The equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
Further explanation:
It is given that the equation of line is [tex]y-1=4\left({x+3}\right)[/tex] and passes through point [tex]\left({4,32}\right)[/tex] .
Rewrite the given equation [tex]y-1=4\left({x+3}\right)[/tex] as follows:
[tex]\begin{aligned}y-1&=4\left({x+3}\right)\\y-1&=4x+12\\y&=4x+12+1\\y&=4x+13\\\end{aligned}[/tex]
Now, compare the obtained equation of line [tex]y=4x+13[/tex] with the standard equation of line [tex]y=mx+b[/tex] .
[tex]\begin{aligned}m&=4\\b&=13\\\end{aligned}[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that both lines are parallel to each other so the product of slope must be equal.
[tex]{m_1}={m_2}[/tex] …… (1)
Substitute [tex]4[/tex] for [tex]{m_1}[/tex] in equation (1) to obtain the value of slope [tex]{m_2}[/tex] .
[tex]{m_2}=4[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that the line passes through point [tex]\left({4,32}\right)[/tex] .
The point-slope form of the equation of a line with slope [tex]m[/tex] passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:
[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex] …… (2)
Substitute [tex]4[/tex] for [tex]{x_1}[/tex] , [tex]32[/tex] for [tex]{y_1}[/tex] and [tex]4[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y-32&=4\left({x-4}\right)\\y-32&=4x-16\\y&=4x-16+32\\y&=4x+16\\\end{aligned}[/tex]
Therefore, the equation of line is [tex]y=4x+16[/tex] .
Now, the four options are given below.
[tex]\begin{gathered}{\text{OPTION A}}\to y=-x+33\hfill\\{\text{OPTION B}}\to y=-x+36\hfill\\{\text{OPTION C}}\to y=4x-16\hfill\\{\text{OPTION D}}\to y=4x+16\hfill\\\end{gathered}[/tex]
Since OPTION D matches the solution that is [tex]y=4x+16[/tex] .
Thus, the equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
Learn more:
1. Which classification best describes the following system of equations? https://brainly.com/question/9045597
2. What is the value of [tex]x[/tex] in the equation [tex]x-y=30[/tex] when [tex]y=15[/tex] ? https://brainly.com/question/3965451
3. What are the values of x? https://brainly.com/question/2093003
Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.
What is the maximum percentage of net spendable income that should be set aside for housing?
Answer:
The maximum percentage of net Spendable income that should be set aside for housing is given by [tex]\frac{28}{36}[/tex] rule,which states that ,if your total gross income after deduction is $ x, then you should use 28% of your income for housing finances and 36 % of your income for debt Purpose.
So, Maximum percentage of net spendable income that should be set aside for housing=28% of total gross income
"1. how many ancestors does a node at level n in a binary tree have? provide justification."
In binary tree there are n ancestor at level n.
Proof :
Take P(0): At node level 0, it has no ancestors since this is a roo tnode.
Take P(1): At node level 1, it has one ancestor. The ancestor is the root, its parents which is at level 0.
Take P(K): A node level K it has K ancestors. Its parent is at level K – 1.
Take P(K+1): At node K + 1 level have more than one ancestor than that of node at k level.
Thus there are n ancestor at level n in binary tree.
A node at level n in a binary tree has n ancestors. This is because there are n nodes on the path from the root to the node itself.
In a binary tree, the ancestors of a node are all the nodes that appear on the path from the root of the tree to that node. The level of a node is defined as its distance from the root node, with the root node being at level 0.
To determine the number of ancestors of a node at level n, consider the following:
The node at the root (level 0) has 0 ancestors.A node at level 1 has the root node as its ancestor (1 ancestor).In general, a node at level n has n - 1 nodes on the path from the root to the node.Therefore, a node at level n in a binary tree has n ancestors because it includes all nodes from the root (level 0) to the node itself (excluding the node itself).Hence, the number of ancestors for a node at level n is simply n.
write the fraction in simplest form 8/10
The simplest form of 8/10 is 4/5.
