The equation in standard form of the line is y+2x+4 = 0.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
Y = mx + c represents the expression of a straight line with slope m and intercept c on the y-axis.Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the topology is described. In analytic geometry, for example, a line in the plane is frequently described as the collection of points whose coordinates satisfy a particular linear equation, whereas in a more abstract context, such as contact geometry, a line may be an autonomous object, separate from the points.We know that the standard form a straight line equation is given by
y-q = m(x-p) where (p,q) is a point on the line and m is the slope.
Therefore
y-0 = -2(x-{-2})
or, y = -2x -4
or, y + 2x + 4 = 0
Therefore the equation of the straight line is y + 2x + 4 = 0 .
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Write in point-slope form an equation of the linethrough each pair of points. 17. (1.0) and (5, 5)19. (0, -1) and (3, -5)21. (1. 9) and (6, 2)
we have the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing:
17. (1, 0) and (5, 5)
[tex]m=\frac{5-0}{5-1}=\frac{5}{4}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=\frac{5}{4}\cdot x-\frac{5}{4} \end{gathered}[/tex]19. (0, -1) and (3, -5)
[tex]m=\frac{-5-(-1)}{3-0}=\frac{-4}{3}=-\frac{4}{3}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{4}{3}\cdot x-1 \end{gathered}[/tex]21. (1, 9) and (6, 2)
[tex]m=\frac{2-9}{6-1}=\frac{-7}{5}=-\frac{7}{5}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{5}\cdot x+10.4 \end{gathered}[/tex]the data below provides a statistical snapshot of the proportion of community college students who majored in different fields of study. a total of 33,150 community college students were included in the study. table 3 displays the total number of community college students who majored in each of the following fields of study. complete the table by filling in the percentages of community college students who majored in each field of study. round to the nearest one percent.
Answer:
Humanities ---> 3%
Social/ Behavioural sciences ---> 8%
Mathematics and Science ---> 16%
Explanation:
The percentage for each value can be calculated by dividing the number of students in that field by the total number of students in college and then multiplying it by 100, so for each field of study, we get
[tex]\frac{850}{33150}\times100=0.03\times100=3\text{ \%}[/tex][tex]\frac{2,600}{33,150}\times100=0.08\times100=8^{}\text{ \% }[/tex][tex]\frac{5,175}{33,150}\times100=0.16\times100=16\text{ \%}[/tex]Therefore, the answers are
Humanities ---> 3%
Social/ Behavioural sciences ---> 8%
Mathematics and Science ---> 16%
find the value of X that would prove y || x. State the converse used to support your answer.
For y to be parallel to x,
[tex]\begin{gathered} (11x-3)+(4x+39)=180^{\circ} \\ 15x=144 \\ x=9.6 \end{gathered}[/tex]Thus, the value of x is 9.6.
a) Let U = {1,2, ., 9} be the universal set, and letA = {1,2,3,4,5),C= {5, 6, 7, 8, 9), E= {2,4,6,8),B = {4, 5, 6, 7),D= {1, 3, 5, 7, 9), F = {1,5,9}.Find: AUC'
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1,2,3,4,5}
B = {4, 5, 6, 7}
C = {5, 6, 7, 8, 9}
D= {1, 3, 5, 7, 9}
E= {2, 4, 6, 8}
F = {1, 5, 9}
What is the question: Find AUC'.
Recall the following:
A ∩ C (read as A intersection C) - are members that are common to both set A and set C.
A ∪ C (read as A union C) - are members that are in set A or set C or both, combining the members of all sets.
C' (read as C complement) - are members that are not in the universal set.
Since what we are about to find is A ∪ C', let's first determine the members of C'.
