well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.
so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x[/tex]
so "x" plus the tax will just be x + 0.08x = 1.08x.
The tip was 15% of that 1.08x, and we happen to know that was $1.05.
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48[/tex]
Letter answer only answer only!
Answer: B
Step-by-step explanation:
When Casey woke up to get ready to go to school, he saw that the temperature was negative five
degrees. Casey knew when he went to bed it was twelve degrees warmer, What was the temperature
when Casey went to bed?
Number Sentence:
Answer:
Based on the difference between the temperature when Casey went to bed and when he woke up, the temperature when he went to bed was 7 degrees, which was 12 degrees warmer than -5 degrees.
What is the difference in temperature?The temperature difference is determined using subtraction.
Subtraction is one of the four basic mathematical operations, involving the minuend, the subtrahend, and the result of the operation called the difference.
The temperature when Casey woke up to prepare for school = -5
The difference between the temperature when Casey went to bed and when he woke up = 12 degrees warmer.
The temperature when Casey went to bed = 7 degrees (12 - 5)
Thus, we can conclude that Casey had a temperature of 7 degrees when he went to bed but woke up when it was -5 degrees.
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Look at the following table then answer the questions below
a. Which of the functions in the table appears to be exponential?
b. What reasoning would you use to justify your answer?
c. Which function(s) would most likely model bacterial growth in a lab culture? Justify your reasoning.
d. Which values would most likely model a tub collecting water from a leaky faucet? Justify your reasoning.
For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, function indicating that the amount of water collected rises by 0.5 for each unit increase in time.
what is function?Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.
A. It appears that the function f(x) = 2x is exponential.
b. The function may be expressed as f(x) = a * bx, where a denotes the starting value, b the growth factor, and x the input value. As can be seen from the table, the values of f(x) = 2x are exponentially growing by a factor of 2 for each input.
d. A linear function may be used to simulate a tub that collects water from a leaking faucet since the amount of water collected grows steadily over time.
For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, indicating that the amount of water collected rises by 0.5 for each unit increase in time.
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if 2 inscribed angles of a circle intercept the same arc, then the 2 angles are equal. If m<1 = 35, then m<2 =__
Answer:
m∠2 = 35°
Step-by-step explanation:
You want to know the measure of angle 2 when angle 1 is 35° and both angles 1 and 2 intercept arc PQ.
Same arcInscribed angles 1 and 2 both intercept the same arc: PQ. The problem statement tells you that such angles are equal.
∠2 = ∠1 = 35°
The measure of ∠2 is 35°.
__
Additional comment
This is a vocabulary and reading comprehension test.
In order to understand the comment and the question, you need to know the meaning of "inscribed angle", "intercept [an] arc", "equal" (as applied to angles). You also need to know the meaning of the notation m∠1, the measure of angle 1.
You pass the test when you understand the question is telling you that angles 1 and 2 are both 35°.
Which of the following rectangles has an area that can be represented by the algebraic expression 9x+9
?
Responses
Image with alt text:
Image with alt text:
Image with alt text:
Image with alt text:
Answer: we can't see the images
Step-by-step explanation:
Answer:
Step-by-step explanation:
be can not see the pictures sir do better ni***
Determine the eccentricity for r=5/2+1sin theta
0. 5
5
2
1
Determine the equation of the directrix of r=26. 4/4+4. 4 cos theta
X=-6
Y=6
X=6
The eccentricity for r=5/2+1sin theta and the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6
To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:
r = 5/2 + 1sin(θ)
r = 5/2 + 1y/r
r^2 = (5/2)r + y
x^2 + y^2 = (5/2)r + y
x^2 + y^2 = (5/2)√(x^2 + y^2) + y
x^2 - (5/2)√(x^2 + y^2) + y^2 = 0
We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:
e = √(1 - b^2/a^2)
Plugging in our values, we get:
e = √(1 - 1/(5/2))
e = √(3/5)
e ≈ 0.5
Therefore, the answer is (A) 0.5.
To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:
r = 26.4/4 + 4.4cos(θ)
r = 6.6 + 4.4x/r
r^2 = 6.6r + 4.4x
x = (r^2 - 6.6r)/4.4
We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:
y = (1/4p)x^2
Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:
y = 1.65
However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:
x = 0
Therefore, the answer is (C) x = 6.
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Sal stands a candle up inside a paper bag, opened at the top. The candle and bag are both in the shape of right rectangular prisms. The dimensions, in inches, are given.
Length Width Height
Bag 2 4 8
Candle 1 2 3
Sal wants to put sand inside the bag surrounding the base of the candle. He wants the sand to be between 12 and 34 inches deep. How much sand, in cubic inches, should Sal put inside the bag? Select your answers from the drop-down lists
Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
Base area of the bag = 4 × 2 = 8 in²
Base area of the candle = 2 × 1 = 2 in²
therefore, we know that base area to be filled with sand:
= 8 - 2 = 6 in²
now, height of sand is known to be between 1/2 and 3/4 inches,
therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³
3 in³ and 4.5 in ³
therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
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Given that both X and Y are independent normal distributionswhere,Prove that Z = X/Y is normally distributed.
Z = X/Y is normally distributed because the ratio of two independent normal variables is itself normally distributed and the same has been proved below:
To prove this, we can use the Central Limit Theorem. This theorem states that if X and Y are independently and identically distributed random variables, then the ratio of the two, Z = X/Y, will be normally distributed regardless of the distribution of X and Y. This is due to the fact that the ratio of two independent normal variables is itself normally distributed.
For example, let X and Y be two independent normal variables. Then their ratio Z = X/Y will follow a normal distribution. This means that the probability density function (pdf) of Z is given by:
f_Z(z) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{z^2}{2\sigma^2}}
where \sigma^2 = \frac{\sigma_x^2}{\sigma_y^2} is the variance of Z.
Therefore, we can conclude that Z = X/Y is normally distributed when X and Y are independent normal distributions.
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Find the area of the triangle. Round your answer to one decimal place. B=115∘,C=29∘,a=52
The area of the triangle is 715.7 square units, rounded off to one decimal place.
The given triangle's side lengths and the angles are a = 52, B = 115°, and C = 29°. The area of the triangle can be determined by applying the formula:A = (1/2) a² sin B sin C, where a is the length of the side opposite to angle A.The area of the triangle is (rounding off to one decimal place)Therefore, the area of the triangle is 715.7 square units, rounded off to one decimal place.
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What will be the coordinates of point G after
a 90° counterclockwise rotation about the
origin?
So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.
To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:
x' = -y
y' = x
This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).
If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.
Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:
x' = -y
y' = x
So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:
G' = (-y, x)
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help would be appreciated
A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small addition, a medium addition and a large addition. If the medical demand is high (there is a favorable market for the addition) they would realize a net profit of $100,000 with a large addition, a net profit of $40,000 with a medium addition and a net profit of $10,000 with a small addition. If the medical demand is low (there is an unfavorable market for the addition) they would realize a net loss of $40,000 with the large addition, a net loss of $10,000 with the medium addition and a net profit of $5,000 with the small addition. The Physicians were also able to assign the following utility preference values to each of the potential payoffs they could encounter. Utility of $100,000 is 1.0, U ($40,000) is 0.9, U ($10,000) is 0.6, U ($5,000) is 0.5, U ($-10,000) is 0.4, and U ($-40,000) is 0.0. The physicians also have a reliable forecast indicating a 40% probability of the high medical demand. Using expected monetary value theory, what should they do and what is the expected value of that decision? Using expected utility theory, what should they do and what is the expected utility of that decision?
Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).
What is probability, exactly?The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
The following formula can be used to determine each option's anticipated financial value:
=> EMV of big addition = (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.
=> EMV of the middle addition is
= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.
=> EMV of a minor addition = (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000
The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.
dividing each outcome's usefulness value by its likelihood, then adding the results:
=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.
=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.
Smaller EU = (0.4 * 0.5) + (0.6 * 0.6) = 0.58
The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.
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Please help me with this needs to be done by today thanks
Answer:
cubic unit eg m³
Step-by-step explanation:
Raised to power 3
Answer:
Units cubed or unit^3
Explanation:
Volume= (base)(width)(height), therefore, this would be cubed. x^3
Area=(base)(height), therefore, this would be squared. x^2
Isabel left her home at 11. 30 A. M. She took 45 minutes to jog to the park.
After exercising for 1 hour 55 minutes, she jogged home. She reached home at 3 P. M.
How long did she take to jog home? Explain how you got to this answer
Answer: 1 hour 50 minutes
Step-by-step explanation: it took her 2 hours to get home
she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for 1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home
PLEASE SHOW WORK!!!!!!!!!
Answer:
The answer is G
what kind of triangle is △ABC? Select all that apply.
A 2-dimensional graph with an x-axis and a y-axis is given. A triangle ABC is drawn on it with co-ordinates (2,1), (4,7) and (6,3) respectively.
The toe of which the triangle is , is called an isosceles triangle and a right angled triangle.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. There are different types of triangle , some of them are ;
Scalene triangle, isosceles triangle , equilateral triangle e.tc.
To know the type of triangle it is, we need to find the length of each sides.
let A = (2,1)
B = (4,7)
C = ( 6,3)
AB = √ (4-2)²+ (7-1)²
AB = √ 2²+ 6²
AB = √2+36
AB = √40
= 2√10
BC = √ (6-4)²+( 3-7)²
BC = √ 2²+4²
BC = √4+16
BC = √20
= 2√5
AC = √ (6-2)²+(3-1)²
AC = √4²+2²
AC =√ 16+2
AC = √20
= 2√5
therefore since AB² = BC² + AC ² ,the triangle is a right angled triangle
And also since two sides of the triangle are equal it is an isosceles triangle.
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The cost price of an article when 22% profit is made after selling it for 's'
The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.
Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:
Profit = Selling price - Cost price
Since a profit of 22% was made on the selling price 's', we can express the selling price as:
Selling price = Cost price + Profit
= Cost price + 0.22 * Selling price
Rearranging this equation, we get:
0.78 * Selling price = Cost price
Substituting the given selling price 's' into this equation, we get:
0.78 * s = c
Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:
c = 0.78 * s
= 0.78 * $100
= $78
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what is 46x squared times 24x squard
Answer:
the answer to ur question is: 1218816
4 - 3x = 16
How do you solve this.... I somehow got -4 but I don't think that is right.
Answer:
yes you are right
Step-by-step explanation:
move 4 to other side so its -3x=12
divide 12 by -3
x=-4
The expression for the nth term of a sequence is 7(3 − n)
What are the first four terms of the sequence? Give your answers in
order.
Answer:
14, 7, 0, -7.
Step-by-step explanation:
To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.
The expression for the nth term of the sequence is 7(3 - n).
Let's find the value of the first term (n = 1):
T₁ = 7(3 - 1) = 7(2) = 14
The first term of the sequence is 14.
Now, let's find the value of the second term (n = 2):
T₂ = 7(3 - 2) = 7(1) = 7
The second term of the sequence is 7.
Next, let's find the value of the third term (n = 3):
T₃ = 7(3 - 3) = 7(0) = 0
The third term of the sequence is 0.
Finally, let's find the value of the fourth term (n = 4):
T₄ = 7(3 - 4) = 7(-1) = -7
The fourth term of the sequence is -7.
Therefore, the first four terms of the sequence are:
To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.
The expression for the nth term of the sequence is 7(3 - n).
Let's find the value of the first term (n = 1):
T₁ = 7(3 - 1) = 7(2) = 14
The first term of the sequence is 14.
Now, let's find the value of the second term (n = 2):
T₂ = 7(3 - 2) = 7(1) = 7
The second term of the sequence is 7.
Next, let's find the value of the third term (n = 3):
T₃ = 7(3 - 3) = 7(0) = 0
The third term of the sequence is 0.
Finally, let's find the value of the fourth term (n = 4):
T₄ = 7(3 - 4) = 7(-1) = -7
The fourth term of the sequence is -7.
Therefore, the first four terms of the sequence are:
14, 7, 0, -7.
The expression (1 - 2x)4 can be written in the form 1 + px + qx^(2) - 32x^(3) + 16x^(4) By using the binomial expansion, or otherwise, find the values of the integers p and q.
Using the binomial expansion theorem, the values of integers p and q are -8 and 24, respectively
Expanding an expression using the binomial theoremFrom the question, we are to use the binomial expansion to expand the given expression and determine the values of p and q.
We can expand (1 - 2x)^4 using the binomial theorem as follows:
(1 - 2x)^4 = 1^4 - 4(1^3)(2x) + 6(1^2)(2x)^2 - 4(1)(2x)^3 + (2x)^4
= 1 - 8x + 24x^2 - 32x^3 + 16x^4
Now, we will compare this expression to the given expression
Comparing the expression to the given expression, 1 + px + qx^2 - 32x^3 + 16x^4
We see that:
p = -8
q = 24
Hence, the values p and q are -8 and 24, respectively.
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1. Correct to the nearest millimetre, the length of a side of a regular hexagon is 3.6 cm. Calculate the upper bound for the perimeter of the regular hexagon.
2. Kelly runs a distance of 100 metres in a time of 10.52 seconds.
The distance of 100 metres was measured to the nearest metre.
The time of 10.52 seconds was measured to the nearest hundredth of a second.
(d) Calculate the lower bound for Kelly’s average speed. Write down all the figures on your calculator display.
3. Steve measured the length and the width of a rectangle.
He measured the length to be 645 mm correct to the nearest 5 mm.
He measured the width to be 400 mm correct to the nearest 5 mm.
Calculate the lower bound for the area of this rectangle.
Give your answer correct to 3 significant figures.
4. The length of the rectangle is 35 cm correct to the nearest cm.
The width of the rectangle is 26 cm correct to the nearest cm.
Calculate the upper bound for the area of the rectangle.
Write down all the figures on your calculator display.
1. The upper bound for the perimeter of the regular hexagon is 21.9 cm.
2. All figures on the calculator display for the calculation of Kelly's average speed is: 99.5 / 10.51 = 9.46717412
3. the lower bound for the area of the rectangle is 2.55 × 10⁵ mm²
4. Upper bound for area = 937.6525 cm²
How to calculate the perimeter of the hexagon1. The upper bound for the perimeter of the regular hexagon can be calculated by multiplying the length of one side by 6 (the number of sides in a hexagon):
Upper bound for perimeter = 6 × (3.6 + 0.05) = 21.9 cm (rounded to one decimal place)
2. Kelly's average speed can be calculated by dividing the distance she ran by the time she took:
Average speed = distance / time
The lower bound for the distance is 99.5 m (since 100 m was measured to the nearest meter, the actual distance could be as low as 99.5 m).
The lower bound for the time is 10.51 s (since 10.52 s was measured to the nearest hundredth of a second, the actual time could be as low as 10.51 s).
Therefore, the lower bound for Kelly's average speed is:
Average speed = 99.5 / 10.51 = 9.4617 m/s (rounded to 4 decimal places)
3. The length of the rectangle is 645 mm correct to the nearest 5 mm, which means it could be as small as 642.5 mm or as large as 647.5 mm. We can express this as:
645 mm ± 2.5 mm, similarly
400 mm ± 2.5 mm
Lower bound for length = 645 - 2.5 = 642.5 mm
Lower bound for width = 400 - 2.5 = 397.5 mm
Lower bound for area = 642.5 × 397.5 = 255393.75 mm²
Rounded to 3 significant figures, the lower bound for the area of the rectangle is 2.55 × 10⁵ mm².
4. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width of the rectangle:
Upper bound for length = 35 + 0.45 = 35.45 cm
Upper bound for width = 26 + 0.45 = 26.45 cm
Upper bound for area = 35.45 × 26.45 = 937.6525 cm²
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There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get?
Answer:
2 ounces per person
Step-by-step explanation:
Use substitution to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]4x+y=14\\y=8+2x[/tex]
Answer:
x = 1 , y = 10
Step-by-step explanation:
Given : y = 8 + 2x
by substitution,
4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1
y = 8 + 2x
y = 8 + 2(1)
y= 10
Proof :
if x = 1,
4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14
if y = 10 and x = 1
4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14
For both equations, LHS = RHS
Therefore Proved.
hope it helps!
PLEASE HELP!! I ONLY NEED HELP WITH THE LAST PART (ASKING AVERAGE SPEED)
Answer:
429
Step-by-step explanation:
The following figure is made of 3 triangles and 1 rectangle.
4
2
B
Figure
Triangle A
Triangle B
Rectangle C
Triangle D
Whole figure
A
2
4
T
6
2C 2D
H
2
Find the area of each part of the figure and the whole figure.
Area (square units)
19
1
I
The areas of each part of the composite figure are;
Triangle A = 20 Square units
Triangle B = 2 Square units
Rectangle C = 4 Square units
Triangle D = 6 Square units
What is area?Area is a measurement of the two-dimensional surface of a shape or object. Area is often used when measuring the size of a plot of land or other physical space, such as a room or an outdoor area.
The area of each part of the figure can be found by adding the areas of the individual shapes that make up the figure. The area of a triangle can be found by using the formula A = 1/2bh, where b is the base and h is the height of the triangle. For a rectangle, the area is equal to the length multiplied by the width.
The composite figure's component parts' respective areas are;
20 Square Units = Triangle A
Triangle B = 2 units of the square
Square units = 4 for the rectangle C.
