The equation of the line where the points (4, -1), (8, -3), and (12, -5) are
collinear is y = [tex]-\frac{1}{2}[/tex]x + 1.
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.
Collinear points are those that are situated along a single or shared straight line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either near or far from one another.
Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. A straight line's equation will be that relationship that:
Any place on the line's coordinates must meet.Any point that is not on the line will not have coordinates that satisfy.The slope of the line is :
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
(x1, y1) = (4, -1)
(x2, y2) = (8, -3)
(x3, y3) = (12,-5)
m = [tex]\frac{-3+1}{8-4}= -\frac{1}{2}[/tex]
In slope intercept form :
Equation of line is y = mx + c
where C is the intercept.
putting (x3, y3) in the equation we get,
-5 = [tex]-\frac{1}{2}[/tex] * 12 + c
⇒ -5 + 6 = c
⇒c = 1
The equation of the line where the points (4, -1), (8, -3), and (12, -5) are
collinear is y = [tex]-\frac{1}{2}[/tex]x + 1.
To learn more about Coordinate Geometry refer to :
https://brainly.com/question/7100287
#SPJ1
Charlotte bought a magazine for $5 and four boxes of candy. She spent a total of $25. How much did each box of candy cost?
Answer: $5
Step-by-step explanation: To calculate how much she spent on the 4 boxes of candy, we need to subtract 5 from 25, because we won't be including the cost of the magazine. So, therefore 25-5 is 20. So, now to find the cost for one, we need to set up a proportional relationship like this:
[tex]\frac{20}{4}[/tex] = [tex]\frac{?}{1}[/tex]
So, with that, we need to divide 4 by 20 to find the cost of 1. So, if you know, 20 divided by 4 = 5. So, therefore the cost of each candy box is $5. We can check our answer if we use the inverse operations, so our new equation would look like this:
5(4) + 5 = 25
We can check this, because we know 5 x 4 = 20, and 20 + 5 = 25. So 25 = 25, so it is $5.00
how would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details
Increases in tolerable misstatement will decrease sample size and assessed level of control risk will Increase sample size in a substantive test of details.
Sample size will be decreased when there is an increase in tolerant misstatement because there is a deviation that does not impact the financial statement. An increase in the assessed level of control risk, on the other hand, will increase sample size because the risk of material misstatements has also increased.
Complete question:-
How would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details?
a. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Decrease sample size
b. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Increase sample size
c. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Decrease sample size
d. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Increase sample size
To know more about sample size visit: brainly.com/question/25894237
#SPJ4
A set of data has a normal distribution with a mean of 47 and a standard deviation of 8. Find the percent of data within the following interval.
from 39 to 55
The percent of data within the interval from 39 to 55 which is normally distributed is 68.26%.
What is Normal and Standard Distribution ?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.However, most price distributions in finance are not quite normal.A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given in the problem mean is 47 and Standard Deviation(SD) is 8
Probability of data within 39 to 55 is
P(x<55) - P(x<39)
Let Z be the standard deviation :
[tex]\phi(Z) = \frac{x - mean}{SD}[/tex].
for X = 39
[tex]\phi(Z) = \phi(\frac{x - mean}{SD})[/tex] = [tex]\phi(\frac{39 - 47}{8}) = \phi(-1) = 1 - \phi(1) = 1-.8413 = .1587[/tex]
for X = 55
[tex]\phi(Z) = \phi(\frac{x - mean}{SD})[/tex] = [tex]\phi(\frac{55 - 47}{8}) = \phi(1) = .8413[/tex]
The percent of data within the interval from 39 to 55
(.8413 - .1587) = .6826 = 68.26%
To learn more about Normal Distribution refer to :
brainly.com/question/2181914
brainly.com/question/1852649
#SPJ1
PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!
The value of x on the equation 2.25 + 0.4x = -2.8 is -0.1375.
How to calculate the value of x?A equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions.
The equation is given as;
- 2.25 + 0.4x = -2.8
Collect the like terms
0.4x = -2.8 + 2.25
0.4x = -0.55
Divide
x = -0.55 / 0.4
x = - 0.1375
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
the variability believed to be in the population, the acceptable margin of sample error, and the level of confidence required in your estimates of the population values describe the basic elements required to calculate the proper sample size for a survey. true false
The statement mentioned in the question is True.
