Which graph represents the solution to the system of inequalities?
x + y ≤ 4
y – x ≥ 1
Answers
The correct answer is C.
EXPLANATION
To find which set represents the solution set of the system of inequalities, the best thing is to graph the inequalities and locate the intersection of the solution region of the two graphs.
The given inequalities are,
[tex]x + y \leqslant 4 \: \: and \: \: y - x \geqslant 1[/tex]
Let us start with,
[tex]x + y \leqslant 4[/tex]
To graph this inequality, we first of all graph the corresponding linear equation,
[tex]x + y = 4[/tex]
using the intercepts,
[tex](0,4) \: and \: (4,0)[/tex]
We plot the above points and draw a solid straight line through them.
We test for the origin to determine which half plane should be shaded.
[tex]0 + 0 \leqslant 4[/tex]
[tex]0 \leqslant 4[/tex]
This statement is true, so we shade the lower half plane.
We repeat the same process to graph,
[tex]y - x \geqslant 1[/tex]
So we graph the corresponding straight line,
[tex]y - x = 1[/tex]
using the intercepts,
[tex](0,1) \: and \: (-1,0)[/tex]
We plot the intercepts and draw a solid line through them.
We test for the origin again to see which half plane to be shaded.
[tex]0 - 0 \geqslant 1[/tex]
[tex]0 \geqslant 1[/tex]
This statement is false, so we shade the
upper half plane.
The intersection of the two region is the region in option C of the graphs provided.
Related Questions
Which shows the expressions in the order they would appear on a number line from least to greatest? 4to the power of 3, square root of 40, square root of 13, square root of 7, 14 over 9 14 over 9, square root of 7, square root of 13, square root of 40, 4 to the power of 3 4 ot the power of 3, square root of 7, square root of 13, 14 over 9, square root of 40 square root of 40, 14 over 9, square root of 13, square root of 7, 4 to the power of 3
Answers
sqrt 40 = 6.32
sqrt 13 = 3.61
14/9 = 1.56
sqrt 7 = 2.66
least to greatest : 14/9 , sqrt 7, sqrt 13, sqrt 40, 4^3
14/9 , sqrt 7, sqrt 13, sqrt 40, 4^3
Subtract (3 + 2i) from (–9 – 8i).
Answers
Evaluate the following expression (a + b)^0
Answers
Answer:
So, [tex](a + b)^0=1[/tex]
Step-by-step explanation:
[tex](a + b)^0[/tex]
To evaluete this expression we apply exponential property
[tex]x^0=1[/tex]
IF any expression has exponent 0 then the value is 1 always
for example, [tex]3^0 =1[/tex]
[tex]5^0=1[/tex]
[tex](x+2)^0=1[/tex] because exponent is 0
So, [tex](a + b)^0=1[/tex]
Answer:
1
Step-by-step explanation:
i just made a B in this class
What is the sum of 5.300 and 3.250
Answers
sum means to add
5.300 + 3.250 = 8.550
what is 10000 more than 46952 and what is the missing
number
Answers
Marisa painted 1/2 of her bedroom in 3/4 of an hour.At this rate how long will it take her to paint the entire room. Please help as fast as possible.
Answers
It will take Marisa 1 1/2 hours to paint the entire room. Hope this helps!
she did 1/2 , so she has 1/2 more to do
it took her 3/4 so multiply that by 2
3/4 x 2 = 1 1/2 hours total
Paul Steve robin and Ryan all play different instruments. Their instruments are guitar, bass
Answers
The record for the boston marathon's weelchair division is 1 hour, 18 minutes, and 27 seconds.The boston Marathon is 26.2 miles long.What's the average speed of the record winner of the weelchair division? At this rate about how long would it take this competitor to complete a 30-mile race?
Answers
1 hour= 60 minutes
60+18
=78 mins and 27 secs.
or 78.45 minutes.
To find the average speed per mile, divide the time by distance.
78.45/26.2
=2.99427481
or 2 minutes and 59.6564886 secs.
It takes 2.99427481 minutes to complete a mile.
To find how long it would take to finish 30 miles, multiply the time per mile by 30 miles.
2.99427481*30
=89.8282443 minutes
or 89 minutes and 49.694658 secs
or an hour and 29 minutes and 49.694658 secs.