Given,
8/10
We need to write it in the simplest form.
What is the simplest form of a given fraction?It means that there is no common factor between the numerator and the denominator other than 1.
Example:
4/8
4 = Numerator
8 = Denominator
4 = 4 x 1
8 = 4 x 2
= 4 x 1 / 4 x 2
Cancel the common factor 4.
= 1/2 is the simplest form of 4/8
Find the simplest form of 8/10.
= 8/10
Look for a common factor.
= 2 x 4 / 2 x 5
Cancel the common factor 2.
= 4 / 5
Now we do not see any common factor.
= 4/5
Thus the simplest form of 8/10 is 4/5.
Learn more about converting given fractions into the simplest form here:
https://brainly.com/question/540029
#SPJ2
Sarah cut 6 yards of ribbon from a spool. How much did she cut in inches?
You want to place a towel bar that is 24 1⁄4 centimeters long in the center of a door that is 70 1⁄3 centimeters wide. How far should you place the bar from each edge of the door?
Answer:
You should place it 23 1/24 centimeters from each edge.
Step-by-step explanation:
The towel bar will be in the center in the door so the space between the edge of the door and each side of the bar is equal in the left and the right of the door. So lets define:
x: distance between edge of door and the towel bar edge.
We see that x is the distance left in both sides of the towel bar from the door so:
x+24 (1/4) +x = 70 (1/3)
2x + 24 (1/4) = 70 (1/3)
2x= 70 (1/3) - 24 (1/4)
To operate the fractions , we need a common denominator that can be obtained simply by multiplying both denominators 4* 3=12
We then subtract the whole numbers and fractions
2x= 70 (4/12) - 24 (3/12) = =( 46 1/12)
x= ( 46 1/12) / 2 = 23 (1/24)
2 out of 10 people have an allergic reaction to a new medicine. What is the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction?
The probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
To find the probability that exactly 4 out of 10 people experience an allergic reaction to the new medicine, we use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
( n ) is the number of trials (in this case, 10 people)
( k ) is the number of successes (in this case, 4 people)
( p ) is the probability of success on each trial (in this case, the probability of having an allergic reaction, which is 2 out of 10, or 0.2)
Now let's calculate:
[tex]\[ P(X = 4) = \binom{10}{4} \times 0.2^4 \times (1 - 0.2)^{10 - 4} \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4!(10-4)!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4! \times 6!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.0016 \times 0.262144 \][/tex]
[tex]\[ P(X = 4) = 0.08704 \][/tex]
So, the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
△EFG≅△JKL . What is m∠K ?
The two triangles are congruent, so the corresponding angles are the same, K is the mid-late phase of JKL, so K is the same as the mid-late phase of EFG. Therefore K = F = 62°.
What is compromise?
If a geometric shape can be placed on top of another so that all its points coincide, the geometry is said to be congruent or harmonious. >
Now that K is JKL, K will be similar to EFG's mid and late game.
Middle and late phase of EFG = F
M∠F = 62°
Therefore m∠K = m∠F = 62°
So "The two triangles are congruent, so the corresponding angles will be the same. K is at the end of JKL, so K will be the same as the end of EFG. So, K = F = 62°."
The probable question maybe:
In a triangle EFG and LJK, we are given angle G = 53 degree and angle F is 62 degree. △EFG≅△JKL. find the value of m∠K ?
An oil spill spreads 25 square meters every 16
hour. How much area does the oil spill cover after 2 hours?
When x = 1 then y equals
If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
4 / x + 3 / y = 5
We have to find the value of y, when the value of x = 1.
Substitute x = 1 in the equation.
4/1 + 3/y = 5
4 + 3/y = 5
3/y = 5 - 4
3/y = 1
y = 3/1
y = 3
Hence the value of y is 3.
Learn more about Equations here :
https://brainly.com/question/10413253
#SPJ2
The question is incomplete. The complete question is as follows.
If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals ?
To do linear regression, there must be paired scores on two variables.
if f(x) =x2-6, find f-1 (x)
The standard deviation of the sampling distribution of x overbarx, denoted sigma subscript x overbarσx, is called the
This is called as the standard error of the mean. Standard error is a numerical term that calculates the accurateness with which a sampling embodies a populace or population. In statistics, a sample mean moves away from the real mean of a population; this deviancy is the standard error.
What is the point slope form of the line with slope 2/5 that passes through the point (−4, −7) ?
The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.
The dimension of the rectangle should be 47cm and 26 cm respectively.
Given that,
The perimeter of the rectangle is 146 cm.And, the length is 5 less than twice the width. Here we assume the length be x and the width be y.Based on the above information,
We know that
The perimeter of the rectangle = 2(l + w)
w = width
(2w - 5) = length
So,
146 = 2(2w - 5 + w)
146 = 4w - 10 + 2w
156 = 6w
w = 26 cm
And, the length is
= 2(26) - 5
= 47 cm
Therefore we can conclude that the dimension of the rectangle should be 47cm and 26 cm respectively.
Learn more: brainly.com/question/16167300
Parks spent 1/3 of his money on a sweater. He spent 3/5 of the remainder on a pair of jeans. If he has $36 left, how much did the sweater cost?
Choose ALL that apply:
The executor of an estate does the following.
creates a will
takes an inventory of the estate's asset's
gives medical advice
gives financial advice
handles financial matters as designated in the will
Choose the correct translation for the following statement it is at most ten
Which of the following statements are equivalent to the statement "price increased by 1/2 "?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2 3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Correct answers to the statement that the price increased by 1/2 are: (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before. All other options either imply the price doubled, decreased, or was halved, which are not equivalent to an increase by half.
When it is stated that the price increased by 1/2, it means that the new price is the original price plus half of the original price. This is equivalent to multiplying the original price by 1.5. Let's evaluate the provided options:
(A) The price doubled - This would mean the new price is twice the original price, or the original price multiplied by 2, which is incorrect.(B) The price is 150% of the price before - This is correct because 150% implies the original price plus 50% of the original price, which matches our initial statement.(C) The price was reduced by a quarter - This would mean the new price is 75% of the original price, which is incorrect.(D) The price became a half of what it was before - This means the new price is half the original price, which is incorrect.(E) The price is now 1.5 of what it was before - This is correct, as it directly states that the new price is 1.5 times the original price.(F) The price now is 66 2/3% of what it was before - This would imply a decrease in price, which is incorrect.(G) The price now is 200% of what it was before - This implies the price doubled, which is not the case.(H) The price is 75% of what it was before - This would mean the price decreased, which is incorrect.Therefore, the correct answers to the statement "price increased by 1/2" are (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before.
The equivalent statements are (B) "The price is 150% of the price before" and (E) "The price is now 1.5 of what it was before".
To determine which statements are equivalent to the statement "price increased by 1/2", let's analyze each option:
(A) The price doubled:
This statement is not equivalent because doubling the price means multiplying it by 2, which is an increase of 100%.
(B) The price is 150% of the price before:
This statement is equivalent. Increasing by 1/2 is equivalent to increasing by 50%, which makes the new price 150% of the original price.
(C) The price was reduced by a quarter:
This statement is not equivalent because reducing by a quarter means subtracting 25%, not adding 50%.
(D) The price became a half of what it was before:
This statement is not equivalent because it implies a decrease to half, whereas the original statement implies an increase by half.
(E) The price is now 1.5 of what it was before:
This statement is equivalent. If the price is increased by 1/2, it becomes 1 + 1/2 = 1.5 times the original price.
(F) The price now is 66 2/3 % of what it was before:
This statement is not equivalent. 66 2/3 % represents a decrease, not an increase.
(G) The price now is 200% of what it was before:
This statement is not equivalent because 200% represents a doubling, not an increase of 1/2.
(H) The price is 75% of what it was before:
This statement is not equivalent because 75% represents a decrease, not an increase.
So, the equivalent statements are (B) and (E).
