Step-by-step explanation:
5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:
5(2 + 1) = 5(2) + 5(1)
Simplifying the expression further, we get:
5(2) + 5(1) = 10 + 5 = 15
Therefore, 5(2 + 1) is equivalent to 15.
GIVING BRAINLIEST look at image and please fill the blanks !
Answer:
see the attachment
Step-by-step explanation:
If
f(x)
X-5
= 4x + 5, find f(x).
Answer:
f(x) = 4+10/x
Step-by-step explanation:
f(x)x-5 = 4x+5
add 5 to both sides
f(x)x = 4x+10
divide both sides by x
f(x) = 4+10/x
still not sure if its the right problem...
Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches. Which statement describes the meaning of the MAD in this situation?
The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.
Mean absolute deviation:The absolute deviation is a measure that quantifies the average deviation of data points from a central point, which can be any point in the data set such as the mean, median, or mode.
Typically, the mean is used as the central point. The formula to calculate the mean absolute deviation (MAD) involves finding the average of the absolute deviation (distance) of each data point from the mean of the data set.
Here we have
Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches
In this situation, the MAD of 2.4 inches means that on average, the stem length of each tomato plant deviated from the mean stem length of 8 inches by 2.4 inches.
Therefore,
The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.
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Find the length of the arc. Round answer to nearest tenth show work pls no.2
Using the length of the arc formula we get the arc's length to be 57.33rad.
Define length of an arc?The following formulas can be used to determine a circle's arc length: Arc Length = r, where r is the radius of the circle and is the central angle that the arc subtends.
When is expressed in radians, this formula is employed. Arc Length is equal to (/180) r, where r is the radius of the circle and is the central angle that the arc subtends.
In the question,
Radius of the circle = 11ft.
Angle created by the arc = 300°.
We need the length of the arc.
Length of the arc = S= 2πr×(θ/360) °
S = 2 × 3.14 × 11 × 300/360
= 57.33 rad
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Which lines best approximate the directrices of the
ellipse? Round to the nearest tenth.
O x= -4.6 and x = 4.6
O x = -3.5 and x = 3.5
O y=-4.6 and y = 4.6
O y = -3.5 and y = 3.5
Option A : The lines that best approximate the directrices of the ellipse are x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.
The directrices of an ellipse are lines that are equidistant from the two foci. In this case, the foci of the ellipse are located at (-5,0) and (5,0). The distance between the foci is 2c, where c is the distance from the center to a focus, and can be found using the equation [tex]c^2 = a^2 - b^2[/tex], where a and b are the lengths of the major and minor axes, respectively.
From the given diagram, we can see that the length of the major axis is 10 and the length of the minor axis is 8. Therefore, a = 5 and b = 4. The value of c can be found as follows:
[tex]c^2 = a^2 - b^2[/tex]
[tex]c^2 = 5^2 - 4^2[/tex]
[tex]c^2 = 9[/tex]
c = 3
Therefore, the directrices are the vertical lines that pass through (-5,-3) and (5,-3) and are equidistant from the foci. These lines are given by x = -5 and x = 5.
Therefore, the lines that best approximate the directrices of the ellipse are A. x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.
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Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.
A. x= -4.6 and x = 4.6
B. x = -3.5 and x = 3.5
C. y=-4.6 and y = 4.6
D. y = -3.5 and y = 3.5
Valeria conducted a survey at the local mall. She
sat and counted 50 people exiting the mall and
noted how many of them were carrying bags of
things they purchased. Using this information,
predict how many of the 4,800 visitors to the
mall on this day purchased something.
With Bag
37
Without Bag
13
We can use the proportion of people carrying bags from the sample of 50 people to estimate the number of visitors who purchased something out of the total 4,800 visitors to the mall.
The proportion of people carrying bags in the sample is:
37/50 = 0.74
This means that 74% of the sample of 50 people were carrying bags.
To estimate the number of visitors who purchased something out of the total 4,800 visitors, we can multiply the proportion by the total number of visitors:
0.74 x 4,800 = 3,552
Therefore, we can predict that approximately 3,552 visitors out of the total 4,800 visitors purchased something on that day.
HELP PLEASE ANYONE !!HELP!!PLEASE :(
Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
What is meant by events?
In probability theory, an event is a set of outcomes or results that can occur when performing a random experiment. An event can consist of a single outcome or multiple outcomes, and it is defined as a subset of the sample space of the random experiment.
