Answers
(i) AB and DC are parallel, so the lines containing these sides have the same slope.
The line containing AB has slope (2 - (-1))/(10 - 4) = 3/6 = 1/2.
Use the point-slope formula to find the equation of the line containing CD:
[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2\implies\boxed{2y=x+4}[/tex]
AP is perpendicular to both AB and CD, and perpendicular lines have slopes that are negative reciprocals of one another. This means the line containing AP has slope -1/(1/2) = -2. Using the point-slope formula again, the equation of the line containing AP is
[tex]y-(-1) = -2(x-4)\implies \boxed{y=-2x+7}[/tex]
(ii) D lies on the x axis, so its y-coordinate is 0. Find the x-coordinate by plugging y = 0 into the equation for the line containing CD:
[tex]2\cdot0=x+4\implies x=-4[/tex]
So D is the point (-4, 0).
P is the intersection of the lines containing CD and AP, so set them equal and solve for x and y :
[tex]y=\dfrac x2+2\text{ and }y=-2x+7[/tex]
[tex]\implies\dfrac x2+2=-2x+7\implies 5x=10\implies x=2[/tex]
[tex]\implies y=-2\cdot2+7\implies y=3[/tex]
So P is the point (2, 3).
(iii) For ASBC to be a parallelogram, we need to find the coordinates of S such that the line containing AS is parallel to the line containing BC, and the line containing SC is parallel to the line containing AB.
BC has slope (8 - 2)/(12 - 10) = 6/2 = 3. Then the line containing AS has equation
[tex]y-(-1)=3(x-4)\implies y=3x-13[/tex]
We already know AB has slope 1/2. Then the line containing SC has equation
[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2[/tex]
S is the intersection of these two lines:
[tex]3x-13=\dfrac x2+2\implies\dfrac{5x}2=15\implies5x=30\implies x=6[/tex]
[tex]\implies y=3\cdot6-13\implies y=5[/tex]
So S is the point (6, 5), and *not* (2, -7) as the answer key suggests. In fact, (2, -7) is located lower than the point A and slightly to the left; if you draw that point and connect it to the other three, there's no way to get a parallelogram.
(iv) Find the lengths of AB, CD, and AP. Then the area is (AB + CD)*AP/2.
[tex]AB=\sqrt{(4-10)^2+(-1-2)^2}=3\sqrt5[/tex]
[tex]CD=\sqrt{(12-(-4))^2+(8-0)^2}=8\sqrt5[/tex]
[tex]AP=\sqrt{(4-2)^2+(-1-3)^2}=2\sqrt5[/tex]
so the area is
[tex]\dfrac{(3\sqrt5+8\sqrt5)2\sqrt5}2=\boxed{55}[/tex]
Related Questions
Consider the system of equations.
y = 3x + 2
y=-fx-4
Explain why these particular equations can be graphed
immediately
Answers
Answer:
Because these are in slope-intercept form which is much easier because y=mx+b means that m=the slope, and b=y intercept so all your information is laid out in front of you.
Step-by-step explanation:
10. The sum of four consecutive integers is at least 18. What's the smallest consecutive integer to make this statement true?
O A.3
O B.4
O C.5
O D.8
Answers
Answer:
A. 3
Step-by-step explanation:
Let the integers be
x
(x+1)
(x+2)
(x+3)
Sum the integers
We have,
x+(x+1)+(x+2)+(x+3)=18
x+x+1+x+2+x+3=18
4x+6=18
Subtract 6 from both sides
4x-6=18-6
4x=12
Divide both sides by 4
4x/4=12/4
x=3
The smallest integer which is x is equal to 3
Check:
3+4+5+6=18
Find the range of the graphed function.
Answers
The range of the curve is from -6 to 10, i.e. -6 ≤ y ≤ 10.
Given is a graph of a curve having endpoints at (-10, -6) and (0, 10), we need to find its range.
To find the range of a curve, we need to determine the set of all possible y-values that the curve can attain.
In this case, we have the endpoints of the curve as (-10, -6) and (0, 10).
The range of the curve is the set of all possible y-values. To find it, we need to identify the minimum and maximum y-values.
The minimum y-value can be found at the lowest point of the curve. From the given endpoints, we can see that the lowest point lies at (-10, -6).
The maximum y-value can be found at the highest point of the curve. From the given endpoints, we can see that the highest point lies at (0, 10).
Therefore, the range of the curve is from -6 to 10, inclusive: [-6, 10].
