A ladder that is 10 yards in length is resting on a branch of a tree, and the base of the ladder is 6 yards from the tree on the level ground. How high up is the branch on which the ladder is resting?
Answers
Given the information, we can make a simple picture to see what we need to measure:
Now, using the pythagorean theorem, we have:
[tex]c^2=a^2+b^2[/tex]In this case, we have that c^2=10 and b^2=6, then we need to solve for a:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \Rightarrow a^2=c^2-b^2 \\ \Rightarrow a^2=(10)^2-(6)^2=100-36=64 \\ \Rightarrow a^2=64 \\ \Rightarrow a=\sqrt[]{64}=8 \\ a=8 \end{gathered}[/tex]Therefore, the branch is 8 yards high.
Related Questions
A surveyor makes a measurement shown in the diagram to find the distance between two observation towers on the opposite sides of the river how far apart are the towers?give an answer to the nearest meter
Answers
To determine the distance between two observation towers:
The distance between the tower 1 and tower 2 = Hypotenuse
[tex]\cos \theta=\frac{adj}{hyp}[/tex][tex]\begin{gathered} \cos \theta=\frac{adj}{hyp} \\ \cos 73^0\text{=}\frac{\text{63}}{hyp} \\ \text{Hyp}=\frac{63}{\cos 73^0} \\ \text{Hyp}=\frac{63}{0.2924} \\ \text{Hyp = 215.48m} \end{gathered}[/tex]Hence the distance between the tower 1 and tower 2 = 216m (nearest meter)
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve.
Answers
Given: An investment of $20,000 for 5 years at an interest rate of 6.5%.
Required: To determine the amount if the money is compounded semi-annually.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here,
[tex]\begin{gathered} P=20000 \\ t=5 \\ n=2 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as follows-
[tex]\begin{gathered} A=20000(1+\frac{0.065}{2})^{2\times5} \\ \end{gathered}[/tex]Further solving for amount gives-
[tex]A=27,537.89[/tex]Final Answer: The accumulated value is $27,537.89
Attempt due: Sep y5 Days, 2 HoursSecondsQuestion 1onnect1 ptsLines k and I are parallel, and the measure of angle ABC is 19 degrees.EmDA1. Explain why the measure of angle ECF is 19 degrees. If you get stuck, considertranslating line l by moving B to C.2. What is the measure of angle BCD? Explain.Edit Insert FormatToolsTable
Answers
Part 1
We know that the angle mAnd taking in count these two conditions is possible to see that corresponding angles so then needs to be congruent.
Part 2
Is possible to see that vertically opposed by the vertex and for this case then are alo congruent and the answer would be:
m
7) Solve the equation.* ух + 3 = 4 оооо
Answers
x = 13
Here, we want to solve the equation;
[tex]\begin{gathered} \sqrt[]{x\text{ + 3}}\text{ = 4} \\ \\ we\text{ square both sides} \\ \\ (\sqrt[]{x\text{ + 3}})^2=4^2 \\ \\ x\text{ + 3 = 16} \\ \\ x\text{ = 16-3} \\ \\ x\text{ = 13} \end{gathered}[/tex]a tree is 160 feet tall. If Francis is standing 74 ft from the tree what is the angle of elevation from the ground where Francis standing to the top of the tree? Round to the nearest tenth
Answers
We shall begin by drawing a sketch of the question.
