The magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
For given question,
Let J(-6, -4) = (x1, y1) and
K(-10,-4) = (x2, y2)
By distance formula, the magnitude of vector is,
[tex]|\vec{JK}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec{JK}|=\sqrt{(-10+6)^2+(-4+4)^2}\\\\ |\vec{JK}|=\sqrt{(-4)^2}\\\\ |\vec{JK}|=4[/tex]
To find the direction of the vector JK:
[tex]tan\theta=\frac{y_2-y_1}{x_2-x_1} \\\\tan\theta=\frac{-4+4}{-10+6}\\\\ tan\theta=0\\\\\theta=0^{\circ}[/tex]
However, the angle is in the fourth quadrant, so we add 360° to obtain a positive angle.
Thus, 0° + 360° = 360°
Therefore, the magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
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Solve each equation for y .
(3/4)y=15 x
After solving the equation, y = 20x is the value of y in (3/4)y=15 x
⇒ (3/4)y=15 x
⇒ y = 15x/(3/4)
⇒ y = 20x
How to solve an equation?To solve Linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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What is the value of 4x² + 2x - 1 when x = 3/4 ? Express the answer as a decimal.
The answer is an decimal form is 2.75
In the given Statement is:
What is the value of 4x² + 2x - 1 when x = 3/4 ?
Express the answer as a decimal.
Let's Come to the solution:
4x² + 2x - 1 __(1)
Now put the value of x = 3/4 in above equation:
4 (3/4)² + 2 (3/4) - 1
Solve the equation, and get the answer
4 x (9/16) + 3/2 - 1
9/4 + 3/2 - 1
Taking the L.C.M
= [tex]\frac{9+6-4}{4}[/tex]
= 11/4
= 2.75 is the answer
Hence, The answer is an decimal form is 2.75
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A certain species of fish costs $5.49 each. You can spend no more than $30. How many of this type of fish can you buy for your aquarium?
Suppose f(x)=2 x-5 and g(x)=|-3 x-1| Find the value. g(2)-f(0)
Suppose f(x)=2 x-5 and g(x)=|-3 x-1| Find the value. g(2)-f(0)
g(2)- f(0) = 12
Given:
f(x)=2 x- 5
g(x)=|-3 x-1|
To find g(2), substitute x=2 in g(x).
g(x)=|-3 x-1|
g(2)=|-3 (2)-1|
=|-6-1|
=|-7|
g(2) = 7
To find f(0), substitute x=0 in f(x).
f(x)=2 x- 5
f(0)=2(0)- 5
f(0) = -5
Now, g(2)-f(0) =7-(-5)
=7+5
=12
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Write in point-slope form an equation of the line through each pair of points. (-10,3) and (-2,-5)
The equation of the line in point-slope form, which passes through the pair of points located at (-10 , 3) and (-2 , -5), is y - 3 = -(x + 10).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-10 , 3) and (-2 , -5).
m = (y2 - y1)/(x2 - x1)
m = (-5 - 3)/(-2 - -10)
m = -8/8
m = -1
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -1 and (x1 , y1) = (-10 , 3)
(y - 3) = -1(x - -10)
y - 3 = -(x + 10)
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2. Amirah, Huixian and Priya make a total of 1530 toys in the ratio 12: 16:17.
(ii) the amount of money Priya earns if she is paid $1.65 for each toy.
Answer:
$953.70
Step-by-step explanation:
sum the parts of the ratio, 12 + 16 + 17 = 45 parts
divide the total number of toys by 45 to find the value of one part of the ratio.
