Given:
Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).
To find:
Whether the parallelogram ABCD is a rhombus, rectangle or square.
Solution:
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]
[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]
[tex]AB=\sqrt{0+64}[/tex]
[tex]AB=8[/tex]
Similarly,
[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]
[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]
[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]
All sides of parallelogram are equal.
[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
Both diagonals are equal.
Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.
We know that, a square is special case of rectangles and rhombus.
So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.
Find the height of the pyramid.
Volume
392 cm3
14 cm
7 cm
The height is
centimeters.
Answer:
12 cm
Step-by-step explanation:
Base area
14 x 7 = 98 cm²
The volume of pyramid
392= 1/3 x height x base area
Height =12 cm
Iooooooooooooookkn ooooo
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Answer:
ok
Step-by-step explanation:
ok
Aaron rolled a fair six-sided number cube, numbered 1 through 6, several times and recorded the data in the table below. Which statement about this situation is true? *
Answer:
Aaron rolled a fair six-sided number cube, numbered 1 through 6 is explained below in details.
Step-by-step explanation:
a. FALSE
Trial possibility of rolling a 6 =1/20 = 0.05
Logical possibility of rolling a 6 = 1/6 = 0.17(approximately.)
So the trial possibility of rolling a 6 is not equal to the logical possibility of rolling a 6.
b. FALSE
Trial possibility of rolling an even number = Trial possibility of rolling number 2,4 or 6 = 4/20+2/20+1/20= 7/20 = 0.35
Logical possibility of rolling an even number = 3/6 = 1/2=0.5
Therefore the Test possibility of rolling an even number is shorter than the logical possibility of the same.
c. TRUE
Trial possibility of rolling a 1= 6/20= 0.3
Logical possibility of rolling a 1= 1/6 = 0.17 (approx.)
So the Trial possibility of rolling a 1 is greater than the logical possibility of rolling a 1.
d. FALSE.
Trial possibility of rolling a 4= 2/20= 0.1
Logical possibility of rolling a 4 = 1/6 = 0.17 (approx.)
So the Trial possibility of rolling a 4 is less than the logical possibility of rolling a 4.
Felipe sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit
$125, how many t-shirts did he sell?
Answer:
He sold 17 shirts at the festival.
The total number of t-shirts Felipe sold is 17 t-shirts.
Consider that the number of t-shirts Felipe sold be "x".
Since He made a profit of $5 for each t-shirt sold. Therefore, his profit from selling t-shirts is 5x. also made a profit of $40 from selling hats.
His total profit is given as $125.
So we can write the following equation:
5x + 40 = 125
Subtracting 40 from both sides;
5x = 85
Dividing both sides by 5, we get:
x = 17
Therefore, Felipe sold 17 t-shirts.
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graph the image of triangle PQR after a reflection across the line y = 2
Answer: Refer to the diagram below
P ' is at (-7, 9)Q ' is at (1, 9)R ' is at (-6, 4)================================================
Explanation:
The diagram shows how point R moves to R'. We move up 2 units going from R(-6,0) to (-6,2). This lands us on the line of reflection. Then we move another 2 units up to land on (-6,4) which is the location of point R'.
The other points P and Q follow the same idea. Though the distances will be different from R. For P and Q, we'll move 7 units up to arrive at the line of reflection, then another 7 units to arrive at the proper locations of P' and Q', which are (-7,9) and (1,9) respectively.
Answer:
If we draw the line of y=2 and if we find the reflections we have the new points of...
R(-6,4)Q(1,9)P(-7,9)Now all we have to do it plot these points, and then we have the triangle PQR
I bought some 60-cent candy bars with c dollars. Then I ate n of them. how many candy bars do I have left?
Thank you!!!!
Answer:
Step-by-step explanation:
60 divided by c-n=how many you have left
HELP MI PORFA<3
Question 1 (4 points)
1. Write a two column proof. (4pts)
Given: 2(3x + 4) = 56
Prove: x = 8.
I
Question 2
Step-by-step explanation:
2(3x+4)=56
<=> 6x+8=56
<=> 6x=48
<=> x=8
-4= d+3/5
Please help this makes no sense to me
need this done fast pls.