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How many 5-digit numbers can be formed using only odd digits?
Answers
Answer:
5^5
Step-by-step explanation:
What is the name of the shape graphed by the function r = 1 + sine ?
A. Cardioid
B. Circle
C. Limaçon
D. Line
Answers
PLEASE HELP!!
Which of the following statements is true for the figures shown?
B
O A A ABC has been dilated using O as the center,
B. A ABC has been reflected using C as the center.
c. A ABC has been dilated using C as the center.
OD. A ABC has been reflected using as the center.
Answers
What is the area of the obtuse triangle below?
다
Answers
B. 49.5 sq. units
Explanation
An area of a triangle is
B • H / 2
Where b = base and h = height.
Substitute base = 11 and h = 9
9 • 11 / 2 = 49.5
<~>\_/<~> Ho_odini <~>\_/<~>
Use the substitution method to solve the following system of equations: 3x + 5y = 3 x + 2y = 0 (1 point) (1, 1) (6, −3) (6, 1) (1, −3)
Answers
Step-by-step explanation:
Given.
[tex]3x+5y=3[/tex]
[tex]x+2y=0[/tex]
Take the second equation and subtract 2y to both sides.
[tex](x+2y)-2y=0-2y[/tex]
[tex]x=-2y[/tex]
Substitute x into the first equation and simplify.
[tex]3x+5y=3[/tex]
[tex]3(-2y)+5y=3[/tex]
[tex]-6y+5y=3[/tex]
[tex]-y=3[/tex]
Invert.
[tex]y=-3[/tex]
Substitute Y into your second equation.
[tex]x+2y=0[/tex]
[tex]x+2(-3)=0[/tex]
[tex]x-6=0[/tex]
Add -6 to both sides.
[tex](x-6)+6=0+6[/tex]
[tex]x=6[/tex]
Answer:
(6, -3)
Answer:
(6,-3)
Step-by-step explanation:
Got it right on the test
Hope this helps :)
Tom counted the number of cards in his collection for 10 weeks. By week 5, he had collected 12 cards. How many cards had he collected by week 9? 5 18 4 20 Tom counted the number of cards in his collection for 10 weeks. By week 5, he had collected 12 cards. How many cards had he collected by week 9? 5 18 4 20 Graph showing how many cards were collected each week. Vertical axis labeled Cards collected. Coordinate pairs plotted at 1,4, 2,6, 3,8, 4,9, 5,12, 6,13, 7,14, 8,15, 9,18, 10,20.
Answers
Answer:
20
Step-by-step explanation:
12/5 means roughly 2 cards per week
In 4 weeks he would get 8 additional cards
12+8=20
Hope this help!
The mad scientist need one third of the eyeball how many eyeball is that
Answers
Answer:
.33 as a decimal or 33%
Step-by-step explanation:
Divide 1/3 and get .33 as your decimal. To convert to a percentage multiply your decimal by 100. (.33 x 100 = 33 )
Answer:
69
Step-by-step explanation:
the graph of y=f(x) is shown on the grid
Answers
Answer:
look below
Step-by-step explanation:
The equation of graph g(x) = f(-x) as it has been rotated along y-axis and the maximum coordinates of g(x) is (-3, 4).
What is a function?A function can be thought of as output for the given set of inputs. The output is called the dependent variable and the inputs are called the independent variable.
We know when we rotate a function along the y-axis sign of x changes.
Given a function y = f(x) after rotation along y-axis it becomes y = f(-x) = g(x)
and if the given function is odd f(-x) becomes -f(x).
Also given that the maximum point of f(x) = (3, 4).
∴ Function g(x) will have maximum at coordinates (-3, 4).
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Find the inequality represented by the graph?
Answers
Answer:
y > -2/3x + 3
Step-by-step explanation:
Well lets first start with the beginning and look at its features.
Features
- Dashed line
- Shaded up
- negative slope
- y intercept at 3
____________________________________________________________
So if the line is dashed with the shade going up that means the inequality starts like this,
y >
We can tell that the y intercept is at 3 because that the point the line touches the y axis.
So we got y > 3,
To find slope we use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex],
So we can use points (0,3) and (3,1).
1 is y2 and 3 is y1 so 1 - 3 = -2
3 - 0 = 3
Slope: -2/3x
Thus,
the inequality is y > -2/3x + 3.
Hope this helps :)
The inequality [tex]y > -\frac{2}{3}\cdot x + 3[/tex] is represented by the graph.