The diagram shows the position of the tree, which is 160 feet tall, the position of Francis which is 74 feet from the tree. The angle of elevation from the ground where Francis is standing to the top of the tree is angle F. Therefore, angle F is calculated as follows;
[tex]\begin{gathered} \tan F=\frac{\text{opp}}{\text{adj}} \\ \text{The opposite is facing the reference angle, which is F} \\ \text{The adjacent lies between the reference angle and the right angle} \\ \tan F=\frac{160}{74} \\ \tan F=2.162162\ldots \\ F=65.179458\ldots \\ F=65.2\text{ (to the nearest tenth)} \end{gathered}[/tex]The angle of elevation is 65.2 degrees (approximated to the nearest tenth)
4x−6x+15−x−4. I don't know
Answers
Which expression is equivalent to sqrt 1-cos(10x) / 2
Answers
The expression is
[tex]\sqrt[]{\frac{1-\cos (10x)}{2}}[/tex]Using the half angle formula:
[tex]\sin \frac{\theta}{2}=\pm\sqrt[]{\frac{1-\cos \theta}{2}}[/tex]If θ=10x then we can replace it in the formula:
[tex]undefined[/tex]Given f(x) = cos^2 (x), find the equation of the tangent line at x = π/6
Answers
GIVEN THE EQUATION :
[tex]f(x)\text{ = cos }^2(x)\text{ }[/tex](i) Find the derivative of cos^2 (x)
[tex]\begin{gathered} f^{\prime}(x)=\frac{d}{dx}(cos\text{ }^2(x)\text{ \rparen.... apply the chain rule } \\ \Rightarrow2\text{ cos \lparen x\rparen }\frac{d}{dx\text{ }}(cos\text{ \lparen x\rparen\rparen} \\ \Rightarrow2cos\text{ x \lparen-sinx\rparen ..... simplify } \\ \Rightarrow-sin(2x)\text{ } \\ \therefore f^{\prime}(x)\text{ = -sin\lparen2x\rparen } \\ \\ \end{gathered}[/tex](ii) Now that we have calculated the derivative of cos^2 (x) = -sin(2x)
at x = /6 :
[tex]\begin{gathered} f(\frac{\pi}{6})\text{ = -sin \lparen2 * }\frac{\pi}{6}) \\ \text{ = -sin }\frac{2\pi}{6} \\ \text{ = -sin }\frac{\pi}{3} \\ \text{ = -0.018} \end{gathered}[/tex]This means that our point is ( /6 ;- 0.018)
(iii) Calculate the slope of the tangent line :
m = f'( /6 )
= -sin2
Really need help with number 16 just started learning this today and still don't quite understand would really appreciate the help
Answers
0. To complete the square, it is easier to move the constants to the other side:
[tex]x^2-\frac{3}{4}x+\frac{1}{8}-\frac{1}{8}=-\frac{1}{8}[/tex][tex]x^2-\frac{3}{4}x=-\frac{1}{8}[/tex]2. Getting the square of both sides:
[tex]x^2-\frac{3}{4}x+(\frac{\frac{3}{4}}{2})^2^{}=-\frac{1}{8}+(\frac{\frac{3}{4}}{2})^2[/tex][tex]x^2-\frac{3}{4}x+(\frac{3}{8})^2=-\frac{1}{8}+(\frac{3}{8})^2[/tex][tex]x^2-\frac{3}{4}x+\frac{9}{64}^{}=-\frac{1}{8}+\frac{9}{64}[/tex]3. Factoring and solving:
[tex](x^{}-\frac{3}{8})^2=\frac{1}{64}[/tex][tex](x^{}-\frac{3}{8})^2-\frac{1}{64}=\frac{1}{64}-\frac{1}{64}[/tex][tex](x^{}-\frac{3}{8})^2-\frac{1}{64}=0[/tex]Answer:
[tex](x^{}-\frac{3}{8})^2-\frac{1}{64}=0[/tex]For the parabola show, what is the symmetry and the vertex?
Answers
Let's put more details in the given graph:
A.) What is the axis of symmetry?
Axis of Symmetry: x = -1
B.) What is its vertex?
Vertex: x, y = -1, -4
6) Use the leading coefficient and degree of the polynomial function todetermine the end behavior of the graph Select all that apply*f(x) = x? - 7x2 + 10xx—+o, f(x) — +0x— too, f(x) —-OptionOption 2
Answers
options 1 and 4
Explanation
when you have a polynomial function :
[tex]f(x)=a_xx^n+a_{x-1}x^{n-1}+a_{x-2}x^{n-2}++++[/tex]When n is even and an is positive the behavior is Graph rises to the left and right
and
When n is odd and an is positive the behavior is :Graph falls to the left and rises to the right
then
[tex]f(x)=x^3-7x^2+10x[/tex]n=3=odds, then
Graph falls to the left and rises to the right
in other words, if x becomes bigger f(x) becomes bigger too,
so the answer are
options 1 and 4
The functions f and g are defined as follows( view the image attached)
Answers
Answer
f(-3) = 36
g(6) = - 10
Explanation:
Given the following functions
f(x) = 3x^2 - 3x
g(x) = -2x + 2
Find f(-3) ?
f(-3) means substitute x = -3
f(-3) = 3(-3)^2 - 3(-3)
f(-3) = 3(9) + 9
f(-3) = 27 + 9
f(-3) = 36
g(6) = -2(6) + 2
g(6) = -12 + 2
g(6) =- 10
Therefore, f(-3) = 36 and g(6) = -10
The diameter of a circle is 10 in. Find the circumference to the nearest tenth?
