3x - 5y = 6
-3x -3x
-5y = -3x + 6
[tex]\frac{-5y}{-5} = \frac{-3x}{-5} + \frac{6}{-5}[/tex]
[tex]y = \frac{3}{5}x - \frac{6}{5}[/tex] ⇒ m = [tex]\frac{3}{5}[/tex]
perpendicular slope (m⊥) = [tex]-\frac{5}{3}[/tex]
Point-Slope equation:
m = [tex]-\frac{5}{3}[/tex] (x₁ , y₁)= (-8, 0)
y - y₁ = m(x - x₁)
y - 0 = [tex]-\frac{5}{3}[/tex](x - (-8))
y = [tex]-\frac{5}{3}[/tex](x + 8)
y = [tex]-\frac{5}{3}x - \frac{40}{3}[/tex]
Derivative of (2x+9)^3
Answer:
[tex]\displaystyle \frac{d}{dx} = 6(2x + 9)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (2x + 9)^3[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = 3(2x + 9)^2 \cdot \frac{d}{dx}[2x + 9][/tex]Basic Power Rule [Addition/Subtraction, Multiplied Constant]: [tex]\displaystyle \frac{dy}{dx} = 6(2x + 9)^2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the average rate of change for the sequence shown below? a coordinate plane showing the points negative 1, 4. 1, 3. 3, 2. 5, 1.
Answer: - 1/2 = - 0.5
Explanation:
1. Make the sequence clear. These are the given points (x,y):
(-1, 4)(1, 3)(3, 2)(5, 1)2. The average rate of change only takes into account the last and the first pairs of your intervals, those are (5, 1) and (-1, 4).
Average rate of change = [change in y] / [change in x] = [1 - 4] / [5 - (-1) ] =
= - 3 / 6 = - 1/2 = - 0.5 ← answer
The averate ratre of change is the slope of the line that joins the first and last points. The fact that the result is negative means that there was a net decrease of the values.
It takes 24 people to pull a 50 ton iron rod. How many people it take to pull a 150 ton iron rod?
72 people.
50 x 3 = 150
24 x 3 = 72
A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground camera and top of the building is 51 feet, and the angel of the camera with respect to the ground is 43 degrees. What is the height of the building?
Answer:
34.78 feet
Step-by-step explanation:
1) using the cosine function, I did cos(43)=x/51
This is because cosine is equal to adjacent over hypotnuse
Once I found x, I used the pythagorean theorem to get 34.78 feet
9c squared -4c squared +2c squared
Answer:
7c^2
Step-by-step explanation:
I'm assuming you meant "9c^2 - 4c^2 + 2c^2." This comes to:
(9 - 4 + 2)*c^2, or 7c^2.
A motorcycle can travel 15 miles on 3/8 of a gallon of gasoline. How far can the motorcycle travel on one gallon of gasoline.
i believe the answer would be 40 miles
the easy way to do it is to look at it as 5 miles for 1/8 gallon of gas and 1 whole gallon is 8/8 so multiply 5 *8=40
40 miles on 1 gallon of gas
PLZZZZZZZZZZZZZZZZZ HELP ASAP WILL GIVE BRAINIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!
Enter the missing numbers in the boxes to complete the table of equivalent ratios.
Number of Servings Liters of Punch
8 2
? 4
20 ?
? 7
answer if u know the answer.
Can someone help me with this
25t = 5( 5t + 1)
That equation has no solutions.
The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat rental fee for the week, plus a charge for each mile driven. The Yu's drove 222 miles; their car cost $110.30 for the week. The Sainz's drove 147 miles; their car cost $99.05. What is the linear equation that represents the cost of a rental car? Round to the nearest hundredth
Answer:
y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Step-by-step explanation:
Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.
Let flat rental fee be c and cost per mile driven = m and miles driven = x
Total cost =y
Then y = mx+C is the linear equation.
to find m and c, we use the fact that y =110.30 when x = 222
i.e. 110.30 = c+222x
and similarly 99.05 = c+147x
Subtract to eliminate c
11.25 = 75 x
0.15 =x
Substitute in I equation
110.30 = c+222(0.15)
c = 77
y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Answer:
y=0.15x + 77.00
Step-by-step explanation:
I did it on edge that is the correct answer promise.
