Answers
Answer:
b = 4,
m = 4/3,
y = 4x/3 + 4
Step-by-step explanation:
We can see the line intercepts the x-axis in (-3,0) and the y-axis in (0,4). So, using the fact that the line equation in the slope-intercept form is:
\(y = mx+b\)
We can substitute the points we know:
→ (0,4):
\(y = mx+b\\\\4 = m\cdot0+b\\\\4 = 0+b\\\\\boxed{b=4}\)
→ (-3,0):
\(y = mx+b\\\\0 = -3m + 4\\\\3m = 4\\\\\boxed{m = \dfrac{4}{3}}\)
So, the line equation in form requested is:
\(\boxed{y=\dfrac{4}{3}x+4}\)
Related Questions
Solve for n: 12nl-4=8
Answers
Answer:
Step-by-step explanation:
12nl-4=8 start by adding 4 to both sides.
12nl=12/l Divide both sides by l.
12n=12 then divide both sides by 12.
n=1/l
1.
ENGINEERING At an engineering school, students are challenged to design
a container that prevents an egg from breaking when dropped from a height of
50 feet. Write an equation giving a container's heighth (in feet above the
ground after t seconds. How long does the container take to hit the ground?
Answers
Answer:
b
Step-by-step explanation:
b
A spinner has five sectors of equal size the sectors are labeled 1, 2, 3, 4 and five the spinner is spun twice X is the number of times three is fun drag each bar on the horizontal axis to the correct location to create a probability distribution for X
Answers
The probability distribution for X is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The distribution gives the probability of each possible outcome, hence it is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.Learn more about the concept of probability at https://brainly.com/question/24756209
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Autumn is making a fruit salad. Peaches cost 0.75 each and blueberries cost $1.50 a package. Autumn spends 11.25 dollars and buys 10 items. How many peaches and blueberries packages were bought
Answers
Blueberries: 5 packages
We’ll have p = number of packages of peaches, b = number of packages of blueberries.
We know:
p + b = 10
And we know:
p(0.75) + b(1.50) = 11.25, which is also:
0.75p + 1.5b = 11.25
First we’ll solve p in terms of b:
p = 10-b
Then we’ll substitute that expression into the other equation to get a numerical value for b.
0.75(10 - b) + 1.5b = 11.25
7.5 - 0.75b + 1.5b = 11.25
0.75b = 3.75
b = 5
Then we substitute that in to solve for a numerical value for p
p + b = 10
p + 5 = 10
p = 5
Check the math:
0.75p + 1.5b = 11.25
0.75(5) + 1.5(5) = 3.75 + 7.5 = 11.25
Let me know if you have any questions.
Help me with this worksheet pls
Answers
The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.
What is exponential function?The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The given function is:
y = 5(2)ˣ
The value of y from x= 0 to x = 3 is:
y = 5(2)⁰ = 5
y = 5(2)¹ = 10
y = 5(2)² = 20
y = 5(2)³ = 40
The most rapid rate of change as x increases beyond 0 is:
y = 7ˣ
This is observed as the graph increases rapidly with change in value of x.
3. y = (1.20)ˣ
The constant 1.20 is greater than 1 thus, the function is exponential growth.
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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The area of the opening of a rectangular window is to be 120 square feet. If the length is to be 2 feet more than the width, what are the dimensions
Answers
Answer:
Width = 10ft
Length = 12ft
Step-by-step explanation:
For a rectangle of length L and width W, the area is calculated as:
A = L*W
In this case, we know that:
The area is 120 ft^2.
The length is 2 ft more than the width.
Then we can write:
L = W + 2ft.
If we use these two equations and replace them in the equation for the area of a rectangle, we get:
A = 120ft^2 = W*L = W*(W + 2ft)
120ft^2 = W*(W + 2ft)
Now we can solve this for W
120 ft^2 = W^2 + 2ft*W
Now we can rewrite this as:
W^2 + 2ft*W - 120ft^2 = 0
The solutions of this equation can be found by the Bhaskara's formula.
