Hello,
We have A(3, 5) and B(5, 6)
[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]
We know the line contain the point (3, 5)
y = 1/2x + b
⇔ 5 = 1/2 × 3 + b
⇔ 5 = 3/2 + b
⇔ 5 - 3/2 = b
⇔ b = 10/2 - 3/2
⇔ b = (10 - 3)/2
⇔ b = 7/2
[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]
Which of the following best describes the graph of the following linear equation?
y − 9 = -9
Horizontal line with y-intercept at (0,0)
Vertical line with y-intercept at (0,0)
Vertical line with x-intercept at (18,0)
Horizontal line with x-intercept at (9,0)
Answer:
Horizontal line with y-intercept at (0,0)
Step-by-step explanation:
y - 9 = -9
Adding 9 to both sides:
y = 0
So it is the x axis.
From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Select one:
a.
36
b.
9
c.
16
d.
6
Answer: d. 6.
Step-by-step explanation:
AD=3 DC=27 BD=x+3 x>0 x=?
1. Consider triangle ABD:
It's rectangular (∡ADB=90°). ⇒
AB²=(x+3)²+3²=(x+3)²+9.
2. Consider triangle BDC:
It's rectangular (∡BDC=90°). ⇒
BC²=(x+3)²+27²=(x+3)²+729.
3. Consider triangle ABC:
It's rectangular (∡ABC=90°).
AC=AD+CD=3+27=30. ⇒
AC²=AB²+BC²
(x+3)²+9+(x+3)²+729=30²
2*(x+3)²+738=900
2*(x²+6x+9)+738=900
2x²+12x+18+738=900
2x²+12x-144=0 |:2
x²+6x-72=0
D=324 √D=18
x₁=-12 ∉ 'cause x>0
x₂=6.
The mass of an electron is approximately 9 × 10-28 grams, while the mass of a neutron is approximately 2 × 10-24 grams. Which of the following is true?
A. The mass of a neutron is approximately 10,000 times the mass of an electron.
B. The mass of a neutron is approximately 1,000 times the mass of an electron.
C. The mass of a neutron is approximately 2,000 times the mass of an electron.
D. The mass of a neutron is approximately 20,000 times the mass of an electron.
Answer: the mass of a neutron is approximately 2,000 times the mass of an electron
Step-by-step explanation:
- the easiest way to solve this (in my opinion) is to simply divide the mass of a neutron by the mass of an electron
- [tex]2 x10^{-24} / (9 x10^{-28} )[/tex]
= [tex](2/9) x10^{-24--28}[/tex]
= [tex](2/9)x10^{-24+28}[/tex]
≈ [tex]0.2222x10^{28-24}[/tex]
≈ [tex]0.2222x10^{4}[/tex]
≈ which is approximately 2222
- so 2222 is approximately 2000 times
- therefore, the mass of a neutron is approximately 2,000 times the mass of an electron
hope this helps :)
Answer:
C. The mass of a neutron is approximately 2,000 times the mass of an electron.
Step-by-step explanation:
Divide the mass of the neutron by the mass of the electron:
[tex]\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}[/tex]
Rewrite:
[tex]\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}[/tex]
Simplify:
[tex]\implies \sf \dfrac{2}{9} \times 10^{4}[/tex]
[tex]\implies \sf 0.\.{2} \times 10^{4} \approx 2000[/tex]
Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.
Check
[tex]\begin{aligned}\textsf{mass of neutron} & = \sf \textsf{mass of electron} \times 2000\\\implies \textsf{mass of neutron} & =\sf 9 \times 10^{-28}\times 2000\\& =\sf 9 \times 10^{-28}\times 2 \times 10^3\\& =\sf 18 \times 10^{-28+3}\\& =\sf 18 \times 10^{-25}\\& = \sf 1.8 \times 10^{-24}\\& \approx \sf 2 \times 10^{-24}\end{aligned}[/tex]
There were some people on a train
17 get off the train at the first stop and 22 people get on the train
Now there are 66 people on the train
How many people were on the train to begin with
If two triangles are congruent which of the following statements must be true
The statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
What are congruent triangles?Congruent triangles are triangles that have corresponding sides, angles which are all equal in measure.
They can be rotated and turned to be look be identical.
Thus, the statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
The complete question is
If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY
A. The triangles have the same size but not the same shape.
B. The triangles have the same size and shape
C. The corresponding sides of the triangles are congruent.
D. The corresponding angles of the triangles are congruent.
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A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or 20% is alcohol. So let's just say that x=alcohol and y=water, this means that: [tex]x+y=c[/tex] where c is the total amount in the glass. This means that: [tex]x=0.20c[/tex]
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: [tex]j+k=c[/tex] and that: [tex]j=0.40c[/tex].