CAN U SOLVE THIS
Find the value of b if the graph the equation y=−3x+b goes through the given point.
A(−2, 4) AND B(5,2)
Hello!
To the value of b, or the y-intercept, we need to substitute an ordered pair/point into the given equation.
Since we are given two points, we can use those two points to find two different equations.
Remember that ordered pairs are written as (x, y).
A(-2, 4)
y = -3x + b
4 = -3(-2) + b
4 = 6 + b (subtract 6 from both sides)
-2 = b
A) Therefore, the equation of the first ordered pair is y = -3x - 2.
B(5, 2)
2 = -3(5) + b
2 = -15 + b (add 15 to both sides)
17 = b
B) The equation of the second ordered pair is y= -3x + 17.
Final answers:
A) y = -3x - 2B) y = -3x + 17Answer:
I got this problem wrong and to all the people out there you are solving for B on both of them
Thank you have a good day.
Step-by-step explanation:
What are the subsets of red blue and yellow
green orange and purple
The length of the segment from –3 to 0 on a number line is shown.
Which equation is represented by the diagram?
A. |–3| = 3
B. |3| = |–3|
C. 3 + 0 = 3
D. 3 – 0 = 3
I believe its A, since the absolute value brackets are used to show how far away a number is from 0. All of the other answers are correct, but A makes the most sense here.
Answer:
a
Step-by-step explanation:
:D
A triangle has side lengths of 7 in., 9 in., and 11 in. Determine whether this is a right triangle and why.
Answer:
Not a right triangle. See below for my reasoning.
Step-by-step explanation:
If this is a right triangle, then the sum of the squares of the two shorter sides will equal the square of the longest side: 7^2 + 9^2 = 11^2 => 49 + 81 = 121 But this is false.
Answer:
It's not a right triangle, because already 7^2 = 7x7 which is 49 so...
Step-by-step explanation:
can you help me solve each compound inequality and graph it's solution? 2 and 4 please and thank you
[tex]\dfrac{k}{4}\geq1\qquad|\cdot4\\\\k\geq4\\\\\dfrac{k}{3}\leq-1\qquad|\cdot3\\\\k\leq-3\\\\k\leq-1\ or\ k\geq4[/tex]
[tex]6\leq x+6\leq11\qquad|-6\\\\0\leq x\leq5[/tex]
Ok so for this one I have to write an equation, solution, and answer.
Two groups hikers start at the same time at the same average speed. Marks group hikes for 2.5 hours. Sally’s group hikes for 4.7 hours and covers another 7.7 miles.
How fast are the hikers going?
Equation:_________
Solution: _________
Answer:___________
Final answer:
To find the hikers' average speed, we use the difference in distance and time between two groups, yielding an average speed of 3.3 miles per hour.
Explanation:
To solve the problem of how fast the hikers are going, we need to calculate the average speed using the distance covered by Sally's group and the time difference between the two groups. The formula for average speed is Average speed = Total distance ÷ Total time.
Let's denote the average speed as v, the distance covered by Marks' group as d (which is the same as Sally's since they start at the same point and hike at the same speed but for different periods), and their respective times as t1 for Marks' group and t2 for Sally's group.
Given:
Sally's group covers 7.7 miles more than Mark's group
t1 = 2.5 hours and t2 = 4.7 hours
Equation: Since they have the same speed, Mark's distance d plus 7.7 miles equals the speed v multiplied by t2 (Sally's hiking time). So, d + 7.7 = v × t2. Also, because speed is constant, v = d ÷ t1. Combining these, we get v = 7.7 ÷ (t2 - t1).
Solution: Substitute the given values into the formula, v = 7.7 ÷ (4.7 - 2.5)
Answer: v = 3.3 miles per hour.
