Given u = (-1,3), v=(2,4) , and w= ( 2,-5), then, by applying scalar multiplication on vector, 2u = (–2, 6)
In the two-dimensional coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector q = (1,–5), which means:
x-component = 1
y-component = –5
Operations on vectors:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1,3), v = ( 2,4) , and w = (2,-5)
Then,
2u = 2 (-1,3)
= (2 . (-1), 2. 3) = (–2, 6)
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Use natural logarithms to solve each equation.
e x+1=30
2.4012 is the value of x after solving equation [tex]e^{x+1}[/tex] = 30 using natural logarithms
We have been asked to solve [tex]e^{x+1}[/tex] = 30 using natural logarithms
⇒ [tex]e^{x+1}[/tex] = 30
⇒ x + 1 = ㏑ 30
⇒ x = ㏑ 30 - 1
≈ 2.4012
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct QuestionUse natural logarithms to solve each equation.
[tex]e^{x+1}[/tex] = 30
For Comic Relief Stamford Green School are taking part in a "Bake Off".
Parents are invited to come and buy cakes. 150 parents attend: 70% donate £1 for their cake and the rest donate £2 for their cake. How much money is donated in total?
Start off with %70 of 150
0.7 • 150 = 105
To find their total donation amount,
105 • £1 = £105
Then we know the rest of the parents account for the last %30 of the attendees
We can find this out by either,
150 - 105
or
0.3 • 150
Either way we end up with 45
45 • £2 = £90
%70 (105) of the parents donated £105
%30 (45) of the parents donated £90
The parents, in total, donated £195
SUPER URGENT!!!
Joel sells ice cream cones at the county fair. He has to rent the equipment for $36 and spend $0.52 on ingredients for each cone. What is the minimum number of ice cream cones Joel must sell at $1.40 each in order to make a profit?
Please explain ALL OF THE STEPS, or your answer is useless. Thanks!!
Denote by x the number of cones sold or produced.
Denote by C(x) the total cost.
Denote by R(x) the revenue made.
Denote by P(x) the net profit accumulated.
[tex]C_{T}(x)=C_{fixed}+C_{variable} \: \\ C_{T}(x)=36+0.52x[/tex]
[tex]R_{T}(x)=selling \: price \: x \\ R_{T}(x)=1.4x[/tex]
[tex]P(x)=R_{T}(x)-C_{T}(x) \\ P(x)=1.4x-(36 + 0.52x) \\ P(x)=1.4x - 36 - 0.52x \\ P(x)=0.88x - 36[/tex]
If there exists profit, then P(x) has to be positive.
[tex]P(x) > 0 \\ 0.88x - 36 > 0 \\ 0.88x > 36 \\ x > \frac{36}{0.88} \\ x > 40.90909 \\ x = 41[/tex]
3 (x - 17) < 9 (1 - 3x)
Answer:
x < 2
Step-by-step explanation:
3(x- 17) = 3x - 51
9(1-3x) = 9 - 27x
3x - 51 < 9 - 27x
30x - 51 < 9
30x < 60
X < 2
Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1) Start: 3 End: 10
2) Start: 9 End: 20
3)Start: 100 End: 85
The percent increase or decrease of the starting and ending quantities below are:
233%122%-15%How to find the percent increase?The percent increase can be found by the formula:
= (End - Start) / Start x 100%
The percent increase of these quantities are:
= (10 - 3) / 3 x 100%
= 7 / 3 x 100%
= 2.3333 x 100%
= 233%
= (20 - 9) / 9 X 100%
= 11/9 x 100%
= 1.222 x 100%
= 122%
= (85 - 100) / 100 x 100%
= -15 / 100 x 100%
= -15%
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Please answer the question in the photo! [ brainliest ] (20 points)
Answer:
1/4
Step-by-step explanation:
or 90/360
At a party store, packages of 12 noisemakers are $2 each. Packages of 9 party hats are $15 each. Mia wants to buy equal numbers of noisemakers and hats.
To get that many noisemakers and hats: How many packages of noisemakers does Mia need to buy?
How many packages of hats? Explain.
Please help due soon.
[tex]a = \pi \: r {}^{2} \\ r {}^{2} = \frac{a}{\pi} \\ r = \sqrt{ \frac{a}{\pi} } [/tex]
Answer: First OptionThe freight elevator has the capacity of 3500 pounds if a barrel averages 50 pounds and a crate 140 pounds write an inequality that describes when x barrels and y crates will cause the elevator to be overloaded
The inequality that describes when x barrels and y crates will cause the elevator to be overloaded is 50x + 140y < 3500.
According to the given question.
Capacity of elevator = 3500 pounds
Average of a single barrel = 50 pounds
capacity of single crate = 120 pounds.
As we know that, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Therefore, the inequality that describes when x barrels and y crates will cause the elevator to be overloaded is given by
50x + 140y < 3500
Hence, the inequality that describes when x barrels and y crates will cause the elevator to be overloaded is 50x + 140y < 3500.
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What is the blue dot on
Find the GCF of
12 and 54
Answer: GCF = 6
Step-by-step explanation:
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
Then the greatest common factor is 6.
plss help me with this
Answer:
Below in bold.
Step-by-step explanation:
7x - 2 + 9x - 2 + 2(5x) = 2(5x + 5) + 2(4x)
7x + 9x + 10x - 4 = 10x + 10 + 8x
7x + 9x + 10x - 10x - 8x = 10 + 4
8x = 14
x = 14/8 = 7/4
So, ST = 5*7/4 + 5
= 55/4
= 13 3/4
Answer:
ST = 13.75
Step-by-step explanation:
The perimeter of a trapezium is calculated with the following formula:
P = a + b + c + d (a, b: bases, c, d: sides)
The perimeter of a rectangle is calculated with the following formula:
P= 2(a + b) (a: base, b: side)
we will write the following equation to find the length of ST
7x - 2 + 9x - 2 + 5x + 5x = 2(5x + 5 + 4x) first do the inside the parenthesis
2(9x + 5) = 18x + 10
Now,
7x - 2 + 9x - 2 + 5x + 5x = 18x + 10 add like terms on the left side of the equation
26x - 4 = 18x + 10 transfer like terms to the same side of the equation
26x - 18x = 10 + 4 add/subtract
8x = 14 divide both sides by 8
x = 1.75 replace x with this to calculate the lentgh of ST
5x + 5 = 5*(1.75) + 5 and ST = 13.75
Japhet is making small rectangular tiles for a mosaic. each tile has an area of 7 cm 2 and is 1 1/4 cm wide. how long is each tile?
Answer:
28/5
Step-by-step explanation:
7 x 4/5 = 28/5
use keep, change, flip
Answer:
28/5
Step-by-step explanation:
just did it on khan academy.
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=(7-x)²
Answer to this question is:
Domain of given function is (-∞,∞),{x|x∈R}
Range of given function is [0,∞),{y|y≥0}
Inverse of given function is -√x+7,√x+7
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(-∞,∞)
Set-Builder Notation:{x|x∈R}
The set of all valid y values constitutes the range.
Interval Notation:[0,∞)
Set-Builder Notation:{y|y≥0}
For calculation of inverse:
Interchange the variables x=(7-y)²Solve for yy=-√x+7,√x+7Replace y with f^-1(x)f^-1(x)=-√x+7,√x+7∴Domain of given function is (-∞,∞),{x|x∈R}
Range of given function is [0,∞),{y|y≥0}
Inverse of given function is -√x+7,√x+7
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Need help please with math
The equation for red graph is y= f(x-1)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
y = f(x)
Here if look at the graph with black with function f(x) = x
Now, if we look at the graph closely to shift the black graph to red.
There is shifting the graph in the right hand side which which gives the function y= f(x-1)
Hence, the equation for red graph is y= f(x-1)
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Write 750 in scientific notation
Answer:
7.5 × 10[tex] {}^{2} [/tex] (scientific notation)
Step-by-step explanation:
➟ 750 = 7.5 × 10[tex] {}^{2} [/tex] (scientific notation)
a bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. after 4 hours there will be 2640 bacteria. (a) express the population after t hours as a function of t. population: equation editor (function of t)
Answer:
T=x(T*2) where X=660
Step-by-step explanation:
If it has been 2 hours than t=2
plug in 2 for t and you get x*4
(x, y) → (x + 5, y − 4), what are the coordinates of point L′?
Answer: (5,-4)
Step-by-step explanation:
start at zero and go right five because of the adding of five
Then go down 4 because of the minus of zero.
z(4−1/2)+4 help please :(((
Answer:
7/2z +4
Step-by-step explanation:
z(4-1/2)+4
=7/2z +4
Answer:
7.5
Step-by-step explanation:
Remove parentheses; z=4-1/2+4
Add the 4s: -1/2+8
convert to fraction: 8*2/2-1/2
combine fractions:8*2-1/2
8*2-1=15
15/2
now convert 15/2 to a decimal, boom, 7.5
Find the LCM of 2 and 6 using lists of multiples.
Answer:
6
Step-by-step explanation:
2,4,6,8,10
6,12,18,24
The least number that is on both lists is 6
At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level.
(a) The expression to represent the difference between the elevations is 5764 - ( - 9).
