12. Given.4(9.2), B(-1,y), C(-5, 16),and D(-8. 11), find the value ofy so that ABCD
Answers
ok, we need to draw both segment of lines... that are parallel.
We need to re draw, because we need more space for point C (-5,16)
The steps to solve this problem are:
1) We draw segment line CD... later,
2) we express the segment line AB,
3) We find the slopes of both segments
4) finally, we found the value of y.
Do you understand? or have questions of the process?
We have done the segment line CD, after that from the graphic we can make a prediction of the value of y, because we need to find a line perpendicular to cd.. like this one (green in the graphic)... line green will be perpendicular to line yellow...
Now, we find the general equation of the yellow line.. that's it:
[tex]\begin{gathered} \text{slope = m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)};\text{ C(x}_1,y_1)=C(-5,16);\text{ D(x}_2,y_2\text{)}=D(-8,11) \\ \text{ m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)}=\frac{\text{(11}-16\text{)}}{(-8-(-5))}=\frac{\text{(11}-16\text{)}}{(-8+5)}=\frac{-5}{-3}=\frac{5}{3} \\ m=\frac{5}{3} \end{gathered}[/tex]After that, we should remember that two lines are paralell when a multiplication of its slopes it's equal to -1, like this:
[tex]\begin{gathered} \text{slope 1 }\cdot\text{ slope 2 = -1} \\ m_1\cdot m_2=-1 \\ \frac{5}{3}.m_2=-1 \\ m_2=\frac{-3}{5} \end{gathered}[/tex]Finally, we find the generall equation of the line green with the point A(9,2) and the value of its slope m2, we apply:
[tex]\begin{gathered} (y-y_1)=m(x-x_1);\text{ A(x}_1,y_1)=A(9,2);\text{ m=}\frac{-3}{5};\text{ We replace and get} \\ y-2=\frac{-3}{5}(x-9) \\ y=\frac{-3}{5}x+\frac{3}{5}\cdot\frac{9}{1}+2 \\ y=\frac{-3}{5}x+\frac{27}{5}+2 \\ y=\frac{-3}{5}x+\frac{37}{5} \end{gathered}[/tex]Now, to find the value of y in the poin B, we replace the value of x = -1 in the equation of the green line, like this:
[tex]\begin{gathered} y=\frac{-3}{5}x+\frac{37}{5};\text{ x=-1} \\ y=\frac{-3}{5}(-1)+\frac{37}{5} \\ y=\frac{3}{5}+\frac{37}{5}=\frac{40}{5}=8 \end{gathered}[/tex]The answer has the value of 8. In graphic is similar.. green line... It's not equal because I do the graphic at inexact way.
Related Questions
7. On the coordinate grid below, show a line that is parallel to y = 2x + 4. 2 5 3 1 2 3 2 -1 4
Answers
Answer
the graph of the line parallel to y = 2x + 4 is presented below
The line has the equation y = 2x + 1
Explanation
Any two parallel lines will have the same slopes.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, for y = 2x + 4, the slope is evidently 2
So, any line that we will pick that will be prallel to the given line has to be of the form
y = 2x + c
c, the y-intercept, can then be any number. Let us use an example where c = 1
The equation of a line parallel to y = 2x + 4 is y = 2x + 1
To plot this, we would need to use the intercepts.
when x = 0,
y = 2x + 1
y = 2(0) + 1
y = 0 + 1 = 1
First point of the line is (0, 1)
when y = 0
y = 2x + 1
0 = 2x + 1
2x = -1
Divide both sides by 2
(2x/2) = (-1/2)
x = -0.5
Second point on the line is (-0.5, 0)
We can then plot the line on the coordinate using these two points (0, 1) and (-0.5, 0)
So, the graph of the line parallel to y = 2x + 4 is presented under 'Answer'
Hope this Helps!!!
The answer and how to do it
Answers
Answer:
v ≈ 4 cm
Step-by-step explanation:
using the Sine rule in Δ VWX
[tex]\frac{v}{sinV}[/tex] = [tex]\frac{w}{sinW}[/tex]
where v = WX and w = VX
∠ W = 180° - (126 + 21)° = 180° - 147° = 33° , then
[tex]\frac{v}{sin21}[/tex] = [tex]\frac{6}{sin33}[/tex] ( cross- multiply )
v × sin33° = 6 × sin21° ( divide both sides by sin33° )
v = [tex]\frac{6sin21}{sin33}[/tex] ≈ 4 cm ( to the nearest cm )
Solve the equation: 7+ 3(2x - 1) = (4x+8)
Answers
Fenelon, this is the solution:
Let's solve the equation:
7+ 3(2x - 1) = (4x+8)
1. Solve the parenthesis
7 + 6x - 3 = 4x + 8
2. Like terms:
6x - 4x = 8 + 3 - 7
2x = 4
3. Dividing by 2 at both sides:
2x/2 = 4/2
x = 2
Solved, Fenelon!!
