Sammy and Pippa's teacher gives them a homework question to solve. She tells them to plot the points A(5, -1), B(9, 4), C(15, 1) and D(11, -4) on a grid and decide whether the shape is a square or a rhombus. Sammy and Pippa do their slope calculations and Sammy insists the shape is a square whereas Pippa insists the shape is a rhombus. Who is right? Show your calculations in your reasoning
Answers
Answer:
Pippa
Step-by-step explanation:
A square has
parallel opposite sides perpendicular adjacent sides perpendicular diagonalsA rhombus has
parallel opposite sides non-perpendicular adjacent sides perpendicular diagonalsThus, we can identify the shape by comparing the slopes of the adjacent sides.
1. Draw the shape
See the graph below
2. Calculate the slope of AB
m = (y₂ - y₁)/(x₂ - x₁) = (4 - (-1))/(9 - 5) = (4 + 1)/4 = 5/4
3. Calculate the slope of BC
If BC⟂AP, its slope should be -4/5 .
m = (y₂ - y₁)/(x₂ - x₁) = (1 - 4)/(15 - 9) =-3/6 = -1/2
½ ≠ -⅘
The two lines are not perpendicular.
Pippa is right. The shape is a rhombus.
Related Questions
Tommy wants to make ice cream for his birthday party. He has 6 cups of cream. Each batch
of ice cream takes 3/4 cups of cream. How many batches can he make? *
Answers
Answer:
8 batches
Step-by-step explanation:
Take the total amount of cream and divide by the amount of cream per batch
6 ÷ 3/4
Copy dot flip
6 * 4/3
6/3 *4
2*4
8 batches
divide $1600 in the ratio of 3:7:10
Answers
Answer:
240, 360, 800
Step-by-step explanation:
We can call the numbers 3x, 7x, and 10x and then we can write:
3x + 7x + 10x = 1600
20x = 1600
x = 80 so the numbers are 3 * 80 = 240, 7 * 80 = 560 and 10 * 80 = 800.
Miguel spent a total of $60 at the grocery store. Of this amount , he spent $18 on fruit. What percentage of the total did he spend on fruit
Answers
Answer:
30%
Step-by-step explanation:
A percent can be found by dividing the part by the whole, or
part/whole
In this case, the part is the amount he spent on fruit. The whole is the total amount he spent.
amount spent on fruit/ total amount spent
He spent $18 on fruit, and $60 in total.
$18/ $60
Divide 18 by 60
18/60
0.3
Convert 0.3 to a decimal by multiplying by 100 or moving the deicaml place two spots to the right.
0.3*100=30
0.3--> 3.0 --> 30
30%
He spent 30% on fruit.
What's the correct answer to both of these?
Answers
Answer:
See explanation.
Step-by-step explanation:
1) The correct answer is B.
2) The correct answer is D.
To find the answer, plug the equations into Desmos.
If this helped, please mark Brainliest :D
Make 'P' the subject in the formula A = P(1+r)T
Answers
P=A/(1+r)T
Step-by-step explanation:
1) p(1+r)=A/T
2)P=A/(1+r)T
Answer:
P=A/(T+Tr)
Step-by-step explanation:
A = P(1+r)T
Multiply P and T
A=PT(1+r)
Clear the bracket by multiplying all bracketed terms by PT
A=PT+PTr
A=P(T+Tr)
Divide both sides by (T+Tr)
A/(T+Tr)=P(T+Tr)
P=A/(T+Tr)
PLEASE HELP!! 85 POINTS!!
Answers
Answer:
20
Step-by-step explanation:
Angle EAC and angle GCJ are corresponding angles.
So angle EAC is equal to 70 degrees.
Angle KAE is a right angle, so it is 90 degrees.
Angles on a line add up to 180 degrees.
x + 90 + 70 = 180
x = 180 - 160
x = 20
Answer:
The measurement of ∠x is 20°
Step-by-step explanation:
From this problem, we are given a few pieces of information. First we know that DE is parallel to FG. We also know that KL is perpendicular to FG. Perpendicular means that the angles from KL and FG are going to form right angles.
So, knowing this, we can start off my saying that the measurement of ∠KAE is 90°.
We can also say that the measurement of ∠IAD is 70° because it is correspondent to ∠JCG and corresponding angles have the same measurements.
So, now we can find x. Set up equation.
