The column vector is discussed below.
What is column vector?In order to write a vector as a column vector: Work out the horizontal component ( x component). Work out the vertical component ( y component). Write the column vector.
Given:
a + b- c
So, If the number is positive, the direction is to the right.
If the number is negative, the direction is to the left.
Also, If the number is positive, the direction is upwards.
If the number is negative, the direction is downwards.
So, according to that 'a' will be in right ( upward) direction and 'b' also be in right ( upward) direction.
Then, 'c' is negative in left ( downward ) direction.
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Marty placed $4000 into an account earning 4% simple interest. At the end of the year he moved the total amount to a new account earning 5% interest. Determine the amount of money Marty would have at the end of the second year.
Simple interest , 4368 is the amount of money Marty would have at the end of the second year.
What does the term "simple interest" mean?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.P = $4000 R = 4% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4000 * 4 * 1}{100}[/tex] = 160
So, the total amount is ( 4000 + 160) = 4160
Second year
P = 4160 , R = 5% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4160 * 5 * 1}{100}[/tex] = 208
So, the total amount is ( 4160 + 208 ) = 4368
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For how many positive integers n, is 3^n+81 the square of an integer?
The number of positive integers n, that satisfy 3^n+81 the square of an integer is infinite.
How to illustrate the information?Based on the information given, let 3n + 82 = p².
Therefore, 3n = p² - 81
= (p - 9)(p + 9)
Let p = 3q.
3n = (3q - 9)(3q + 9(
= 9(q - 3)(q + 4)
n = 3(q - 3)(q + 3)
n > 0 ; q >= 4 for n = 4, 5, 6....
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A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856
How find the probability of the lot that will fail inspectionGiven data
p = 20%
sample drawn = 19 bulbs
20% of the bulbs in the lot are defective
n = 19
p = 20% = 0.20
if 20% of the bulbs are defective to find the non defective bulbs we solve as follows
q = 1 - p
= 1 - 0.20
= 0.80
Using binomial theorem,
[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]
[tex]= 1 - P ( x < 1 )[/tex]
[tex]= 1 - P ( X = 0)[/tex]
[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]
[tex]= 1 - 1 * 1 * 0.01441[/tex]
[tex]= 1 - 0.01441[/tex]
= 0.98559
= 0.9856 (to four decimal place)
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At 7:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 28270 ft. and is descending at the rate of 550 ft/min. Airplane #2 has an elevation of 5270 ft. and is climbing at the rate of 700 ft/min.
(1) Let
t
represent the time in minutes since 7:00 am, and let
E
represent the elevation in feet. Write an equation for the elevation of each plane in terms of
t
.
plane #1:
E
(
t
)
=
plane #2:
E
(
t
)
=
(2) At what time will the two airplanes have the same elevation?
t
=
minutes after 7:00 am
(3) What is the elevation at that time?
E
=
feet
Question HelpQuestion 25: Message Message instructor
Using linear functions, it is found that:
1. The functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.2. They will have the same elevation after 18.4 minutes.
3. At that time, the elevation is of 18,150 feet.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The initial heights are the intercepts.The rates are the slopes, climbing positive and descending negative.Hence the functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.They will have the same elevation when:
E1(t) = E2(t)
28270 - 550t = 5270 + 700t
1250t = 23000
t = 23000/1250
t = 18.4.
They will have the same elevation after 18.4 minutes.
This elevation will be of:
28270 - 550(18.4) = 18150.
At that time, the elevation is of 18,150 feet.
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Hello can someone please help
The correct statements for this problem are given as follows:
20. Plane N contains line l.
21. Point P lies in line l.
22. PQ lies on plane N.
23. Line l and line m are coplanar.
24. Line l passes through P and Q.
25. Line m and line l intersect at P.
26. Points P and Q are colinear.
What is each thing in this problem?From the graph, we have these following items:
Plane N.Lines m and l.Segment PQ.Points P and Q.For item 20, we have that:
Line l is on plane N, hence:
Plane N contains line l.
For item 21, we have that point P is on both lines, m and l, hence:
Point P lies in line l.
For item 22, we have that points P and Q are on the plane N, hence:
PQ lies on plane N.
For item 23, we have that the lines are on the same plane, hence:
Line l and line m are coplanar.
For item 24, we have that points P and Q are both on line l, hence:
Line l passes through P and Q.
From it, we can also solve item 26, as follows:
Points P and Q are colinear.
And for item 25, the two lines intersect at point P, hence:
Line m and line l intersect at P.
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10. 1.4810 irrational number
Answer:
List A: 2√2, 3√2, 4√2, …
List B: 2π, 3π, 4π, …
List C: 2log35, 3log35, 4log35, …
Step-by-step explanation:
from the graph of each parabola, determine whether the parabola opens upward or downward, and find the vertex, axis of symmetry, and range of the function. find the maximum and minimum value of the function and the intervals on which the function is increasing and decreasing. URGENT 20 POINTS!
A quadratic function is one that has the formula f(x)=ax2+bx+c, where a, b, c, and an are all real values and a 0 a 0. The conventional form of a quadratic function is this form.
The quadratic function's graph is a U-shaped curve known as a parabola.
Below is a graph of the equation y=x2y=x2; it is a parabola.
The parabola rises if a>0a>0 in f(x)=ax2+bx+cf(x)=ax2+bx+c. In this case, the vertex is the smallest or lowest point of the parabola.
The vertex of the y=x2y=x2 graph is (0, 0). (0,0).
The parabola opens downhill if a0a0 in f(x)=ax2+bx+cf(x)=ax2+bx+c is true. The maximal or highest point of the parabola in this instance is called the vertex.
The value of cc for an equation in standard form yields the graph's yy-intercept.
The axis of symmetry is the line that divides the parabola into two symmetric sections and runs through the vertex.
In the case of the graph y=ax2+bx+cy=ax2+bx+c, where a=0a=0, the equation for the axis of symmetry is x=b2ax=b2a.
The yy-axis, with x=0x=0, is the axis of symmetry in all of the graphs above. The axis of symmetry in the graphs below is different (marked in red.) As you can see, cc still provides the yy-intercept.
If you write a quadratic function like x=f(y)=ay2+by+cx=f(y)=ay2+by+c, instead of writing yy as a function of xx, you obtain a parabola with a horizontal axis of symmetry.
Hence, that the xx-intercept in this situation is cc. When aa is positive, the graph opens to the right; when aa is negative, it opens to the left.
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How to do domain and range
Answer:
bjuk
Step-by-step explanation:
ftftrtt987652123456789
Solve the equation.
Question 1, 9.3.1
-6y+6= -2(4y + 4)
Solve
Solution : y = -7
One Variable in the linear equation :
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equations in two variables, it has two solutions.
-6y+6= -2(4y + 4)
-6y = -8y -8 -6
-6y +8y = -14
2y = -14
y = -14/2
y = -7
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Michael is playing a game of chance in which he tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random.
Answer:
6 I belive it should land on 6
17x12 help what do it equal
Answer:
Step-by-step explanation:
17
12
-----
do 7 x 2
14
then carry the 1
2x1 is 2 plus the 1 from before. it becomes 3
then do 1 x 7 then 1 x 1 but with an extra zero
so it becomes
17
12
---------
34
170
---------
then add it all together
34+170=204
Answer: 17*12=204
Step-by-step explanation: because of G O O G L E
John's test grade is 5 points less than twice Ariana's test grade. If x represents Ariana's test grade, write an expression for John's test grade.
In linear equation, 2x - 5 is an expression for John's test grade.
What is linear equation in one variable?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Ariana's test grade = x
twice Ariana's test grade = 2x
then, John's test grade = 2x - 5
an expression for John's test grade = 2x - 5
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D(7,3) is the midpoint, (MP), of AB.
E(10, 4) is the MP of BC.
F(5,5) is the MP of AC
Find the coordinates of A, B, and C
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
Midpoint :
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
x= x1+x2/2
y=y1+y2/2
Now ,
D(7,3) is the midpoint of AB.
D (x',y') = (7,3)
vertex of A = (x1,y1)
vertex of B = (x2,y2)
x' = x1+x2/2
7 = x1+x2/2
14 = x1+x2 ...1
y' = y1+y2/2
3= y1+y2/2
6= y1+y2 .....2
E (x'',y'') = (10,4)
vertex of c = (x3,y3)
vertex of B = (x2,y2)
x''= x3+x2/2
y''=y3+y2/2
20= x3+x2 ....3
8 =y3+y2.......4
F (x''',y''') = (5,5)
vertex of c = (x3,y3)
vertex of A = (x1,y1)
10= x1 +x3 ...5
10 =y1+y3 .....6
For 1 & 3 & 5
14 = x1+x2 ...1
20= x3+x2 ....3
10= x1 +x3 ...5
Add all 1 & 3 & 5
44 = 2(x1+x2+x3)
22 = (x1+x2+x3) .....7
For 1 & 7
x3 = 8
For 3 & 7
x1 = 2
For 5&7
x2 = 12
For 2 , 4 & 6
6= y1+y2 .....2
8 =y3+y2.......4
10 =y1+y3 .....6
Add all 2 & 4 & 6
24 = 2 (y1+y2+y3)
For 2 & 8
y3 = 6
For 4 & 8
y1 = 4
For 6 & 8
y2 = 2
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
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Ken is playing with building blocks. He wants to put all 64 blocks into the same number of stacks. How many blocks could he put in each stack
Answer: He could put 8 blocks in 8 stacks
Step-by-step explanation:
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.
So we have:
Number of blocks = 64
Number of stacks = x
To find out how many blocks can be put in each stack, we can set up the following equation:
64 / x = y
where y is the number of blocks in each stack.
Solving for y, we get:
y = 64 / x
So if Ken wants to put all 64 blocks into the same number of stacks, he can put:
64 blocks in 1 stack
32 blocks in 2 stacks
16 blocks in 4 stacks
8 blocks in 8 stacks
4 blocks in 16 stacks
2 blocks in 32 stacks
1 block in 64 stacks
Therefore,
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
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What is the size of the sample space for
the outcomes of rolling two 20 sided
dice?
Step-by-step explanation:
So, the total number of joint outcomes (a,b) is 6 times 6 which is 36. The set of all possible outcomes for (a,b) is called the sample space of this probability experimentWhat are the two equations to set up to solve the equation
Answer:
X is 21 (3x = 3*7) and 3x - 2 = 19.Step-by-step explanation:
Solve for X:
3x - 2 = 19= 3*7Solve for 19:
3 * 7 - 2 = 19= 21 - 2 = 19= 1919 = 19.So 3x - 2 = 19 is (3 * 7) - 2 = 19.help meeeeeeeeeeeeeeee please !!
Answer: 59
Step-by-step explanation:
(2x+3) + 7 and 2x + (3+7)? Expressions equivalent
The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.
f(x) = 3(x2 – 8x) + 10
(StartFraction negative 8 Over 2 EndFraction) squared = 16
What is the function written in vertex form?
f(x) = 3(x + 4)2 – 6
f(x) = 3(x + 4)2 – 38
f(x) = 3(x – 4)2 – 6
f(x) = 3(x – 4)2 – 38
The function is written in vertex form the equation for is mathematically given as
f(x) = 3(x – 4)2 – 38
This is further explained below.
What is the function written in vertex form?Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.
y = 3(x² - 8x) + 10
We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:
y = 3(x² - 8x + 16 - 16) + 10
y = 3((x - 4)² ) - 48 + 10
y = 3(x - 4)² - 38
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Answer: option D
Step-by-step explanation:
Help ASAP! 25 Points! What theorem allows you to prove line f is parallel to line g? For what value of x is line f parallel to line g?
PLEASE FIND X FOR ME TOO :) Thank you if you help!
Answer:
Theorems are stated below
x = 6
Step-by-step explanation:
The following theorems can prove that 2 lines are parallel
Two lines are parallel if they’re cut by a transversal such that
Two corresponding angles are congruent.Two alternate interior angles are congruent.Two alternate exterior angles are congruent.Two same-side interior angles are supplementary.Two same-side exterior angles are supplementary.The two angles shown are corresponding angles. They are corresponding because each is in the same position left side) in its group of four angles.
Corresponding angles are equal
Therefore,15x + 9 = 21x - 27
Subtract 9 from both sides:
15x = 21x - 27 - 9
15x = 21x - 36
Subtract 21x from both sides
15x - 21x = - 36
-6x = 36
Divide by -6 both sides
-6x/-6 = 36/-6
x = 6
The two angles are
15x + 9 = 15(6) + 9 = 90 + 9 = 99°
and
21x - 27 = 21(6) - 27 = 126 - 27 =99°
And indeed they are equal
whats 26/7 as a mixed number
Answer:3 and 5/7
Step-by-step explanation:
2.12 rounded to the nearest hundedth.
Answer: 2.12
Step-by-step explanation:
it's in the hundredths place
2 . 1 2
ones tenths hundredths
In simplest terms, Adam can see a√b feet farther than Pam. a = , b =
It is recommended that the expressions
d = 400 - 256 and
d = 256 - 400 be considered when attempting to determine how much farther Adam can see to the horizon.
The calculation for the expression is as follows:Since, the eye-level height of Pam is 256 feet above sea level, whereas the eye-level height of Adam is 400 feet above sea level.
Therefore, the formula that indicates how much farther Adam can see to the horizon should be taken to be
d = 400 - 256 and
d = 256 - 400.
This expression may be found by subtracting 400 from 256.
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CQ
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.
Answer:
A= 2 B= 6
Step-by-step explanation:
the dude above me is wrong
Solve system of equations using substitution method
2x-3y=6
x + y = -12
work this out please
Answer:
1/16
Step-by-step explanation:
32= 2^5
Thus:
(2^5) ^-4/5
= (2)^ - 4
= (16) ^ - 1
= 1/16
chapter 7 /pt3
10.Find the value of each trigonometric ratio.
What lowest terms fraction equal to 15%
Answer:
3 / 20
Step-by-step explanation:
Take only after the decimal point part for calculation.
.15
Then, divide that value by 1.
.15
1
Multiply both numerator and denominator by 100 (because there are 2 digits after the decimal point so that is 102 = 100).
.15 × 100
1 × 100
=
15
100
;
To simplify
15
100
its lowest terms, find GCD (Greatest Common Divisor) for 15 & 100, which is 5. Here's How to Find GCD of 15 and 100?
15/5
100/5
After simplify or reduce the fraction.
3
20
HELP PLESSE i need to hrr it turned in 4 horus
Answer: 5358
Step-by-step explanation:
282
x 18
----------
2538
+282
-----------
5358
←
If a single fair die is rolled, find the probability of the following result.
An even number, given that the number rolled was 1.
Answer: so assuming this is a d6, it's 3/6
Step-by-step explanation:
on a d6, there are 6 sides (duh). three out of the six numbers are even, two four and six. so, three out of the six numbers you can roll are even.
esse rode his bike for 2 hours at a constant rate. During the first 1.5 hours, he rode 12 miles. How many miles did Jesse ride his bike during the last half hour? (Enter an exact number.)
mi
In the last half hour 4 miles did Jesse ride his bike.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Jesse rode his bike for 2 hours at a constant rate.
First 1.5 hours, he rode 12 miles.
According to given question we have
1.5 hours=12 miles
1 hours=12/1.5
0.5 hours=12*0.5/1.5
0.5 hours=4 miles
Therefore, in the last half hour 4 miles did Jesse ride his bike.
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