The equation of the line is y = ( 1/2 )x + 1 and the y intercept is b = 1
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 1 )
Let the second point be Q ( 4 , 3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 1 ) / ( 4 - 0 )
Slope m = 2/4
Slope m = 1/2
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = ( 1/2 ) ( x - 0 )
y - 1 = ( 1/2 )x
Adding 1 on both sides , we get
y = ( 1/2 )x + 1
Hence , the equation of line is y = ( 1/2 )x + 1
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A triangle has integer side lengths 2, 5 and x. What is the median of all possible
values of x?
The median of all possible values of x is 5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
To find the median of all possible values of x, we need to find all the possible values of x first.
By the triangle inequality, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write:
2 + 5 > x
2 + x > 5
5 + x > 2
Simplifying each inequality, we get:
7 > x
x > 3
x > -3
The smallest possible integer value for x is 4 and the largest possible integer value for x is 6.
Therefore, the possible integer values for x are 4, 5, and 6.
Since we have an odd number of values, the median is simply the middle value, which is 5.
Therefore, the median of all possible values of x is 5.
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20. A popular pizza parlor charges $12 for a large cheese pizza plus $1.50 for each additional topping. The
total cost, C, of a pizza with T toppings can be represented by C = 1.50T + 12. What is the domain in
the context of the problem situation?
Answer:
efgdfhncdrt gguhd r g sixtieth sex
Using the Rule of 70, what approximate interest rate would be needed for an investment
of $14,000 to double by the end of 32 years?
A22.49
B 45.7%
C 2.19%
What are four solutions of this equation that are ordered pairs? y=2x+4
Answer: (0,4), (1,6), (2,8), (3,10)
Step-by-step explanation:
you can plug this equation into a graphing calculator (if you don't have a physical one, you can use desmos online graphing calculator) or just graph it on paper.
If you graph it on paper, start at (0,4) because that is the y-intercept. Then go up 2 and right 1 and plot a point there. Up 2 and right 1 and plot a point, etc.
Some points on this line are (0,4), (1,6), (2,8), (3,10)
For what value of x is the given parallelogram a rhombus?
The value of x the given parallelogram a rhombus is 18
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The quadrilateral that is a rhombus
The diagonals of rhombus bisect each other
Using the above as a guide, we have the following:
Angle 1 = A
Substitute the known values in the above equation, so, we have the following representation
5x - 30 = 3x + 6
Evaluate
2x = 36
Divide
x = 18
Hence, the value is 18
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what is 10% of 500000?
Answer:
Step-by-step explanation: the answer is 50000.
……………Help with 22-27…………
The equations of the lines in slope-intercept form are:
22. y = -1/2x + 3.
23. y = 2x - 3.
24. y = -x
25. y = -2x + 4.
26. y = 3/2x - 2.
27. y = 5/2x - 1/2
28. y = x + 3
29. y = -x + 2
30. y = -1/4x + 9/4
How to Find the Equation of a Line in Slope-intercept Form?The equation of a line is y = mx + b, in slope-intercept form, where:
m = slope = rise/run = change in y / change in x
b = y-intercept or the point where the graph intercepts the y-axis.
22. Slope (m) = rise/run = -1/2
y-intercept (b) = 3
Substitute m = -1/2 and b = 3 into the equation, y = mx + b:
y = -1/2x + 3.
23. Slope (m) = rise/run = 4/2 = 2
y-intercept (b) = -3
Substitute m = 2 and b = -3 into the equation, y = mx + b:
y = 2x - 3.
24. Slope (m) = rise/run = -2/2 = -1
y-intercept (b) = 0
Substitute m = -1 and b = 0 into the equation, y = mx + b:
y = -x + 0
y = -x
25. Slope (m) = rise/run = -2/1 = -2
y-intercept (b) = 4
Substitute m = -2 and b = 4 into the equation, y = mx + b:
y = -2x + 4.
26. Slope (m) = rise/run = 3/2
y-intercept (b) = -2
Substitute m = 3/2 and b = -2 into the equation, y = mx + b:
y = 3/2x - 2.
27. Slope (m) = rise/run = 5/2
y-intercept (b) = -0.5 = -1/2
Substitute m = 5/2 and b = -1/2 into the equation, y = mx + b:
y = 5/2x - 1/2
28. Slope (m) = change in y / change in x = (5 - 3) / (2 - 0) = 2/2 = 1
y-intercept (b) = 3
Equation is, y = x + 3
29. Slope (m) = change in y / change in x = (-1 - 4) / (3 -(-2)) = -5/5 = -1
Substitute (x, y) = (3, -1) and m = -1 into y = mx + b, to find b:
-1 = -1(3) + b
-1 = -3 + b
-1 + 3 = b
2 = b
b = 2
The equation would be: y = -x + 2
30. Slope (m) = change in y / change in x = (3 - 2) / (-3 - 1) = 1/-4 = -1/4
Substitute (x, y) = (1, 2) and m = -1/4 into y = mx + b, to find b:
2 = -1/4(1) + b
2 = -1/4 + b
b = 2 + 1/4
b = 9/4
The equation would be: y = -1/4x + 9/4
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Which inequality represents all the solutions of 4(3x + 2) < 5(3x − 2)? Select the correct answer.
