what is the answer ?
Answers
i) y ≤ –0.75x
ii)y ≤ 3x – 2
since [tex]0.75= \frac{75}{100}= \frac{3}{4} [/tex], we can write the system again as
[tex]i) y \leq - \frac{3}{4}x [/tex]
[tex]ii) y \leq 3x-2[/tex]
Whenever we are asked to sketch the solution of a system of linear inequalities, we:
1. Draw the lines
2. Color the regions of the inequalities.
3. The solution is the region colored twice.
A.
to draw the line [tex] y =- \frac{3}{4}x[/tex]
consider the points: (-4, 1) and (0, 0), or any 2 other points (x,y) for which [tex] y =- \frac{3}{4}x[/tex] hold.
since we have an "smaller or equal to" inequality, the line is a solid line (not dashed, or dotted).
In order to find out which region of the line to color, consider a point not on the line, for example P(1, 1), which is clearly in the upper region of the line.
For (x, y)=(1, 1) the inequality [tex]y \leq - \frac{3}{4}x[/tex], does not hold because
[tex]1 \leq - \frac{3}{4}*1= -\frac{3}{4} [/tex] is not true,
this means that the solution is the region of the line not containing (1, 1), as shown in picture 1.
B.
similarly, to draw the solution of inequality ii) y ≤ 3x – 2,
we first draw the line y=3x-2, using the points (0, -2) and (2, 4), or any other 2 points (x,y) for which y=3x-2 holds.
after we draw the line, we can check the point P(1, 7) which clearly is above the line y=3x-2.
for (x, y) = (1, 7), the inequality y ≤ 3x – 2 does not hold
because 7 is not ≤ 3*1-2=1, so the region we color is the one not containing P(1, 7), as shown in picture 2.
The solution of the system is the region colored with both colors, the solid lines included. Check picture 3.
the lines intersect at (0.533, -0.4) because:
–0.75x=3x-2
-0.75x-3x=-2
-3.75x=-2, that is x= -2/(-3.75)=0.533
for x=0.533, y=3x-2=3(0.533)-2=-0.4
Answer: Picture 3, the half-lines included. So the graph is in the 3rd and 4th Quadrants
Related Questions
Find the value of 4 + (27 - 12·2) ÷ 2.
Answer's are 3.5,5.5 and 19
Which one is it
Answers
The value of 4 + (27 - 12·2) ÷ 2 would be 5.5.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
A Simplification usually involves making the expression simple and easy to use later.
WE follow the rule PEMDAS parenthesis, exponent, multipy, divide, add, substart.
4 + (27 - 12·2) ÷ 2
4 + (27 - 24 ) ÷ 2
4 + (3) ÷ 2
4+3/2, do 3/2=1.5
then add it
4+1.5 = 5.5.
Therefore, the correct answer is 5.5
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How did he get this 1/2i ? I dont remember studying this definition in calc 1 neither calc 2!
Answers
[tex]\sin at=\dfrac{e^{iat}-e^{-iat}}{2i}[/tex]
This follows from
[tex]e^{iat}=\cos at+i\sin at[/tex]
[tex]e^{-iat}=\cos at-i\sin at[/tex]
[tex]\implies e^{iat}-e^{-iat}=2i\sin at[/tex]
[tex]\implies \sin at=\dfrac{e^{iat}-e^{-iat}}{2i}[/tex]
Final answer:
The term 1/2i most likely pertains to complex numbers, where 'i' is the imaginary unit. It's not typically covered in Calculus I or II but in pre-calculus or algebra courses. The principles of working with fractions apply similarly for complex numbers as they do with real numbers.
Explanation:
The term 1/2i likely refers to the fractional unit in the context of complex numbers, where 'i' is the imaginary unit. This concept is not commonly taught in Calculus I or II but is a part of complex number arithmetic, which is sometimes covered in pre-calculus or algebra. When calculating with complex numbers, it is crucial to remember that 'i' represents the square root of -1.
