Find the equation of the line passing through the points (-5,-9) and (4,7)
Answers
The formula for calculating the equation of a line is expressed as:
y = mx + b
where:
• m is the, slope, of the line
,• b is the ,y-intercept
Given the coordinate points (-5,-9) and (4,7)
Determine the slope
\(\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ Slope=\frac{7-(-9)}{4-(-5)} \\ Slope=\frac{7+9}{4+5} \\ Slope=\frac{16}{9} \end{gathered}\)Determine the y-intercept of the line
Recall that y = mx + b
\(\begin{gathered} 7=\frac{16}{9}(4)+b \\ 7=\frac{64}{9}+b \\ b=7-\frac{64}{9} \\ b=-\frac{1}{9} \end{gathered}\)Determine the required equation
\(\begin{gathered} y=mx+b \\ y=\frac{16}{9}x+(-\frac{1}{9}) \\ y=\frac{16}{9}x-\frac{1}{9} \end{gathered}\)Related Questions
Solve 3^5x=10
HELP PLS
Answers
Answer:
x = 10/243
Step-by-step explanation:
3^5x = 10
243x = 10
Divide 243 on both sides
10/243
89,235 written in expanded form? (2 points)
a
8 x 10,000 + 9 x 1,000 + 2 x 100 + 3 x 10 + 5 x 1
b
8 x 10,000 + 9 x 1,000 + 2 x 100 + 3 x 10 + 5 x 5
c
8 x 100,000 + 9 x 10,000 + 2 x 1,000 + 3 x 100 + 5 x 10
d
8 x 80,000 + 9 x 9,000 + 2 x 200 + 3 x 30 + 5 x 5
Answers
Ally collects stickers as a hobby. She gives her sisters of her stickers.
She then gives her cousin of the remainder.
Ally says that she has 3/5 of the stickers in the end because 1-1/5-1/5=3/5
• Explain why Ally's reasoning is incorrect.
What should the correct answer be?
Explain how you arrived at your answer.
Answers
Answer:
\(\frac{16}{25}\)
Step-by-step explanation:
Ally gives her sister = 1/5 stickers
Ally gives her cousin = 1/5 of the remainder stickers
Assume Number of sticker Ali has = 1
Remainder after giving stickers to her sister = 1 - 1/5 = 4/5
Number of stickers she gave her sister = \(\frac{1}{5}\times\frac{4}{5}\)
=\(\frac{4}{25}\)
Sticker she has = \(1-\frac{1}{5}-\frac{4}{25}\)
=\(\frac{25-5-4}{25}\)
=\(\frac{16}{25}\)
Sticker left with Ally is equal to \(\frac{16}{25}\).
A two-child family is selected at random. Let B denote the event that at least one child is a boy, and let D denote the event that
the genders of the two children differ. Find the union of B and D. (1 point)
The union is (bb, gg); the first letter denotes the gender of the firstborn child, and the second letter denotes the gender of the
second child.
The union is (bg. gb); the first letter denotes the gender of the firstborn child, and the second letter denotes the gender of the
second child.
The union is {bb, bg, gb, gg); the first letter denotes the gender of the firstborn child, and the second letter denotes the gender of
the second child.
The union is (bb, bg. gb); the first letter denotes the gender of the firstborn child, and the second letter denotes the gender of the
second child.
Answers
With the help of probability we can say that, DUM={GG,BB,GB,BG).
What is Probability?Probability is the concept that describes the likelihood of an event occurring.
In real life, we frequently have to make predictions about how things will turn out.
We may be aware of the result of an occurrence or not.
When this occurs, we state that there is a possibility that the event will occur.
In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence
The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.
hence, DUM={GG,BB,GB,BG)
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Describe the transformation of ƒ(x) = ex which is given by g(x) = −e2x + 6.
A)
g(x) is reflected across the y-axis and translated 6 units to the right compared to ƒ(x).
B)
g(x) is reflected across the x-axis and translated 6 units up compared to ƒ(x).
C)
g(x) is reflected across the y-axis and translated 6 units to the left compared to ƒ(x).
D)
g(x) is reflected across the x-axis and translated 6 units down compared to ƒ(x).
Answers
Answer:
g(x) is reflected across the x-axis and translated 6 units up compared to ƒ(x).
Step-by-step explanation:
Answer:
Step-by-step explanation:
g(x) is reflected across the x-axis and translated 6 units up compared to ƒ(x).
Rewrite 9 2/7 as an improper fraction. 25/2 65/7 25/7 23/7 Rewrite 2 4/5 as an improper fraction. 10/4 13/5 14/5 22/5 Find the product of 9 2/7 and 2 4/5. Express your answer in simplest form. 26 130/5 910/35 15
Answers
Answer:
1. 9 2/7 = (63+2)/7 = 65/7
2. 2 4/5 = (10+4)/5 = 14/5
3. 65/7 * 14/5 = 910/35 = 26
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
Answers
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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Pls help with this question. I will give brainlest thank youuu
Answers
-7x + 7y - 2
Hope this helps! :D
What does kcf stand for in math?
