Write an equation of the line that has a slope of 3 and contains the point (2,5) in point-slope form.
Answers
y - y1 = m(x-x1)
where m is the slope and (x1,y1) is the point the line goes through
The slope is 3, so let's replace m with 3
y - y1 = m(x-x1)
y - y1 = 3(x-x1)
The given point is (2,5) so let's replace x1 with 2 and y1 with 5
y - y1 = 3(x-x1)
y - y1 = 3(x-2)
y - 5 = 3(x-2)
Answer: y-5 = 3(x-2)
Related Questions
5x^2+-8x^2 how to simplify
Answers
5+(-8)=-3
Final answer: -3x^2
if a quadrilaterals diagonals bisect its vertices, what kind of quadrilateral must it be?
A - Rhombus
B - trapezoid
C - rectangle
D - parallelogram
Answers
A man drives from home to the store, shops, and then drives back home. Click on the graph until the graph that best represents the given statement appears.
Answers
Click the third graph (check the picture attached)
ExplanationRemember that [tex]speed=\frac{distance}{time}[/tex], so the line in the first part of the graph means that the man is driving his car at certain speed (different form zero) from home to the store. The horizontal graph in the middle of the graph means that he man is sopping at the store; therefore his driving speed is 0. The third part of the graph means that the man is driving again from the store to home.
Check the picture bellow to visualize it more easily.
If x2 + kx + 18 is factorable, what are the possible values of k?
Answers
The factors of 18 are
(1 x 18); (2 x 9); (3 x 6).
If we use (1, 18) as factors, then
(x - 1)(x - 18) = x² - 19x + 18 => k= -19
or
(x + 1)(x + 18) = x² + 19x + 18 => k = 19
If we use (2,9) as factors, then
(x - 2)(x - 9) = x² - 11x + 18 => k = - 11
or
(x + 2)(x + 9) = x² + 11x + 18 => k = 11
If we use (3, 6) as factors, then
(x - 3)(x - 6) = x² - 9x + 18 => k = - 9
or
(x + 3)(x + 6) = x² + 9x + 18 => x = 9
Answer:
The possible values of k are -9,+9, -11, +11, -19, +19.
Final answer:
The possible values of k in the factorable quadratic expression x^2 + kx + 18 can be determined by finding the factors of 18 that can be multiplied to obtain the constant term.
Explanation:
If the quadratic expression x^2 + kx + 18 is factorable, the possible values of k can be determined by finding the factors of 18 that can be multiplied to obtain the constant term.
The factors of 18 are:
1 and 18
2 and 9
3 and 6
Therefore, the possible values of k are -19, -10, -3, 3, 10, and 19.
A broken faucet leaks 1 gallon of water every 1 and1/3 months the amount of months that pass m varies directly with the amount of gallons leaked g. Find the equation that models this direct variation. How many months will it take for the faucet to leak 7 gallons of water?
Answers
[tex]\bf \textit{\underline{m} varies directly with the amount of gallons}\implies \stackrel{months}{m}=k\stackrel{gallons}{g} \\\\\\ \textit{we also know that } \begin{cases} m=1\frac{1}{3}\\ \qquad \frac{4}{3}\\ g=1 \end{cases}\implies \cfrac{4}{3}=k1\implies \cfrac{4}{3}=k \\\\\\ \boxed{m=\cfrac{4}{3}g}\\\\ -------------------------------\\\\ \textit{what's \underline{m} when g=7?}\qquad m=\cfrac{4}{3}\cdot 7\implies m=\cfrac{28}{3}\implies m=9\frac{1}{3}[/tex]
Answer:
m = [tex]\frac{4}{3}[/tex]g, k= 9[tex]\frac{1}{3}[/tex] months
Step-by-step explanation:
Each week, Christian earns $x fixing bicycles and receives $10 as his allowance. To find how much he will earn in total over 2 weeks, Christian calculates: x + 10 + x + 10. What is another way Christian can calculate how much he will earn in total over the 2 weeks?
A. x + 10
B. 2x + 10
C. x + 20
D. 2(x + 10)
Answers
If he earns $x in one week, then you need 2x to calcualte 2 weeks, add that with his allowance and there you have it.
Christian can calculate his total earnings over 2 weeks by simplifying the expression x + 10 + x + 10 to 2(x + 10). This method combines his earnings from fixing bicycles and his allowance for each week. Therefore, the correct answer is D. 2(x + 10).
