The equation of the line which is perpendicular to 5x - 4y = 16 is [tex]y = -\frac{4}{5}x -4[/tex].
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:
The intersection of perpendicular lines is always at a right angle.Two lines will always be parallel to one another if they are perpendicular to the same line.Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.
If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.
As a result, the following is the formula for the perpendicular's slope:
m1.m2 = -1
The equation of the line be "y = mx + c".
Equation of the line Perpendicular to the line is 5x - 4y = 16
Therefore, 4y = 5x - 16
⇒ [tex]y = \frac{5}{4}x -4[/tex]
Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].
Slope of the required ine be m .
Therefore, m * [tex]\frac{5}{4} = -1[/tex]
⇒ [tex]m = -\frac{4}{5}[/tex].
Equation of the line is ,
[tex]y = -\frac{4}{5}x + c[/tex]
The line passes through (5,-8)
Therefore,
[tex]-8 = \frac{-4}{5}*5 + c[/tex]
⇒ c = -4
The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].
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when finding 6.1 divided by 0.1 how is the decimal point moved?
well, let's just divide them anyway and check it out.
hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets one "0".
That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61. We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.
If 65% of a number is 208 and 15% of the same number is 48, find 80% of that number.
The number is 320 and 80 % of the number is 256
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation A is
65% of a number is 208 and 15% of the same number is 48
So , 65% of n = 208 be equation (1)
15% of n = 48 be equation (2)
Now , on simplifying the equations , we get
( 15 / 100 ) x n = 48
15n/100 = 48
Multiply both sides by 100 . we get
15n = 4800
Divide by 15 on both sides of the equation , we get
n = 320
The number n can also be determined by
( 65% - 15% ) of n = 208 - 58
50 % of n = 160
So , 100 % on n = 160 x 2
n = 320
Therefore , the number n is 320
Now , the 80 % of the number n is A = 80/100 x 320
A = 320 x 0.8
A = 256
Therefore , the value of A is 256
Hence , The number is 320 and 80 % of the number is 256
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One angle measures 27°, and another angle measures (8d − 9)°. If the angles are complementary, what is the value of d?
d = 72
d = 21
d = 3
d = 9
Answer:
d = 9°
Step-by-step explanation:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
soln
27° + (8d – 9)° = 90°
27° + 8d – 9° = 90°
27°–9° + 8d = 90°
18° + 8d = 90°
8d = 90° – 18°
8d = 72°
divide both sides by (8)
d = 9°
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write an equation of the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9
An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Here, slope of a line y=-1/5x-9 is m=-1/5.
The slope of a line perpendicular to given line is m1=-1/m2
So, slope =5
Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get
10=5(7)+c
⇒c=-25
Substitute m=5 and c=-25 in y=mx+c, we get
y=5x-25
Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
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A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.
Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
n(s)=4
n(e)=1
Probability of choosing a sock, replacing it, and then choosing another sock,
=1/4*1/4
=1/16
Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.
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O
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and
each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a
system of equations that could be used to determine the number of games Nolan
played and the number of rides Nolan went on. Define the variables that you use to
write the system.
Answer: g + r = 17
2.5g + 3.5r = 52.5
Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:
g + r = 17
2.5g + 3.5r = 52.5
We can solve this system of equations using elimination, substitution, or graphing.
What is the solution of the equation?:
-2(3x+1)-2x=-4(2x)-4
it doesn't have solution
Pls answer it quickly
The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;
Statements [tex]{}[/tex] Reasons
1. AC ≅ BC [tex]{}[/tex] 1 Given
2 D is the midpoint of AB [tex]{}[/tex] 2 Given
3. CD ≅ CD [tex]{}[/tex] 3 Reflexive property → CD = CD
4 ∠ACD ≅ ∠BCD [tex]{}[/tex] 4 Median line of an isosceles triangle bisects the vertex angle
5 ΔACD ≅ ΔBCD [tex]{}[/tex] 5. SAS congruency postulate
What is the two-column method used to prove statements in geometry?The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.
The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;
Reflexive property
The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.
