The distance between the two points in simplest radical form is 5.
What is meant by distance between two points?The length of the line segment connecting two points in a plane is the distance between them. The formula for calculating the distance between two places is typically d=((x₂ - x₁)² + (y₂ - y₁)²). This formula is used to calculate the distance between two locations on a coordinate plane or the x-y plane.
In geometry, distances are usually positive unless the points coincide. Consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).
The linear distance between two points is equal to the square root of the sum of the squared x-axis and y-axis distances. To continue with the example, the distance between (3,2) and (7,8) is sqrt (52), or 7.21 units.
Given,
The two points are (7,1), (4,5)
Distance between two points
AB=√(x₂-x₁)²+(y₂-y₁)²
AB=√(4-7)²+(5-1)²
=√3²+4²
=√9+16
=√25
=5
Distance between two points=5
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A deli owner sold 90 sandwiches in one day. Of those sandwiches,
36 were pastrami. What percent of sandwiches sold were NOT
•pastrami with work showing
60 percent of the sandwiches were not pastrami with work showing.
What do you mean by percentage?
percentage, a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified, percentage.
The total number of sandwiches sold by the deli owner is 90
total number of pastrami is 36.
total number of pastrami is 54.
so, the percentage of sandwiches sold that were NOT pastrami is,(54/90)×100
Hence, 60 percent pastrami with work showing.
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1. What are the different methods you can use to find the vertex of a parabola?
2. How can the axis of symmetry formula be used to find the minimum and maximum values?
3. Use the quadratic formula to find the solutions to ^2 + 3 = 2 − 2.
The vertex of your parabola lies at those two coordinates .The axis of symmetry, x is 1, was already discovered.
1. What are the different methods use to find the vertex of a parabola?To locate a parabola's vertex, you must first determine x (or y, if your parabola is sideways) using the axis of symmetry formula. The quadratic equation will then be used to solve for y (or x, if your parabola opens to the side) using that value. The vertex of your parabola lies at those two coordinates.
2. How do you find the maximum or minimum value of axis of symmetry?The axis of symmetry is shown as a line, hence x=1. Since it is the highest or lowest point of the parabola, the vertex of a quadratic equation also serves as its maximum and minimum. We need to do a few things in order to locate the vertex: The axis of symmetry, x=1, was already discovered.
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Bro this is so weird. If Jayden has 19 dollars and idek
Answer:
if i have 19
Step-by-step explanation:
Drag the ordered pairs to match the points shown on the coordinate grid. A coordinate plane has an x-axis from 0 to 9 in increments of 1 and a y-axis from 0 to 9 in increments of 1. Point A is plotted 3 units to the right and 6 units above the origin. Point B is plotted 2 units to the right and 3 units above the origin. Point C is plotted 4 units to the right and 2 units above the origin. Point D is plotted 6 units to the right of the origin. (6, 0)(3, 6)(4, 2)(2, 3) Point Coordinates A B C D
Answer:
the answer is 3,6 6,0 2,3 4,2 that is the answer :)
Step-by-step explanation:
becuase that is the answer
What is the Domain and Range?
Answer:
Domain: all real numbers >= 4
Range: all real numbers >= 3
How much greater is the sum of the first 50 counting numbers greater than the sum of the first 100 counting numbers?.
The difference between the sum of the first 50 counting numbers and the sum of the first 100 counting numbers is 3775.
Here we have to find the difference between the first 50 counting numbers and first 100 counting numbers.
Formula to find the sum of the number n is:
[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)
a = first number of the series
d = common difference
n = number of series
Sum of first 50 counting numbers:
[tex]S_{50}[/tex] = 50/2( 2× 1 + (50-1) 1)
= 25 × 51
= 1275
Sum of first 100 counting numbers:
[tex]S_{100}[/tex] = 100/2 ( 2×1 + (100- 1) 1)
= 50 × 101
= 5050
Now the difference between them:
[tex]S_{100}[/tex] - [tex]S_{50}[/tex] = 5050 - 1275
= 3775
Therefore the difference is 3775.