According to the figure, we have an inequation of the form [tex]y > f(x)[/tex], where [tex]f(x)[/tex] is a linear function.
The linear function can be found by using the point-slope formula:
[tex]y-y_{1} = \left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\cdot (x-x_{1})[/tex] (1)
If we know that [tex](x_{1}, y_{1}) = (0, 3)[/tex] and [tex](x_{2}, y_{2}) = (3, 1)[/tex], then the linear function is:
[tex]y -3 = \left(\frac{1-3}{3-0} \right)\cdot x[/tex]
[tex]y = -\frac{2}{3}\cdot x+3[/tex] (1b)
The inequality [tex]y > -\frac{2}{3}\cdot x + 3[/tex] is represented by the graph.
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Marlene brought a can of polyurethane varnish that was stored at 40°F into her shop, where the
temperature was 74°F. After 2 hours, the temperature of the varnish was 58°F. If the varnish must be
68°F for best results, then how much longer must Marlene wait until she uses the varnish?
Please show explanation:(
Answers
Answer:
1 hour and 6 minutes
Step-by-step explanation:
A temperature difference of 58-40 = 18°F was obtained in 2 hoursA temperature difference of 68-40 = 28°F will be obtained in x hoursThe next proportion must be satisfied:
18 °F / 28 °F = 2 hours / x hours
x = 2*28/18
x = 3.1 hours in total
Given that she has already waited 2 hours, she must wait 3.1 - 2 = 1.1 extra hours. 1 hour is equivalent to 60 minutes, then 0.1 hours is equivalent to 0.1*60 = 6 minutes.
Honeydew lemons sell in a market place for $24.95 per box. One box contains 9 melons. How much would you have to pay for 17 melons?
Answers
Answer:
47.13 for 17 melons
Step-by-step explanation:
We can use a ratio to solve
24.95 x dollars
---------------- = ----------------
9 melons 17 melons
Using cross products
24.95 * 17 = 9x
Divide by 9
24.95 * 17/9 = x
47.127777777 = x
Rounding to the nearest cent
47.13 for 17 melons
Answer:
$47.12
Step-by-step explanation:
We know that 1 box has 9 lemons and each box is $24.95. Therefore, 1 lemon costs 24.95/9 dollars. That leads us to know that 17 lemons cost (24.95/9 * 17). Once we plug that into the calculator and round to the nearest hundreth place, we get $47.12.
Gemma is creating a histogram based on the table below. Salary Range Number of People 0 - $19,999 40 $20,000 - $39,999 30 $40,000 - $59,999 35 Which scale can she use for the vertical axis such that the difference in the heights of the bars is maximized? 0–50 0–40 10–50 25–40
Answers
Answer:
Hello!
~~~~~~~~~~~~~~~~~~~~~
Your answer would be (D) 25–40
Step-by-step explanation: The largest amount od people is 40 the lowest amount is 35 so to maximize the bars you would want the smallest range.
Thus, (D) is the correct answer.
Answer:
Its D
Step-by-step explanation:
for all the ppl who don't care how they got it
Help pleaseeeeeeeeeeeeee and write it descriptively
Answers
Answer:
14) [tex]\frac{1}{2} n-1[/tex] (half of n is [tex]\frac{1}{2} n[/tex] and subtract that with 1)
15) 3o+4 ( multipy o with 3, it becomes "3o" and add that with "4")
16) 5p-2 (same concept as No.15)
17) 7+r ( add 7 with "r")
18) s+7 (same concept with No.18)
19) t-10 (subtract 10 from "t")
20) 10-u ( subtract "u" from 10)
21) 2v ( multiply 2 with v)
22) 2w (same concept as No.21)
23) [tex]\frac{x}{5}[/tex] (divide x with 5 and show the result in fractions)
24) [tex]\frac{5}{y}[/tex] ( divide 5 with y and show the result in fractions)
Tip : Alphabets and numbers never combine unless you multiply them with it (eg. 3*x = 3x) but ( 3+x stays like that ).
What is the value of f(6) in the function below?
f(x) = 2x
HELP ASAP PLS
Answers
Answer:
f(6) = 64
Step-by-step explanation:
f(x) = 2^x
Let x = 6
f(6) = 2^6
= 2*2*2*2*2*2
= 64
Answer:
B. 64
Step-by-step explanation:
[tex]f(x)=2^x[/tex]
Plug x as 6 and solve.