Answer:
x > 6
Step-by-step explanation:
4(3x+2) < 5(3x-2)
12x+8 < 15x-10
12x-15x < -10-8
-3x < -18
3x > 18
x> 6
can anyone please help me do this? I need it done asap but nothing makes sense
Answer:
Skip it bro this fin be hard and i can do the next one i tryed to do this and it hard
Step-by-step explanation:
4.) You roll a number cube twice. Find the probability that the first roll shows a five, and then
che second roll shows a six.
The probability of rolling a 5 and then 6 is 1/36
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Number cube rolled twice
The sample space of each number cube is
Sample space = {1. 2. 3. 4. 5. 6}
From the above entries, we have
P(5) =1/6
P(6) = 1/6
Using the above as a guide, we have the following:
P = 1/6 * 1/6
Evaluate
P = 1/36
Hence, the probability is 1/36
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E = (children who go to the park),
T = {children who play tennis) ,
G = {children who play golf}
120 children go to the park. 50 play tennis. 75 play golf. 25 do not play tennis or golf.
(a) Show this information in the Venn diagram.
(b) How many children play both golf and tennis?
Answer:
125 children play tennis and golf
don't forget to follow me ,
please help!! Describe an octant's main features
An octant's main features are :
Axes Positive and negative regions Quadrants What are the main features of an octant ?An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.
Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.
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Part C: Charlie designs a square garden. Each side length is 3x + 5.
The perimeter of Charlie's garden is how much larger than the perimeter of Shawn's
garden?i
The requried difference between the perimeters of the two gardens would be, 12x + 20 - 4s.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
Let's assume that Shawn's garden is also a square with side lengths. Therefore, the perimeter of Shawn's garden would be 4s.
The perimeter of Charlie's garden would be 4(3x + 5), which simplifies to 12x + 20.
The difference between the perimeters of the two gardens would be,
12x + 20 - 4s
We can't simplify this expression any further without knowing the value of s.
Therefore, we can conclude that the difference between the perimeters of the two gardens depends on the side length of Shawn's garden.
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(Likelihood MC)
A collector has items including baseball cards, gold coins, and stamps in a box. If P(gold coin) 50%, interpret the likelihood of randomly selecting a gold coin from the box.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer: The likelihood of randomly selecting a gold coin from the box is "Likely."
When the probability of an event is 50%, it means that there is an equal chance of the event happening or not happening. In this case, the probability of randomly selecting a gold coin from the box is 50%, so it is likely to occur.
Step-by-step explanation:
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
The quotient of the division is 3x - 11 with a remainder of 37x + 21
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
Using the long division method of quotient, we have
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
The division steps are as follows
3x - 11
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
3x³ + 9x² + 9
------------------------------------------------
-11x² + 4x - 12
-11x² - 33x - 33
------------------------------------------------
37x + 21
Hence, the quotient is 3x - 11
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Leo replaces the strings on some guitars. He puts 6 new strings on Each guitar. He uses 18 strings. How many guitars does leo put Strings on?
Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
So, we know that:
6 new strings are put on each guitar.
He uses 18 strings.
Then, the number of guitars:
⇒ 18/6 = 3
Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
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Which one of the following best defines the notion of the P-value of a hypothesis test? a. The probability of rejecting H_o, whether it's true or not b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true c. The probability of the type I error d. The probability of the type II error
P-value of a hypothesis test is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about rejecting or failing to reject the null hypothesis.
A hypothesis test is a statistical method used to test the validity of an assumption or a hypothesis about a population based on a sample data.
The correct answer is b. The P-value of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
In hypothesis testing, we start with a null hypothesis, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.
The P-value is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.
A high P-value indicates that the sample data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.
In mathematical terms, the P-value is calculated as the probability of observing a test statistic Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.
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3. In one pond in the forest, scientists found that a sample of pond water contained 45 minnows for every 27 tadpoles. How many tadpoles would they expect to find in a sample that contained 315 minnows? Show all work and explain how you got your answer
Answer: 189
Step-by-step explanation:
for every 45 minnow there will be 27
315 minnow is 7 times 45 minnow 27*7 is 189
What is the value of (2^(2014)+2^(2012))/(2^(2014)-2^(2012))? (A) -1 (B) 1 (C) (5)/(3) (D) 2013 (E) 2^(4024)
The value of the exponential equation is A = 5/3
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ] be equation (1)
On simplifying the equation , we get
Taking the common factor as 2²⁰¹² , we get
A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]
On further simplification , we get
A = ( 2² + 1 ) / ( 2² - 1 )
A = ( 4 + 1 ) / ( 4 - 1 )
A = 5/3
Therefore , the value of A is 5/3
Hence , the equation is A = 5/3
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Question 9
Triangle ABC has vertices of
A (2,4)
B (3,7)
C (7,4)
What will be the vertices of Triangle A'B'C' after a dilation of k = 2, centered at point A?