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Write the equation of the
line passing through (5,3)
that has a slope of 1/2.
A) Mrs. Reynolds y = 1/2x + 1/2
B) Mr. Preston y = 1/2x + 5/2
C) Coach Taylor y = -1/2x + 11/2
D) Ms. Greene y = 1/2x + 2
E) Mr. Moulden y = -2x + 13
Answer: The correct answer is A) Mrs. Reynolds y = 1/2x + 1/2
Step-by-step explanation:
In the slope-intercept form of y=mx+b, m=the slope of the line
Therefore, y=1/2x + 1/2 has a slope of 1/2
As noted in the graph below, it is the only option listed that also intersects the point (5,3).
in order to estimate the mean 30-year fixed mortgage rate for a home loan in the united states, a random sample of 28 recent loans is taken. the average calculated from this sample is 5.25%. it can be assumed that 30-year fixed mortgage rates are normally distributed with a population standard deviation of 0.50%. compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. (you may find it useful to reference the z table. round your final answers to 2 decimal places. enter your answers as percentages, not decimals.)
The 90% confidence interval is (5.09% , 5.41%) and the 99% confidence interval is (52.24% , 52.76%) .
In the question ,
it is given that ,
number of sample of loans taken = 28
the average of the sample is = 5.25%
the standard deviation of the normally distributed population is 0.5 %
The formula to find the Confidence Interval (CI) for the population mean is written as
[tex]\bar{x}[/tex] ±[tex]t_{n-1} , _{\alpha /2} \frac{\sigma}{\sqrt{n} }[/tex]
it is given that the 30 year fixed mortgage rates are normally distributed .
the sample size (n) = 28
Since sample size is less than 30 , the t - test is applied .
Sample mean ( [tex]\bar{x}[/tex] ) = 0.0525
the standard deviation (σ) = 0.005
the significance level : α = 1 - 0.90 = 0.1
critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.05}[/tex] = 1.703
So , 90% confidence interval will be :
= 0.525 ± (1.703)×(0.005/√28)
≈ 0.0525 ± 0.0016
= (0.0525 - 0.0016 , 0.0525 + 0.0016)
= (0.0509 , 0.0541)
= (5.09% , 5.41%)
For the 99% confidence interval ,
the significance level : α = 1 - 0.99 = 0.01
critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.005}[/tex] = 0.2771
So , 99% confidence interval will be :
= 0.525 ± (0.2771)×(0.005/√28)
≈ 0.0525 ± 0.00026
= (0.0525 - 0.00026 , 0.0525 + 0.00026)
= (0.05224 , 0.05276)
≈ (52.24% , 52.76%)
Therefore , The 90% confidence interval is (5.09% , 5.41%) and the 99% confidence interval is (52.24% , 52.76%) .
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solve for x 48= x/2 Simplify your answer as much as possible.
x⁴⁸ = x/2
Multiply to remove the fraction, then set equal to
0
and solve.
Exact Form:
x
=
0
,
1
47
√
2
Decimal Form:
0,0.98536040
what is the equation of line m
Equation of the line 'm' is 5x - 6y - 30 = 0.
According to graph,
A(6,0) and B(0,-5) lies on the line m.
Slope-intercept form -> y = mx + c
Putting B(0,-5) in slope-intercept form,
-5 = m(0) + c
c = -5
Putting A(6,0) in slope-intercept form,
0 = m(6) - 5
6m = 5
m = 5/6
Putting the values of m and c in slope-intercept form,
y = (5/6)x - 5
6y = 5x - 30
5x - 6y - 30 = 0
Hence, equation of the line is 5x - 6y - 30 = 0.
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Use a Pythagorean Identity (not triangles) to find sin theta if you're given cos theta =
4/5 with theta in quadrant IV.
The value of the sinθ is -3/5.
What is the Pythagorean identity?