Answers
The circumference can be calculated using the formula
C = 2πr
where r is the radius
From the question, diameter =10, this implies radius = 5
π is a constant which is equal to 22/7
substitute the values into the formula and evaluate
[tex]C=2\times\frac{22}{7}\times5[/tex][tex]C\approx31.4\text{ cm}[/tex]Find the first 4 terms of the sequence.t(n) = -3n- 1b. t(15)=
Answers
Answer:
(a)-4, -7, -10 and -13.
(b) -46
Explanation:
Given the sequence:
[tex]t\mleft(n\mright)=-3n-1[/tex](a) The first four terms are obtained by substituting n=1,2,3 and 4 respectively.
[tex]\begin{gathered} t\mleft(1\mright)=-3(1)-1=-3-1=-4 \\ t(2)=-3(2)-1=-6-1=-7 \\ t(3)=-3(3)-1=-9-1=-10 \\ t(4)=-3(4)-1=-12-1=-13 \end{gathered}[/tex]The first 4 terms of the sequence are -4, -7, -10 and -13.
(b)t(15)
[tex]\begin{gathered} t(15)=-3(15)-1 \\ =-45-1 \\ =-46 \end{gathered}[/tex]A rectangular prism has a length of 6 ft, a height of 15ft, and a width of 6ft. What is its volume, in cubic feet?
Answers
The formula of the volume of a rectangular prism is
[tex]V=l\cdot w\cdot h[/tex]where l is the length, w is the width and h is the height
In our case we have
l=6ft
w=6ft
h=15ft
we substitute the values
[tex]V=6\cdot6\cdot15[/tex]the volume is
[tex]V=540ft^3[/tex]the volume is 540 cubic feet
Dustin and Mabel have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Dustin earns a base wage of $15 per hour, as well as $2 for every subscription that he sells. Mabel gets $3 per subscription sold, in addition to a base wage of $5 per hour. If they each sell a certain number of subscriptions in an hour, they will end up earning the same amount. How many subscriptions would that be?Write a system of equations, graph them, and type the solution.
Answers
The system of equations:
y = 15 + 2n...............(1)
y = 5 + 3n..................(2)
The graph is plotted below
Each of Dustin and Mabel sell 10 subscriptions in 1 hour
They earn $35 each in 1 hour
Explanations:Let the number of subscriptions made by each of Dustin and Mabel in 1 hour be n
Let the amount earned by each of them be y
Dustin earns a base wage of $15 per hour, as well as $2 for every subscription that he sells.
Total amount earned by Dustin is:
y = 15 + 2n
Mabel gets $3 per subscription sold, in addition to a base wage of $5 per hour
Total amount earned by Mabel
y = 5 + 3n
The system of equations is:
y = 15 + 2n...............(1)
y = 5 + 3n..................(2)
The graph representing the system of equations is:
The red line represents y = 15 + 2n
The blue line represents y = 5 + 3n
The point where the two lines meet is the solution to the system of equations
The solution to the system of equations is:
n = 10, y = 35
Therefore, each of Dustin and Mabel sell 10 subscriptions in 1 hour
They earn $35 each in 1 hour
5. Keisha collected and weighed 5 soil samples for a science project. What is the mean weight of thesoil sample?Sample 1112.345Weight37.2g43.6g29.8840.1g39.4g
Answers
The mean of a group of numbers is the division of the sum of each individual value by the number of samples. With this in mind, we have:
[tex]\mu=\frac{34.2+43.6+29.88+40.1+39.4}{5}[/tex][tex]\mu=\frac{187.18}{5}=37.436[/tex]The mean weight of the samples is 37.436 kg.
8. Nate wrote the polynomial shown below on the board. Which value(s) of "n" would make the polynomial factorable? 16x2 - I. q 9 II. -9 III. 25 a. I only b. I and III only w c. I and II only d. I, II and III
Answers
By definition, a Perfect square trinomial has the following form:
[tex]a^2\pm2ab+b^2[/tex]Perfect square trinomials can be expressed in Squared-binomial form, as following:
[tex](a\pm b)^2[/tex]In this case, you know that the first term of the Perfect square trinomial Tia wrote on the board, is:
[tex]4x^2[/tex]And the last term is:
[tex]25[/tex]Then you can identify that:
[tex]a^2=4x^2[/tex]Solving for "a", you get:
[tex]\begin{gathered} a=\sqrt[]{4x^2} \\ a=2x \end{gathered}[/tex]Notice that:
[tex]b^2=25[/tex]Solving for "b", you get:
[tex]\begin{gathered} b=\sqrt[]{25} \\ b=5 \end{gathered}[/tex]Knowing "a" and "b", you can write the following Squared-binomial:
[tex](2x+5)^2[/tex]And determine that the missing term is:
[tex]2ab=2(2x)(5)=20x[/tex]Therefore, the missing value is not a Perfect square, because it is not obtained by multiplying two equal Integers.