Let's consider the calculation of 'half' of something in more familiar terms. If you have half a pie, and you're looking to find half of that, you would intuitively know that you now have one-quarter of a pie. Likewise, if you are trying to understand how to combine fractions such as 1/2 and 1/3, you look for a common denominator. Multiplying denominators can often provide this common base for addition, just like multiplying 2 and 3 to get 6 as a common denominator.
However, when working with complex numbers and encountering a term like 1/2i, it can seem less intuitive. Nonetheless, the basic principles of fraction manipulation remain the same. The student might be looking at a problem involving complex fractions, which would require familiarity with the algebraic rules governing complex numbers.
In △ABC, m∠A=72°, c=61, and m∠B=16°. Find a to the nearest tenth.
Answers
make sure your calculator is in Degree mode.
Using the law of sines, the length of side a to the nearest tenth is 58.1 units.
What is law of sines?Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.
In ΔABC,
∠A=72°
∠B=16°
∠A + ∠B + ∠C = 180° (angle sum property)
72° + 16° + ∠C = 180°
∠C = 180° - (72° + 16°) = 92°
Using sine law, (refer to the figure attached)
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]
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Which is equivalent to “12 chairs for every 3 tables”?
Answers
Answer:
A 12 chairs per 3 table
Step-by-step explanation:
4/1 is equivalent to 12 chairs for every 3 tables.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given a statement, 12 chairs for every 3 tables.
The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1
Therefore, there are 4 chairs for every table.
Hence, 4/1 is equivalent to 12 chairs for every 3 tables.
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a mechanic charges 50 am hour plus parts if a bill is 450 including 150 in parts how many hours did it take
Answers
total = 450
parts = 150
450-150 = 300
50 per hour
300/50 = 6
it took 6 hours
Tessa had $110 in her checking account. She paid her cable/internet bill for $75. She deposited $50 from her part-time job before writing a check for $85 to pay her credit card bill. What is Tessa's account balance?
Answers
110-75+50-85 =
110+50=160
75+85 = 160
160-160=0
her balance is 0
If the total price paid for an item is $20.25 and the cost of the item before sales tax is $18.90, what is the rate of sales tax?
Answers
20.25 -18.90 = 1.35
1.35 / 18.90 = 0.071428571
= 7.14%
check:
18.90 x 1.34946 Round to 1.35
18.90 + 1.35 = 20.25
Sales tax = 7.14%
((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify
Answers
[tex]\bf \cfrac{\left( 81x^3y^{-\frac{1}{3}} \right)^{\frac{1}{4}}}{(x^2y)^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{3\cdot {\frac{1}{4}}}y^{-\frac{1}{3}\cdot {\frac{1}{4}}}}{x^{2\cdot {\frac{1}{4}}}y^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}y^{-\frac{1}{12}}}{x^{\frac{2}{4}} y^{\frac{1}{4}}}[/tex]
[tex]\bf \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}x^{-\frac{2}{4}}}{ y^{\frac{1}{4}}y^{\frac{1}{12}}}\implies \cfrac{(3^4)^{\frac{1}{4}}x^{\frac{3}{4}-\frac{2}{4}}}{y^{\frac{1}{4}+\frac{1}{12}}}\implies \cfrac{3^{4\cdot \frac{1}{4}}x^{\frac{1}{4}}}{y^{\frac{4}{12}}}\implies \cfrac{3^{\frac{4}{4}}x^{\frac{1}{4}}}{y^{\frac{1}{3}}} \\\\\\ \cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}[/tex]
A person 5.4 feet tall stands in line of a shadow cast from the top of the house. The shadow hits the top of the person's head, and continues until the shadow ends on the ground 2.4 feet from the person's shoes. The distance along the ground from the tip of the shadow to the house is 14.6 feet. Find the height of the house. Do not round your answer.
Answers
Let h = the height of the building.
