Approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
The perpendicular line to a point is the path that travels the shortest distance between them.
The equation for the indicated line is -x + 2y = 14, which can be expressed as the following in slope and intercept form:
-x + 2·y = 142·y = 14 + xy = 14/2 + x/2 = x/2 + 7y = x/2 + 7The y-intercept is 7, and the slope, m1, is 1/2.
As a result, the slope, m2, of the line perpendicular to the line y = x/2 + 7 (y = -x + 2y = 14) is m2 = -1/m1 = -1/(1/2) = -2.As a result, we know that the line from A(-1/4, 5) to the line -x + 2y = 14 has a slope of -2.Consequently, the line's equation is:
y - 5 = -2(x - (-1/4))y - 5 = -2·x - 1/2y = -2·x - 1/2 + 5 = -2·x + 9/2y = -2·x + 9/2Therefore, the coordinates of the point on line A(-1/4, 5) that coincides with the perpendicular from the line -x + 2y = 14 (y = x/2 + 7) are as follows:
-2·x + 9/2 = x/2 + 79/2 - 7= x/2 + 2·x-2.5 = 2.5·xx = -2.5/2.5 = -1x = -1y = x/2 + 7 = -1/2 + 7 = 6.5y = 6.5The location on the line -x + 2y = 14 (y = x/2 + 7) that is perpendicular to the point A(-1/4, 5) has the coordinates: (-1, 6.5)
The following formula is used to calculate the distance between points A and B:
[tex]l=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]Where: (x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)
Using the values as plug-ins, we have;
[tex]\begin{aligned}&I_{A B}=\sqrt{(6.5-5)^2+((-1)-(-1 / 4))^2}=\sqrt{(-0.75)^2+(1.5)^2}=\sqrt{\frac{45}{16}}=\frac{3}{4} \cdot \sqrt{5} \\&l_{A B}=\frac{3}{4} \cdot \sqrt{5} \approx 1.677\end{aligned}[/tex]
Therefore, approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
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PLEASE HELP WILL GIVE 150 POINTS IF HELPED
what is the anwer
What is an era
a a time period consisting of distinct historical events
b the effect of a historical event
c a visual representation of historical events
d the cause of a historical event
Answer:
Its A
Step-by-step explanation:
I will answer so you can give the other person brainliest :)
Can someone help me please? This is imporant
The solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622. (Correct choice: B)
How to solve graphically a system of equations
In this question we find a system formed by one nonlinear equation and one linear equation, which can be resolved by using a graphic approach. g(x) = f(x) represents the point of intersection of the two curves. First, we plot the graphs of the two curves and, second, the point of intersection is marked on the Cartesian plane.
According to the result given by the graphing tool, there are two solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622.
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ΔABC has coordinates of A (–5, –7), B (6, –3), and C (2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
The coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .
Let
OA vector = ( - 5 , - 7 )
OA' = 2 ( -5 , - 7 )
A' = ( - 10 , - 14 )
OB vector = ( 6 , - 3 )
OB' vector = 2 ( 6 , - 3 )
B' = ( 12 , - 6 )
OC vector = ( 2 , 7 )
OC' vector = 2 ( 2 , 7 )
c' = ( 4 , 14 )
Hence , the coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .
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1/6(6+18)-2 to the 2nd power
The value of the given expression using PEDMAS is 0
Simplifying expressions using PEDMASThe meaning of PEDMAS is expressed as shown below;
P is parenthesis
E is exponent
D is division
M is multiplication
A is addition
S is subtraction
Given the expression below;
1/6(6+18)-2²
Solve the parenthesis
1/6(6+18)-2²
1/6(24)-2²
Then exponent
1/6(24) - 4
Multiplication
(1/6*24) - 4
4 - 4
Then subtract to have:
4 - 4 = 0
Hence the value of the given expression using PEDMAS is 0
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4=q+13. Solve the equation using addition or subtraction A. q=4. B.q=17 C.q= -9 D. q= -2
Answer:
C. q= -9
Step-by-step explanation:
4=q+13
-13 -13 (4-13= -9)
q=-9
hope this helps :)
The solution of the given equation 4=q+13 is -9. Thus option C is correct.
