Which graph represents the solution set of the system of inequalities?
{y<2/3x
y≥−x+2
Answers
y≥−x+2
It's the last graph
Answer:
Last graph is the answer.
Step-by-step explanation:
The inequalities are y < [tex]\frac{2}{3}x[/tex] and y ≥ -x + 2
Now first inequality y < [tex]\frac{2}{3}x[/tex] will represent a dotted line passing through origin and a point (3, 2)
This inequality will be in the form a dotted line and shaded area will be below the line.
Second inequality is y ≥ -x + 2
Line representing the inequality will be solid in shape and shaded area will be above this line.
Common shaded area of both the inequalities matches with the last option.
Therefore, Last option (second row last figure) will be the answer.
Related Questions
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 110 kilograms. A delivery of 2 large boxes and 6 small boxes has a total weight of 74 kilograms. How much does each type of box weigh?
Answers
5x + 3y = 110 .....multiply by -2
2x + 6y = 74
------------------
-10x - 6y = - 220 (result of multiplying by -2)
2x + 6y = 74
-----------------add
-8x = - 146
x = -146/-8
x = 18.25 <== large box weighs 18.25 kg
2x + 6y = 74
2(18.25) + 6y = 74
36.50 + 6y = 74
6y = 74 - 36.50
6y = 37.50
y = 37.50/6
y = 6.25 <=== small box is 6.25 kg
E bisects DF, DE=2y, and EF=8y-3. Find DE, EF, and DF
Answers
DF=2
EF=1
DE=1
12x > 9(2x-3) -15
solve the inequality for x. show each step of the solution.
Answers
-6x>-42
x<7
12x > 18x - 27 -15 (distribute)
12x > 18x - 42 (simplify)
12x - 18x > 18x - 18x - 42 (subtract -18x from each side)
-6x/-6 > -42/-6 (divide, isolate the x)
x < 8 (answer, when you divide a negative, flip the sign)
hope this helps
A student has two test scores. the difference between the scores is 44 and the mean, or average, of the scores is 8484. what are the two test scores?
Answers
andre placed 7/8 gallon of water in a pot near his wood burning stove 1/5 gallon of water evaporates each hour how many hours would it take for the entire pot of water to evaporate
Answers
To divide, you just want to reverse the second fraction and then multiply.
1/5 reversed is 5/1.
7/8 * 5/1 = 35/8
35/8 converted to a mixed number would be 4 3/8.
So it would take 4 3/8 hours for the entire pot of water to evaporate.
A single little brown bat can eat up to 1,000 mosquitoes in a single hour. Express in scientific notation how many mosquitoes a little brown bat might eat in 10.5 hours.
Answers
I hope this helps!
A trout swims 1 2/3 miles in 25 minutes. How far can it's swim in one hour
Answers
60minutes per hour
25/60 = 5/12
1 2/3 / 5/12 =
5/3 / 5/12 =
5/3 * 12/5 = 60/15 = 4 miles
What is the result of dividing x^3-4 by x+2
A. x^2-2x+4+12/x+12
B. x^2-2x+4+4/x+2
C. x^2-2x+4-4/x+2
D. x^2-2x+4-12/x+2
What is the result of dividing 2x^3+x^2-2x+8 by x+2
A. 2x^2+5x+8
B. 2x^2-3x+16
C. 2x^2-3x+4
D. 2x^2+5x-8
What is the remainder when the polynomial 6x^2+11x-3 is divided by 2x-1
Jorge wasnt to divide 3x^2-x-2 by x+4 using synthetic division. (has picture)
Which answer shows the correct process?
What is the remainder when the polynomial 6x^2+11x-3 is divided by x+2
Answers
Write x^3-4 as 1x^3 + 0x^2 + 0x + (-4)x^0
The coefficients here are 1, 0, 0, and -4
note how the exponents step down one at a time (3, 2, 1, 0)
Write the coefficients 1, 0, 0, -4 in that order along a single row. Write the test root x = -2 in a box off to the left of the row of coefficients. See Figure1A (attached) to see how the set up is done so far.
-------------------------
Now we will follow the steps to perform synthetic division. The first step is to drop the first coefficient (which is 1) down below the horizontal line. This is shown by the letter A in red. See Figure1B (attached).
