The point-slope form of equation of the line perpendicular to the line y = 5x + 6 nd passing through (-3,3) is x + 5y = 12.
If two lines are perpendicular to each other, then the product of slopes of these two lines is equal to -1.
The provided line is y = 5x + 6,
The slope M₁ of the line is equal to the coefficient of x,
M₁ = 5
Let the slope of the perpendicular line is M₂,
So, we can write,
M₁M₂ = -1
M₂ = -1/5.
Now, we can use the point slope form of the equation of line, according to which is if line passes through (a,b) and have slope m then the equation of the line will be,
(y-a) = m(x-a)
This form of line is called Point-slope form of line.
Then, the equation of the line with slope -1/5 and passing through (-3,3) will be,
(y-3) = -1/5(x+3)
-5y+15 = x+3
x + 5y = 12
The above equation is the required equation of line in point slope form.
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A triangle has side lengths of (10f+6)(10f+6) centimeters, (2f-4)(2f−4) centimeters, and (9g+1)(9g+1) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The formula predicts that the triangle's perimeter will be 12f+9g+3.
What is a triangle?
A triangle is a polygon with three sides and three angles. The triangle has angles that add up to 180 degrees.The perimeter of the triangle is determined by adding together all of its sides.The sides of a triangle are (10f +6) centimetres, (2f-4) centimetres, and (9g+1) centimetres long, respectively.
The expression for the triangle's perimeter will be
P = (10f+6) + (2f- 4) + (9g+1)
P = 12f+9g+3
The formula predicts that the triangle's perimeter will be 12f+9g+3.
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2. Ron's car left four skid marks on the road after he slammed his foot
on the brake pedal to make an emergency stop. The police measured
them to be 55 ft, 55 ft, 62 ft, and 62 ft. What skid distance will be
used when calculating the skid speed formula?
The skid distance value that will be used when calculating the skid speed formula is 58.5 ft.
What is average of values and how is it defined?
The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. As a result, the following is the mathematic average formula:
Average = Sum of values/Set of values = (x₁ + x₂ + ... + xₙ)/n
Given, the first skid distance calculated, in feet = x₁ = 55
The second skid distance calculated, in feet = x₂ = 55
The third skid distance calculated, in feet = x₃ = 62
The fourth skid distance calculated, in feet = x₄ = 62
Therefore using the formula for average mentioned in the literature at n=4, we have,
Average skid distance = (55 + 55 + 62 + 62)/4 = 234/4 = 58.5 ft.
Thus, the skid distance value that will be used when calculating the skid speed formula is 58.5 ft.
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help please with this question
Gagu will be paid £1248 per month after the increase.
Given,
The amount Gagu is paid = £1200 per month
The increase he is going to get = 4%
We have to find the amount Gagu gets after the increase:
First we have to find the increment amount:
That is,
4% of 1200
= 1200 × (4/100)
= 12 × 4
= 48
Here,
£48 is the increment amount Gagu will get.
Now we can calculate the monthly amount gagu will be paid after the increase.
That is,
1200 + 48 = 1248.
Therefore,
Gagu will be paid £1248 per month after the increase.
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can someone help me solve this math problem with solution?? TYY! you
Answer: n + 3
Step-by-step explanation:
Solution
n+3
Evaluate
(n 2 +n−6)
(n−2)
Remove the parentheses
n−2n 2 +n−6
Factor the expression
n−2
(n+3)(n−2)
PLEASE HELP! I ONLY HAVE A FEW MINUTES!! The amount of money put in the cash register, y, after selling x hotdogs at the snack shack. The slope is 2 1/4 and the y-intercept is 10
Explain what the slope and the y-intercept mean in this situation.
The interpretations are
Slope = Amount per hot dogIntercept = Initial amount of moneyHow to explain the slope and the y-intercept?The slope
From the question, the slope is given as
Slope = 2 1/4
From the question, we have
y = Amount of money
x =Number of hot dogs
This means that the amount of money per 1 hot dog is $ 2 1/4
The y-intercept
From the question, the y-intercept is given as
y-intercept = 10
From the question, we have
y = Amount of money
x =Number of hot dogs
This means that the initial amount of money is $10
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PLEASE HURRYYYY
The coordinates of midpoint M and endpoint E of a segment are M(35, –3) and E(15, 26). Students were asked to find two equations that could be used to find the coordinates of the other endpoint, F(x2, y2).
Josiah set up the equations as follows:
Which statement best describes Josiah’s work?
The −3 and 35 should be switched.
The 15 and 26 should be switched.
The equations should be
The equations are correct.
The equations for the coordinates of the endpoint F should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.