The sample size of a survey is determined by the variability believed to be in the population, the acceptable margin of sample error, and the level of confidence required in estimates of the population values. These elements are important considerations when designing a survey because they help to ensure that the results of the survey are reliable and accurately reflect the characteristics of the population being studied.
To calculate the proper sample size for a survey, you need to first determine the size of the population being studied and the level of precision you want to achieve in your estimates. You also need to consider the level of confidence you want to have in your estimates and the acceptable margin of error for your survey. Once you have all of this information, you can use a sample size calculator or a statistical formula to determine the appropriate sample size for your survey.
To learn more about sample size,
visit; brainly.com/question/29922928
#SPJ4
6) Which transformation or set of transformations will map a point (x, y) onto the point (3x, 3y+4 )
a
a dilation of scale factor 3 through the origin followed by a translation of up 4 unit
b
a dilation of scale factor 3 through the origin followed by a translation of right 4 unit
c
a dialation of scale factor 3 through the point ( 4, 0 )
d
a dialation of scale factor 3 through the point ( 0, 4 )
5) Which discription of a figure and its image match the transformation described by (x, y) → (x+5, y )
a
The figure and its image are neither similar nor congruent, and the image has been streched horizontally.
b
The figure and its image are similar, and the image has been translated 5 unit up.
c
The figure and its image are similar, and the image has been translated 5 unit to the right.
d
The figure and its image are neither similar nor congruent, and the image has been streched vertically.
6. The transformation or set of transformations which map a point (x, y) onto the point (3x, 3y+4 ) is; Choice A; a dilation of scale factor 3 through the origin followed by a translation of up 4 unit.
5. The description of a figure and its image match the transformation described by (x, y) → ( x+5, y ) is; The figure and its image are similar, and the image has been translated 5 unit to the right.
Which transformations maps the given pre-image and image points?It follows from transformations that a transformation using a scale factor, k about the origin is represented as; ( x, y ) → ( kx, ky ).
Also a shift in the horizontal or vertical direction by k units is represented by; ( x, y ) → ( x ± k, y ± k ) intuitively and respectively.
On this note, the given transformations are as represented in the answer section above.
Read more on transformations;
https://brainly.com/question/5020733
#SPJ1
What is the partial sum of terms 12 to 15 of the arithmetic sequence 100, 88, 76, 64, …?
The provided sequence's 12th through 15th terms add out to -200.
The formula is used to get the sum of n terms in an arithmetic sequence.
Sn = ((2×a₁)+(d×(n -1)))×(n/2)
where d is the common difference and a₁ is the first number in the series.
Finding the total of four words in a series that starts with 100, 88, 76 is necessary to solve this issue. These are the 12th through 15th terms.
General Term
The formula indicates what an arithmetic sequence's general term is.
aₙ = a₁ +d(n-1)
where d is the common difference and a is the first term.
The first term in the above sequence, a₁ is 100, and the common difference is...
d = 88 -100 = -12
Then the general term is
aₙ = 100 -12(n -1)
The 12–15 term total is what we need. This sub-first sequence's phrase is
a₁₂ = 100 -12(12 -1) = 100 -132 = -32
The following words in the series will all share a -12 common difference. The following sum formula may be used to get the total of the four terms:
Sₙ = (2·a₁+d(n -1))(n/2) . . . . . . . for a₁=-32, d=-12, and n=4
S₄ = (2·(-32) -12(4 -1))(4/2) = (-64 -36)(2) = -200
To learn more about Arithmetic Expression, visit:
brainly.com/question/29594290
#SPJ1
On Thursday the Meat King Market sold 210 pounds of ground beef. On Friday they sold twice
that amount. On Saturday they only sold 130 pounds. How much more meat did they sell on
Friday than Saturday?
Answer:
290
Step-by-step explanation:
210 x 2 = 420
420 - 130 = 290
(9x -38)= (2x+42) find mf this exam is crazy
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x=80/7
Decimal Form: x=11.428
or 11.44
Mixed Number Form: x=11 3/7
If f(x) = x³ - 5x² - 2x + 24 and x + 2 is a factor of f(x), then find all of the
zeros of f(x) algebraically.
