Answers
The distance between the two points is 10 units and the slope of the line is -78/25
Distance Between Two Points
To find the distance between two points, we can simply use the formula of distance between two which is given as
[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}[/tex]
Let's substitute the values and solve for the distance.
[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}\\d = \sqrt{(1-7)^2 + (-3 - 5)^2} \\d = 10[/tex]
2)
The slope of the line can be found using the two points given.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]
let's substitute the values and solve.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = -\frac{78}{25}[/tex]
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Related Questions
When 4a-a is simplified it’s equivalent to
Answers
Answer: 3a
Step-by-step explanation: 4a - 1a = 3a
Find the length of the missing side.
Answers
Answer:
13 cm
Step-by-step explanation:
You can use the pythagorean theorem to solve this problem. The pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where and b are the legs of a right triangle and c is the hypotenuse.
In the problem, we are given two legs, 12 and 5, so we can substitute them in for a and b and solve from there:
[tex]5^2+12^2=c^2[/tex]
[tex]25+144=c^2[/tex]
[tex]c^2=169[/tex]
[tex]c=13[/tex]
The missing side is 13 cm long
At the school 460 of the students walk to school.
1The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
2The number of students who bike to school is 5% of the number of students who walk. How many students bike to school
3The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
Answers
Answer:
92 public transit
23 bike
Step-by-step explanation:
460 / 5 = 92
460 / 20 = 23
how do i convert (x+3)(x-4) to standard form
Answers
Answer:
solving the bracket
x×x = x²
x×-4= -4x
3×x= 3x
3×-4= -12
x²-x-12=0
Work out the area of this semicircle.
Take to be 3.142 and write down all of the digits given by your calculator.
18 cm
Answers
Answer:
A = 127.251 cm²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( where r is the radius )
the area (A) of a semicircle is then
A = [tex]\frac{1}{2}[/tex] πr²
given diameter = 18 then r = 18 ÷ 2 = 9 cm , so
A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²
(1 × 10¹)(8 × 10^4) help
Answers
Answer:
800000
Step-by-step explanation:
(1 x 10^1) = 10
(8 x 10^4) = 80000
10 x 80000 = 800000
The diagram below shows the first four of a series of designs that an artist draws on artwork.
The artist wants to use a design with a maximum of 15 shaded circles. What number of design should the artist use?
Answers
Using an arithmetic sequence, the number of design that the artist should use is:
b. Design 6.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sequence for the number of circles is:
(4, 6, 8, ...)
Hence the common difference is given by:
d = 8 - 6 = 6 - 4 = 2.
Then the rule for the nth term is:
[tex]a_n = 4 + 2(n - 1)[/tex]
As the first term is of 4.
The maximum number is of 15 shaded circles, hence:
4 + 2(n - 1) ≤ 15
4 + 2n - 2 ≤ 15
2 + 2n ≤ 15
2n ≤ 13
x ≤ 6.5.
Hence the maximum number is of 6, meaning that Design 6 is chosen, given by option b.
Missing informationThe complete problem is given by the image at the end of the answer.
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w=0.75f.
What does 0.75 tell us in this situation?
Answers
Answer:
it should be in the ratio of 3:4
Step-by-step explanation:
100w= 75f
w/f = 75/100
= 3/4
= 3:4
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)
Answers
From the given sequence, it is found that:
a) It is a geometric sequence, as the ratio between consecutive terms is the same.
b) Station 5 will be completed in 48 minutes.
c) Station 9 will be completed in 768 minutes.
What is a geometric sequence?In a geometric sequence, the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by the following rule:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, the ratio between consecutive terms is given by:
r = 24/12 = 12/6 = 6/3 = 2.
Hence it is a geometric sequence.
Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:
24 x 2 = 48 minutes.
The first term of the sequence is of 3, hence the explicit formula is given by:
[tex]a_n = 3(2)^{n-1}[/tex]
Hence the time for the 9th station, in minutes, is given as follows:
[tex]a_9 = 3(2)^{8} = 768[/tex]
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A race car driver
travels 34 ft in the first second of a race.
If the driver travels 3.5 additional feet each
subsequent second, how many feet did the
driver travel in 52 s?
Answers
The number of distance in feet the driver travel in 52 seconds is 216 feet.
How to find the distance in feet the driver can travel in a particular time?The race car driver travels 34 feet in the first second of a race.
The driver travels 3.5 additional feet each subsequent second.
The number of feet the driver travel in 52 seconds can be solved as follows:
Therefore,
the distance travel = 34 + 3.5x
where
x = number of time in seconds the driver travelsTherefore,
the distance travel = 34 + 3.5(52)
the distance travel = 34 + 182
the distance travel = 216 feet
Therefore, if the driver travels 34 feet in the first seconds of the race and travels an additional 3.5 feet each subsequent second, the number of distance in feet the driver will travel in 52 seconds is 216 feet.
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The mass of a textbook is approximately 0.0165 metric tons. If this number were written in scientific notation, what would the
exponent be?
Answers
If the number were written in scientific notation, the exponent will be -2.
What is scientific notation?Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The number of times a number is multiplied by itself is referred to as its exponent.
In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.
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What is the constant of proportionality in the equation y=3xy=3xy, equals, 3, x?
constant of proportionality ==equals
Answers
The constant proportionality is 3
What is Proportionality Constant ?
The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.
Now, We have the equation is:
y = 3xy
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k = y/x or y = kx
To get the constant of proportionality,
we will derive both sides of the equation by x.
y/x = 3x/x
y/x = 3
Hence, The constant proportionality is 3
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Solve it , I need help
Answers
y < 2
can't be y <= 2 or y<=1 because the dot is open meaning the point is not included.
the range is talking about the y value, the point is at y = 2. The graph is also negative; therefore, range will be anything less than y = 2
Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars. A. 3x+2=30B. x+2+3x=30C. 2x+3=30D. x+2x+3=30
Answers
We can represent the length in Zach's car model by x
Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow
[tex]\begin{gathered} 3\text{ times the length of Zach's car is} \\ 3\times x=3x \\ \end{gathered}[/tex][tex]\begin{gathered} 2\text{ more than 3 times the length of Zach's car will be} \\ 2+3x \end{gathered}[/tex]Therefore,
Ginny's model will be 2 + 3x
Next, we are told that the sum of the lengths of both cars is 30 inches
Then
[tex]\begin{gathered} Zach\text{+}Ginny=30 \\ x+2+3x=30 \end{gathered}[/tex]Therefore,
The answer is
[tex]x+2+3x=30[/tex]Thus, the answer is Option B
A group of friends wants to go to the amusement park. They have no more than $155 to spend on parking and admission. Parking is $18, and tickets cost $24 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answers
Answer:
5
Step-by-step explanation:
155-18=137
137/24=5.70833333
5 people are able to join max
mathhhh helppp pleasee
Answers
not to intrude but is that big ideas math?
What is the value of x?
Answers
Answer:
x=27
Step-by-step explanation:
Alan is ordering uniforms for his flag football team. Each uniform costs $14. All orders over $150 receive a 15% discount.
If Alan buys 12 uniforms, what will be the cost?
Answers
Answer:
$142.80
Step-by-step explanation:
smarts
which best describes why you might want to rewrite a literal equation?
To solve for a different indicated variable.
To solve for the variable x.
To solve for a different number.
To solve for the variable y.
Answers
Sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
What are literal equations?A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v = Dt) and the area of a circle (A = r₂).So, as in the description, it is given that A literal equation is one that is mostly made up of letters.
Therefore, sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
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The correct question is given below:
Which best describes why you might want to rewrite a literal equation?
(A) To solve for a different indicated variable.
(B) To solve for the variable x.
(C) To solve for a different number.
(D) To solve for the variable y.
If a and b are the roots of 2x²+3x-1=0,find the values of a³-b³
Answers
Answer:
Step-by-step explanation:
Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.
a³/b³=1001/1024+45*sqrt(23)/1024*i
b³/a³=1001/1024-45*sqrt(23)/1024*i
Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!
If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.
It is -2c=-2*1001/1024=-1001/512, and
c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.
two trains leave the station at the same time, one heading west and the other east. the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours, what is the rate of the westbound train?
Answers
if the two trains are miles apart after hours, then the rate of the westbound train is 79 miles per hour
two trains leave the station at the same time, one heading west and the other east.
the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,
what is the rate of the westbound train?
Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:
4 (e + (e - 12)) = 680
4 (2e + 12) = 680
8e - 48 = 680
8e = 728
e = 91 mph
e - 12 = w
91 - 12 = w
79 = w
Therefore, the westbound train travels at 79 miles per hour.
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look at attachment please MATHHHHHHHHHHHHHHHHH
Answers
Answer: 89%
[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]
8x-5x+21 = 36-6y
Write the equation so that y is a function of x.
Answers
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Given Data
Function
8x-5x+21 = 36-6y
6y = 36 - 21 - 8x +5x
6y = -3x + 15
y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
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Create a division equation that represents the question: How many \frac{3}{8} are in \frac{5}{4} ?
Answers
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
Given,
Fractions : 3/8 and 5/4
We have to find a division equation for number of 3/8 in 5/4
Number of 3/8 in 5/4 = x
Now,
Number of a in b = b/a
So here,
Number of 3/8 in 5/4, x = 5/4 / 3/8
Number of 3/8 in 5/4, x = 5/ 3/2
Number of 3/8 in 5/4, x = 5 × 2 / 3
Number of 3/8 in 5/4, x = 10/3
That is,
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
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Math for Homework
Question Help Challenge You buy 1.09 pounds of apples, 0.99pounds of grapes, and 1.29 pounds of oranges. What is your total bill?
Grocery Store Prices
Item
Cost
Apples
$0.99 per
pound
Grapes
$1.19 per
pound
$1.09 per
Oranges
Savvar Egge Rigid muiago
Your total bill is $
(Round to the nearest cent as needed.)
Clasroom Continks Schoonet: math
Answers
0.99 x 1.19 = $1.18 grapes
1.29 x 1.09 = $1.41 oranges
Total bill = $3.67
There are 20 balloons in Emma's hand. Four-fifths are red
balloons. How many red balloons are in Emma's hand?
Answers
Answer:
16
Step-by-step explanation:
4/5=0.8
20*0.8=16
easy 8th grade math
with explanation pls
Answers
Answer:
x: (40,0)
y:(0,30)
Step-by-step explanation:
hope this helped
have a good day :)
2y - 16 = 12 solve for y and simplify your answer as much as possible
Answers
Answer:
y = 14
Step-by-step explanation:
2y - 16 = 12
add 16 to both sides:
2y - 16 + 16 = 12 + 16
2y = 28
divide both sides by 2:
2y/2 = 28/2
y = 14
Answer: y = 14 is the solution.
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.The probability of rolling a number less than 7 is
Answers
Probability is the quantitative measure of the likelihood of the occurrence of an event.
It is mathematically expressed as:
[tex]P=\frac{number\text{ of selected outcome}}{number\text{ of total outcome}}[/tex]We can decide to call the set of numbers below 7 "A".
A = {1, 2, 3, 4, 5, 6}
|A| = 6
We call the universal set, the set containing all the numbers rollable "U"
|U| = 12
Our probability is therefore:
[tex]undefined[/tex]axline computers manufactures personal computers at two plants, one in texas and the other in hawaii. the texas plant has 45 employees; the hawaii plant has 15. a random sample of 10 employees is to be asked to fill out a benefits questionnaire. (round your answers to four decimal places.) (a) what is the probability that none of the employees in the sample work at the plant in hawaii?
Answers
The probability that none of the employees in the sample work at the plant in hawai is 0.0112
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
PH= 20/60 = 1/3
P(T) = 2/3
It is hypergeometric distribution
P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},
where
N = 60
K = 20 for Hawai; 40 for Texas
n = 10
P(X=0) = 0.0112
Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112
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