How to derive the equations for the missing endpoint of a line segment
In this problem we know the coordinates of the endpoint E and the midpoint M of the line segment EF and we need to derive expressions of the coordinates of the endpoint F by the midpoint formula:
M(x, y) = 0.5 · E(x, y) + 0.5 · F(x, y)
2 · M(x, y) = E(x, y) + F(x, y)
F(x, y) = 2 · M(x, y) - E(x, y)
If we know that M(x, y) = (35, - 3) and E(x, y) = (15, 26), then the coordinates of the endpoint F are:
F(x, y) = 2 · (35, - 3) - (15, 26)
F(x, y) = (70, - 6) + (- 15, - 26)
F(x, y) = (55, - 32)
The equations should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.
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The endpoint F's coordinates should be given by the formula
x = 2×35 - 15 and y = 2×(- 3) - 26.
What is the procedure to find the other endpoint?In order to solve this problem, we need to derive expressions for the coordinates of the endpoint F using the midpoint formula.
We know the coordinates of the endpoint E and the midpoint M of the line segment EF.
M(x, y) = 0.5×E(x, y) + 0.5×F(x, y).
2×M(x, y) = E(x, y) + F(x, y).
F(x, y) = 2×M(x, y) - E(x, y).
Given that M(x, y) = (35, -3) and E(x, y) = (15, 26), the endpoint F's coordinates are,
F(x, y) = 2×(35, - 3) - (15, 26).
F(x, y) = (70, - 6) + (- 15, - 26).
F(x, y) = (55, - 32).
The equations should be x = 2×35 - 15 and y = 2×(- 3) - 26.
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= 18cm
c1 =
cm
XÑ
b1 = 25cm
Material Type
6²
163
c2=
b2 = 40cm
b3 = 55cm
b4 = 75cm
Quantity
c3 =
Total:
cm
Length (total)
Answer:
7.08661
Step-by-step explanation:
What is the equation of the line perpendicularto y = 1/2x + 6 that passes through the point(4, 1)?
Two lines are perpendicular when their slopes are opposite.
You have the equation;
[tex]y=\frac{1}{2}x+6[/tex]You can identify the slope as the number next to the x (y=mx+b, m is the slope)
the slope in the given equation is 1/2
The slope of the perpendicular line will be the opposite
Ruben thinks of a whole number.
When he divides his number by 4, the result has 1 decimal place and is
greater than 6 but less than 7.
What is ruben’s original number
Solve for x :
ax+b=0 where a,b are any integers
Plus solution please
The solution for x of the given equation ax + b = 0 is x = -b/a.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given equation,
ax + b = 0
Add -b both side
ax + b - b = 0 - b
ax = -b
Divide by both side
ax/a = -b/a
x = -b/a
Hence "The solution for x of the given equation ax + b = 0 is x = -b/a".
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Class 7. Fractions & decimals
1/2 of 2 3/4
Answer:
11/8 or 1.375
Step-by-step explanation:
2 3/4 => 11/4
1/2 x 11/4 = 11/8
Work out the following calculations and give your answer to the nearest 10. A)23x46 b)25x68
Answer:
A) 1060 (corrected to the nearest 10) B) 1700
Step-by-step explanation:
A) the answer is 1058 which taken to the nearest 10 is 1060
B) the answer is 1700 which does not need to be corrected
lect the correct answer.The equation of a line is y=-3x - 2. What are the slope and the y-Intercept of the line?
Given the equation of a line as shown below :
[tex]y=-3x-2[/tex]To determine the slope and the y - intercept of the line, compare the equation with straight line equation
[tex]y\text{ = mx+c}[/tex]After comparing the equation of a line
[tex]\begin{gathered} m\text{ = slope} \\ c\text{ = y-intercept} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = -3x-2 } \\ y=mx+c \\ m\text{ = -3 } \\ c\text{ = -2} \end{gathered}[/tex]Therefore slope = -3 and y - intercept = -2
1.1 Complete the table.
Length (cm) Length (mm)
4
12
50
88.49
What is the constant of proportionality?
The constant of proportionality in the given representation is 3 .
The proportionality constant is the ratio that connects two given numbers in a connection that is thought to be proportional. The proportionate constant is also known as constant ratio, unit rate, variable of variation, and even rate of change.
The proportionality constant is calculated by a proportionality constant illustration.
Finding the proportionality constant begins with identifying the x and y elements. To figure out the weight to stick ratio, x will stand for size and Y for the number of butter sticks. We use the equations k = y/ x to calculate the proportionality constant.
Given the value of x is 4 and the value of y is 12
therefore using the equation we get
k= 12 / 4 = 3 .
Therefore the complete table will be
length (x) (y)
4 12
50 150
88.49 265.47
Hence the proportionality constant is 3 .
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Engl Write the linear equation that gives the rule
for this table.
Hon
Sch
Dire
Sch
Cale
Con
Car
Sup
X
0
1
2
3
y
23
24
25
26
Write your answer as an equation with y first,
followed by an equals sign.
y=x+23 is the linear equation that gives the rule for the given table .
