Hannah is experimenting with a new drawing program on her computer. She created quadrilateral MATH with coordinates M(1, 2). A(-5, 3), T(- 6,-3), and H(0,- 4). Hannah believes that she has created a square. Prove that Hannah is correct.
Answers
The square MATH has equal side lengths MA, TH, AT and HM
Hanna's claim is correct because
The side lengths are equal.Opposite sides have the same slopeThe slopes of adjacent sides are opposite reciprocalsHow to prove that Hannah is correct?The coordinate points are given as:
M(1, 2), A(-5, 3), T(-6,-3), and H(0,- 4).
Calculate the side lengths of the square using the following distance formula
d = √[(x2 - x1)^2 + (y2 - y1)^2]
So, we have:
MA = √[(1 + 5)^2 + (2 - 3)^2] = √37
AT = √[(-5 + 6)^2 + (3 + 3)^2] = √37
TH = √[(-6 + 0)^2 + (-3 + 4)^2] = √37
HM = √[(0 - 1)^2 + (-4 - 2)^2] = √37
The side lengths are equal.
Next, we calculate the slopes using:
m =(y2 - y1)/(x2 - x1)
So, we have:
MA = (2-3)/(1+5) = -1/6
AT = (3+3)/(-5+6) = 6
TH = (-3+4)/(-6+0) = -1/6
HM = (-4-2)/(0-1) = 6
See that opposite sides have the same slope
i.e MA = TH and AT = HM
And adjacent sides have their slopes to be opposite reciprocals
i.e. MA = -1/AT and TH = -1/HM
The calculated distances and slopes implies that Hanna's claim is correct
Read more about quadrilaterals at:
https://brainly.com/question/3050890
Related Questions
Lucia is using energy at a rate of 210 kilocalories (kcal) per hour (h) ice skating. At what rate is Lucia using energy in calories per minute ( / min ) ?
Answers
Answer:
3500cal/min
Step-by-step explanation:
You have 210kcal/h. There are 1000cal in 1kcal, and 60 minutes in 1 hour:
[tex] \frac{210}{1} \frac{kcal}{hour} \times \frac{1000}{1} \frac{cal}{kcal} \times \frac{1}{60} \frac{hour}{minutes} [/tex]
The units kcal cancel and hours cancel, leaving cal per min:
[tex] \frac{210 \times 1000}{60} \frac{cal}{minute} = 3500 \frac{cal}{min} [/tex]
A group of people walk 62 in week 1 in week 2 they walked 14 miles less than during week 1 how many miles did the group walk in week 2 weeks
Answers
The graph below represents the proportional relationship between the weight of dog food, in pounds, and the price of dog food, in dollars.
How much money will 6lbs of dog food cost?
$8.75
$6.00
$5.50
$7.50
Answers
Answer:
The answer is 8.75<3
Answer:
the correct answer is 7.50
Step-by-step explanation:
because they are telling to measure how much will 6lbs will scost them in the chart when you look at six and go up to the line it lines up with 7.50
HELP FOR A BRAINLIESTTTTT
Answers
Step-by-step explanation:
solve for y pretty much just move the negative x and turn it into a positive x because from there now you have a solid variable solved and you can just plug into the y so 3x - 2 x - 3 that'll be your equation then just do what you would normally do for a distributive multi-step equation and then take the answer you get from that and plug it into your newly solved simple equation which would be y = x - 3 that's as far as I'm going to get you but I do hope this helps
Answer:
(6, 3 )
Step-by-step explanation:
3x - 2y = 12 → (1)
- x + y = - 3 → (2)
multiplying (2) by 2 and adding to (1) will eliminate y
- 2x + 2y = - 6 → (3)
add (1) and (3) term by term to eliminate y
x = 6
substitute x = 6 into either of the 2 equations and solve for y
substituting into (1)
3(6) - 2y = 12
18 - 2y = 12 ( subtract 18 from both sides )
- 2y = - 6 ( divide both sides by - 2 )
y = 3
solution is (6, 3 )
A sporting goods store specializes in mountain bikes. Each week, two dozen mountain bikes are randomly selected from the store's warehouse to undergo a performance test.
What is the population for the performance test?
A.
The population is all of the mountain bikes in the store's warehouse.
B.
The population is the salespersons at the store.
