Answers
Answer:
see the attachment for a graph
Step-by-step explanation:
You seem to want a graph of the inequalities ...
y ≤ -3/2x -2y > 1/2x +6Boundary linesThe equations of the boundary lines are given by replacing the inequality symbol with an equal sign:
y = -3/2x -2y = 1/2x +6These are graphed in the usual way. It is often convenient to find the y-intercept, then use the slope to locate other points on the line.
y = -3/2x -2
The y-intercept is (0, -2). The line has a rise/run of -3/2, so goes down 3 units for each 2 to the right. Another point on the line is (2, -5).
y = 1/2x +6
The y-intercept is (0, 6). The line has a rise/run of 1/2, so goes up 1 unit for each 2 to the right. Another point on the line is (2, 7).
Line typeWhen the "or equal to" symbol (≤ or ≥) is used, the boundary line is solid. When the "or equal to" case is not part of the solution, the boundary line is dashed.
The line with negative slope through (0, -2) is solid; the line with positive slope through (0, 6) is dashed.
ShadingAll you need to determine shading is a variable with a positive coefficient, and the inequality symbol.
y ≤ . . . . . tells you shading is below the solid line
y > . . . . . tells you shading is above the dashed line
We notice x has a positive coefficient in the second inequality, so we could determine shading from ...
> x . . . . . tells you shading is left of the line (where x values are less than those on the line)
Of course, you can rearrange the inequality so a variable of interest has a positive coefficient. For example, we could add 3/2x to the first inequality to get ...
3/2x + y ≤ -2
Then, looking at the x-variable, we see ...
x ≤ . . . . . tells you shading is to the left of the line
Answer:
See attachment.
Step-by-step explanation:
When graphing inequalities:
< or > : draw a dashed line.≤ or ≥ : draw a solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.
Inequality 1
\(y \leq -\dfrac{3}{2}x-2\)
\(\begin{aligned}x=0 \implies y&=-\dfrac{3}{2}(0)-2\\y&=-2\end{aligned}\)
\(\begin{aligned}x=2 \implies y&=-\dfrac{3}{2}(2)-2\\y&=-5\end{aligned}\)
Plot the points (0, -2) and (2, -5).
Draw a solid straight line through the points.
Shade under the line.
Inequality 2
\(y > \dfrac{1}{2}x+6\)
\(\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+6\\y&=6\end{aligned}\)
\(\begin{aligned}x=4 \implies y&=\dfrac{1}{2}(4)+6\\y&=8\end{aligned}\)
Plot the points (0, 6) and (4, 8).
Draw a dashed straight line through the points.
Shade above the line.
The solution to the two inequalities is the overlap of the shaded parts.
Related Questions
A package of 25 fishing hooks costs $9.95 , while a package with 40 hooks costs $13.99 . Which is the better buy? Round your answer to the nearest cent if necessary.
Answers
Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.
To determine which package is the better buy, we need to compare the cost per hook for each package.
For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:
Cost per hook = $9.95 / 25 = $0.398
Rounding to the nearest cent, the cost per hook is $0.40.
For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:
Cost per hook = $13.99 / 40 = $0.3498
Rounding to the nearest cent, the cost per hook is $0.35.
Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.
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A square prism is 12 cm tall. The side length of the square base is 5 cm.
What is the volume of the prism?
Answers
Answer:
300cm^3
Step-by-step explanation:
volume of a prism is
V=area of the base xH
find the area of base
A= 5x5
= 25cm^2
V=25x12
300cm^3
Which of the following shows the graph of the parent function of
Answers
The given function is:
\(f(x)=4\sqrt[]{-5x+7}+2\)Notice that the function is a Square Root function.
The parent function of the square root function is:
\(y=\sqrt[]{x}\)Hence, the graph that matches this function is the graph shown below:
Which of the following z-scores is NOT outside the middle 68% of the data for a normal distribution?
a.) -0.8
b.) -2.8
c.) 1.8
d.) 3.8
Answers
Answer:
Step-by-step explanation:
A, use three_digite rounding arithmetic to compute 13- 6 and determine the absolute,relative ,and percentage errors.
tepeat part (b) using three – digit chopping arithmetic.