Answer:
45°Step-by-step explanation:
85 + 50 + ? = 180
? = 180 - 85 - 50
? = 45
n order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? --> It must be
Complete Question
In order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? -->
It must be that the resulting P-value must be
A) Greater than 0.2
B) Between 0.19 and 0.10
C) Between 0.09 and .05
D) Between .049 and .02
E) Less than 0.02
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The mean of sample 1 is [tex]\= x_1 = 10[/tex]
The standard deviation is [tex]s_1 = 6[/tex]
The mean of sample two is [tex]\= x_2 = 16[/tex]
The standard deviation is [tex]s_2= 4[/tex]
The sample size for both samples is [tex]n_1 = n_2 = n = 6[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x_1 - \= x_2 }{ \sqrt{ \frac{s^2_1}{n_1} +\frac{s^2_1}{n_2} } }[/tex]
=> [tex]z = \frac{ 10 - 16 }{ \sqrt{ \frac{6^2}{6} +\frac{4^2}{6} } }[/tex]
=> [tex]z = -1.3646[/tex]
From the z table the area under the normal curve to the left corresponding to -1.3646 is
[tex]P(Z < -1.3646) = 0.086189[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P(Z < -1.3646)[/tex]
=> [tex]p-value = 0.086189 * 2[/tex]
=> [tex]p-value = 0.1724[/tex]
So the p-value is Between 0.19 and 0.10
Solve for n in the following equation. A=P(1+n) show all work
Answer:
n = A/P - 1
Step-by-step explanation:
1st step: subtract P from each side to get A/P = 1+n
2nd step: subtract 1 from each side to get the answer above
My last oneeeeee help please
Answer:
C HOPE THIS HELPS MARK BRain leist
Step-by-step explanation:
EX 1) Games Galore Super Store buys the latest video game at a wholesale price of $30.00. The markup rate at Game's Galore Super Store is 40%. You use your allowance to purchase the game at the store. How much will you pay, not including tax?
Answer:
$42
Step-by-step explanation:
Given that,
Galore Super Store buys the latest video game at a wholesale price of $30.00.
The markup rate at Game's Galore Super Store is 40%.
We need to find the price from the store. It can be calculated as follows :
[tex]C=30+\dfrac{40}{100}\times 30\\\\=30+12\\\\=\$42[/tex]
Hence, we will pay $42.
I need help please :D Thanks
Answer:
Step-by-step explanation:
HII do the parentheses first then carry on if you need more help i suggest you go to caculatorsoup and search mixed number caculator and it should help u its a web
Brooke measures the height of her bean plant for a science project. The bean plant is 12.5 inches tall.
How many centimeters tall is Brooke’s bean plant?
Answer:
its 31.75
Step-by-step explanation:
12.5 inch = 31.75 cm
There are six doors in a hostel .In how many ways a student enters the hostel and leave by different door
Answer:
5 times
Step-by-step explanation:
Because he enters through the front door.
I really need some help with this my brain is dead at the moment
What do I write as an answer?
Answer: I got no clue brother.
Step-by-step explanation: Brother
Pls work out and give detail. Use the slope formula to determine the slope of each line.
4. AB
ТУ
41
2
2ТА
B
Х
— 4 — 2
O|
2
N
т
-4 +
Answer:
[tex]m=0[/tex]
Step-by-step explanation:
Given
See attachment
Required
Determine the slope of the line
From the attachment, we have the following points
[tex](x_1,y_1) = (-4,1)[/tex]
and
[tex](x_2,y_2) = (3,1)[/tex]
The slope m is then calculated using:
[tex]m = \frac{y_2- y_1}{x_2 - x_1}[/tex]
Substitute values for the x's and y's
[tex]m = \frac{1-1}{3 - (-4)}[/tex]
[tex]m = \frac{1-1}{3 +4}[/tex]
[tex]m = \frac{0}{7}[/tex]
[tex]m=0[/tex]
Hence, the slope is 0
Which expression is equal to 1-12|- |-3|?
О-15
9
o 9
o 15
Answer:
15 i think 15 or 9 is the answer
Sam is reading a book. He finishes 6 pages of the book in 18 minutes. How many pages would Sam have finished reading in 36 minutes?
Answer:
12 pages
Step-by-step explanation:
This is a fairly straight forward question.
Sam read 6 pages in 18 minutes, and we want to know how many pages he could have finished if he read for 36 minutes.
36 minutes is double the time of 18 minutes.
So we just have to double the 6 pages Sam read into 12 pages and that is the answer.
A boat traveled 54 km with the stream and 42 km against the stream spending a total of as much time as it would spend while travelling 96 km in a lake. Find the speed of boat while it is travelling in the lake, if the current of the river is 3 km/hour.
Answer:
18 miles / hour
Please I will give you 10 plus 5 more for brainliest
Answer:
1-12
Step-by-step explanation:
1. left 2. right 3. equal 4. left 5. left 6. equal
sry i was running out of time.
What is a real estate investment group?
a.
A collection of investors who pool their resources in order to purchase and manage property for a profit.
b.
An investment trust which uses investors’ money to purchase property, which it then manages in the investors’ stead.
c.
A category of real estate, such as “houses” or “apartment buildings.”
d.
A set of several properties purchased all at once.