All the zeroes of the polynomial x³ - 5x² - 2x + 24 are -2, 3, and 4.
What are the zeroes of a polynomial?The polynomial can be expressed as [tex]ax^{2} +bx+c=0[/tex], where a, b and c are real numbers. The numbers by which the polynomial expression values equal zero are termed zeroes of the polynomial.
The number of zeroes of the polynomial depends on the highest power of the polynomial.
Calculation:As x + 2 is one of the factor of f(x),
Now, dividing x³ - 5x² - 2x + 24 by x + 2, we get
Quotient = [tex]x^2-7x+12[/tex]
Remainder = 0
Now, factorizing the quotient by splitting the middle term,
[tex]x^2-3x-4x+12=0[/tex]
[tex]x(x-3)-4(x-3)=0[/tex]
[tex](x-3)(x-4)=0[/tex]
Now, equating both values to 0, we get
x = 3 and x = 4
All the zeroes of the polynomial x³ - 5x² - 2x + 24 are -2, 3, and 4.
To know more about zeroes of the polynomial, visit:
https://brainly.com/question/1398039
#SPJ1
Plssssssssssssssssssss
Select the correct text in the passage.
iS John is a journalist. He went to a product demonstration for a new computer. Some of what he heard was informative, while the rest was meant to
persuade consumers to buy the product. Which two statements in the excerpt are persuasive rather than informative?
At the latest launch by the computer manufacturer Mintel Corporation, they demonstrated the latest smart technology in their new computer. The
computer has voice recognition software that can adapt the user's experience to his or her preferences. This is something no other computer can
do at present.
The computer also has touchscreen technology, is loaded with the latest apps, and comes with a free year's subscription to Adobe
Photoshop. This is the best buy on the market.
The two sentences meant to persuade are the following:
"This is something no other computer can do at present.
"This is the best buy on the market".
What are the sentences for persuasion?It should be noted that persuasion is used to make someone agree to a particular point. From the information, at the latest launch by the computer manufacturer Mintel Corporation, they demonstrated the latest smart technology in their new computer.
The computer has voice recognition software that can adapt the user's experience to his or her preferences. This is something no other computer can do at present.
Learn more about persuasion on:
https://brainly.com/question/3764126
#SPJ1
juan is trying to save pizza from dinner, so he can bring pizza to school for lunch he bought 1 3/7 od pepperoni pizza and ate 1 1/3 of the pepperoni pizza how much pizza does he have left to bring to school?
Answer:
i think 2/21 i think im wrong
Step-by-step explanation:
PLEASE HURRY
Given:
1 = 4
2 = 3
Prove:
AB = CD
Which of the following triangle congruence theorems would be used in this proof?
ASA
AAS
SSS
ASA triangle congruence theorems would be used in this proof.
What is ASA rule ?
According to the ASA rule, two triangles are said to be congruent if any two of the angles and sides that make up one triangle are equal to the corresponding two angles and sides that make up the other triangle.
When two or more triangles are congruent, their corresponding angles and sides are also congruent, according to the formula CPCTC, which stands for "corresponding parts of congruent triangles are congruent".
So, AB=CD
Thus, ASA triangle congruence theorems would be used in this proof.
To learn more about the ASA postulate from the given link
https://brainly.com/question/2938476
#SPJ1
The ratio of females to males at a movie is 8 7 If there are 28 males how many females
are in the movie
Answer: 32 females
Step-by-step explanation:
28 divided by 7 = 4
so, multiply 8 by 4 as well.
Answer: 32 females are at the movie
Step-by-step explanation:
8(females):7(males)
x:28
28/7= 4
x=4x8
x=32
There are 32 females
Write the linear equation in slope intercept form
[tex]y= - \frac{1}{3} z +2[/tex] is slope intercept form of given equation.
How do you write slope intercept form?Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is typically simple. The standard form and the point-slope form are other formats for linear equations.Y equals mx plus b is actually the slope intercept form. Because it provides both a slope and an intercept, the form is known as a slope intercept form.Given liner equation :
[tex]\frac{1}{3} z + y = 2[/tex]
[tex]y = 2 - \frac{1}{3} z[/tex]
[tex]y= - \frac{1}{3} z +2[/tex]
To learn more about slope intercept form refer,
https://brainly.com/question/1884491
#SPJ1
The school's math team has 14 new members this year, which makes a total of 34. The number of new members represents about what percent of the total membership?
