The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
The given points are (2,3) and (5, -2)
The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex] [tex](x_{2} ,y_{2} )[/tex] is
D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]
For evaluating the distance between the points (2,3) and (5, -2)
The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]
Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.
In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.
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find the value of b/a if a+1/b-1=5/1 and a-1/b+1=1/1
Answer:
1/2
Step-by-step explanation:
You want the value of b/a when (a+1)/(b-1)=5/1 and (a-1)/(b+1)=1/1.
SolutionThe latter equation tells you ...
a -1 = b +1
b = a -2
Then the first equation tells you ...
a +1 = 5(b -1)
a +1 = 5(a -2 -1) substitute for b
a +1 = 5a -15 . . . . eliminate parentheses
16 = 4a . . . . . . . . add 15 -a
4 = a . . . . . . . . . divide by 4
b = a -2 = 4 -2 = 2 . . . . find the value of b
b/a = 2/4 . . . . . . . . . . find the desired ratio
b/a = 1/2
Write the given expression as an algebraic expression in x. tan(2 sin^-1(x))
The trigonometric ratio tan(2 sin⁻¹(x)) is expressed as 2sec(x)
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In the question given, we have;
tan(2 sin⁻¹(x))
tan = sin / cos
sin/cos(2 * 1/sin x)
The expression becomes 2/cosx or 2cos⁻¹(x)
But cos⁻¹ = sec
tan(2 sin⁻¹(x)) = 2sec(x)
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10. Sean promotes certain brands on his social media page for compensation. His monthly profit can be modeled using
the quadratic function p(x) = -0.00425x² +7z-1000, where p(x) is the amount of profit earned over
number of days. The graph of the function is shown. Use the graph to find the zeros of the function and interpret
them in context.
Answer:
The zeros are (158.017, 0) and (1489.042, 0)
The profit earned in 158.017 days and 1489.042 days is equal to 0. This means that Sean only earns money (makes a profit) when the amount of days he promotes a brand is greater than 158.017 but less than 1489.042 days.
Helen had $330 in her savings account when Vince
opened a savings account with zero
dollars.
Helen deposited $30
into her account each week for x week;
Vince deposited $50 into his account
each week for x weeks.
The accounts did not earn
interest.
Which inequality represents this situation when the amount of money in Helen's account wa
greater than the amount of money in Vince's account?
Answer:
Step-by-step explanation:
50x < 330 + 30x
Q12) 150 Chinese Yuan is about $21 US dollars. How much (in US dollars) will an item cost in 700 Chinese Yuan?
Answer:
Step-by-step explanation:
Set up the equation:
21/150=x/700
Cross multiply 150*x and 21*700
14700=150x
Divide each side by 150
98=x
An isosceles triangle with congruent sides of length
49.3 inches has a perimeter of 121.7 inches Find the
length of the base.
The length of the base is 22.1
An isosceles triangle with congruent sides of length 49.3 inches has a perimeter of 121.7 inches
An triangle is said to be isosceles if two sides of the trainagle have same length.
The two sides of this triangle is congurent that is they have same length = 49.3
perimeter of a triangle is the summation of all three sides.
Perimeter = length + base + length
121.7 = 49.3 + base + 49.3
base = 121.7 - 99.6
base = 22.1
Therefore, the length of the base is 22.1
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(a) The school sells pens for $1.50 and notebooks for $2.50. The equation 1.50x+2.50y=601.50x+2.50y=60 describes the number of pens, x, and notebooks, y, that you can but for $60. Part A: Find the x- and y-intercepts. Tell what they represent. x-int: What does the x-intercept represent in the context of the problem? (b) BoldItalicUnderlineAlign Align Left Align Center Align Right Align Justify Increase IndentIncrease IndentSpecial Characters $$ 0 Words (c) y-int: What does the y-intercept represent in the context of the problem?
The x-intercept of the equation, 1.50 x + 2.50y = 60, is x = 40
The y-intercept of the equation, 1.50 x + 2.50y = 60, is y = 24
Determining the x-intercept and y-intercept of an equationFrom the question, we are to determine the x-intercept and y-intercept of the given equation.
The given equation is
1.50 x + 2.50y = 60
The x-intercept is the point where y = 0
and
The y-intercept is the point where x = 0
Determining the x-intercept
1.50x + 2.50y = 60
Put y = 0
1.50x + 2.50(0) = 60
1.50x + 0 = 60
1.50x = 60
x = 60/1.50
x = 40
The x-intercept is x = 40
Determining the y-intercept
1.50x + 2.50y = 60
Put x = 0
1.50(0) + 2.50y = 60
0 + 2.50y = 60
2.50y = 60
y = 60/2.50
y = 24
Hence, the y-intercept is y = 24
The x-intercept represent the number of pens that could be bought for $60 when one is not buying any notebooks.
The y-intercept represent the number of notebooks that could be bought for $60 when one is not buying any pens
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Logan's family drinks a total of 12 gallons of milk every 6 weeks.
a. How many gallons of milk does the family drink per week?
Answer: 2 gallons
Step-by-step explanation:
If they drink 12 gallons of milk every 6 weeks, to find how many gallons they drink per week, you need to divide the number of gallons by the time.
So,
12/6 = 2 gallons
Thus, they drink 2 gallons per week.
What is 4x6x26x376x466 equal to
see picture for question
The percentage error is 0.67%
What is Linear approximation ?
A linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
The formula is
L(x) = f(a) + f'(a) (x - a)
Given,
y = sin(2x)
Δx = 0.1 at x = 0
y'(x) = dy/dx = 2 cos 2x
As, x = 0
y'(0) = 2 cos 0
we know, cos 0 = 1
y'(0) = 2
Δy = y'(x) * Δx
= y'(0) * Δx
= 2 * 0.1
Δy = 0.2 (Approx value)
Exact value of Δy = sin(2 * 0.1) - sin 0
= sin(0.2) - 0
= 0.19867
% error = [ (Exact value - Approx value) / Exact value ] * 100
= [ (0.2 - 0.19867) / 0.19867 ] * 100
= 0.66945 or 0.67%
Hence, the percentage error is 0.67%
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explain what a,h, and k do to transform the parent absolute function y=|x| to the function y= a|x|…
The a ,h and k values affect the parent absolute function ,by altering the the size , causing horizontal and vertical movements respectively.
How do the a , h and k values affect the function?a )a values
a values affect the size of the graphed parent absolute function and they have a scalar factor.When a is greater than 1 , we have a vertical stretch (Taller appearance )and a horizontal compression (Thinner appearance).When a is between 0 and 1 , we have a vertical compression( Shorter appearance) and a horizontal stretch ( wider appearance).b ) h values
h values cause left or right movement of the graph, which is known as the horizontal shift or translation.When h is negative, the graph moves right.When h is positive , the graph moves left.c ) k values
k values cause up and down movement ,which is known as the vertical shift or translation.When k is negative, the graph moves down.When k is positive , the graph moves up.To learn more about parent absolute function, refer:
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Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3. What is the smallest total number of pets each could be walking?
The smallest total number of pets each could be walking is 2.
Given:
Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3.
from the given statements:
Juan pets groups = 9
Malia pets groups = 3
so they both can same total number of pets is maximum 3.
so minimum number for each is 1.
Total = 1+1
= 2
Therefore The smallest total number of pets each could be walking is 2.
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SAFSADFASDSADSA HELPPPPPPP
Answer:
y = - [tex]\frac{10}{3}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{10}[/tex] x - 8 ← is in slope- intercept form
with slope m = [tex]\frac{3}{10}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{10} }[/tex] = - [tex]\frac{10}{3}[/tex] , then
y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation of line h
to find c substitute (3, - 9 ) into the partial equation
- 9 = - 10 + c ⇒ c = - 9 + 10 = 1
y = - [tex]\frac{10}{3}[/tex] x + 1 ← equation of line h
Wha is the y intercept of the line given by the equation below y=4x - 6
State what additional information is required in order to know that the triangles are congruentfor the reason given.
44 POINTS !
The additional information is required in order to know that the triangle are congruent is, GW ≅ WX.
What is congruent triangles?
If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.
We have to show that the the triangles ΔVWX and ΔEWG are congruent by using the AAS (angle, angle, side) criteria.
From the given reasons,
∠V ≅ ∠E
∠VWX ≅ ∠EWG
From this the AA criteria is satisfied.
We want sides of the triangle are congruent.
From the figure, GW ≅ WX
Therefore, by AAS the two triangles ΔVWX and ΔEWG are congruent.
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in a class of 50 student 35 are girls what is the probability that a student selected at random is a boy
Find the y intercept
Because there is a slope of 0, the graph is a horizontal line.
Plug into the slope-intercept form: y=mx+b
Where
m = slope & b = y-intercept
m=0
y=-1
So,
y=(0)x+(-1)
therefore your final answer is:
y=-1
Find the final balance earned in an account with $845 invested at 4% annual simple
interest for 18 months.
The final balance is $895.7.
What is simple interest?
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Interest = principal ×rate× time
Given, principal = $845
rate = 4%
time = 18 months = 3/2 years.
After substituting the values, we get
Interest = 845(4)(3/2)/100
= 50.7
Final balance = initial balance + interest
Therefore,
Final balance = 845 + 50.7
= $895.7
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