Write the sequence of transformations that changes figure ABCD to figure A’B’C’D. Explain your answer and write the coordinates of the figure obtained after each transformation. Are the two figures congruent? Explain your answer.
Answers
SOLUTION:
We can compare a point to get the translation.
We can use the point;
[tex]A(-4,4)[/tex]which transforms to;
[tex]A^{\prime}^^{\prime}(3,-4)[/tex]The first transformation is a reflection over the x-axis to map point A to;
[tex]A^{\prime}(-4,-4)[/tex]The next transformation is a translation 7 units to the right.
Therefore, the sequence of transformations are;
Part B: The two figures are congruent because the transformations used are non-rigid.
what is the answer to 3+2q+6-q
Answers
To simplify the expression 3+2q+6-q, we have to combine like terms, we do this by combining the terms that are multiplied by the same variable (y) and the terms that are not being multiplied by any variable, we can do it, like this:
3+2q+6-q = (3 + 6) + (2q - q) = (9) + (q) = 9 + q
Then, the answer is 9 + q
Find the zeros of the function.7x^2-28=0
Answers
14. Hotel Rates You rent a hotel room for $72 a night. The hotel adds a charge for using its parking lot to the total bill, Afterstaying at the hotel for 3 nights, your total bill is $231.a. Write an equation in slope-intercept form that gives your total bill (in dollars) as a function of the number ofnights you stay in the room.b. How much of your bill was for the parking fee?c.How much does it cost to stay at the hotel for 7 nights?d. If your bill was $591, how many nights did you stay at the hotel?
Answers
Answer:
(a)y=72x+15
(b)$15
(c)519
(d)8 nights
Explanation:
Let the number of nights which you stay = x
The cost of renting a room for a night =$72
Therefore, the costs for x nights = $72x
If the charge for using its parking lot = c
Then, the total cost, y=72x+c
Part A
When the total bill = $231
x=3 nights
[tex]\begin{gathered} 231=72(3)+c \\ 231=216+c \\ c=231-216 \\ c=15 \end{gathered}[/tex]Therefore, an equation in slope-intercept form that gives your total bill as a function of the number of nights, x is:
[tex]y=72x+15[/tex]Part B
Your packing fee, c=$15
Part C
When the number of nights, x=7
[tex]\begin{gathered} \text{Total Cost,y}=72(7)+15 \\ =504+15 \\ =\$519 \end{gathered}[/tex]Part D
When the total cost, y = $591
[tex]\begin{gathered} 591=72x+15 \\ 72x=591-15 \\ 72x=576 \\ \frac{72x}{72}=\frac{576}{72} \\ x=8 \end{gathered}[/tex]If your bill was $591, you stayed for 8 nights.
the volume of the right triangular prism is ______ in3 . use the formula V=Bh
Answers
First, we need to obtain the area of the triangle B
[tex]B=\frac{5\cdot12}{2}=\frac{60}{2}=30in^2[/tex]Then we can use the formula given
[tex]V=\text{ B}\cdot h=30\cdot10=300in^3[/tex]Kaizen is a Japanese word that means continuous development. It says that each day we should focus on getting1% better on whatever we're trying to improve.How much better do you think we can get in a year if we start following Kaizen today?Note: You can take tilf value of (1.01)365 as 37.78
Answers
If at day 1 we get 1% better than in the day 0, we will be:
[tex]\frac{101}{100}\times1=1.01\times1=1.01[/tex]1.01 better on day 1 than on day 0.
If we get 1% better on day 2 than on day 1, then by day 2 we would be:
[tex]\frac{101}{100}\times1.01=1.01\times1.01=(1.01)^2=1.0201[/tex]1.0201 times better on day 2 than on day 0.
After n days, we would have to multiply 1 by 1.01 n times, so by day n we would be:
[tex]1.01^n[/tex]times better than on day 0.