C.
The population is all of the merchandise sold by the store.
D.
The population is the mountain bikes that are not randomly selected
Answers
Answer:
A
Step-by-step explanation:
A population is a set of similar items or events which is of interest for some question or experiment.
PLEASE HELP 70 POINTS & WILL GIVE BRAINLIEST Mayerlin volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 319 people went to The Youth Wing, 401 people went to Social Issues, and 398 went to Fiction and Literature.
On Sunday, the library had 1500 total visitors. Based on what Mayerlin had recorded on Saturday, about how many people should be expected to go to Fiction and Literature? Round your answer to the nearest whole number.
Answers
Answer:
413
Step-by-step explanation:
413 people should be expected to go to Fiction and Literature
Step-by-step explanation:
Proportion of people who went to Fictions and Literature on Saturday:
342 out of 467 + 433 + 343 = 1243
The proportion is:
342/1243 = 0.275
On Sunday:
Based on Saturday, so 0.275 out of 1500(number of visitors on Sunday).
0.275*1500 = 412.5
Rounding to the nearest whole number:
413 people should be expected to go to Fiction and Literature
Solve each equation. Identify the solutions as rational or irrational numbers.
Answers
[tex]\textbf{a)}\\\\~~~~~~~x(3x-4)=5\\\\\implies 3x^2 -4x = 5\\\\\implies 3x^2 -4x=5\\\\\implies x^2 - \dfrac 43 x = \dfrac 53\\ \\\implies x^2 - 2\cdot \dfrac 23 \cdot x + \left( \dfrac 23 \right)^2 - \left( \dfrac 23 \right)^2 = \dfrac 53\\\\\implies \left(x-\dfrac 23 \right)^2 = \dfrac 53 + \dfrac 49\\\\\implies \left(x-\dfrac 23 \right)^2= \dfrac{19}{9}\\\\\implies x- \dfrac 23 = \pm\dfrac{\sqrt{19}}3\\\\\implies x=\dfrac 23 \pm\dfrac{\sqrt{19}}3\\\\[/tex]
[tex]\text{The solutions are irrational.}\\\\\\\textbf{b)}\\\\~~~~~~~(3x-2)^2 = \dfrac 14\\\\\implies 3x -2 = \pm \dfrac 12\\\\\implies 3x = 2\pm \dfrac 12\\\\\implies x = \dfrac 23 \pm \dfrac 16\\\\ \implies x = \dfrac 56 ,~~ x =\dfrac 12 \\ \\\text{The solutions are rational .}[/tex]
Which sets of measurements could be the interior measures of a triangle?
(answer choices)
A. 10*, 10*, 160*
B. 15*, 75*,90*
C. 20*, 80*, 100*
D 35*, 35* 105*
E 60*, 60*, 60*
Answers
Answer:
A, B, E
Step-by-step explanation:
the 3 angles of a triangle must add up to 180
A. 10 + 10 + 160 = 180
B. 15 + 75 + 90 = 180
C. 20 + 80 + 100 = 200
D. 35 + 35 + 105 = 175
E. 60 + 60 + 60 = 180
The actual length of a machine is 12.25cm. The measured length is 12.2cm. Round the amswer to part(b) to the nearest hundreth of a percent. Find the absolute error. Find the percent error.
Answers
Answer:
ABS Error: 0.05 cm
PERC Error: 0.40%
Step-by-step explanation:
Absolute error: Absolute difference between the actual dimension, and its measure. Measured in the same dimension as what we're measuring
(Remember the absolute)
ABS Err: | 12.25 cm - 12.2 cm | = 0.05cm
Percent error: Percentual difference between the actual dimension and its measure. Always measured in Percents
PERC Err: | (12.25 - 12.20) | / 12.25 = 0.0040 ≈ 0.40%
Please help me solve
Answers
a) 66%
b) 42%
hope it really helps..!!!
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 147, 21, 3, ... This is sequence and the is equal to
Answers
Answer:
geometric sequence
Step-by-step explanation:
an arithmetic sequence has a common difference d between consecutive terms.
21 - 147 ≠ 3 - 21
Hence the sequence is not arithmetic
A geometric sequence has a common ratio r between consecutive terms
[tex]\frac{21}{147}[/tex] = [tex]\frac{1}{7}[/tex] and [tex]\frac{3}{21}[/tex] = [tex]\frac{1}{7}[/tex]
there is a common ratio thus the sequence is geometric
I need help to find the area of this problem.