70 + x + 90 = 180
Add 70 to 90.
x + 160 = 180
Subtract 160 on both sides.
x = 20
So, the value of x is 20°
[tex](5 {x }^{2} + 2 {y}^{2} ) \times (3 {x}^{2} - 7 {y}^{2}) [/tex]
Answers
Answer:
[tex]15x^4 - 29x^2y^2 - 14y^4[/tex].
Step-by-step explanation:
(5x^2 + 2y^2) * (3x^2 - 7y^2)
= 15x^4 + 6x^2y^2 - 35x^2y^2 - 14y^4
= 15x^4 - 29x^2y^2 - 14y^4
= [tex]15x^4 - 29x^2y^2 - 14y^4[/tex]
Hope this helps!
The company calculates that 500 g of titanium dioxide should produce 1.2 kg of titanium chloride. However, the company finds that 500 g of titanium dioxide only produces 900 g of titanium chloride. Calculate the percentage yield.
Answers
Answer:
75%
Step-by-step explanation:
Percent yield = experimental yield / theoretical yield * 100
= 900 / 1200 * 100 (remember that 1,000 g = 1 kg)
= 75
For a proof by induction of the math statement below, identify the correct step for proving the theorem is true for n = k + 1. HELP ASAP THANKS!!
Answers
What we do is simply replace every n with k+1. So (3n)^2 turns into (3(k+1))^2
We see that only choice A has the correct term mentioned on the left hand side, so this must be the answer.
The right hand side is treated the same way. We plug in n = k+1. Your teacher did a bit of algebraic manipulation to get what is shown for choice A.
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?
Answers
Answer:
3.95m + 8.95b = 47.65
Step-by-step explanation:
m is the number of magazines, and b is the number of books. If it costs $3.95 for each magazine, you will get 3.95m. If it costs $8.95 for each book, you will get 8.95b. Both of these values add up to the total, which is $47.65.
3.95m + 8.95b = 47.65
Answer:) 3.95m+8.59b=47.65
Step-by-step explanation:) edge 2023
Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?
A. (-6, 0)
B. (0, -6)
C. (0, 2)
D. (2, 0)
The graph of the question is attached.
Answer:
The point is (x, y) = (0, 2)
The correct option is C.
Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.
Step-by-step explanation:
From the given graph, the points A and B are
[tex](x_1, y_1) = (-2, 4) \\\\(x_2, y_2) = (2,-8) \\\\[/tex]
The slope of the equation is given by
[tex]m_1 = \frac{-8 - 4 }{2 -(-2)} \\\\ m_1 = \frac{-12 }{2+2} \\\\m_1 = \frac{-12 }{4} \\\\m_1 = -3 \\\\[/tex]
We know that the slopes of two perpendicular lines are negative reciprocals of each other.
[tex]m_2 = - \frac{1}{m_1}[/tex]
So the slope of the other line is
[tex]m_2 = \frac{1 }{3} \\\\[/tex]
Now we can find the equation of the line that is perpendicular to the line AB and passes through the point C.
From the graph, the coordinates of point C are
[tex](x_1, y_1) = (6, 4)[/tex]
The point-slope form is given by,
[tex]y - y_1 = m(x -x_1)[/tex]
Substitute the value of slope and the coordinates of point C
[tex]y - 4 = \frac{1 }{3} (x - 6)\\\\[/tex]
To get the y-intercept, substitute x = 0
[tex]y - 4 = \frac{1 }{3} (0 - 6) \\\\y - 4 = \frac{-6 }{3}\\\\y - 4 = -2\\\\y = 4 -2 \\\\y = 2 \\\\[/tex]
So, the point is
[tex](x, y) = (0, 2)[/tex]
The correct option is C.
Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.
Answer:
C (0, 2)
Step-by-step explanation:
Giselle has $40 to spend on parking this month. Parking costs her $2.50 each day. After Giselle parks for 9 days, which statement is true? 1.Giselle has spent less than 12 of her parking money. 2.Giselle has spent 12 of her parking money. 3.Giselle has spent more than 12 of her parking money. 4.Giselle has spent almost all of her parking money.
Answers
Answer:
Giselle has spent more than 1/2 of her parking money.