Consider the following relation:(1,12) (3.8) (3,11) (6,9) (7,11) . Which ordered pair could be removed so that the relation is a function.
You could remove 3,11)
Jenny can send texts on her phone at the rate of 32 words per minute. if she sends 8 texts that average 80 words each how long would it take her?
8×80= 640
640/32= 20.
your answer is 20 minutes
How to do this question?
Remark
Drawing that diagram was a very good idea. If you can picture something happening, you are half way there. I tend to use a table, but the diagram will come to the same thing.
Olivia Dawn
Start 176 80
Donate x x Subtract
What's left 176 - x 80 - x
Equation
176 - x = 5*(80 - x) Olivia had 5 times as many books as Dawn did. Remove the brackets.
Solution
176 - x = 400 - 5x Add 5x to both sides
176 + 5x - x = 400 Combine terms on the left
176 + 4x = 400 Subtract 176 from both sides
4x = 400 - 176 Combine terms on the right.
4x = 224 Divide by 4
x = 224/4
x = 56 Answer
(02.01)Polygon ABCD slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what is the measure of angle A'?
Answer:
Option A. 75 Degrees
Step-by-step explanation:
Juan y Marta tienen que hacer un trabajo de 24 páginas. Juan hace 1/3 del trabajo y Marta 1/2. ¿Cuántas páginas ha hecho cada uno?
Tenemos.
Total paginas = 24
Lo que hace Marta = 24/2 = 12
Mara hace 12 paginas
Lo que hace Juan = = 24/3 = 8
Lo que hace Juan es 8 paginas
La fraccion de lo que hizo Marta
12/24 = 1/2
La fraccion de lo que hizo Juan = 8/24 = 1/3
La fraccion de lo que hicieron los 2:
1/2 + 1/3 =
3/6 + 2/6 =
(3 + 2)/6 =
5/6
Lo que hicieron los 2 es 5/6 de 24
Les queda por hacer.
1 - 5/6 =
6/6 - 5/6 =
(6 - 5)/6 =
1/6
Les falta por hacer 1/6 de 24
Las pagina que quedan por hacer son:
24 - 12 - 8 = 4
Faltan por hacer 4 paginas
What is the answer for (-6)(-3) can you you please walk me through it then answer. I think it’s 2 -2 -18 or 18 please help me!
When you Multiply Two Negative numbers you will get a Positive Number When you Multiply Two Positive Numbers You get a Positive number, but when you multiply a Positive to a Negative you get a Negative Number. Hope this Helps ( The answer is 18)
true or false, every relation is a function
Final answer:
The statement that every relation is a function is false, as a function requires each input from the domain to be associated with exactly one unique output in the range, unlike a general relation which can associate a single input with multiple outputs.
Explanation:
A function is a special type of relation where each element in the domain is paired with exactly one unique element in the range. This specificity is illustrated by considering a relation that contains ordered pairs sharing the same first element but with different second elements; such a relation cannot be a function since it violates the definition that each input (domain) must be associated with a unique output (range).
On the other hand, if a relation has pairs where the second elements (outputs) are the same but the first elements (inputs) are distinct, it still qualifies as a function. This is because the foundation of a function's definition pertains solely to the uniqueness of mapping from the domain to the range, without regard to the uniqueness of the range itself.
Solve for v in terms of s, t, an u. U=tsv
Final answer:
To solve for velocity v in the provided equation U=tsv, divide both sides by ts to isolate v, resulting in v = U / (ts).
Explanation:
Solving for v in Terms of s, t, and u:
To solve for v in terms of s, t, and u given the equation U=tsv, we can rearrange the equation to isolate v. We start by dividing both sides of the equation by ts, which results in:
v = U / (ts)
This equation shows that the velocity v can be calculated if we know the initial velocity u, the time t, and the displacement s.
B is the midpoint of AC. If AB = 3x + 2 and BC = 5x - 10, find AC
If B is the midpoint of AC, then |AB| = |AC|.
|AB| = 3x + 2
|BC| = 5x - 10
Therefore we have the equation:
3x + 2 = 5x - 10 |subtract 2 from both sides
3x = 5x - 12 |subtract 5x from both sides
-2x = -12 |divide both sides by (-2)
x = 6
The measure of line segment AC is 40 units.
