The slope of the line that passes through the points (9,8) and (2,3) is 5/7.
What is a slope in a graph?The slope of a line in a graph is a measure of its steepness or slant. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line can be represented as the difference in the y-coordinates of two points on the line divided by the difference in the x-coordinates of the same two points.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
slope = (3 - 8) / (2 - 9) = -5 / -7 = 5/7
So, the slope of the line that passes through the points (9,8) and (2,3) is 5/7.
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Use the area model to factor 9c + 30d.
First, find the terms of the factors. The factor on the left must be a whole number greater
than 1, and all coefficients must be integers.
Factor the Greatest Common Factors out and then we are left with the expression 3(3c+10d).
What is expression term factor?Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression.
The terms are the numbers or the variables added together, factors are the numbers or the variables that are multiplied together and the coefficient is the number multiplied to the variable.
The numbers or variables that are multiplied to form a term are called its factors. For example, 5xy is a term with factors 5, x and y. The factors cannot be further factorized.
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Need as fast as possible
The graph of g(x) = 5x+9 can be obtained from the graph of f(x) by shifting the graph of f(x) up by 9 units.
What is graph?A graph is a visual representation of data points or connections between them. It is a mathematical structure used to represent relationships among data points. Graphs are used in various fields, such as mathematics, physics, engineering, computer science, and economics. They are also used to visualize complex information and to make it easier to understand. Graphs can be used to show relationships between two or more variables, to show how different variables are connected, and to illustrate trends in data.
This is because the equation of g(x) is the same as f(x) but with an added constant of 9. This addition of 9 causes the graph of g(x) to be shifted up by 9 units compared to the graph of f(x).
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when there are two coefficients, the resulting confidence sets are: part 2 a. rectangles. b. trapezoids. c. squares. d. ellipses.
Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses.
When a confidence set contains two coefficients, the coefficients determine the shape of the confidence set. Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses. When the coefficients are the same, as in a linear regression, rectangles are created. When the coefficients are different, as they are in a quadratic regression, trapezoids are created. When the coefficients are inversely connected, squares are created. Finally, ellipses are created when the coefficients, as in a cubic regression, are both distinct. The resulting confidence set can therefore take any of the four previously described shapes depending on the coefficients.
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(1 point) given the augmented matrix a=⎡⎣⎢⎢13−3−1−20−6−61−663⎤⎦⎥⎥, perform each row operation in the order specified and enter the final result. first: r2−3r1→r2, second: r3 3r1→r3, third: r3 3r2→r3.
Row 1 and Row 2 were divided by three in the initial row operation. Row 1 was multiplied by 3 in the second row operation, and row 3 was then updated with the result. The augmented matrix, 13 3 1 20 3 31 303, is the end result.
The provided augmented matrix is 13 3 1 20 6 61 666. Row 1 and Row 2 were divided by three in the initial row operation. This implies that each value in row 2 is subtracted from each element in row 1 by the factor of 3. The augmented matrix 133120331303 is the outcome of this row action. Row 1 was multiplied by 3 in the second row operation, and row 3 was then updated with the result. Thus, each element in row 1 is multiplied by three and the resulting value is added to its corresponding element in row 3, with the result. The augmented matrix 133120331303 is the outcome of this row action. Row 2 was multiplied by 3 in the third row operation, and row 3 was then updated with the result. Accordingly, each element in row 2 is multiplied by three and the resulting value is added to its corresponding element in row 3, with the result. The augmented matrix 133120331303 is the outcome of this row action. The augmented matrix 13 3 1 20 3 31 303 is the outcome of the row operations.
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an arithmetic sequence $2,5,8, 11, 14,\ldots$ is written in order in a book, one hundred numbers per page, beginning on page one. on which page will the number $11{,}111$ appear? if you are having trouble with this question, read problem 10.4 in the textbook.
The page where the number 110 appears will be 37.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
An arithmetic sequence 2, 5, 8, 11, 14,... is written in the order in a book. Then the first term is 2 and the common difference is 3. Then the number of terms if the nth term is 110. Then we have
110 = 2 + (n - 1) x 3
108 = (n - 1) x 3
n - 1 = 36
n = 37
The page where the number 110 appears will be 37.