We get,
C' = {1, 2, 3, 4}
A = {1,2,3,4,5}
Therefore, AUC' = {1,2,3,4,5}.
arc TQ =arc QR =arc TS =arc SQR =arc RQTBackNext
What transformations to the linear parent function, f(x) = x, give the functiong(x) = -6X? Select all that apply.A. Vertically stretch by a factor of 6.B. Horizontally stretch by a factor of 6.O C. Shift 6 units down.D. Reflect over the x-axis.
Looking at f(x) and g(x), we can see that g(x) is made by f(x) multiplied by -6.
Since the function was multiplied by a negative value, that means we had a reflection over the x-axis.
Also, if the function was multiplied by a constant value, that means we had a vertical stretch by a factor equal to the absolute value of the constant.
Therefore the correct options are A and D.
on spirit day 63 fewer 7th graders wore green and white then 8th grade. the total number of students wearing green and white was 561. find the number of 7th and 8th graders who wore green and white
I got the answer of 505 students
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain can be best described using interval notation. The domain is [1,∞].
A continuous function is graphed here. The function is continuous only on where it is defined. That is, the graph of the function does not have any discontinuities from 1 to infinity.
The domain of a function is the x-values for which the function is defined. That is for such x-values, the function will attain some y-value, which is called the function value. This function values corresponding to each x-value sketches the graph.
From the figure, the graph is started from x = 1 and is extended to infinity.
So it is better to express the domain in an interval form.
Graph of the function is a curve. So the domain is [1,∞].
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Mrs. Danforth packed $5$ bags of fun-sized candies for her family's picnic. Each bag contains $16$ pieces. She had intended to pass out the same number of candies to each of her $4$ children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
From the information given in the word problem, the oldest child of Mrs. Danforth must be 13 years old.
What is the calculation showing the above?
Given:
Each bag contains $16 CandiesThere are 5 bagsThere are four children.Since the bags are distributed according to the proportion of their ages, then, we say
5 bags x 16 candies =80 candies.
80 / 4 = 20 candies per child
Given that his 4-year-old sister gets 20 -12 = 8 candies, then:
8/4 = 2 candies per year for each child's age.
Given that Cameron will gain 20 + 2 =22 candies, then:
22 / 2 = 11 years is Cameron's age.
22 candies of Cameron + 8 candies for youngest sister=30
80 - 30 = 50 candies for the remaining older children.
Since Cameron is the 2nd youngest, it means the remaining 2 siblings must be 12 and 13 years respectively:
So that: 12 x 2 = 24 candies for the 3rd oldest
And 13 x 2 = 26 candies for the oldest child. So, the total allocations of all the candies would be:
8 + 22 + 24 + 26 = 80 candies.
Therefore, the most senior child must be 13 years old.
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Full Question
Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
Fill in the frequency distribution below
The frequency for the given distribution of the class interval 1.00 - 1.09 is 3, which are 1.07, 1.05 and 1.07.
What is frequency?The frequency of a repeating event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to emphasise differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is expressed.
The period is the reciprocal of the frequency because it is the length of time for one cycle in a repeating event. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).
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Question in picture will give brainlist
The angle addition postulate is the best justification for m∠XPD + m∠DPE = m∠XPE.
What is an angle bisector?An angle bisector is a line segment that divides an angle into two equal parts.
The angle addition postulate states, if a line segment is in between an angle sum of two smaller angles created by the line segment, is equal to the measure of the larger angle.
We have an ∠XPE that is divided by a line segment PD which creates two smaller angles ∠XPD and ∠DPE.
∴ By angle addition postulate m∠XPD + m∠DPE = m∠XPE.
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A chess player won 63 games of the games he played. if his ratio was 9:2 how many games did he play in total
From the ratio given, the number of games won is 77
RatiosTo solve this problem, we simply need to use the ratio of games won to find the total number of games played.
Let x represent the total number of games played;
The fraction of games won can be written as
[tex]\frac{9}{9 + 2} * x = 63\\\frac{9}{11}* x = 63[/tex]
Let's solve for x here;
[tex]\frac{9x}{11} = 63\\ 9x = 63 * 11\\9x = 693\\x = 77[/tex]
From the calculations above, the chess played a total of 77 games.