Explanation of the concept of linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
The following is how the linear equation can be expressed in a slope-intercept form:
y = mx + b
where
slope = m
y-intercept = b
Using the table we get two points:
(1,24) and (2,25)
slope= y2-y1/x2-x1
= 25-24/2-1
=1
Now we have to calculate B using the point (1,24) and putting values in equation y=mx+b
24=1+b
b=23
So the equation is :
y=x+23
Therefore the linear equation for the given set of data table is y=x+23.
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Alina and Cesar estimated the number of miles they drove during a trip.
Alina estimated the number of miles they drove in the morning.
Cesar estimated the number of miles they drove in the afternoon.
Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.
The statements about Alina's and Cesar’s estimates should be completed as follows:
Alina is 5 miles off the actual mileage of 50 miles. That is a percent error of 10%. Cesar is 10 miles off the actual mileage of 200 miles. That is a percent error of 5%. Because Alina's mileage is lesser than Cesar's mileage, each mile of error results in a greater percent error.What is percentage error?Percentage error is also referred to as percent error and it can be defined as a measure of the extent to which an experimental numerical value differs from the actual (theoretical) numerical value.
Mathematically, percentage error can be calculated by using this expression;
[tex]Percent\; error = \frac{Actual\;value - Experimental\;value}{Experimental\;value} \times 100[/tex]
For the Alina's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 50 miles - 45 miles
Difference = 5 miles.
Next, we would determine Alina's percentage error as follows:
Percentage error = 5/50 × 100
Percentage error = 500/50
Percentage error = 10%.
For the Cesar's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 200 miles - 190 miles
Difference = 10 miles.
Next, we would determine Cesar's percentage error as follows:
Percentage error = 10/200 × 100
Percentage error = 1000/200
Percentage error = 5%.
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Complete Question:
Alina and Cesar estimated the number of miles they drove during a trip. Alina estimated the number of miles they drove in the morning. Cesar estimated the number of miles they drove in the afternoon. Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.
Alina's Estimate Actual Mileage
45 miles 50 miles
Cesar's Estimate Actual Mileage
190 miles 200 miles
Alina is ___ miles off the actual mileage of 50 miles. That is a percent error of %.
Cesar is ___ miles off the actual mileage of 200 miles. That is a percent error of %.
Because Alina's mileage is _____ than Cesar's mileage, each mile of error results in a ____ percent error.
sarah, the yearbook editor, and mrs. moore, the yearbook sponsor, are reviewing costs to produce the yearbook new yearbook design software costs $800, and it costs $15 to print each yearbook.
A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.
Explain the variables in mathematics?A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).
The price to produce x yearbooks will be 15x.
Additionally, software has a fixed cost of $800.
So the total price would be:
y = 800 + 15x
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Find CX. C(6,-4), X(1, -2)
The value of CX as asked will be √29 when two points are given as (6,-4) and (1,-2) by using the distance formula √((x2-x1)²+(y2-y1)²).
What is point?In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that extends in both directions indefinitely. It has a single length dimension.
What is distance?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here,
distance formula =√((x2-x1)²+(y2-y1)²)
CX=√((x2-x1)²+(y2-y1)²)
=√((1-6)²+(-2+4)²)
=√(25+4)
=√29
When two points are given as (6,-4) and (1,-2) by the distance formula √((x2-x1)²+(y2-y1)²), the value of CX as asked will be 29.
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Michael is driving to Hollywood, California. Hollywood is 1,375 miles from Michael's. home. If Michael spends 4 days driving to Hollywood, what is the fewest number of miles he can drive each day?
Answer:
343.75
Step-by-step explanation:
dividing the number of miles by the number days to get fewest equal number miles per each day
A quadratic function passes through the points (−1,−1), (2,−19), and (3,−33).
What is the equation of the function in standard form?
A) f(x)=−2x^2−4x−3
B) f(x)=−2x^2+4x−3
C) f(x)=−2x^2−4x+3
D) f(x)=−2x^2+4x+3
The quadratic function has an equation of f(x) = -2x² - 4x - 3
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(−1,−1), (2,−19), and (3,−33).
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (-1, -1), we have
a(-1)²+ b(-1) + c = -1
So, we have
a - b + c = -1
Using the point (2, -19), we have
a(2)²+ b(2) + c = -19
So, we have
4a + 2b + c = -19
Using the point (3, -33), we have
a(3)²+ b(3) + c = -33
So, we have
9a + 3b + c = -33
So, we have
a - b + c = -1
4a + 2b + c = -19
9a + 3b + c = -33
Using a graphing tool, we have
a = -2, b = -4 and c = -3
Substitute a = -2, b = -4 and c = -3 in f(x) = ax²+ bx + c
So, we have
f(x) = -2x² - 4x - 3
Hence, the equation is f(x) = -2x² - 4x - 3
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A person placed $4080 in an investment
The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount but after 1 year it will convert into $550.