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Gennaro is considering two job offers as a part-time salesperson. Company A will pay him $12.50 for each item he sells, plus a base salary of $500 at the end of the month. The amount Company B will pay him at the end of the month is shown in the table. Compare the functions’ initial values and rates of change. Then determine how much more Gennaro would make at Company A if he sells 28 items by the end of the month
Answer:
Answer: 80
Step-by-step explanation:
Solution:
salary of A: yA = 12.5x+500
suppose salary of B: YB= kx+ b
5455 = 3446
= Sk= It
500=10kth
b=350
YB = 15x + 350
When
X=28
УA = 830
48=770
УА -43 = 80
:)
PLEASE HELP WILL GET BRAINLY
The table below shows the ratio of materials in a composting container.
Brown Material (gallons) 12.75 18.6 24 E
Green Material (gallons) 4.25 B D 11.5
Total (gallons) A C 32 46
If Jeremy needs 52 gallons of compost to plant his garden in the spring, how much brown material will he need? How much green material will he need?
Jeremy will need 40 gallons of brown material and 12 gallons of green material.
Jeremy will need 13 gallons of brown material and 39 gallons of green material.
Jeremy will need 39 gallons of brown material and 13 gallons of green material.
Jeremy will need 37 gallons of brown material and 15 gallons of green material.
The amounts needed of brown and green material for 52 gallons of compost are
Brown material: 39 gallons.
Green material: 13 gallons.
What is a proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
On the first column of the table, the total amount is:
12.75 + 4.25 = 17 gallons.
The fractions of each material are given as follows:
Brown material: 12.75/17 = 0.75
Green material: 4.25/17 = 0.22.
Thus, the amount of brown material needed with 52 gallons is:
0.75 x 52 = 39 gallons.
and, the amount of green material needed with 52 gallons is:
0.25 x 52 = 13 gallons.
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Answer:
Brown material: 39 gallons
Green material: 13 gallons.
Step-by-step explanation:
the null and alternative hypotheses for a hypothesis test of the difference in two population means are: null hypothesis:mu 1 equals mu 2 alternative hypothesis:mu 1 does not equal mu 2 notice that the alternative hypothesis is a two-tailed test. suppose ttest ind method from scipy module is used to perform the test and the output is (-1.99, 0.0512). what is the p-value for this hypothesis test? select one.
As the alternate hypothesis is a two-tailed test the p-value for this hypothesis test is 0.0512.
Here the null hypothesis, H₀, is μ₁ =μ₂
Alternate hypothesis, H₁ , is μ₁ ≠ μ₂
The statistical test is said to be a two-tailed test. So the critical area of of distributions are on both sides of the range.
Here t test-ind method for spicy module is used.
The output is given as (-1.99 , 0.0512)
In such an output the first value is the test statistic value and second value is the p-value.
So the test statistic value = -1.99
p-value = 0.0512.
So the p-value is 0.0512.
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Use the diagram as a reference to answer the question below.
If arctan 3/3 = B find the measures of angles a and b and side lengths h, k, and r.
The measures of angles α and β and the side lengths h, k, and r, found using trigonometric ratios and the Pythagorean Theorem are;
α = 60°, β = 30°, h = √3, k = 3, r = 2·√3
Pythagorean Theorem states that the square of the length of the hypotenuse side is equivalent to the sum of the squares of the lengths of the legs of a right triangle.
The triangle formed by the sides h, k, and r, is a right triangle
The hypotenuse side of the right triangle = r
The legs of the right triangle are h and k
The measure of arctan(√(3)/3) = β...(1)
The tangent of angle β = h/k
Therefore; arctan(h/k) = β...(2)
Comparison the equations (1) and (2), we get;
h/k = (√3)/3
When h = √3, k = 3
Arctan(√3)/3 = 30°
Therefore;
β = 30°Angle α and angle β are complementary angles, therefore;
α + β = 90° (definition of complementary angles)
α = 90° - β
α = 90° - 30° = 60°
α = 60°Pythagorean Theorem indicates that we get;
r² = h² + k²
Therefore; r² = (√3)² + 3² = 3 + 9 = 12
r = √(12) = 2·√3
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let g be the successor function defined from z to z by the formula g(n) = n 1. g(−4,000) = g(0) = g(3,999) =
The value of g(−4,000) is −4,001, the value of g(0) is −1, and the value of g(3,999) is 3,998.