The answer is: Option B.
Which of the following is an extraneous solution of V-3x-2-X+2?O x=-6O x = -1O X = 1O x = 6
Answers
We have the expression:
[tex]\sqrt[]{-3x-2}=x+2[/tex]The square root, to be defined in the domain of real numbers, has to have a 0 or positive argument. Then, -3x-2 has to be greater or equal than 0.
We can write:
[tex]\begin{gathered} -3x-2\ge0 \\ -3x\ge2 \\ x\le-\frac{2}{3} \end{gathered}[/tex]Then, solutions for x that are greater than -2/3 are not valid.
We are left with x=-6 and x=-1.
We can test both:
[tex]\begin{gathered} x=-6\Rightarrow\sqrt[]{-3(-6)-2}=-6+2 \\ \sqrt[]{18-2}=-4 \\ \sqrt[]{16}=-4 \\ 16=(-4)^2 \\ 16=16 \end{gathered}[/tex]x=-6 is a valid solution.
We now test the other solution:
[tex]\begin{gathered} x=-1\longrightarrow\sqrt[]{-3(-1)-2}=-1+2 \\ \sqrt[]{3-2}=1 \\ \sqrt[]{1}=1 \\ 1=1 \end{gathered}[/tex]x=-1 is also a valid solution.
find the equation of the circle with the given center and radius:a. Center (0,0) and r = √13b. Center (-8, -1) and r = 9
Answers
ANSWER:
[tex]x^2+y^2=13[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of the circle is given by the following equation
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h, k) is the center and r is the radius} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=\sqrt[]{13}^2^{} \\ x^2+y^2=13 \end{gathered}[/tex]what is the equivalent degree measure for [tex] \frac{3\pi}{4} [/tex]radians?
Answers
Given:
[tex]\frac{3\pi}{4}[/tex]Required: Equivalent in degree
Solution:
Let the equivalent of
[tex]\frac{3\pi}{4}[/tex]be represented as X.
Thus,
[tex]\frac{3\pi}{4}\text{ = X}[/tex]But
[tex]\pi radians=180^{\circ}[/tex]This implies that
[tex]\begin{gathered} \pi=180^{\circ} \\ \frac{3\pi}{4}\text{ = X} \end{gathered}[/tex]By cross-multiplication, we have
[tex]\begin{gathered} \pi\text{ }\times\text{ X = 180 }\times\text{ }\frac{3\pi}{4} \\ X\pi\text{ = }\frac{180\times3\pi}{4} \end{gathered}[/tex]Divide both sides by the coefficient of X.
The coefficient of X is π.
Thus,
[tex]\begin{gathered} X\text{ = }\frac{180\times3\pi}{4}\times\frac{1}{\pi} \\ \Rightarrow X\text{ = 135} \end{gathered}[/tex]Hence, the equivalent of
[tex]\frac{3\pi}{4}\text{ radians}[/tex]is 135°
x+y=2 y=2x+5write the solution as an ordered pair
Answers
We are given the following system of equations:
[tex]\begin{gathered} x+y=2,(1) \\ y=2x+5,(2) \end{gathered}[/tex]To solve this system we will use the method of substitution. We will replace the value of "y" from equation (2) into equation (1).