Triangle D = 6 units of the square
How can I calculate the composite figure's area?The formula for a triangle's area is straightforward;
A = 0.5 × base × height
Triangle A's area is;
Triangle A: (6 + 2 + 2) × 4 × 1/2
= ¹/₂ × 10 × 4
equals 20 square units
Triangle B's perimeter is;
Triangle A equals 1/2 × 2 × 2
equals 2 square units
Length × Width = Area of Rectangle C
= 2 × 2
equals 4 square units
Triangle D's area is;
Triangle D is equal to.5 × 6.
equals 6 square units
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Complete question -
Relative to the origin O, the position vectors of two points A and B are a and b respectively. b is a unit vector and the magnitude of a is twice that of b. The angle between a and b is 60°. Show that [a×[ob + (1-o)a] =√k, where k is a constant to be determined.
Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
What is the proof that [a * [ob + (1 - o)a] = √kThe vector OB can be expressed as OB = b since b is a unit vector and O is the origin.
The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.
The angle between a and b is 60°, so we have:
|a| |b| cos 60° = a · b
2|b| · 1/2 = a · b
|b| = a · b
We can now express the vector [OB + (1 - O)A] as:
[OB + (1 - O)A] = b + (1 - O)2b
= (2 - O) b
The cross product of a and [OB + (1 - O)A] is:
a × [OB + (1 - O)A] = a × [(2 - O) b]
= (2 - O) (a × b)
The magnitude of the cross product is:
|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|
= |2 - O| |a| |b| sin 60°
= √3 |2 - O| |b| |a| / 2
= √3 |2 - O| |b|^2 |b| / 2
= √3 |2 - O| |b|^3 / 2
Substituting |b| = a · b, we get:
|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2
Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:
√k = √3 |2 - O| (a · b)^3 / 2
Squaring both sides, we get:
k = 3 (2 - O)^2 (a · b)^6 / 4
Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
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A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water.
5 liters of yellow tint are added to the original mixture.
The percent of yellow tint in the new mixture is ____?
Answer must be correct to 1 decimal place
From the given information provided, the percent of yellow tint in the new mixture is 36.4%.
The total amount of yellow tint in the original mixture is:
0.30 × 50 liters = 15 liters
When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:
15 + 5 = 20 liters
The total amount of new mixture is:
50 + 5 = 55 liters
To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:
(20/55) × 100 = 36.4%
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b. If there are 440 towers, how many customers does the company have? Write a proportion you can use to solve. Choose the correct proportion.
Answer:
What's your question
Step-by-step explanation:
How many customers in each tower
Solve the equation by using the square root method:
9x^2 - 36x = 0
Answer:
Step-by-step explanation:
To solve the equation 9x^2 - 36x = 0 by using the square root method, we first need to rearrange the terms to get x^2 and x on one side:
9x^2 - 36x = 0
Factor out 9x from the left-hand side:
9x(x - 4) = 0
Now we have two factors: 9x = 0 and x - 4 = 0. Solving for x in each factor gives us:
9x = 0: x = 0
x - 4 = 0: x = 4
Therefore, the solutions to the equation are x = 0 and x = 4.
Answer:
x = 0, x = 4
Step-by-step explanation:
Unfortunately, the equation 9x^2 - 36x = 0 cannot be solved using the square root method directly. The square root method is used to solve quadratic equations of the form ax^2 + bx + c = 0 by isolating the x^2 term, taking the square root of both sides, and solving for x. However, in the given equation, there is no constant term (c = 0), and therefore, we need to use a different method to solve it.
As I mentioned earlier, we can factor the equation and use the zero product property to solve for x. This method involves finding two factors of the quadratic equation that multiply to give 0, setting each factor equal to 0, and solving for x. In this case, we can factor out x and obtain the factors x and (9x - 36), which multiply to give 0. By setting each factor equal to 0 and solving for x, we obtain the solutions x = 0 and x = 4.
To solve the equation 9x^2 - 36x = 0 using the factorization method:
Factor out x from the left-hand side of the equation to get:
x(9x - 36) = 0
Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for x:
x = 0 or 9x - 36 = 0
For the second equation, solve for x:
9x - 36 = 0
9x = 36
x = 4
Therefore, the solutions to the equation are x = 0 and x = 4.
Note that this method involves factoring the quadratic equation and then using the zero product property to obtain the solutions. It works for any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.