Answers
Answer:
keep-flip-change
Step-by-step explanation:
This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem.
Answer:
keep-flip-change
Step-by-step explanation:
This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem.
Graph and find the area of the figure with the vertices (-3, 0), (1,4), (2, 0)
Answers
Answer:
10
Step-by-step explanation:
The sum of two numbers is negative sixteen. One number is seven times the other. Find the numbers
Answers
The two numbers are \(-2\) and \(-14\).
It is given that,
Sum of two numbers is negative sixteen.One number is seven times the other.Explanation:
Let \(x\) be the one number. Then the second number is \(7x\).
Sum of two numbers is negative sixteen.
\(x+7x=-16\)
\(8x=-16\)
\(x=\dfrac{-16}{8}\)
\(x=-2\)
The value of other number is:
\(7(-2)=-14\)
Thus, the two numbers are \(-2\) and \(-14\).
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I need helppppppppp please help me
Answers
We know interior angles in a Pentagon sum to 540 degrees.
We can add all 5 angles and expressions to sum 540.
148 + 3x + 10 + x + 112 + 90 = 540
Combine like terms
4x + 360 = 540
Subtract 360 from both sides to isolate x
4x + 360 - 360 = 540 - 360
Simplify
4x = 180
Divide both sides by 4 to solve for x
4/4 x = 180/4
x = 45
Now find angle B = 3x + 10
Substitute value of x = 45 into expression
B = 3 * 45 + 10
B = 135 + 10
B = 145
Leila has a deck of 10 cards numbered 1 through 10 . She is playing a game of chance.
This game is this: Leila chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $6 if an odd numbered card is drawn.
(a) Find the expected value of playing the game.
(b) What can Leila expect in the long run, after playing the game many times?
(She replaces the card in the deck each time.)
Leila can expect to gain money.
Leila can expect to lose money.
Leila can expect to break even (neither gain nor lose money).
Answers
a. The expected value is $12
b. She is expected to win money
What is the expected value of playing the game?To find the expected value of playing the game, we need to calculate the average value of the winnings or losses.
(a) Expected Value:
The probability of drawing an even-numbered card is 5/10 (since there are 5 even-numbered cards out of 10), and the probability of drawing an odd-numbered card is also 5/10.
If Leila draws an even-numbered card, she wins an amount equal to the value of the card. So the expected value of winning is:
(5/10) * (2 + 4 + 6 + 8 + 10) = (5/10) * 30 = 15/10 = $15
If Leila draws an odd-numbered card, she loses $6. So the expected value of losing is:
(5/10) * (-6) = -3
To find the overall expected value, we subtract the expected value of losing from the expected value of winning:
Expected value = (15) + (-3) = 12
Therefore, the expected value of playing the game is $12
(b) In the long run, after playing the game many times, Leila can expect to lose money. Since the expected value is positive $12 , on average, she will win $12 per game.
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A dairy needs 258 gallons of milk containing 7% butterfat how many gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 258 gallons
Answers
Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.
The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.
To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.
For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).
For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).
Since we want the final mixture to contain 7% butterfat, we can set up the following equation:
0.08x + 0.02y = 0.07(258)
Simplifying the equation, we have:
0.08x + 0.02y = 18.06
To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.
Substituting this value into the equation above, we get:
0.08x + 0.02(258 - x) = 18.06
Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.
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Please help with these math questions I really need it ! Don't just do it for points pls
Answers
Answer:
wouldn't that be 81 but i dont know
Answer:
1. d 2. 43.5 3. 817.5
Step-by-step explanation:
If a = -3, find the value of (the 2 on b and c is squared) a) 2a b) a2 c) 3a2
Answers
Answer:
4, -4, 36
Step-by-step explanation:
a) a*2 = -2*-2 = 4
b) a^2 = -2^2 = -4
c) a*3^2= 3*-2^2 = -36
Solve for f.
3<
f
–
1
+7
Answers
Answer:
F will be +5
Step-by-step explanation:
Predict the population in 2016, as a decreases at a constant rate
Answers
Answer:
We need more information to accurately predict the population in 2016. The following information is needed:
The initial population (population in a given baseline year)
The known population decrease rate as a percentage or absolute number per year
For example, if:
The initial population (in 2010) was 10,000
The population is decreasing at a constant rate of 100 people per year
Then we can calculate the population in 2016 as follows:
2010 population: 10,000
2011 population: 10,000 - 100 = 9,900
2012 population: 9,900 - 100 = 9,800
2013 population: 9,800 - 100 = 9,700
2014 population: 9,700 - 100 = 9,600
2015 population: 9,600 - 100 = 9,500
2016 population: 9,500 - 100 = 9,400
Therefore, based on this information, the predicted population in 2016 would be 9,400.