PLS HELP ASAP ILL GIVE 5 STARS
Answers
Hey there!
(5 * 6) * 4
= 30 * 4
= 120
So you’re basically looking for something that’s equivalent to 120
CHOICE A.
5 * (5 * 6)
= 5 * 30
= 150
So, Choice A is probably NOT the answer you’re looking for!
CHOICE B.
4 * (5 * 6)
= 4 * 30
= 120
Choice B. is probably the answer you’re probably looking for.
So, I recommend you to color it apricot. :)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Change 9/3 to percentage
Answers
Answer:
300%
Step-by-step explanation:
because 9/3×100=900/3=300 so it is 300%
Answer:
300%
Step-by-step explanation:
9/3 * 100%
900%/3 = 300%
50, 60, 72, ...
Find the 8th term.
Answers
I found because it seems to be multiplied by 1.2.
find an equation that passes through (1 ,2) and is parallel y=3x-9
Answers
Answer:
A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (1, 2)
Substituting the values we get:
y - 2 = 3(x - 1)
Simplifying the equation we get:
y - 2 = 3x - 3
y = 3x - 1
Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .
;>
Find the geometric mean of 36 and 64.
Answers
Given the numbers:
36 and 64
Let's find the geometric mean of both numbers.
To find the geometric mean, apply the formula:
\(\sqrt[]{a\ast b}\)Please answer this correctly
Answers
Answer:
Step-by-step explanation:
Area = area of triangle + area of rectangle 1 + area of rectangle 2 + area of rectangle 3
= (1/2)*10*20 + 9 * 14 + 21* 3 + 5*7
= 100 + 126 + 63 + 35
= 324 sq.in
a line which joins the midpoints of two sides of a triangle is _?
Answers
A line which joins the midpoints of two sides of a triangle is Midsegment
A triangle's midsegment is a line formed by joining any two of the triangle's sides at their midpoints. All three sides of a triangle can be divided (split in half) in any triangle, whether it be right, isosceles, or equilateral. The midpoint of each side is the point that is equally spaced from either vertex.
Triangles can have three midsegments because they have three sides. Any two sides can be joined at their midpoints. Half the length of the base is represented by one midsegment (the third side not involved in the creation of the midsegment). That is the only intriguing aspect. It also:
Is consistently parallel to the triangle's third side; the base
Creates a tiny triangle that resembles the primary triangle.
The area of the smaller, comparable triangle is one-fourth that of the larger triangle.
Half of the original triangle's circumference is contained within the smaller, comparable triangle.
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could i get some help in next few minutes?
sketch is another part of question but not necessary
Answers
Answer:
a) - 8 and 2b) (- 3, - 75)Step-by-step explanation:
Given relation
y = 3x² + 18x - 48a)
Find its zero's
3x² + 18x - 48 = 0x² + 6x - 16 = 0x² + 8x - 2x - 16 = 0x(x + 8) - 2(x + 8) = 0(x + 8)(x - 2) = 0x + 8 = 0 ⇒ x = - 8x - 2 = 0 ⇒ x = 2b)
The vertex of qudratic function is determined at x = - b/(2a)
Applied to this relation, the x- coordinate of vertex is
x = - 18/(3*2) = - 18/6 = - 3Find its y- coordinate
y = 3(-3)² + 18(-3) - 48 = 27 - 54 - 48 = -75The vertex is (- 3, - 75)
Zeros:-
x=-8 and 2#Vertex
y=x²+6x-16y=x²+2(3x)-16+25-25y=x²+2(3x)+9-25y=(x+3)²-25Multiply 3 which we deduced
y=3(x+3)²-75Vertex (-3,-75)
A crew of highway workers paved
mile in minutes. If they work at the same rate, what portion of a mile will they pave in one hour?
Answers
I don't know .............
a cow heart beat 325 in 5 minutes. about how many times does a cow's heart beat in 2 minutes?
Answers
Answer:
130
Step-by-step explanation:
You can make a ratio - 325:5, then we can simplify it to 65:1, where we are comparing # of beats in 1 minute. Now, we can just multiply both sides by two, getting us 130:2, which is just 130 beats.