1530 ÷ 45 = 34 , then
Priya makes 17 × 34 = 578 toys
she is paid $1.65 per toy, so is paid
578 × $1.65 = $953.70
the product of two consecutive number is 18 more than 8 times a number
Using algebra, The product of two consecutive numbers is 18 more then 8 times a number
What is Algebra ?Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics
The two consecutive numbers are :
x and x+1
x(x+1) = 8(x+1) + 18
x^2 + x = 8x + 8 + 18
x^2 + x = 8x + 26
x^2 + x - 8x - 26 = 0
x^2 - 7x - 26 = 0
Substitute a=1,b=−7 and c=−26 into the quadratic formula
- B ± √ B2-4AC
x = ————————
2A
Accordingly, B^2 - 4AC = 49 - (-104) = 153
Applying the quadratic formula :
7 ± √ 153
x = —————
2
x = ( 7 ± 3 × 4.123 ) / 2
Two real solutions:
x =(7+√153)/2=(7+3√ 17 )/2= 9.685
or:
x =(7-√153)/2=(7-3√ 17 )/2= -2.685
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rewrite each fraction
A. 5/20
B. 9/25
C. 6/7 - 2/5
Solve each system by elimination.
2x - 3y = -1 3x + 4y = 8
The solution of the given system of equations is (20/17, 19/17)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
2x - 3y = -1 ...... (1)
3x + 4y = 8 ...... (2)
To be able to use the elimination method, multiply equation (1) by 3 and equation (2) by 2.
2x - 3y = -1 (⨉3)
⇔ 6x - 9y = -3 .........(3)
3x + 4y = 8 (⨉2)
⇔ 6x + 8y = 16 .........(4)
Substract equation (3) from (4)
6x + 8y = 16
6x - 9y = -3 –
17y = 19
y = 19/17
Substitute y = 19/17 into equation (1)
2x - 3y = -1
2x - 3(19/17) = -1
2x - 57/17 = -17/17
2x = (-17 + 57) / 17
2x = 40/17
x = 20/17
Thus, the solution is (20/17, 19/17)
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This can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days. how many phone calls should she expect after a week?
From the given equation y = 30(0.92)d, she should expect 193 phone calls after a week.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "="..
If the number of phone calls she should expect can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days, then we can calculate the expected amount phone calls after a week.
To determine how much phone calls she should expect after a week, substitute the value of d.
y = 30(0.92)d
where d = 1 week = 7 days
y = 30(0.92)(7)
y = 193.2
Rounding off to the nearest whole number,
y = 193
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When placed in the box below, what expression will complete an example of the commutative property of addition 7(2+9)= ?
The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.
Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition
A + B = B + A Which is Commutative property of addition
A.B = B.A, which is a commutative property of multiplication.
Distributive property is A(B+C) =AB+AC
The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.
from the given data 7(2+9) =7*2+7*9
=14+63
=77
Now, we can clear that 7(2+9) =7(9+2)
Hence, the expression for commutative property of addition is A(B+C) = AB+AC.
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Write a flow proof.
Given: ΔQ R S /RT is isosceles with QR ≅ SR.
RT bisects QS at point T .
Prove: QRT ≅ ΔS R T
We came to the conclusion that ΔQRT ≅ ΔSRT is under the side-side-side (SSS) condition.
What accurately does "triangle congruency" mean?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: ΔQRS/SRT is isosceles with QR ≅ SR; RT bisects QS at point T.
To prove: ΔQRT ≅ ΔSRT
QR = SR = GivenQT = QS = Given: (RT bisects QS at point T)RT = RT = Common baseSo, we can say that ΔQRT ≅ ΔSRT under SSS condition.
Therefore, ΔQRT ≅ ΔSRT is congruent under SSS condition.
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Please help if you can
Solve the equation
W^2+2w-15=0?
Answer:
w = 3,−5
Step-by-step explanation:
If ur solving for w then that i presume.
4. A conveyor belt moves at a constant rate
of 12 feet in 3 seconds. A second conveyor
belt moves 16 feet in 4 seconds. guys help !!!!
Solution :
Yes, the conveyors are in a proportional relationship.
Given,
A conveyor belt moves at a constant rate of 12 feet in 3 seconds.
A second conveyor belt moves 16 feet in 4 seconds.
There is a proportional relationship if the ratios of each pair of values are the same.
- First conveyor belt
12 feet in 3 seconds.
Ratio = 12 / 3 = 4
- Second conveyor belt
16 feet in 4 seconds.