[tex]f(6)=2^{(6)}[/tex]
[tex]f(6)=2^6[/tex]
[tex]f(6)=2 \times 2 \times 2 \times 2 \times 2 \times 2[/tex]
[tex]f(6)=64[/tex]
The first four terms of a sequence are: 1/6 4/7 9/8 16/9
Find the nth term of this sequence.
Answers
Answer:
n^2/(n + 5)
Step-by-step explanation:
The numerators are 1^2, 2^2, 3^2, 4^2, etc.
The denominators are 6, 7, 8, 9, etc.
The nth numerator is n^2.
The nth denominator is n + 5.
Answer: n^2/(n + 5)
A new brand of gym shoe claims to add up to 2 inches to an athlete vertical leap. Design an experiment to test this claim. State the objective of the experiment
Answers
Answer:
I'd think the first one would be correct. To determine whether or not athletes have an increase in vertical leap when wearing the shoes.
I'm not totally sure but this answer just seems the most correct. It would prove if the manufacturers clam is valid. You would have to other brand and models of shoes. You would also have to test the same kind of shoes ie, gym shoe vrs gym shoe instead of gym shoe vrs flip flop.
You would also have to use the different shoe on the same test group of users/athletes to keep a constant.
Hope I help.
Please help me I would appreciate it
Answers
Answer:
m<1= 50 degrees
m<2= 130 degrees
m<3= 50 degrees
m<4= 130 degrees
m<5= 40 degrees
m<6= 30 degrees
Step-by-step explanation:
All of the angles of triangles equal to 180 degrees, so you can solve all of the angles based on that info :)
pls hurry the answer is not 36.......Given a * b=ba−ba+ab, find (2*3)×(3*2).
Answers
Answer:
36
Step-by-step explanation:
In the above question, we have been given a rule to follow
Given a * b = ba−ba+ab
We are to find (2*3)×(3*2)
Let simplify each bracket first
a * b = ba−ba+ab
2*3, a = 2, b = 3
2*3 = 3×2 - 3×2 + 2×3
= 6 - 6 + 6
= 6
a * b = ba−ba+ab
3*2, a = 3, b = 2
3*2 = 2×3 - 2×3 + 3×2
= 6 - 6 + 6
= 6
(2*3)×(3*2)
= 6 × 6
= 36
The answer is 36
Solve this system using the substitution method: y = 6x – 5; y = (2/3)x + 1
Answers
Answer:
x = 1.125
Step-by-step explanation:
6x – 5 = (2/3)x + 1
6x - (2/3)x = 1 + 5
(16/3)x = 6
x = 9/8
x = 1.125
12/ y + 8 = 4/9 Thats the question. Im dyin for help. :)
Answers
Answer:
-1 10/17
Step-by-step explanation:
Answer:
y = 1 10/17
Step-by-step explanation:
The LCD is 9y. Multiply all three terms by 9y:
(9y)(12) (9y)(4)
----------- + 8(9y) = -----------
y 9
This reduces to 108 + 72y = 4y, or 108 = -68y
Dividing both sides by 68, we get y = 1 10/17
-125>-135 divide each side by -5 what is the resulting true inequality
Answers
Answer: 25<27
Step-by-step explanation:
-125/-5=25
-135/-5=27
25<27
Answer:
[tex]\boxed{25<27}[/tex]
Step-by-step explanation:
[tex]-125 > -135[/tex]
Dividing both sides by -5
=> [tex]\frac{-125}{-5} < \frac{-135}{-5}[/tex]
=> [tex]25 < 27[/tex]
Question 6 Essay Worth 5 points)
(05.02) In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle.
40
SO
Write and solve an equation to determine the measure of angle y.
I
Answers
The value of y will be 90°. The sum of angle of the two right angle is 180°. The property of the adjacent angle is used.
How can we find the solution to an equation?We do same operations on both the sides so that equality of both expressions doesn't get disturbed.
Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are an infinite number of solutions.
The angles subtended by a circle is 360°, then;
The equation is found as;
[tex]\rm 40^0+50^0+x+y+z=360^0 \\\\ x+y+z=270^0[/tex]
The sum of angle of the two right angle is 180°;
x°+40°+50°=180°
x=90°
y+50°+40°=180°
Y=90°
Hence, the value of y will be 90°.
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Evelyn flips three coins simultaneously. The theoretical probability that only two of the coins will turn up heads 3/8. If Evelyn flips the three coins simultaneously 200 times, how many times can she expect only two heads to turn up
Answers
Answer:
75
Step-by-step explanation:
200 ÷ 8 = 25
25 x 3 = 75
The number of times 2 coins will turn heads up is 75, the correct option is D.
