Answer:
Let’s take a point each on the x, y, and z-axis as follows:
A (1, 0, 0) on x-axis
B (0, 1, 0) on y-axis and
C (0, 0, 1) on z-axis
unit vector
So, we have
|OA→| = 1 , |OB→| = 1, and |OC→| = 1
These vectors OA→, OB→, and OC→, each having magnitude 1 are Unit Vectors along the axes OX, OY, and OZ respectively. They are denoted by i⃗ , j⃗ , and k⃗ as shown in Fig. 1 above.
Step-by-step explanation:
use the quadratic formula to solve 4x²-9x=2x²-2x-4
[tex]4x^2-9x = 2x^2 -2x -4\\\\\implies 4x^2 -9x -2x ^2 +2x +4 =0\\\\\implies 2x^2 -7x +4=0\\\\\text{Apply quadratic formula,}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case,} ~a =2, b = -7 ~ \text{and}~ c =4\\\\\\x =\dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 4}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{17}}4\\\\\\\text{Hence,}~ x = \dfrac{7 +\sqrt{17}}4~ \text{and}~x = \dfrac{7 -\sqrt{17}}4[/tex]
URGENNTTT PLEASE ILL GIVE 50
Take Triangle ABC, A(2,-1), B(1,4) and C(-2,2). Do
the series of mappings to find A'B'C'.
First translate
it 3 units to the right and 2 units up, next reflect
about the x-axis, and finally rotate 180 degrees.
Answer:
(3-2)
Step-by-step explanation:
Write the sphere in standard form. 4x2 + 4y2 + 4z2 − 24x + 16y = 1
Answer:
(x -3)^2 +(y +2)^2 +z^2 = 13.25
Step-by-step explanation:
Divide by 4 and complete the squares.
x^2 -6x +y^2 +4y +z^2 = 1/4
(x^2 -6x +9) +(y^2 +4y +4) +z^2 = 13 1/4
(x -3)^2 +(y +2)^2 +z^2 = 13.25
Indira was measuring the length of her school's hallway. The first part of the hallway
was 132 inches long. The next part was 3 yards long. How long is the hallway in
feet?
Answer:
132 in /12 in/ft + 3 yd(3ft/yd) = 11 + 9 = 20 ft
Step-by-step explanation:
Answer:
20 ft
Step-by-step explanation:
12 inches = 1 foot
12 : 1 = 132 : y
[tex]\frac{132:y}{12:1}[/tex]
12 × y = 132 × 1
12y = 132
12y ÷ 12 = 132 ÷ 12
y = 11
11 ft
1 yard = 3 feet
1 : 3 = 3 : y
[tex]\frac{1:3}{3:y}[/tex]
1 × y = 3 × 3
1y = 9
y = 9
9 ft
11 ft + 9ft = 20 ft
lines that meet each other at a right angle are called ____
Answer: Perpendicular
Explanation:
One example of a pair of perpendicular lines would be having one horizontal line and one vertical line. They form a right angle which is 90 degrees.
Answer:
Perpendicular lines
Step-by-step explanation:
I think that when two lines meet each other in right angle it ie calledDivide 5.6 by 0.7 the quotient is what ?
the marked price of a table fan is Rs 1400 and 10% discount is allowed on it. Find it's cost with 15%VAT.
Answer:
marked price=1400
discount=10%
VAt= 15%
selling price=?
Now
we know that,
sp= mp - discount%of mp
1400- 10% of 1400
1400 - 10÷100* 1400
1400
Could someone help me solve this please? With explanation?
Answer:
x=109 degrees
Step-by-step explanation:
By alternate interior angles, the measure of angle ADE is the same as that of EAB, both of which are 38.
Because ADE is an isosceles triangle, the measure angle EAD is equal to that angle EDA; let that measure be x.
Because the angles of a triangle add up to 180, x+x+38=180 -> 2x+38=180 -> 2x=142 -> x=71
That means that angle EDA is 180 degrees
Because x is supplementary to angle EDA, the measure of angle x is 180-71=109 degrees
which of the following is NOT a rational number, -n its like on top of it, -4/7, 3/5 or 2/3
Step-by-step explanation:
i am very sorry but I don't know the answer
Select All equivalent expressions to 4( x + 2)
Answer:
3x 3-x and 3+x
are the following expressions equivalent 5(2z+3) and (5x2)+(z+3)
Answer: yes they are
Step-by-step explanation:
someone pleaseeee answer!!!
Answer:
7.79
Step-by-step explanation:
in 30, 60, 90 triangle, hypotenuse is equal to "2x", shortest length is equal to "x" and second longest is equal to "x × square root of 3". hope this helps
expand and simplify
5(3y+2)+5(5y+2)
Answer:
Step-by-step explanation:
15y + 10 + 25y + 10
Answer:
Solution here,
Step-by-step explanation:
For simplify
First multiply the terms inside the brackets with the term outside the bracket i.e 5.
5(3y+2)+5(5y+2)
15y+10+25y+10
35y+20
What is the distance between points A and B?
A. 1/3
B. 1/2
C. 1 1/3
D. 1 1/2
Answer:
A. 1/3
Step-by-step explanation:
From 1 to ___, ____, and 2 is half and half that would be 2 and a half. the only solution would be 1/3
Answer:
boom
Step-by-step explanation:
ALOT OF POINTS FOR THIS ONE
Admission to the state fair is $12, and each ride ticket costs $3.50. Write an
expression to represent the situation and explain what the variable means.
3.50t + 12 where t represents the number of ride tickets
3.50a + 12 where a represents the cost of admission
12a + 3.50 where a represents the cost of admission
12t + 3.50 where t represents the number of ride tickets
Answer : 3.50t + 12
Step - by - step explanation :
the reason why I think the answer is " 3.50t + 12 " is because . . . since the admission to the state farm is only ONCE - there doesn't need to be a variable there to tell us that it MIGHT repeat more than once. and because we don't know how many ride ticket will be purchased - there is a variable there to tell us unknown.
please help asap!!!!!!!!