The equation is defined as an expression consisting of an equality sign.
let us consider an example :
[tex]2x - 5 = 13.[/tex]
The given equation is:
[tex]4 = q + 13 \rightarrow 1[/tex]
For part A when q = 4 (given)
on substituting the value in equation 1 we get,
On transposing 13 to opposite side we get,
[tex]4 -13 = q[/tex]
[tex]-9 = q[/tex]
rewrite the equation as,
[tex]q =9[/tex]
The solution of the given equation [tex]4=q+13[/tex] is -9.
Thus option C is correct.
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Suzy's kitchen measures 17 feet by 4 feet She would like to add a small tile border around the entire room. How much should she expect to pay
if the tile strip costs $0.95 per foot
Total Cost = $
Preview My Answers Submit A
Room DimensionsLiving Room:·Room: 12 feet x 19 feet·Wall Height: 8 feet 4 walls painted
Step-by-step explanation:
A/b= 3/5 and b/c= 4/5
The answer of the following fraction which involves ABC is said to be 12:20:25
The transformation of a ratio into a fraction is known as the simple fraction form. In order to convey the relative size of two or more variables, the ratio is utilized. The fraction similarly identifies the components of the total. A:B or a/B are two ways to represent the ratio. As an illustration, the ratio is 12: 15.
Express the ratio in terms of a
a/b = 3/5 (cross-multiply)
3b = 5a (Divide the total both sides by 3)
b= 5/3 a
b/c = 4/5 (cross-multiply)
4c = 5b (divide the total both sides by 4)
c= 5/4 b=5/4×5/3 a=25/12a
then
a:b:c
=a:5/3 a:25/12 a (multiply each part by 12 to clear the fractions)
=12a:20a:25a (divide each part by a)
=12:20:25
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If p and q are positive integers such that pxq = 37, find the value of p + q. Show your working clearly and explain your answer. Please explain ty
Using a letter to represent the unknown number, select the equation that matches the problem.
A stick is 5 m long. A rope is 4 times as long as the stick. If the rope is divided into 2 pieces, how many meters long is each piece of rope?
The length of each piece of rope is 10m.
What is the length of each peace of rope?The first step is to determine the length of the rope before it was cut. In order to determine the length of the rope, multiply the length of the stick by the number of times the rope is as long as the stick.
Multiplication is the process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.
Length of the rope = length of the stick x 4
4 x 5 = 20m
lf the length of the rope is divided into two prices, divide the length of the rope by 2. Division is the mathematical operation that is used to determine the quotient of two or more numbers. It entails grouping a number into equal groups using another number.
Length of each piece = Length of the rope / 2
20m / 2 = 10m
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At a large university it is known that 30% of the students eat at dinning halls on campus. The director of student life is going to take a random sample of 300 students. What is the probability that less than a quarter of the sampled students eat at dinning halls on campus?.
What is the decimal equivalent of 1/7 and how can you do the order and how it goes?
Answer:
Answer: 1/7 as a decimal is 0.143
Step-by-step explanation:
Let us understand the division method to write 1/7 as a decimal. Explanation: To convert any fraction to its decimal form, we just need to divide the numerator by the denominator. Irrespective of the methods used, the answer to 1/7 as a decimal will always remain the same
A sample of size n = 10 is drawn from a population. The data is shown below. 119.1 95.2 119.1 86.5 78.4 107.1 86.8 119.1 96.2 90.1 What is the range of this data set? range = What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data. Please, please, please do not calculate the value by hand. stdev = Question Help: Message instructor Submit Question
[tex]range = 119.1 - 78 .4 = 40.7[/tex]
Part 2First determine the mean average:
[tex]mean = \frac{119.1 + 95.2 + ... + 90.1}{10} = 99.76[/tex]
[tex]stdev = \sqrt{ \frac{ \sum(x - mean) {}^{2} }{n - 1} } = \sqrt{ \frac{(119.1 - 99.76) {}^{2} + ... }{10 - 1} } = 15.285[/tex]
The perimeter of a rectangle is 102 feet. Find the length and width if the length is an integer and the width is 3 times the next consecutive integer.
Length = [_] feet
Width = [_] feet
The length of the rectangle is 12feet and the width is 26feet.
