Why are inequalities like the last two problems graphed on a number line while the ones in the
Set portion of this assignment are graphed on a coordinate plane? What difference is there
between the inequalities in the last two problems and the ones found in problems 13-16?
It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.
Why some inequalities are graphed on a number line?The type of diagram that we need to use depends on the number of variables that we have.
A single variable ----> number linetwo variahbles ----> a coordinate plane.3 variables ---> a volume.That is the main reason, for example:
x > 2
Is graphed on a number line.
y > 3x + 4
is graphed on a coordinate plane.
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name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
I need help with my math
Step 1: Pick any two points
The points are represented as (x1,y1), (x2,y2).
where x1= -4, y1= -8, x2= 0, y2= 4
Step 2: Write out the formula of the equation to use
\(\frac{y-y_1}{x-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}\)Step 3: Substituting the values and to get the equation
\(\begin{gathered} \frac{y-(-8)_{}}{x-(-4)}=\text{ }\frac{4-(-8)}{0-(-4)} \\ \frac{y+8}{x+4}=\frac{4+8}{0+4} \\ \frac{y+8}{x+4}=\text{ }\frac{12}{4} \end{gathered}\)\(\begin{gathered} \frac{y+8}{x+4}=\text{ 3} \\ \text{Cross multiply} \\ y+8=\text{ 3(x+4)} \\ y+8=\text{ 3x+12} \\ \text{Collect like terms} \\ y=\text{ 3x+12-8} \\ y=\text{ 3x + 4} \end{gathered}\)The equation that represents the graph is y= 3x+4.
Option A is the correct answer.
Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.
Answer:
\(\displaystyle a = \frac{8}{5}\).
Step-by-step explanation:
Two vectors \((x_1,\, y_1)\) and \((x_2,\, y_2)\) are parallel to one another if and only if the ratio between their corresponding components are equal:
\(\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}\).
Equivalently:
\(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\).
For the two vectors in this equation to be parallel to one another:
\(\displaystyle \frac{a}{4} = \frac{2}{5}\).
Solve for \(a\):
\(\displaystyle a = \frac{8}{5}\).
\(\displaystyle \frac{8}{5}\) would be the only valid value of \(a\); no other value would satisfy the \(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\) equation.
mega mart sells a large 5kg cake for $2500 while a 2kg chocolate cake cost $1200 what is the cheapest price sam would payfor 10kg of cake for the party
The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.
To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.
At Mega Mart, a 5kg cake costs $2500.
Therefore, the price per kilogram for this cake is:
Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.
At the same time, a 2kg chocolate cake costs $1200.
So, the price per kilogram for this cake is:
Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.
Now, let's calculate the total price for 10kg of cake from each option:
Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.
Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.
Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.
Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.
Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.
In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.
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Solve: 13x+310x=−17+17.
Answer:
x = 0
Step-by-step explanation:
323 x = 0
x = 0
Look at the image for the question:
9514 1404 393
Answer:
te, tm, (m-e), t
Step-by-step explanation:
The problem statement tells you how to interpret the expressions and their parts.
Swap the top two expressions on the right and the list will be in the appropriate order:
tetmm-et
If x is increased by 20%.
then what
will be the increased percent if there will be x^2?
Answer:
the area will be increased by 44%
Step-by-step explanation:
What value of b will cause the system to have an
infinite number of solutions?
=====================================================
Explanation:
Let's solve the second equation for y to get it into slope intercept form.
\(-3x + \frac{1}{2}y = -3\\\\\frac{1}{2}y = 3x-3\\\\y = 2(3x-3)\\\\y = 6x-6\\\\\)
Compare this to \(y = 6x-b\) and we see that b = 6
Therefore, if b = 6, then the first equation will be exactly identical to the second original equation. The two equations would produce infinitely many solutions.
All of the infinitely many solutions would be of the form (x,y) = (x, 6x-6) where x is any real number.
A sign by the pears reads, "Buy 1/4 pound for only 1/2 dollar!" Ms. Morales thought that the pears cost more than $1.00 per pound. Her daughter, Jasmine, thought that the pears cost less than $1.00 per pound. Who is correct?
Answer:Ms. Morales is right
Step-by-step explanation: it is 1/2 a dollar = to 50 cents 50 cents x 4 =2.00$
its math's question pleases help me to solve
The domain of the composite function f(g(x)) is equal to (x - 2)/(4 + 4x).
What is composite functionA function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function f(g(x)) as follows:
f(g(x)) = 1 ÷ 12/[(x - 2) + 4]
f(g(x)) = 1 ÷ [12 + 4(x - 2)]/(x - 2) {simplify the denominator to a single fraction}
f(g(x)) = 1 ÷ (12 + 4x - 8)/(x - 2) {open bracket for 4(x - 2)}
f(g(x)) = 1 ÷ (4 + 4x)/(x - 2) {simply like terms}
f(g(x)) = 1 × (x - 2)/(4 + 4x) {changing division to multiplication}
f(g(x)) = (x - 2)/(4 + 4x)
Therefore, the result (x - 2)/(4 + 4x) is the domain of the composite function f(g(x)).
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Highest common factor of 42,72,and 56
Answer:
the HCF is 2
Step-by-step explanation:
Solve by Factoring:
2x^2 - x - 3 = 0
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1
packaging idaho produce company ships potatoes to its distributors in bags whose weights are normally distributed witb. nean weight of 50 pounds and a standard deviation of .5 pounds. if a bag of potatoes is selected at random from a shipment, what is the probability that it weighs more than 51 pounds
The probability that it weighs more than 51 pounds exactly 53 pounds.
Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.
We need to find the probability that it weighs more than 51 pounds,
P(X = 53) = 0
z = (51 - 50) / 0.5 = 2.00
P(X > 51) = P(z > 2.00) = 0.0228
z1 = (49 - 50) / 0.5 = -2.00
z2 = (51 - 50) / 0.5 = 2.00
P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544
Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.
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I want you to find the answer
The value of length BC is 18.9
What is cosine rule?Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
Therefore,
c² = a² + b² - 2abcosC
To find the length BC we use cosine rule.
c² = 13² + 7² - 2(13)(7)cos140
c² = 218 - 182cos140
c² = 218-(-139.42)
c² = 218+139.2
c² = 357.2
c = √357.2
c = 18.9
Therefore, the length of BC is 18.9
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In the triangle, the value of the side BC is 18.9cm to 1 decimal place
How to determine BC?The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The cosine formula states that
c² = a² + b² - 2abcosC
To find the length BC we use cosine rule.
c² = 13² + 7² - 2(13)(7)cos140
c² = 218 - 182cos140
c² = 218-(-139.42)
c² = 218+139.2
c² = 357.2
c = √357.2
c = 18.9
In conclusion, the value of the length of BC is 18.9cm
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I need helppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!
I need help please.
Answer:
B
Step-by-step explanation:
Benjamin is planning what to wear tomorrow evening.
• He has 3 shirts to choose from: red, white, and green.
• He has 2 pairs of pants to choose from: blue jeans and khaki pants.
• He has 3 pairs of shoes to choose from: sneakers, flip flops, and boots.
Benjamin randomly chooses one item from each group. What is the probability that he chooses
sneakers and the green shirt? Type in simplest form!!! Anything else will be considered correct, no exceptions
Answer:
1/9
Step-by-step explanation:
P =
\((no \: of \: favorable \: outcomes) \div (total \: numeber \: of \: outcomes \: )\)
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Peace
Solve the radical equation.
√3x-2-√11+x= -1
Answer:
\(x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } \)
3 mi 1,622 yd − 3 mi 1,038 yd =
mi
yd
Answer: 584 yds
Step-by-step explanation:
3mi-3mi=0
1622-1038=584yds
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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In a lottery game, a player picks six numbers from 1 to 28. If the player matches all six numbers, they win 20,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?
Answer:
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.You can calculate the exact number by using the exact probability of picking the winning number stated in the first line of this answer.
Step-by-step explanation:
I hope it's helpful
Interpretation: On average, we lose about 95 cents each time we play the game.
This is not a fair game because the expected value is not 0.
=============================================================
Explanation:
There is only one way to win the game which is to match all the numbers.
This is out of 376,740 different ways to select 6 items from a pool of 28. The steps on how to get this value are shown below
\(_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{28} C _{6} = \frac{28!}{6!*(28-6)!}\\\\_{28} C _{6} = \frac{28!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23*22!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6*5*4*3*2*1}\\\\_{28} C _{6} = \frac{271,252,800}{720}\\\\_{28} C _{6} = 376,740\\\\\)
I used the nCr combination formula. n = 28 is the pool size and r = 6 is the sample size.
Therefore, the probability of winning is 1/376740 and the probability of losing is 1-1/(376740) = 376739/376740
Multiply the odds found by each corresponding net winnings
Win: (1/376740)*(20,000) = 0.05308700960874
Lose: (376739/376740)*(-1) = -0.99999734564951
Then add up those results
0.05308700960874 + (-0.99999734564951) = -0.94691033604078
Rounding to the nearest cent, we get -0.95
The expected value is -0.95
We expect to lose, on average, 95 cents every time we play the game. The game is considered not fair because the expected value is not 0. The game is in favor of the lotto company.
Which is not a true statement about 4x^2 + 5x - 1 ?
Answer:
ndidnfnfjkfnfb
Step-by-step explanation:
nxbcudnbdbdhdikd
Answer:
where is the statement
When rolling a 6-sided die twice, determine P(sum of 5).
two sixths
four thirty sixths
five thirty sixths
ten thirty sixths
The probability of getting a sum of 5 will be 4 /36. The correct option is B.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
Probability = Number of favorable outcomes / Number of samples
Given that the die is rolled twice has six sides. The probability of getting a sum of 5 will be calculated as:-
Number of favourable outcomes = { 1,4 } { 4,1 } { 2,3}{3,2} = 4
Total outcomes = 36
Probability = Number of favorable outcomes / Number of samples
Probability = 4 /36
Therefore, the likelihood of getting a sum of 5 is 4/36. The best choice is B.
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Find the surface area of
the prism.
Answer:
\(\text{D. }464\:\mathrm{ft^2}\)
Step-by-step explanation:
The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:
Rectangle 1 (top base): \(12\cdot 14=168\)
Rectangle 2 (bottom base): \(6\cdot 14 = 84\)
Trapezoids 1 and 2 (lateral): \(2\cdot 9 \cdot 4=72\)
Rectangles 3 and 4 (lateral): \(2\cdot 14\cdot 5=140\)
Thus the total surface area is equal to
\(168+84+72+140=\boxed{\text{D. }464\:\mathrm{ft^2}}\)
Area of a trapezoid please help
Answer:
A= 30
Step-by-step explanation:
A= a+b over 2
h= 5+15 over 2 times that by 3 to get 30
Question 14(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle LMN, mL = (4c + 47). If the exterior angle to L measures 69°, determine the value of c.
Oc= 36
Oc=34
Oc=16
Oc=11
The required value of c is 16 which is the correct answer that would be an option (C).
In triangle LMN, m∠L = (4c + 47). If the exterior angle to L measures 69°,
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
In the case of triangle LMN, we can use the given information to write the following equation:
⇒ 180 - 69 = (4c + 47)
⇒ 111 = 4c + 47
⇒ 4c = 111- 47
⇒ 4c = 64
⇒ c = 64/4
Apply the division operation, and we get
⇒ c = 16
Thus, the value of c is 16.
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Find the output, y, when the input, x, is -9.
y =
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
Help me please I need this done quick
the volume of a pyramid is given by the formula V=1/, where B is the area of the base and h is the height?
Answer:
Step-by-step explanation:
The volume of this pyramid in cubic inches is 16.
Given that,
The base and height is 8 and 6.
Based on the above information, the calculation is as follows:
The volume is
= 16