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Natalie walked 1.4 miles in one hour. How far did she walk in kilometers?
The distance covered by Natalie in kilometers will be 2.24 kilometers.
What is a unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that Natalie walked 1.4 miles in one hour. The distance covered by Natalie in kilometers will be calculated as:-
The value of 1 mile is equal to 1.4 kilometers.
1 miles = 1.6 kilometers
1.4 miles = 1.4 x 1.6 kilometers
1.4 miles = 2.24 kilometers
Therefore, the distance covered by Natalie in kilometers will be 2.24 kilometers.
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Sara drives 171 miles on 7.6 gallons of gas. She uses this information to calculate how man miles per gallon she can drive. Using this result, how many miles can Sara drive on 12.5 gallons of gas?
A unit rate means a quantity at a rate of one of something.
The number of miles Sara can drive on 12.5 gallons of gas is 281.25 miles.
Option D is the correct answer.
What is a unit rate?A unit rate means a quantity at a rate of one of something.
It is written with a denominator of one.
We have,
Sara drives 171 miles on 7.6 gallons of gas.
This can be written as:
171 miles = 7.6 gallons
Multiply 12.5/7.6 on both sides.
12.5/7.6 x 171 miles = 12.5/7.6 x 7.6 gallons
281.25 miles = 12.5 gallons
Thus,
The number of miles Sara can drive on 12.5 gallons of gas is 281.25 miles.
Option D is the correct answer.
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As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail 2 sloshes of the water out of her cup before 3 she gets a chance to drink any. 8 cm T 3 cm:n What is the volume of water remaining in Abigail's cup? Hint remember to subtract?
First we have to find the volume of the cone so we use the formula:
[tex]V=\frac{\pi r^2h}{3}[/tex]and we replace pi by 3.14, h by 8 and r by 3 so:
[tex]\begin{gathered} V=\frac{3.14\cdot3^2\cdot8}{3} \\ V=\frac{3.14\cdot9\cdot8}{3} \\ V=75.36 \end{gathered}[/tex]now she sloshes 2/3 of the water, so we need to calculate the remaining 1/3 of the volume so:
[tex]\frac{75.36}{3}=25.12[/tex]the remaining volume of water is 25.12 cubic centimeters
How do I solve for 10?It says to leave in the simplest radical form
the length of th diagonal is 10√2
Explanation:side length = 10 inches
We need an illustration to solve the question:
Using pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = diagonal
opposite = 10 in, adjacent = 10 in
diagonal² = 10² + 10²
diagonal² = 100 + 100
diagonal² = 200
diagonal = √200
diagonal = 10√2
Hence, the length of th diagonal is 10√2
Find the
28th term of
3,11, 19, 27
The 28th term of the given arithmetic sequence is 219
any arithmetic sequence can be solved once we identify the aa1 term and the an term because then we have to simply find the common difference and solve further by substituting the value in the below mentioned equation.
Given the arithmetic sequence = 3,11, 19, 27
a₁ = 3
a₂ = 11
a₃ = 19
a₄ = 27
the common difference or d = a₂ - a₁
this implies d = 11 - 3 = 8
Therefore the 28th term of the given arithmetic sequence is
a₂₈ = a₁ + ( n - 1 ) d
a₂₈ = 3 + ( 28 - 1 ) 8
= 3 + 27 × 8
= 3 + 216
= 219
Thus a₂₈ = 219
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4.There are 30 students in the classroom competing for classroom prizes. Only the first two students whose name is drawn will win a prize. The first student wins 5 bonus points and the second student wins 2 bonus points, both on the upcoming test. If you are one of the 30 students, what is the probability you will win the top prize and your best friend wins the second prize?
Out of 30 students, the probability of one student winning the top prize is 1/30.