1.Rolling a dice and flipping a coin are two independent events. The probability of rolling any particular number on a dice is 1/6, and the probability of flipping heads on a coin is 1/2. Since the outcome of rolling a dice does not affect the outcome of flipping a coin and vice versa, these events are considered independent.
2.Spinning two spinners each round are independent events. The probability of each spinner landing on a particular section is fixed, and the outcome of one spinner does not affect the outcome of the other spinner. Therefore, these events are considered independent. The probability of the first spinner landing on a specific section and the second spinner landing on another specific section at the same time is the product of their individual probabilities.
3.Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. In the beginning, there are 12 S tiles and 9 M tiles in the bag. The probability of drawing an S tile is initially 12/21 or 4/7. If an S tile is drawn first, the number of S tiles in the bag decreases to 11, and the probability of drawing an M tile on the second draw becomes 9/20. Therefore, the probability of drawing an S tile and then an M tile is (4/7) x (9/20) = 18/70 = 9/35.
4.Pulling a candy, eating it, and then pulling another out of a bag are dependent events. Initially, there are a certain number of candies in the bag. After one candy is drawn and eaten, the number of candies in the bag decreases, affecting the probability of drawing a specific candy on the second draw. Therefore, these events are considered dependent.
Therefore, Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
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Solve the arithmetic operation.
4* 3+9-8 ^ 3 %4+9*4
Answer: 57
It won't let me show the steps, since I've already edited my answer once...
The fraction 3 8 is a multiple of what unit fraction?
Answer: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8
Step-by-step explanation:
someone please help me. alg 2. spam comments will be reported and deleted.
Answer:
hope this helps
Step-by-step explanation:
At the ' Grub shrub, the following orders were placed: 3 burgers and 6 fries, which cost $30 in total 3 burgers and 2 fries, which cost $18 in total Find the cost, in dollars, of 2 burgers and 3 fries.
The total cost of 2 burgers and 3 fries, considering a system of equations, is given as follows:
$17.
How to obtain the costs?The costs are obtained by a system of equations, for which the variables are given as follows:
Variable x: cost of a burger.Variable y: cost of a fry.3 burgers and 6 fries, which cost $30, hence:
3x + 6y = 30
x + 2y = 10
x = 10 - 2y.
3 burgers and 2 fries, which cost $18 in total, hence:
3x + 2y = 18
1.5x + y = 9
Replacing the first equation into the second, the value of y is given as follows:
1.5(10 - 2y) + y = 9
2y = 6
y = 3.
Then the value of x is given as follows:
1.5x + 3 = 9
x = 6/1.5
x = 4.
Then the cost, in dollars, of 2 burgers and 3 fries, is given as follows:
2 x 4 + 3 x 3 = $17.
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Find the product.
a.
b.
8 15 19
7 -4 12
1
-15 19
-12-19
0-13
-600 -760
-114 106
-120 -114
-760
106
C.
d.
-354 -406
-111 27
57 71
3
17
The product of the values can be obtained by multiplying as follows:
1. 8 * 15 * 19 = 2280
2. 7 * -4 * 12 = -41
How to find the product of a valueTo find a product simply means to multiply the figures in order to arrive at a value. The question asks that we get the product of some values. To get these values, we are to multiply the numbers given to arrive at the answers.
It is possible to multiply two, three, or more values at the same time. So, another word that is used in place of multiplication is "product" as is the case in the question given.
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1) Find the minimum and maximum values for the function with the given domain interval.
c(x) = √x, given 1/121 <_x<_17
Answer:
√17 good luck
Step-by-step explanation:
The function c(x) = √x is a continuous and increasing function over the interval [0, ∞), which means that its minimum and maximum values on the given domain interval [1/121, 17] will occur at its endpoints.
At x = 1/121, we have c(1/121) = √(1/121) = 1/11.
At x = 17, we have c(17) = √17.
Therefore, the minimum value of c(x) on the given domain interval is 1/11, and the maximum value is √17.
Question Details
To earn full credit, you must show ALL
of your steps and calculation leading to
your solution. You will be assessed on
your mathematical communication, use
of mathematics and accuracy of your
results.
A rectangular prism and a square
pyramid were joined to form a
composite figure. What is the surface
area of the figure?
3 workers can do a job in 28 hours, how many more workers are needed to complete the job in 12 hours
Answer:
7 workers are required, so we need 7-3 or 4 more workers.