As per the given,
Principle amount P = $4080
Rate of interest r = 5.7% = 0.057
Time period t = 4 years.
The formula for total value is given as,
V = P[tex]e^{rt}[/tex]
V = 4080[tex]e^{(0.057\times4)}[/tex]
V = $5124.83
Hence "The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83".
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The given question is incomplete complete question follows;
A line is drawn so that it passes through the points (-6,0) and (8,5). What is the slope of the line? Round the answer
to the tenths place. If the answer is a whole number than make the tenths place a zero to be counted as correct.
Answer:0.4
Step-by-step explanation:
just do y2-y1 over x2-x1 which gives 5/14
and convert that to a decimal which is .3571 and round it to get .4
It is given that the equation (mx)²+ 5nx+4=0 has two equal real roots while the quadratic equation px²-x+m=0 has two distinct roots where m,n and p are constants. Express the range of n in terms of p
Given:
[tex](mx)^2+5nx+4=0\text{ has two equal real roots}[/tex][tex]px^2-x+m=0\text{ has distict roots. }[/tex]Taking the first equation:
[tex]a=m^2\text{ ; b=5n ; c=4 }[/tex][tex]b^2-4ac=0[/tex][tex]25n^2-4m^2(4)=0[/tex][tex](5n)^2-(4m)^2=0[/tex][tex](5n+4m)(5n-4m)=0[/tex][tex]5n+4m=0\text{ ; 5n-4m=0}[/tex][tex]m=-\frac{5}{4}n\text{ ; m=}\frac{5}{4}n[/tex][tex]4m=-5n\text{ ; 4m=5n}[/tex]Taking the second equation:
[tex]a=p\text{ ; b=-1 ; c=m}[/tex][tex]b^2-4ac>0[/tex][tex]1-4pm>0[/tex]If 4m=5n,
[tex]1-p(5n)>0[/tex][tex]1>p(5n)[/tex][tex]\frac{1}{5p}>n[/tex]If 4m=-5n,
[tex]1-p(-5n)>0[/tex][tex]1+5pn>0[/tex][tex]5pn>-1[/tex][tex]n>-\frac{1}{5p}[/tex]Range of n in terms of p:
[tex]\frac{1}{5p}>n>-\frac{1}{5p}[/tex][tex]-\frac{1}{5p}please help me I don't get this
Answer:
(10, 1) is a solution to this equation.
Answer: your answer will be (10, 1)
Step-by-step explanation:
i just watch a mathematics video
(7a
3
−2a−2)+(−5a+3)
Answer: 14a + 1
Step-by-step explanation:
( 7a x 3 - 2a - 2 ) + ( -5a + 3 )
( 21a - 2a - 2 ) + ( -5a + 3 )
21a - 2a - 2 - 5a + 3
14a + 1
what 10 + 10 -2+123-85544
Answer: -85403
Step-by-step explanation:
Which graph best represents Sarah total earnings for babysitting
Answer:
Sarah earned $10 per hour for babysitting
Step-by-step explanation:
Levi and James collect baseball cards. Levi
has four times as many cards as James. If
the total number of cards they have is 600,
how many cards does each boy have? Write an equation
Step-by-step explanation:
l = number of Levi's cards
j = number of James' cards
l = 4j
l + j = 600
whey we use the first identify in the equation we get
4j + j = 600
5j = 600
j = 120
l = 4j = 4×120 = 480
Levi has 480 cards, James has 120 cards.
answer this solve 2k+6k=h for k
The value of the variable k in the equation given as 2k + 6k = h is k = h/8
How to determine the solution for k?From the question, the equation is given as
2k + 6k = h
Evaluate the like terms
i.e. We add 2k and 6k together.
This gives 8k
So, we have the following equation
8k = h
Divide both sides of the equation by 87
So, we have the following equation
8k/8 = h/8
Evaluate the quotient in the equation
k = h/8
The equation cannot be further simplified
Hence, the solution for k is k = h/8
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¿What is the constant term missing in the perfect square that begins with x ^ 2-20xx
2
−20xx, squared, minus, 20, x?
Some of the terms of an equation that has missing terms will be eliminated.
100 is the missing term that transforms (x² - 20) into a perfect square.
What is a perfect square?
A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent. For instance, the number 25, which is the product of the integer 5 multiplied by itself, is a perfect square because 5 x 5 = 25.
The missing term will be calculated in the next step.
Use k to represent the x-coefficient.
We thus have:
k = -20
Divide both sides by 2
k/2 = - 10
squaring both the sides,
(k/2)² = (- 10)²
=> (k/2)² = 100
This means that the term that is lacking is 100.
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Question:
What is the missing constant term in the perfect square that starts with x^2 -20x?