Step-by-step explanation:
2x + y = -4
-3y = 2x + 12
convert to regular line equations, when we have only y on one side :
y = -2x - 4
y = -2/3 x - 12/3 = -2/3 x - 4
remember, the general line equation is
y = ax + b
a is the slope (y coordinate change / x coordinate change). and b is the y-intercept (the y value when x = 0).
that means, both lines have the same y-intercept : y = -4
and that means only F is the right representation of the 2 lines.
Which equation in standard form has a graph that passes through the point (15,3) and has a slope of ¼?
Answer:
2y - 9x - 40 = 0
Step-by-step explanation: i already done the test
You have 90.43 in your bank account and you make a deposite. Your account will:
Answer:
be adding more money
Step-by-step explanation:
deposit means to add withdraw means to take out
Answer:
increase
Step-by-step explanation:
Correct answer please
Answer:
50.75
Step-by-step explanation:
We have:
\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)
\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)
Study this table.
x
y
–3
–2
–2
0
0
4
4
12
Which best describes the function represented by the data in the table?
linear with a common ratio of 2
linear with a common first difference of 2
quadratic with a common ratio of 2
quadratic with a common first difference of 2
Miles draws three cards at random from a standard deck of 52 cards, without replacement.
(a) Find the probability that all three cards are red.
(b) Find the probability that all three cards have the same rank.
Answer:
P( red, red, red no replacement ) = 2/17
P( 3 cards with same rank, no replacement) = 1/425
Step-by-step explanation:
There are 52 cards, 26 are red
P( red) = red/total =26/ 52 = 1/2
Now draw the second card without replacement
There are 51 cards, 25 are red
P( red) = red/total =25/51
Now draw the third card without replacement
There are 50 cards, 24 are red
P( red) = red/total =24/50 = 12/25
P( red, red, red no replacement ) = 1/2 * 25/51 * 12/25 = 2/17
P ( all have the same rank)
There are 52 cards, 4 of each rank
We don't care what the first rank is, now the second and third draw have to have the same rank as the first
P( rank) = 1/1
Now draw the second card without replacement
There are 51 cards, 3 are left with the same rank
P( same rank) = cards with same rank/total = 3/51
Now draw the third card without replacement
There are 50 cards, 2 are left with the same rank
P( same rank) = cards with same rank/total = 2/50 = 1/25
P( 3 cards with same rank, no replacement) = 1 * 3/51*1/25 = 1/425
I am shopping for stocking stuffers. I have $45 to spend and can buy bags of candy for $2.50 each and fuzzy socks for $7.50. 1. Write an equation to represent the situation.2. Find the x and y intercepts and explain what they represent.
Assuming that all $45 will be spent, no more no less, is will be equal to the sum of what is spent on candy and socks.
Ley x represent the number of bag of candy bought and let y be the number of fuzzy socks bought.
Since each bag of candy costs $2.50, the total spent on candy is:
\(2.5x\)Since each fuzze sock costs $7.50, the total spent on socks is:
\(7.5y\)Adding them, we have to get a value equal to the total spent, $45, so this is the equation that represents the situation:
\(2.5x+7.5x=45\)The x intercept is the x value when y = 0:
\(\begin{gathered} 2.5x+7.5\cdot0=45 \\ 2.5x=45 \\ x=\frac{45}{2.5} \\ x=18 \end{gathered}\)The y intercept is the y value when x = 0:
\(\begin{gathered} 2.5\cdot0+7.5y=45 \\ 7.5y=45 \\ y=\frac{45}{7.5} \\ y=6 \end{gathered}\)Since x is the number of bag of candy bought and y is the number of fuzzy socks bought:
- the x-intercept represents the situation where all the money was spent on bag of candy and no fuzzy sock was bought.
- the y-intercept represents the situation where all the money was spent on fuzzy socks and no bag of candy was bought.
(3х — у = 2
(x+2y = 3
if someone can help me with solving with system of elimination please that would be amazing
Answer:
x=1 y=1
Step-by-step explanation:
You want to chose either x or y to cancel out of both equations. I chose y, so I multiplied the entire equation of 3x-y=2 by 2 to get 6x-2y=4
6x-2y=4
x+2y=3
The -2y and 2y cancel each other out, the 6x and x can be added, and the 4 and 3 can be added.