A'
B’
C’
I NEED HELP
The coordinates of the triangle after the dilation of k = 2 is given by
A' ( 4 , 8 ) , B' ( 6 , 14 ) and C' ( 14 , 8 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , let the dilated triangle be represented as A'B'C'
And , the coordinates of the triangle ABC are
The coordinate of A = A ( 2 , 4 )
The coordinate of B = B ( 3 , 7 )
The coordinate of C = C ( 7 , 4 )
And , the dilation factor k = 2
So , the new coordinates of the dilated triangle are
The coordinate of A' = A' ( 4 , 8 )
The coordinate of B' = B' ( 6 , 14 )
The coordinate of C' = C' ( 14 , 8 )
Hence , the triangle is dilated by a scale factor of 2
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A car salesman earns 5% on the sale of a BMW sold for $103,100. What is his take home pay that day?
Answer:
$5155
Step-by-step explanation:
We know
A car salesman earns 5% on the sale of a BMW sold for $103,100.
5% = 0.05
What is his take-home pay that day?
We take
103,100 times 0.05 = $5155
SO he takes home $5155.
Step-by-step explanation:
Looks like we're trying to find out what 5% of 103,100 is. We first need to convert the percent into a decimal and then multiply.
[tex]5\% = 0.05[/tex]
Now we can multiply
[tex](0.05)(103100) = 5155[/tex]
What is the cost of 0. 85 pound of imported cheese at $7. 90 per pound
Answer:
Step-by-step explanation:
Cost = 0.85 x $7.90
Cost = $6.72
What is the prime factorization of 51?
The prime factorization of 51 is 3 * 17.
Graph the line that has a slope of 1/4 and includes the point (0,4).
.
Answer: y = mx+b
y = -1x+1/4
Step-by-step explanation:
Leo's rent is due a few days before he expects to receive his paycheck from work. He takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck. The lender charges $15 for every $100 borrowed, which needs to be paid back in 2 weeks.
Leo needs to pay back a total of $215 in two weeks.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Leo takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck and the lender charges $15 for every $100.
Now, (15/100)×100% = 15%.
Therefore, He has to pay back,
[(100 + 15)/100]×200.
= (115/100)×200.
= 1.15×200.
= $230.
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the scale of a map is 1:50000 find the area in square km of a square field 4cm² on the map.
The area in square km of a square field 4 cm² is given as follows:
1 km².
How to obtain the area?The area is obtained applying the proportions in the context of the problem.
The scale is of:
1 cm : 50000 cm -> 1 cm = 0.5 km, as 1 cm = 10^-5 km.
Hence, for the areas, in square units, the scale is obtained squaring both sides, as follows:
(1 cm)² = (0.5 km)²
1 cm² = 0.25 km².
Meaning that the area of the square field is of:
4 x 0.25 = 1 km².
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Mayerlin has xx dimes and yy nickels. She has no more than 20 coins worth no less than $1.30 combined. Solve this system of inequalities graphically and determine one possible solution.
what are the inequalities?
Answer: look at the image for the answers and solutions
Step-by-step explanation:
3
The volume of a sphere is given by V = Tr³, where r is the radius.
Find the inverse function. Describe what it represents.
The inverse function is v⁻¹ = ( v/T)^1/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that the formula of the volume of the sphere is,
⇒ v = 4/3 πr³
T = 4/3π
Now,
To determine the inverse function we can solve the formula for the term r as;
⇒ v = 4/3 πr³
Multiply by 3/4 we get;
⇒ 3v/4 = πr³
Divide by π both side, we get;
⇒ 3v/4π = r³
Substitute r = v⁻¹ in above equation, we get;
⇒ v⁻¹ = ( v/T)^1/3
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The function C approximates the number of calories recommended per day for
a dog, based on the weight, in pounds, of the dog.
The table gives values of C for selected values of p, where C(p) represents the
recommended number of calories per day for a dog that weighs p pounds.
Recommended Number of Calories for Dogs
p (pounds) C(p)
A2.F.BF.A.la
a.
C(x) = 18p +22
b. C(x) = 22p+ 18
?
11
22
33
Which of the equations shown most closely approximates C?
44
55
66
77
88
250
450
750
1000
1250
1500
1700
1880
C.
C(x) = 40(1.06)
d. C(x) = 48(1.07)"
The equation most closely approximates C is C(x) = 22p+ 18.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that function, C calculates the number of calories recommended per day for a dog based on the dog's weight in pounds.
The equation can be written as:-
C(x) = 22p+ 18.
Here the dependent variable is C(x) and the dependent variable is p. So the value of C(x) will always depend upon the variable p.
Therefore, the correct equation will be C(x) = 22p+ 18.
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A tiling pattern is defined by the pattern rule equation n = 5+ 3p, where p is the
position number and n is the number of tiles. How many tiles would there be in
position 26?
Step-by-step explanation:
n=5+3p
when p=26,
n=5+3×26=83