Mia drew a map of a park. Mia’s map shows the endpoints of the walking paths at A(2, 2), B(2, 6), C(8, 6), and D(8, 2). There are 6 walking paths: AB, BC, CD, AD, AC, and BD.
1. Are walking paths AB and CD parallel? Explain.
2. Are walking paths AC and BD perpendicular? Explain.
3. Mia also drew path FG that goes through (12, 2) on her map and is parallel to path AC. Write an equation for path FG.
4. Mia also drew path MN that goes through (10, 10) on her map and is perpendicular to path BD. Write an equation for path MN.
Answers
Answer:
1. yes, because they both have the same undefinite slopes. They are both vertical lines.
2. no, because their slopes are not negative reciprocals.
3. [tex]y=\frac{2}{3}x-6[/tex]
4. [tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
In order to solve this problem, we can start by drawing a diagram of the paths Mia drew. (See attached picture the red lines are the original paths).
1. In order to determine if the paths are parallel or not, we need to first know what the slope of the paths is. The slope of the paths can be found by using the equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
So, for path AB we get:
[tex]m_{AB}=\frac{6-2}{2-2}[/tex]
which yields:
[tex]m_{AB}=\frac{4}{0}[/tex]
Now, since we have a denominator of 0 in that friction, this means that the division is not defined for the real number, therefore, we are dealing with a vertical line.
for the path CD we get:
[tex]m_{CD}=\frac{2-6}{8-8}[/tex]
which yields:
[tex]m_{AB}=-\frac{4}{0}[/tex]
Now, since we have a denominator of 0 in that friction, this means that the division is not defined for the real number, therefore, we are dealing with a vertical line.
Therefore, since both slopes are the same, this means that the two lines will be parallel.
2. The procedure is the same as in the previous problem:
[tex]m_{AC}=\frac{6-2}{8-2}[/tex]
which yields:
[tex]m_{AC}=\frac{2}{3}[/tex]
for the path BD we get:
[tex]m_{BD}=\frac{2-6}{8-2}[/tex]
which yields:
[tex]m_{BD}=-\frac{2}{3}[/tex]
This two fractions are just opposite in sign. But for the lines to be perpendicular, their slopes should be negative reciprocal. In this case they are not reciprocal, so the lines are not perpendicular to each other.
3. For part 3, we know that for two lines to be parallel, their slopes must be the same. We already found the slope of AC to be:
[tex]m_{AC}=\frac{2}{3}[/tex]
we also know the line must go through the point (12,2), so we can use the point-slope form of the equation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
so we can go ahead and substitute the pertinent data:
[tex]y-2=\frac{2}{3}(x-12)[/tex]
So now we can solve it for y so it gets the slope-intercept form, which is:
[tex]y=\frac{2}{3}x-6[/tex]
4. In this part of the problem, we will need to follow a similar process, but this time, we need the slope to be negative reciprocal to slope of the line BD.
[tex]m_{BD}=-\frac{2}{3}[/tex]
so:
[tex]m_{MN}=\frac{3}{2}[/tex]
so now we can build our equation with the point-intercept form and the given point so we get:
[tex]y-10=\frac{3}{2}(x-10)[/tex]
So now we can solve it for y so it gets the slope-intercept form, which is:
[tex]y=\frac{3}{2}x-5[/tex]
Related Questions
9. Antonio loves to go to the movies. He goes both at night and during the day. The cost of a daytime movie(x) is $6.00. The
cost of an evening show is $8.00(X). If Antonio went to see a total of 12 movies and spent $86.00, how many night movies
did he attend? Identify a system to represent this scenario and use desmos to graph the system and find the solution
Answers
SOMEONE DO NUMBER 1 AND 2 FOR ME, ILL GIVE BRAINLIEST
Answers
Answer:
1. The second number line, the third number line, the first number line.
2.