41% of the math team's total members are brand-new recruits.
What is percentage ?It is the ratio of two integers expressed as a decimal fraction of a whole number. It is a statistic for contrasting two sets of data, and the % sign is used to describe it as a percentage.
Percentages are often and creatively used. For instance, a lot of data is published as percentages in the media, including bank interest rates, retail discounts, and inflation rates. Percentages are essential for grasping the financial aspects of daily living.
The percentage of the entire membership that the number of new members represents is determined to be
=(14/34)×100
=41 %
0.41 x 100 = 41%
This means that 41% of the club is new members!
Thus, the number of new members is 41% of the total membership of the maths team.
Learn more about the percentage here:
brainly.com/question/26352729
#SPJ1
Go step by step to reduce the radical
The reduced form of the radical √192 is 8√3.
How to reduce radicals?A radical is a symbol that represents a particular root of a number. Radical simply means square root of a number.
Therefore, the symbols for radical is √.
Let's reduce the radical accordingly,
√192
Let's find number you can multiply to get 192. One of the numbers will be a perfect square.
Therefore, the numbers are 64 and 3. 64 is the perfect square.
Therefore,
√192 = √64 × 3 = √ 8² × 3 = 8√3
learn more on radicals here; https://brainly.com/question/21792967
#SPJ1
n- ? 1) When loan officers speak to people about taking out a loan for a certain principal, P at a certain monthly rate, they always have to balance two quantities, the monthly payment, m] with the number of payments, n] it takes to pay off the loan. These two vary inversely. All of these quantities can be related by the formula: Por 1-(1+r)¯" m= Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20-year period.. 110
[tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex] is the monthly payment
What is Compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
According to given question:
Principle Amount (P) = $200, 000
Rate(r) = 4% yearly
Rate(r) = 4/12 % Monthly
Rate(r) = 1/3 % Monthly
Time = 20 years = 240 months
⇒ 240 is the number of payment needed to pay
n = 240
Therefore, the monthly payment needed to pay
⇒ [tex]m = \frac{P.r}{1-(1-r)^{-n} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(1-1/3)^{-240} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex]
To learn more about Compound interest , check out
https://brainly.com/question/14295570
#SPJ1
g(x) = x² - 4x²+x+6
The simplified expression of g(x) = x² - 4x² + x + 6 is g(x) = -3x² + x + 6
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
g(x) = x² - 4x²+x+6
Rewrite properly
So, we have the following representation
g(x) = x² - 4x² + x + 6
Evaluate the like terms
g(x) = -3x² + x + 6
The above expression cannot be further simplified
Hence, the solution is g(x) = -3x² + x + 6
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
Fractions on number line help!!!!!
Answer:
There are four small lines between 0 and 1 in the number line, they denote the decimals : 0.2, 0.4, 0.6 and 0.8. Put the SUM on the 0.4 line
9. A straight line passes through points (2, 12) and (3, 8). What is the equation of the
line?
a philosophy professor assigns letter grades on a test according to the following scheme. a: top 12 % of scores b: scores below the top 12 % and above the bottom 63 % c: scores below the top 37 % and above the bottom 22 % d: scores below the top 78 % and above the bottom 7 % f: bottom 7 % of scores scores on the test are normally distributed with a mean of 72 and a standard deviation of 8.1. find the numerical limits for a b grade. round your answers to the nearest whole number, if necessary.
Rounding to the nearest whole number, the limits for a 'b' grade are 75 and 81
In this question we have been given a philosophy professor assigns letter grades on a test according to the given scheme.
We need to find the numerical limits for a b grade.
b: scores below the top 12 % and above the bottom 63 % which means scores between the 63th and 88th percentile.