Answers
Answer:
119 square yards
Step-by-step explanation:
assuming that the parallelograms height is 8 (11 - 3) we can find the area of the bottom
13 * 8 = 104
assuming that the rectangles length is 5 (13 - 8) we can find the area of the top
3 * 5 = 15
then add those
104 + 15 = 119
Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. a square is split into 3 sections. the bottom section is 5 acres, the middle section is 30 acres, and the top section is 15 acres. the top and bottom sections are shaded. what is the probability that his model rocket has landed in a grassy area? 0.2 0.3 0.4 0.6
Answers
The probability that his model rocket has landed in a grassy area will be equal to 0.4.
What is probability?The extent to which an event is likely to occur, is measured by the ratio of the favorable cases to the whole number of cases possible.
The total area of the land will be = 5+15+30=50 acres
Now the total grassy area will be =15+5=20 Acres
Now the probability of the model rocket to land on the grassy land will be:
[tex]P=\dfrac{Grassy\ area}{Total\ area}[/tex]
[tex]P=\dfrac{20}{50}=0.4[/tex]
Hence the probability that his model rocket has landed in a grassy area will be equal to 0.4.
To know more about probability follow
https://brainly.com/question/24756209
Answer:
C.10.0%
Step-by-step explanation:
Edge 2023!
Can someone help me with this problem?
Answers
Answer:
4(17+5)
Step-by-step explanation:
GCF is 4
68/4 = 17
20/4 = 5
so,
4(17+5)
HELPPPPPPPPP PLEASE!!! :(
Answers
Answer:
x = 25
Step-by-step explanation:
Given:
∠A = ∠B (Vertically opposite angles)∠A = (7x - 8)°∠B = (6x + 17)°Since ∠A is equivalent to ∠B...
[tex]\implies (7x - 8)= (6x + 17)[/tex]
Open the parenthesis:
[tex]\implies 7x - 8= 6x + 17[/tex]
Add 8 both sides:
[tex]\implies 7x - 8 + 8= 6x + 17 + 8[/tex]
Simplify both sides:
[tex]\implies 7x = 6x + 25[/tex]
Subtract 6x both sides:
[tex]\implies 7x - 6x = 6x - 6x + 25[/tex]
Simplify both sides:
[tex]\implies x = 25[/tex]
Answer:
x = 25
Step-by-step explanation:
Putting Both angels together:
Since,
m∠A = (7x - 8)°
m∠B = (6x + 17)°
Then,
(7x-8) = (6x+17)
Solving for x:
7x - 8 = 6x + 17
+ 8 +8
--------------------------
7x = 6x + 25
-6x -6x
-------------------
x = 25
Hence Answer is 25
~Lenvy~
Please help ASAP I’ll give brainliest
Answers
Answer:
D. y-9 = 2(x-1) (This is wrong dont use lol)
Answer:
C is your correct answer.
Step-by-step explanation:
Point Slope Formula:
y - y1 = m(x -x1)
Your Coordinate Points: (-2, 3) and (1,9)
The first "y" is 3 so the y1 should be 3.
The First "x" is -2 which is what x1 should be.
**But -x1 and -2 have to be + because negative and negative should cancel out and become an addition problem.
Point Slope Form Right Now:
y - 3 = m ( x + 2)
We're missing the "m" which is the slope.
Here's the specific formula:
y2 - y1/ x2 - x1
The "y2" is 9
The "y1" is 3
The "x2" is 1
The "x1" is -2
Now, do 9-3 over 1- (-2)
9-3 = 6 and 1-(-2) = 3
6/3 should be the answer for slope but it needs to be simplified
So, do 6 divided by 3 which is 2.
2 is your slope.
Plug it in and finalize!!
y - 3 = 2 ( x + 2)
**The answer is C but the writing of the answer choice is wrong.
helppppppp meeee plsssss
Answers
z = 50/3
[tex]\bold{EXPLANATIONS:}[/tex]
How many cubes are in the prism (Its surface area and i'm confused)
Answers
Answer:
432 cubes
Step-by-step explanation:
(9)(8)(6)=432
Hope this helps
Answer:
432
Step-by-step explanation:
The front face of the prism (green) is 6 cubes high and 8 cubes wide. So, the front layer of cubes is 6×8 = 48 cubes.