In summary, to accurately predict population changes over time, we need to know the initial population and population decrease rate. With that information, we can calculate the population for each subsequent year by subtracting the decrease amount from the population in the previous year.
Hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3 of the remaining cookies, and when Carla came home, she ate 1/2 of the cookies on the plate. When their mother came home, there were 5 cookies on the plate. How many did each child eat?
Answers
Answer: Children ate 15 cookies and 5 each because Alex ate 1/4 and bernice ate 1/3 and carla ate 1/2
and 5 were left
5 into 3 is 20
and 5 are left so
20-5 is 15
15 divide by 3 is 5
Frame calculation process in your words but the final answer is each child ate 5 cookies.
PLS, 20 POINTS BRAINLIEST Jamie biked m miles at a speed of k miles per hour. What distance did she cover during the last 15 minutes of her trip?
Answers
Answer:
0.25 k miles
Step-by-step explanation:
15 minutes =1/4 of an hour
Distance= speed*time= k (1/4)= (1/4) k= 0.25 k miles
The distance is the multiplication of speed and time thus the speed covered in 15 minutes with a speed of k miles per hour will be k/4.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Average velocity = total distance / total time taken
Units of velocity are given by ⇒ meter/second
As per the given,
Number of miles covered = m
Speed = k miles per hour.
1 hour = 60 mint
15 mint = 1/4 hour.
Since, speed = distance/time
Distance = speed × time
Distance = k × 1/4 = k/4
Hence "The distance is the multiplication of speed and time thus the speed covered in 15 minutes with a speed of k miles per hour will be k/4".
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Please answer this Calculus webwork question about differential equations:
Answers
Answer:
a)
\(4ydy = xdx\)
\(2 {y}^{2} = \frac{1}{2} {x}^{2} + c\)
\( {y}^{2} = \frac{1}{4} {x}^{2} + c \)
\( {y}^{2} - \frac{1}{4} {x}^{2} = c \)
b)
c = 4, so
\( {y}^{2} = \frac{1}{4} {x}^{2} + 4\)
\(y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} \)
\(y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} \)
Please answer! I will give you the brainliest :)
Answers
Answer:
K
Step-by-step explanation:
(1*500 * 5) + (10 * 3*500)
matt had 4/6 bag of peanuts. He ate a quarter of what was in the bag. How much of a full bag of peanuts did Matt eat?
Answers
Matt ate 1/6 of the bag of peanut
How to calculate the amount of peanut that matt ate?
Matt had 4/6 bag of peanut
He ate a quarter of what was in the bag
The amount of peanut he ate can be calculated as follows
= 4/6 × 1/4
= 4/24
= 1/6
Hence Matt ate 1/6 of the bag of peanut
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Given that h(x) = -2x + 5, g(x) =
2x – 7; compute g(h(x))
Answers
-4x+10-7
-4x+3
Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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Select the correct answer.
Solve the following equation for x.
x2 - 36 = 0
A.
x = 1; x = -36
B.
x = -1; x = 36
C.
x = -6; x = 6
D.
x = -18; x = 18
Answers
Answer: D
Step-by-step explanation:
2x-36=0
+36 +36
___________
2x=36
x=18
Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.
Which of the following is equivalent to the expression (3x² + 2x-8)-(2x² - 4x + 7)?
Answers
Answer: x^2+6x-15
Step-by-step explanation:
SA = 2rr2 + 2nrh (Use 3.14 for .) How much metal is needed to create a cylindrical can with a heart of 5 inches and a base diameter of 3 inches? square inches Do NOT round your answer.
Answers
ANSWER:
61.23 square inches
STEP-BY-STEP EXPLANATION:
We will know the necessary metal by calculating the surface area, which is given by the following formula:
\(SA=2\cdot\pi\cdot r^2+2\cdot\pi\cdot r\cdot h\)The formula is based on the radius, therefore we calculate the radius that is equivalent to half the diameteum and then we replace:
\(\begin{gathered} r=\frac{d}{2}=\frac{3}{2}=1.5 \\ \text{replacing} \\ SA=2\cdot3.14\cdot1.5^2+2\cdot3.14\cdot1.5\cdot5 \\ SA=14.13+47.1 \\ SA=61.23 \end{gathered}\)why do the hands on the clock form an angle?
Answers
Answer:
The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)
I hope this helps you!
-8/9 + (-2)/57
find the absolute value of the following rational number
Answers
The absolute value of the Rational number -474/513 is 474/513.
To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:
-8/9 = (-8/9) * (57/57) = -456/513
-2/57 = (-2/57) * (9/9) = -18/513
Now, you can add the fractions:
-456/513 + (-18/513) = (-456 - 18)/513 = -474/513
To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:
| -474/513 | = 474/513
Therefore, the absolute value of the rational number -474/513 is 474/513.
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