Hope this helps.
-Benjamin
Mr. and Mrs. McClurrie are debating on whether or not to remove a tall tree in their front yard. Mr. McClurrie is concerned that the tree could fall during a storm and land on their home. Mrs. McClurrie disagrees. She thinks the tree poses no danger to their home and wants to keep the tree because of the wonderful shade it provides. They decide to estimate the height of the tree using special right triangles.
They stood 25 feet from the base of the tree to create a 30° angle from the ground to the top of the tree.
If their home is 20 feet from the base of the tree, could the McClurrie's wait a few more years before cutting down the tree or does it pose a risk now?
Answers
Let A be the point where Mr. and Mrs. McClurrie are standing, let B be the base of the tree and C the top of the tree. Let H be the point representing the house.
ABC is a right triangle, with m(BAC)=30°.
so by special triangles, if the length of the hypotenuse is 2x, the length of BC is x, since it is the side opposite to the 30° angle.
by the pythagorean theorem :
[tex](AC)^{2}= (AB)^{2}+(BC)^{2} [/tex]
[tex](2x)^{2}= (25)^{2}+(x)^{2} [/tex]
[tex]4x^{2}= (25)^{2}+x^{2}[/tex]
[tex]3x^{2}= (25)^{2}[/tex]
[tex]x= \sqrt{ \frac{(25)^{2} }{3}}= \frac{25}{ \sqrt{3} }= \frac{25 \sqrt{3} }{3} [/tex]
[tex]\frac{25 \sqrt{3} }{3}=25* \frac{ \sqrt{3} }{3}=25*0.577= 14.43[/tex] (feet)
so even if the tree falls, it falls more than 5 feet away from the house.
Answer: they can wait a few more years.
the lines shown below are perpendicular. if the green line has a slope of -2/3, what is the slope of the red line?
Answers
Answer:other guy was correct 3/2
Step-by-step explanation:
In a 30-60-90 triangle, the hypotenuse is the shorter leg times the square root of two.
a.always
b.sometime
c.never
Answers
The hypotenuse in a 30-60-90 triangle is the shorter leg doubled. So, it's 2x where x is the shorter leg.
In fact, the square root of two is not used to calculate any other sides in a 30-60-90 triangle. The shorter leg is x, the medium leg is x√3, and the hypotenuse is 2x.
1. A sum of money doubles in 20 years on simple interest. It will get triple at the same
rate in:
a. 40 years
b. 50 years
c. 30 years
d. 60 years
e. 80 years
Answers
2p=p (1+rt)
2=1+rt. T=20 years
2=1+20r
Solve for r to get the simple interest rate
2-1=20r
20r=1
R=1÷20
R=0.05
Now find how long will get triple at the same rate
3p=p (1+rt)
3=1+rt. R=0.05
3=1+0.05t
Solve for t
3-1=0.05t
0.05t=2
T=2÷0.05
T=40 years. .....answer
I WILL GIVE BRAINLIEST please answer correctly
Answers
Isabella wrote 0.0135<0.01350 because 135 <1350.Is Isabella correct?Why or Why not?
Answers
HELP PLEASE ASAP!!!!
What are the 3 methods for solving systems of equations?
If a system has no solution, how does it look on a graph?
Answers
THE SOLUTIONS OF A SYSTEM OF EQUATIONS
A system of equations refers to a number of equations with an equal number of variables. We will only look at the case of two linear equations in two unknowns. The situation gets much more complex as the number of unknowns increases, and larger systems are commonly attacked with the aid of a computer.
A system of two linear equations in two unknowns might look like
This is the standard form for writing equations when they are part of a system of equations: the variables go in order on the left side and the constant term is on the right. The bracket on the left indicates that the two equations are intended to be solved simultaneously, but it is not always used.
PLEASE HELP!!
Factor completely: x2 + 6x + 8
Answers
Let's simplify this...
x² + 6x + 8 --------> Now, we need to find two numbers that multiply to 8 and also add up to 6
factors of 8
1
2 ---->
4 ----> These two multiply to 8 and add up to 6
8
Let's solve this now!
x² + 6x + 8
(x + 4)(x + 2) ----> If you want to check your answer just FOIL them
Your x-intercepts will be -4 and -2
Hope this helps! :D
Please vote me for Brainliest if there is a second answer!