We know that for an equation of the form:
a*x^2 + b*x + c = 0
The two solutions are given by:
\(x = \frac{-b +\sqrt{b^2 - 4*a*c} }{2*a}\)
in our case, we have:
a = 1
b = 2ft
c = -120ft^2
Then the solutions for the equation W^2 + 2ft*W - 120ft^2 = 0 are:
\(W = \frac{-2ft + -\sqrt{(2ft)^2 - 4*1*(-120ft^2)} }{2*1} = \frac{-2ft +- 22ft}{2}\)
Then the two solutions are:
W = (-2ft - 22ft)/2 = -12ft (this is a negative measure, does not have a real meaning in this case, so this solution can be discarded)
The other solution is:
W = (-2ft + 22ft)/2 = 10ft (this is the correct solution)
Then the width is 10ft, and we know that the length is 2 ft longer than the width, then the length is:
L = W + 2ft = 10ft + 2ft = 12ft
the difference of a number and 6 is the same as 5 times the sum of the number and 2
Answers
Answer:
n - 6 = 5 * ( n + 2 ) ; n = -4
Step-by-step explanation:
For this problem, we will use the words to create an equation. The left hand side of the equation will be the difference of a number and 6 and the right hand side of the equation will be 5 times the sum of the number and 2. Hence, we can build the equation:
n - 6 = 5 * ( n + 2 )
If we wanted, we can solve the equation for the number, n.
n - 6 = 5 * ( n + 2 )
n - 6 = 5 * n + 5 * 2
n - 6 = 5n + 10
-16 = 4n
-4 = n
Thus, we have found the missing number to be negative four.
Cheers.
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
1/3(-9 - 24h) = 37 help please!
Answers
Answer:
h = -5
Step-by-step explanation:
1/3(-9 - 24h) = 37
Multiply each side by 3
3*1/3(-9 - 24h) = 37 *3
-9-24h = 111
Add 9 to each side
-9-24h+9 = 111+9
-24h = 120
Divide by -24
-24h/-24 = 120/-24
h = -5
Answer:
h = -5
Step-by-step explanation:
\(\frac{1}{3}\left(-9-24h\right)=37\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\3\times\frac{1}{3}\left(-9-24h\right)=37\times\:3\\\\Simplify\\-9-24h=111\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-9-24h+9=111+9\\\\Simplify\\-24h=120\\\\\mathrm{Divide\:both\:sides\:by\:}-24\\\frac{-24h}{-24}=\frac{120}{-24}\\\\Simplify\\h=-5\)
Need help ASAP on a timer
Answers
Answer:
1/2
Step-by-step explanation:
The odds in favor of an event are given. Compute the probability of the event. (Enter the probability as a fraction.)
2 to 3
Answers
The probability from the odds is 2/5
How to determine the probability?The value of the odds is given as
Odds = 2 to 3
Represent the odds as a fraction
So, we have the following representation
Odds = 2/3
To convert the odds to probability, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
Probability = (2/3)/(2/3 + 1)
Evaluate the sum
Probability = (2/3)/(5/3)
Evaluate the probability
Probability = 2/5
Hence, the probability = 2/5
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Find the value of y for the given value of x.
y=2−9x;x=2/3
Answers
Answer:
-4
Step-by-step explanation:
y=2-9×(2/3)=2-6= -4
tìm các đường tiệm cận của hàm số sau y=1/x+7
Answers
Answer:
i dont speak...that language can u translate to english?
Step-by-step explanation:
The halt-lime performance of a marching band includes a performance in which the band members form a circle with point J at the center. This formation can he modeled by the equation 2° +1? + 10z 12y - 83 = 0.
Answers
The required values are as follows:
Center = (-5, 6), Radius = 12, Domain: x ∈ (-17, 7), Range: y ∈ (-6, 18)
Given equation: x² + y² + 10x - 12y - 83 = 0
To convert it into standard form, complete the square for both the x and y terms:
(x² + 10x) + (y² - 12y) = 83
(x² + 10x + 25) + (y² - 12y + 36) = 83 + 25 + 36
(x + 5)² + (y - 6)² = 144
Comparing this with the standard form, we have:
Center (h, k) = (-5, 6)
Therefore, the coordinates for the point J are (-5, 6).