The successor function g, is a mathematical operation that takes any integer, n, and returns the next integer in the sequence. This is defined in terms of the formula g(n) = n + 1. This means that when we plug in a number, n, the function returns the number that comes after n in the sequence. The successor function g from Z to Z is defined by the formula g(n) = n - 1. To find the value of g(−4,000), we plug in -4,000 into the formula. g(−4,000) = −4,000 - 1 = −4,001. To find the value of g(0), we plug in 0 into the formula. g(0) = 0 - 1 = -1. To find the value of g(3,999), we plug in 3,999 into the formula. g(3,999) = 3,999 - 1 = 3,998. Therefore, the value of g(−4,000) is −4,001, the value of g(0) is −1, and the value of g(3,999) is 3,998.
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exercise 4 (20 points). in a certain population, the percentage of deaths due to car accidents is 1.2%, and the percentage of deaths due to shark attacks is 0.0005%. the percentage of surfers is: 1% among those who die in car accidents, 60% among those who die in shark attacks, and 0.5% among those who die by other causes. for a randomly chosen deceased person from this population, what is the probability that the person (a) (5 points) did not die due to a shark attack? (b) (5 points) was a surfer, given that the person did not die due to a shark attack? (c) (5 points) died due to a shark attack, given that the person was a surfer (d) (5 points) did not die due to a shark attack, given that the person was not a surfer?
For a randomly chosen deceased person from this population in a certain population,
the probability that the person (a) (5 points) did not die due to a shark attack is 6/5.the probability that the person (b) (5 points) was a surfer, given that the person did not die due to a shark attack is 3/200.the probability that the person died due to a shark attack, given that the person was a surfer is 3/5.the probability that the person did not die due to a shark attack, given that the person was not a surfer 6/5.Probability can be defined as the rate of the number of favorable issues to the total number of issues of an event. For an trial having 'n' number of issues, the number of favorable issues can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability( Event) = Favorable issues /Total issues = x/ nProbability of car accidents was 1.2% i,e 12/10 → 6/5
Probability of deaths due to sharks are 0.0005% → 1/2000
If a person is a surfer then,
Probability of surfer dying in a car accident is 1% → 1/10Probability of surfer dying by shark attack is 60%→ 3/5 Probability of surfer dying by other causes is 0.5%→ 1/200Learn more about Probability:
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Ratios-Item 35044 p Ravi makes lemonade by mixing lemon juice and water For every 1 cup of lemon juice, he uses 4 cups of water Drag the correct number of each ingredient into the box that would make 10 cups of lemonade Lemon p Water Ravi's Lemonade CLEAR
According to the information, to make 10 cups of lemonade Ravi needs 10 cups of lemon juice and 40 cups of water.
How to find the amount of lemon juice and water that Ravi needs for 10 cups of lemonade?To find the amount of lemon juice and water that Ravi needs to prepare 10 cups of lemonade we must take into account the following information.
For every cup of Ravi lemonade you should use 1 cup of lemon juice and 4 cups of water.
Therefore, the operation that we must perform is multiplication, in this case we must multiply the number of cups of lemon juice and water that he needs for each lemonade by the number of lemonades that he wants to prepare:
1 * 10 = 104 * 10 = 40So we can infer that Ravi needs 10 cups of lemon juice and 40 cups of water to make 10 lemonades.
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A bag factory is to produce 2 000 bags in four different colors-red, white, yellow,
and black in the ratio 3:4:5:8. How many bags of each color should be made?
To find out how many bags of each color should be made, we need to first find the total ratio of bags, which is 3+4+5+8=20.
Next, we find the number of bags in each color by dividing the color's ratio by the total ratio and multiplying by the total number of bags to be made (2000):
Red bags: (3/20) * 2000 = 300 bags
White bags: (4/20) * 2000 = 400 bags
Yellow bags: (5/20) * 2000 = 500 bags
Black bags: (8/20) * 2000 = 800 bags
So the factory should produce 300 red bags, 400 white bags, 500 yellow bags, and 800 black bags.
If u put 3500 in a bank account, with 2% interet for 5 year, how much money will have in the bank account
In 5 years after depositing 3500, the bank account will have 3850
What is simple interest?It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.
The formula for simple interest and procedure we will use to solve this exercise is:
S.I.= (P*R*T)/100
Where:
P = principalR = rate of interest in % per annumT = timeInformation about the problem:
P = 3500R = 2%T = 5 yearsTotal amount = ?Applying the simple interest formula, we get:
S.I.= (P*R*T)/100
S.I.= (3500*2*5)/100
S.I.= 350
Calculating the total amount that would be in my savings account, we get:
Total amount = P + S.I.
Total amount = 3500 + 350
Total amount = 3850
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two unit squares share the same center. the overlapping region of the two squares is an octagon with perimeter $\frac{10}{3}$. what is the area of the octagon?
Two unit squares share the same center. the overlapping region of the two squares is an octagon with perimeter 10/3. The area of the octagon is 0.833 square unit.
Let the octagon's eight successive vertices be A, B, C, D, E, F, G, and H.
Connect the squares' vertices to the shared center O by drawing the segments OA, OB, OC, OD, OE, OF, OG, and OH.
The octagon is divided into 8 triangles by the segments.
The bases of these triangles are AB, BC, CD, DE, EF, FG, GH, and HA; each triangle's height equals 1/2 of a unit.
Consequently, the octagon's surface area is
Area = (1/2) × (1/2) × (AB + BC + CD + DE + EF + FG + GH + HA)
Area = (1/4) × Perimeter of the octagon
Perimeter of the octagon = 10/3
Area = (1/4) × (10/3)
Area = 10/12
Area = 0.833 square unit.
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Find the length of side x to the nearest tenth.
suppose you deposit $1,000 into an account which pays 4 nnual interest, compounded quarterly. approximately how long will it take for the amount of money in the account to double?
The number of years will be 5 years, will it take for the amount of money in the account to double.
Here, we have,
The number of years will be computed using the excel formula as:
=N per(rate,pmt,pv,fv,type)
where
N per is number of years
rate is 4%
But is compounded quarterly,
So,
rate = 4% × 4
rate = 16%
pmt is $0
pv is Present value which is -$1,000
fv is future value which is $2,000 (as it will get doubled)
Putting the values above:
=N per(4%× 4,0,-1000,2000,0)
= 4.67 years or 5 years
Therefore, the amount will get double in 5 years will it take for the amount of money in the account to double.
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find the domain of the function. f(x)=√(7 x)/(-4 3x) write your answer as an interval or union of intervals.
The domain of the given function f(x) is = [-7,∞)∩(R-{3/4}).
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)
The domain of the function. f(x)=√(7 +x)/(-4 +3x)
[tex]f(x)=\frac{\sqrt{(7+x)}}{(-4+3x)}[/tex]
The domain of [tex]\sqrt{7+x}[/tex] is [-7,∞)
and the domain of -4+3x is R-{4/3}
the domain of the given function f(x) is = [-7,∞)∩(R-{3/4})
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find the volume and surface area of three-dimensional shapes (examples: rectangular and right prisms, cylinders, right pyramids). find the side lengths, radius, or diameter of a three-dimensional figure when given the volume or surface area
To find the volume and surface area of three-dimensional shapes, you can use the following formulas:
Rectangular Prism:
Volume: V = lwh (l = length, w = width, h = height)
Surface Area: A = 2lw + 2lh + 2wh
Right Cylinder:
Volume: V = πr^2h (r = radius, h = height)
Surface Area: A = 2πrh + 2πr^2
Right Pyramid:
Volume: V = (1/3)Bh (B = base area, h = height)
Surface Area: A = B + pl (B = base area, l = slant height)
Given the volume or surface area, you can find the side lengths, radius, or diameter of a three-dimensional figure by solving the formulas for the desired variable.
For example, if you are given the volume of a cylinder and want to find the radius, you can use the formula for the volume of a cylinder and solve for the radius:
V = πr^2h
r^2 = V / (πh)
r = √(V / (πh))
In a similar manner, you can find the side lengths, radius, or diameter of any three-dimensional shape by using the relevant formulas and solving for the desired variable.
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Can someone help me with this
The quantity of possible outcomes is known as probability.All events that could possibly occur.
What are examples and probability? The quantity of possible outcomes is known as probability.All events that could possibly occur.For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail).P(heads) = 12 is the formula.Three main categories of probability are as follows:Possibility theory.Probabilistic experimentation.Probability based on axioms.There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.To learn more about probability refer
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UREGNT!!! NEED ANSWER NOW!!! SEE BELOW!!!!!!
The required number of rhombi that can be made through two adjacent triangles is 300 rhombi.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
The given figure grid consists of 25 small triangles,
Since to make a rhombus we have to add 2triangles.
So the number of ways rhombi can be formed from 25 triangles
= 25C2
= 25!/2!
= 300 rhombus
Thus, the required number of rhombi that can be made through two adjacent triangles is 300 rhombi.
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I need help I will award 40 points!
The value of QS is 56 ft if Point Q is the midpoint of PS. And PQ = 56 ft
What is mid point ?
A midpoint is a factor mendacity among points and is within the middle of the line joining the 2 factors. If a line is drawn becoming a member of the two points, then the midpoint is a factor on the middle of the line and is equidistant from the two factors.
Given any factors, say A and C, the midpoint is a factor B that is located halfway among points A and C. therefore, to calculate the midpoint, we are able to truly degree the duration of the line section and divide through 2.
Given ,
Point Q is the midpoint of PS.
And PQ = 56 ft; so we have to find the value of QS.
Midpoint means that Q is between the points of P and S. Meaning the line QP and QS would be equal.
So the answer would be 56 ft,
Hence, The value of QS is 56 ft if Point Q is the midpoint of PS. And
PQ = 56 ft
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PLEASE HELP!! INFO IS IN PIC. WILL GIVE BRAINLIEST!!
The trigonometry function represented on the graph is
y = -0.5 sin (4x - π/2 ) - 1How to write the trigonometry functionSine waves or sinusoidal waves are the graphs of functions that are defined by the equation y = sin x.
The graph repeats itself as it advances along the x-axis, as you can see. Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.
How to interpret sine graph
The sine graph in the problem starts at (0, 0)
The equation is y = -0.5 sin (4x - π/2 ) - 1
The amplitude of the graph is 0.5The negative sign reverts the curveThe graph completes 4reolutions in 2πThe phase shift is π/2 to the leftA translation down one unitLearn more on sine graphs at:
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(T<3, –2> ◦ D5)(ΔTUV) for T(–1, –1), U(–1, 2), V(2, 1)?
Points T''(x, y) = (10, - 15), U''(x, y) = (10, 0) and V''(x, y) = (25, - 5) are the images of vertices T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2) and V(x, y) = (2, 1).
How to apply rigid transformations
In this problem we need to make use of rigid transformations on a triangle, rigid transformations are transformations applied on geometric locus such that Euclidean distance is conserved in every site of the locus. We need to make use of the following two operations:
Translation
P'(x, y) = P(x, y) + T(x, y)
Dilation
P'(x, y) = k · P(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectork - Dilation factorFirst, write the three vertices of the triangle:
T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2), V(x, y) = (2, 1)
Second, apply translation on every vertex:
T'(x, y) = (- 1, -1) + (3, - 2)
T'(x, y) = (2, - 3)
U'(x, y) = (- 1, 2) + (3, - 2)
U'(x, y) = (2, 0)
V'(x, y) = (2, 1) + (3, - 2)
V'(x, y) = (5, - 1)
Third, apply dilation on every image:
T''(x, y) = 5 · (2, - 3)
T''(x, y) = (10, - 15)
U''(x, y) = 5 · (2, 0)
U''(x, y) = (10, 0)
V''(x, y) = 5 · (5, - 1)
V''(x, y) = (25, - 5)
Vertices T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2) and V(x, y) = (2, 1) have the following images T''(x, y) = (10, - 15), U''(x, y) = (10, 0) and V''(x, y) = (25, - 5), respectively.
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A fair coin is tossed four times. What is the probability of getting at least two heads among all four tosses, given that at least one head came up among the first two tosses?
my work:
first, we know that the probability of getting at least one head among the first two tosses is 1 - (probability of getting no heads in the first two tosses) = 1 - (0.5 * 0.5) = 0.75.
next, we can use this information to find the probability of getting at least two heads among all four tosses, given that at least one head came up among the first two tosses. We can use the formula:
P(A | B) = P(A and B) / P(B)
where A is the event of getting at least two heads among all four tosses, and B is the event of getting at least one head among the first two tosses.
P(A and B) is the probability of getting at least two heads among all four tosses, given that at least one head came up among the first two tosses. We can find this by finding the probability of getting two or three or four heads among the four tosses, and adding them up.
to find the probability of getting two heads we can use binomial probability distribution:
P(X=2) = C(4,2) * (1/2)^2 * (1/2)^2 = 6 * (1/16) = 3/8
to find the probability of getting three heads we can use binomial probability distribution:
P(X=3) = C(4,3) * (1/2)^3 * (1/2) = 4 * (1/8) = 1/4
to find the probability of getting four heads we can use binomial probability distribution:
P(X=4) = C(4,4) * (1/2)^4 = 1 * (1/16) = 1/16
So P(A and B) = 3/8 + 1/4 + 1/16 = 21/32
now, we can substitute this into our formula:
P(A | B) = P(A and B) / P(B) = 21/32 / 0.75 = 28/42 = 2/3
so the probability of getting at least two heads among all four tosses, given that at least one head came up among the first two tosses, is 2/3.
The probability of getting at least two heads among all four tosses, given that at least one head came up among the first two tosses is given as follows:
p = 5/6.
How to obtain the probability?A probability is given by the division of the number of desired outcomes by the number of total outcomes.
Four the toss of four fair coins, the 16 total outcomes are given as follows:
H - H - H - H.H - H - H - T.H - H - T - H.H - H - T - T.H - T - H - H.H - T - H - T.H - T - T - H.H - T - T - T.T - H - H - H.T - H - H - T.T - H - T - H.T - H - T - T.T - T - H - H.T - T - H - T.T - T - T - H.T - T - T - T.There are 12 outcomes that result in at least one heads during the first two trials.
Among those, 10 outcomes result in at least two heads, hence the probability is defined as follows:
p = 10/12
p = 5/6.
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Write the equation of the line that passes through the points (4,−2) and (6,3). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
To find the equation of a line that passes through two given points, we can use the point-slope form of a line.
The first step is to find the slope of the line. We can do this by using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for the two given points:
m = (3 - (-2)) / (6 - 4) = 5 / 2
Next, we can use the point-slope form of a line to find the equation of the line:
y - y1 = m (x - x1)
Plugging in the values we have:
y - (-2) = 5/2 (x - 4)
Expanding the right side:
y + 2 = 5/2 x - 4
Multiplying both sides by 2:
2y + 4 = 5x - 8
Adding 8 to both sides:
2y + 12 = 5x
Dividing both sides by 2:
y + 6 = 2.5x
So the equation of the line that passes through the points (4, -2) and (6, 3) is y + 6 = 2.5x.
Are the triangles similar?
The two given triangles are not similar. The correct option is D.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Given that there are two triangles one triangle has sides 20 and 24. The second triangle has sides 36 and 42.
If the ratio of the two lines should be equal to the other two lines then the triangle will be similar.
( 20 / 36) = ( 24 / 42 )
4 / 9 = 6 / 7
Hence, the two triangles will not be similar.
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2.A container holds marble . A marble will randomly selected from the bag.
-!7 red marbles
-8 blue
-16 green
-9 black
What is the probability in decimal form that the selected marble will be green or black.
Answer:
To find the probability of selecting a green or black marble, we need to add the number of green marbles (16) to the number of black marbles (9) and divide by the total number of marbles (7 + 8 + 16 + 9 = 40). So the probability is:
(16 + 9) / 40 = 0.625 or 62.5% in decimal form.
A 2-yard piece of aluminum wire costs $13.50. What is the price per foot?
Answer:
Step-by-step explanation:
What is the relation between yard and feet?
The value of one yard is equal to 3 feet.
That is given by,
1 yard=3ft.
We have 2 yards piece of aluminum wire
Firstly, we have to find the cost for 2 pieces of wire.
2x3=6
The cost is 13.80
13.80/6=2.5.
Therefore the price per foot will be $2.5.
Solve the following initial value problems for y(t) by antidifferentiation or by
aseparation of variables:
e-21 dt =y(1-e); y(0) = 0
On Solving the initial value problem y(t) , e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0 , we get the solution is y² = e^(2t) - 2t - 1 .
The function is : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t) ;
⇒ e^(-2t)dy/dt = (1/y)(1-e⁻²t) ..because y⁻¹ = 1/y ;
⇒ ydy = e^(2t)[1-e^(-2t)) dt ;
⇒ ydy = (e^(2t) - 1)dt ;
now integrating both sides of the problem ;
⇒ y²/2 = [e^(2t)/2 - t]+c ;
Now we know that initial value : y(0) = 0 ;
Substituting y(0)= 0 , we get ;
⇒ 0²/2 = [e⁰/2 - 0]+c ;
⇒ c = -1/2 ;
So , the solution is y²/2 = [e^(2t)/2 - t] - 1/2 .
it can be written as : y² = e^(2t) - 2t - 1 .
Therefore , the solution of the initial value problem is y² = e^(2t) - 2t - 1 .
Solve the following initial value problems for y(t) by antidifferentiation or by aseparation of variables : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0 .
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