[tex]a) \: 1 \frac{7}{8} > \frac{7}{4} [/tex]
[tex]b) \: \frac{21}{5} = 4 \frac{1}{5} [/tex]
[tex]c) \frac{13}{4} < 3 \frac{5}{6} [/tex]
find the scale factor between each pair of similar shapes
Answers
Answer:
Step-by-step explanation:
For the pairs of sides to be proportional to each other, they must have the same scale factor. In other words, similar figures have congruent angles and sides with the same scale factor. A scale factor of 2 means that each side of the larger figure is twice as long as its corresponding side is in the smaller figure.
orginal price $1.29 Sold for $3.00
Answers
Answer:
$1.71 is the difference
Step-by-step explanation:
3.00 - 1.29 = 1.71
Answer:
Suplly and demand buddy boy
Step-by-step explanation:
2. A ratio that relates two quantities with different units of measure is
a
Answers
Answer: A rate
Step-by-step explanation:
A rate is a ratio that compares two different quantities with different units of measure
Determine which quadrant each point will be located (-8,2)
Answers
Answer:
The point (-8, 2) is in Quadrant 2.
Step-by-step explanation:
Quadrant 1: (x, y)
Quadrant 2: (-x, y)
Quadrant 3: (-x, -y)
Quadrant 4: (x, -y)
Answer:
The point, -8,2, will be located in quadrant II.
A historian took a count of the number of people in a Gold Rush town for six years in the 1870's find a quadratic function that models the data as a function of x the number of years since 1870. Use the model to estimate the number of people in the town in 1878
Answers
Solution :
The model is :
Year 1870 1871 1872 1873 1874 1875 1876
Population 365 384 393 392 381 360 329
It is given that a historian counted the number of people in the Gold Rush town for a 6 years staring from 1870.
Therefore the quadratic function which models a data as a function of the number of years from 1870 i.e. x is given by
[tex]$P(x) = -5x^2+24x+365$[/tex]
And the number of people present the town of Gold Rush in the year 1878 can be found by using the model is 237.
Answer:
Step-by-step explanation:
I think it's d, I hope this helps and If I'm wrong please correct me.
I need help with these 2 questions
Answers
Answer:
1. a
2. c
Step-by-step explanation:
help! if you do this and my other queston 53 points
101 202 505 1010 . . . ? . . .10100 50500
2 . . ? . . . . ? . . .10 . . .50 . . 100 . . . . . ? . .
what are the ?'s
Answers
Answer:
5050, 4, 10, 500
Step-by-step explanation:
Seven friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
Answers
Answer:
Step-by-step explanation:
if 7 friends share 8 cups of lemonade
each will receive 7/8 of the lemonade
Each friend will receive 7/8 of the lemonade
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
From the given question, we are informed that Seven friends are sharing 8 cups of lemonade and that they share the lemonade equally.
The number of cups that each friend gets can be calculated by dividing the number of cups of lemonade by the number of friends.
This will be:
= 7/8
We can conclude that Each friend will receive 7/8 of the lemonade
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ5
The formula for the volume of a sphere is V space equals space 4 over 3 Ïr cubed. Find the radius to the nearest hundredth of a sphere with each volume. 20 ft 3 i really need to know the answer
Answers
Answer:
r = 1.68 ft
Step-by-step explanation:
Volume of a sphere, V = 4/3πr³
V = 20 ft³
π = 3.14
r = ?
V = 4/3πr³
20 = 4/3 × 3.14 × r³
20 = (4×3.14×r³)/3
Cross product
20 × 3 = 4 × 3.14 × r³
60 = 12.56r³
r³ = 60/12.56
= 4.7771
r = 3√4.7771
= 1.6842
Approximately
r = 1.68 ft to the nearest hundredth
solve the equation x2-4x+6=0 by completing the square
Answers
Answer:
X= i√2
Step-by-step explanation:
x2-4x+6=0
We add all the numbers together, and all the variables
x^2-4x+6=0
a = 1; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·1·6
Δ = -8
Delta is less than zero, so there is no solution for the equation
What is the simplified form of
of (-7xº+5x²-x+6)-(-8x2 + x +3)?
ОА.
-x + 4x2 - x+3
OBX + 4x² - x+3
ocx - 4x² – 2-3
D. -15x + 6x? - X+9
Please I need help immediately
Answers
Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.
Answer:
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)[/tex]
solving the expression
[tex]=-7x^0+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]
apply the rule: [tex]a^0=1,\:a\ne \:0[/tex]
[tex]=-7+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]
[tex]=-7+5x^2-x+6+8x^2-x-3[/tex]
simplify
[tex]=13x^2-2x-4[/tex]
Therefore, the simplified form is:
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]
Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.
Simplify the following surd expressions
a)
[tex]6 \sqrt{2} - 5 \sqrt{2} [/tex]
b)
[tex] \sqrt 11 + 3 \sqrt{11} [/tex]
Answers
Answer:
A) [tex]\sqrt{2}[/tex]
B) [tex]4\sqrt{11}[/tex]
Step-by-step explanation:
A) You can add these expression because they contain the same square root:
[tex]6\sqrt{2} - 5\sqrt{2} = (6 - 5)\sqrt{2} =\sqrt{2}[/tex]
B) Same as above:
[tex]\sqrt{11} + 3\sqrt{11} = (1 + 3)\sqrt{11} = 4\sqrt{11}[/tex]
Answer:
[tex]A) \: 6 \sqrt{2} - 5 \sqrt{2} = (6 - 5) \sqrt{2} = \sqrt{2} \\ [/tex]
√2 is the right answer.[tex]B) \sqrt{11} + 3 \sqrt{11} = (1 + 3) \sqrt{11} = 4 \sqrt{11} [/tex]
4√11 is the right answer.please someone help me with this question
4x-3=2x+7
Answers
more words because it wont send ;-;
Whoever answers gets brainly
Answers
Answer:
The function y = 5 [tex](.98)^{x}[/tex] represents exponential decay
The percentage rate of change is 2%
Step-by-step explanation:
The formula of the exponential growth is y = a [tex](1+r)^{x}[/tex], where
a is the initial valuer is the rate of increase in decimal ⇒ (1 + r) > 1The formula of the exponential decay is y = a [tex](1-r)^{x}[/tex], where
a is the initial valuer is the rate of decrease in decimal ⇒ (1 - r) < 1Let us solve the question.
∵ y = 5 [tex](.98)^{x}[/tex]
→ Compare it with the forms above
∴ a = 5
∵ The rate of change is .98
∵ .98 < 1
→ That means the rate of change is decreasing
∴ The function y = 5 [tex](.98)^{x}[/tex] represents exponential decay
→ From the 2nd form above
∵ (1 - r ) = .98
→ Subtract 1 from both sides
∴ 1 - 1 - r = .98 - 1
∴ - r = - .02
→ Divide both sides by -1
∴ r = .02
→ Multiply it by 100% to change it to a percentage
∵ .02 × 100% = 2%
∴ r = 2%
∴ The percentage rate of change is 2%
2x+-2y=14
x+4y=13
Elimination Method to Solve Linear Equations
Answers
Answer:
(41/5, 6/5)
Step-by-step explanation:
2x+-2y=14
x+4y=13
You can multiply the first equation by 2 so you can eliminate the y:
2(2x+-2y=14)
4x+-4y=28
Then you can set up both equations to be added together:
4x+-4y=28
+ x+4y=13
5x=41
x=41/5
Then you can substitute 41/5 for x in the original equation:
x+4y=13
41/5+4y=13
5(41/5+4y)=5(13)
41+20y=65
20y=24
y=24/20
y=6/5
Check:
2x+-2y=14
2(41/5)+-2(6/5)=14
82/5+-12/5=14
70/5=14
14=14
I need help with this
Answers
Adam can paint 38 feet of fence per hour. How many yards of fence can he paint per hour? 12 yards per hour 456 yards per hour 114 yards per hour 3 yards per hour
Answers
Answer:
12.66 yards/hour
Step-by-step explanation:
38 feet/3 feet per yard=12.66 yards
Answer:
12 2/3 is the answer...
