Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]then, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}[/tex]The measures of the exterior angles of an octagon are x°x°, 2x°2x°, 3x°3x°, 4x°4x°, 5x°5x°, 6x°6x°, 9x°9x°, and 10x°10x°. Solve for xx.
Answer:
x=10
Step-by-step explanation:
Given: =The exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°,8x°.
Then, x°+2x°+3x°+4x°+5x°+6x°+7x°+8x° =360°
⇒ 36x = 360
⇒ x= 10
Find x of the triangle
Answer:
x=65
Step-by-step explanation:
47+68+x=180
x=65
:]
Answer: 65 = x
Step-by-step explanation:
1) First find the mini triangles, left and right angles
We will be calling the left one A and the right one B.
2) Next use triangle sum to find B.
62 + 50 + b = 180
b=68
3) Use triangle sum again to find A.
53 + 80 + a = 180
a = 47
4) Use triangle sum to find the top mini angle.
47 + 68 + c = 180
c = 65
5) Since x is in the vertical angle of c, they are equal
c = x
65 = x
(2x^2+4x-7)(3x-1) use a table
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
Given,
The binomials; (2x² + 4x - 7) (3x - 1)
We can use FOIL method to solve this;
FOIL method;
Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.
Here,
(2x² + 4x - 7) (3x - 1)
= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7
= 6x³ + 12x² - 21x - 2x² + 4x - 7
= 6x³ + 10x² - 17x - 7
That is,
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
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How can you determine which of the numbers below is greatest 13/20, 5/8, 3/5, 3/10
Answer:
13/20 is the greatest because it is equal to 65% of 100%.
Step-by-step explanation:
5/8 = to 12.5x5=62.5%. 3/5= 20x3=60%. 3/10 = 10x3=30%. So 13/20 is the greatest.
when was the temperature decreasing
Answer:
I need you to be more specific and answer options. That is the only way anyone can answer this question.
Step-by-step explanation:
the population of rabbits on an island is growing exponential in the year 2008, the population of rabbits was 7100 and by the year 2013 the population had grown to 8900 . Predict the population of rabbits by the year 2023 to the nearest whole number
The population of rabbits by the year 2023 is 13985.
What will the population be?We have to use the following exponential function. This will be:
y = a b^t
In 2008 means, t=0
So we have 7100 = a b^0
a = 7100
y = 7100b^t
In 2013 means t = 2013-2008 =5
8900 = 7100 b⁵
b⁵ = 89/71
b = 1.046
So the equation will be
y = 7100 (1.046)^t
For 2023, t=2023-2008= 15
y = 7100(1.046)¹⁵
= 13985
The population is 13985.
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On a standardized exam, the scores are normally distributed with a mean of27 and a standard deviation of 4. Find the Z-score of a person who scored 17on the exam.
mean = 27
standard deviation = 4
n = 17
z = ?
[tex]\begin{gathered} \text{ z = }\frac{X\text{ - }\mu}{\sigma} \\ \text{ z = }\frac{27\text{ - 17}}{4} \\ \text{ z = }\frac{10}{4} \\ \text{ z = 2.5} \end{gathered}[/tex]Result :
z = 2.5
Find x of the triangle
Answer: x = 22
Step-by-step explanation:
We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.
(6x - 7) = (2x) + (103 - x)
6x - 7 = 2x + 103 - x
6x - 7 = x + 103
5x = 110
x = 22
The point-slope form of a line that has a slope of 2/3 and passes through point (6,0) is shown?
y-0=2/3(x-6)
What is the equation in slope-intercept form?
y-2/3x-12
y-2/3x-6
y-2/3x-4
y-2/3x-8
Answer:
See below
Step-by-step explanation:
y-0=2/3(x-6) (expand L side)
What is the equation in slope-intercept form?
y = 2/3 x - 4
f(x) = −3|x −1| + 4
Answer:
Find the Inverse f(x)=3x-1/4. f(x)=3x−14 f ( x ) = 3 x - 1 4. Step 1. Write f(x)=3x−14 f ( x ) = 3 x - 1 4 as an equation. y=3x−14 y = 3 x - 1 4.
