Given:
ABCD is a parallelogram, A(-3,-1), B(1,4), C(4,-1).
To find:
The x-coordinate of point D.
Solution:
Let the point D be (x,y).
We know that the diagonals of a parallelogram bisect each other. So, third midpoints are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
In parallelogram ABCD, AC and BD are two diagonals.
Midpoint of AC = Midpoint of BD
[tex]\left(\dfrac{-3+4}{2},\dfrac{-1+(-1)}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},\dfrac{-2}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},-1\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1}{2}=\dfrac{1+x}{2}[/tex]
[tex]1=1+x[/tex]
[tex]1-1=x[/tex]
[tex]0=x[/tex]
Similarly,
[tex]-1=\dfrac{4+y}{2}[/tex]
[tex]-2=4+y[/tex]
[tex]-2-4=y[/tex]
[tex]-6=y[/tex]
The coordinates of point D are (0,-6).
Therefore, the x-coordinate of point D is 0.
I need help on number 26
Answer:
The number of required shelves is 5
You have to find the HCF of 45, 105, and 75.
How many digits are in 385,604 ?
Answer:
6
Step-by-step explanation:
because 385,604 there is 6 digits
The circle graph shows the results of a survey about favorite hobbies. A total of 1,000 people
were surveyed.
Favorite Hobbies
8%
Scrapbooking
24%
Playing Sports
16%
Collecting
22%
Cooking
12%
Reading
18%
Traveling
a. How many selected traveling as their favorite hobby?
Answer:
180 people
Step-by-step explanation:
Total of people surveyed = 1,000
% of people that selected travelling as their favorite hobby = 18 %
Number of people that selected travelling = % that selected travelling of 1,000
= 18% of 1,000
= 18/100 × 1,000
= 180 people
Therefore, 180 people selected travelling as their favorite hobby.
If a bakery produces 1,215 cupcakes during a 9 hour shift, what is the production rate of cupcakes per hour?
Answer:
135
Step-by-step explanation:
Answer:
135 cupcakes
Step-by-step explanation:
You would do 1,215 divided by 9 to get your answer. So the answer would be 135 cupcakes.
Amir has 5 cups of water. He uses it to water 12 plants. Each plant gets
the same amount of water. How much water does each plant get?
Answer:
5/12 cup of water per plant
On a certain hot summer's day, 321 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $634.25. How many children and how many adults swam at the public pool that day?
Answer:
31 children and 290 adults
Step-by-step explanation:
Let a = number of adults and c = number of children.
a + c = 321
2a + 1.75c = 634.25
Multiply both sides of the the first equation by -2 and add it to the second equation.
-2a - 2c = -642
(+) 2a + 1.75c = 634.25
--------------------------------------
-0.25c = -7.75
Divide both sides by -0.25
c = 31
Use the first equation to find a.
a + c = 321
Substitute 31 for c.
a + 31 = 321
Subtract 31 from both sides.
a = 290
Answer: 31 children and 290 adults
Which graph shows the solution to the following system of inequalities?
{x - y = 1
y - x = 1
The lines are parallel.
The lines are coinciding.
The lines intersect at (1, 0).
The lines intersect at (–1, 0).
I NEED HELP ASAP PLEASEEEE!!!!! Given the cube, what is the total surface area and volume?
Answer:
864
Step-by-step explanation:
144x6
Answer:
b
Step-by-step explanation:
Select all of the given trigonometric equations that are true statements. sin(180°) = cos(0°) cos(74°) = sin(16°) sin(20°) = cos(70°) sin(A°) = cos(90° - A°) sin(A°) = cos(180° - A°) cos(140°) = sin(40°)
Answer:
Cos 74°= Sin 16°
Sin 20°= Cos 70°
Sin A°=Cos (90°- A°)
Step-by-step explanation:
This is because the three pairs are complementary i.e they add up to 90° and in trigonometric ratios, complementary ratios are equal.
A wheel with radius 1 foot makes 1 revolution in 4 seconds. What is the linear velocity, in feet per second, of a point on the edge of the wheel? 4π 8π
Answer:
[tex]v=\dfrac{\pi}{2}\ ft/s[/tex]
Step-by-step explanation:
Given that,
A wheel with radius 1 foot makes 1 revolution in 4 seconds
We need to find the linera velocity of a point on the edge of the wheel. We know that, the linear velcity is given by :
[tex]v=r\omega[/tex]
Where
[tex]\omega[/tex] is angular velcocity,[tex]\omega=2\pi\ rad[/tex]
[tex]\omega=\dfrac{1}{4}\times 2\pi\\\\=0.5\pi\ rad/s[/tex]
So
[tex]v=1\times 0.5\pi\\\\v=\dfrac{\pi}{2}\ ft/s[/tex]
So, the linear velocity of the wheel is equal to [tex]\dfrac{\pi}{2}\ ft/s[/tex].
Answer:
pi/2
B
Step-by-step explanation:
Got it right on EG
Question 6
Simplify the following expression.