Median of an isosceles triangle
In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent
SAS congruency postulate
The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
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Find the equation of the line, in lope-intercept form, containing the point ( 5,2. 2) and (9,2. 6)
The equation of the line, in slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.
What is an example of a slope intercept form?Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.
What is the slope and y-intercept?The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b
Here, m = (y2-y1)/(x2-x1)
So, m = (2.6-2.5)/(9-5)
m= 1/40
m=0.025
Now finding b by using formula y=mx+b using x= 5 and y= 2.5
2.5=(0.025)(5)+b
2.5=(0.125)+b
b=2.375
so equation of line is y=0.025x+2.375 in slope-intercept form.
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Find the equation of the line that passes through (4,4) and is parallel to y = 3 x + 4.
The line's equation that is parallel to the given line is= 3x - 8
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
The line's equation in the form of the slope intercept is,
y = mx + c
m is the line's slope, and c is its y-intercept.
line equation provided that,
Therefore, the line's slope is
Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.
Because all parallel lines have the same slope.
Equation for the necessary line is,
Replace point (4,4) in the line above.
In order for the line equation to become,
3x - 8
Hence, The line's equation that is parallel to the given line is= 3x - 8
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Janet made 7 1/3 pounds of trail mix. If she puts 1 5/6 pounds into each bag, how many
bags can Janet fill?
Kona work at a bakery. She baked 3308 muffin. She diplayed the muffin on tray that each hold 12 muffin. How many tray did Kona ue to diplay the muffin?
Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.
So, a tray will be needed to display all the cakes:
The total number of muffins is 3308.
Each tray can have 12 muffins.
The total trays needed are:
3308/12
275.66
Rounding off: 276
Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.
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X is a normally distributed random variable with mean 26 and standard deviation 1.
What is the probability that X is between 24 and 28?
Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.
Answer: give me brainliset
(
X
>
42
)
=
P
(
Z
>
−
1.1429
)
=
1
−
P
(
Z
<
1.1429
)
=
1
−
Φ
(
1.1429
)
=
1
−
0.8729
(from tables)
=
0.1271
Step-by-step explanation:
The diameter of a circle is 6 cm. Find its area to the nearest whole number.
Answer:
28.26
Step-by-step explanation:
A=3.14r^2
A=3.14(3)^2
A=3.14(9)
A=28.26
Answer: 28 cm
Step-by-step explanation: Area=π·r² and diameter =2r
So if we need to find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.
Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26
Now round to the nearest whole number ⇒ 28.
what goes in the missing box
Answer:
10
Step-by-step explanation:
in the first one, 6 16 8, (6×8)/3=16
in the third one, 9 21 7, (9×7)/3=21
using the same comcept, 5 ? 6, (5×6)/3=10
so, ?=10
The diameter of a circle is 12 ft. Find its area to the nearest whole number.
Answer:
77.04
Step-by-step explanation:
A=3.14r^2
a=3.14(6)^2
A=3.14(36)
A=77.04
Answer: 113 ft^2
Step-by-step explanation:
how many ways are there to list the letters of the word mathematics so that no two consecutive letters are the same?
There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the ordering of the selection is irrelevant. You can choose the components of combos in any order.Total number of ways to organize the word "mathematics".
The same letter does not appear twice.
The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.
We will first organize H,E,I,C,S in five different ways;
−H−E−I−C−S−
No, we could arrange 2M, 2T, and 2A as we have 6 gaps;
= 6!/(2!.2!.2!)
So there are a total of;
= 5 x 6!/(2!.2!.2!)
= 22.5
= 22 ways
Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
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42 out of the 84 teachers in a school staff meeting were first-year teachers. What percentage of the teachers in the meeting were first-year teachers? Write your answer using a percent sign (%).
If x=6 what is 4x
??????????????
Answer:
24
Step-by-step explanation:
6*4=24
Order these numbers from least to greatest.
1.4 comma space 1.04 comma space 16 over 10 comma space 1 1 half
Answer:
1.04, 1.4, 1.5 (one and a half), 10, 16
Answer:
1.04, 1.4, 1.5, 1.6
Step-by-step explanation:
1 1 half = 1.5
16 over 10 = 1.6
hope this helps!
if 14 meter of ribbion cost 19$ how much will 21 meters cost
Answer: 21 meters cost $28.5
Step-by-step explanation:
divide 19 by 14 and multiply by 21
21 meters cost $28.5
Show your work, (I am stuck on this because I’m not smart lol)
Answer:
She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.
Step-by-step explanation:
(97+78+89+?) divided by 4 at\geq 90
It is divided by 4 because it is the average of 4 test scores.
To Solve: (97+78+89+?) divided by 4 at\geq 90
Multiply by 4 on both sides 97+78+89+? at\geq 360
Isolate variable: ? at\geq 96
If [tex]$4^x = 3$[/tex], what is [tex]$4^{2x-2}?$[/tex]
[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]
Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. If caroline keeps planting flowers at this rate, how long will it take her to plant all 70 flowers that she has?.
It will take 40 minutes for her to plant all 70 flowers that she has. By using proportions, we can find this value.
How to calculate a word problem using proportions?To calculate a word problem using proportions is as follows:
Consider the details of the word problem in proportions as
a : b = c : d
Here, a: b is the ratio of an event, and c : d is the ratio of another event.
Then, to find the value of c we need to reframe the above proportion into
c = ad/b
This is also said to be a cross formula in terms of word problems.
Calculation:It is given that, Caroline is planting flowers in her garden.
She plants her first 7 flowers in 4 minutes.
After 12 minutes, she planted 21 different flowers.
Then, she takes x minutes for planting 70 flowers.
(Since the rate of planting is the same)
So, we can write
70 : 21 = x : 12
⇒ x = (70× 12)/21 = 40 minutes
Therefore, Caroline takes 40 minutes for planting all 70 flowers.
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Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
What is radioactive decay?
The release of energy in the form of ionizing radiation occurs during radioactive decay.
Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.
We know that decay behaves exponentially and follows this model
[tex]m(t) = m_{0} . e^{t/T} \\[/tex]
The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression
T = t1/2 /In2
If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:
τ ≈ 11.541 min
t = -τ .In m(t)/m₀
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
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Neha drives a car that gets 25 miles per gallon when she is driving in the city and 40 miles per
gallon when she is driving on the highway. Her car's fuel tank will hold 15 gallons of gas. What
equation can we write to represent all the combinations of city miles and highway miles she can
drive on one tank of gas?
1. Record an equation that is a prediction.
Answer:
C/25 + H/40 = 15
Step-by-step explanation:
Let's call C the number of city miles, and H the number of highway miles.
The total gas used is therefore:
C/25 + H/40
The fuel tank holds 15 gallons, so:
C/25 + H/40 = 15
please help meeeee!!
Answer:
f(2) = 9
Step-by-step explanation:
to evaluate f(2) substitute x = 2 into f(x) , that is
f(2) = 4(2) + 1 = 8 + 1 = 9
Find the x- and y-intercepts of the graph of -3x + y = 6. State each answer as an
integer or an improper fraction in simplest form.
Answer:
X-intercept : (-2,0)
Y-intercept : (0,6)
Answer:y-intercept (0,6),x-intercept (-2,0)
Step-by-step explanation:
To find the y-intercept set x=0
-3(0)+y=6
y=6
y-intercept (0,6)
To find the X-intercept set y=0
-3x+0=6
-3x=6
x=-2
x-intercept (-2,0)
Jermaine plays classical guitar at a local restaurant in the evenings. If jermaine plays 23 songs per evening, how many songs does he play in 73 evenings?.
Answer:
1679 songs
Step-by-step explanation:
23
x73
----------------------------
69
+ 1610
-------------------------------
1679
16 miles out of 40 miles
The 16 miles out of 40 miles. Then the percentage will be 40%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The 16 miles out of 40 miles. Then the percentage is calculated as,
P = (16 / 40) x 100
P = 0.40 x 100
P = 40%
The 16 miles out of 40 miles. Then the percentage will be 40%.
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The missing part of the question is given below.
Determine the percentage.