Ratio = 16 / 4 = 4
Ratios are the same.
4 = 4
Thus the conveyors are in a proportional relationship.
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A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Education and Health Services - All Employees, 2000-2009
A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.
The number of new jobs gained is 2,842.
How many new jobs are gained?A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis.
Percentage can be described as a fraction of an amount expressed as a number out of hundred. The sign used to represent percentage is %.
Percentage increase from 2009 to 2016 = percentage increase x number of employees in 2009
14.8% x 19,200
0.148 x 19,200 = 2,842
Here is the complete question:
A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
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Answer:
c. 16,273,200
Step-by-step explanation:
Edge 2022
Find the first five terms of each sequence. a n =-n²+2 n
The first five terms of the sequence. an=n2 +2 are 3, 6, 11, 18 and 27.
The sequence is given as n² + 2.
The first term will be:
= n² + 2 = 1² + 2 = 1 + 2 = 3
The second term will be:
= n² + 2 = 2² + 2 = 4 + 2 = 6
The third term will be:
= n² + 2 = 3² + 2 = 9 + 2 = 11
The fourth term will be:
= n² + 2 = 4² + 2 = 16 + 2 = 18
The fifth term will be:
= n² + 2 = 5² + 2 = 25 + 2 = 27
Therefore, the first five terms of the sequence. an=n2 +2 are 3, 6, 11, 18 and 27.
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7) in one week, you earned $75.00 at your afterschool tutoring job. after working 8 more hours the following week, you had a total of $195.00. a) how much do you make per hour as a tutor?
Solving for the rate, you make $15 per hour as a tutor.
Rate is defined as the ratio between two quantities of different units.
Let x = rate
n = total amount you've earned = $195.00
t = time you've worked = 8 hours
If in one week, you earned $75.00 at your afterschool tutoring job, and after working 8 more hours the following week, you had a total of $195.00, then we can express this as
n = xt + $75.00
Substitute the values to solve the rate, x.
n = xt + $75.00
$195.00 = x(8 hours) + $75.00
8hours (x) = $195.00 - $75.00
8hours (x) = $120.00
x = $15/hr
rate = $15 per hour
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Find the volume of the candle in Exercise 4 . Round to the nearest tenth if necessary.
The volume of the candle is 36.9 cubic inches.
Given that the candle is in a circular pillar shape. That is it is in cylindrical shape.
Height of the candle, h = 6 inches
Width of the candle = Diameter of the base circle = 2.8 inches
Radius of the circle, r = 2.8/2 = 1.4 inches
We need to calculate the volume of the cylindrical candle.
Volume of a cylinder = Area of the base circle x height of the cylinder
Therefore, volume of the candle, V = [tex]\pi r^2 h[/tex]
= 3.14 x 1.4 x 1.4 x 6
= 36.9264
= 36.9 cubic inches
The question is incomplete. Find the complete question below:
A circular pillar candle is 2.8 inches wide and 6 inches tall. Find the volume of the candle. Round to the nearest tenth if necessary.
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Refer to ®N . If CN = 8 centimeters, find D N .
CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.
What is a circle?A circle is defined as the collection of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). A radius is any interval that connects a point on a circle to its center. Any two radii have the same length according to the definition of a circle.
A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "center."
A circle is a shape formed by all points in a plane that are at a given distance from the center. It is the curve traced out by a point moving in a plane so that its distance from a given point remains constant.
Here, CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.
The complete question is:
If CN = 8 centimeters, find DN.
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Evaluate each logarithm. log₃ 1/27
In mathematics, the logarithm is the reciprocal of a power. This means that the logarithm of a given number x is the exponent by which another fixed number (the base b) must be increased to get that number x. The simplest logarithm counts the number of times the same element occurs when multiplying repeatedly. The logarithm of x to base b is denoted by log b (x), or log b x without parentheses. Also, if confusion is impossible or the base doesn't matter, log x shows that even without an explicit base: B. In big O notation.
