The equation for the line parallel to the given line and passing through the given point is y = -4x + 5.
Given:
3y = -12x + 4 and point (1,1)
3y = -12x+4
divide by 3 on both sides
3y/3 = -12x/3 + 4/3
y = -4x + 4/3.
m = -4.
y = mx + c
substitute m and (1,1)
1 = -4*1 + c
1 = -4 + c
c = 1 + 4
c =5
substitute c and m value in y = mx+c
y = mx + c
y = -4x + 5.
Therefore the equation for the line parallel to the given line and passing through the given point is y = -4x + 5.
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The doctor orders 100 units of a medication to administer daily. The vial is labeled 50 units/mL. How many mL will be administered if the patient stays in the hospital for a week?
350mL will be administered in a week.
A bag has 2 red, 3 green, and 6 orange balls. If a ball is randomly selected from the bag, what is the theoretical probability
that it is the color specified in parts (a) through (d).
Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.
In the given question,
A bag has 2 red, 3 green, and 6 orange balls.
So total number of balls = 2+3+6 = 11
We have to find the theoretical probability.
(a) We have to find the theoretical probability of selecting green ball.
P(G) = Total number of green balls/Total number of balls
P(G) = 3/11
Hence, the probability of selecting green ball is 3/11.
(b) Now we have to find the theoretical probability of not selecting green ball.
Except green ball there is having red and orange i.e.
Total remaining balls except green = 2+6 = 8
P(G) = Total number of balls except green balls/Total number of balls
P(G) = 8/11
Hence, the probability of not selecting green ball is 8/11.
(c) Now we have to find the theoretical probability of selecting orange ball.
P(G) = Total number of orange balls/Total number of balls
P(G) = 6/11
Hence, the probability of selecting green ball is 6/11.
(d) Now we have to find the theoretical probability of not selecting orange ball.
Except orange ball there is having red and green balls i.e.
Total remaining balls except orange = 2+3 = 5
P(G) = Total number of balls except orange balls/Total number of balls
P(G) = 5/11
Hence, the probability of not selecting orange ball is 5/11.
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Does the line for y = 6 have a negative slope ?
No, the slope of a horizontal line y=6 is, zero not negative.
What is a Slope?
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.
Slope Formula
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope, m = Change in y-coordinates/Change in x-coordinates = Δy/Δx
m = (y2 – y1)/(x2 – x1)
In the given equation of line y=6 .
The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is zero.
The equation y = 6 means for each and every value of x, y will be equal to 6.
This is the definition of a horizontal line.
By definition, the slope of a horizontal line is m = 0
When x = 0 then y = 6
Therefore, the y-intercept is: (0, 6).
Hence , the the slope of a horizontal line , m = 0.
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[tex]\sqrt{3p^{9}q^{7} r^{6}\\/ 16x^{6}y^{12}[/tex]
Using Laws of exponents, the solution to the expression √(3p⁹q⁷r⁶)/(16x⁶y¹²) is; (p⁴q³r³/(x³y⁶))√(3pq/16)
How to use laws of exponents?The different laws of exponents are;
1) Product With the Same Bases; a^m × a^n = a^(m+n)
where;
m and n are real numbers.
2) Quotient with Same Bases;
a^m/a^n = a^(m-n)
where;
a is a non-zero term and m and n are integers.
3) Power Raised to a Power; (a^m)^n = a^(mn)
where;
a is a non-zero term and m and n are integers.
4) Product to a Power; a^n * b^n = (ab)^(n)
where;
a is a non-zero term and n is the integer.
5) Quotient to a Power; It states that the fraction of two different bases with the same power is represented as; a^n/b^n = (a/b)^n
where;
a and b are non-zero terms and n is an integer.
6) Zero Power; When the power of any integer is zero, then it means that its' value is equal to 1, such that;
a⁰ = 1
where;
a is any non-zero term.