Answer:
Your answer would be A
Step-by-step explanation:
I got it right on edge!
a. A collection of investors who pool their resources in order to purchase and manage property for a profit.
100% on edge 2021 c:
An 8-foot rope is tied from the top of a pole to a stake in the ground,as shown in the diagram below.
If the rope a 57° angle with the ground, what is the height of the pole, to the nearest tenth of a foot?
A 4.4
B 6.7
C 9.5
D 12.3
The height of the pole, to the nearest tenth of a foot is given by: Option B: 6.7 feet
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
How to use right triangles to find the height of the specified pole?Remember that we assume that pole is vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.
Referring to the attached figure below, we get:
Length of the rope = length of AC = |AC| = 8 feetThe angle of elevation of rope from ground: 57°Using the tangent ratio, we get:
[tex]\sin(x) = \dfrac{\text{Length of perpendicular}}{\text{Length of hypotenuse}} = \dfrac{|AB|}{|AC|}\\\\|AB| = \sin(x) \times |AC|\\\\|AB| = \sin(57^\circ) \times 8 \approx 6.71 \approx 6.7\: \rm feet[/tex]
Thus, the length of the pole is approx 6.7 feet (option B).
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are the equations 2x - y = - 4 and 3x + y = -1 dependent, independent or neither
Answer:
From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}2x-y=-4\\ 3x+y=-1\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}2x-y=-4\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:6x-3y=-12[/tex]
[tex]\mathrm{Multiply\:}3x+y=-1\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:6x+2y=-2[/tex]
[tex]\begin{bmatrix}6x-3y=-12\\ 6x+2y=-2\end{bmatrix}[/tex]
[tex]6x+2y=-2[/tex]
[tex]-[/tex]
[tex]\underline{6x-3y=-12}[/tex]
[tex]5y=10[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}6x-3y=-12\\ 5y=10\end{bmatrix}[/tex]
solving 5y = 10 for y
[tex]5y=10[/tex]
Divide both sides by 5
[tex]\frac{5y}{5}=\frac{10}{5}[/tex]
simplify
[tex]y=2[/tex]
[tex]\mathrm{For\:}6x-3y=-12\mathrm{\:plug\:in\:}y=2[/tex]
[tex]6x-3\cdot \:2=-12[/tex]
[tex]6x-6=-12[/tex]
Adding 6 to both sides
[tex]6x-6+6=-12+6[/tex]
[tex]6x=-6[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{-6}{6}[/tex]
[tex]x=-1[/tex]
Therefore, the solution to the system of equations be:
[tex]x=-1,\:y=2[/tex]
From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.
f(x) = 2x3 + 6x2 – 5x – 3
g(x) = 3x – 4
Find (f - g)(x).
O A. (f - g)(x) = 2x3 + 6x2 – 2x – 7
O B. (f - g)(x) = 2x3 + 6x2 – 2x + 1
O c. (f - g)(x) = 2x3 + 6x2 – 8x – 7
O D. (f - g)(x) = 2x3 + 6x2 – 8x + 1
Answer:
D) is the answer
Step-by-step explanation:
It is taught in 5th class in India
Mark as Brainliest.
Because I am Indian and solving your question from India.
The correct answer is option D which is (f - g)(x) = 2x³ + 6x² – 8x + 1.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Given that:-
f(x) = 2x³ + 6x² – 5x – 3
g(x) = 3x – 4
The function (f-g)x will be calculated as follows:-
(f - g)(x) = f(x) - g(x)
(f - g)(x) = ( 2x³ + 6x² – 5x – 3 ) - ( 3x – 4 )
(f - g)(x) = 2x³ + 6x² – 5x – 3 - 3x + 4
(f - g)(x) = 2x³ + 6x² – 8x + 1
Therefore the correct answer is option D which is (f - g)(x) = 2x³ + 6x² – 8x + 1.
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What is an equivalent fraction to 2/7
4/14 is equivalent. This was found by multiplying both the numerator and denominator by 2.
Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -170 feet. Then she continued to hike down another 20 minutes at a different rate. Her change in elevation for this part of the hike was -260 feet. During which portion of the hike did she walk down at a faster rate?
PLEASE HELP
order the numbers from least to greatest -20 3/4 -14 3/4 -1/4 and -15 1/2
Answer:
3/4 3/4 1/2 1/4 -14 -15 -20
Step-by-step explanation:
Answer:
-20,-15,-14,-1/4,1/2,34
Step-by-step explanation:
Sean has a beginning balance of $328.15 in his account. He writes checks for the following amounts: $20.75, $43.58, $30.45, and $29.72. What is the new balance in Sean’s account?
Answer:
20.75+43.58+30.45+29.72= 124.5
328.15-124.5=
203.65.Answer:
198
Step-by-step explanation: