Answer:
Remember that a vector translation can be written as:
T(a, b)
And if we apply this to a random point, (x, y), the translation gives:
T(a, b)(x, y) = (x + a, y + b)
now, remember that a general line can be written as:
y = m*x + s
Then a point of that line can be written as: (x, m*x + s)
Then if we apply the translation to a point in the line, we get:
T(a, b)(x, m*x + s) = (x + a, m*x + s + b)
Here we have two lines:
2x - 3y - 1 = 0
2x - 3y + 5 = 0
First, let's rewrite both of these in the slope-intercept form:
y = (2/3)*x - 1/3
y = (2/3)*x + 5/3
Now let's assume that we apply a translation to the first line, that has points of the form (x, (2/3)*x - 1/3), such that we want to get points of the form:
(x, (2/3)*x + 5/3).
Then we must have:
T(a, b)(x, (2/3)*x - 1/3) = (x + a, (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).
Then we need to solve:
(x + a, (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).
This means that:
x + a = x
(2/3)*x - 1/3 + b = (2/3)*x + 5/3
From the first equation, we can see that a = 0
Now we can solve the second one to find the value of b.
(2/3)*x - 1/3 + b = (2/3)*x + 5/3
subtracting (2/3)*x in both sides, we get:
-1/3 + b = 5/3
b = 5/3 + 1/3
b = 6/3 = 2
b = 2
Then the vector translation is:
T(0, 2)
So it moves the whole line 2 units upwards.
The first term in an arithmetic sequence is 9 and the tenth term is 45. Use the first and tenth terms to find the sun of the first 10 terms. The equation of the sequence is an=4n+5
Answer:
270.
Step-by-step explanation:
If the first term = a and 10th term = a + 9d where d = the common difference.
a + 9d - a = 45 - 9
9d = 36
d = 4.
Sum of first 10 terms = (10/2)[2*9 + (10-1)*4]
= 5 * (18 + 36)
= 5 * 54
= 270.
If the right angle triangle LMN.
L=30°, MN = 4cm and diagonal LM.
Find the LM and LN.
convert solar days into minutes
Answer:
1 Solar day = 86,400 seconds (SI Base Unit)
1 day = 1,440 minutes
Step-by-step explanation:
If need anymore help just ask I'm not really good at explaining but I'll try just comment haha ☺️
f(4) = ______
If g(x) = 2, x = _____
Answer:
-11
0
Step-by-step explanation:
Jessica is traveling at a speed of 60 miles per hour in her truck. After 4 hours, how far will she have traveled?
Answer:
240 miles
Step-by-step explanation:
60*4=240
Answer: 240
Step-by-step explanation: If she is traveling 60 miles per hour you can multiply it by 4, which is 240.
Determine el radio vector del punto medio del segmento que se forma al unir los puntos (-8, 7) y (6, 3).
Es para hoy
Answer:
The radius vector is (-8, 7) and (-1 , 5).
Step-by-step explanation:
Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).
The end points are (- 8, 7) and (6, 3) .
The mid point is given by
[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]
So, the radius vector is (-8, 7) and (-1 , 5).
A shopkeeper sells house numbers. She has a large supply of the digits, 1, 2, 7, and 8, but no other digits. How many different three-digit house numbers could be made using only the digits in her supply?
Answer:
64.
Step-by-step explanation:
The digits used are 1 , 2, 7 and 8
To make a number of three digits, the digits are repeated.
To make the three digit number
The ones place is filled by 4 ways.
The tens place is filled by 4 ways.
The hundred place is filled by 4 ways.
So, the total number of ways to make a three digit number is 4 x 4 x 4 = 64.
Find the area of triangle ABC.
A. 35.92 units²
B. 43.79 units²
C. 21.39 units²
D. 22.91 units²
Answer:
[tex]\text{C. }21.39\:\mathrm{units^2}[/tex]
Step-by-step explanation:
The area of a triangle with sides [tex]a[/tex] and [tex]b[/tex] and angle [tex]\gamma[/tex] between them is given by [tex]A=\frac{1}{2}ab\sin \gamma[/tex].
Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as [tex]36.43^{\circ}[/tex]. Assign values:
[tex]a\implies 7.39[/tex] [tex]b\implies 9.75[/tex] [tex]\gamma \implies 36.43^{\circ}[/tex]Substituting these values into our area formula, we get:
[tex]A=\frac{1}{2}\cdot 7.39\cdot 9.75\cdot \sin (36.43)^{\circ},\\A=21.3938371858,\\A\approx \boxed{21.39\:\mathrm{units^2}}[/tex]
-9-13+2+13−9−13+2+13minus, 9, minus, 13, plus, 2, plus, 13.
me lo pueden resolver porfa es para mañana antes de la 12:59
Answer:
-21
Step-by-step explanation:
comments
A company has 500 computers that are used by its employees. A sample of 40 of these computers finds that 12 of them require an update to the printer driver. What is the best estimate of the percent of the company's computers that require an update to the printer driver
Answer:
I think the answer might be 30%
Step-by-step explanation:
The best estimate of the percent of the company's computers that require an update to the printer driver is 30%.
What is unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
According to the question
A company has 500 computers that are used by its employees. A sample of 40 of these computers finds that 12 of them require an update to the printer driver.
Using unitary method,
[tex]\frac{40}{12} =\frac{500}{x}[/tex]
Where x is the best estimate of the number of the company's computers that require an update.
x = [tex]\frac{12.(500)}{40}[/tex]
x = 150
To convert it into percentage,
[tex](\frac{150}{500} ).100[/tex]
= 30 %
Hence, the best estimate of the percent of the company's computers that require an update to the printer driver is 30%.
Find out more information about unitary method here
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Finding the missing length in a figure
Answer:
11
Step-by-step explanation:
because you have to add 5+6=11
what is the measure of angle A
Answer:
a = 53
Step-by-step explanation:
Start with d
The ends of d + 53 are diameter ends. That means that d + 53 is a right angle
d + 53 = 90
d = 90 - 53
d = 37
Next, find b. The end points of b are the same end points as for 53 degrees. B is the central angle of 53 which means b = 2 * 53
b = 106
c is the supplement of b
c + b = 180
b = 106
c + 106 = 180
c = 180 - 106
c = 74
The triangle containing a and c is isosceles because 2 of the 3 angles are opposite radii. The lowest angle is also a because it is opposite one of the radii.
a + a + 74 = 180
2a = 180 - 74
2a = 106
a = 106/2
a = 53
Hard to believe, but there it is.
Type the correct answer in the box. If necessary, use / for the fraction bar.
Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the center of dilation. Square A B C D is dilated to created square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub?
Answer:
The length of one side of the hot tub is 4.8ft
Step-by-step explanation:
Given
Shape: Square
[tex]k = 5[/tex] -- scale factor
[tex]B'C' = 24[/tex]
Required
Side length of ABCD (the hot tub)
From the question, we understand that
[tex]ABCD \to D_5 \to A'B'C'D[/tex] ABCD dilated by 5 to A'B'C'D
This implies that:
[tex]BC * 5 = B'C'[/tex] i.e. the sides of ABCD is multiplied by 5 to get A'B'C'D
So, we have:
[tex]BC * 5 = 24[/tex]
Divide by 5
[tex]BC = 4.8[/tex]
A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and two black marbles. If it lands tails, a marble is drawn from Box 2, which contains two white and two black marbles. Find P(black|coin fell tails).
Answer:
P(black|coin fell tails) = ¼
Step-by-step explanation:
Since a coin has a head and a tail, then probability of landing tail is;
P(tail) = ½
Now, if it falls tails, a marble is drawn from Box 2, which contains two white and two black marbles.
Thus, probability of getting a black marble is; 2/4 = ½
Thus;
P(black|coin fell tails) = ½ × ½ = ¼
Someone plz help me on this
Answer:
9²+x²=13²
81+x²=169
x²= 169-81
x²=88
X= 9.38
x=9.4[tex]x = \sqrt{88} [/tex]
when three times a certain number is subtracted from 5 the result is more than 9 find the range of the values of the number.
Answer:
] 14/3 ; ♾ [
Step-by-step explanation:
3x-5>9
3x>9+5
3x>14
x>14/3
wich make it ] 14/3 ; ♾ [
when three times a certain number is subtracted from 5 the result is more than 9 find the number.
Solution :Let us assume :
The number be x
Data :
A number is 3 times = 3x
Subtracted from 5
The result = 9
Henceforth, the equation we got is :
3x - 5 = 9Transposing 9 to the other side
3x = 14 x = 14/3Hence, the value of x is 14/3 respectively
The GCF of 10 and 18 is 6.
TRUE
FALSE
Answer:
False
Step-by-step explanation:
Because the gcf of 10 and 18 is 2
Answer:
False
Step-by-step explanation:
Any factor of a number must evenly devide into the number. 6 does not even divide into 10, so no. The GCF of 10 and 18 is 2.
Ashipment department on time ships 500 boxes per day. Approximately 97% of those shipments are shipped on time. The remaining 3% are shipped later. Approximately how many shipments are shipped later per day?
Answer:
15 boxes were shipped late
Step-by-step explanation:
late = 3% = 0.03
500 x 0.03 = 15 boxes
find formula of s in terms of a, b, cos(x)
Answer:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
Step-by-step explanation:
We want to find a formula for s in terms of a, b, and cos(x).
Let the point where s intersects AB be D.
Notice that s bisects ∠C. Then by the Angle Bisector Theorem:
[tex]\displaystyle \frac{a}{BD} = \frac{b}{AD}[/tex]
We can find BD using the Law of Cosines:
[tex]\displaystyle BD^2 = a^2 + s^2 - 2as \cos x[/tex]
Likewise:
[tex]\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x[/tex]
From the first equation, cross-multiply:
[tex]bBD = a AD[/tex]
And square both sides:
[tex]b^2 BD^2 =a^2 AD^2[/tex]
Substitute:
[tex]\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)[/tex]
Distribute:
[tex]a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x[/tex]
Simplify:
[tex]b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x[/tex]
Divide both sides by s (s ≠ 0):
[tex]b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x[/tex]
Isolate s:
[tex]b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x[/tex]
Factor:
[tex]\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x[/tex]
Therefore:
[tex]\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}[/tex]
Factor:
[tex]\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}[/tex]
Simplify. Therefore:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
Can anybody explain how you can use the absolute value to tell whether the sum of two integers is positive or negative
Giá Trị tuyệt đối của tổng hai số nguyên có hai kết quả là số âm và số dương.Nhưng Giá trị tuyệt đói luôn luôn ra kết quả là số dương nên ta cần kết quả là cả âm và dương khi phá dấu tuyệt đối. khi âm -dương =âm. khi dương- âm=dương
PLEASE HELP!!! geometry!
Answer:
A' (-3,12)
B' (9,6)
C' (-6,-6)
Answered by GAUTHMATH
I need help please!!!!
Insert seven rational numbers between 2 and 3.
Answer:
5/2, 7/3, 9/4, 11/5, 13/6, 15/7,17/8
Step-by-step explanation:
Answer:
2/1
2.5
2whole number6/4
on the number line, which of the following numbers below can be found on the right of 2.26??
A.2.30
B.-2.25
C.2.25
D.1.26
Answer:
2.25
Step-by-step explanation:
The lower number will always be on the right side unless its negative numbers , So the lower number is 2.25 , Why it isn't 1.26 is because its much far from 2.26 and so cannot be counted . Thanks
I don't understand plz help out
Step-by-step explanation:
V(-2,1)
U(1,3)
E(0,1)
the dilation is by 1/2 so multiply all numbers by a half, hope you pass!!
What is the volume of the solid? Let π=3.14
.
The volume of the solid as shown in the task content is; 2786.2cm³.
What is the volume of the solid?It can be obtained from the task content that the solid given is a Cone.
On this note, the volume of the cone can be evaluated by means of the formula;
V = (1/3)π r²h where(r =22/2 = 11 and h=22).
Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.
Read more on volume;
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) If a 480 pupils in a school are boys representing 80% of the school's enrolment . Find the total number of pupils in the school
Answer:
Total student= 600
Step-by-step explanation:
Let x be the number of students
[tex]x \times \frac{80}{100} = 480 \\ = 480 \times \frac{10}{8} \\ x = 600[/tex]
Brainliest please~
Answer:600
Step-by-step explanation:
by taking total number of pupils x
80/100×x=480
48000/80=600
x=600
The area of a trapezium is 6y⁵.
The sum of its parallel sides is 4y² .
Derive an expression for the perpendicular distance between the parallel sides.
================================================
Work Shown:
A = area = 6y^5
b1+b2 = sum of the parallel bases = 4y^2
h = unknown height, i.e. distance between the parallel sides
------
A = 0.5*h*(b1+b2)
6y^5 = 0.5*h*4y^2
6y^5 = 0.5*4y^2*h
6y^5 = 2y^2*h
2y^2*h = 6y^5
h = (6y^5)/(2y^2)
h = (6/2)*y^(5-2)
h = 3y^3
The parallel sides are separated by a distance of 3y^3 units.
What type of conic section is the following equation?
5x^2-y=12
Answer:
The conic section for the equation 5x^2 - y = 12 is parabola