Solution:
Your problem → log (3,1/27)
log (3, (127)) =-3
Solution steps:
=log (3,127)
=log (3,0.037037)
=log3(0.037037)
=-3
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The age of a woman is four times the age of her daughter. Five years h:t 1ce, the age of the woman wili be three times the age of her daughter. What is the present age of the daughter
The present age of the daughter is 10 years old.
How to find the age of the daughter?The age of a woman is four times the age of her daughter.
let
x = age of the daughter
Therefore,
age of the woman = 4x
Five years later, the age of the woman will be three times the age of her daughter.
Therefore,
4x + 5 = 3(x + 5)
4x + 5 = 3x + 15
4x - 3x = 15 - 5
x = 10
Therefore, the present age of the daughter is 10 years old.
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53(2x−6)+18=23(x+3)−4.
Answer:
365/83
Step-by-step explanation:
Distribute where we can
106x - 318 + 18 =23x + 69 - 4
Get variables on one side and constants on the other
106x - 23x = 65 + 300
Do the math
83x = 365
Divide both sides by 83
365/83
Answer:
x = 365/83
Step-by-step explanation:
53(2x−6)+18=23(x+3)−4
106x-318+18=23x+69-4
106x-23x=69-4+318-18
83x = 365
x = 365/83
There is a number such that for times the number plus 3 is equal to 19. Find the number
Answer:
4
Step-by-step explanation:
let the number be n then four times the number is 4n and
4n + 3 = 19 ( subtract 3 from both sides )
4n = 16 ( divide both sides by 4 )
n = 4
then the number n is 4
If w = 22, what is the value of 4w − 12?
Answer: 76
Step-by-step explanation:
4 * 22 = 88
88-12 = 76
sustitucion de 18-3x=9
Answer: x=+9
Step-by-step explanation:
18=3x-9 18-(3x-9)=0 3x+9+18=0 -3x+27=0
-3x=-27
x=-27/-3
x=+9
Hope this helps! :) Have a great day! ^-^
Answer:
x=3
Step-by-step explanation:
18-3x=9
-18 -18 Subtract 18 from both sides of the equation to leave 3x by itself.
3x=9
/ /
3 3 Divide both sides by 3 to isolate x.
x=3 Final answer.
Why is the slope of a vertical line undefined.
The slope of a line can be positive, negative, zero, or undefined. The horizontal line does not rise vertically (y1 − y2 = 0), so the slope is zero, but the vertical line does not extend horizontally (that is, x1 − x2 = 0), so the slope is undefined. As mentioned above, the horizontal line has zero slopes. This does not mean that the horizon has no slope. Since the horizontal line is m=0, it is represented symbolically by the expression y=b. Functions defined by horizontal lines are often called constant functions. The slope of the vertical line is undefined. Any two points on the vertical line have the same x-coordinate, so the gradient cannot be computed as a finite number according to the equation
M=(y2-y1)/(x2-x1)
This is because division by zero is an undefined operation.
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Multiple the question bellow
Answer:
1
Step-by-step explanation:
We have to convert the whole number into an improper fraction :
4 = 4/1
Now we multiply the numerators together and the denominators together :
4 × 1 = 4
1 × 4 = 4
Our new fraction is 4/4 = 1
Hope this helped and have a good day
Determine the slope of the line that contains the given points.
C(3,1), D(-2,1)
The slope of the line containing (3,1) and (-2,1) is Zero(0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = 1 , [tex]y_{1}[/tex] = 1 , [tex]x_{2}[/tex] = -2 , and [tex]x_{1}[/tex] = 3 .
On substituting the values of variables in equation1, we will get
m = ( (1)-(1) ) / ( (-2)-(3) ) = (0/(-5)) = 0.
As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
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please help i'm stuck
Answer:
- 1 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
substitute x = - 5 into f(x)
f(- 5) = [tex]\frac{1}{4}[/tex] × - 5 = - [tex]\frac{5}{4}[/tex] = - 1 [tex]\frac{1}{4}[/tex]
