The distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.
Two points J(-2 , 6) and K(1 , 4) are given .
We have to find out the distance between two points.
What is the distance formula ?
The distance formula is [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] where two points are ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]).
As per the question ;
J ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) = J (-2 , 6) and K ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = K (1 , 4)
and
The distance formula is ;
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex]
So ,
The distance between points J(-2 , 6) and K(1 , 4) will be ;
= [tex]\sqrt{(-2-1)^{2} + (6-4)^{2} }[/tex]
= [tex]\sqrt{(-3)^{2} + (2)^{2} }[/tex]
= [tex]\sqrt{(9)+ (4)}[/tex]
= √13
= 3.6 ( round to nearest tenth)
Thus , the distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.
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Simplify each expression. 3[2(x-3)+2]+5(x-3)
The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
According to the given question.
We have an expression 3[2(x - 3) + 2] + 5(x - 3).
To simplify the above expression we will use the distributive law and add and subtract the like terms.
Therefore,
3[2(x - 3) + 2] + 5(x - 3)
= 3[2x - 6 + 5x - 15] (distributive rule)
= 3[7x - 21] (adding the like terms)
= 21x - 63
Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
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1 orange tree grows 3 oranges. How many oranges trees will grow 15 oranges? (its for my cousin ;-;)
Answer:
Step-by-step explanation:
t = number of trees per 3 oranges
3t = 15
3t/3 = 15/3
t = 5 trees
5. A rock is thrown straight up from a 224-foot tall cliff. The height of the rock as a
function of time is given by the equation h(t) = -16t² + 80t+224. How many
seconds until the rock hits the ground?
By finding the positive root of the quadratic equation, we conclude that the rock will hit the ground 7 seconds after it is thrown.
How many seconds until the rock hits the ground?
We know that a rock is thrown from a cliff whose height is 224 ft. And the equation that models the height of the rock as is the quadratic equation:
h(t) = -16t² + 80t + 224
The rock will reach the ground when its height is equal to zero, so what we need to find is the positive root of the quadratic equation, so what we need to solve is:
-16t² + 80t + 224 = 0
Solving it we get:
t = (-80 ± √(80² - 4*(-16)*224)/(2*-16)
t = (-80 ± 144)/(-32)
The positive solution is:
t = (-80 - 144)/(-32) = 7
This means that the rock will hit the ground 7 seconds after it is thrown.
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Kelly is designing a new quilt. It will be made of squares that are sewn together at the sides with a circle sewn on top of each square. a. Kelly decides that the quilt will be a rectangle 7ft 4in by 6ft 5in. How many squares will she need to make for the quilt? Round the answer to the nearest tenth, if necessary.
Answer:
14ft 8in by 12ft 10in
Please help!! ;-; I cannot figure this out
to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]
question in the picture
Answers:
14 rides: 52
and
r rides: 3r + 10
Step-by-step explanation:
3(14) + 10
52
Simplify each rational expression. State any restrictions on the variable. x²+4 x+3 / x²-3 x-4
Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.
Solution:
To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X
So,
X+1 = 0
X = -1
X-4 = 0
X = 4
When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables
= (x2+4x+3)/(x2-3x-4)
= (x+1) (x+3)/(x+1) (x-4)
Now cancel the common factor (x+1)
= x+3x-4
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Find the future value and interest earned if $8704.56 is invested for 9 years at 5% compounded (a) semiannually and (b) continuously.
The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.
The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.
What is the future value and interest earned compounded semiannually and continuously?Compound interest is mathematically expressed as;
A = P(1 + r/n)^nt
Given the data in the question;
Principal P = $8704.56Annual rate r = 5% = 5/100 = 0.05Time t = 9 yearsCompounded n = (a) semiannually and (b) continuouslyAccrued amount and interest = ?a) Determine the accrued amount and interest when compounded semiannually ( n = 2 )
A = P(1 + r/n)^nt
A = 8704.56(1 + 0.05/2)^( 2× 9 )
A = 8704.56(1 + 0.025)¹⁸
A = 8704.56(1.025)¹⁸
A = 8704.56(1.025)¹⁸
A = $13,576.14
Note that; A = Principal + Interest.
Interest = $13,576.14 - $8704.56 = $4,871.58
b) Determine the accrued amount and interest when compounded continuously.
A = P × e^(r × t)
A = 8704.56 × e^(0.05 × 9)
A = 8704.56 × e^0.45
A = $13,651.47
Note that; A = Principal + Interest.
Interest = $13,651.47 - $8704.56 = $4,946.91
The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.
The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.
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Find the sum: 435,098 + 37,987
Answer:
473085 is the answer
Step-by-step explanation:
Hope it helps you
What is the probability that a randomly chosen diameter is greater than or equal to 10?
probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)
=0.14+0.02 = 0.16
What is probability?
Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.
Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.
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State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.
Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
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Please can someone help me? It’s due trmw
Answer:
Yes OFC
Step-by-step explanation:
As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height
Which angles are obtuse?
D
AB
C
Check all that apply.
A. ZMLK
B. ZGFE
C. ZDBC
D. ZOBA
K
G
24
H
PREVIOUS
M
SUBMIT
Answer:
dbc
Step-by-step explanation:
thats the only one that is obtuse
The depth and the corresponding pressure form an arithmetic sequence, where the depth
represents the number of the term and the corresponding distance represents the value of
the term. What is the pressure, in pounds per square inch, that a scuba diver will
experience when they are 130 feet underwater?
Answer:
40 psi
Step-by-step explanation:
We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth
The data is given from depth of 40 feet
At 40 feet, pressure = 10 psi
At 55 feet, pressure = 15 psi
At 70 feet pressure = 20 psi
We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]
But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi
So the equation that connects depth (d) and pressure (p) is:
[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]
If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3
Hope that helps
Type in one, none or infinite
What is 4x -2 = -12
[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]
28-6x+4=30-3x what is the answer ?
Answer: x=2/3
Step-by-step explanation:
A triangle has vertex coordinates (0,0) and (a, 0) . If the coordinates of the third vertex are in terms of at, and the triangle is isosceles, identify the coordinates and position the triangle on the coordinate plane.
The coordinate of another point will be (a/2,y) where y can be any value.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
An isosceles triangle is a triangle whose two sides are equal.
Let's say AB = AC
So,
Distance associate to AB = Distance associate to AC
(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²
x² + y² = (x - a)² + y²
x = a/2
So the coordinate of the third vertex is (a/2,y)
Hence "The coordinate of another point will be (a/2,y) where y can be any value".
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Round 1.602 to the nearest
whole number.
Answer:
2
Since the numbers after the decimal are above 500 , thereby rounding it to nearest whole number is 2.
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 10+7+4+ . . . ; n=5
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
The given arithmetic series is 10+7+4+ . . .
The summation notion of given series is ∑10-3n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=5, [tex]a_{1}[/tex] = 10
To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .
[tex]a_{5} = a_{1} + (n-1)d[/tex]
d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{5}[/tex] = 10 + (5-1)(-3)
[tex]a_{5}[/tex] = 10-12 =-2
On substituting values in sum of arithmetic series formula, we get
[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
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The equation 8x − 12 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. what is the distance, in miles, between the cars? x = 48 x = 30 x = 3 x = 1
Answer:
its option C: x = 3
Step-by-step explanation:
The distance between the cars, x = 3 miles
The equation representing two cars traveling in opposite directions is given by, 8x-12 = 4x,
where 'x' is the distance (in miles) between the cars.
We need to find 'x'.
The equation given is a linear equation in x. So we will solve for 'x'.
8x-12 = 4x
⇒ 8x-4x = 12
⇒ 4x = 12
⇒ x = 12/4
⇒ x = 3
So the distance between the cars = 3 miles
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HELP ME WITH THIS QUESTION PLS
Answer:
49π in²
Step-by-step explanation:
Formula for Area of a Circle: A = πr²
The image shows the radius (r) = 7in
A = πr² → A = π(7)²→ A = π(49)
A = 153.94 in²
Step-by-step explanation:
Area of circle with radius of r is given by:
[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]
Solve each system by substitution.
4y - 6 = 2x , y - 3x = 9
Using substitution method, the solution of the given system of equations is (-3,0)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
4y - 6 = 2x ............ (1)
y - 3x = 9 .............. (2)
We need to find the solution using substitution method.
In equation (2), add 3x to both sides:
y - 3x + 3x = 9 + 3x
y = 9 + 3x ........ (3)
Substitute y = 9 + 3x into equation (1):
4y - 6 = 2x
4.(9 + 3x) - 6 = 2x
36 + 12x - 6 = 2x
12x - 2x = 6 - 36
10x = -30
x = -3
Substitute back x = -3 into equation (3)
y = 9 + 3x
= 9 + 3.(-3)
= 9 + (-9) = 0
Hence, the solution is (-3, 0)
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What 8.1+2.53 with shown work
Answer:
10.63
Step-by-step explanation:
Which angles of rotation will map the figure onto itself? Explain your reasoning
and/or show your work.
Square each of the binomials and place them into perfect square trinomial form, then subtract the trinomial‘s
Answer: #11? y^2-14 #12 m^2-64
Step-by-step explanation:
Factor each of the binomials: (2y-5)^2 -> 2 (y-5) (y+5) and (y+6)^2 -> (y+6) (y-6) Multiply the each factored binomial into perfect squares: (since the second numbers are opposites it will be binomials since they cancel out) 2 (y-5) (y+5) would be 2y^2-10y+10y-50 or 2y^2-50 and (y+6) (y-6) will become y^2-6y+6y-36 or y^2-36 Subtract the binomials: Remember when you are subtracting polynomials you are changed the sign to addition and invert the operations of the second polynomial (so if the term was positive it would be negative and vice versa) so it would be 2y^2-50 + ‐y^2+36 and that would equal y^2-14- For the second question you apply the same steps to #12 to get m^2-64
Which of the following functions is graphed below?
Answer:
The answer is A because both equations are true
[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]
An angle is a figure formed by two rays with a common initial point called a
of the angle.
An angle is a figure formed by two rays with a common initial point called a of the angle.
What does a math angle mean?
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.What is type of angle ?
There are three different types of angles in geometry: acute angles, which range from 0 to 90 degrees. Right angle, or a 90° angle. A 90–180 degree angle is referred to as an obtuse angle. a 180 degree angle, or a straight angle.What is acute angle?
Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.Learn more about acute angle
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The graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9). What is the value of y in the equation y= f(2)
The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2
Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).
The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.
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Determine the smallest integer value of x in the solution of the
Following inequality.
2x - 82 -11
The smallest integer is 1 and solution is (₋1)
Given, the inequality is 2x ₋ 8 ≥ ₋11
The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. A statement that two things are not equal is what is meant by the word "inequality." It's possible for one of the items to be more than, smaller than, equal to, or equal to the other things.
now add 8 on both sides.
2x ₋ 8 ₊ 8 ≥ ₋11 ₊ 8
2x ≥ ₋3
dividing both sides by 2.
2x/2 ≥ ₋3/2
⇒ x ≥ ₋3/2
₋3/2 is not an integer.
hence the smallest integer value of x is 1, and solution is (₋1)
Hence we get the integer value as 1.
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Solve the equation x²+10 x+40=5 by completing the square.
So we are provided with the equation,
x2 + 10x + 40 = 5
To simplify it, we will first reorder the terms,
40 + 10x + x2 = 5
Now we will solve the equation to find the value of the unknown variable that we declared here as x.
40 + 10x + x2 = 5
Solving for variable 'x.'
40 + -5 + 10x + x2 = 5 + -5
We will combine similar terms; the variables and the constants.
40 + -5 = 35
35 + 10x + x2 = 5 + -5
Combine the like terms again:
5 + -5 = 0
35 + 10x + x2 = 0
Adding -35 on both sides
35 + 10x + -35 + x2 = 0 + -35
35 + -35 + 10x + x2 = 0 + -35
35 + -35 = 0
0 + 10x + x2 = 0 + -35
10x + x2 = 0 + -35
0 + -35 = -35
10x + x2 = -35
The x term is 10x.
Take half its coefficient (5) to make it a perfect square.
Square it (25) and add it to both sides.
10x + 25 + x2 = -35 + 25
25 + 10x + x2 = -35 + 25
-35 + 25 = -10
25 + 10x + x2 = -10
Perfect square on the left side:
(x + 5) (x + 5) = -10
We can see that the Square root of the right side can’t be calculated.
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