Calculate 1.01^365 to find how many times better we would be one year after day 0:
[tex]1.01^{365}=37.78343433\ldots[/tex]Therefore, we would get 37.78 times better by day 365, which is after one year.
a. Reflect y = x^2 – 2 across the x-axis.
Answers
Given;
We are to reflect the function:
[tex]y=x^2\text{ -2}[/tex]Given a function f(x), the rule for reflecting across the x-axis is:
[tex]\begin{gathered} f(x)\text{ }\rightarrow\text{ -f'(x)} \\ \text{where the arrow represents the transformation} \end{gathered}[/tex]Hence, the reflection of the given function gives:
[tex]\begin{gathered} y=f(x)=x^2\text{ -2} \\ f^{\prime}(x)=-(x^2-2) \\ =-x^2+2 \end{gathered}[/tex]Thus the reflected function would be:
[tex]y^{^{\prime}}=-x^2+2[/tex]What is the approximate length of the edge that Tasha will cover with tile
Answers
Given:
length=16
width=12
radius=4.5
So total length is:
length of half circle is:
circumference of circle:
[tex]\begin{gathered} C=2\pi r \\ \text{half circle=}\frac{2\pi r}{2} \\ =\pi r \end{gathered}[/tex][tex]\begin{gathered} r=4.5 \\ =\pi r \\ =\pi(4.5) \\ =14.137 \end{gathered}[/tex]For there sides of circle is:
[tex]\begin{gathered} \text{length}+\text{width}+\text{width} \\ =16+12+12 \\ =40 \end{gathered}[/tex]for circle side length is:
[tex]\begin{gathered} =16-(\text{diameter of circle)} \\ =16-(2\times4.5) \\ =16-9 \\ =7 \end{gathered}[/tex]So total length is:
[tex]\begin{gathered} =14.137+40+7 \\ =61.137 \\ \approx61 \end{gathered}[/tex]Approximate length of the edge that Tasha will cover with tile is 61.
………………………………………………………….
Answers
you made 66 dots or periods i
think
Identify the polynomial by selecting the most accurate name for the example: 3x² + 6x - 10
Answers
Notice that the degree of the polynomial
[tex]3x^2+6x-10[/tex]is 2. Then it is called a trinomial expression.
Find the slope of the line that passes through all of the points
on the table.
X
2
3
4
5
6
Y
3
13
23
33
43
Please help
Answers
HEEEEELPPPP
The population of a town is modeled by the equation P=3485e0.12t, where “P” represents the population as of the year 2000.
According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
show step bye step explanation
Answers
There are 11571 people in the world as of 2010, and would take about 22 years for that number to reach 50,000 of population.
What is termed as the exponential increase?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits greater increases over time. Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (that is raised to a power).Let P stand for the population in 2000 (or any other time period). Considering the equation:
P = 3485e∧0.12t,
The population in 2010 (t = 10 years) would be:
P = 3485e∧0.12×10
P = 3485e∧12
P = 11571
When there are 50,000 people in the population:
50,000 = 3485e∧0.12t,
Solving, by log property.
t = 22 years.
Thus, there are 11571 people in the world as of 2010, and would take about 22 years for that number to reach 50,000.
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If carpeting costs R75,50/m and an entrance hall has a length of 468,cm. Determine the cost of carpenting the hallway?
Answers
The cost of carpeting the hallway is Rs. 35,334.
The cost of carpeting is Rs. 7,550 per meter. We have an entrance hall. The length of the entrance hall is 468 cm. We need to find out the total cost of carpeting the hallway.
First of all, we will convert all the quantities to the same units. The length of the entrance hall is 468/100 = 4.68 meters.
The total cost of carpeting the hallway is the product of the length of the hallway and the cost of carpeting per unit length. Let the cost be represented by the variable "C".
C = Rs. 7,550*4.68
C = Rs. 35,334
Hence, the cost of carpeting the hallway is Rs. 35,334.
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A population of beetles are growing accordingto a linear growth model. The initial population (week 0) isPo = 5, and the population after 7 weeks is P = 82.Find an explicit formula for the beetle population after n weeks..Pn-After how many weeks will the beetle population reach 258?weeks
Answers
Answer:
P(n) = 5 + 11n
n = 23 weeks
Explanation:
The equation for the population as a linear growth model has the form
P = P0 + an
Where P0 is the initial population, n is the number of weeks and a is the rate of increase per week. We know that P0 = 5, so
P = 5 + an
Additionally, when n = 7 the value of P = 82, so we can use this to find the value of a as follows
82 = 5 + a(7)
82 = 5 + 7a
82 - 5 = 5 + 7a - 5
77 = 7a
77/7 = 7a/7
11 = a
Therefore, the equation for the population after n weeks is
P(n) = 5 + 11n
Finally, to know the number of weeks to reach a population of 258, we need to replace P by 258 and solve for n, so
258 = 5 + 11n
258 - 5 = 5 + 11n - 5
253 = 11n
253/11 = 11n/11
23 = n
So, after 23 weeks the population will be 258.
x^3-6x^2+12x-8=27
thnk kiu
Answers
x^3−6x^2+12x−8=0
⇔x^3−3x^2.2+3.x.2^2−2^3=0
⇔(x−2)^3=0
⇔(x−2)=0
⇔x=2
2.Each year on the same day, Susan deposits $100 into a savings account that earns simple interest at a rate of 3%. She makes no withdrawals. How much interest has Susan’s account earned after 2 years?3.Each year on the same day, Susan deposits $175 into a savings account that earns simple interest at a rate of 3.5%. She makes no withdrawals. How much interest does Susan’s account earn after 5 years?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
P = $100
r = 3% = 0.03
t = 2 years
Step 02:
Simple Interest = P * r * t
= 100 * 0.03 * 2
= 6
The answer is:
Susan earned $6 as simple interest after 2 years.
what percent of 28 is 35? the answer is (blank)%
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What is 2 8/10 in decimal form?
Answers
Okay, here we have this:
We are going to convert the following mixed number to decimal: 2 8/10, so we obtain the following:
[tex]\begin{gathered} 2\frac{8}{10} \\ =\frac{2\cdot10+8}{10} \\ =\frac{28}{10} \end{gathered}[/tex]Finally we obtain that 2 8/10 expressed as a fraction is equal to 28/10.
Help me simplify I don’t understand homework and I have to show work .
Answers
The Solution:
Given the expression below:
[tex]\frac{\left(sin\theta+cos\theta\right)^2}{1+2sin\theta\:cos\theta}[/tex]We are required to simplify the above expression.
[tex]\begin{gathered} (\sin \theta+\cos \theta)^2=\sin ^2\theta+2\sin \theta\cos \theta+\cos ^2\theta=\sin ^2\theta+\cos ^2\theta+2\sin \theta\cos \theta \\ =1+2\sin \theta\cos \theta \\ \text{ Since }\sin ^2\theta+\cos ^2\theta=1 \end{gathered}[/tex]So,
[tex]\frac{(sin\theta+cos\theta)^2}{1+2sin\theta\: cos\theta}=\frac{1+2sin\theta\: cos\theta}{1+2sin\theta\: cos\theta}=1[/tex]Therefore, the correct answer is:
[tex]\frac{(sin\theta+cos\theta)^2}{1+2sin\theta\: cos\theta}=1[/tex]write the given equation in slope intercept form. 5x-3y = -9
Answers
Thae equation is given as :
5x - 3y = -9
The equation can be written in slope intercept form as;
y= mx + c where m is the gradient and c is the y-intercept
So this will be;
5x = 3y -9
5x + 9 = 3y
5/3 x + 9/3 = 3y/3
5/3 x + 3 = y
y= 5/3 x + 3
Answer
y = 5/3 x + 3
Suppose a jar contains 20 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answers
The probability that they are both are red is 0.15.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
The jar contains 20 red marbles and 31 blue marbles. The total marble is 51.
Therefore, the probability will be:
= P(red) × P(red)
= 20/51 × 19/50
= 380 / 2550
= 0.15
The probability is 0.15.
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First, rewrite8/9 and 7/8so that they have a common denominator
Answers
we have
8/9 and 7/8
9=3*3
8=2*2*2
LCM=9*8=72
therefore
8/9 multiply by 8/8-----> (8/9)*(8/8)=64/72
7/8 multiply by 9/9 ----> (7/8)*(9/9)=63/72
8/9 and 64/72 are equivalent fractions
7/8 and 63/72 are equivalent fractions
Given the function and the graph below, which of the following best describes the continuity, interval of increase and interval of decrease?
Answers
Given the function:
[tex]f(x)=(-x-1)^2+3[/tex]As we can see, there is no restriction for x, it can be any real value. Additionally, looking at the graph, we do not see any discontinuity ("jumps" or "holes"). We conclude that the function is always continuous.