The figure shows you there are 9 layers like this making up the whole prism.
Then the volume of the prism is ...
(9 layers) × (48 cubes/layer) = 9×48 cubes = 432 cubes
There are 432 cubes currently in the prism.
_____
Additional comment
The picture here does not ask for the surface area of the prism. The area would be the sum of the areas of each of the surfaces.
The three surfaces we can see (red, green, blue) have areas of 9×8 = 72, 6×8 = 48, and 6×9 = 54 square units, respectively. These areas total 174 square units, but represent only half of the total area.
The other half of the area is the same (each hidden face has the same area as its visible opposite). So, the total surface area of this prism is 2×174 = 348 square units. (1 unit = small cube edge length).
A group of campers were polled about whether they like swimming and whether they like playing baseball. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table. a circle labeled swimming 24 overlaps a circle labeled baseball 18. overlap is labeled 15. 4-column table with 3 rows. first column has no label with entries likes baseball, does not like baseball, total. second column is likes swimming with entries a, c, 39. third column is does not like swimming with entries b, 13, e. fourth column is labeled total with entries 33, d, 70. which values are correct? select three options. a = 15 b = 18 c = 23 d = 35 e = 31
Answers
The missing values a, b, c, d and e are included in the given two-way table. The correct values from the options are: a =15, b=18,e=31
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]
List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
For this case, the table given is:
[tex]\begin{array}{cccc}\rm &\rm \text{Likes swimming}&\rm \text{Doesn't like swimming}&\rm Senior\\\rm \text{Likes baseball}&a&b&33\\\rm \text{Doesn't likes baseball}&c&13&d\\\rm Total & 39& e& 70 \end{array}[/tex]
From this table, we can make 5 equations as:
[tex]a+b = 33\\a+c=39\\b+39=e\\33+d = 70\\39+e=70[/tex]
From the last two equations, we get the values of d and e as:
[tex]d = 70-33 = 37\\e = 70-39 = 31[/tex]
Putting this value of 'e' in last third equation, we get:
[tex]b + 13 = 31\\b = 31-13= 18[/tex]
From this, and first equation, we get:
[tex]a +18 = 33\\a=33-18=15[/tex]
And from this value of a, and second equation, we get:15+c = 39
[tex]c = 39-15 = 24[/tex]
Thus, the correct values are: [tex]a =15, b=18,e=31[/tex]
Learn more about two-way table here:
https://brainly.com/question/26788374
Answer:
a,b,e
Step-by-step explanation:
help me please HeLp
i already tried 18.85 and 28.27
i don't know what it could be so i need heLP
Answers
Answer:
18.84
Step-by-step explanation:
C = 2pi × r
C = 2 × 3.14 × 3
C = 18.84
Answer:
It would be 18.84. There is no rounding
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
so it would be
C = 2[tex]\pi[/tex]3
in exact form it would be
6[tex]\pi[/tex] but as a deciamal its
18.849555.....
it says no rounding so it would be 18.84
A cylinder has a base radius of 10in and a height of 20in. What is its volume in cubic in, to the nearest tenths place?
Answers
Answer:
6283.2
Step-by-step explanation:
[tex]V=\pi r^{2} h[/tex]
=[tex]=\pi *10^{2} *20[/tex]
=6283.18531
=6283.2(correct to the tenths place)
Answer:
6,283.2 in^3
Step-by-step explanation:
The volume formula for a cylinder is V = (pi)r^2*h
and in this case r = 10 in, h = 20 in
so the volume of this cylinder is
V = 3.14159(10 in)^2*(20 in) = 6,283.2 in^3
What is the factored form of a2 – 121?
(a – 121)(a – 1)
(a – 11)(a + 11)
(a + 11)(a + 11)
(a – 121)(a + 1)
Answers
Answer:
(a-11) (a+11)
Step-by-step explanation:
Hope it helps you
Answer:
(a+11)(a-11)
Step-by-step explanation:
we all need help sometimes dude
Which fraction would you find marked on a ruler?