Step-by-step explanation:
What is the answer to 15a + 9 =
Answers
Answer:
[tex]a=-\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]15a-9=0\\\\15a=-9\\\\a=-\frac{9}{15} \\\\a=-\frac{3}{5}[/tex]
Answer:
Step-by-step explanation:
Use distributive property
15a + 9 = 3*5*a + 3*3
= 3 (5a + 3)
Your roommate loves to eat Chinese food for dinner. He estimates that on any given night, there’s a 30% chance he’ll choose to eat Chinese food. Although he loves Chinese food, he doesn’t like to eat it too much in a short period of time, so on most weeks he eats several different kinds of foods for dinner. Suppose you wanted to calculate the probability that, over the next 7 days, you friend eats Chinese food at least 3 times. Which of the following is the most accurate statement about calculating this probability?
A. Because he doesn’t like to eat Chinese food too much in a short period of time, p is not really the same for each trial and so we cannot use the binomial distribution to calculate the desired probability.
B. Because "success" or "failure" have no real meaning in the context of this problem, we cannot use the binomial distribution to calculate the desired probability.
C. Because we do not know the probabilities of your roommate eating any other types of foods, we cannot use the binomial distribution to calculate the desired probability.
Answers
Answer:
A. Because he doesn’t like to eat Chinese food too much in a short period of time, p is not really the same for each trial and so we cannot use the binomial distribution to calculate the desired probability.
Step-by-step explanation:
As it is mentioned in the question that he doesn't like the Chinese too much in a very short interval so he prefers various other foods for dinner
So now we have to determine the probability for the next 7 days
So based on the options mentioned, we prefer option A as we do not use the binomial distribution here as it shows only success results that are not confirmed in the given case
Therefore, the correct option is A.
1) Expand the following expressions
(a) 2(x + 6)
Answers
Answer:
2x + (2 × 6)
since we are expanding, we represent 2 multiplying to every expression in the given parentheses
Answer:
2x+12
Step-by-step explanation:
2(x + 6)
Distribute
2*x + 2*6
2x+12
A car travels at a speed of 41 meters/second using 756 joules of energy every second. Suppose we know that the car uses 52,700 joules of energy. Set up a calculation to find the number of meters the car travels with this amount of energy.
Answers
Answer:
Heres a screenshot with the answers I got from someone who commented:
Edit: Credits- saltern20333
Answer:
Step-by-step explanation:
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 8y2, y ≥ 0, x = 8; about y = 2
Answers
Answer:
Step-by-step explanation:
If you were to graph this on a coordinate plane, it looks like a log function. It starts at (0, 0) and ends, according to the boundaries given, at x = 8. Because we are to solve for the volume using the shell method, we need x = y equations (which we have, thankfully!) and y intervals. The y-interval is given to us within the problem as 0≤y≤2. If we are to revolve this solid about the line y = 2, the line of rotation is above the solid, so we have to go backwards to get there. That's very important. The formula we need for shells is
[tex]2\pi\int\limits^2_0 {p(y)h(y)} \, dy[/tex]
where p(y) is the distance between the axis of rotation and the solid, and h(y) is the height of the representative rectangle. Since we are using the shell method, the representative rectangle is parallel to the axis of rotation, so it is 8 units long (or high).
p(y) is the distance from y = 2 to the solid, so p(y) = 2 - y
h(y) is the length of the representative rectangle, so h(y) = 8
and filling in the formula:
[tex]2\pi\int\limits^2_0 {(2-y)(8)} \, dy[/tex] and simplifying a bit:
[tex]2\pi\int\limits^2_0 {16-8y} \, dy[/tex]
Integrating we get
[tex]2\pi[16y-4y^2][/tex] from 2 to 0. Using the First Fundamental Theorem of Calculus:
[tex]2\pi[(32-16)-(0)][/tex] simplifies to
[tex]2\pi(16)[/tex] which is, finally,
[tex]V=32 \pi[/tex]
In this exercise we have to use the fundamental calculus theorem to calculate the volume of a rotating cylinder, thus we find that:
[tex]V=32\pi[/tex]
If you were to graph this on a coordinate plane, it looks like a log function. It starts at (0, 0) and ends, according to the boundaries given, at x = 8. Because we are to solve for the volume using the shell method, we need x = y equations and y intervals. The y-interval is given to us within the problem as 0≤y≤2. If we are to revolve this solid about the line y = 2, the line of rotation is above the solid, so we have to go backwards to get there. That's very important. The formula we need for shells is
[tex]2\pi \int\limits^2_0 {p(y)h(y)} \, dy[/tex]
Where p(y) is the distance between the axis of rotation and the solid, and h(y) is the height of the representative rectangle. Since we are using the shell method, the representative rectangle is parallel to the axis of rotation, so it is 8 units long (or high).