Step-by-step explanation:
Sloan Transmissions, Inc., has the following estimates for its new gear assembly project: price = $1,700 per unit; variable costs = $480 per unit; fixed costs = $4.1 million; quantity = 95,000 units. Suppose the company believes all of its estimates are accurate only to within :t15 percent. What values should the company use for the four variables given here when it performs its best- case scenario analysis? What about the worst-case scenario?
The company should use the following values: Price per unit = $1,445; Variable costs per unit = $552; Fixed costs = $4.715 million ; Quantity = 95,000 units.
what is variables ?In algebra, a symbol (typically a letter) is used to represent an undetermined quantitative score in an expression or algebraic expression. Simply put, a variable is a number that may be changed yet remains fixed. Categorical and numeric variables are the two main types of variables. Then, discrete or continuous categories are made for each category for numerical and categorical variables, respectively. An overview of various types is given in this section. a metric that has a wide range of possible values. Something that can change; a variable's sign; an element of a science experiment that could vary.
To perform a best-case and worst-case scenario analysis, we need to adjust the estimates for each variable based on the given percentage error of 15%.
Best-case scenario analysis:
Price per unit = $1,700 + (15% x $1,700) = $1,955
Variable costs per unit = $480 - (15% x $480) = $408
Fixed costs = $4.1 million - (15% x $4.1 million) = $3.485 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Worst-case scenario analysis:
Price per unit = $1,700 - (15% x $1,700) = $1,445
Variable costs per unit = $480 + (15% x $480) = $552
Fixed costs = $4.1 million + (15% x $4.1 million) = $4.715 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Therefore, for the best-case scenario, the company should use the following values:
Price per unit = $1,955
Variable costs per unit = $408
Fixed costs = $3.485 million
Quantity = 95,000 units
And for the worst-case scenario, the company should use the following values:
Price per unit = $1,445
Variable costs per unit = $552
Fixed costs = $4.715 million
Quantity = 95,000 units
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Concerns about climate change and C02 reduction have initiated the commercial production of blends of biodiesel eg from renewable sources and petrodiesel from fossil fuels. Random samples of 35 blended fuels are tested in a lab to ascertain the bio total carbon ratio
URGENT ANSWER BOTH A/B and C
The answer of the given question is (a) 95% of the sample means will fall within the interval from 0.9448 to 0.9512. (b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. (c) We used the central limit theorem to answer part (b).
What is Central Limit theorem?The central limit theorem is a fundamental concept in statistics that states that for a sufficiently large sample size, the distribution of the sample mean will be approximately normal, regardless of the distribution of the population from which the sample is drawn. This means that if we take repeated random samples from a population, the distribution of the means of those samples will approach a normal distribution, even if the population itself is not normally distributed.
(a) We can use the formula for the confidence interval of a mean:
σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.
Substituting the given values, we get:
CI = 0.9480 ± 1.96*(0.0060/√35)
CI = (0.9448, 0.9512)
Therefore, 95% of the sample means will fall within the interval from 0.9448 to 0.9512.
(b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. This is because the central limit theorem states that for a sufficiently large sample size (n[tex]\geq[/tex]30), the sampling distribution of the sample mean will be approximately normal, regardless of the distribution of the population.
(c) We used the central limit theorem to answer part (b).
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Use the Quadratic Formula to solve the equation x² - 6x = - 18.
x = −3+3i or x = -3-3i
x = −3+3√√3 or x = -3-3√3
x = 3 + 3i or x = 3 - 3i
x = 3 + 3√3 or x = 3−3√√3
These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex] is[tex]x = 3 + 3i or x = 3 - 3i[/tex].
What are equations used for?A linear formalism is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or explain the whole situation, this is known as an equation.
What sort of equation would that be?The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 consists of the two numbers 3x + 5 and 14, which are separated by the 'equal' sign.
we have a = 1, b = -6, and c = 18
[tex]x = (-(-6) +- \sqrt{-6^{2} } - 4(1)(18))) / 2(1)[/tex]
[tex]x = (6 +/- \sqrt{36-72} / 2[/tex]
[tex]x = (6 +/- \sqrt{36} / 2[/tex]
[tex]\sqrt{-36} = \sqrt{36} * \sqrt{-1} = 6i[/tex]
Therefore, the solutions are:
[tex]x = (6 + 6i) / 2 or x = (6 - 6i) / 2[/tex]
Simplifying:
[tex]x = 3 + 3i or x = 3 - 3i[/tex]
These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex].