A. 1/8 inch
B. 1/10
C. Inch D. 1/5 inch
D. 1/9 inch
Answers
Answer:
1/8
Step-by-step explanation:
Generally, rulers, yardsticks and tape measures are marked in 16ths 8ths and quarter inches
Answer:
1/8
Step-by-step explanation:
that is the answer
The fish population of a receding pond is 8,000. The population is
expected to decrease at a rate of 8% each year.
Which function represents the population of the fish in the pond after x
years?
f(x) = 8,000(0.08)
f(0) = 92(1.08)
f(2) = 92(0.8)
Of(x) = 8,000(0.92)*
f(3) = 8,000(0.2)
f(x) = 8,000(1.08)*
Answers
Answer:
f(x)=8,000(0.08)
Step-by-step explanation:
I am not 100% sertin but 8% = 0.08 so to find the percentage you would just multiple that by the given 8,000.
The formula t = 2 pi startroot startfraction l over 32 endfraction endroot relates the time, t, in seconds for a pendulum with the length, l, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for pi. 2 feet 4 feet 11 feet 19 feet
Answers
The length of this pendulum that makes one full swing is 3.93 meters.
How to calculate the length of the pendulum?Mathematically, the time taken by this pendulum is given by this formula:
[tex]\rm T=2\pi \sqrt{\dfrac{L}{32}}[/tex]
Making L the subject of the formula, we have:
[tex]\rm T=2\pi \sqrt{\dfrac{L}{32}}\\\\32T^2=4\pi ^2L\\\\L=\dfrac{32T^2}{4\pi ^2}\\\\[/tex]
Substitute all the values in the formula
[tex]\rm L=\dfrac{32T^2}{4\pi ^2}\\\\ L = \dfrac{32 \times 2.2^2}{4 \times 3.14 ^2\\}\\\\ L =\dfrac{154.88}{39.43}\\\\L=3.93 \ m[/tex]
Hence, the length of this pendulum that makes one full swing is 3.93 meters.
Read more about pendulum here:
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Answer:
Basically if your coming from edge its 4 ft so B
Step-by-step explanation:
Which of these expressions represent the
sum of the areas of the triangles shown?
Answers
Answer:
C. 3((x+4) + (x-2))
Step-by-step explanation:
Area of a triangle: [tex]\frac{1}{2}bh[/tex]
Area of the left triangle:
[tex]\frac{1}{2}(x+4)(6)[/tex]
The 6 multiplied by the 1/2 equals 3, so:
[tex]A = 3(x+4)[/tex]
Area of the right triangle:
[tex]\frac{1}{2}(x-2)(6)\\[/tex]
Again, the 6 multiplied by the 1/2 equals 3, so:
[tex]A= 3(x-2)[/tex]
Adding the two areas together equals:
[tex]3(x+4) + 3(x-2)[/tex]
We can factor out the 3 from both, giving us the final answer:
[tex]A = 3((x-4)+(x-2))[/tex]
Which model and number line show the same fraction? Answer and explain why
Answers
can you help me know how to get the answer i don’t need the answers just how to solve the problem
Answers
Answer:
I guess 21
Step-by-step explanation:
Because if you find the other side by trigonometric theorem-
[tex]x^2 = c^2 - a^2\\x^2 = 12^2 -8^2\\x^2= 144 - 64\\x^2=80\\\sqrt{x} =\sqrt{80}\\ x=8.94[/tex]
which is almost 9
9 is a possible value
they ask you to find the value which doesn't fit in the triangle
so the answer is 21 which doesn't make any sence
Hopefully, the answer would be work
Find the value of the missing variable(s)?
Answers
Answer:
x = 163°
Step-by-step explanation:
The sum of interior angles of a pentagon is 540°. The missing value will bring the total to that. It can be found by subtracting the known values from 540°.
__
x = 540° -85° -103° -121° -68°
x = 163°
_____
Additional comment
The sum of interior angles of a simple n-gon is found from the formula ...
angle sum = 180°·(n -2)
For n = 5, this is 180°×3 = 540°.
what is 3/4 of 4/9 kilogram?
Answers
Answer:
0.333333333kilograms
Step-by-Step explanation:
3 x 4 = 12
4 x 9 = 36
3/4 ÷ 4/9 = 12 ÷ 36 = 1/3 = 0.333333333 kilograms