The radius represents the distance from each band member to the center of the circle. In this case, the radius of the circle is the square root of the constant term on the right side of the standard form equation:
Radius = √144 = 12
The domain of the circle is the set of all possible x-values that lie on the circle. Since the circle is centered at (-5, 6) and has a radius of 12, the domain can be expressed as:
Domain: x ∈ (-5 - 12, -5 + 12) or -17 ≤ x ≤ 7
The range of the circle is the set of all possible y-values that lie on the circle. Using the same information, the range can be expressed as:
Range: y ∈ (6 - 12, 6 + 12) or -6 ≤ y ≤ 18
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A pizza shop is running a special on 4 topping pizzas there are 15 toppings total to choose from each topping can be chosen at most once how many different 4 topping pizzas could be chosen
Answers
Answer:
1365 different pizzas
Explanation:
The number of ways to select 4 toppings from the 15 toppings in total can be calculated using combinations.
So, we will use the following equation
\(nCx=\frac{n!}{x!(n-x)!}\)Where n = 15 and x = 4. So, we get
\(\begin{gathered} 15C4=\frac{15!}{4!(15-4)!} \\ \\ 15C4=\frac{15!}{4!(11!)} \\ \\ 15C4=\frac{15\cdot14\cdot13\cdot12\cdot11!}{4\cdot3\cdot2\cdot1\cdot11!} \\ \\ 15C4=1365 \end{gathered}\)Therefore, there are 1365 different 4 topping pizzas.
The customer service department of a company found that the relationship between the number of minutes a customer spends on hold when telephoning and the customer's level of satisfaction on a 10-point scale can be approximated by the equation y=10−0.1x
, where x
is the number of minutes on hold and y
is the level of satisfaction. What does 0.1 represent in the equation?
Answers
In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.
Define slopeit represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.
In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.
In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.
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NEED HALP!!! Find the ordered pair $(s,t)$ that satisfies the system
Answers
Answer:
(-8/7 ; 5/7)
Step-by-step explanation:
5t + 1/2s = 3 - - - (1)
3t - 6s = 9 - - - - - (2)
Multiply (1) by 12 and (2) by 1
Add the result to eliminate s
60t + 6s = 36
3t - 6s = 9
____________
63t = 45
t = 45 / 63
t = 5/7
Put t = 5/7 in either (1) or (2) to obtain the value of s
3(5/7) - 6s = 9
15/7 - 6s = 9
-6s = 9 - 15/7
-6s = (63 - 15)/7
-6s = 48/7
s = 48/7 * - 1/6
s = - 8/7
Which property will help to find these sums?
57/80+21/80 and 21/80+57/80
the Associative Property
the Commutative Property
the Identity Property
Answers
Answer:
Associative Property
Step-by-step explanation:
Associative Property is the ability to change the order of an equation, and get the same result.
For example:
(1 + 2) + 3 = 6
If you were to take this equation, and this equation:
3 + 2 + 1 = 6
These numbers are in a different order, but the answer is the same!
It goes the same way for your problem.
57/80 + 21/80 and 21/80 + 57/80.
Therefore, the property to help you would be Associative Property.
Multiply (3a + 5)2
A9a2 + 30a + 25
B 25a2 + 15a + 9
C a2 + 3a + 25
D 5a2 + 15a + 9
Answers
Answer:
9 a^2 + 30 a + 25 the anwser is A
Step-by-step explanation:
Expand the following:
(3 a + 5)^2
(3 a + 5) (3 a + 5) = (3 a) (3 a) + (3 a) (5) + (5) (3 a) + (5) (5) = 9 a^2 + 15 a + 15 a + 25 = 9 a^2 + 30 a + 25:
Answer: 9 a^2 + 30 a + 25
The graph shows equivalent ratios. Khalid plots a point to show a fourth equivalent ratio. If the x-value of Khalid’s point is 35, what is the y-value? 20 25 28 35
Answers
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Which expression describes the area in square units of a rectangle has a width of 4x^3y^2 and a length of 3x^2y^3
Answers
Area is length x width:
4x^3y^2 x 3x^2y^3
Apply the exponent rule: a^b x a^c = a^(b+c)
4 x 3 = 12
x^3 x x^2 = x^5
y^2 x y^3 = y^5
Combine for final answer: 12x^5y^5
Annabel's water bottle holds 6 cups of water. How many fluid
ounces does it hold?