7) Negative Exponent Rule; a^(-m) = 1/(a^m)
We are given the expression as;
√(3p⁹q⁷r⁶)/(16x⁶y¹²)
Applying the laws of exponents, we will have;
√(3p⁹q⁷r⁶)/(16x⁶y¹²) = (p⁴q³r³/(x³y⁶))√(3pq/16)
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This is a safe space please answer how you are feeling today and why!!
Answer:
feeling good
Step-by-step explanation:
I am just happy
BIG IDEAS MATH
# 30 i
A coordinate plane is superimposed on a property map. Each unit in the coordinate plane represents 1 foot. The
location of a wellhead on the property is given by the point (12, 6). How close is the wellhead to a property line
modeled by the line y = x - 14? If necessary, round your answer to the nearest tenth place.
feet
The distance between point (12,6) and the line y = x - 14 is given as follows:
5.6 feet.
How to obtain the distance of a point to a line?The standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the point which we want to find the distance from the line are given as follows:
(x0,y0).
The equation that obtains the shortest distance of the point (x0, y0) to the line ax + by + c = 0 is presented as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
The line for this problem is given by the rule presented as follows:
y = x - 14.
In standard notation, it is defined by the rule presented as follows:
x - y - 14 = 0.
Hence the coefficients are presented as follows:
a = 1, b = -1, c = -14.
The point has the coordinates given as follows:
(12,6).
Hence:
x0 = 12, y0 = 6.
Thus the distance from the point to the line is obtained as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
D = |1(12) -1(6) - 14|/sqrt(1²+(-1)).
D = 8/sqrt(2)
D = 5.6 feet.
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NO LINKS!! Use the diagram below, classify the angle pairs as corresponding, alternate interior, consecutive interior, or none
Answer:
a) Consecutive interior angles.
b) Alternate exterior angles.
c) Corresponding angles.
d) Alternate interior angles.
e) Corresponding angles.
f) None.
g) Alternate exterior angles.
h) Consecutive interior angles.
i) None.
j) Corresponding angles.
k) Corresponding angles.
l) Alternate exterior angles.
m) Alternate interior angles.
n) Consecutive interior angles.
Step-by-step explanation:
Transversal
A line that crosses two other lines in the same plane at two distinct points.
Corresponding angles
A pair of angles that are in the same position relative to both lines crossed by the transversal.
Alternate interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Alternate exterior angles
A pair of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Consecutive interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.
a) Lines p and q are crossed by transversal line s.
Therefore, ∠4 and ∠7 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
b) Lines r and s are crossed by transversal line p.
Therefore, ∠2 and ∠11 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal p.
c) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠16 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
d) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠13 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.
e) Lines p and q are crossed by transversal line s.
Therefore, ∠11 and ∠15 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
f) ∠7 and ∠10 have no relationship.
g) Lines p and q are crossed by transversal line r.
Therefore, ∠1 and ∠14 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal r.
h) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠15 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
i) ∠6 and ∠7 have no relationship
j) Lines r and s are crossed by transversal line p.
Therefore, ∠1 and ∠3 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal p.
k) Lines r and s are crossed by transversal line q.
Therefore, ∠14 and ∠16 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal q.
l) Lines r and s are crossed by transversal line q.
Therefore, ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.
m) Lines p and q are crossed by transversal line r
Therefore, ∠5 and ∠10 are alternate interior angles as they are on the inner side of lines p and q, but on opposite sides of the transversal r.
n) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠14 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal q.
Solve the system of equations by graphing
u=v
4u=2v-12
By using the graphing method, a solution to the given system of equations is equal to -6 and -6.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would simplify the equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have:
4u/4 = (2v - 12)/4
u = v/2 - 3
By critically observing the graph of this system of equations, we can logically deduce that the point of intersection is at (-6, -6).
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A company orders 20 boxed lunches from a deli for $234.00. If each boxed lunch
costs the same amount, how much do 16 boxed lunches cost?
16 boxed lunch cost $187.2.
Given that a company orders 20 boxed lunches from a deli for $234.00.
