Write the equation of the
line that is parallel to
y = 1.5x – 6 and passes
through the point (4,2).
Answers
:)
The equation of the line is (y - 2) = 1.5(x - 4)
What is line ?
Euclid described a line as an "unextended length" that "stands equally with respect to its points"; he introduced the postulates as the main unprovable properties from which he constructed all of geometry, now called Euclidean geometry to avoid confusion with other geometries introduced from the late 19th century (such as non-Euclidean, projective and affine geometry).
In modern mathematics, given the multiplicity of geometries, the concept of line is closely related to the way geometry is described. For example, in analytic geometry, a plane line is often defined as a set of points whose coordinates correspond to a given linear equation, but in a more abstract setting, such as drop geometry, the line may be an object other than the set. of the points located on it.
When geometry is described by a set of axioms, the concept of line is usually left undefined (so-called primitive object). The properties of the lines are then determined by the axioms that refer to them. One of the advantages of this approach is the flexibility it gives users of the geometry. Thus, in differential geometry a line can be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and allows physicists, for example, to think of the path of a light ray as a line.
Given, [tex]y = 1.5x - 6....(1)[/tex]
We are comparing equation (1) with y = mx+c and get m = 1.5
It is also given required equation passes through the point (4,2)
We know, if slope of a equation m and the equation passes through (a,b) then equation of the line (y-b) = m (x-a)
Here,
[tex]m = 1.5 \\ a = 4 \\ b = 2[/tex]
So, required equation of the line [tex](y - 2) = 1.5(x - 4)[/tex]
Line related one more question:
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Related Questions
This is due in 15 minutes help.
Answers
The probability that the next student he sees will be a boy with brown eyes is 25%. All of them are the exact same so 100 divided by 4 is 25.
What is the volume of the can below? Use Pi = 3.14 and round your answer to the nearest tenth. A cylinder with height 96 millimeters and diameter of 66 millimeters.
Answers
Answer
328,268.2 mm cubed is correct!
Step-by-step explanation:
If you use the formula V=πr²h with these steps:
1. Calculate the area of the base (which is a circle)
2. use the equation πr² where r is the radius of the circle.
3. Then, multiply the area of the base by the height of the cylinder
4. The volume is found!
Answer:
328,268.2 cubic millimeters
Step-by-step explanation:
I did it on edge
please help
In the parallelogram below,
x = [? ]
3х+7
5x-17
Answers
Answer:
x = 12
Step-by-step explanation:
3х+7 = 5x-17
-2x = -24
Question 3 of 3
Carlita has a swimming pool in her backyard that is rectangular with a length of 28 feet and a width of 12
feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she
wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood
deck.
Answers
The perimeter of the wood deck can be expressed, based on the length and width of the swimming pool to be 80 + 8c + 8w feet.
How to find the perimeter ?The perimeter of a rectangle is given by the formula 2x ( length + width ). With the walkway installed, the length becomes (28 + 2c) feet and the width becomes ( 12 + 2c ) feet.
Therefore, the length with the wood deck is ( 28 + 2c + 2w ) feet and the width with the deck is ( 12 + 2c + 2w ) feet.
The perimeter would therefore be:
P = 2 x [ ( 28 + 2c + 2w ) + (12 + 2c + 2w )]
P = 2 x [ 40 + 2c + 2w + 2c + 2w ]
P = 80c + 8 c + 8 w
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82,78,86,82,94,84,90.What is the mode
Answers
Answer:
82 ☺️
Step-by-step explanation:
Can you help me please thank you
Answers
6. 4x^2 + x - 1
7. 3x^2 + 4x + 4
Explanation:
(3x^2 + x + 8) + (x^2 - 9)
4x^2 + x - 1
(5x^2 + 8x - 2) - (2x^2 - 4x + 6)
3x^2 + 4x + 4
Someone pls help me I’ll give out brainliest please dont answer if you don’t know.