Since the student who won the top prize cannot be the student who wins the second prize, then the probability of a student winning the second prize is 1/29.
So, the probability that you will win the top prize and your best friend wins the second prize is:
[tex]P=\frac{1}{30}\times\frac{1}{29}=\frac{1}{870}[/tex]Answer:
The probability that you will win the top prize and your best friend wins the second prize is 1/870.
In decimal form, this is 0.001149.
In percent form, this is approximately 0.11%.
I really need help is there any one that can help me rn ?
Given:
a function f(x) = (x-2)^2 is given.
Find:
we have to find the function whose graph is a result of horizonal shift of 2 units of the original graph.
Explanation:
Since the given graph of the function is shifted 2 units horizontally,
and we know y is vertical axis, x is horizontal axis.
So put x = x+2 in the given function, we get
[tex]\begin{gathered} f(x)=(x+2-2)^2 \\ f(x)=x^2 \end{gathered}[/tex]Therefore the graph of f(x)=(x-2)^2 is a result of horizontal shift of 2 units of f(x) = x^2.
The graphs are given for the reference
a spinner has four equal spaces: one is blue , one is red , one is green and one is yellow. What is the probability of spinning the spinner and having it land on blue (Give your answer as a percent, round to the nearest whole number if necessary) Please hurry on this question.
Answer: 25%
Explanation:
Probability is expressed as
number of favorable outcomes/number of total outcomes
From the information given, the spinner has 4 equal spaces. Thus,
number of total outcomes = 4
number of favorable outcomes = number of blue spaces = 1
Thus,
the probability of spinning the spinner and having it land on blue = 1/4 x 100
the probability of spinning the spinner and having it land on blue = 25%
Maria wants to put new carpet on her living room floor which is shaped like a square. If the length of one side of the floor in the living room is 19 feet, what is the area of the floor that will be re-carpeted?
The area to be recarpeted is 361 sq. m.
What is area?
The measurement that describes the size of a location on a horizontal or contour is called area. Surface area refers to the area of an extended surface or the border of a tri object, whereas the area of a horizontal region or flat area corresponds to the area of a form or planar laminate. Area can be interpreted as both the amount of substance with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
given the area is in form of square
So, the area of floor = 19x19 = 361 sq. m.
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I AQUIRE INFORMATION, please
What is the product of the radical expression? (7- square root of 7) (-6+ square root of 7)
The product of the given expression will be -49 + 13√7.
Product of two entities may be used to increase the amount of those entities. A radical expression may be defined as an expression which along with numbers and variables contain square root symbol. Instead of square root there can be cube root, fourth root or of root with any power. For example, 1 + √4, 1 + ∛4 etc. We have the expression (7 - √7) (-6 + √7). The product of this expression will be
Product = (7 - √7) (-6 + √7)
Product = -42 + 7√7 + 6√7 - 7
Product = -49 + 13√7 which is the required expression.
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Answer:
[tex]-49 + 13\sqrt{7}[/tex]
Step-by-step explanation:
[tex](7 - \sqrt{7} )(-6 + \sqrt{7})\[/tex] Distribute.
[tex]7 * -6 + 7 * \sqrt{7} - \sqrt{7} * -6 - \sqrt{7} * \sqrt{7}[/tex] Multiply. Keep in mind [tex]- \sqrt{7} * \sqrt{7} = (-\sqrt{7})^{2} = - 7[/tex].
[tex]-42 +13\sqrt{7} - 7[/tex] Combine like radicals/terms.
[tex]-49 +13\sqrt{7}[/tex]
convert the following improper fraction to a mixed number-11/4
We are given the improper fraction
[tex]-\frac{11}{4}[/tex]And told to express it as a mixed number. To do so, we take the denominator (4) and look for the closes multiple of it that is less than the numerator (11).Then, we write the numerator as the sum of that multiple of the denominator and another number.