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Rearrange b=4+5g2 to make g the subject
Answer:
b-4/5×2 =g
Step-by-step explanation:
if u wrote down the equation correctly
Calculate the area of the shape below
Answer:
[tex]225 \: {m}^{2} [/tex]
Step-by-step explanation:
I added a photo of my notes
This figure is formed from a rectangle and a trapezoid
Since the opposite sides of a rectangle are equal, we can find the its area:
A (rectangle) = 9 × 17 = 153 m^2
In order to find the area of a trapezoid, we have to know the length of its altitude:
H = 15 - 9 = 6 m
We know the lengths of both bases, now we can find the area:
A (trapezoid) = 0,5(7 + 17) × 6 = 0,5 × 24 × 6 = 12 × 6 = 72 m^2
Now add these two areas together and we'll get the total area of this figure:
A = 153 + 72 = 225 m^2
A discounted amusement park ticket costs $44 dollars, which is $12.95 less
than the original price p. Write and solve an equation to find the original
price.
Answer:
p-(p*.2274)
Step-by-step explanation:
P is the original price
P multiplied by .2274 gives the discount that's taken off
So the answer is P minus the discounted sum
According to 2015 census data, 40 percent of Colorado residents were born in
Colorado. If a sample of 250 Colorado residents is selected at random, what is
the standard deviation of the number of residents in the sample who were born in
Colorado?
60
12.23
0.24
7.75
10
Option D is correct. The Standard Deviation of the number of residents in the sample who were born in colorado is 7.75
How to find Standard Deviation of a given sample ?
Let x be the standard deviation for the sample, n =250
p = probability of success, q = probability of failure = 1 - p
q = 1 - 0.40 = 0.60
[tex]x = \sqrt{n \times p \times q}\\= \sqrt{250 \times 0.40 \times 0.60}\\= \sqrt{60}\\=7.75[/tex]
Therefore, Option D is correct. Standard Deviation is 7.75.
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option (d) the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.
what is standard deviation formula?The standard deviation of a binomial distribution is given by the formula:
σ = √(np(1-p))
binomial distribution with parameters n = 250 and p = 0.4—where n is the sample size and p is the probability of success—can be used to approximate the distribution of the number of Colorado residents who were born in Colorado in a sample of 250 residents.
Substituting n = 250 and p = 0.4, we get:
σ = √(250 x 0.4 x 0.6) ≈ 7.75
Therefore, the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.
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A study by the department of education of
a certain state was trying to determine the
mean SAT scores of the graduating high
school seniors. The study examined the
scores of a random sample of 250
graduating seniors and found the mean
score to be 538 with a standard deviation
of 96. Determine a 95% confidence
interval for the mean, rounding all values
to the nearest tenth.
The 95% confidence interval for the mean SAT scores is CI = (526.2, 549.8)
What is confidence interval?It is a statistical tool used in inferential statistics to estimate the unknown population parameter based on the sample data.
According to question:To find the 95% confidence interval for the mean SAT scores, we can use the formula: CI
where:
sample mean (538)
population standard deviation (96)
n = sample size (250)
z = z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96)
Plugging in the values, we get:
CI = 538 ± 1.96*(96/√250)
Simplifying, we get:
CI = 538 ± 11.8
Rounding to the nearest tenth, the 95% confidence interval for the mean SAT scores is:
CI = (526.2, 549.8)
For example, a 95% confidence interval for a population mean means that if we were to repeat the sampling process multiple times and calculate a 95% confidence interval each time, about 95% of the intervals would contain the true population mean.
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52. The height of an isosceles triangle is 8 feet. The base of the isosceles triangle is 23 feet. What is the
measure of one of the base angles of the triangle? Round your answer to the nearest degree
As a result, the triangle's base angle is roughly 72 °
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides.. Sometimes it is said that it must have exactly two sides that are the same length, and other times it must have at least two sides that are the same length, with the latter version adding the equilateral triangle as an exception.
Let x represent the size of one of the triangle's base angles.
Hence, we may apply the following equation to determine x:
angle = ((b/2)/h) arccos
where h is the height and b is the length of the base of one of the equal sides.
B in this instance equals 23 feet, while h is 8 feet.
Filling up the formula with these values:
angle = ((23/2)/8) arccosine
angle ≈ 72°
Consequently, one of the triangle's base angles is roughly 72 °
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Question What is the volume of this figure? Enter your answer in the box. ft³ Three-dimensional figure that could be formed by placing two rectangular prisms together to form an L shape where the wider part of the L is on the bottom and the L extends up from the left side. The wider part of the L has a length of 6 ft and a width of 2 ft and a height of 3 ft. The L extends up on the left side with the total height of the figure labeled 8 ft. The taller part of the L has a length of 4 ft and a width of 2 ft.
The volume of the figure is 76 ft³.
What is a prism?In geometry, a prism is a three-dimensional solid object that has two parallel bases that are congruent polygons, and rectangular faces connecting the bases. The rectangular faces are also called lateral faces or sides, and the edges where the bases and lateral faces meet are called lateral edges. The number of sides in the bases and the shape of the bases determine the name of the prism.
To find the volume of the figure, we can break it down into two rectangular prisms and add their volumes.
The first rectangular prism has dimensions 6 ft x 2 ft x 3 ft, so its volume is:
V1 = 6 ft x 2 ft x 3 ft = 36 ft³
The second rectangular prism has dimensions 4 ft x 2 ft x 5 ft (8 ft - 3 ft), so its volume is:
V2 = 4 ft x 2 ft x 5 ft = 40 ft³
The total volume of the figure is the sum of these volumes:
V = V1 + V2 = 36 ft³ + 40 ft³ = 76 ft³
Therefore, the volume of the figure is 76 ft³.
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Find the missing numbered angle
(5x-2)
The missing numbered angle is 80 degrees.
In the given diagram, we can see that angles A and B form a linear pair (they are adjacent angles whose sum is 180 degrees). So we can write:
A + B = 180 degrees
Substituting the given value of angle A, we get:
(3x + 10) + B = 180 degrees
Simplifying this equation, we get:
3x + B = 170 degrees
We are also given that angle C is a complementary angle to angle B, which means that angle C + angle B = 90 degrees. We can substitute the value of angle B from the above equation to get:
C + (3x + B) = 90 degrees
Simplifying this equation, we get:
C + (3x + 170 - 3x) = 90 degrees
Simplifying further, we get:
C + 170 = 90 degrees
Subtracting 170 from both sides, we get:
C = 80 degrees
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A convenience store sold 14 half-gallon containers of milk and 28 quars of orange juice. Write a sentence comparing the total number of gallons of milk sold to the total number of gallons of orange juice sold. Explain how you know that your comparison is correct without multiplying.
Who ever answers nicely gets 40 points
Answer:
The total number of gallons of milk sold is equal to the total number of gallons of orange juice sold. This is because there are 2 quarts in a half-gallon, so the 14 half-gallon containers of milk sold is equal to 28 quarts. Therefore, the total amount of milk sold is the same as the total amount of orange juice sold, which is 28 gallons.
The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet wide and 90 feet high. (i)Find the equation describing the door’s shape. (3) (ii)If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head? (2)
Step-by-step explanation:
So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...
Vertex at 60,90 <=====given
Vertex form y = a (x-h) ^2 + k
y = a ( x -60)^2 + 90 to find 'a' substitute in a point on the parabola...I'll use 0,0
0 = a ( 0-60)^2 + 90 shows a = - 1/40
so the equation is y = -1/40 ( x -60)^2 + 90
( or expanded to y= -1/40 x^2 + 3x )
Solve for 'x' when y = 6 ft ( to keep from hitting your head)
6 = -1/40x^2 +3x
0 = -1/40 x^2 + 3x - 6 Use Quadratic Formula to find x = ~ 2 feet
The equation of a line is y=1/4x-2. What is the equation of the line that is parallel to the first line and passes through (4, –2)?
A. y=-4x+14
B. y=-1/4x-1
C. y=-4x+3
D. y=1/4x-3
Two parallel lines have the same slope, so we need to find the slope of the first line y = (1/4)x - 2, and then use it to find the equation of the parallel line that passes through (4, -2).
The slope of the first line is 1/4, so the slope of the parallel line will also be 1/4.
Using the point-slope form of the equation, we can write the equation of the parallel line as:
y - (-2) = (1/4)(x - 4)
Simplifying this equation, we get:
y + 2 = (1/4)x - 1
Subtracting 2 from both sides, we get:
y = (1/4)x - 3
Therefore, the equation of the line that is parallel to y = (1/4)x - 2 and passes through (4, -2) is y = (1/4)x - 3, which is option D.
Is 4p + 7n+ 3p and 14pn equal
Answer:
yes
Step-by-step explanation:
4p+ 3p= 7p
7p+7n=14pn