(b) The answer will be a positive integer.
(c) The difference between the highest and lowest point is 5773 feet.
The elevation of a county is 5764 feet above sea level.
The elevation of the county is 9 feet below sea level at the lowest point.
(a) The highest point = 5764 feet
The lowest point = 9 feet
Then the difference between the highest and the lowest point will be:
difference = Highest - lowest
difference = 5764 - ( - 9)
(b) The answer will be written as a positive integer.
(c) The difference between the highest and lowest points of the county will be:
difference = Highest - lowest
difference = 5764 - ( - 9)
difference = 5764 + 9
difference = 5773 feet
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The complete question is mentioned below:
At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level. Answer parts (a) through (c).
a. Write an expression using integers to represent the difference between the elevations.
b. Will the answer be written as a positive or negative integer?
c. What is the difference between the highest and lowest points of the county?
A submarine was 200 feet below sea level. Then it dove down another 370 feet so the biologists could study a squid. After that, the submarine ascended 500 feet to get closer to the surface. What is the current depth of the submarine? Express your answer as an integer.
Answer:
70 feet
Step-by-step explanation:
Depth
200 + 370 - 500 = 70 feet
Sheridan Street and Richmond Street are parallel, and both are intersected by University Boulevard.
Two cars are heading west, one on Sheridan St. and one on Richmond St. Both cars turn north onto University Blvd.
What is the measure of the angle of their turn on to University Blvd.
The measure of the angle of their turn on to University Blvd is; 80°
How to interpret corresponding angles?
Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.
Thus, from the given diagram when we apply the concept of corresponding angles, we can say that;
17x + 15 = 19x + 5
19x - 17x = 15 - 5
2x = 10
x = 5
Thus;
19x + 5 = 19(5) + 5 = 100°
Now, the sum of the angles on a straight line is 180 degrees. Thus, the measure of the angle of their turn on to University Blvd is;
180 - 100 = 80°
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The radius of a circle can be expressed as r=√A/π inches where r is the radius and A is the area of the circle. If the area of a circle is 169 π in.², what is its radius?
The radius is 169 inches.
As per the known fact, the radius and area of circle are related by the formula -
Area = πr²
So, rewriting the expression in equation -
r=√(A/π)²
As mentioned, r is the radius and A is the area of the circle and π is constant
Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.
r = √(169π/π)²
On solving the above equation we get the new equation, which is as follows -
r = 169π/π
Cancelling π as it is common in both numerator and denominator
r = 169 inches
Hence, the radius of circle is 169 inches.
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The figure shows relationships of the dimensions of a square pool with an attached patio. Complete the equations and reasons to show that AC= BD
For the given square pool the relationship between the line segment will be BD = BC + CD and AB + BC = CD + BC and it will go to proves that AC = BD.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given that,
AB = CD
By segment addition postulate
AC = AB + BC
Again by segment addition postulate
BD = BC + CD
In addition property of equality
AB + BC = CD + BC
So,
AC = BD
Hence "BD = BC + CD and AB + BC = CD + BC will proves that AC = BD".
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A puppy weighs 2.8 pounds at birth and gained about 0.5 pounds per week. A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week. In how many weeks will the weight of the kitten be no less than the weight of the puppy?
The weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.
What is Inequality?Statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
A puppy weighs 2.8 pounds at birth and gained about 0.5 pounds per week.
A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week.
puppy: 2.8 + 0.5x
Kitten: 1.4 + 1.2x
As, kitten is no less than puppy.
Kitten ≥ puppy
1.4 + 1.2x ≥ 2.8 + 0.5x
hence, the weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.
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Expand each binomial.
(2 x-y)⁴
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (2x - y)⁴
By using binomial expansion theorem, we get
(2x - y)⁴ = 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴
(2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴
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-7/10 + 1/5 (please help)
Answer: 2
Step-by-step explanation:
Show that at least three of any 25 days chosen must fall in the same month of the year.
The proof that at least three of any 25 days chosen must fall in the same month of the year holds true because; there are twelve months in a year.
What is the proof that three of any twenty-five, 25 days chosen must fall in the same month of the year as required in the task content?This proof required for the statement in the task content follows from the fact that, there are 12 months in a year.
Hence, the proof that at least three of any twenty-five, 25 days chosen must fall in the same month of the year is because, there are 12 months in a years and after choosing two days from each month, amounting to 24 days, the 25th day would fall into a month and hence, such month has 3 days already.
Ultimately, the statement that at least three of any 25 days chosen must fall in the same month of the year holds true because there are 12 months in a year.
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from x-2 subtract 4x +9
Answer:
I'm pretty sure it is -3x+7