-3 + 4a - 3b + 2) - 5(2-a + 3b)
3. What is the axis of symmetry of the graph of function f(x) = x² - 6x – 1
Answer:
guihnijiop;kl;lkm
Step-by-step explanation:
Answer:
A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.
f(x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2)^2 - 5/4 => vertex = (-3/2, -5/4)
f(x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2)^2 - 21/4 => vertex = (3/2, -21/4)
f(x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3)^2 - 6 => vertex = (-3, -6)
f(x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3)^2 - 10 => vertex = (3, -10)
Therefore, f(x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.
Step-by-step explanation:
plz mark me as brainlist
helpppppppppppppppppppp
Answer:
c
Step-by-step explanation:
Use GCF and the distributive property to write equivalent
expressions.
A) 6x + 9y
B)3c +11c
Answer:
Step-by-step explanation:
Greatest common factor of 6x and 9y is 3.
6x + 9y = 3(2x + 3y)
:::::
Greatest common factor of 3c and 11c is c.
3c + 11c = (3+11)c
Translate this sentence into an equation.
54 is the sum of 15 and Jenny's age.
Use the variable j to represent Jenny's age.
Answer:
54= 15 + J
Step-by-step explanation:
j= 39
Please help I’ll give brainliest! Due today. I need Sin Z, Tan z, and Cos Z
Mr. Jamison bought a toaster oven that was originally priced at
$89. He received a 20% discount. What is the sale price of the
toaster oven?
please help
Answer: $71.20
Step-by-step explanation: 20% discount means 20% of the original price is subtracted from the original price, so to find 20% of the original price multiply 89 by 0.2 and you will get 17.8. Subtract the 17.8 from 89 and you get the answer, $71.20!
Graph the line.
Y= 4/3 x
Answer:
hope this helps :)
Step-by-step explanation:
4. The radius of a circle is 6 inches. What is
the area?
a. 18.84 in?
b. 37.68 in
c. 87.98 in
d. 113.04 in
2. Find the GCF of: - 4x^2 and 28x^3
Answer: 4x^2
Step-by-step explanation: Multiply that by -1 to get -4x^2 and multiply by 7x to get 28x^3
Find the measurement indicated. Round to the nearest tenth.
9514 1404 393
Answer:
22.015.030.0°137.0°Step-by-step explanation:
These are all Law of Cosine problems. A generic expression for the length of side 'c' opposite angle C, which is defined by sides 'a' and 'b' is ...
c² = a² +b² -2ab·cos(C)
The square root of this gives the side length:
c = √(a² +b² -2ab·cos(C))
Rearranging the equation, we can obtain an expression for the angle C.
C = arccos((a² +b² -c²)/(2ab))
These two formulas are used to solve the offered problems.
__
1) AC = √(13² +14² -2·13·14·cos(109°)) ≈ √483.506
AC ≈ 22.0
__
2) BC = √(7² +10² -2·7·10·cos(123°)) ≈ √225.249
BC ≈ 15.0
__
3) ∠B = arccos((24² +28² -14²)/(2·24·28)) = arccos(1164/1344)
∠B ≈ 30.0°
__
4) ∠B = arccos((6² +9² -14²)/(2·6·9)) = arccos(-79/108)
∠B ≈ 137.0°
What is the area of this figure? (I give brainliest!)
Answer:
726
Step-by-step explanation:
(22*25)+(16*11)=
550+176=
726
2.45 divided by 0.17 =
Its not 14.41176470588235
Answer:
0.06938775
Step-by-step explanation:
This is the correct answer.
Which expression is equivalent to ( + )?
Answer:
No entiendo que es lo que hay qué hacer
Missing length..Area 90mm to the second power with base at 10mm. What is the millimeters
Answer:
5
Step-by-step explanation:
Quinn correctly answered 72 questions on a test, getting a score of 80%. How many questions were on the test?
Answer:
90
Step-by-step explanation:
7.2.8 Scientists at the Hopkins Memorial Forest in western Mas- sachusetts have been collecting meteorological and environmen- tal data in the forest data for more than 100 years. In the past few years, sulfate content in water samples from Birch Brook has averaged 7.48 mg/L with a standard deviation of 1.60 mg/L. a. What is the standard error of the sulfate in a collection of 10 water samples
Answer:
The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 1.60 mg/L.
This means that [tex]\sigma = 1.6[/tex]
Collection of 10 samples:
This means that [tex]n = 10, s = \frac{1.6}{\sqrt{10}} = 0.506[/tex]
The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
An aircraft seam requires 29 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 23% of all seams need reworking, what is the probability that a rivet is defective
Answer:
0.9995 = 99.95% probability that a rivet is defective
Step-by-step explanation:
For each rivet, there is only two possible outcomes. Either they are defective, or they are not. Rivets are defective independently of one another, each with the same probability, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
An aircraft seam requires 29 rivets.
This means that [tex]n = 29[/tex]
23% of all seams need reworking
This means that [tex]p = 0.23[/tex]
What is the probability that a rivet is defective?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{29,0}.(0.23)^{0}.(0.77)^{29} = 0.0005[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0005 = 0.9995[/tex]
0.9995 = 99.95% probability that a rivet is defective
Write down an irrational number with a value between 6 and 7.
Answer:
Three irrational numbers between 6 and 7 are
i )6.2020020002...
ii) 6.5010010001....
iii)6.9010010001.... etc.
•••♪
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
3 irrational numbers with a value between 6 & 7 can be :-
6.101001000....6.533533353333....6.122122212222...