Answers
Answer:
-12n - 6
Step-by-step explanation:
6(-2n - 1 ) -12n - 6 You need to multiply the 6 by the numbers inside the Parenthesis.A firm's marginal revenue and marginal cost functions are given by MR = R'(x) = 205 -0.5x2 and MC = C'(x) = 85 +0.7x2. Fixed costs are 10. a) Write down an expression for total revenue and deduce the corresponding demand function. Write down an expression for the total cost function. c) Determine the maximum profit.
Answers
a) The expression for total revenue is:
[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]
The demand function is:
[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]
b) The expression for the total cost function is:
[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]
c)The maximum profit, is 1079.56
How to write an expression for total revenue and deduce the corresponding demand function?a) Total revenue is the integral of marginal revenue. Thus, expression for total revenue is:
[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]
The demand function is the inverse of the total revenue function:
[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]
b) Total cost is the integral of marginal cost:
[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]
c) Profit is total revenue minus total cost:
P(x) = R(x) - C(x) = 205x - 0.25x³ - (85x + 0.21x³ + 10) = 120x - 0.46x³ - 10
To find the maximum profit, we need to find the point where marginal profit is zero. Marginal profit is the derivative of profit:
P'(x) = 120 - 1.38x² = 0
Solve for x:
120 - 1.38x² = 0
1.38x² = 120
x² = 120/1.38
x = √(120/1.38)
x = 9.33
We find that the maximum profit is achieved when x = 9.33. Thus, the maximum profit:
P(9.33) = 120(9.33) - 0.46(9.33)³ = 1079.56
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If cos theta = 0.3090, which of the following represents approximate values of sin thetha for 0 degrees <90 degrees?
A. sin thetha =0.9511;tan theta = 0.3249
B.sin thetha =0.9511 ;tan thetha =3.0780
C. sin thetha 3.2362 ; tan thetha=0.0955
D. sin thetha = 3.2362;tan thetha=10.4731
Answers
The approximate value of sin(theta) for 0 degrees < theta < 90 degrees, given cos(theta) = 0.3090, is approximately ±0.9511. The correct answer from the given options is A, which states sin(theta) = 0.9511 and tan(theta) = 0.3249.
To determine the value of sin(theta) given that cos(theta) is 0.3090, we can use the identity [tex]\(\sin^2(\theta) + \cos^2(\theta) = 1\)[/tex].
Since we know cos(theta) is 0.3090, we can substitute it into the identity:
[tex]\(\sin^2(\theta) + 0.3090^2 = 1\)[/tex]
[tex]\(\sin^2(\theta)\)[/tex] + 0.095481 = 1
[tex]\(\sin^2(\theta)\)[/tex] = 0.904519
Taking the square root of both sides, we get:
sin(theta) = √(0.904519)
sin(theta) ≈ ±0.9511
So, the approximate value of sin(theta) is approximately ±0.9511.
Now let's evaluate the given options:
A. sin(theta) = 0.9511; tan(theta) = 0.3249
B. sin(theta) = 0.9511; tan(theta) = 3.0780
C. sin(theta) = 3.2362; tan(theta) = 0.0955
D. sin(theta) = 3.2362; tan(theta) = 10.4731
We can eliminate options C and D immediately since the value of sin(theta) cannot be greater than 1.
Now, let's consider options A and B. Both options have sin(theta) = 0.9511, which matches our approximate value. However, the value of tan(theta) in option A is 0.3249, while in option B it is 3.0780.
Since we're looking for values of sin(theta) and tan(theta) that are consistent with the given cos(theta) = 0.3090, we can conclude that option A is the correct answer.
Therefore, the approximate values of sin(theta) and tan(theta) for 0 degrees < theta < 90 degrees are:
sin(theta) ≈ 0.9511
tan(theta) ≈ 0.3249
Therefore, the correct answer is A. sin(theta) = 0.9511; tan(theta) = 0.3249.
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factor 5a2 – 30a 40. question 17 options: a) 5(a – 2)(a 4) b) 5(a – 2)(a – 4) c) (5a – 5)(a – 8) d) (a – 20)(a – 2)
Answers
The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)
The following procedures can be used by us while factoring polynomials:
Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.
Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.
Eliminate any factors that are frequent.