In this case, note that 4*2 = 8 and 4*3=12. So 8 is the multiple of 4 that is the closest to 11, such that it is less than 11.
In this case, we can write the following
[tex]\frac{11}{4}=\frac{8+3}{4}[/tex]Then, we can split the sum as follows
[tex]\frac{8+3}{4}=\frac{8}{4}+\frac{3}{4}=2+\frac{3}{4}[/tex]We see that there is one number that is not a fraction. This is the whole number of the mixed number. So we have
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Finally, we add the negative sign, so we get
[tex]-\frac{11}{4}=-2\frac{3}{4}[/tex]Consider the expression. (-3)^-3 divided by 1/-6^2Which Three choices are equivalent to the expression givenA. 4/3B. 1/-(6)^2(-3)^3C. 36/-27D. -6^2/-27E. -36/(-3)^3
Solution
For this case we have the following:
[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex][tex](\frac{1}{-6})^2=\frac{1}{36}[/tex]When we apply the division we got:
[tex]\frac{\frac{1}{27}}{\frac{1}{36}}=\frac{36}{27}=\frac{4}{3}[/tex]Option A is correct
Option D is correct
Option E is correct
Final answer: A, D, E
hi hope your doing great. can you please show me the quick easiest way to solve math problem (work the problem with numbers)thank you kindly
Given:
The graph shows the XY plane where x shows the number of T shirts bought and Y shows the number of stickers received.
The plotted points on the graph have the coordinates:
[tex](1,2),(2,4)\text{ , (3,6) ,(4,8) , (5,10)}[/tex]Clearly, we can see the y coordinate is double of x coordinate here, so the equation of graph shown will be : y = 2x
Now we will check the points given in tables in the options if they satisfy this equation or not.
Check option (F),we get:
[tex](6,6)\text{ ,(7,7) , ( 8,8), (9,9)}[/tex]Which doesnot satisfy the equation y=2x hence, option F is wrong.
Now chcek option G ,
[tex](6,12)\text{ , (7,14), (8,16), (9,18).}[/tex]These points clearly satisfy y= 2x, hence,
Option (G) is correct.
Similarly, if we check option (H) and (I) they will not satisfy the equation, Hence , option (G) is only correct.
Hancox Homes Hancox Homes is a popular construction company that builds affordable housing. When the company first started, they sold 1 home the first month, 3 homes the second month, 9 homes the third month, and 27 homes the fourth month. What is the sequend pattern?
The sequence in the question may be given as
1, 3, 9, 27
From this, the first term is 1 and the common ration is 3
Common ratio = 3/1 = 9/3 = 27/9
= 3
List all the elements of the following set using set notation
We are told to list all the elements of whole numbers not greater than 8 using both the set notation and the listing method.
SET NOTATION
Let 'x' be used to represent the whole numbers.
[tex]\lbrace x\colon x\leq8\rbrace[/tex]LISTING METHOD
[tex]\mleft\lbrace\ldots,-2,-1,0,1,2,3,4,5,6,7,8\rbrace\mright?[/tex]Evaluate: open parentheses 3 y minus 2 close parentheses plus open parentheses fraction numerator 2 x y over denominator 3 end fraction space minus 30 space close parentheses space w i t h space x equals 10 comma space y equals 6 ANS.____________________ __________.
In order to evalute this expression, replace the variable placeholders with the numerical values, that is,
[tex](3(6)-2)+(\frac{2(10)(6)}{3}-30)[/tex]which gives
[tex]\begin{gathered} (18-2)+(\frac{120}{3}-30) \\ (16)+(40-30) \\ 16+10 \\ 26 \end{gathered}[/tex]then, the answer is 26.
Come onnnnSimplify fast help
Answer:
i know that if i just answered the question quick then it would have been better for you but i also need help with something but i know something that will help you
Step-by-step explanation: go to cymath ans type it in it will help you and you can use it on school laptops so im kind of helping future you
