I’m doing my geometry homework and don’t remember the formula or way to solve the lengths of a triangle side with graph points. How do I solve both parts of #1?
Answers
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]
Related Questions
A company gives yearly raises to their employees. The salaries at the company are based on the equation below, where S is the salary before taxes and t is the time since the date of hire in years.
S = $33,113 + $600t
What is the minimum number of years an employee would have to stay to make a salary of over $40,000 per year?
A. 13 years
B. 12 years
C. 11 years
D. 1 year
Answers
Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.
What is an equation?An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.
Equations show equality using the equation symbol (=).
When one expression is more or less than, or not equal to another expression, it is an inequality.
If S = $33,113 + $600t
Where S = the salary before taxes
t = the time since the date of hire in years.
For S ≥ $40,000:
$33,113 + $600t ≥ $40,000
$600t ≥ $40,000 - $33,113
$600t ≥ $6,887
t ≥ 11.48
t = 12 years
Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.
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5. The diagram shows a rectangular field ABCD has a path of uniform width around it. AB and BC are 6m and 4 m respectively. Given that area PQRS is twice the area of ABCD. Find the length of PQ and QR.
Answers
Tthe length of PQ and QR. is 6 and 8 m
Area of rectangular field ABCD is = 4m x 6m = 24m2
Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)
= 24 + 4x + 6x + x²
48 = 24 + 10x + x²
x² + 10x - 24 = 0
x² + 12x - 2x - 24
x(x + 12) - 2(x + 12)
(x - 2)(x + 12) = 0
x - 2 = 0
x = 2
PQ = 4 + 2 = 6
QR = 6 + 2 = 8
Therefore, the length of PQ and QR. is 6 and 8 m
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I need answer help please
Answers
For given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
In this question we have been given a function f(x) = 7/(x² - 5)
We need to evaluate f(a + 4)
Substitute x = a + 4 in given function.
f(a + 4)
= 7/((a + 4)² - 5)
= 7/(a² + 8x + 16 - 5)
= 7/(a² + 8x + 11)
Therefore, for given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
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Emory walks one lap on the
track every 7 minutes. Madison
walks one lap on the track every
8 minutes. How many minutes
will pass before they meet on
track at the same time?
Answers
Answer: 56 minutes
Step-by-step explanation:
7 = 7, 14, 28, 35, 42, 49, 56
8 = 8, 16, 24, 32, 40, 48, 56
7 and 8 have 56 in common so it would take them 56 minutes
Write 3.278 correct to 1 decimal place.
Answers
Answer: 0.3278
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!
The CDC is investigating if the average blood pressure of the US population is
different from 123. A hypothesis test is conducted which returns a sample mean of
128 and a p-value of 0.0037. What is the appropriate conclusion at the 5%
significance level?
Answers
Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123
How to test the hypothesisH0: mean = 123
H1 : mean ≠ 123
We have the p value of the statistics stated already in the question as p value = 0.0037.
The level is significance that we have been given in the question is 5% = 0.05
We are to test here if the true mean is different from 123.
Hence we would be testing the p value against the significance level.
We can see that P value is < level of significance.
0.0037 < 0.05
Hence we would reject the null hypothesis.
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Fill in the table using this function rule. y=-2x-3
Answers
Answer:
6
Step-by-step explanation:
the answer is 6
Directions - Write an equation in slope-intercept (y = mx + b) form for each line.
Answers
The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2
How to determine the equation of the line?From the graph, we have the points to be given as
(-3,0) and (0,2)
Start by calculating the slope of the points using the following slope equation
m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3,0) and (0,2)
So, we have
m = (2 - 0)/(0 + 3)
Evaluate
m = 2/3
The equation is then calculated as
y = m(x - x₁) + y₁
Where
(x, y) = (0, 2) and m = 2/3
So, we have
y = 2/3(x - 0) + 2
Expand
y = 2/3x + 2
Hence, the equation in slope intercept form of the line is y = 2/3x + 2
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How many dogs do they need to walk in order to pay for the box of treats?
hint:In the equation for the function representing the profit, substitute 5 for y and solve the equation for x.
hint:Round up to the nearest whole number of dogs.
Answers
The number of dogs do they need to walk in order to pay for the box of treats is 4
The function that representing the profit is
y = 3x - 5
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here the cost for buying a box of treat = $5
Substitute the value in the function and find the number of dog that they need to walk
5 = 3x - 5
3x = 5 + 5
3x = 10
x = 10 / 3
x = 3.33
x ≈ 4
Hence, the number of dogs do they need to walk in order to pay for the box of treats is 4
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David and Vicky share £36 in the ratio 2:7. How much do they each
receive?
Answers
David share is £8
Vicky share is £28
From the question, we have
David and Vicky share £36 in the ratio 2:7.
David share = £36 *2/9 = £8
Vicky share = £36 *7/9 = £28
Multiplication:
The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.