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed according to the equation below:
Perimeter = 2(length + width)
If the width is 3 times the next consecutive integer, then;
w = 3(x+1)
l = x
Substitute
102 = 2(x + 3x + 3)
102 = 2(4x + 3)
102/2 = 4x+ 3
51 = 4x + 3
4x = 48
x = 12 = length
For the width
width = 2(x+1)
width = 2(12+1)
width - 26 feet
Hence the length and the width of the rectangle are 12 feet and 26 feet respectively
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Question: 18 The auditorium at McCaskey East High School in Lancaster, PA has 800 seats. Suppose that the drama club has a goal of making $3400 each night of their spring play to cover expenses and raise money for the club. Adult tickets are $7 and students/senior tickets are $4.
Based on the information, it should be noted that there be 67 adults and 733 students in the auditorium.
How to calculate the value?Let adults tickets = a
Let students tickets = s
The auditorium at McCaskey East High School in Lancaster, PA has 800 seats. This will be:
a + s = 800 ..... i
Therefore, suppose that the drama club has a goal of making $3400. This will be:
7a + 4s = 3400 ..... ii
From equation i, a = 800 - s.
7a + 4s = 3400
7(800 - s) + 4s = 3400
5600 - 7s + 4s = 3400
Collect like terms
-7s + 4s = 3400 - 5600
3s = -2200
s = 2200 / 3
s = 733
a = 800 - 733 = 67
Therefore, there'll be 67 adults and 733 students.
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Brad, a teenager, saves up his monthly allowance over a period of six months to buy a pair of high-resolution headphones. He lends his friend, Jorge $10 from his savings. If Brad has $272 now, calculate his monthly allowance
If Brad has $272 now and lent his friend Jorge $10, his monthly allowance is $47.00
What is the total monthly allowance over 6 months?
Brad total monthly allowance over 6 months is the sum of the amount lent to Jorge and the balance Brad has currently which is $272
total allowances for 6 months=$272+$10
total allowances for 6 months=$282
monthly allowance=total allowances for 6 months/6 months
monthly allowance=$282/6
monthly allowance=$47.00
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7-20 pleaseeee need help asap..no explanation needed answer only please
all answers can be written multiple ways
7. 65/140, 13/28, or 46.43%
8. 18/140, 9/70, or 12.86%
9. 110/140, 11/14, or 78.57%
10. 95/140, 19/28, or 67.86%
Please help me need help
Answer:
81 100 121 144 169 196 225 256
17 19 21 23 25 27 29 31
Step-by-step explanation:
the formula is to square the number then subtract the preceding number in the box
What is the employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year?
A. $2480
C. $1160
FICA Taxes
Social Security
12.4%
employer exployee
6.2%
6.2%
Medicare
2.9%
employer employee
1.45% 1.45%
B. $4960
D. $580
The employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year is $580.
Medicare is a federal employment tax that helps pay the Medicare insurance program.
The Medicare duty, occasionally known as the" sanitarium insurance duty," is a civil employment duty that contributes to the Medicare insurance program. Medicare duty, like Social Security duty, is taken from an hand's payment or paid as a tone- employment duty.
Part A of the Medicare program, which covers sanitarium insurance for grown-ups 65 and aged, as well as persons with certain impairments or medical conditions, is funded by the Medicare duty. Medicare sanitarium insurance includes hospitalization, lodge care, nursing home care, and certain home healthcare.
Anyone working in the United States is obliged to pay Medicare levies.
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What is the midpoint of (3,5) and (6,0)
The midpoint of (3,5) and (6,0) is (9/2, 5/2)
How to calculate the midpoint of (3,5) and (6,0)?The points are given as
(3,5) and (6,0)
The midpoint of the points is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
So, we have
Midpoint = 1/2 * (3 + 6, 5 + 0)
Evaluate the sum
So, we have
Midpoint = 1/2 * (9, 5)
Evaluate the product
So, we have
Midpoint = (9/2, 5/2)
Hence, the midpoint of (3,5) and (6,0) is (9/2, 5/2)
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Una elevación de 10 pies está más cerca o más lejos de la superficie del océano que una elevación de -8 pies?
Answer:
farther
Step-by-step explanation:
2 feet farther from the surface of ocean than elevation of -8feet
help me please
show your solution
Hello,
[tex]1) \: - 24[/tex]
[tex] 2) \frac{ - 24}{2} = - 12[/tex]
[tex] 3)\frac{ - 12}{2} = - 6[/tex]
[tex]4) \frac{ - 6}{2} = - 3[/tex]
[tex]5) \frac{ - 3}{2} = - 1.5[/tex]
Answer → -1,5
Point D is the image of A after a reflection using the y-axis, then a translation two units to the right.