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answers
Answer:
Option D: 5591.93
Step-by-step explanation:
The best way to understand this question is to apply the formula in an indirect manner;
P - Principle number, Starting Value
T - Time
I - Interest
Let us convert the interest into decimal form, such that 3.8% is shifted two decimal points to the right ⇒ 0.038. Now add 1 to this value to get ⇒ 1.038. By PEDMAS, you would first raise this value to the span of 3 years as such:
(1.038)^3 = 1.118386872.......
The final step would by to multiply the starting value (investment $) $ 5,000 by this continuing value of 1.118386872:
5,000(1.118386872) = 5591.93436 ⇒ Rounded to (About) 5591.93
Answer:D
Step-by-step explanation:
principal=p=$5000
Rate=r=3.8%
Time=n=3 years
amount=a
a=p(1+r/100)^n
a=5000(1+3.8/100)^3
a=5000(1+0.038)^3
a=5000(1.038)^3
a=5000 x 1.038 x 1.038 x 1.038
a=5591.93
a=$5591.93
blank minus 1/2 equls to 3/4
Answers
Answer:
5/4
Step-by-step explanation:
We can start but setting the blank as x.
x - 1/2 = 3/4
we can put a common denominator on both of the.
2, 4
4, 8
4 is a common denominator.
1/2 times 2/2 = 2/4
x - 2/4 = 3/4
add on both sides.
x = 5/4
Answer:
5/4
Step-by-step explanation:
____ - 1/2= 3/4
____= 3/4+1/2
= 3+2/4 ( LCM of 2,4 is 4)
5/4
Check
5/4-1/2=3/4
Which point on the number line represents two and one-half degrees below zero?
A. point A
B. point B
C. point C
D. point D
Answers
Answer:
B
Step-by-step explanation:
Answer:
it would be D because it didn't say one and one-half it said two and one-half
Please pick me for brainlyest
A special CPI is constructed to measure the variation of these products, so that coffee and bread have a weight of 0.35 of the total and egg, ham and cheese 0.1 of the total. variation of the CPI?
Answers
9514 1404 393
Answer:
The CPI increased 3.42% in Month 2.
Step-by-step explanation:
In a spreadsheet, the weighted sum is easily computed using the SUMPRODUCT( ) function. It multiplies the corresponding values of two arrays, then returns the sum of those products. If one of the values is a weight, then the result is a weighted sum.
Your CPI is computed as the weighted sum of the prices of the individual products. The percentage change is computed in the usual way:
pct change = ((new value)/(old value) -1) × 100%
Of course, the spreadsheet can format a fraction as a percentage, so the computation of the change can stop after 1 is subtracted from the ratio.
Gavyn & Raj share a lottery win of £950 in the ratio 1 : 4.
Gavyn then shares his part between himself, his wife & their son in the ratio 5 : 3 : 2.
How much more does his wife get over their son?
Answers
Answer:
£19
Step-by-step explanation:
Gavyn:Raj=1:4£950 to be split in 1:4, so Gavyn=£190 and Raj=£760Gavyn:Wife:Son=5:3:2£190 to be split in 5:3:2, so Gavyn=£95, Wife=£57, and Son=£38Wife gets £57-£38=£19 more than her sonwould like some help
Answers
Answer:
A
Step-by-step explanation:
-4x²+7x+8=0
4x²-7x-8=0
a = 4, b = -7, c = - 8
x= (−b ± √b²−4ac) ÷ 2a
x= [ −(−7) ± √(−7)²−4(4)(−8) ] ÷ 2(4)
x = 7±√177
Hence,
x = 7+√177 and x = 7-√177
It has two solutions
express 72 1/2 as a percentage
Answers
Answer:
7250%
Step-by-step explanation:
To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.
72 1/2 is equivalent to 72.5 as a decimal.