In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).
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Find the perimeter of this complex shape.
Answers
Add are the sides
Which quadrilateral has four right angles and four sides of equal length?
Answers
Answer:
Square.
Step-by-step explanation:
A square is a rectangle, but a rectangle is not a square.
Answer:
A square
Step-by-step explanation:
The file below can help you out understand the properties of the square better!
a student performed the following steps to find the solution to the equation x^2 + 14x + 45=0
where did the student go wrong?
Step 1. Factor the polynomial into (x + 5) and (x + 9)
Step 2. x + 5 = 0 or x - 9 = 0
Step 3. x = -5 or x = 9
a. in Step 2
b. in Step 3
c. The student did not make any mistakes, the solution is correct
d. in Step 1
Answers
While factoring the given equation, the mistake occurred in Step 1 (option d.)
Upon reviewing the steps, we can see that the student made a mistake in Step 1. The factorization of the polynomial should be (x + 5)(x + 9), not (x + 5)(x - 9).
The correct factorization should be:
[tex]x^2 + 14x + 45 = (x + 5)(x + 9)[/tex]
The mistake occurred when the student incorrectly wrote (x - 9) instead of (x + 9) as one of the factors.
As a result, the subsequent steps are also affected. In Step 2, the student incorrectly set x - 9 = 0 instead of x + 9 = 0. This leads to an incorrect value in Step 3, where the student states that x = 9 instead of the correct value x = -9.
Therefore, the student made a mistake in Step 1, which caused subsequent errors in Step 2 and Step 3. The correct answer is d. The mistake occurred in Step 1.
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10 POINTS !! :( ANSWER BOTH PLS !! DUE BEFORE 11:59 PM
Answers
Answer:
Easy,
1) To find the area you need to multiply. Therefore 10 x 4 = 40 square centimeters.
2) 20, why? A calculator online for area of a triangle, it really helps! :) just look up triangle area in the future.
Step-by-step explanation:
Find the distance between 2 and -2.
A) -6
B) -4
C) 0
D) 4
Answers
Answer:
4
Step-by-step explanation:
We can do this problem by doing the absolute value of the difference between 2 and -2.
2-(-2)=4. Absolute value of 4 is 4.
Hope this helped.
~cloud
Answer:
4
Step-by-step explanation:
Plz help!!!!
Josh conducted an experiment with the bag of
marbles shown below. He will draw a marble out of the bag, record the result, return the marble to the bag, and draw another marble, continuing the process.
If he completes this process 600 times, about how many
times should he expect to draw a striped marble?
A.Approximately 400 times
B.Approximately 250 times
C.Approximately 200 times
D.Approximately 150 times
Answers
Answer:
Step-by-step explanation:
There are 12 marbles in total with three of them being striped. The chance of pulling out a striped marble is 3/12 which can be reduced to 1/4. And 1/4 of 600 is 150.
Use Wilson's theorem to find the least nonnegative residue modulo m of each integer n below. (You should not use a calculator or multiply large numbers.) n = 861, m = 89 (b) n = 64!/52!, m = 13 m=
Answers
The least nonnegative residue of 64!/52! modulo 13 is 4.
Wilson's theorem states that for any prime number 'p', the factorial of (p-1) is congruent to -1 modulo p. This can be written as (p-1)! ≡ -1 (mod p).
Using Wilson's theorem, we can find the least nonnegative residue modulo 89 for the integer 861.
For n = 861 and m = 89, we need to calculate (n mod m) as follows:
861 mod 89 = 861 - (89 * (861 // 89))
= 861 - (89 * 9)
= 861 - 801
= 60
Therefore, the least nonnegative residue of 861 modulo 89 is 60.
Now let's move on to the second part.
For n = 64!/52! and m = 13, we can simplify the expression using cancelation:
64!/52! = (64 * 63 * 62 * ... * 53 * 52!)/52!
Most of the terms in the numerator and denominator cancel out, leaving:
64 * 63 * 62 * ... * 53
To find the least nonnegative residue modulo 13, we can calculate the product of the remaining terms and take the result modulo 13.
(64 * 63 * 62 * ... * 53) mod 13 ≡ (11 * 12 * 1 * 2 * ... * 3) mod 13
≡ (11 * (-1) * 1 * 2 * ... * 3) mod 13
≡ (-11 * 1 * 2 * ... * 3) mod 13
Since (-11) ≡ 2 (mod 13), we have:
(-11 * 1 * 2 * ... * 3) mod 13 ≡ (2 * 1 * 2 * ... * 3) mod 13
Calculating the product, we find:
(2 * 1 * 2 * ... * 3) mod 13 ≡ 4 (mod 13)
Therefore, the least nonnegative residue of 64!/52! modulo 13 is 4.
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Please answer correctly! I will mark you as Brainliest!
Answers
Answer:
I have actually done this before, I got it right and I chose C!
hope this helps. love u guys!
Answer:
The 4th answer choice
Explain:
195 divided by 3 is 65. Then the diameter of 307 needs to be divided by 2 to get the radius. Now take the radius and square it to get 23562.25. Now times 3.14. Lastly, multiply by the 65 to get 4809055.225. Hope that helps! :)
What is the value, to the nearest tenth, of 15 x 3 - 12 x 2 when x = 2.5
Answers
Answer:
159.4
Step-by-step explanation:
I'm assuming that it's supposed to be 15x^3-12x^2 because when you copy and paste the "^" gets cut out
15*2.5^3 - 12*2.5^2 = 234.375 - 75 = 159.375
rounded is 159.4
A cone has a volume of 602.88 cubic centimeters and a radius of 6 centimeters. What is its height? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Answer:
15.98cm
Step-by-step explanation:
Given data
Volume= 602.88cm^3
Radius= 6cm
The formula for the volume of a cone is
V= 1/3 πr^2h
substitute
602.88= 1/3*3.142*6^2*h
602.88=1/3*3.142*36*h
602.88=37.704*h
h= 602.88/37.704
h= 15.98cm
Hence the height is 15.98cm
Simplify: 36.6 ÷ (12)
Answers
Answer:
Hi! The answer to your question is [tex]3.05[/tex]
Step-by-step explanation:
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☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.
According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD . Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles ______________ are congruent by the Alternate Interior Angles Theorem. Angles ______________ are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the Alternate Interior Theorem. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality,∠ ABC is congruent to∠ CDA. Consequently, opposite angles of parallelogram ABCD are congruent. What angles accurately complete the proof? (5 points) 1. BCD and CDA 2. CDA and BCD 1. BCD and PBC 2. PBC and BAD 1. PBC and CDA 2. CDA and BAD 1. PBC and BAT 2. BAT and BAD
Answers
To accurately complete the proof, the angles that can be filled in are: BCD and CDA; ABC and BAT.
Let's go step by step to understand why these angles are congruent. Given that segment AB is parallel to segment DC and segment BC is parallel to segment AD, we extend segment AB to point P above point B and extend segment AD to point T to the left of point A.
According to the Alternate Interior Angles Theorem, angles BCD (angle at point C) and CDA (angle at point D) are congruent. This is because these angles are formed by a transversal (segment AD) intersecting two parallel lines (AB and DC).
Next, applying the Corresponding Angles Theorem, angles ABC (angle at point A) and BAT (angle at point T) are congruent. This is because these angles are corresponding angles formed by a transversal (segment AB) intersecting two parallel lines (AD and BC).
By the Transitive Property of Equality, we can conclude that angle ABC is congruent to angle CDA. Therefore, opposite angles of parallelogram ABCD are congruent, and the proof is complete.
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nobody is helping me on this pls answer and ty
Answers
Answer:
38.7
Step-by-step explanation:
[tex]\frac{sinA}{A}=\frac{sinB}{B}=\frac{sinC}{C}[/tex]
A, B and C are the sides of the triangle and sinA, sinB and sinC are the opposing angles
[tex]\frac{sin95}{43}=\frac{A}{27}[/tex]
[tex]A = sin^{-1} (\frac{27*sin95}{43} )=38.72018809[/tex]
A lottery consists of selecting 7 numbers out of 35 numbers. You win $10 if exactly three of your 7 numbers are matched to the winning numbers chosen. What is the probability of winning the $10?
Answers
the number of favorable outcomes is 35 * 20475 = 716,625.
Probability = 716,625 / (35! / (7!(35 - 7)!)).
To determine the probability of winning the $10 prize by matching exactly three numbers, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be calculated using combinations. Since we are selecting 7 numbers out of 35, the total number of possible outcomes is given by the combination formula:
C(n, r) = n! / (r!(n - r)!)
In this case, n = 35 (total numbers) and r = 7 (numbers selected). Substituting these values into the formula:
C(35, 7) = 35! / (7!(35 - 7)!)
= 35! / (7!28!)
The number of favorable outcomes is determined by choosing 3 winning numbers from the 7 numbers selected and 4 non-winning numbers from the remaining 28 numbers. The number of favorable outcomes can be calculated using combinations as well:
C(7, 3) * C(28, 4)
Substituting the values into the formula:
C(7, 3) * C(28, 4) = (7! / (3!(7 - 3)!)) * (28! / (4!(28 - 4)!))
Calculating these values:
C(7, 3) = 7! / (3!(7 - 3)!)
= 7! / (3!4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
C(28, 4) = 28! / (4!(28 - 4)!)
= 28! / (4!24!)
= (28 * 27 * 26 * 25) / (4 * 3 * 2 * 1)
= 20475
Therefore, the number of favorable outcomes is 35 * 20475 = 716,625.
Now, we can calculate the probability of winning the $10 prize by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 716,625 / C(35, 7)
Calculating this value:
Probability = 716,625 / (35! / (7!(35 - 7)!))
It is important to note that calculating the factorial of 35 might result in very large numbers, which may be computationally intensive. Alternatively, you can use numerical methods or estimation techniques to approximate the probability.
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Can someone help me please
Answers
Answer:
its C
Step-by-step explanation:
Answer:
c. I believe
Step-by-step explanation:
because all of the other options dont go in a consistent order/pattern. C. matches the vertical side
please consider marking me as brainliest. as I explained my answer!
Please and thanks!
NEED HELP FAST
Find the arc length of the partial circle
Answers
Answer:
The arc length is about 12.57.
Step-by-step explanation:
Formula for arc length: 2πr( degrees/360)
For ours lets do 2π8(90/360)
Simplify the 90 and 360: 16π(1/4)
This gives you: 16π/4
Divide by 4
You get: 4π
4π ≅ 12.57
I really need help with this
Answers
Answer:add 11 on both sides sorry
Answer: subtract 11 from both sides
Step-by-step explanation: this was an assigned assignment for me two days ago
Simplify the following expression when x=14 y=10 z=6 .
3x+3y divided by z
Answers
A rectangular box is 6 inches wide 10 inches long and 2 inches tall how much wrapping paper is needed to cover the box exactly
Answers
Answer:
184 in²
Step-by-step explanation:
Given :
Width, w = 6 inches
Length, l = 10 inches
Height, h = 2 inches
To obtain how much wrapping paper is needed ; we take the surface area of the box
Surface area = 2(lw + lh + wh)
Surface area = 2((6*10) + (6*2) + (10*2))
Surface area = 2(60 + 12 + 20)
Surface area = 2(92)
Surface area = 184 in²
The amount of wrapping paper needed = 184 in²
The mean pulse rate (in beats per minute) of adult males is equal to 69 pm. For a random sample of 152 adultes the map 68 4 bpm and the standard deviation is 105 bpmFind the value of the test statistic
Answers
The test statistic for this problem is given as follows:
t = -0.7.
How to calculate the test statistic?We have the standard deviation for the sample, hence the t-distribution is used to calculate the test statistic.
The equation for the test statistic is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 68.4, \mu = 69, s = 10.5, n = 152[/tex]
Hence the test statistic is given as follows:
[tex]t = \frac{68.4 - 69}{\frac{10.5}{\sqrt{152}}}[/tex]
t = -0.7.
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