[tex]x+2x+5=2[/tex]Now we will add like terms:
[tex]3x+5=2[/tex]Now we will subtract 5 to both sides of the equation:
[tex]\begin{gathered} 3x+5-5=2-5 \\ 3x=-3 \end{gathered}[/tex]Now we will divide by 3:
[tex]x=-\frac{3}{3}=-1[/tex]Now we will replace the value of "x" in equation (2):
[tex]y=2(-1)+5[/tex]Solving the operations:
[tex]\begin{gathered} y=-2+5 \\ y=3 \end{gathered}[/tex]The solution of the system is:
[tex](x,y)=(-1,3)[/tex]Find the probabilities of the events below. Write each answer as single fraction
Answers
Part A:
a) P(A) = 1/2 b) P(B) = 4/7 c) P(A and B) = 1/7 d) P(A or B) = 13/14 e) P(A or B) = 13/14
Part B:
P(A) + P(B) - P(A and B) = P(A or B) (last option)
Explanation:Given:
A Venn diagram of the 14 students in Ms. Patterson's class
To find:
Part A:
a) P(A) b) P(B) c) P(A and B) d) P(A or B) e) P(A) + P(B) - P(A and B)
Part B:
To find the probability equal to P(A) + P(B) - P(A and B)
a) P(A) = number students in A/total
Total students = 14
number of students in A = 7
P(A) = 7/14 = 1/2
b) P(B) = number students in B/total
number of students in B = 8
P(B) = 8/14 = 4/7
c) P(A and B) = number of students in A and B
P(A and B) = 2/14 = 1/7
d) P(A or B) = P(A) + P(B) - P(A and B)
[tex]\begin{gathered} P(A\text{ or B\rparen = }\frac{1}{2}\text{ + }\frac{4}{7}\text{ - }\frac{1}{7} \\ P(A\text{ or B\rparen = }\frac{7(1)\text{ + 2\lparen4\rparen - 2\lparen1\rparen}}{14} \\ P(A\text{ or B\rparen}=\text{ }\frac{7+8-2}{14} \\ P(A\text{ or B\rparen = }\frac{13}{14} \end{gathered}[/tex]e) P(A) + P(B) - P(A and B) = P(A or B)
P(A) + P(B) - P(A and B) = 13/14
Part B:
P(A) + P(B) - P(A and B) = P(A or B) (last option)
what is the angle formed by the hillside and theo's line of sight p?1 Approximately 104.8 degree2 Approximately 20 degree3 Approximately 55.2 degree 4 Approximately 180 degree
Answers
We have to find the angle formed by the hillside and Teo's line of sight (P).
We know two side lenghts and one angle measure.
We can use the Law of sines to relate angles and sides: the quotient between the sine of an angle and its opposite side length is constant for the three pair of angles and opposite sides of the triangle.
In this case we can write:
[tex]\begin{gathered} \frac{\sin20\degree}{100}=\frac{\sin P}{80} \\ \sin P=\frac{80}{100}\sin20\degree \\ \sin P\approx0.8\cdot0.342 \\ \sin P\approx0.274 \\ P\approx\arcsin(0.274) \\ P\approx15.9\degree \end{gathered}[/tex]As the two sides are approximately the same length (80 yd vs 100 yd), we can expect for the opposite angle to have similar measures.
Then, as one of the opposite angles is 20°, the other opposite angle (P) will have a measure that is approximately 20° too.
Answer: 2. Approximately 20 degrees
ACTIVITY 4. THINK THINK THINK! Given are congruent triangles, find the uknown values.
Answers
d) SZ = 5cm
e) f)
Explanations:According to the given diagram, triangle QSZ is similar to the triangle NKH. This shows that:
[tex]\begin{gathered} SZ=KH \\ NK=QS \\ KH=SZ \\ \end{gathered}[/tex]Similarly for the angles:
[tex]\begin{gathered} m\angle N=m\angle Q \\ m\angle K=m\angle S \\ m\angle H=m\angle Z \end{gathered}[/tex]d) Since SZ = KH and the measure of KH is 6cm, hence the measure of SZ will also be 5cm i.e SZ = 5cm
e) Similarly for the angles, we know that measure of angle K will be 87 degrees based on the similarity theorem.
f) To get the measure of the vertex angle Q, we know that the sum of an interior angle of a triangle is 180 degrees, hence;
[tex]\begin{gathered} m\angle Q+m\angle S+m\angle Z=180^0 \\ m\angle Q+87^0+68^0=180^0 \\ m\angle Q+155=180 \\ m\angle Q=180-155 \\ m\angle Q=25^0 \end{gathered}[/tex]
the graph below represents the dimensions of a rectangle. what type of variation do the adjacent side lengths exhibit? A. no variation B. combined variation C. inverse variation D. direct variation
Answers
SOLUTION:
The area of the rectangle is given by;
[tex]A=l\times b[/tex]For constant area, the length can be written in terms of the breadth as;
[tex]l=\frac{A}{b}[/tex]But this is clearly an inverse variation.
Therefore, the answer is Inverse Variation
hi i don't understand this but jay jt means range
Answers
Using the Triangle inequality which states: The sum of the lengths of any two sides of a triangle is greater than the third side.
So:
[tex]\begin{gathered} zTherefore, the range of the 3rd side is:[tex](0,17)[/tex]find three pointsthen plot them on thegraph.x-3y=6
Answers
Answer
Check Explanation.
Step-by-step explanation
The equation of the straight line is given, we are then told to obtain 3 points and plot it on the graph.
The equation of the straight line given is
x - 3y = 6
The equation of straight lines are usually best represented in the form
y = mx + c
So, we will put the given equation in that format.
x - 3y = 6
-3y = -x + 6
Multiply both sides by -1
3y = x - 6
Divide through by 3
(3y/3) = (x/3) - (6/3)
y = (x/3) - 2
y = 0.3333x - 2
So, we now find 3 points on the line in order to plot it on your graph.
In picking points while plotting graphs, it is easier to
- first pick the point where x = 0, calculate y
- Then pick the point where y = 0, calculate x,
- We can then pick one more arbitrary point and calculate the corresponding other coordinates there.
So, when x = 0,
y = 0.3333x - 2
y = (0.3333 × 0) - 3 = 0 - 2 = -2
when x = 0, y = -2.
First point is (0, -2)
when y = 0,
y = 0.3333x - 2
0 = 0.3333x - 2
0.3333x = 2
x = (2/0.3333) = 6
when y = 0, x = 6.
Second point is (6, 0)
Then for the third point, we arbitrarily pick when x = 3,
y = 0.3333x - 2
y = (0.3333 × 3) - 2 = 1 - 2 = -1
when x = 3, y = -1
Third point is (3, -1)
Hence, the three points that will help us plot the graph of the straight line are
(0, -2), (6, 0) and (3, -1)
Now, I'll need you to mark these points on the graph provided and join the points together to form a straight line as shown in the image I will attach now.
So, this is the graph of x - 3y = 6.
Hope this Helps!!!
Which of the following equations represents a line that is perpendicular toy = -2x+4 and passes through the point, (4,2)?O A. y= -1/2x+2O B. y= 1/2x+4O C. y= -2xO D. y= 1/2x
Answers
Given that
The equation is y = -2x + 4 and we have to find the line perpendicular to the given line and pass through the point (4, 2).
Explanation -
Since the two lines are parallel when the product of their slopes is -1.
[tex]\begin{gathered} Let\text{ the slope of given line is m}_1\text{ and slope of line to be found is m}_2. \\ Then,\text{ } \\ m_1\times m_2=-1 \end{gathered}[/tex]On comparing the given line with the general equation,
y = mx + c
we have m = slope = -2
[tex]\begin{gathered} So\text{ we have} \\ m_1=-2 \\ Then \\ -2\times m_2=-1 \\ m_2=\frac{1}{2} \end{gathered}[/tex]Now we have to find the line with a slope 1/2 and pass through the point (4, 2).
[tex]\begin{gathered} y-2=m_2(x-4) \\ y-2=\frac{1}{2}(x-4) \\ y-2=\frac{x}{2}-\frac{4}{2} \\ y-2=\frac{x}{2}-2 \\ y=\frac{x}{2}=\frac{1}{2}x \end{gathered}[/tex]So the required line is y = x/2 and the correct option is D.
Final answer -
Hence the final answer is y = x/2what is the mean, median, and mode?80.6, 60.8, 54.5, 61.4, 99.2, 71.1, 79.6, 79.8, 99.2,99.2
Answers
mean=78.54
median=79.7
mode=99.2
Explanation
Step1
mean
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set
Let
sum of the data
[tex]\begin{gathered} 80.6+60.8+54.5+61.4+99.2+71.1+79.6+79.8+99.2+99.2 \\ =785.4 \\ \end{gathered}[/tex]and
number of data=10
so
[tex]\operatorname{mean}=\frac{785.4}{10}=78.54[/tex]Step 2
to find the median,
1)Arrange your numbers in numerical order.
2)Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
[tex]\begin{gathered} 80.6,60.8,54.5,61.4,99.2,71.1,79.6,79.8,99.2,99.2 \\ 54.5,60.8,,61.4,71.1,79.6,79.8,80.6,99.2,99.2,99.2 \\ so,\operatorname{median}\text{ =79. 7} \end{gathered}[/tex]Step 3
The mode is the value that appears most frequently in a data set
then, check for the value that most frequently appear is
[tex]99.2(3\text{ times)}[/tex]I hope this helps you