What is Probability?Probability is the measure of the likeliness of an event to happen.
The probability has a range from 0 to 1, 0 denotes uncertainty and 1 indicates certainty.
When 3 coins are flipped, there is two probabilities,
The probability of getting a head or a tail is 1/2.
The probability that there will be 2 coins that will turn up heads is 3/8
Probability is defined as the ratio of favorable outcomes to total outcomes.
If Evelyn flips the three coins simultaneously 200 times, the number of times she can expect only two heads to turn up is given by,
= (3/8) * 200
= 75
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Given that P(B|A)=0.88 and P(A)=0.46, what is P(B AND A)? Round to three decimal places.
Answers
===============================================
Work Shown:
The notation P(B|A) has a vertical line separating the B and A
Given values
P(B|A) = 0.88P(A) = 0.46----------
P(B|A) = P(B and A)/P(A) ... conditional probability formula
P(B and A) = P(B|A)*P(A) ... solve for P(B and A)
P(B and A) = 0.88*0.46 ... plug in given values
P(B and A) = 0.4048
P(B and A) = 0.405 .... rounding to three decimal places
This is the same as P(A and B).
write the equation of a line that is perpendicular to x=3 and that passes through the point (0 -4) will mark brainliest asap!!!
Answers
Answer:
y = -4
Step-by-step explanation:
x = 3 is a vertical line.
The perpendicular line passes through (0, -4) (x, y)
y = -4
The line is perpendicular, so the line should be also horizontal.
Answer:
y = -4
Step-by-step explanation:
The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).
Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.
What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5)?
y=34x−92
y=34x+72
y=34x−74
y=34x+174
Answers
Answer:
y = 3/4x + 17/4
Step-by-step explanation:
Step 1: Find slope m
m = (5 - 2)/(1 + 3)
m = 3/4
y = 3/4x + b
Step 2: Find b
5 = 3/4(1) + b
5 = 3/4 + b
b = 17/4
Step 3: Rewrite equation
y = 3/4x + 17/4
Answer:
y = 3/4x + 17/9
Step-by-step explanation:
Find the slope:
5 - 2/ 1 - (- 3)
3/ 1 + 4
3/4
Find the y-intercept:
2 = 3/4(-3) + b
2 = -9/4 + b
17/4 = b
Put it in an equation:
y = 3/4x + 17/9
I have some red , blue, and green marbles. I have 5 less blue marbles than 4 times the red marbles. I have 3 more green marbles than 2 times the number of red marbles. All together I have 61 marbles. How many red , blue, and green marbles do I have? PLEASE ANSWER! I"LL GIVE CORRECT ANSWER AS THE BRAINLIEST ANSWER! I NEED HELP
Answers
Answer:
You have 9 red marbles, 21 green marbles, and 31 blue marbles.
Step-by-step explanation:
Let r equal the number of red marbles
Let b equal the number of blue marbles
Let g equal the number of green marbles.
"I have 5 less blue marbles than 4 times the red marbles."
4r-5=b
"I have 3 more green marbles than 2 times the number of red marbles."
2r+3=g
" All together I have 61 marbles."
r+b+g=61
Substitute the b and g for 4r-5 and 2r+3
r+(4r-5)+(2r+3)=61
5r-5+2r+3=61
5r+2r-5+3=61
7r-2=61
7r=63
r=9
2r+3=g
2(9)+3=g
21=g
4r-5=b
4(9)-5=b
36-5=b
b=31
You have 9 red marbles, 21 green marbles, and 31 blue marbles.
Let me know if this helps :)
Answer:
There are 9 red, 21 greens and 31 blues
Step-by-step explanation:
Set up equations
Let
R=# red
G=# green
B=# blue
I have 5 less blue marbles than 4 times the red marbles.
B=4R-5 .............(1)
I have 3 more green marbles than 2 times the number of red marbles.
G=2R+3..............(2)
All together I have 61 marbles.
R+G+B=61 ..................(3)
Solution:
substitute (1) & (2) in (3)
R + 2R+3 + 4R-5 = 61
Simplify
7R = 61+2 = 63
R = 63/7 = 9 ..........(4)
Substitute (4) in (1)
B = 4R-5 = 4(9) - 5 = 36-5 = 31
Substitute (4) in (2)
G = 2R+3 = 2(9) + 3 = 18+3 = 21