List two actions a person can take to minimize the fees paid to a bank.
ANSWER:
1. Keep good records to avoid overdraft fees.
2. Be sure to check banks carefully. Look at the services to see if the bank charges fees for those services. Compare multiple banks before settling with one.
Answer:
First, keep good records to avoid overdraft fees. Second, be sure to check banks out carefully. Look at the services you will most likely need and see whether the bank charges fees for those services. Compare several different banks before opening an account in one of them.
Step-by-step explanation:
Plato answer
Use the formula for Interest:
P = 100
r = 7.2%
Y = 5
A = ?
Your computer monitor has a width of 14.80 inches and a height of 11.10 inches. what is the area of the monitor display in square meters?
A boat heads south at 1,200 mph while a steamer heads east at 500 mph. If they started from the same dock and at the same time, when will the distance between them be 1,300 mi?
Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.
Step-by-step explanation:
Given the speed of boat = 1200 mph
the speed of steamer =500 mph
Distance traveled by boat in time "t"=[tex]\frac{distance}{time}=\frac{1200}{t}[/tex]
Distance traveled by steamer in time time "t"=[tex]\frac{500}{t}[/tex]
As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)
By Pythagoras theorem
[tex](Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow(\frac{1200}{t})^2+(\frac{500}{t})^2=(1300)^2\\\\\Rightarrow\frac{1440000}{t^2}+\frac{250000}{t^2}=1690000\\\\\Rightarrow\frac{1690000}{t^2}=1690000\\\\\Rightarrow\ t^2=\frac{1690000}{1690000}=1[/tex]
⇒t=1 hour
Thus, after t= 1 hour the distance between them be 1300 mi.
Any polygon with two pairs of parallel opposite sides is a parallelogram. True or False.
Answer:
the answer is false.
Step-by-step explanation:
Determine the number of solutions for the system y-3x=2 and 2y-6x=2
How many radians are in one degree, accurate to three decimal places?
One radian is approximately 0.0175 degrees. To convert from radians to degrees, multiply the radians value by 57.3°. This conversion is commonly used in mathematics and physics.
Explanation:One radian is equal to approximately 0.0175 degrees. To convert from radians to degrees, you can use the conversion factor of 1 radian = 57.3°. So, to convert an angle from degrees to radians, you can multiply the degrees value by 0.0175. This conversion can be used when working with angular measurements in mathematics and physics.
Learn more about Radians and degrees here:https://brainly.com/question/30033928
#SPJ2
The product of two integers is 72. One number is two less than five times the other.
Which of the following equations could be used to find one of the numbers?
2x^2 - 5 = 72
2x^2 - 5x = 72
5x^2 - 2x = 72
5x^2 - 2 = 72
Answer:
[tex]5x^{2}-2x=72[/tex]
Step-by-step explanation:
Let
y------> one integer number
x----> the other integer number
we know that
[tex]xy=72[/tex] ----> equation A
[tex]y=5x-2[/tex] -----> equation B
substitute equation B in equation A
[tex]x(5x-2)=72[/tex]
[tex]5x^{2}-2x=72[/tex]
Determine the linear factors for x4-2x^2+1
22x(4+16)-78x3 how do solve GEMDAS
Answer: 206
Step-by-step explanation:
22(4+16)-(78)(3)
(22)(20)-(78)(3)
440-(78)(3)
440-234=
206
°ω°
This is the range of sample statistics obtained when many samples are selected?
Explain how you can use doubles when multiplying with 4 to find 4x8
Answer:
Here,
4 × 8 = 32
Now,
using the doubles when multiplying with 4
2 × (4 × 4)
= 2 × 16
= 32
Hence,
we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4
Step-by-step explanation:
Here,
4 × 8 = 32
Now,
using the doubles when multiplying with 4
2 × (4 × 4)
= 2 × 16
= 32
Hence,
we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4
or
double the number 4 i.e 2 × 4 = 8
then again double the result i.e 2 × 8 = 16
and, again double the result i.e 2 × 16 = 32 which the required answer.