The Pythagorean trigonometric identity, also known as the Pythagorean identity, is a trigonometric identity that expresses the Pythagorean theorem. It is one of the fundamental relationships between the sine and cosine functions, along with the sum-of-angles formulae.
We have,
cosθ = 4/5
sin θ = ?
We'll use the definition of cos to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
[tex]cos\theta = \frac{Adjacent}{hypotenuse} = \frac{4}{5}[/tex]
We know the hypotenuse and adjacent sides and we'll use the Pythagorean theorem to find the remaining side(opposite side).
opposite = √hypotenuse² − Adjacent²
opposite = √(5)² − (4)²
opposite = √25 - 16
opposite = √9
opposite = 3
[tex]sin\theta = \frac{opposite}{hypotenuse}[/tex]
sin θ = 3/5
In the fourth quadrant, the sine and tangent ratios are negative and the cosine ratio is positive.
Hence, the value of the sinθ is -3/5.
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A parabola can be drawn given a focu of (−3,−3) and a directrix of x=5. Write the equation of the parabola in any form
The equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).
According to the question,
We have the following information:
A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5.
Now, let's take (x,y) to be the points of parabola.
So, we have the following expression:
Distance between (-3,-3) and (x,y) = Distance between (x,y) and x = 5
Distance between (x,y) and x = 5 will be Ix-5I
Now, we will use distance formula to solve this expression further.
[tex]\sqrt{(y+3)^{2}+ (x+3)^{2} }= (x-5)} }[/tex]
Squaring on both sides of the equation:
[tex]{(y+3)^{2}+ (x+3)^{2} }= (x-5)^2} }[/tex]
[tex]y^{2}[/tex]+9+6y+[tex]x^{2}[/tex]+9+6x = [tex]x^{2}[/tex]+25-10x
[tex]y^{2}[/tex]+6y+6x+18-25+10x = 0
[tex]y^{2}[/tex]+6y+16x-7 = 0
16x = [tex]-(y^{2}[/tex]+6y-7)
x = -1/16([tex]y^{2}[/tex]+6y-7)
Hence, the equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).
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In 60 econd, Darrell walk 90 meter. Select the two anwer that decribe the unit rate at which he walk
The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.
Given:
Darrell is walking for a distance of 90 meters in time 60 seconds.
To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.
Unit rate = Distance traveled / Time taken
= 90 meters / 60 seconds.
= 1.5 meters per second.
Therefore , The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.
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true or false 4. the expected value of a random variable must equal one of the values that the random variable can have.
The statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False
In this question, we have been given a statement.
We need to state whether given statement is true or false.
Given statement : the expected value of a random variable must equal one of the values that the random variable can have.
We know that the expected value of a random variable is the mean of all possible values of the variable.
It is denoted by E(x).
E(x) can not be one of the values that the random variable have, because it is a average of all values of random variable.
Therefore, the statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False
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Tom bought 3 T-shirts at a sale price of $14.50. If he saved up $2.47 because of the sale, what would be the percentage of the money he saved?
Tom saved 14.55% money in this sale.
Given that the sale price of 3 T shirts is $14.50.
And Tom saved in this sale $2.47.
So original selling price of that 3 T shirts is = 14.50+2.47 = 16.97
So the percentage of savings = (2.47/16.97)*100% = 14.55% (approximately)
Hence he saved approximately 14.55% in this sale.
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Find the perimeter and area of the triangle.
The perimeter = yds. The area = yd2
Step-by-step explanation:
perimeter:
74 + 74 + 48 = 196 yd
area:
48/2=24
√74^2+√24^2 = 77.79 (2dp)
77.79 x 48 = 3734.14
3734.14/2=1867.07yd^2
Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members, if it must have the same number of men and women?.
A department needs to choose six members consists of 3 women and 3 men from 10 men and 15 women. The number of ways it can be selected is 54,600.
If r persons need to be selected from total n members and the order does not matter, the number of ways it can be selected is calculated using the combination formula:
ⁿCr = n! / [(n-r)! r!]
Data from the problem:
Total man = 10
Man to be chosen = 3
Total woman = 15
Woman to be chosen = 3
Hence,
The number of ways men can be selected = ¹⁰C₃ = 10! /(3! 7!)
= 120
The number of ways women can be selected = ¹⁵C₃ = 15! /(3! 12!)
= 455
The number of ways men and women selected:
= ¹⁰C₃ x ¹⁵C₃
= 120 x 455 = 54,600 ways
Hence, the number of ways the members can be selected = 54,600 ways.
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Question A line passes through the points (−6,−8) and (−3,−7). What is the equation of the line in Slope-Intercept Form?
y=1/3x+6y
y=3x−6y
y=1/3x−6y
y=3x+6
The equation of the line in Slope-Intercept Form is y = 1/3x - 6
Given,
A line passes through the points (−6,−8) and (−3,−7).
To find the equation of the line in Slope-Intercept Form
Now, According to the question:
Write the slope formula :
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Substitute x1 = -6 , x2 = -3 and y1 = -8 , y2 = -7 into above slope formula:
Calculate;
[tex]m = \frac{-7-(-8)}{-3-(-6)}[/tex]
Determine the sign :
m = (-7+8)/ (-3+6)
m = 1/3
Substitute m = 1/3 , x = -6 and y = -8 into y = mx + b
Calculate:
-8 = 1/3 x (-6) + b
Reduce the expression:
-8 = -2 + b
-b = 6
b = -6
Again , Substitute
y = 1/3x - 6
m = 1/3 into y = mx +b:
y = 1/3x - 6
Hence, The equation of the line in Slope-Intercept Form is y = 1/3x - 6
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consider the line y=7/3x-3
Find the equation in slope-intercept form of the line that is perpendicular to this line and passes through the point (-2, -3).
Equation of perpendicular
line:
Answer: 3x-3
Step-by-step explanation:
EX1. Prints It charges $2.25 per box of business
cards plus a $11.25 shipping cost. We Print it
Better charges $3.50 per box but has free
shipping. How many boxes would you have to
order for the price for both printing companies
to be the same?
Answer:
[tex]5x {}^{2} - 5y { = }0 [/tex]
Melissa was able to do 25 sit ups in 30 seconds if she keeps at the same rate approximately how many set ups come out to complete is 150 seconds
Answer:
125
Step-by-step explanation:
150/30=5
25x5=25
if you want to figure out how much box office revenue each genre earned, which function in the values menu would you use to summarize the data?
The function in the values menu would you use to summarize the data is SUM
Because
I would use the SUM function to figure out how much box office revenue each genre earned. In the pivot table, the SUM function would add the total revenue separately for each genre.
This function, as clear from the name, is used to add all the values provided as arguments and to display the result in the cell-containing function. Argument Type All Numbers Return Type Number. Syntax = SUM(number 1 , number2, ).
The SUM function will sum hardcoded values and numbers that result from formulas. If you need to sum a range and ignore existing subtotals, see the SUBTOTAL function.
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Last week, a chocolate shop sold $6\frac{1}{6}$ ounces of white chocolate. It sold $\frac{2}{9}$ times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell? Express your answer as a simplified mixed number.
The ounces of milk chocolate that the shop sells is 1/27 ounces.
What is fraction?A fraction is a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the chocolate shop sold 1/6 ounces of white chocolate and it sold 2/9 times as much milk chocolate as white chocolate.
The milk chocolate sold will be:
= 1/6 × 2/9
= 2/54.
= 1/27
The ounces is 1/27 ounces.
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What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
15
2
O
O
O
0
2
22
24
By using the concept of slope, it is obtained that
Slope of the required trend line is [tex]\frac{22}{9}[/tex]
What is slope of a line?
Slope of the line is the tangent of the angle that the line makes with the positive direction of x axis
If the angle is [tex]\theta[/tex], the slope of the line is given by
[tex]m = tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]), then the slope of the line is given by
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
The line passes through (1, 3) and (10, 25)
[tex]x_1 = 1, y_1 = 3, x_2 = 10, y_2 = 25[/tex]
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}\\[/tex]
= [tex]\frac{25 - 3}{10 - 1}[/tex]
= [tex]\frac{22}{9}[/tex]
Slope of the required trend line is [tex]\frac{22}{9}[/tex]
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Find the constant rate of change and interpret its meaning a complete sentence. 
The constant rate of change of the altitude of the Hawk is -10 ft/s. The meaning of the -10 ft/s rate of change in altitude is the hawk is diving vertically down towards the prey with a speed of 10 feet per second
What is the rate of change of a function?The average rate of change of a function is the rate at which the output values of the function changes with regards to the change in the argument of the function.
A function that has a constant rate of change is a linear function.
The rate of change of a linear function or equation that gives a straight-line graph is found from the slope, m, of the function.
The formula for the slope of a function, using the points (x₁, y₁), and (x₂, y₂), is presented as follows;
[tex]Slope, \, m = \dfrac{y_2-y_1}{x_2- x_1}[/tex]
The points on the graph are; (x₁, y₁) = (3, 60) and (x₂, y₂) = (6, 30)
Which gives;
[tex]Slope, \, m = \dfrac{30\, ft-60 \, ft}{6\, s- 3\, s} = -10 \, ft/s[/tex]
The constant rate of change of the the function in the graph is -10 feet per secondThe meaning of the constant rate of change of -10 feet per second is that the Hawk is diving towards the prey at a rate of decrease of altitude of 10 ft/sLearn more about the rate of change of a function here:
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a box contains 12 batteries of which 6 are still working. anne starts picking batteries one at a time from the box and testing them. find the probability that she has to pick 5 batteries in order to find one that works.
The probability that she has to pick 5 batteries in order to find one that works is 5/12.
What is probability?
Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No of out comes=5
No. of total possible outcome=12
Therefore probability P= 5/12
P=5/12
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Q.57 help me please please pleaseeee
The value of the expression are as follows
30-218How to solve an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols.
Let's solve the expression by substituting the actual values of the variables.
a.
5x when x = 6
5x = 5(6) = 30
b.
3y when y = -7
3y = 3(-7) = -21
c.
10z when z = 0.8
10z = 10(0.8) = 8
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The graph of y = x2 + 11x + 24 is equivalent to the graph of which equation?
y = (x + 8)(x + 3)
y = (x + 4)(x + 6)
y = (x + 9)(x + 2)
y = (x + 7)(x + 4)
Ax^2 +Bx + C
x^2 +11x +24
Using the number in place of C gives us what values could be inside the brackets.
For 24 the multiples are
1 and 24
2 and 12
3 and 8
4 and 6
We want the one that can add or subtract to give the number in place of B, which is 11.
The only multiples that add to 11 are 3 and 8
Therefore we know that 8 and 3 need to be in the brackets.
Giving us (x+8)(x+3)
Xavier buys 18 bottles of orange juice at the corner store for a total cost of $14.04. If each bottle costs the same amount, how much is each bottle of juice?
The cost of each bottle of orange juice is 0.78 dollars.
How to find the cost of each bottle of orange juice?Xavier buys 18 bottles of orange juice at the corner store for a total cost of $14.04. Each bottle costs the same amount.
Therefore, the cost of each bottle of orange juice can be found as follows:
cost of each bottle of orange juice = total cost of the whole orange juice / number of orange juice bought
cost of each bottle of orange juice = 14.04 / 18
Therefore,
cost of each bottle of orange juice = $ 0.78
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what is the 4 digit number in which the first digit is one fifth of the last and the
second and third digits are the last digit multiplied by 2
Answer:
1,105
Step-by-step explanation:
since the first digit is 1/5 them the last digit it can only be 1 because if it was 2 then the last digit will be 10 which isn’t possible
So we know the last digit is 5 so we multiply by 2 to get the second and third digit of 10
Hopes this helps please mark brainliest