Because triangles ABC and ADE are similar (due to AAA), therefore
DE/BC = AD/AB
That is,
h/5.4 = 14.6/2.4
h/5.4 = 6.0833
h = 6.0833*5.4 = 32.8498 ft
Answer: The height of the house is 32.8498 ft
three tables are placed side by side. one table is 6 feet 9 inches, another is 5 feet 11 inches wide, and the third is 2 feet 10 inches wide. how wide are they combined
Answers
6+5+2=13 feet
10+9+11=30 inches
30 inches in feet is 2 and 6 inches.
What is the greatest common factor of 28 and 42 and 70
Answers
Product A is an 8 oz bottle of cough medication that sells for $1.36. Product B is a 16oz bottle of cough medication that cost $3.20. Which product has the lower unit price
Answers
^^^^^^^^^^^^^^^^
is a kiloliter greater than one liter
Answers
Kiloliters is a metric unit of volume equivalent to 1000 liters or 1 cube meter.
-------------------------------------------------------------------------------------------
Yes, a kiloliter is greater than one liter.
------------------------------------
1 kiloliter = 1000 liters
I hope that helps!
What is the probability of rolling a number less than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?
Answers
And the probability of roll a two or less is:
P(≤2)=2/6=1/3
Cos (pi/11)+cos (3pi/11)+cos (5pi/11)+cos (7pi/11)+cos(9pi/11)
Answers
Answer:
1/2
Step-by-step explanation:
A home has dimensions of 35 feet by 57 feet that include an attached 24-foot by 22-foot garage and a 200-square-foot screened porch. how many square feet of gross living area does the home have
Answers
1995 - ((24*22)+200) = 1267
1267 is your answer.
"apply quickselect to find the median of the list of numbers 9, 12, 5, 17, 20, 30, 8."
Answers
Final answer:
To find the median using quickselect, choose a pivot value, partition the list, and repeat the process with the appropriate partition until the pivot index matches the desired median index.
Explanation:
The median of a list of numbers is the middle value when the numbers are arranged in ascending order. To apply quickselect to find the median, start by choosing a pivot value from the list. Partition the list and move all values smaller than the pivot to the left and all values larger than the pivot to the right. If the pivot index is equal to the desired median index, then the pivot value is the median. Otherwise, if the pivot index is smaller, repeat the process with the right partition; if the pivot index is larger, repeat with the left partition.
In the given example, let's apply quickselect to find the median:
Choose a pivot value, let's say 17.
Partition the list: 5, 8, 9, 12, 17, 20, 30
The pivot index is 4, which is less than the desired median index.
Repeat the process with the right partition: 17, 20, 30
Choose a new pivot value, let's say 20.
Partition the list: 17, 20, 30
The pivot index is 1, which is equal to the desired median index.
Therefore, the median of the list of numbers 9, 12, 5, 17, 20, 30, 8 is 17.
Find the area of the shaded region when r = 4 feet and the area of the triangle is: 123√ square feet
Use 1.73 for 3√ and 3.14 for π. Round your answer to two decimal places.
Answers
A ( shaded ) = A ( circle ) - A ( triangle ) =
= r² π - 12 √ 3 =
= 4² π - 12 √ 3 =
= 16 π - 12 √ 3 =
= 16 · 3.14 - 12 · 1.73 =
= 50.24 - 20.76 = 29.48
Answer: Area of the shaded region is 29.48 ft².
A bike is bought for $1200 and sold 10 months later for $940.
a) Find the depreciation equation.
b.) Value
Answers
Value
Depreciation is defined as the reduction in value of an asset over time. In this case, value reduction is due to wear and tear of an equipment (bicycle).
a. The depreciation value would simply be the difference in initial and salvage value divided by time in years.
Depreciation = (Initial value – Salvage value) / Number of years
b. Substituting the given values into the equation where:
Initial value = $1200
Salvage value = $940
Number of years = 10 months = 10/12 years
Calculating:
Depreciation = ($1200 - $940) / (10/12 years)
Depreciation = $312 / year
or
Depreciation = $26 / month
Could one prove that a shape is a square by finding the slopes of each side?
Answers
Yes,
If a quadrilateral has four congruent facets and 4 right angles, then it's a square (reverse of the square definition).