So if we're going to add the two glasses, we simply add the two sides, and get: [tex]j+x+k+y=2c[/tex]. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: [tex](0.4c+0.2c)+x+k=2c[/tex] Now we can add like terms to get the equation: [tex]0.6c+y+k=2c[/tex]. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Answer:
3 : 7
Step-by-step explanation:
We can do this question using a easier way.
For example, A glass contains sugar and water, the ratio to sugar to water is 2 : 5. And the second glass's sugar to water is 2 : 3. The mixture of the first glass is 200 mL. The mixture of the second glass is the same as the first glass.
This kind of glass question, is very important to Math.
Try using this to solve this question.
A math teacher randomly assigns seats in the classroom to students each quarter. Each student randomly chooses their row number out of a hat. In the classroom, there are 4 desks in each row and 27 students in your class. What is the probability that you and your 3 friends will get to sit together in the same row?
Using the combination formula, it is found that the probability that you and your 3 friends will get to sit together in the same row is given by:
[tex]p = \frac{1}{17550}[/tex].
We do not consider the order, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 students will be taken from a set of 27, hence the number of ways they can sit is given by:
[tex]C_{27,4} = \frac{27!}{4!23!} = 17550[/tex]
Only one outcome is desired, hence the probability is given by:
[tex]p = \frac{1}{17550}[/tex].
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Of the cartons produced by a company, 5% have a puncture, 8% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
In this problem, the events are:
Event A: Puncture.
Event B: Smashed corner.
The "or" probability is given by:
[tex]P(AUB)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]
5% have a puncture, hence [tex]P(A)=0.05[/tex]
8% have a smashed corner, hence [tex]P(B)=0.08[/tex]
0.4% have both a puncture and a smashed corner, hence[tex]P(AUB)=0.004[/tex]
Then:
[tex]P(AUB)=0.05+0.08-0.004= 0.126[/tex]
Therefore, The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
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As strange as it may seem, it is possible to give a precise-looking verbal definition of an integer that, in fact, is not a definition at all. The following was devised by an English librarian, G. G. Berry, and reported by Bertrand Russell. Explain how it leads to a contradiction. Let [tex]n[/tex] be “the smallest integer not describable in fewer than [tex]12[/tex] English words.” (Note that the total number of strings consisting of [tex]11[/tex] or fewer English words is finite.)
Worth 10 points.
YOUR ANSWER MUST BE UNIQUE
The statements hold the contradiction, just by confusion in keep meaning of statements and get confused with "12" which is string in quotes
Let be “the smallest integer not describable in fewer than English words.” (Note that the total number of strings consisting of or fewer English words is finite.)
What do you mean by contradiction?
Contradiction means that couple of statements that opposes each other.
Here,
The statement says let n be “the smallest integer not describable in fewer than English words.” which implies that n is connected with string mentioned in "" quotes, which is not a definition but contain 11 words in the quotes.
and another statement - Note that the total number of strings consisting 11 or fewer English words is finite which implies that:
the limit of words inside the quotes ≤ 11 words
Thus, strings implies in quotes is simple meaning with 11 word in it
While in statement in brackets implies the limit of words as a string should be ≤ 11. the string "12" create the contradiction in minds.
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Keilantra has a toy car collection of 400 toy cars. She keeps 268 of the toy cars on her
wall. What percentage of Keilantra's toy car collection does she keep on her wall?
Answer:
15
I
Submit Answer
MacBook Air
33
attempt 1 out of 2
4
Answer:
67%
Step-by-step explanation:
268 ÷ 400 = 0.67 = 67%
[tex]\huge\boxed{67\%}[/tex]
This can be solved just with division.
[tex]\dfrac{268\ \text{cars on the wall}}{400\ \text{total cars}}=0.67[/tex]
Multiply the result by [tex]100[/tex] to get a percentage.
[tex]0.67=\boxed{67\%}[/tex]
A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A - K). Two cards are pulled in order from this deck of 52 playing cards. What is the probability that the cards will be two 10's?
A) 1/663
B) 9/26
C) 1/252
D) 1/221
The probability of drawing two 10's is P = 1/221, so the correct option is D.
How to find the probability?
We know that in the deck of 52 cards, we have 4 10's.
Then, the probability of drawing the first 10 is:
p = 4/52.
At this point, we have 3 10's in the deck, and a total of 51 cards (because we already took one 10).
The probability of getting another is:
q = 3/51
The joint probability (of getting both 10's, one after the other) is given by the product of the individual probabilities:
P = p*q = (4/52)*(3/51) = (1/13)*(1/17) = 1/221
Then the correct option is D.
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The second highest point measured above sea level is the summit of
Kangchenjunga which is 8,586m above sea level and the lowest point is
challenger deep at the bottom of Mariana Trench which is 10,911 m below
the sea level. What is the vertical distance between these two points? Collect
some more information about these two points and present them withimages
Answer:
To find the vertical distace between both points you will have to add both. 8,586+10,911= 19 497.
Hence, the vertical distance is 19,497 feet.
Here is a picture:
Hope this helps and please mark as brainliest!!
Write as an equation: The product of a number and 12 is 78.
A. 12n=78
12
n
=
78
B. n+12=78
n
+
12
=
78
C. 12−n=78
12
−
n
=
78
D. 12=78n
Can someone give me the answer to this?
[tex]\frac{FI}{IG}=\frac{14}{28}=\frac{1}{2}\\\\\frac{FE}{EH}=\frac{12}{26}=\frac{6}{13}[/tex]
So, IE is not parallel to GH.
Look At The Graph. How many nails are less than 1 1/2 inches long?
A)7
B)17
C)6
D)15
Answer:
D 15
Step-by-step explanation:
Count all of the x's less than 1 1/2 = 15
Find the tangent of angle Θ in the triangle below.
Answer: 4/3
Step-by-step explanation:
[tex]\tan \theta=\frac{20}{15}=\boxed{\frac{4}{3}}[/tex]
Select each row where the property is being used correctly.
-3x - 4x + 4
2(x - 5) + 1 ≤ 5
-4x ≥-24
x = 2y and 2x + 2y > 60
y+ 2 ≤4-x and 4 - x ≤ 3y
➜
➜
-3x < x
2(x - 5) ≤ 4
x≤6
X> 27
6y > 60
y + 2 ≤ 3y
The correct rows in the inequalities are
2(x - 5) + 1 ≤ 5 ⇒ 2(x - 5) ≤ 4-4x ≥ -24 ⇒ x ≤ 6x = 2y and 2x + 2y > 60 ⇒ 6y > 60y + 2 ≤ 4 - x and 4 - x ≤ 3y ⇒ y + 2 ≤ 3yHow to determine the correct rows?The rows are given as:
-3x - 4 < x + 4 ⇒ -3x < x
2(x - 5) + 1 ≤ 5 ⇒ 2(x - 5) ≤ 4
-4x ≥ -24 ⇒ x ≤ 6
x = 2y and 2x + 2y > 60 ⇒ 6y > 60
y + 2 ≤ 4 - x and 4 - x ≤ 3y ⇒ y + 2 ≤ 3y
To determine the correct rows, we simply solve each inequality.
This is done as follows:
-3x - 4 < x + 4
Collect like terms
-3x - x < 4 + 4
Evaluate the like terms
-4x < 8
Divide by -4
x > -2
This means that:
-3x - 4 < x + 4 ⇒ -3x < x is false.
2(x - 5) + 1 ≤ 5
Subtract 1 from both sides
2(x - 5) ≤ 4
This means that:
2(x - 5) + 1 ≤ 5 ⇒ 2(x - 5) ≤ 4 is true.
-4x ≥ -24
Divide through by -4
x ≤ 6
This means that:
-4x ≥ -24 ⇒ x ≤ 6 is true.
x = 2y and 2x + 2y > 60
Substitute 2y or x in 2x + 2y > 60
2(2y) + 2y > 60
Evaluate the product
4y + 2y > 60
Evaluate the like terms
6y > 60
This means that:
x = 2y and 2x + 2y > 60 ⇒ 6y > 60 is true.
y + 2 ≤ 4 - x and 4 - x ≤ 3y
We have:
y + 2 ≤ 4 - x and 4 - x ≤ 3y
This can be rewritten as:
y + 2 ≤ 3y
This means that:
y + 2 ≤ 4 - x and 4 - x ≤ 3y ⇒ y + 2 ≤ 3y is true
Hence, the correct rows are 2, 3, 4 and 5
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A cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462. Model the numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality.
The numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality is x ≥ 2,052 and x ≤ 2,462.
How to illustrate the inequality?From the information given, we are told that the cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462.
Learn x be the number of people that can be accommodated. Therefore, the model is x ≥ 2,052 and x ≤ 2,462.
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a
Find tan a.
r
√5,-√7)
✓[?
Enter
Answer:
[tex]tan(\alpha)=-\frac{\sqrt{35}}{5}[/tex]
Step-by-step explanation:
Tan can be defined as: [tex]\frac{sin(\theta)}{cos(\theta)}[/tex] as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.
Using this we can define tan
[tex]sin(\alpha)=-\sqrt{7}\\cos(\alpha)=\sqrt{5}\\\\tan(\alpha)=-\frac{\sqrt{7}}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}\\tan(\alpha)=-\frac{\sqrt{7*5}}{5}\\tan(\alpha)=-\frac{\sqrt{35}}{5}\\[/tex]
Answer:
tan α = -√35/5
Step-by-step explanation:
tan α = y/x
tan α = -√7/√5
tan α = -√7/√5 × √5/√5
tan α = -√35/5
In the following exercises, multiply the binomials. Use any method.
254. (10a − b)(3a − 4)
Answer:
Hence the expression [tex]$$(10a-b)(3a-4)=30a^2-3ab-40a+4b$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (10a-b)(3 a-4).We have to multiply the given expression.Multiply the (10a-b) by -4, multiply the (10 a-b) by 3a then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 10a & - & b \\ \times & {} & {} & {} & 3a & - & 4 \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}{} & {} & {} & - & 40a & + & 4b \\ 30{{a}^2} & - & 3ab & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}30{{a}^2} & - & 3ab & - & 40a & + & 4b \\ \end{matrix}$$[/tex]
Find the radius of the given circle with the given central angle and arc length. Round your answer to the nearest tenth.
Show work for full credit.
130*
19.6 cm
Answer: 8.6
Step-by-step explanation:
[tex]19.6=2\pi r\left(\frac{130}{360} \right)\\\\r=\frac{19.6}{2\pi \left(\frac{130}{360} \right)}\\\\r \approx 8.6[/tex]
The height of an
equilateral triangle is
11√12. What is a side
of the triangle?
Answer:
I don't know the answer
Step-by-step explanation:
it's hard solve it for me
Find the value of x.
[tex]x + 4x + 4x + 135 + 135 = 540[/tex]
[tex]9x + 270 = 540[/tex]
[tex]9x = 540 - 270 \\ 9x = 270[/tex]
[tex]x = \frac{270}{9} = 30[/tex]
Anthony is planning a trip using a map with the scale of 1 cm to 15 miles it’s a destinations 15 cm away on the map how far away in Miles as the destination
The distance of Miles' destination is 225 miles.
What is the distance of the destination?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The map is a scale drawing of a larger town. The scale drawing is reduced by constant dimensions.
Actual distance = (15 x 15) / 1 = 225 miles
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Can someone solve it step by step for me please?
What is the domain of function m based on the graph?
Answer:
let why is equal to FX b and function with an independent variable X and dependent variable y if a function of f provide a way to successfully produced the single value using for the prepos a value of x then the chosen X value is called belong to domain f
The perimeter of the rectangle below is 130 units. Find the length of side VY.
Write your answer without variables.
Y
4y
V
5y + 2
X
W
VY
Answer:
VY = 28 units
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2 ( length + breadth )
given P = 130 , then
2(5y + 2 + 4y) = 130 ( divide both sides by 2 )
9y + 2 = 65 ( subtract 2 from both sides )
9y = 63 ( divide both sides by 9 )
y = 7
Then
VY = 4y = 4 × 7 = 28
20 POINTS!!! PLEASE HELP
Find the logarithm base 10 of each number:
10
Please show work. Thanks!!
The logarithm of 10 to base 10 is 1
How to determine the logarithm?The given parameters are:
Base = 10
Number = 10
So, the expression is:
[tex]\log_{10}10[/tex]
As a general rule;
[tex]\log_{a}a = 1[/tex]
The above means that;
When the base and the number are the same, the logarithm is 1
So, we have:
[tex]\log_{10}10 = 1[/tex]
Hence, the logarithmic value is 1
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The length of an inflatable swimming poll is 2 meters 12 centimeters. How long is the pool in millimeters?
Answer:
2120 mm
Step-by-step explanation:
→ Convert 2.12 metres into centimetres
2.12 × 100 = 212 cm
→ Multiply by 10 to get into mm
212 × 10 = 2120 mm
(bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home.
The probability that he will use both bus and the train among bus, cab, train is 0.11.
Given There are 3 choices to people each among bus, cab, train for his trip home.
Probability is the likeliness of happening an event among all the events possible. The value of probability lies between 0 and 1. The formula to calculate probability is as under:
Probability= number of things/ total things.
The value of probability cannot be negative.
Number of buses=3
Number of cab=3
Number of train=3
Probability that he will go through train and bus is 3/9*3/9
=9/81
=1/9
=0.11
Hence the probability that he will travel with bus and train is 0.11.
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Question is incomplete as it includes:
What is the probability that he will use both train and bus?