Each boxed lunch costs the same amount.
20 boxed lunches from a deli for $234
1 boxed lunches from a deli for $234/20 = $11.7
Hence the cost of 16 boxed lunch is = $11.7*16 = $187.2
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A 2-pound bag of candy costs $6.04. What is the unit price?
per pound
Answer:
it would be $3.02
Step-by-step explanation:
you pretty much do $6.04/2 Ib
therefore, your answer would be $3.02
Answer:
Step-by-step explanation:
6.04 divded by 2= 3.02 per pound
Can someone help me with this question please like explain it to me ?
Using the trigonometry relation, the value of sin2x=4√2/9, cos2x=7/9 and tan2x=4√2/7.
In the given question, we have to find the value of sin(2x), cos(2x) and tan(2x).
The given value of six=1/3, x in quadrant first.
We firstly finding the value of cosx.
cosx = √1-(sinx)^2
Now putting the value of sinx
cosx = √1-(1/3)^2
cosx = √1 -1/9
cosx = √(9-1)/9
cosx = √8/9
cosx = 2√2/3
We know that;
sin2x=2sinxcosx
sin2x=2* 1/3 * 2√2/3
sin2x=4√2/9
Now finding the value of cos2x
We know that;
cos2x=1-2(sinx)^2
cos2x=1-2(1/3)^2
cos2x=1 -2/9
cos2x=(9-2)/9
cos2x=7/9
Now finding the value of tan2x
As we know that
tan2x=sin2x/cos2x
tan2x=(4√2/9)/(7/9)
tan2x=4√2/7
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The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
point a and point e are the two points representing extreme points on graph
Dave and LaVontae are saving money. Dave has $10, and LaVontae has $5. Write an
equation expressing the relationship between the amount that LaVontae has, x, and
the amount that Dave has, y.
what's the constant of proportionality: the table represent the linear relationship between the number of seconds a paper airplane is in the sky and the total distance it will fly
PLEASE HURRY!!!!!!!!!!!!!!!!!!! i need to complete this it im studying it for my test tomorrow
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
What is constant of proportionality?When two or more parameters are directly or indirectly proportional to one another, their relationship is expressed as a = kb or a = k/b, where k indicates the nature of the relationship between the two variables. This k is referred to as the proportionality constant.
For example, the number of apples in a crop is proportional to the number of trees in an orchard, with the ratio of proportionality being the average number of apples per tree.
This can be illustrated as:
Let's say y = 4
Let's say x = 2
y = kx
4 = 2k
Divide
k = 4/2
k = 2
The constant is 2.
Note that an overview was given as the information is incomplete.
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7. Select all of the numbers that are multiples of 12.
22
26
36
42
48
60
Answer:
36
48
60
Reason:
Since it is multiples of twelve, we can find out and multiply
12*3= 36
12*4= 48
12*5= 60
I hope this helps!
Answer: 36, 48, and 60.
Step-by-step explanation:
36, 48, and 60 are the only numbers that can be divided by 12 into a whole number.
36/12 = 3
48/12 = 4
60/12 = 5
Julia is a motived worker, and she is caring, considerate and cooperative most times. These are just a few of her positive,
A. typical responses
B. inherited responses
C.personality traits
D.measurable traits
In an economy, the price index in 2006 was 100 and the real gross domestic product (GDP) was $1,000. In 2010, the price index was 110 and the nominal GDP was $2,200. Based on that information, which of the
following can be inferred about the economy's nominal GDP in 2006 and real GDP in 2010?
A. Nominal GDP in 2006 = $2,000; Real GDP in 2010 = $1,000
B. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000
C. Nominal GDP in 2006= $1,100, Real GDP in 2010 = $2,420
D. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,420
E. Nominal GDP in 2006 = $1,100; Real GDP in 2010 = $2,200
Please show your work.
The economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
What does GDP Price Index mean?