To convert it to a percentage:
72.5 * 100 = 7250
Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.
let me know it is helpful for you or not
Step 2) Multiply 72.5 by 100 to work out the percentage
Step 3) 72.5 multiplied by 100 gives you 7250%
Fill in the missing statements and reasons for the proof. Given ∠2 ≅ ∠3 proof ∠1 ≅ ∠4
Answers
The proof is given as follows:
∠1 ≅ ∠2 - Vertical Angles are ≅∠2 ≅ 3 - Given∠3 ≅4 - Vertical Angles are ≅Thus, ∠1 ≅ 4 Transitive properties.What are transitive properties?The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".
The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.
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lucinda weighs two bags of apples at the grocery store. the first weighs 3 1/5 pounds. the second bag weighs 2 4/5 pounds. what's the difference in weight of the two bags?
Answers
Answer:
2/5 pound
Step-by-step explanation:
The first bag is 1/5 pound more than 3 pounds. The second bag is 1/5 pound less. The difference in weight is 1/5 +1/5 = 2/5 pounds.
If you'd like to see that as an equation, you could write ...
Δw = (3 +1/5) -(3 -1/5)
= (3 -3) +(1/5 -(-1/5))
= 0 +1/5 +1/5 = 2/5
The weight difference is 2/5 pounds.
You have saved $1500 to buy a TV you notice the store is offering one year same as cash deal you can take the TV home today and pay nothing until one year from now when you’re out of the store $1500 purchase price if your savings account earns 5% a year what is the NPV of this offer
Answers
Answer:
The net present value of 1,500 a year from now at 5% interest is $1,428.57.
Step-by-step explanation:
NPV = 1,500 / 1.05 = 1,428.57
Please help me please thank
Answers
Answer:
x=20
Step-by-step explanation:
<2 = <3 when the lines are parallel
3x-10 = x+30
Subtract x from each side
3x-10 -x = x+30-x
2x-10 = 30
Add 10 to each side
2x-10 +10 = 30+10
2x = 40
Divide by 2
2x/2= 40/2
x =20
Please help me with this
Answers
Step-by-step explanation:
Flip f(x) about the x-axis by multiplying it by -1
- f(x)
the squish it skinnier by multiplying it by 4
g(x) = - 4 f(x) = -4 x^2
4,400 is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 22 years to the nearest cent
Answers
After 22 years the amount in the account will be 12,386.
What is simple interest?Simple interest is an interest amount calculated on the principal amount with certain interest rate. It is given by the formula,
\(S.I.=\frac{P*n*r}{100}\)
Where P is the principal amount, n is the number of years, r is the rate of interest.
4,400 is placed in an account i.e., Principal amount, P=4400
With an annual interest rate, r=8.25%
Number of years, n=22 years.
Amount in the account after 12 years will be,
By using simple interest formula,
\(S.I.=\frac{P*n*r}{100}\)
= \(\frac{4400*8.25*22}{100}\)
=7,986
Interest amount = 7,896.
Total amount after 22 years= interest amount + principal amount
= 7896+4400
= 12,386.
Hence, after 22 years the amount in the account will be 12,386.
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Brent starts with 16 identical white socks in his sock drawer. Imagine he receives 2 identical black socks as a gift and mixes them in with his 16 white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?
Answers
Answer: Its high
Step-by-step explanation: It just is
The probability that Brent draws mismatched socks is 32/153.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.
Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.
For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.
Let's consider the first case.
There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.
For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.
Therefore, the probability of Brent drawing mismatched socks is:
= (32 + 32) / 306
= 64 / 306
= 32 / 153
Thus, the probability that Brent draws mismatched socks is 32/153.
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Solve the equation for X 3(x+2)=2(2-x)
Answers
Answer:
x = - 2/5Step-by-step explanation:
\(3(x+2)=2(2-x)\\\\\mathrm{Expand\:}3\left(x+2\right):\quad 3x+6\\\\\mathrm{Expand\:}2\left(2-x\right):\quad 4-2x\\\\3x+6=4-2x\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\3x+6-6=4-2x-6\\\\3x=-2x-2\\\\\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\\\3x+2x=-2x-2+2x\\\\Simplify\\\\5x=-2\\\\Divide\:both\:sides\:by5\\\\\frac{5x}{5}=\frac{-2}{5}\\\\x=-\frac{2}{5}\)
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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