Answers
Annabel's water bottle can hold \(48\) fluid ounces of water.
To determine the number of fluid ounces in 6 cups of water, we need to know the conversion rate between cups and fluid ounces.
In the United States customary system, there are \(8\) fluid ounces in \(1\) cup. Therefore, we can use this conversion rate to calculate the number of fluid ounces in \(6\) cups.
Since \(1\) cup is equal to \(8\) fluid ounces, we can set up a proportion:
\(\(\frac{1 \text{ cup}}{8 \text{ fluid ounces}} = \frac{6 \text{ cups}}{x \text{ fluid ounces}}\)\)
By cross-multiplication, we find:
\(\(1 \text{ cup} \cdot x \text{ fluid ounces} = 8 \text{ fluid ounces} \cdot 6 \text{ cups}\)\)
Simplifying the equation:
\(\(x \text{ fluid ounces} = 48 \text{ fluid ounces}\)\)
Therefore, Annabel's water bottle holds \(48\) fluid ounces of water.
To convert \(6\) cups of water to fluid ounces, we use the conversion rate of 1 cup equals \(8\) fluid ounces. Setting up a proportion, we find that \(6\) cups is equal to \(48\) fluid ounces. Hence, Annabel's water bottle can hold \(48\) fluid ounces of water.
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lender requires a minimum down payment of 18% of the value of the home. You have $29,000 cash available to use as a down payment toward a home. Determine the maximum home value that you can finance.
Answers
The maximum home value that can be financed is approximately $35,365.85.
Let's represent the maximum home value that can be financed by H.
If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.
Therefore, we have:
H × 82% = $29,000
Multiplying both sides by (1/82%), we get:
H = $29,000 / 82%
= $35,365.85
Hence, the maximum home value that can be financed is approximately $35,365.85.
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A triangle has a side with length 9 feet and another side with length 7 feet. The
angle between the sides measures 69°. Find the area of the triangle. Round your
answer to the nearest tenth
Answers
Answer:
63
Step-by-step explanation:
help me find the volume because im bad at math :)
Answers
Answer:
v=2144.66
Step-by-step explanation:
V=4/3πr^3
sub in r which is 8
V=4/3 * π * 8^3
V=4/3 * π * 512
math mystery case of the bee bandits clue 5
Answers
Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays the other. For example, if Deven owes Laura 189 dollars, he can give her 6 Harry Potter stickers ($6 \cdot 49 = 294$ dollars), and she can return 3 Twilight stickers ($3 \cdot 35 = 105$ dollars). This trade is like a transfer of $294-105=189$ dollars. What is the smallest positive debt, in dollars, that can be paid off using sticker trading?
Answers
The smallest positive debt that can be paid off using sticker trading is $7$ dollars.
To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.
Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.
The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.
In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.
Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.
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Samuel's family took a road trip to Mount Rushmore. Samuel fell asleep after they
had travelled 990 miles. If the total length of the trip was 1000 miles, what
percentage of the total trip had they travelled when Samuel fell asleep?
Answers
Answer:
99%
Step-by-step explanation:
For which value of k does the system have no solutions?
Answers
Given:
\(\begin{gathered} 4x+y=3 \\ kx+y=-2 \end{gathered}\)To find the k value which the system has no solutions:
If the system has no solution, then
\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\)So, we get
\(\begin{gathered} \frac{4}{k}=\frac{1}{1}\ne\frac{-3}{2} \\ \therefore k=4 \end{gathered}\)Hence, the answer is k=4.