A metric for gauging price inflation for American-made goods and services. The prices of American goods and services exported to other nations are included in the gross domestic product price index. This index excludes the costs Americans pay for imports.A country's gross domestic product that has been accounted for inflation is known as real GDP. Compare this to nominal GDP, which calculates GDP using today's prices without taking inflation into account.Nominal GDP in 2006=$1,000;
Real GDP in 2010=$2,000
Price index = (nominal GDP/real GDP) ×100
thus, nominal GDP in 2006=(price index × real GDP)/100
= (100×$1,000)/100
=$1,000
Real GDP in 2010= (nominal GDP/price index) ×100
= ($2,200/110) ×100
=$2,000.
Hence, the economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
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Macmillan Learning
Holly is deciding between 2 yoga studios. If she chooses Life Studio, she will pay a $60 initial sign-up fee and $30 each
month. If she chooses Yoga Mind, she will pay $40 each month and no initial sign-up fee. If Holly thinks she will do yoga
for 6 months, which studio should she join to pay less money?
She will pay the same amount at both.
Life Studio
Yoga Mind
Answer:
She will pay the same amount at both
Step-by-step explanation:
For Life Studio,
the initial sign up fee + $30 each month
= $30 = 30 × 6 = $180
Hence, $60 + $180 = $240
For Yoga Mind,
$40 each month for 6 months
= $40 × 6
$40 × 6= $240
Therefore, she will pay the same amount at both
Nate and Gavin are playing a video game. Gavin has scored eleven more than twice the number of points Nate has. If they scored 692 points altogether, have many points has Gavin scored?
Answer: gavin scored 465 points
Step-by-step explanation:
Please help me! Christian, Freddy, and Skyler are all drinking orange juice from the same-size cartons in the cafeteria. Christian's carton is 3/7 packed. Freddy's carton is 3/10 complete. Kevin's carton is 3/4 full. Who has the least milk left in their carton?
Answer: Freddy
Step-by-step explanation:
Choose a common denominator for all the fractions. Let's use 140.
Christian: 3/7 = 60/140
Freddy: 3/10 = 42/140
Skyler: 3/4 = 105/140
The least value is 42/140
This square root equation has 2 solutions. What is the extraneous solution?
√x+12 −6=x
Enter your answer in the box.
x = - 8 is not a root of √(x + 12) - 6 = x, since it is an extraneous solution.
How to find the extraneous solution of a radical equation
In this question we have a radical equation that offer two possible roots. A root is an extraneous solutions when it brings out an absurd (i.e. 1 = 4) when the expression is evaluated. First, write the radical equation:
√(x + 12) - 6 = x
Second, use algebra properties to find the possible roots of the radical equation:
√(x + 12) - 6 = x
√(x + 12) = x + 6
x + 12 = x² + 12 · x + 36
x² + 11 · x + 24 = 0
(x + 3) · (x + 8) = 0
x = - 3 or x = - 8
Third, evaluate the radical equation at each root:
√(- 3 + 12) - 6 = - 3
√9 - 6 = - 3
3 - 6 = - 3
- 3 = - 3 (TRUE)
√(- 8 + 12) - 6 = - 8
√4 - 6 = - 8
2 - 6 = - 8
- 4 = - 8 (FALSE)
x = - 8 is an extraneous solution.
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Finding the slope and y-intercept of a line.
Answer:
Slope = -5/2
Y-intercept = -9
Step-by-step explanation:
Hello!
The equation is given in Slope-Intercept Form: y= mx + b
m = slopeb = y-interceptSince the slope is the coefficient of the x-term, the slope of this equation is -5/2, or -2.5
The y-intercept is the numerical constant, which is given the by the integer -9.
the equation of the trend line is y= 0.36x + 12.6 use the equation of the trend line to predict the wind chill for a wind speed of 4 mi/h. Round your answer to the nearest degree. The wind chill at 4 mi/h is?? PLease help!!!! need this answer in less than 10 min!