The image of point D after the transformation of the point A is
(6,3)
How to determine the image of point D after the transformation of the point A?The complete question is added as an attachment
From the question, we have the coordinate of point A to be
A = (-4, 3)
The sequence of transformations is given as:
Reflection across the y-axisTranslation two units to the rightThe rules of the above transformations are
reflection across the y-axis
(x, y)= (-x, y)
So, we have
A' = (4, 3)
translation two units to the right
(x, y)= (x + 2 , y)
So, we have
A'' = (6, 3)
This means that
D = (6,3)
Hence, the image of point D after the transformation of the point A is
(6,3)
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Solve each equation. If necessary, round to the nearest ten-thousandth. 12⁴⁻x=20
The solution of the given equation by rounding off it to the nearest ten-thousandth is 20716.0000.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: 12⁴ - x = 20
We are given that 12⁴ - x = 20 —- 1
We know that 12⁴ = 20736
So, equation 1 becomes,
20736 - x = 20
x = 20736 - 20
= 20716
Hence, the solution of the given equation to the nearest ten-thousandth is 20716.0000.
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Nathaniel is an insurance underwriter. He earns $31.45 per hour, is paid weekly, and works 40 hours per week. His current federal withholding per week is
$106. Nathaniel lives in a state with a flat-rate income tax of 5.3%. He will receive a 5.25% raise and his new federal withholding will be $117. Determine
the following after taxes:
Answer:
Step-by-step explanation:
yyyyyyyyyyyyyyyyyyyyyyyyyyyy
can someone help quick I will give brainlest.
Answer:
The answer is -2
Step-by-step explanation:
8-4 = 4
4÷-2 = -2
1¼ x 3.14 x ¾ to the second power
2 133/640 or 2.2078125
Solve. Check for extraneous solutions. (2 x)¹/₂=(x+5)¹/₂
x = 5 is not an extraneous solution of the equation.
[tex](2x)^{1/2} = (x+5)^{1/2}[/tex]
Taking square on both the side of the equation, we get
[tex]((2x)^{1/2})^{2}[/tex] = [tex]((x+5)^{1/2})^{2}[/tex]
2x = x + 5
Subtracting x on both the sides of the equations, we get
2x - x = 5
x = 5
Check for Extraneous Solution by putting x = 5 in the original equation, we get
[tex](2(5))^{1/2} = (5+5)^{1/2}[/tex]
[tex]10^{1/2}[/tex] = [tex]10^{1/2}[/tex]
⇒ LHS = RHS
∴ x = 5 is not an extraneous solution of the equation.
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A precipitate is the name for the ______ that forms when liquids are mixed.
*Hard lumps
*Gas
*Metal
*Element
swer.
At the beginning of the month, Sarah had $600 in her bank account. Within the month she
made two deposits of $40 and $25. She also made three withdrawals of $100, $50, and $20.
How much was in her account at the end of the month?
Sarah have $495 in her account at the end of the month.
Given,
The amount Sarah had in her bank account at the beginning of the month = $600
The deposits she made within the month = $40 and $25
The withdrawals she made = $100, $50 , $20
We have to find the balance amount in Sarah's account after all these transactions made:
The deposits Sarah had = 600 + 40 + 25 = 665
Sarah had $665 in her account in a month.
Withdrawals made by Sarah = 100 + 50 + 20 = 170
Sarah made a total withdrawal of $170 in the month.
Now, we have to find the account balance of Sarah:
Account balance = Total deposits - Total withdrawals
Account balance = 665 - 170 = 495
That is, Sarah have $495 in her account at the end of the month.
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Set up an equation and solve for x.
Answer:
Equation: [tex]14x + 2 = 15x - 3[/tex]
Solution: [tex]x = 5[/tex]
Step-by-step explanation:
The two lines are parallel, therefore, the two given angles are equal alternate exterior angles.
[tex]14x + 2 = 15x - 3 \text{ / Subtract 14x}\\14x + 2 - 14x = 15x - 3 - 14x\\\to 2 = x - 3 \text{ / Add 3}\\2 + 3 = x - 3 + 3\\\to 5 = x[/tex]