Find the first six terms of the sequence.
a1 = -8, an = 5 • an-1
8, -40, -200, -1000, -5000, -25,000
-8, -40, -35, -30, -25, -20
0, 5, -40, -35, -30, -25
-40, -200, -1000, -5000, -25,000, -125,000
Plz help me
Answers
a1 = first term = -8
r = common ratio = 5
a(2) = -8 * 5^(2-1)
a(2) = -8 * 5^1
a(2) = -40
a(3) = -8 * 5^(3 - 1)
a(3) = -8 * 5^2
a(3) = -8 * 25
a(3) = -200
a(4) = -8 * 5^(4 - 1)
a(4) = -8 * 5^3
a(4) = -8 * 125
a(4) = -1000
a(5) = -8 * 5^(5 - 1)
a(5) = -8 * 5^4
a(5) = -8 * 625
a(5) = -5000
a(6) = -8 * 5^(6-1)
a(6) = -8 * 5^5
a(6) = -8 * 3125
a(6) = -25,000
the first 6 terms are : -8, -40, -200, -1000, -5000, -25,000
Answer:
the answer is B
Step-by-step explanation:
Can someone help me with these two questions about Logarithms? If you can, please don't just tell me the answer. I really want to understand how to do these so please add an explanation. Please and thank you. ^^
My phone wouldn't let me send the photos so here are the questions:
1. The loudness, L, of a sound in decibels is given by L=10logR, where R is the sound's relative intensity. if the intensity of a certain sound is tripled, by how many decibels does the sound increase?
2. An earthquake rated at 3.5 on the Richter scale is felt by many people and an earthquake rated at 4.5 may cause local damage. The Richter scale magnitude reading, m, is given by m=logx, where x represents the amplitude of the seismic wave causing ground motion. How many times greater is the amplitude of an earthquake that measures 4.5 than one that measures 3.5?
Answers
plug in numbers so use R=1500 and 3R=1500(3)
so you get 36.53-31.76=about 4.77
2.
so put put 4.5 in the formula and 3.5 in the formula and divide them
4.5=logx
10^4.5=x
then 3.5=logx
10^3.5=x
(10^4.5)/(10^3.5)
= 10
(08.01)Which of the following questions is a statistical question?
a How many professional sport leagues are there?
b Where do the professional sport leagues play?
c How many hours of professional training took place over the weekend?
d How many hours do you spend each week training for a sports league?
Answers
A box of photographs contains 13 wedding photographs 4 vacation photographs and 8 holiday photographs one is randomly selected what is the probability that the photograph is a holiday photograph given that it is not a wedding photograph
Answers
so
desired outcomes is the 'not wedding' photos
there are 4 vacation and 8 holiday
so 12 'not wedding' photos
12=desired outcomes
total outcomes is 13+4+8=25
so the probablity would be 12/25 or about 48%
The probability that a randomly selected photograph from the box is a holiday photograph, given that it is not a wedding photograph, is 2/3 or approximately 0.67.
The question involves calculating the probability of drawing a holiday photograph from a box, given that the photograph is not a wedding photograph. First, we determine the total number of non-wedding photographs, then we find the probability that a photo selected is a holiday photograph from that subset.
There are 13 wedding photographs, 4 vacation photographs, and 8 holiday photographs. Given that we're not selecting a wedding photograph, we're only considering the vacation and holiday photographs, which total 4 + 8 = 12 photographs. The event of selecting a holiday photograph then has 8 favorable outcomes (since there are 8 holiday photographs).
The probability that the photograph is a holiday photograph given that it is not a wedding photograph is calculated by dividing the number of holiday photographs by the total number of vacation and holiday photographs:
Probability = Number of holiday photographs / Total number of non-wedding photographs = 8 / 12 = 2/3 or approximately 0.67
Using the following data, calculate the mean absolute deviation:
7 2 8 5 9 9 5 6 8 1
What is the mean absolute deviation for these data?
Answers
7+2+8+5+9+9+5+6+8+1=60
60/10=6 = mean
To calculate MAD, find the mean of the differences between each value and the mean.
1+4+2+1+3+3+1+0+2+5=22
22/10=2.2
Final answer: 2.2
Answer:
kphung76127 is right. It is 2.2
Step-by-step explanation:
I got it right on a test.