The prediction of the wind chill for the wind speed 4 mi/h is 14 degrees
How to predict the wind chill for the wind speed?Here, we have the following parameters:
Equation of the trend line: y = 0.36x + 12.6
Where
x = Wind speed
y = Wind chill
Also, we have
x = 4 mi/h i.e. the wind speed
Substitute x = 4 in the equation y = 0.36x + 12.6
So, we have
y = 0.36 x 4 + 12.6
Evaluate the equation
y = 14.04
Approximate
y = 14
Hence, the wind chill is 14 degrees
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Write equations for the horizontal and vertical lines passing through the point (2, -6).
horizontal line: 0
vertical line:
Continue
0
00
X
0=0
3
The equation of the horizontal line passing through the point (2, -6) is :
y = -6
and the equation of the vertical line passing through the point (2, -6):
x = 2
We need to write equations for the horizontal and vertical lines passing through the point (2, -6)
For a vertical line the value of x will never change. This will be true for any value of y.
So, the equation for a vertical line passing through this point is:
x = 2
Similarly, for a horizontal line the value of y will never change. This is true for any value of x.
So, the equation for a horizontal line passing through this point is:
y = -6
Therefore, the equation of the horizontal line passing through the point (2, -6) is y = -6
and the equation of the vertical line passing through the point (2, -6) is x = 2
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HELP ASAP!! Find the sum of the series
Answer:
225
Step-by-step explanation:
a1 = 1
a15 = 29
sum = n/2 ( a1 + a15) = (15/2) ( 1 + 29) = 225
identify the slope. pls help asap
Answer:
Step-by-step explanation:
Slope: 6/3 = -2
since the line is going from left to right, it is a negative slope
Answer:
-7/3 or 2.3333333333333
Step-by-step explanation:
X= -1 – -4 = 3
Y= -4 – 3 = -7
y = -2.3333333333333x – 6.3333333333333
or
y = -7/3 x - 19/3
So when y= -6.33 that will mean x= -2.71
Annie's current earnings are shown in the table.
She was offered a new job that will pay $7.25 per hour. Assume
that her earnings vary directly with the number of hours worked.
Which job pays more an hour?
Answer:
Annie's new job pays more an hour.
Step-by-step explanation:
They tell us that her new job pays $7.25 per hour. So to determine which job pays her more, we need to find how much she earns in her current job.
There are a few ways to find this (none of them are hard.) But this is the easiest way in my opinion.
The chart tells you that Annie earns $13 in 2 hours. We need to find how much she earns in 1 hour. All you need to do is divide $13 by two.
13/2 = 6.5
6.5 = $6.50
If her current job pays her $6.50 an hour and her new job pays $7.25 an hour, she should consider higher paying jobs.
But, yes, the new job pays her more an hour.
-9x+2y =24
x = 10-4y
Answer: x = -2, y = 3
Step-by-step explanation:
Given that,
-9x+2y = 24..................................(i)
x = 10-4y.......................................(ii)
From equation (i)
-9(10-4y) + 2y = 24 [as x = 10-4y]
=> -90 +36y + 2y = 24
=> 38y = 90 + 24
=> 38y = 114
=> y = 114/38
Therefore, y = 3
Again,
x = 10 - 4(3) [as y = 3]
=> x = 10-12
Therefore, x = -2
Here, x = -2 and y = 3
Which of the following expressions has the greatest value
Answer:
2⁵ that is my answer for the question
Answer: 2^5
Step-by-step explanation:
3^3 = 27
1^10 = 1
2^5 = 32
5^2 = 25
Robert bought a used car for $10,332 with an added sales tax of 2.5%. What was the
original price of the car?
A $11,080
B. $10,080
C. $20,800
D. $15,416
If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
Option (B) is correct.
What is a percentage?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is the one-hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Robert bought a used car for $10,332 with an added sales tax of 2.5%.
so the additional amount would be = 10,332 * 2.5%
= 10332 * 0.025
= $258.3
So the original price of the car would be = 10332 - 258.3
≈ $10,080.
Hence, If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
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