Step-by-step explanation:
Which is the graph of g(x) = (two-thirds) Superscript x – 2?
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
Answers
Answer:
-2 , 0.25
-1 , -0.5
0 , -1
1 , -1.333
2 , -1.556
Step-by-step explanation:
By checking the y-intercept, we will see that the correct option is the first graph.
How to find the graph of the function?Here we have the function:
g(x) = (2/3)^(x - 2).
To see which one is the correct graph, first we should evaluate it in x = 0, we will get:
g(0) = (2/3)^(-2) = (3/2)^2 = 9/4 = 2.25
The only graph that intercepts the y-axis at y = 2.25 is the first one, so that is the correct option.
If you want to learn more about exponential functions, you can read:
https://brainly.com/question/11464095
Can someone help me with this ASAP
Answers
9514 1404 393
Answer:
x = 45
Step-by-step explanation:
If we assume that ray GJ lies between rays GF and GH, then the angle sum theorem tells us ...
∠FGH = ∠FGJ +∠JGH
140° = 95° +x°
45° = x° . . . . . . subtract 95° from both sides
x = 45
_____
Alternate solution
There is an alternate solution if ray GF lies between ray GH and ray GJ.
∠JGH = ∠FGJ +∠FGH
x° = 95° +140°
x° = 235°
x = 235
Without some additional information, we cannot tell which assumption we should make about the geometry.
1.
What type of polynomial is this?
- 3x3 - x2 - 10x + 12
O a) Monomial
c) Trinomial
O b) Binomial
d) Polynomial
Answers
Answer:
monomial
Step-by-step explanation:
50 points
Use the vertical line test to determine if the graphed relation is a function.
Yes. One output results in one input.
No. At least one output results in two inputs.
No. At least one input results in two outputs.
Yes. One input results in one output.
Answers
Answer:
The answer is C. "No. At least one input results in two outputs."
Step-by-step explanation:
Please help please please ASAP please please
Answers
Step-by-step explanation:
ac is the answer
.............
The sum of the measures of angle A and angle B is 90 degrees.
The measure of angle A is (5x + 10)
The measure of angle B is 3x degrees
What is the value of x?
Answers
Answer:
x=10
Step-by-step explanation:
5x+10+3x=90
8x+10=90
8x=80
x=10
:)
HELP PLEASE ASAPPPPPPPP
Answers
Answer:
c
Step-by-step explanation:
2+3x-18
Answer: the last one
Step-by-step explanation:
HELP PLS <3 ASAP
KSKXNXNNmxmx
Answers
Answer:
sbshsbsbhshsndjdudbdjdjdjdb
Step-by-step explanation:
shsbshshudhdbdudjdjdsbsbsb
Given m|n, find the value of x
Answers
Answer:
x = 17
Step-by-step explanation:
x and 163 are same- side interior angles and are supplementary, sum to 180°
x + 163 = 180 ( subtract 163 from both sides )
x = 17
x
Solve ONE of the following two equations. YOU decide
which one you want to solve for this Cool Down. Show
all of your steps in the line paper provided. YOU GOT
THIS! Don't forget to check your answer.
Equation #1: 5(a + 1) = 2a - 3
OR
Equation #2: 10 - 2b = 16
Answers
Answer:
Equation 1 a=-8/3
Equation 2 b= -3
Step-by-step explanation:
Equation 1
5a+5=2a-3
5a-2a=-3-5
3a=-8
a=-8/3
Equation 2
-2b=16-10
-2b=6
b=6/-2
b=-3
In a class of 25 students, 80% attended a field trip. How many students went on the field trip? 20 15 05 8
Answers
Answer:
McDonald'sssssssssssssss
20 students went on a field trip and 5 did not.