We then multiply that dropped value (1) by the test root (-2) to get 1 times -2 = -2. This result of -2 is placed where you see the red letter B (Figure1B)
Now add straight down: 0 plus -2 = -2
The result -2 is placed just below the previous result. It is placed where you see the red letter C
-------------------------
Repeat these steps over and over until the bottom row is filled out. By that, I mean we have the bottom row terms line up with the right most value in the top row. See figure1C to have a look at what I mean. We stop once we get to -12 in the bottom row as there are no more terms to fill out.
The last term in the bottom row (-12) is the remainder. The other terms help construct the quotient.
In this case, the quotient is 1x^2 + (-2)x + 4x^0 which simplifies to x^2 - 2x + 4
The remainder is -12
Put this all together and we have the final answer of [tex]x^2 - 2x + 4 - \frac{12}{x+2}[/tex]
So the final answer is choice D
===================================================================================================
Problem 2)
Follow the same kind of steps shown in problem 1. This time we'll have the synthetic division table you see in the image Figure2 (attached)
The last value in the bottom row is the remainder. The remainder of 0 indicates (x+2) is a factor of 2x^3+x^2-2x+8
The quotient is the other values in the bottom row. The other values in that bottom row are (in order) 2, -3, 4 so the quotient is 2x^2 - 3x + 4
This makes the final answer to be choice C
===================================================================================================
Problem 3)
We can use the remainder theorem and skip synthetic division
2x-1 = 0 leads to x = 1/2 = 0.5
Plug x = 0.5 into the function f(x) = 6x^2 + 11x - 3 to get
f(x) = 6x^2 + 11x - 3
f(0.5) = 6(0.5)^2 + 11(0.5) - 3
f(0.5) = 4
So the remainder is 4
Answer: 4
Side Note: if you wish to use synthetic division, then check out "Figure3" in the attachments
===================================================================================================
Problem 4)
The answer is choice with the bottom row of 3, -13, and -54. This looks to be choice C. The same steps are followed as done in problems 1 through 3.
===================================================================================================
Problem 5)
Plug x = -2 into f(x) = 6x^2 + 11x - 3
f(x) = 6x^2 + 11x - 3
f(-2) = 6(-2)^2 + 11(-2) - 3
f(-2) = -1
Final Answer: -1
ann took a taxi home from the airport. the taxi fare was $2.10 per mile and she gave the driver a $5 tip. Ann paid a total of $49.10. What is an equation to determine the distance in miles from Anns home to the airport?
Answers
(49.1/5)/2.1 = amount of miles it takes to reach Ann's home
Hope this helps!
Need help please !
Thanks !
Answers
1/20 = 0.05
30*0.05= 1.5 years
Final answer: 1 1/2 years
Math Plzz HELP ASAP!!!!!!
(−213+515)+113
Answers
The solution of (−213+515)+113 is 415
Add -213 and 515:
-213 + 515
= 302
Add 113 to the result:
302 + 113
= 415
So, the final answer is 415.
Question:
Solve: (−213+515)+113
.help me please thanks
Answers
A jet travels 500 miles in 2 hours. At this rate, how far could the jet fly in 8 hours? What is the rate of speed of the jet?
Answers
500 / 2 = 250 miles per hour ( rate of speed)
250 * 8 = 2,000 miles in 8 hours
What's the principal square root of 169
Answers
The principal square root of 169 is 13.
The principal square root of a number is the non-negative square root.
The principal square root of 169 is the non-negative number that, when multiplied by itself, equals 169.
We are looking for a number such that when it is squared (multiplied by itself), it equals 169.
This can be expressed mathematically as:
x² = 169
The solution to this equation is
x = √169.
169 is a perfect square, and its square root is 13 because:
13 × 13 = 169.
Therefore, the principal square root of 169 is 13.
The answer to this question
Answers
Use substitution to go from
Angle T = Angle R
to
3x+36 = 6x-9
Now let's solve for x
3x+36 = 6x-9
3x+36-3x = 6x-9-3x
36 = 3x-9
36+9 = 3x-9+9
45 = 3x
3x = 45
3x/3 = 45/3
x = 15
Since x = 15, we can say,
Angle T = 3x+36
Angle T = 3*x+36
Angle T = 3*15+36 ... x is replaced with 15 (since x = 15; found above)
Angle T = 45+36
Angle T = 81
The final answer is 81 degrees
Find the distance between the points 6 + 5i and 1 – 2i.