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JMP made a profit of $85,000 last year. If the profit margin increased by 20% this year what is the amount of profit made by JMP
Answers
The amount of profit made by JMP is 102000.
Given,
In the question;
JMP made a profit of $85,000 last year.
If the profit margin increased by 20% this year.
To find the amount of profit made by JMP.
Now, According to the question:
Based on the given condition:
Formulate:
= 85000 x (20% + 1)
Calculate;
85000 x (0.2 + 1)
Calculate the sum or difference
85000 x 1.2
= 102000
Hence, The amount of profit made by JMP is 102000.
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What is the equation of this line in slope intercept form?
2x+3y=−6
Answers
3y=-2x -6
y = -2/3x - 2
A combination lock uses 4 numbers, each of which can be 0 to 32. If there are no restrictions on the
numbers, how many possible combinations are available?
Answers
If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.
What is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Here,
There are 4 numbers needed for the combination and one can pick between 0 and 32.
This means that there are 33 numbers that can be used for the lock including 0.
The number of possible combinations is:
= Number that can be used with no restrictions on the number combination lock limit
= 33 ⁴
= 1,185,921 combinations
Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.
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A cube box is 20 cm x 20 cm x 20 cm. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.
Answers
The surface area of the largest size sphere that can fit in this box is 400π
What is the surface area of the sphere?
The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.
Here, we have
The diameter of the biggest sphere will be equal to the side of the sphere.
radius = 20/2
= 10
The surface area of the sphere = 4πr²
=4π(10)²
= 400π
Hence, the surface area of the largest size sphere that can fit in this box is 400π.
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An Olympic-size swimming pool holds approximately 6×105 gallons of water. The capacity of this swimming pool is between which interval?
Answers
The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.
What is the capacity?Capacity refers to the product of the length, width, and height of a three-dimensional object or space.
The capacity of an object means the same as its volume.
Olympic-size swimming pools have the following standard dimensions:
Length = 50 m
Width = 25 m
Height = 2 m
Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)
= 660,000 gallons (2,500 x 1,000 ÷ 3.785)
An interval estimate shows the lower and upper limits.
6 x 105 gallons = 630 gallons
Thus, the capacity of the swimming pool is Option B.
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Question Completion with Answer Options:A. 100 gallons to 500 gallons
B. 500 gallons to 1,000 gallons
C. 1,000 gallons to 1,500 gallons
D. 1,500 gallons to 2,000 gallons
-8b+ 2 + 6b = -3b + 7
Answers
Answer:
b = 5
Step-by-step explanation:
Add 8b to both sides :
2+6b = 5b+7
Subtract 5b from both sides :
2+b = 7
Subtract 2 from both sides :
b = 5
Let's check :
-8(5) + 2 +6(5) = -3(5) + 7
-40 + 2 + 30 = -15 + 7
-38 + 30 = -8
-8 = -8
Correct
Hope this helped and have a good day
Answer:
b = 5
Step-by-step explanation:
to solve this you must first combine like terms
-8b + 2 + 6b = -3b + 7
combine (add) -8b and 6b
that makes -2b
-2b + 2 = -3b + 7
now add 3b to both sides to put b on one side
-2b + 2 + 3b = -3b + 3b + 7
b + 2 = 7
now subtract 2 to both side
b + 2 - 2 = 7 - 2
b = 5
that is your answer
Compute the value of the expression C (8,5)
Answers
The value of C (8,5) is 56.
What is the combination?A combination is made up of n different items that are taken one at a time without repeating itself.
The given expression is C(8,5).
The expression C (8,5) can be denoted as ₈C₅.
The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)
Therefore, the value of ₈C₅ is:
₈C₅ = 8!/( (8-5)! 5 !)
= 8!/( 3! ×5!)
= (8×7×6×5!)/( 3! ×5!)
= (8×7×6)/(3!)
= (8×7×6)/(6)
= 8×7
=56
Hence, the value of C (8,5) is 56.
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6th grade problem i need help
Answers
Answer:
Step-by-step explanation:
1. First multiply to get the number of hours for 5 painters.
5*21= 105 minutes for 5 painters.
2. Divide by 7 for hours taken for the 7 painters!
105/7=15
3. Answer=15 hours
Because you would need to do a proportion table and do 7x21=147
147/5= 29.4
Round it??
A street light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?
Answers
The tip of his shadow moving when he is 50 ft from the pole is 10ft/s
What is meant by differentiation?The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions
I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.
(y-x)/y =6/15
15(y-x)=6y
9y=15x
y=(5/3)x
Differentiating both sides with respect to t,
dy/dt=(5/3)dx/dt
We know that, dx/dt= 6 ft/s
((5/3)*6=10 ft/s
Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s
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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8. What are the two numbers?
Answers
The first number is 3 and the second number is -5.
According to the question,
We have the following information:
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.
Now, let's take the first number to be x and the second number to be y.
So, we have the following expressions:
6x+4y = - 2
6x = -2-4y ...(1)
6x+2y = 8
Putting the value of 6x from equation 1:
-2-4y+2y = 8
-2-2y = 8
-2y = 8+2
-2y = 10
y = -10/2
y = -5
Putting this value of y in equation 1:
6x = -2-4y
6x = -2-4*(-5)
6x = -2+20
6x = 18
x = 18/6
x = 3
Hence, the first number is 3 and the second number is -5.
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What is the correct answer
Answers
Answer: See coordinate graph below.
Step-by-step explanation: The black point is the original point and the red point is the reflected point.
Ordered pair of the reflected point:
A': (1, -4)
Let me know if this is right! :)
Which of the following is the inverse of f(x) =
2x+4/3
Answers
By using the concept of function, it can be calculated that
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, the function is
[tex]f(x) = 2x + \frac{4}{3}\\[/tex]
Let f(x) = y
[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]
6x + 4 = 3y
6x = 3y - 4
[tex]x = \frac{3y - 4}{6}[/tex]
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
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there are three consecutive odd integers such that if the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. find the sum of the first and second
Answers
The sum of the first and second integer is 44.
How to illustrate the information?Let the numbers be x, x+2 and x+4.
If the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. This will be:
2(x + 2 + x + 4) - (x + 2) = x + 52
2(2x + 6) - (x + 2) = x + 52
4x + 12 - x - 2 = x + 52
Collect like terms
4x - x - x = 52 - 12 + 2
2x = 42
Divide
x = 42/2
x = 21
Second Integer = x + 2 = 21 + 2 = 23
Third integer = x + 4 = 21 + 4 = 25
Sum = 21 + 23 = 44
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During the WMS Presidential elections, candidate #1 received 75 votes whereas candidate #2, who
promised better lunches and longer seminar class times received 165 votes. What is the percentage
difference between the WMS Presidential Candidate # 1 and WMS Presidential Candidate # 2's total
number of votes?
Answers
Answer: candidate 2 has 90 votes
Step-by-step explanation:
165-75=90
Given the inequality 4x ≤ 28, determine the value of x.
Answers
Step-by-step explanation:
Given the inequality 4x ≤ 28, determine the value of x.
4x ≤ 28
divide both sides by 4:
4x/4 ≤ 28/4
x ≤ 7
set builder notation: (-∞, 7]
answer:
The value of x is 7.
Step-by-step explanation:
4x ≤ 28 | divide both sides by 4
4x / 4 = x and 28 / 4 = 7
therefore, x ≤ 7
For every pull-up Mark completes, he does 4 push-ups. If he did 48 push-up, how many pull-ups did he do?
Answers
Answer:
Mark did 12 pull ups
Step-by-step explanation:
48 / 4 = 12
Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?
-51
63
119
175
Answers
Answer: 119
Step-by-step explanation:
(4^2+1)(3*4-5)
=(16+1)(12-5)
=17*7
=119
Answer:
g(4) = 119
Step-by-step explanation:
g(x) = (x² + 1) (3x - 5)
Substitute x for 4 in the equation
g(4) = (4² + 1) (3(4) - 5)
g(4) = (16 + 1) (12 - 5)
g(4) = (17) (7)
g(4) = 119
Hence, the value of g(4) is 119
Assume that a hat contains four bills: a $1, a $5, a $10,
and a $20 bill. Two bills are to be selected at random with
replacement. Find the probability that both bills are $20 if
the first selected is a $20 bill?
The probability that both bills are $20 if the first selected is
a $20 bill is
(Simplify your answer. Type an integer or a fraction.)
Answers
The probability that both bills are $20 if the first selected is a $20 bill is 1/16.
What is probability ?The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to occur P (E) =
[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]
Hat contains four bills: a $1, a $5, a $10, and a $20 bill.
Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;
After Replacement,
Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;
So, the probability that both bills are $20 if the first selected is
a $20 bill = 1/4 * 1/4 = 1/16,
Hence we get 1/16 as the probability of getting both bills of $20.
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HELPPP FOR BRAINLEST????
Answers
Answer:
[tex]2,8,14,20[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:
[tex]a_n=6n-4[/tex]
Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].
the variables x and y are related such that each time x decreases by 5 , y increases by 2 .if y is a positive value when x=0. which of the following equations could express the relationship between x and y
Answers
The linear function that could express the relationship between x and y is given as follows:
y = -0.4x + b, b > 0.
What is a linear function?The slope-intercept representation of a linear function is given by the rule presented below as follows:
y = mx + b
The coefficients of the function, along with their meaning, are listed as follows:
m is the slope of the function, being obtained by the division of the change in y by the change in x.b is the y-intercept of the function, representing the values of the output variable y when the input variable x assumes a value of zero.In the relationship, we have that each time x decreases by 5 , y increases by 2, hence the slope is obtained as follows:
y = -2/5 = -0.4.
The y-intercept is positive, hence the definition of the function is given as follows:
y = -0.4x + b, b > 0.
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