Given that the scores on the test are normally distributed with a mean of 72 and a standard deviation of 8.1
μ = 72, σ = 8.1
z-score at the 63th percentile: 0.332
z-score at the 88th percentile: 1.175
The lower limit of a 'b' grade is:
0.332 = X - μ/σ
0.332 = (X - 72)/8.1
2.67 = X - 72
X = 74.67
X ≈ 75
The upper limit of a 'b' grade is:
1.175 = X - μ/σ
1.175 = (X - 72)/8.1
9.52 = X - 72
X = 81.52
X ≈ 81
Therefore, you get a 'b' if you have a grade between 75 and 81
Learn more about the normal distribution here:
brainly.com/question/29509087
#SPJ4
help me pleaseeeeeeee
Answer:
Step-by-step explanation:if angle a is 42 then b is 42 which means its 42 right, so its cos(42)=AB over 10, the last one its a educated guess.
Find the number of degrees for the sum of the interior angles of a regular 12-sided figure.
Answer:
Sum of 12-sided polygon=1800°
Measure of each interior angle of a regular12-sided polygon=150°
Given: Angle R is congruent to Angle Q Segment AS is congruent to Segment AT Which of the following may not be true?
Angle 5 is congruent to Angle 6
Segment AR is congruent to Segment AQ
Segment RS is congruent to Segment TQ
Angle 2 is congruent to Angle 3
please helppppp :(((
Answer: Crust and asthenosphere should be switched
Step-by-step explanation:
Brainliset please?
Answer:
Step-by-step explanation:
crust is the surface of the earth and the asthenosphere below it with currents that cause earthquakes.
if d is the standard deviation of x, y, and z, what is the standard deviation of x 5, y 5, and z 5 ?
If we add any constant term in the variable then the standard deviation remains same. So it is not change.
In the given question, d is the standard deviation of x, y, and z.
We have to find the standard deviation of x+5, y+5, and z+5.
As we know that;
Data distribution in reference to the mean is measured by a standard deviation, or. Samples are said to be more narrowly collected around the mean when the standard deviation is minimal and more dispersed when the standard deviation is higher.
While a high or low standard deviation implies that data points are, respectively, above or below the mean, a standard deviation that is close to zero suggests that data points are, on the other hand, relatively close to the mean.
If we see that in each variable x, y, z a constant value 5 is added.
If we add any constant term in the variable then the standard deviation remains same. So it is not change.
To learn more about standard deviation link is here
brainly.com/question/29088233
#SPJ4
The right question is:
If d is the standard deviation of x, y, and z, what is the standard deviation of x+5, y+5, and z+5?
The function p(x) = x³ + x² = x³ + x²-x+ 5 is graphed on the coordinate plane. As x approaches positive infinity, what value does p(x) approach?
A. 0
B. 5
C. +infinity
D. -infinity
As x approaches positive infinity, the function r(x) approaches negative infinity.
What is a function approaches infinity?
In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero.
As x approaches positive infinity, the term x^3 becomes dominant, and the value of the function p(x) approaches positive infinity as well.
In general, when the highest-order term in a polynomial function has a positive coefficient, the function will approach positive infinity as x approaches positive infinity.
Similarly, if the highest-order term has a negative coefficient, the function will approach negative infinity as x approaches positive infinity.
For example, consider the function q(x) = 3x^3 - 2x^2 + x - 5. As x approaches positive infinity, the term 3x^3 becomes dominant, and the function q(x) approaches positive infinity. On the other hand, if we consider the function r(x) = -3x^3 + 2x^2 - x + 5, the highest-order term is -3x^3, which has a negative coefficient.
Therefore, as x approaches positive infinity, the function r(x) approaches negative infinity.
To learn more about the function approaches infinity visit,
https://brainly.com/question/26385044
#SPJ1
set the two equations to each other then solve for x y=2x-3
Answer:
The value of x is (y + 3)/2
Step-by-step explanation:
y = 2x - 3
y + 3 = 2x - 3 + 3
y + 3 = 2x
2x/2 = (y + 3)/2
x = (y + 3)/2
Thus, The value of x is (y + 3)/2
Answer:
x = (y + 3)/2
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ y = 2x - 3
Then the value of x will be,
→ y = 2x - 3
→ 2x - 3 = y
→ 2x = y + 3
→ x = (y + 3)/2
→ x = (y/2) + (3/2)
Hence, answer is x = (y + 3)/2.