7x=7
x=1
Now that we know x=1, plug in x to one of the original equation.
1+2y=3
2y=2
y=1
A surveyor in a canyon takes measurements and draws the diagram shown.
Determine the length of a bridge that would stretch across the canyon to 1 decimal
place.
Answer:
\(\approx 118.4\)
Step-by-step explanation:
We know two sides and the angle between the sides, so we can use the Law of Cosines. Recall that the Law of Cosines states that:
\(c^2=a^2+b^2-2abcos(C)\), where a and b are the sides and C is the angle in between.
Let's substitute 115 for a, 178 for b, and 41 for Angle C.
Thus:
\(c^2=115^2+178^2-2(115)(178)cos(41)\)
\(c^2=44909-40940cos(41)\)
\(c=\sqrt{44909-40940cos(41)}\)
\(c \approx 118. 4\)
…name three points that are collinear
Answer:
D. Points D, C and AStep-by-step explanation:
Points D, C and A are collinear as DC, CA and DA have same slope of 1/3.
Mrs. Hilt has 6 boxes of markers. Each box has 19 markers in it. If she sold each maker for $0.75, how much money would Mrs. Hilt earn?
Answer:
85.50
Step-by-step explanation:
6 times 19 = 114 markers then times .75= 85.50
Question 10 (1 point)
A
33
7 in.
B
C
The value of AB is,
⇒ AB = 5.9
(rounded to nearest tenth)
We have to given that,
A right triangle ABC is shown.
Now, By trigonometry formula,
we get;
⇒ cos 33° = Base / Hypotenuse
Substitute all the values, we get;
⇒ cos 33° = AB / 7
⇒ 0.84 = AB / 7
⇒ AB = 0.84 × 7
⇒ AB = 5.88
⇒ AB = 5.9
(rounded to nearest tenth)
Thus, We get;
AB = 5.9
(rounded to nearest tenth)
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3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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convert 2.64 to a fraction
please don't just give the answer. can please give some explanation
Answer:
2 and 16/25
Step-by-step explanation:
first: change 0.64 into a fraction which is 64/100
second: simplify by dividing by four which is:
64/4 = 16
100/4 = 25
so...
2.64 = 2 16/25
HOPE THIS HELPS :)
Answer:
2 and 16/25 OR 66/25
Step-by-step explanation:
As a mixed fraction, 2.64 is 2 and 64/100 because you have 2 whole 100s and a 64/100. Simplify 64/100 to 16/25 (divide both 64 and 100 by 4) and you're left with 2 and 16/25.
In improper form, you have 264/100. Simplify that (divide 264 and 100 by 4) and you're left with 66/25.
Quan likes to exercise by running every day. On average, he runs 5 miles each day. This varies by about 0.3 mile. What are the maximum and minimum numbers of miles Quan is expected to run each day?
Answer:
Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.
Step-by-step explanation:
Let x= the actual measurement.
|actual − ideal|≤ tolerance
Use an absolute value inequality to express this situation.
|x−5|≤0.3
Rewrite as a compound inequality.
−0.3≤x−5≤0.3
Solve the inequality.
4.7≤x≤5.3
Answer the question. Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.
Suppose a professional baseball player hit 55 home runs his first season, 58 his second,
and 69 his third. How many home runs would he need to hit in the current season so that
his average for the 4 years is no less than 59?
Answer:
About 54
Step-by-step explanation:
To work backwards from average, you need to multiply the average by the total number of cases, which is 4, since there are 3 current cases/seasons and you want the 4th.
59 * 4 = 236
You then subtract the total home runs that you know of from 236.
236 - 55 - 58 - 69 = 54
To find average, you are adding to the total and then dividing by the number of groups, which is essentially mean (mean is basically the average).
a town's population was 7500 at the beginning of the year 2000 and has been decreasing by 3.2 % each year thereafter.
Answer:
In 2022, the town's population is 2220.
Step-by-step explanation:
It currently the year 2022. Hence, 22 years have passed since 2000.
2022 − 2000 = 22
To solve for the town's population today, first multiply the years passed since 2000 by the percent decrease each year.
\(22 \, \textrm{years} \times \dfrac{3.2 \, \%}{\textrm{year}} = 70.4 \, \%\)
Then, subtract that percent of the population in 2000 from the population in 2000.
\(7500-(70.4 \,\% \cdot 7500)\)
\(= 7500 - 5280\)
\(=2220\)
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
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You are __________ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance.
a. twice as likely b. less likely c. equally likely d. more likely
You are more likely to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance.
What is meaning of level of significance?
The measurement of statistical significance is called degree of significance. It specifies whether or not the null hypothesis is thought to be true.
If the outcome is statistically significant, it should be possible to conclude that the null hypothesis is either incorrect or invalid.
What does "0.05 level of significance" mean?
The likelihood that the null hypothesis will be rejected when it is true is the significance level. For instance, a significance level of 0.05 suggests a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.
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Never mind i got it!
Answer:
OOk
Step-by-step explanation:
Jake left the gym at 6:22 he exercised for 45 mins. What time did he arrive
What is the solution to 4 x + 6 less-than-or-equal-to 18?
Answer:
a
Step-by-step explanation:
edge 2020-2021 <3333
(have an amazing day lovely)
While at a beach, Daniel buys lunch for his family from a food stand. He purchases one hot dog for $2.50 and 3 hamburgers. If he spent $13 total, write and solve an equation to find h, the amount each hamburger cost
Answer:
h= $3.50 ($13-$2.50)/3 = h
Step-by-step explanation:
$13 total. He spends $2.50 on a hotdog which leaves him at $10.50. He buys 3 hamburgers so $10.50/ 3 = $3.50
what would be your first step in completely factoring 6a^2-15a+6
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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You are playing in the NBA Playoffs and attempt a 3-point shot as the buzzer sounds for the end of the
game, if you make the shot your team wins! Your basketball is is traveling on a path described by the
following function: b(x) = -x2 +1.36x + 2. The net is on a level described by the following function:
n(x) = 3 between (8 < x < 8.5). Will you make the shot and win the playoffs?
You may work alone or in a group of up to 3 students total.
BONUS: How high in the air will the basketball be at its highest point?
UNITS: x is in meters, y is in meters
Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.
Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.
Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.
Assuming that the basketball follows a parabolic path, we can use the formula:
y = ax² + bx + c,
where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.
To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.
Therefore, the points on the trajectory of the basketball are:
(0, 1.5), (8.5/2, h), and (8.5, 0),
where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,
we get:
1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)
Simplifying equations (1) and (2),
we get:
c = 1.5...(4)b = -a(8.5)²/8.5...(5)
Substituting equation (4) in equation (3), we get:
h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5
Substituting the value of a from equation (5) in the above equation,
we get:
h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5
Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,
we can use the formula:
x = ut + 0.5at²,
where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.
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solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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John bought new headphones originally listed for $ 80.99 . They are \(35\%)| off. Which equation can be used to find the amount John will save?
Answer:
$28.35
Step-by-step explanation:
The headphones are $80.99 and are 35% off. To find the amount he will save, change the 35% to a decimal by moving it two times to the left, which is 0.35. Multiply 80.99 and 0.35 to get 28.3465. Round to get $28.35.
Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box
Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)
How to determine the key features?Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:
Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).
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-5p = -40 solve for t
Answer:
p = 8
Step-by-step explanation:
Divide -5 to both sides
-5p = -40
5p = 40
p = 8
So p = 8
What is the m∠J, to the nearest tenth? JLK is right angle triangle. The length of JL is 9.4 and length of LK is 15.1. explaination?
The angle m∠J in the right angle triangle is 58.1 degrees.
How to find the angle of a triangle?One of the angle of a right tangle triangle is 90 degrees. The sum of
angles in a triangle is 180 degrees.
Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.
Hence,
tan ∠J = opposite / adjacent
tan ∠J = 15.1 / 9.4
∠J = tan⁻¹ 1.60638297872
∠J = 58.0909229196
Therefore,
m∠J = 58.1 degrees
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Help please *an image is attached*
Answer:
what grade????????????