Mr. Brown owned a house a house, which he rented for $60 a month. The house was assessed for $9000. In 1975 the rate of taxation was increased from $25 to $28 per $1000 assessed valuation. By what amount should the monthly rent have been raised to absorb the increase in that year's taxes?
Answers
Old value = 25×9 = 225 ⇒ The value 9 represents the 9 lots of thousands of the house's value
New value = 28×9 = 252
Increase in tax = 252 - 225 =27
Percentage increase = (27÷225) ×100 = 12%
The amount of yearly rent would be then increased by 12%
Monthly rent = $60
Yearly rent = 60×12 = $720
Increase by 12% = 720×1.12 = 806.4 ⇒ The value 1.12 is the multiplier, obtained from 100%+12%=112%=1.12
The monthly rent is 806.4÷12 = $67.20 which is an increase of $7.20 per month
Jeremy opens a chocolate shop in the city. He pays $1,500 a month for rent and maintenance of the shop. The price of raw materials and manufacturing the chocolates is $6,000 a month. He sells the chocolates individually and in boxes of a dozen. Jeremy understands that his business needs a little time to become a success and decides that he wants to build a customer base initially. He is happy to break even for the first year. After a year, Jeremy prices his chocolates at $3 apiece. He offers a discount of 10% on boxes of chocolate to promote the sale of boxes. How many boxes of chocolate would he have to sell to recover the cost of running the business this year per month? (Assume that he sells no individual chocolates.)
A. 188 boxes
B. 208 boxes
C. 226 boxes
D. 232 boxes
Answers
after a year, hr prices his chocolates at $ 3 a piece....there are 12 pieces in each box....so each box cost (3 * 12) = $ 36......but he offers a discount of 10%....so ur actually paying 90%....0.9(36) = 32.40 per box
7500 = 32.40x
7500 / 32.40 = x
231.48 = x....so he would have to sell 232 boxes to break even <=
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
Answers
The reason for the 2 is that the new car was twice that the new car was twice the old car.
Answer:
The Equation would be P(x) = [tex]\frac{x}{2}[/tex]
Step-by-step explanation:
The Equation states that the price of the old car P is equal to half the price that she paid for her new car (x). Since she paid $22,500 for her new car, we can use the equation to figure out how much she paid for her previous car.
[tex]P(x) = \frac{22,500}{2}[/tex]
P = $ 11,250
So $11,250 is what Ms. Banerjee paid for her previous car.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
find the product of 6 and 4296
Answers
6*4296=25776
hope this helps!
What two numbers make the product of 12 and have the sum of 7?
Answers
product: 3x 4 = 12
sum: 3+4 = 7
3x+2y+4z=12 X+y+2z=6 (X=0,y=4,z=1) Determine if the given 2 lines intersect at the given point. Explain your reasoning. -2x-4y+z=8 4x+2y=-5 (x=-2,y=0,z=3) same as up above
Answers
Equation 2: x + y + 2z = 6
Substituting x = 0, y = 4 and z = 1 into equation 1 and equation 2 and if the answer equals to 12 and 6 then the two lines intersect at the given point
Equation 1 ⇒ 3(0) + 2(4) + 4(1) = 0 + 8 + 4 =12
Equation 2 ⇒ 0 + 4 + 2(1) = 4 + 2 = 6
We have the answer of 12 and 6, hence the two lines intersect at the given point
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Equation 1: -2x - 4y + z = 8
Equation 2: 4x + 2y = -5
Given point: x = -2, y = 0, and z = 3
Equation 1 ⇒ -2(-2) - 4(0) + 3 = 4 - 0 +3 = 7
Equation 2 ⇒ 4(-2) + 2(0) = -8 + 0 = -8
The answers are not 8 and -5 hence the lines don't intersect at given point
What happens to a horizontal line if you rotate it 90 degrees counterclockwise ?
Answers
hope this helps, and sorry if im wrong
An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below. What is the value of b in the equation? (Enter a positive number.)
Answers
Answer: 12
Step-by-step explanation:
The four people at Carla's birthday will get one-quarter (one fourth) of the cake each. Carla puts 16 candies on the cake so that each person gets the same number on their piece of cake. How many candies will each person get on their piece of cake?
Question 4 options:
4
8
12
16