To calculate how much Christian will earn in total over 2 weeks, you can simplify the expression x + 10 + x + 10:
First, combine like terms for the amount he earns from fixing bicycles: x + x = 2x.Next, combine the constants for his allowance: 10 + 10 = 20.This gives us the total expression: 2x + 20.Rewriting this, you get 2(x + 10). Therefore, the correct answer is D. 2(x + 10).
A runner wants to run 10.0 km. she knows that her running pace is 7.5 miles per hour. how many minutes must she run?
Answers
7.5=10/time
Time =1.3333 hour=60+.3333*60=80 minutes
A runner must run for 50 minutes to cover the distance of 10 kilometers.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
A runner wants to run 10.0 km. she knows that her running pace is 7.5 miles per hour.
7.5 miles = 12 kilometers
Speed = 12 kilometers/hours
1 hour = 60 minutes
Speed = 12 / 60 kilometers per minute
Speed = 0.2 kilometers per minute
Time = distance/speed
Time = 10 / 0.2
Time = 50 minutes
Thus, A runner must run for 50 minutes to cover the distance of 10 kilometers.
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What is the algebraic expression for the quotient of a number and nine
Answers
Find an equation of the line with the given slope and containing the given point. express your answer in slope-intercept form.
Answers
an equation is : y - b = a(x - c) ... the point is : A ( c , b) and slope : a
A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
The function that models the height of the ball is given by :
[tex]f(x)=-10x^2+20x+8[/tex]
When we plug x as 1.5 , we could get the height f(1.5) as :
[tex]f(1.5)=-10(1.5)^2 +20*1.5 +8[/tex]
[tex]f(1.5)=-22.5+30+8[/tex]
[tex]f(1.5)=15.5[/tex]
So the height of the ball after 1.5 second is 15.5 meters. : Answer
Hope it will help :)
Answer:
It is c on edge just took the test
Step-by-step explanation:
Jo is flipping a fair coin. If the coin is truly fair, how many times should it land on heads if he flips the coin 200 times
Answers
a coin has a 1/2 probability of landing on heads
so it should land on heads 1/2 of the time
1/2 of 200 = 100
Final answer:
With a fair coin, theoretical probability suggests that Jo should expect to land on heads roughly 100 times out of 200 flips. Actual results may vary slightly due to random chance, but should approximate 50 percent heads over a large number of trials.
Explanation:
If Jo is flipping a fair coin, on average, we would expect the coin to land on heads 100 times out of 200 flips. This expectation is based on the theoretical probability of getting heads, which is 0.5 or 50% for a fair coin. Therefore, if Jo flips the coin 200 times, the expected number of heads is calculated by multiplying the total number of flips by the probability of getting heads (0.5), which is 200 * 0.5 = 100.
However, it's important to note that while the theoretical probability suggests that Jo should get heads approximately 100 times, the actual result might be slightly more or slightly less due to random chance. The larger the number of flips, the closer the actual results are likely to get to the expected 50 percent heads, as demonstrated by the law of large numbers. But for any finite number of flips, there is always potential for some variation from the expected value.
It is predicted that the population of a particular state will double every 25 years. a) Determine the annual and monthly growth rates. Express your answers as percents. b) Determine the continuous growth rate per year. Express your answer as a percent.
Answers
The annual growth rate is 41.4% and the monthly growth rate is 3.45%. The continuous growth rate per year is 2.77%.
Explanation:To determine the annual growth rate, we need to find the growth factor by taking the square root of the doubling factor. Since the population is predicted to double every 25 years, the annual growth rate would be the square root of 2, which is approximately 1.414. To express it as a percentage, we can subtract 1 from the growth factor and multiply by 100, resulting in an annual growth rate of 41.4%.
The monthly growth rate can be calculated by dividing the annual growth rate by 12. In this case, the monthly growth rate would be approximately 3.45%.
To determine the continuous growth rate per year, we use the formula: r = ln(2)/t, where r is the continuous growth rate and t is the doubling time in years. In this case, the continuous growth rate would be ln(2)/25, which is approximately 0.0277. Multiplying this by 100, we get a continuous growth rate per year of 2.77%.
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Mr Webster is buying carpet for an exercise room in his basement the room will have an art of 230 square feet the width of the room is 12 1/2 what is the length
Answers
The length of Mr. Webster's exercise room is 18.4 feet, calculated by dividing the area (230 sq ft) by the width (12.5 ft).
To find the length of the room, we can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given that the area is 230 square feet and the width is 12 1/2 feet, we can plug these values into the formula:
[tex]\[ 230 = \text{Length} \times 12 \frac{1}{2} \][/tex]
To solve for the length, divide both sides by 12.5:
[tex]\[ \text{Length} = \frac{230}{12 \frac{1}{2}} \]\[ \text{Length} = \frac{230}{\frac{25}{2}} \]\[ \text{Length} = 230 \times \frac{2}{25} \]\[ \text{Length} = 18.4 \][/tex]
So, the length of the room is [tex]\( \boxed{18.4} \)[/tex] feet.
1.3 divided by 0.0338 step by step please
Answers
338*30=338*3*10
1 2 (what I carry is at the top)
338
x3
____
1114
Multiplying that by 10, I get 11140, which isn't enough. Trying 338*40, which is 338*4*10, we can add 338 to 338*3 to get 338*4 to get
2
1114
+338
____
1462
Multiplying that by 10, we get 14620, which is more than 13000 - something we don't want. Repeating this for 338*35 (which is 338*3.5*10, and 3.5 is 3*338+338/2)=11830 and which isn't enough, we then move on to something between 35 and 40 (the number doesn't matter), say 39. 338*39=338*3.9*10, and 338*3.9 is 338*3+338*9/10, and
338*39 results to 13182, which is more than 13000 , but only by a tiny bit, so we can try 38 using the same method, getting 12844, which is smaller, so we know it's between 38 and 39. Finding the difference between 13000 and 12844, we get 13000-12844=156 and the answer is therefore 38+156/338
chance to get brainliest What are the lower bound estimate and the upper bound estimate found by rounding to the greatest place? 764 – 241 A. lower bound 400 upper bound 600 B. lower bound 400 upper bound 500 C. lower bound 500 upper bound 600 D. lower bound 200 upper bound 800
Answers
The lower bound estimate and upper bound estimate are found by rounding 764 to 700 and 241 to 200, then subtracting to get 500. However, the mistake in the options seems that both the lower and upper bound estimates are 500. Based on the given options, the right answer should be option C with lower bound 500 and upper bound 600, albeit the upper bound estimate is not correctly represented.
Explanation:The lower bound and upper bound estimate of a calculation are found by rounding each number involved to the greatest place value then performing the calculation. In the case of the subtraction 764 - 241, the lower bound estimate will be calculated by underestimating both figures, and the upper bound will be calculated by overestimating.
Round down 764 to 700 and 241 to 200, then subtract: 700 - 200 = 500.Round up 764 to 800 and 241 to 300, then subtract: 800 - 300 = 500.Therefore, both the lower bound estimate and the upper bound estimate are 500 and the correct option is C. lower bound 500 upper bound 600
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The length of a rectangle is 3 inches more than the width. the perimeter is 30 inches. find the length and width.
Answers
9/10 and -9/10 determine if parallel, perpendicular, or neither
Answers
Perpendicular means they have opposite reciprocal slopes.
We can apply these concepts to this question. Although they are opposites of each other, they are not reciprocals.
So, the answer is neither
Hope this helps!
Describe how to derive the quadratic formula from a quadratic equation in standard form. edginuity
Answers
[tex]ax^2+bx+c=a(x^2+ \dfrac{b}{a}x+ \dfrac{c}{a} )\\ =a(x^2+2* \dfrac{b}{2a}x +( \dfrac{b}{a} )^2- (\dfrac{b}{a} )^2+\dfrac{c}{a})\\ =a((x+ \dfrac{b}{2a} )^2- \dfrac{b^2-4ac}{4a^2} )\\ =a(x+ \dfrac{b}{2a} )^2- \dfrac{b^2-4ac}{4a} [/tex]
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.
Step-by-step explanation:
Need help please help
Answers
Notice how on the graph, the y value peaks at 7. The y values to the left and right are symmetrical, meaning that the x value for the y value of 7 is the axis of symmetry, and the point (105,7) is the vertex.
LeAnn wants to giftwrap a present she got for her little brother. How many square inches of giftwrap will be needed to cover a box that is 4in x 6in x 2in? In your final answer, include all of your calculations.
Answers
The answer, also in the picture, is 88 square inches (or 88 in.^2)
Hope this helps!
there are 6 sides to a cube
2 are 4*6 = 24*2 =48
2 are 4*2 = 8*2 = 16
2 are 6*2 = 12*2 =24
48 +16 +24 = 88 square inches total
Please help me out!! ☮✌
Answers
180 = 93 +3x +18
180 =111 +3x
3x = 180-111
3x = 69
x = 69/3
x = 23
Let f(x) = 3x + 5 and g(x) = x2. Find g(x)/f(x) and state its domain.
Answers
g(x)/f(x) = x^2 / (3x + 5)
set denominator equals 0.
so
3x + 5 = 0
3x = -5
x = -5/3
Therefore x cannot equal -5/3
Domain (-∞ , -5/3) ∪ (-5/3, ∞)
hope it helps
Which is bigger 30% or 1/3
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Is the number of bottles of juice sold at lunch continuous or discrete?
Answers
the product of 15 and 7 added to 8
Answers
Final answer:
To calculate the requested expression, multiply 15 by 7 to get 105, and then add 8 to this product to find the sum, which is 113.
Explanation:
The question asks to calculate the result of the mathematical expression where a product is first found by multiplying 15 and 7 and then that product is added to 8. To solve this, you need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the product of 15 and 7 to get 105.
Next, add this product to 8 to find the final result.
So, 105 + 8 equals 113.
The correct answer to the question is 113, which is the sum of the product of 15 and 7, with 8 added.
Fill in 2 to 10 so every row and column adds up to 18
Answers
7| 8 | 3
9| 4 | 5
Hope this helps love! :)
Consider points R, S, and T. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points.
Answers
c- one plane can be drawn so it contains all three points.
(i just took this on a mastery test)
Answer: The answer is (c) One plane can be drawn so that it contains all three points.
Step-by-step explanation: We are given three points R, S and T in a coordinate plane. Considering all these three points to be distinct and non-collinear, we can draw the following conclusions.
(i) Since each pairs of points. i.e., (R,S), (S,T) and (T,R) give rise to a straight line when joined, so option (a) is incorrect.
(ii) Through any two given points, we can always draw a line. If we consider a third point and since we are dealing with non-collinear points, so one line cannot be drawn through three points.
(iii)We can always draw a line by joining two points and when we join the two ends of the line to a third point which does not lie on the line, it will give rise to a plane. So, option (c) is correct.
(iv) We cannot draw two different planes through three given points. If we do so, the new plane will coincide with the previous one. This proves that option (d) is not correct.
Please see the attached figure, where P, Q and R are three non-collinear points. They give rise to a plane.
Thus, the correct option is (c).
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.
What it looks like: two circles touching at one point. Larger circle has radius of 8 inches. Smaller circle has radius of 2 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation? Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear? Show all work.
Answers
ω₁ and ω₂ are the angular velocities of the larger and smaller gears respectively.
Part 1.
When the smaller gear makes one revolution, it turns through an angle of 2π radians or 360°.
Because the gears do not slip, the larger gear turns through an angle of θ, so that
(θ radians)*(8 in) = (2π radians)*(2 in)
or
8θ = 4π
θ = π/2 radians = 90°
Answer: 90.0°
Part 2.
When the larger gear makes one revolution, it turns through an angle of 2π radians.
Because the gears do not slip, the smaller gear turns through an angle φ, such that
(2 in)*(φ radians) = (8 in)*(2π radians)
or
2φ = 16π
φ = 8π radians
= (8π radians)*(1/2π rotations/radian)
= 4 rotations
Answer: 4 rotations
I need help with the following problem
Answers
The first aircraft has 73 more seats than the second aircraft. The third aircraft has 57 fewer seats than the second aircraft. If their total number of seats is 427 find the number of seats for each aircraft.
Answers
second aircraft seats : y
third aircraft seats : z
The first aircraft has 73 more seats than the second aircraft: x = y + 73
The third aircraft has 57 fewer seats than the second aircraft: z = y - 57
Their total number of seats is 427: x + y + z = 427
solve these three equations, you will get:
x = 210 seats
y = 137 seats
z = 80 seats
-------------------------
you can check your answer by:
x - y = 210 - 137 = 73 correct
and
z + 57 = 80 + 57 = 137 = y correct