Answer:
$3192.5.
Step-by-step explanation:
First $3000 tax is 3000 * 0.02 = $60.
Second $2000 tax is 2000 * 0.03 = $60.
Third $12000 tax is 12000 * 0.05 = $600.
Last $43,000 tax is 43000 * 0.0575 =$2472.5
Total income tax = $3192.5.
x^2+2x+8=0, Find x?aaaaaaa
Lashonda finished a race in 5 minutes. How many seconds is this
Answer:
300 seconds
Step-by-step explanation:
There are 60 seconds in a minute. If there are 5 minutes, you have to multiply 5 by 60.
5 x 60 = 300
-hope it helps
Answer:
360 sec
Step-by-step explanation:
this is because 60sec is one mintute
so 60x5= 360
What is the answer to this : Simplify 4 4128
Answer:
1032/1
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 4128 and 4 is 4
Divide both the numerator and denominator by the GCD
4128 ÷ 4
4 ÷ 4
Reduced fraction:
1032
1
Therefore, 4128/4 simplified to lowest terms is 1032/1.
Try changing these improper fractions to mixed numbers.
16/5?
( teach me how to solve this please!)
Answer:
3 1/5
Step-by-step explanation:
The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):
As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as
3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)
mom left $5.00 for his 7 children. how much did each child receive
a.0.17
b.0.70
c.17
d.71
please answer it correctly.
Answer:
.71
Step-by-step explanation:
Answer:
B. 0.70
Step-by-step explanation:
Just divide the total amount of money by the total amount of people.
5/7=0.71428...
if you round up correctly, you get 0.70; thus, it is B.
Also, his is for he, mom is a she, so use her instead of his...
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). (a) If a single student is randomly selected, find the probability that the sample mean is above 500. (b) If a sample of 35 students are selected randomly, find the probability that the sample mean is above 500. These two problems appear to be very similar. Which problem requires the application of the central limit theorem, and in what way does the solution process differ between the two problems?
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.281 = 28.1% probability that the sample mean is above 500.
b) 0.0003 = 0.03% probability that the sample mean is above 500.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 430, hence [tex]\mu = 430[/tex].The standard deviation is of 120, hence [tex]\sigma = 120[/tex].Item a:
The probability is the p-value of Z when X = 500, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 430}{120}[/tex]
[tex]Z = 0.58[/tex]
[tex]Z = 0.58[/tex] has a p-value of 0.719.
1 - 0.719 = 0.281
0.281 = 28.1% probability that the sample mean is above 500.
Item b:
Sample of 35, hence [tex]n = 35, s = \frac{120}{\sqrt{35}}[/tex]
Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{500 - 430}{\frac{120}{\sqrt{35}}}[/tex]
[tex]Z = 3.45[/tex]
[tex]Z = 3.45[/tex] has a p-value of 0.9997.
1 - 0.9997 = 0.0003
0.0003 = 0.03% probability that the sample mean is above 500.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Beatrice has two coins. The first coin is fair and the second coin is biased. The biased coin comes up heads with probability 2/3 and tails with probability 1/3. Beatrice selects one of the two coins at random and flips the selected coin 4 times. The result is HHTH. What is the probability that the fair coin was selected?
Help me pllllllllllease! I have only got 2 minutes!
When I divide an integer by 15, the remainder is an integer from 0 to 14. When divide an integer by 27, the remainder is an integer from 0 to 26. For instance, if the integer is 100 then the remainders are 10 and 19, which are different. How many integers from 1 to 1000 leave the same remainders after division by 15 and after division by 27?
Answer:
Two minutes for what???
Determine if the two triangles are congruent. If they are, state how you know
Answer:
yes the two triangles are congruent by the SSS theorum.
Step-by-step explanation:
it is given that two of the sides are congruent. they also share a side making that side also congruent. so, all three sides are equal, making the two triangles congruent by SSS/side-side-side theorum.
Steve checked out a book and a video from the local library. They were three days overdue when he returned them. The fine was 15 cents for each day the book was overdue, and 25 cents for each day the video was overdue. How much did Steve owe?
Answer:
1.20 or 120 cents
Step-by-step explanation:
First, we need to calculate the total due for the book. 15 cents(3 days) = 0.45
Next, we need to calculate the total due for the video. 25 cents(3days) =0.75
0.75+0.45=1.2 dollars, or 120 cents
Cho ma trận 4 1 21 0 13 2 1A= −−−−Tính 25AI−Câu 2(3điểm)Tìm ma trận nghịch đảo của ma trận sau−=123020112ACâu 3(3điểm)Giải hệ phương trình=+−−=+−=−+02347213321321321xxxxxxxxxCâu 4(1điểm)Giải và biện luận hệ phương trìnhsau theo m1 2 31 2 31 2 3222 2 6 62 3 4 5xx xxxxxxxm− + =− + − = −− + = +HẾT.
Hi can you translate into English then I would be happy to help
What is the slope of the function?
–10
- 5
5
10
Answer:
?
Step-by-step explanation:
what is the function?
a slope going up means it is positive and a slope going down means it is negative
X=[-1,+∞),Y=R,f(x)=y sao cho y^2-2y=x∀x∈X
Answer:
30
Step-by-step explanation:
sh well cm to cm et FL to
Can anyone please help? im running out of time and im so confused.
Answer:
x=8
Step-by-step explanation:
x+x+5=x+x+x-3
2x+5=3x-3
Subtract 2x from both sides.
5=x-3
Add 3 to both sides.
8=x
-hope it helps