Step-by-step explanation:
WILL GIVE BRAINLIEST
find all values of x for which (f∘g)(x)=(g∘f)(x).
f(x)=x/(x+2), g(x)=x^2
Step-by-step explanation:
(f○g)(x) means f(g(x))
(g○f)(x) means g(f(x))
f(g(x)) means to use the expression of g(x) as input to f(x). so, we replace all simple x in f(x) by g(x) = x².
f(g(x)) = x²/(x² + 2)
using the same principle we get for
g(f(x)) = (x/(x + 2))² = x²/(x + 2)²
now we need to solve
x²/(x² + 2) = x²/(x + 2)²
let's multiply both sides with both denominators :
x²(x + 2)² = x²(x² + 2)
x²(x² + 4x + 4) = x²(x² + 2)
so, one solution is clear : x = 0.
because then we have 0 = 0.
for x <> 0 we can divide both sides by x² and get
x² + 4x + 4 = x² + 2
4x + 4 = 2
4x = -2
x = -2/4 = -1/2
both expressions are equal for x = 0 and x = -1/2
Write the equation of a line in slope-intercept form that goes through points (1,5) and (9, -6).
Answer:
y-21 = 4(x+9)
Write a polynomial P(x) of degree 4 and with zeros 1, 3/2, (which of multiplicity one) and 0 (of multiplicity 2).
Answer
The polynomial is
P(x) = 2x⁴ - 5x³ + 3x²
Explanation
We are told to write a polynomial of degree 4 with zeros (roots)
x = 1
x = (3/2) = 1.5
x = 0
x = 0 (multiplicity of 2 means it appears twice)
So, we can piece together the polynomial
P(x) = (x - 1) (x - 1.5) (x) (x)
We can write this as
P(x) = x² (x - 1) (x - 1.5)
= (x³ - x²) (x - 1.5)
We can multiply through by 2 to turn the 1.5 into a whole number
P(x) = (x³ - x²) (2x - 3)
= x³ (2x - 3) - x² (2x - 3)
= 2x⁴ - 3³ - 2³ + 3x²
= 2x⁴ - 5x³ + 3x²
Hope this Helps!!!
x 8 x 7 x 5 x 6 a planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. the owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. what will be the new length of this building?
The new length of the building will be 110 feet.
Volume of Cuboid:
Volume of cuboid is
V = length x breadth x height cubic unit
Given,
The building was going to be 100 feet long, 75 feet deep, and 30 feet high.
Therefore, the volume will be:
= 75 × 100 × 30 ft³
= 225000 ft³
Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.
There was an increase by 10%,
New volume will be,
V' = 225000 + (10% × 225000)
= 247500 ft³
Therefore, the new length will be:
as,
Volume = length x breadth x height
length = Volume/ (breadth x height)
New length will be
= 247500/(30 × 75)
= 110 feet
Thus the new length of the building will be 110 feet.
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Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and
includes the point (-4, 14) on the boundary?
Answer:
(a) y < 3(x +2)² +2
Step-by-step explanation:
You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).
Vertex formThe vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...
y = a(x -h)² +k
For the given vertex (-2, 2), the boundary line equation is ...
y = a(x -(-2))² +2 = a(x +2)² +2
Scale factorThe value of 'a' is positive when the curve opens upward.
Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).
The only reasonable answer choice is ...
y < 3(x +2)² +2
On a tour of a old gold mine, you find a nugget containing 0.82 ounce of gold. Gold is worth $1323.80 per ounce. How much is your nugget worth
For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.
As given in the question,
On a tour of a gold mine,
Ounce of gold contained by nuggets found in the mine = 0.82 ounce
Worth of gold per ounce = $1323.80 per ounce
Worth of nuggets containing 0.82 ounce of gold
Worth of 1 ounce of gold = $1323.80
⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )
= $1085.516
Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.
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Help!!! With this math question
Answer:
QPR SAS
Step-by-step explanation:
As you can see. Hope it can help
10-2y=46 solve for y
Answer:
-18
Step-by-step explanation:
first subtract ten from both sides now you're left with -2y=36 ,lastly divide both sides by -2 and you're left with y= -18
If the area of a square is 139cm squared, what would the length of the side be?
The length of the side is 11.79cm
How to find the area of the square?The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.
On a sheet of paper, draw a square with a pencil.
It is a two-dimensional figure.
The area of a shape on paper is the area it occupies.
Area of a square i= 139cm^2
a^2 = 139
The length of the side (a) = [tex]\sqrt{139}[/tex] = 11.79cm
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-24 = -12v solve for v and simplify as much as posible
Answer:
divide both sides by the coefficient of v which is 12
-24/-12=-12v/-12
-2=v
a rectngular piece of paper measures 96 cm by 84 cm. it is cut into square pieces of equal lenght such that no paper is wasted. what is the maximum lenght of a square?
89 squares will be present.
Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and
its total area is 8064 square centimeters, we may deduce that the maximum square area
[tex]\sqrt[2]{8064}[/tex]
that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.
In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.
How do square roots work?Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.
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. let ???? be a discrete random variable that is uniformly distributed over the set of integers in the range [????, ????], where ???? and ???? are integers with ???? < 0 < ????. find the pmf of the random variables max(0,????) and min(0,????).
Filling in the blanks, I assume you're talking about a random variable [tex]X[/tex] distributed uniformly over the integers [tex]a\le x\le b[/tex]. Let both [tex]a,b>0[/tex] so we can write the support of [tex]X[/tex] as the set
[tex]S = \{-a, -a+1, -a+2, \ldots, -1, 0, 1, \ldots, b-2, b-1, b\}[/tex]
Note that [tex]|S| = a+b+1[/tex], so the PMF of [tex]X[/tex] is
[tex]\mathrm{Pr}(X=x) = \begin{cases}\frac1{a+b+1} & \text{if } x\in S \\ 0 & \text{otherwise}\end{cases}[/tex]
Let [tex]Y=\max\{0,X\}[/tex]. Then
[tex]Y = \max\{0,X\} = \begin{cases}0 & \text{if } X\le0 \\ X & \text{if } X>0 \end{cases}[/tex]
which tells us
[tex]\displaystyle \mathrm{Pr}(Y=0) = \mathrm{Pr}(X\le0) = \sum_{x=-a}^0 \mathrm{Pr}(X=x) = \frac{a+1}{a+b+1}[/tex]
and
[tex]\displaystyle \mathrm{Pr}(Y\neq0) = \mathrm{Pr}(X>0) = \sum_{x=1}^b \mathrm{Pr}(X=x) = \frac b{a+b+1}[/tex]
Hence the PMF of [tex]Y[/tex] is
[tex]\mathrm{Pr}(Y=y) = \begin{cases}\frac{a+1}{a+b+1} & \text{if } y=0 \\\\ \frac b{a+b+1} & \text{otherwise}\end{cases}[/tex]
Let [tex]Z=\min\{0,X\}[/tex]. The same reasoning applies, but this time
[tex]Z = \min\{0,X\} = \begin{cases} 0 & \text{if } X \ge 0 \\ X & \text{if } X < 0 \end{cases}[/tex]
Now
[tex]\displaystyle \mathrm{Pr}(Z=0) = \mathrm{Pr}(X\ge0) = \sum_{x=0}^b \mathrm{Pr}(X=x) = \frac{b+1}{a+b+1}[/tex]
and
[tex]\displaystyle \mathrm{Pr}(Z\neq0) = \mathrm{Pr}(X<0) = \sum_{x=-a}^{-1} \mathrm{Pr}(X=x) = \frac a{a+b+1}[/tex]
so that
[tex]\mathrm{Pr}(Z=z) = \begin{cases}\frac{b+1}{a+b+1} &\text{if }z=0 \\\\ \frac a{a+b+1} & \text{otherwise}\end{cases}[/tex]
Mike and Raymond each read the same book.Mike reads 182 pages in 7 hours.Raymond reads 168 pages in 6 hours. Based on the rates which statement is true? select TWO correct choices
A.Mike reads faster than Raymond.
B.Raymond reads faster than mike.
C.Mike reads 2 more pages than raymond in one hour.
D.Raymons reads 52 pages in 3 hours.
E.Mike can read 13 pages in half an hour.
Answer:
B and c
Step-by-step explanation:
182/7=26
168/6=28
17x-5
16x + 3 what is x
Answer:
x = 8
Step-by-step explanation:
17x-5 = 16x + 3
Step 1: Subtract 16x from both sides.
17x−5−16x=16x+3−16x
x−5=3
Step 2: Add 5 to both sides.
x−5+5=3+5
x=8
The solution to the equation is x = 8.
To solve the equation 17x - 5 = 16x + 3 and find the value of x, we can follow these steps:
Start by simplifying both sides of the equation by combining like terms. Add 5 to both sides to move the constant term to the right side of the equation:
17x - 5 + 5 = 16x + 3 + 5
17x = 16x + 8
Next, we want to isolate the x term on one side of the equation.
Subtract 16x from both sides:
17x - 16x = 16x - 16x + 8
x = 8
Therefore, the solution to the equation is x = 8.
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y=-x+7
Graph it also if you can
Answer:
Hope this helps!!
The speeders soccer team charge $12 to watch each car at a fundraiser car wash. The team collected a total of $672 by the end of the day. How many cars did the team was?
Answer:
they washed 55 cars
Step-by-step explanation:
I did the math good luck
The distance between Q(-1, a) and P(3, -2) is 4√5. Find all possible values of a
The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are 6 and -10.
What is the numerical value of a?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point Q( -1, a )
x₁ = -1y₁ = aPoint P( 3, -2 )
x₂ = 3y₂ = -2Distance D = 4√5To find the numerical value of a, plug the given coordinates into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )
4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )
Square both sides
( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²
( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²
( 4√5 )² = ( 4 )² + ( -2 - a )²
80 = 16 + ( -2 - a )²
80 - 16 = ( -2 - a )²
64 = ( -2 - a )²
( -2 - a )² = 64
Expand the parenthesis
( -2 - a )( -2 - a ) = 64
a² + 4a + 4 = 64
a² + 4a + 4 - 64 = 0
a² + 4a - 60 = 0
solve for a
( a - 6 )( a + 10 ) = 0
a - 6 = 0, a + 10 = 0
a = 6, a = -10
Therefore, the values of a are 6 and -10.
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Calculate the number of students per teacher at West Elementary school
Ok, so
We know that, at West Elementary school, there are 438 students and 22 full-time teachers. We want to know the number of students per teacher. This is:
[tex]\frac{438\text{students}}{22\text{teachers}}=19.91\frac{students}{teacher}[/tex]"Complete the table" can someone help on thi thank you!
Answer:
2000 pounds is 1 ton
6 tons is 12,000
7 tons is 14,000
16,000 pounds is 8 tons
solve for x: square root of 3x-4 = 2 times the square root of x-5
The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.
Given,
The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]
We have to solve this equation to get the value of x.
That is,
[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]
Square both sides to remove square root.
[tex]\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}[/tex]
We get,
3x - 4 = 4 (x - 5)
That is,
3x - 4 = 4x - 20
Here,
20 - 4 = 4x - 3x
Then,
x = 16
That is,
The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.
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