\pi\times14^2 \\ A=\frac{7}{12}\times196\times\pi \\ A=359.2ft^2 \end{gathered}[/tex]Hence, the area in the nearest tenth is
Tell which set or sets the number below belongs to:natural,whole,integer,rational,irrational, or real number -4/9
Given
[tex]-\frac{4}{9}[/tex]
Procedure
Rational numbers: In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Real numbers: In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).
Find the equation of the tangent line e^-4t at t=0
Given -
y = e^-4t
To Find -
The equation of the tangent =?
Step-by-Step Explanation -
y = e^-4t
So, dy/dx =
y' = -4e^-4t
also,
m = y'(0) = -4e^-4(0)
= -4
So,
when x = 0, y = e^0 = 1
So, point of tangency is (0,1)
Slope of tangent is -4
Using point-slope form:
y - 1 = -4(x - 0)
y = -4x +1
Final Answer -
The equation of the tangent =
y = -4x +1 or at x = t
y = -4t +1
2. What is the product of m^3, 2m^5, and 1/m^2?
the expression is given as follows,
[tex]=m^3\times2m^5\times\frac{1}{m^2}[/tex][tex]\begin{gathered} =m\times2m^5 \\ =2m^6 \end{gathered}[/tex]so the answer is 2m^6
At the start of a trip, a car’s gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 LaTeX: \frac{1}{8}1 8 gallons of gasoline. How much gasoline is left in the tank?
At the beginning we have 12 gallons and during the trip the car consumes 10 1/8 of the tank. Then the expression we are looking for is
[tex]12-10\text{ 1/8}[/tex]The football players had to sell DEVIL FOOTBALL t-shirts to raise money for their next uniforms.
They charged $17 for short sleeve shirts and $13 for long sleeve shirts.
At the end of the fund raiser, they had sold 46 shirts and had made $718..
How many of each type of shirt did they sell?
Your job is to setup two equations to answer this question (we will not solve this system right now)
Use S as the number of short sleeve shirts and L as the number of long sleeve shirts.
Write your two equations below.
Your 1st equation:
Your 2nd equation:
Question Help: Message instructor
Jump to Answer
Check All Parts
Answer:
- From the information given, S and L was sold into a total of 46 shirts to get $718
- In terms of quantity of shirts; [1 st equation]
[tex]{ \rm{S + L = 46 \: - - - (eqn \: a)}} \\ [/tex]
- In terms of money income and outcome; [2 nd equation]
[tex]{ \rm{17S + 13L = 718 - - - (eqn \: b)}} \\ [/tex]
- Further more as per the question;
- From 1st equation;
[tex]{ \rm{S = 46 - L - - - (eqn \: c)}}[/tex]
- From equation c, substitute for S in equation b;
[tex]{ \rm{17(46 - L) + 13L = 718}} \\ \\ { \rm{782 - 17L + 13L = 718}} \\ \\ { \rm{ - 4L = - 64}} \\ \\ { \rm{L = 16}}[/tex]
- Substitute for L in equation c;
[tex]{ \rm{S = 46 - 16}} \\ { \rm{S = 30}}[/tex]
30 Short sleeved shirts were sold, earned $510
16 Long sleeved shirts were sold, earned $208
Question 2: Attached in screenshot below: If chart from question 1 is needed just tell me.
EXPLANATION
The slope field can be obtained by applying a graph drawing as shown as follows:
Which of the following equation(s) are equivalent to y − 4 = 2/3(x − 1)?
A y= 2/3x - 10/3
B y= 2/3x - 3 1/3
C y= 2/3x + 3
D y= 2/3 + 10/3
Answer:
D) y = 2/3x + 10/3Step-by-step explanation:
GivenEquation of the line in point-slope form:
y - 4 = 2/3(x - 1)Convert the equation into slope-intercept form of y = mx + b:
y - 4 = 2/3(x - 1)y - 4 = 2/3x - 2/3y = 2.3x + 4 - 2/3y = 2/3x + (12 - 2)/3y = 2/3x + 10/3Correct choice is D
Answer:
[tex]\textsf{D.} \quad y=\dfrac{2}{3}x+\dfrac{10}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]y-4=\dfrac{2}{3}(x-1)[/tex]
Distribute the parentheses on the right side of the equation:
[tex]\implies y-4=\dfrac{2}{3}x-\dfrac{2}{3}[/tex]
Add 4 to both sides:
[tex]\implies y-4+4=\dfrac{2}{3}x-\dfrac{2}{3}+4[/tex]
[tex]\implies y=\dfrac{2}{3}x-\dfrac{2}{3}+4[/tex]
Rewrite 4 as 12/3:
[tex]\implies y=\dfrac{2}{3}x-\dfrac{2}{3}+\dfrac{12}{3}[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{12}{3}-\dfrac{2}{3}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{12-2}{3}[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{10}{3}[/tex]
Therefore, the equation that is equivalent to the given equation is:
[tex]\boxed{y=\dfrac{2}{3}x+\dfrac{10}{3}}[/tex]
What is the answer to this 8x+10y=20
We need to find the value of x and y:
[tex]8x\text{ + 10y = 20}[/tex]First, let solve the x variable:
Subtract 10y on both sides
[tex]8x\text{ +10y -10y = 20-10y}[/tex][tex]8x\text{ =20-10y}[/tex]Then divide by 8 into both sides :
[tex]\frac{8x}{8}=\text{ }\frac{20-10y}{8}[/tex][tex]x\text{ = }\frac{20-10y}{8}[/tex]Replace the x value into the first equation:
[tex]8x\text{ + 10y = 20}[/tex][tex]8(\frac{20-10y}{8})+10y\text{ = 20}[/tex]Now, solve the equation for y:
[tex]20-10y\text{ +10y = 20}[/tex]