If consecutive aspects of a rectangle are congruent, then it is a square neither the reverse of the definition nor the speak of a assets.
How do you show a form is a rectangle with the usage of the slope?If we can display that the slopes of the alternative sides are identical, then the other facets are parallel. The slopes of the opposites have been the same, so ABCD is a parallelogram. Step three: subsequent, show that the parallelogram is a rectangle.
what's the slope of a side?
The slope is just the upward thrust over the run, which is defined as the change in y over the change in x meaning the distinction of the y coordinate factors divided with the aid of the distinction of the x-factors? So we have the two x-factors, so this is six minus two, divided by the, the x-factors 3 minus one.
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A group of ladies meet for an afternoon tea party. They bring all their cats. In all, there are 26 heads and 84 feet. How many ladies and how many cats are in the room
Answers
X= ladies y = number of cats
Each lady has 2 feet and each cat has 4 feet
<=>
x + y = 26 (1) => number of characters
2x + 4y = 84 (2) => number of feet
<=> operation : (1) * 2
2x + 2y = 52 (1')
2x + 4y = 88 (2')
<=> operation : (2') - (1')
2y = 26
<=>
y = 20 and x = 32- 16 = 16
10 ladies and 16 cats
p+c=26, solve for c, subtract p from both sides
c=26-p, now for feet...
2p+4c=f, using c found above gives you:
2p+4(26-p)=f and we are told that there are 84 feet so:
2p+4(26-p)=84 perform indicated multiplication on left side
2p+104-4p=84, combine like terms on left side
-2p+104=84 subtract 104 from both sides
-2p=-20 divide both sides by -2
p=10, and since c=26-p
c=26-10
c=16
So there are 10 people and 16 cats in the room.
95 is described as what
Answers
answer is option 2
a rational number is any number that can be expressed as the quotient or fraction
so 0.95 = 95/100
hope that helps
Cylindrical soup radius 4 centimeters height 12 centimeters what is the volume of the soup to the nearest tenth?
Answers
V=(pi)(4^2)(12)
V=(pi)(16)(12)
V=(pi)(192)
V=603.2 centimeters^3
V = π × r² × h
r = 4
h = 12
V = π × 4² × 12
V = π × 16 × 12
V = π × 192
V = 603.19
The volume of the soup to the nearest tenth is 603.2 cm³.
how do you make a equivalent ratio?
Answers
what is the square root of -1?
Answers
If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.
Answers
-n. -n
n-4=-10
+4. +4
n=-6
Final answer: -6
What is the next number in the series? 83 79 75 71 67 ?
Answers
Answer:
Given the series : 83 , 79 , 75 , 71 , 67, ?
Difference of two consecutive terms;
79 -83 = -4
75 -79 = -4
71-75 = -4
67-71= -4
Since, you can see that the number is decreases by 4 every time.
Let unknown term be x
then;
x - 67 = -4
x = 67-4
x = 63.
Therefore, the next term in the series is 63.
The next number in the series is 63.
In the given series, each number is decreasing by 4.
We can observe that the first number, 83, is decreased by 4 to get the next number, 79.
Similarly, each subsequent number is obtained by subtracting 4 from the previous number.
Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.
67 - 4 = 63
Therefore, the next number in the series is 63.
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You deposit $70 in a savings account that pays an annual interest rate of 30%. How much simple interest would you earn in 2.5 years?
Answers
I=prt
I interest earned?
P principle 70
R interest rate 0.3
T time 2.5 years
I=70×0.3×2.5
I=52.5
How is a calculation of net worth different from a day-to-day or month-to-month tallying of expenses?
Answers
A businessman has 10 employees. His salary is equal to 6 times the average of employees salaries. If the 11 of them receive a total of $64,000 in one year, what was the business mans salary that year ??
Answers
x = business man's salary
y = employee's salary
x + 10y = 64000
x = 6y
6y + 10y = 64000
16y = 64000
y = 64000/16 = 4000
x = 6*4000
x = 24000
business man's salary was $24,000