Given that, B is the midpoint of AC.
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
Since, B is the midpoint of AC, we get
AB=BC
⇒ 3x + 2 = 5x - 10
⇒ 5x-3x=2+10
⇒ 2x=12
⇒ x=6
So, AC=AB+BC
= 3x + 2 + 5x - 10
= 8x-8
= 8(x-1)
= 8(6-1)
= 40 units
Therefore, the measure of line segment AC is 40 units.
To learn more about the mid point of line segment visit:
https://brainly.com/question/27656385.
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Please help. I need help with B.
Andrew is wrong The mat is only 100 times bigger than the unit, hope this helps :D
What is the perimeter of the polygon shown?
The perimeter of a polygon is calculated by adding up the lengths of all its sides. In the case of a regular polygon (all sides equal), it's the length of one side times the number of sides. To answer the specific question, each side must be measured and added up.
Explanation:In mathematics, the perimeter of a polygon is the sum of the lengths of its sides. If the polygon has all equal sides, like a square or regular hexagon, you just multiply the length of one side by the number of sides. If not, you have to add up the lengths of all the sides individually.
For example, if we have a triangle with sides 3, 4, and 5 units long, the perimeter would be 3+4+5 = 12 units. Or, for a square with each side 4 units long, the perimeter would be 4*4 = 16 units. Without seeing the actual polygon in your question, I can't provide the exact perimeter, you’d need to measure each side and add them together or use a formula if it’s a regular shape with equal sides.
Learn more about Perimeter here:https://brainly.com/question/30252651
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It's not B or C and can you explain the work please and thanks
The temperature at the start (2:00 AM) is -6°C
It furthered decreased by 8°C
-6 - 8 = -14
(B) -14°C is your answer
~Senpai
name the property for the given statement 2+4=2+4
it is the identity property because it states that 2+4=2+4 and 2+4 will always equal itself, 2+4
another example of this would be 5=5
The correct option is A.
The property for the given statement "2 + 4 = 2 + 4" is the Addition Property of Equality.
The property demonstrated in the given statement "2 + 4 = 2 + 4" is the addition property of equality. Here's why:
A. **Addition Property of Equality**: This property states that if you add the same number to both sides of an equation, the equality remains true. In the given equation, both sides are identical, with 2 + 4 on each side. Therefore, adding the same quantity (in this case, zero) to both sides keeps the equation true.
B. Distributive property involves multiplication and addition, which is not applicable here.
C. Multiplication Property of Equality involves multiplication, which is not present in the given equation.
D. Subtraction Property of Equality is not relevant since there is no subtraction involved in the given equation.
So, the correct option is A. Addition Property of Equality.
The complete question is here:
Name the property for the given statement.
2 + 4 = 2 + 4
A. addition property of equality
B. distributive property
C. multiplication property of equality
D. subtraction property of equality
In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50 cm. Find the lengths of all sides.
The length of the base is 10 and the length of each leg is 20.
In order to find this, we can start by making the length of the base x. Now we know that the legs are twice as long, which would make them 2x. Since there are two of them, we can add x + 2x + 2x and set equal to 50 to find the value of x.
x + 2x + 2x = 50
5x = 50
x = 10
Now we can plug this in for our leg length as well to find that.
2x = Leg
2(10) = Leg
20 = leg
help mee plsss & thank youu
The answer to your question is,
5.
-Mabel <3
For this case, we have the following expression:
[tex]3x ^ 6yz + x ^ 4y ^ 2 + 2xz ^ 5-6x ^ 2y ^ 3-7y\\[/tex]
Where for example, 3x ^ 6yz represents a polynomial term that consists of:
3: Represents the coefficient of the term
x, y, z: Represent the associated variables
6: Represents the exponent associated with the variable x. (y, z have exponent 1)
Therefore, the expression has 5 terms.
Answer:
Option c