p(y) is the distance from the solid, so: [tex]p(y) = 2 - y[/tex] h(y) is the length of the representative rectangle, so: [tex]h(y) = 8[/tex]
and filling in the formula:
[tex]2\pi \int\limits^2_0 {16-8y} \, dy[/tex]
Integrating we get;
[tex]2\pi [ 16y-4y^2][/tex]
Using the First Fundamental Theorem of Calculus:
[tex]2\pi [ (32-16)-(0)][/tex]
[tex]2\pi (16) \\V=32\pi[/tex]
See more about volume at brainly.com/question/1578538
John can cut the yard on a riding lawn mower in 2 hours. Sandy can cut the yard with a push mower in 5 hours. How long would it take to cut the yard if John and Sandy work together? (Express in hours and minutes)
Answers
Answer:
2x/5x= 7
Step-by-step explanation:
The vertices of are D(7, 3), E(4, -3), and F(10, -3). Write a paragraph proof to prove that is isosceles.
Answers
Answer:
See explanation
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x2 - x1)^2+(y2-y1)^2}[/tex]
Isosceles Triangle: 2 sides are the same
[tex]d = \sqrt{(4 - 7)^2+(-3-3)^2} = 3\sqrt{5}[/tex]
[tex]d = \sqrt{(10-4)^2+(-3+3)^2} = 6[/tex]
[tex]d = \sqrt{(10-7)^2+(-3-3)^2} = 3\sqrt{5}[/tex]
Since we have 2 distances between the vertices the same, we have an isosceles triangle.
Elle, Jonah and Mandy shared some game cards in the ratio 2:3:7. Each of
them would have received 152 game cards each if the game cards were
distributed equally. How many more game cards did Mandy receive than Elle? Please do a step by step explanation.
Answers
Answer:
190 cards
Step-by-step explanation:
Elle, Jonah and Mandy shared the game cards in the ratio 2 : 3 : 7. The total ratio is:
2 + 3 + 7 = 12
If they were shared equally, they would each receive 152 cards, this means that the total number of cards they received is:
152 * 3 = 456 cards
Elle's share is therefore:
2 / 12 * 456 = 76 cards
Mandy's share is:
7 / 12 * 456 = 266 cards
Therefore, the number of cards that Many received more than Elle is:
266 - 76 = 190 cards
ABCD is a rectangle.
Use the diagram to answer the questions.
The length of AB is __
The length of BC is __
The length of AC is __
Answers
BC = 5
AC = 3
To find AC, we can use the pythagoras theorem, square root of 12 power of 2 + 5 power of 2 and we can get 12. Hope this help!
Answer:
12
5
13
Step-by-step explanation:
Use a calculator to find the correlation coefficient of the data set. PLEASE HELP!
Answers
Answer:
The correlation coefficient of the data set is -0.901
Step-by-step explanation:
x y xx xy yy
1 20 1 20 400
3 14 9 42 196
5 10 25 50 100
9 6 81 54 36
15 4 225 60 16
[tex]\sum x = 1+3+5+9+15=33\\\sum y =20+14+10+6+4=54\\\sum x^2 =1+9+25+81+225=341\\\sum y^2=400+196+100+36+16=748\\\sum xy=20+42+50+54+60=226[/tex]
Formula :[tex]\frac{N \sum XY - (\sum X)(\sum Y)}{\sqrt{N\sum X^2 - (\sum X)^2}\sqrt{N \sumY^2 - (\sum Y)^2)}}[/tex]
[tex]= \frac{5 (226) - (33)(54)}{\sqrt{5(341)- (33)^2}\sqrt{5 (748) - (54)^2}}\\=-0.901[/tex]
So, Option D is true
Hence the correlation coefficient of the data set is -0.901
The length of a rectangle is 2 less than 3 times its width. If the area of the rectangle is 96cm², what is the length of the rectangle?
Answers
Answer: The length is 16 cm
Step-by-step explanation:
L= 3w -2 w × L = 96 substitute for L
w(3w -2) =96
3w² -2w = 96
3w² -2w - 96 = 0 factor this
(3w + 16)(w -6) = 0 Set the w-6 factor equal to 0 and solve for w (The 3w + 16 will yield a negative number; real rectangles can't have negative dimensions!)
w-6 = 0 so w = 6
Original equation for L L =3w -2 substitute 6 for w
L = 3(6) - 2 = 18 -2
L = 16
Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest. A) How much will Mr. Hughes have in total in his RRSP account? B) How much did Mr. Hughes contribute? C) How much will be interest?
Answers
Answer:
A) $93,504.818
B) $40,000
C) $53,504.818
Step-by-step explanation:
Yearly contribution ( periodic payment) = $4000
Period (p) = 10years
Additional period(y) = 5years
Annual interest(r) = 9% = 0.09
Future value (FV) =
periodic payment [(1 + r)^y - 1] / r
4000 [(1 + 0.09)^10 - 1 / 0.09]
4000[1.09^10 - 1 / 0.09]
4000[1.3673636 / 0.09]
4000(15.192929)
= 60771.716
If left for five more years:
FV = 60771.716(1 + r)^n
FV = 60771.716(1 + 0.09)^5
FV = 60771.716(1.09)^5
FV = 60771.716(1.5386239549)
FV = $93,504.818
B) MR. HUGHES CONTRIBUTION :
Periodic payment × p ; $4000 was deposited annually for 10 years.
$4000 × 10 = $40,000
C) Interest = Future value - contribution
$93,504.818 - $40,000
= $53,504.818
A car trip is 1/2h shorter that a bus trip. How long is the car trip if the bus trip is 3/4h?
Answers
Answer:
1/4h
Step-by-step explanation:
The car trip is 1/2h shorter than the bus trip.
The bus trip is 3/4h long.
Therefore, the length of the car trip is:
3/4h - 1/2h = 1/4h
The car trip is 1/4h long.
Which equation has no solution A.) 4(x+3)+2x=6(x+2) B.) 5+2(3+2x)=x+3(x+1) C.) 5(x+3)+x=4(x+3)+3 D.) 4+6(2+x)=2(3x+8)
Answers
Answer:
B. 5+2(3+2x)=x+3(x+1)
Step-by-step explanation:
Expand the brackets.
5 + 6 + 4x = x + 3x + 3
11 + 4x = 4x + 3
Add -4x and -11 on both sides.
4x - 4x = 3 - 11
0 = -8
There are no solutions.
Answer:
B
Step-by-step explanation:
I could explain this to you by using process of elimination but I think it would be easier to explain to you straight forward why answer choice B has no possible answers. First I did the equation out on a piece of paper:
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 +4x = x + 3x +3
11 + 4x = 4x +3
Now we have 4x + 3 = 4x + 11. It is impossible for 4x to be added to two entirely different numbers and still produce the same outcome, so that is why B is the correct answer choice.
Which number is a perfect cube?
O9
O 18
0 27
O 36
Answers
Answer:
27
Step-by-step explanation:
9 is not a perfect cube.
18 is not a perfect cube.
27 is a perfect cube.
∛27 = 3
36 is not a perfect cube.
Answer:
27
Step-by-step explanation:
We want a number time itself times itself
27 = 3*3*3
27 = 3^3
Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE. A horizontal line has points C, F, E, G. 2 lines extend from the line at points F and E to form an isosceles triangle with point D. Angle DEF measures 75°. What is the measure of angle CFD? 105° 125° 150° 165°
Answers
Answer:
105 degrees
Step-by-step explanation:
Angle DEF measures 75°.Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE.
the angles all together is 180 degrees
so 180 - 75 = 105 degrees
The measure of angle CFD is 105 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Angle DEF = 75°.
Triangle DEF is isosceles, so Angle DEF Is-congruent-to Angle DFE.
Angle DFE + Angle CFD = 180 (angle on a straight line)
so 180 - 75 = 105 degrees
Thus, Angle CFD = 105 degree
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ2
Please answer this question fast in two minutes
Answers
Answer:
lines NP and OP are intersecting
Step-by-step explanation:
they touch at point P
Sum of four consecutive multiplies of 7 is 70.Find these multiplies.
please
Answers
Answer: 7, 14, 21, 28
Step-by-step explanation:
Let first multiple = x
So, second multiple = x + 7
Third = x + 14
Fourth = x + 21
According to the question,
=>x + (x + 7)+ (x + 14) + (x + 21) = 70
=>4x + 42 = 70
=>4x = 28
=>x = 7
So, the multiples are 7(x), 14(x+7), 21(x+14), 28(x+21)