The vertex of the parabola is at (-1, 3), so x = 1 separates the intervals of increase and decrease. Going from -∞ to -1, we see a decrease in the y-values. Similarly, from -1 to +∞, we see an increment. Then:
Interval of increase: -1 < x < +∞
Interval of decrease: -∞ < x < -1
solving right triangle find the missing side. round to the nearest tenth number 15
Answers
To solve the triangle we are going to first find the measures of all the angles:
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree}\Rightarrow\text{ Because is a right triangle} \\ A+B+C=180\text{\degree} \\ \text{Because the sum of the internal angles of a triangle is 180 degrees} \\ 47\text{\degree}+90\text{\degree}+C=180\text{\degree} \\ 137\text{\degree}+C=180\text{\degree} \\ \text{ Subtract 137\degree from both sides of the equation} \\ 137\text{\degree}+C-137\text{\degree}=180\text{\degree}-137\text{\degree} \\ C=43\text{\degree} \end{gathered}[/tex]Now to find the measures of the sides you can use trigonometric ratios because it is a right triangle:
Side a: you can use the trigonometric ratio tan(θ)
[tex]\tan (\theta)=\frac{\text{ opposite side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan (47\text{\degree})=\frac{a}{28} \\ \text{ Multiply by 28 from both sides of the equation} \\ \tan (47\text{\degree})\cdot28=\frac{a}{28}\cdot28 \\ 30=a \end{gathered}[/tex]Side b or side x: you can use the trigonometric ratio cos(θ)
[tex]\cos (\theta)=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos (47\text{\degree})=\frac{28}{b} \\ \text{ Multiply by b from both sides of the equation} \\ \cos (47\text{\degree})\cdot b=\frac{28}{b}\cdot b \\ \cos (47\text{\degree})\cdot b=28 \\ \text{ Divide by cos(47\degree) from both sides of the equation} \\ \frac{\cos (47\text{\degree})\cdot b}{\cos (47\text{\degree})}=\frac{28}{\cos (47\text{\degree})} \\ b=\frac{28}{\cos(47\text{\degree})} \\ b=41.1 \end{gathered}[/tex]Therefore, when solving the triangle you have
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree} \\ C=43\text{\degree} \\ a=30 \\ b=41.1 \\ c=28 \end{gathered}[/tex]and the missing side is
[tex]\begin{gathered} b=x \\ x=41.1 \end{gathered}[/tex]A trapezoid has legs that are 13 cm and 15 cm long. The parallel sides are 11 cm and 25 cm long. The distance between the bases is 12 cm. What is the area of the trapezoid?
Answers
The formula for the area of trapezoid is
[tex]A=\frac{1}{2}\times\sum ^{\square}_{}\text{parallel sides }\times base\text{ height.}[/tex]The area of trapezoid is
[tex]A=\frac{1}{2}\times(11+25)\times12=6\times36=216cm^2[/tex]
What is the relationship among proportional relationships, lines, rates of change, and slope? The graph of a (select) unit (select) is a line through the origin whose (select) is the
Answers
The graph of a proportional relationship.
Whose slope
is the unit rate of change
Find the mean, median, and mode of the set of data.10, 11, 4, 7, 12, 11, 16, 6, 9, 15
Answers
Before we begin we will order the data set given
4, 6, 7, 9, 10, 11, 11, 12, 15, 16
Mean.
The mean of a data set is given by:
[tex]\operatorname{mean}=\frac{\sum ^{}_{}x_i}{n}[/tex]where the denominator means that we have to add the points on the data and then divide them result by the number of points in the data. In this case we have:
[tex]\begin{gathered} \operatorname{mean}=\frac{4+6+7+9+10+11+11+12+15+16}{10} \\ \operatorname{mean}=\frac{101}{10} \\ \operatorname{mean}=10.1 \end{gathered}[/tex]Hence the mean of the data set is 10.1
Median.
The median is the central value of the ordered data set. In this case we have an even number of values which means that the median is the average of the central values. The central values in this set are the the fifth and sixth term, that is, 10 and 11. The median is then:
[tex]\begin{gathered} \operatorname{median}=\frac{10+11}{2} \\ \operatorname{median}=\frac{21}{2} \\ \operatorname{median}=10.5 \end{gathered}[/tex]Mode
The mode is value that occur most frequently. In this case only the 11 repeats itsefl, hence the mode is 11.
Summing up we have:
Mean 10.1
Median 10.5
Mode 11