Answers
let : z = 6+5i z' = 1-2i
the distance between the points 6 + 5i and 1 – 2i is : |z - z' |
|z - z' | = |6+5i -1+2i| = |5+7i | =√(5²+7²) =√74
Answer:
Approximately 8.6
Step-by-step explanation:
Polynomial Factorization Help!
Can 2x^2-3x-5 = 0 be factorized? I solved it with the Quadratic Formula but I can't find two numbers that multiply to -5 but add to -3
Answers
Five cans of tomatoes cost $6.50. At this rate, how much will nine cans of tomatoes cost?
Answers
The cost of one can of tomatoes is $1.30, so nine cans at this rate would cost $11.70.
If five cans of tomatoes cost $6.50, to find the cost of nine cans, we first need to find the cost of one can of tomatoes. We do this by dividing the total cost by the number of cans.
Cost per can = Total cost / Number of cans
Cost per can = $6.50 / 5
Cost per can = $1.30
Now that we know how much one can costs, we can find out how much nine cans will cost by multiplying the cost per can by nine.
Total cost for nine cans = Cost per can × Number of cans
Total cost for nine cans = $1.30 × 9
Total cost for nine cans = $11.70
Therefore, nine cans of tomatoes will cost $11.70.
Simply the product -7x/5y * 5x/-7
Answers
= x^2/y
(-) times(-) = positive
and canceled out 7, 5
so answer is
x^2/y
what we do is, we form a single fraction where the numerator is the product of the numerators, and the denominator is the product of the denominators, that is:
[tex] \frac{-7x}{5y} \cdot \frac{5x}{-7}= \frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y} [/tex]
simplify the common numbers and terms in the numerator and denominator:
[tex]\frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}=\frac{5 \cdot x \cdot x}{5 \cdot y}=\frac{x \cdot x}{y}= \frac{ x^{2} }{y} [/tex]
Answer: [tex]\frac{ x^{2} }{y} [/tex]
A worker can assemble 3 shelf units each hour. the same worker can assemble 6 tv stands each hour. if x = hours assembling shelf units, y = hours assembling tv stands, and 24 = total number of furniture pieces made, write a function in standard form modeling the situation.
Answers
mrs perry shares out 30 biscuits between gemma and zak in the ration 1:4 how many biscuits does each child get
Answers
Gemma gets 6 biscuits, and Zak gets 24 biscuits when Mrs. Perry shares out 30 biscuits between them in the ratio 1:4.
To solve this problem, we need to divide the 30 biscuits according to the ratio 1:4 between Gemma and Zak.
Calculate the total parts in the ratio.
Total parts = 1 (from Gemma) + 4 (from Zak) = 5 parts
Find out how many parts each child gets.
For Gemma:
Gemma's share = (1 part ÷ 5 parts) × 30 biscuits
= (1/5) × 30
= 6 biscuits
For Zak:
Zak's share = (4 parts ÷ 5 parts) × 30 biscuits
= (4/5) × 30
= 24 biscuits
Verify the result.
Gemma gets 6 biscuits, and Zak gets 24 biscuits.
6 + 24 = 30 biscuits (which is the total), so the division is correct.
Thus, Gemma gets 6 biscuits, and Zak gets 24 biscuits when Mrs. Perry shares out 30 biscuits between them in the ratio 1:4.
A gumball machine has just been filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. sue and jim each purchase one gumball. what is the likelihood that both sue and jim will get red gumballs?
Answers
Final answer:
To calculate the likelihood of both Sue and Jim getting red gumballs, we multiply the probability of each event occurring sequentially. After Sue gets a red gumball, the chances are 1/4, and then 99/399 for Jim. The final probability of both getting red gumballs is 99/1596 or about 6.203%.
Explanation:
The likelihood that both Sue and Jim will get red gumballs from the gumball machine can be calculated using basic probability principles. First, we need to determine the total number of gumballs in the machine. This is the sum of black, white, red, and yellow gumballs, which are 50, 150, 100, and 100 respectively, making a total of 400 gumballs.
The probability that Sue gets a red gumball is the number of red gumballs divided by the total number of gumballs in the machine, which is 100/400, simplifying to 1/4. When Sue takes a gumball, assuming she gets a red one, there are now 399 gumballs left with 99 being red. Therefore, the probability that Jim also gets a red gumball is 99/399. To find the likelihood of both events occurring, we multiply these probabilities:
P(Both Sue and Jim get red gumballs) = P(Sue gets a red gumball) × P(Jim gets a red gumball after Sue) = (1/4) × (99/399).
Now we simplify and multiply these fractions to get the final probability. After simplifying, the final probability is 99/1596, which is approximately 0.06203 or 6.203% chance that both Sue and Jim will get red gumballs.
How do you write a piecewise function
Answers
To write a piecewise function, you need to define different equations for different intervals of the independent variable.
Explanation:To write a piecewise function, you need to define different equations for different intervals of the independent variable. Each equation represents a different part or piece of the function. Here's an example:
f(x) =
2x + 1, if x ≤ 0x^2, if 0 < x ≤ 54 - x, if x > 5In this function, the equation 2x + 1 is used for values of x that are less than or equal to 0, the equation x^2 is used for values of x between 0 and 5 (inclusive), and the equation 4 - x is used for values of x greater than 5.
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A bag contains eight green marbles and four blue marbles. what is the probability of drawing a green marble on the second draw?
Answers
A balloon is released on top of a building. The graph shows the height of the balloon over time. What does the slope and y-intercept reveal about the situation?
Answers
1.5/10=3/20=0.15. Since it's based off of 1000 feet, we multiply 0.15 by 1000 to get 150 as the rate of change for every x value. In addition, since we start at 0.5, 1000*0.5=500 and we therefore start at 500 ft. Using the information we have, we therefore have C as our answer
Answer:
C. The balloon starts at a height of 500 ft and rises at a rate of 150 ft.
Step-by-step explanation:
We have been given a graph which represents the height of the balloon over time.
We can see from our graph that y-intercept, which represents the height of the balloon (in thousand feet) at time equals zero, is 0.5. To find the correct y-intercept we will multiply 0.5 by 1000 as height of the balloon is given in thousand feet.
[tex]\text{y-intercept}=(0.5\times 1000)\text{ feet}=500\text{ feet}[/tex]
Therefore, y-intercept represents that the balloon starts at a height of 500 feet.
Now let us find slope of our given line using slope formula.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2-y_1[/tex] is vertical change or rise.
[tex]x_2-x_1[/tex] is horizontal change or run.
Upon substituting given values in above formula we will get,
[tex]\text{Slope}=\frac{3.5-0.5}{20-0}[/tex]
[tex]\text{Slope}=\frac{3}{20}[/tex]
[tex]\text{Slope}=0.15[/tex]
Now let us multiply 0.15 by 1000 as height of balloon is given in thousand feet.
[tex]\text{Slope}=0.15\times 1000=150[/tex]
Therefore, slope of our line is 150 which means that height of balloon is increasing 150 feet per second or balloon is rising at a rate of 150 feet per second.
Upon looking at our given options we can see that option C is the correct choice.
How many ounces of gold are in anan 18-karat gold chain that weighs 2.7 ounces?
Answers
A karat is a measure of the amount of gold in the gold chain. The karat has a maximum value of 24 karats. This means that an 18 karat of gold chain contains 18 parts of pure gold for every 24 parts of gold chain. Therefore:
gold = (18 / 24) * 2.7 ounces
gold = 2.025 ounces
What is the measure of <JHG?
The measure of <JHG is _____ degrees
Answers
The measure of ∠JHG is 70 degree.
What is an Angle?An angle is formed by two rays called the arms of the angle meeting at a common endpoint called the vertex of the angle.
There are three types of angles, acute angle, right angle and obtuse angle.
Protractor is used to measure angles, it is of semicircular shape with degrees of angles engraved upon it.
Acute Angle : The angle whose measure is less than 90 degree is called the acute angle.
Right Angle : The angle whose measure is equal to 90 degree is called right angle.
Obtuse Angle: The angle whose measure is greater than 90 degree is called obtuse angle.
The ∠JHG has JH and HG are the arms of the angle.
The measure of ∠JHG = 70 degree, it is less than 90 degree, it is an acute angled triangle.
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What is the distance in km between two cites that are 7.5 cm apart on a 1:24 000 scale
Answers
7.5 cm on the map represents 7.5 x 24000 = 180000 cm on the ground.
180000 cm = 1800 m (dividing by 100 cm per m)
1800 m = 1.8 km (dividing by 1000 m per km)
Those "cities" are really close together!
Jim and Sarah are running for class president. Cayla and Daniel are running for Vice President. What combinations of president and Vice President could there be?
Answers
An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
Answers
Answer:
third option
Step-by-step explanation:
I just got a 100
Answer:
C
Step-by-step explanation: