When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.
How to calculated the slope intercept?Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).
Solution
Step 1: Replace the provided in the formula.
Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.
y = mx + b
y = 2 3 x + 4
2 /3 x – y = - 4
(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)
3( 2 /3x – y) = (- 4) (- 4)
3/2x – 3y = - 12
This is the line's determined equation.
Verify is the second step.
Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12
Let y = 2 Let y = - 6
2x – 3(2) = - 12 2x – 3(-6) = - 12
2x – 6 = - 12 2x + 18 = - 12
2x = - 6 2x = - 30 \sx = - 3 x = - 15
P1 therefore equals (-3, 2) and P2 equals (-15, -6).
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jeff jogged 4 miles today, and larry biked 2 1/3 miles. how many times the length of jeff's bike ride was larry's bike ride?
583 times the length of jeff's ride was larry's bike ride
Word problem in maths is a maths question written as one sentence or more that requires children to apply their maths knowledge to a ‘real-life’ scenario. a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.Word problems are usually made up of a few sentences describing a scenario that needs to be solved through maths. These scenarios are usually ‘real-life- ones, situations that people might find themselves in every day. For example, it could be the division of pizza between party members or working out how long a train might take from one place to another.
This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.
Given,jeff jogged 4 miles today, and larry biked 2 1/3 miles.
Let x times the length of jeff's ride was larry's bike ride.
4x= 7/3
x=.583 times
So, .583 times the length of jeff's ride was larry's bike ride.
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Find the value of x in the triangle shown below: 2.5 6.5 Choose 1 answer: I =6 3 = V48.5 x = 9 x = V9
Answer:
x = 6 units
Step-by-step explanation:
We know that, By pythagoras theorem,
Hypotenuse2 = base2 + perpendicular2
Given, Hypotenuse = 6.5
perpendicular = 2.5
base = x
So, by putting the values,
6.52 = 2.52 + x2
42.25 = 6.25 + x2
36 = x2
Hence, x = 6 units
Which expression is equivalent to (10+7r-r2)+(-6r2-18+5r)
Answer:
8−72+12−8
Step-by-step explanation:
Complete. If m∠6=x,m∠7=x−20, and m∠11=80, then x=______?
The value of x = 50
Exterior angle:
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.
If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.
In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
given that
m∠6 = x
m∠7 = x-20
m∠11 = 80
we solve this by using exterior angles
sum of 2 interior angles is equal to one exterior angle
m∠6 + m ∠7 = m∠11
x + x - 20 = 80
2x = 80 + 20
2x = 100
x = 100/2
the value of x = 50
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In triangle ACE points B, D and F are midpoints of the sides. If AC=48 and FB=23 Find EC.
Answer: In ΔABF & ΔACE
AB/FB = AC/EC (As both the triangles are similar)
as B is the midpoint of AC = 48
AB = 24
So,
24/23 = 48 / EC
EC = 46
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The value of EC is equal to 69 units
What is the triangle midpoint theorem?Triangle Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Given here, AX=24 And FB=23
Now applying the triangle midpoint theorem we get the value of
AC =3×23
= 69 units
Hence, The value of EC is equal to 69 units
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Question Graph the linear function d(x)=−1/2x−3.
Answer:
Step-by-step explanation:
The required graph of the given function d(x)=−1/2x−3 has been shown.
Given that, to plot the graph of the linear function, d(x)=−1/2x−3.
What is the graph?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The graph of the liner function d(x)=−1/2x−3 can be plot by putting the values of the x in the equation which gives the value of y by calculating such an ordered pair we can plot the curve of the liner equation on the graph. i.e.
At x = 0
d(0) = -1/2 * (0) - 3
d(0) = -3
So, the ordered pair will be (0, -3).
Now, put x = 2
d(2) = -1/2 * 2 - 3
d(2) = -1 - 3
d(2) = - 4
So the ordered pair will be (2, -4)
joining these two points will show the graph of the given equation d(x)=−1/2x−3.
Thus, the required graph of the given function d(x)=−1/2x−3 has been shown.
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which best describes the reason we use summary statistics to describe our data? group of answer choices summary statistics provide evidence of associations we may not have considered. even for relatively small datasets, it is difficult or impossible to analyze data simply by looking at it. summary statistics prove whether our public health interventions are having an impact. our goal in biostatistics is to conduct complex and sophisticated analyses.
The information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.
What are the components of summary statistics? The essence of the information about the sample data is summarized and provided by summary statistics, a subset of descriptive statistics.By identifying a measure of location or central tendency, such as the arithmetic mean, statisticians frequently attempt to define and classify the observations.The technique of inferring statistically from a sample or subset of data is known as statistical inference.Most of the time, it is not feasible to collect all the measurements from a population.Quick summaries of data are provided by summary statistics, which are especially helpful when comparing one project to another or before and after.Measures of dispersion and central tendency are the two primary categories of summary statistics used in appraisal.To learn more about summary statistics refer
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What is the ratio between 1 1/4 hours and 25 minutes?
Answer: 75 minutes to 25 minutes
Step-by-step explanation:
To find the ratio between 1 1/4 hours and 25 minutes, we first need to convert both quantities to the same unit of time. Since 1 hour is equal to 60 minutes, 1 1/4 hours is equal to 1.25 * 60 = 75 minutes. Therefore, the ratio between 1 1/4 hours and 25 minutes is 75 minutes to 25 minutes, or 3 to 1.
Find the sum of ten terms of the G. P 1,1.3,1.69
Answer:
Sum of G.P. series is given by,
Sum=
r−1
a(r
n
−1)
when r>1
Where a= first term, n=n
th
term and r is common ratio.
Here, a=1,n=10,r=
3
S
10
=
(
3
−1)
1×{(
3
)
10
−1}
=
(
3
−1)
(3
5
−1)
×
(
3
+1)
(
3
+1)
=
(3−1)
242(
3
+1)
=121(
3
+1).
What is the slope for (-5, 8); (-4, 2)
Answer: -10
Step-by-step explanation:
y2-y1
---------
x2-x1
How do you convert 22/55 into a percent and decimal?
Answer:
22/55 = 40% = 0.4
Step-by-step explanation:
22/55
Reduce the fraction by dividing the numerator and denominator by 11.
22/55 = 2/5
Now use a calculator, or long division, to divide 2 by 5.
22/55 = 2/5 = 0.4
To change a decimal to a percent, multiply the decimal by 100%.
0.4 × 100% = 40%
Answer: 22/55 = 40% = 0.4
Consider the line y = -5x + 1. Write the equation of the line that is perpendicular to this line and that contains the point (2, -1)
Considering the definition of perpendicular line, the equation of the perpendicular line is y= 1/5x - 13/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= -5x +1.
In this case, the line has a slope of -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:
(-5)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-5)
slope perpendicular line= 1/5
So, the perpendicular line has a form of: y= 1/5x + b
The line passes through the point (2, -1). Replacing in the expression for perpendicular line:
-1= 1/5× 2 + b
-1= 2/5 + b
-1- 2/5= b
-13/5= b
Finally, the perpendicular line is y= 1/5x - 13/5.
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The graph of y=h(x)y=h(x)y, equals, h, left parenthesis, x, right parenthesis is a line segment joining the points (-7,-5)(−7,−5)left parenthesis, minus, 7, comma, minus, 5, right parenthesis and (-1,-2)(−1,−2)left parenthesis, minus, 1, comma, minus, 2, right parenthesis.
Drag the endpoints of the segment below to graph y=h^{-1}(x)y=h
−1
(x)y, equals, h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis.
Answer:
(-5, -7) and (-2, -1)
Step-by-step explanation:
The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2). (Blue line on the attached graph).
The graph of the inverse function is a reflection in the line y = x.
Therefore, the endpoints of the inverse function are:
(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.
Answer:
(-5, -7) and (-2, -1)
Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2). (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.
Step-by-step explanation:
Vladmir sketches the graph of the function f(x)=12(x+6)2−3
as shown below
He then translates this function 11 units to the right and 4 units down to obtain the new function g(x)=12(x−h)2+k
. Which function correctly shows integer values for h and k?
The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7
How to determine the function correctly?From the question, we have the following parameters that can be used in our computation:
f(x) = 12(x + 6)² - 3
The transformation is given as
11 units to the right and 4 units down
This is represented as
(x - 11, y - 4)
So, we have the following representation
g(x) = 12(x + 6 - 11)² - 3 - 4
Evaluate
g(x) = 12(x - 5)² - 7
Hence, the function is g(x) = 12(x - 5)² - 7
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jerry is driving 35 mph as he approaches a park. A dog darts out into the street between two parked cars, and jerry reacts in about three-quarters of a second. what is his approximate reaction distance?
The distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.
What is distance?Distance is the total movement of an object without any regard to direction.
To calculate the approximate reaction distance, we use the formula below.
Formula:
d = Vt............... Equation 1Where:
d = Reaction distanceV = Speed at which jerry was drivingt = TimeFrom the question,
Given:
V = 35 mph = 15.6464 m/st = 3/4 seconds 0.75 secondsSubstitiute these values into equation 1
d = (15.6464×0.75)d = 11.73 mHence, the distance of the reaction is 11.73 m.
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She makes $3,200 as a base salary each month. She gets 8.5% of everything she sells. If she sold $60,000 worth of items this month, what are her earnings for the month, including commission?
Her total salary for the month would be $8300.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have a women with $3,200 as a base salary each month. She gets 8.5% of everything she sells. If she sold $60,000 worth of items this month.
Assume her total salary to be y = $(3200 + x). Then, we can write -
y = $(3200 + {8.5/100} x 60000}
y = $(3200 + 5100)
y = $8300
Therefore, her total salary for the month would be $8300.
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pls help with this homework
The solution of the system of equation 2x + 4y = 16, 2x - 4y = 0 is (4, 2). The correct option is A.
How to solve the system of equation?System of equations can be solved using different method such as substitution method, elimination method and graphical method. The system of equation can be solved with the elimination method as follows:
2x + 4y = 162x - 4y = 0
add equation(ii) to equation(i)
2x + 2x = 16 + 04x = 16
divide both sides by 4x = 16
x = 4
Let's find y
2x - 4y = 0-4
y = -2x-4y = -2(4)
-4y = -8
divide both sides by -4y = -8 / -4y = 2
Therefore, the solution is (4, 2)
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solve the equation.34(2a − 6) 12 = 25(3a 20)a =
Answer:a=6,25
Step-by-step explanation:
i did the test yesterday
The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
34(2a − 6) + 12 = 25(3a + 20) + a
Simplify the equation, then the value of the variable 'a' is given as,
34(2a − 6) + 12 = 25(3a + 20) + a
68a − 204 + 12 = 75a + 500 + a
68a − 192 = 76a + 500
Simplify the equation further, then the value of the variable 'a' is given as,
76a − 68a = − 192 − 500
8a = − 692
a = − 692 / 8
a = −86.5
The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.
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Please help needing assistance
Answer:
Step-by-step explanation:
its ab
activity a1 takes 5 weeks, a2 takes 7 weeks, and a3 takes 3 weeks with a 50% probability and 9 weeks with a 50% probability. what is the expected project completion time?
The probability to determine the time needed to complete the project, we simply added the time required for activities 1 and 2.
1 (1): the chance that a given event will occur
(2): the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes a branch of mathematics concerned with the study of probabilities
2 : something (such as an event or circumstance) that is probable
3: the quality or state of being probable
4: a logical relation between statements such that evidence confirming one confirms the other to some degree
The best-case scenario's calculation of the project's completion time is displayed below;
= Week spent on Activities A1 + Week spent on Activities A2.
= 5 weeks plus 7 weeks.
= 12
To determine the time needed to complete the project, we simply added the time required for activities 1 and 2.
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solve each of these equations. explain or show your reasoning.
2(x+5)=3x+1
3y-4=6-2y
3(n+2)=9(6-n)
Answer: n = 4
9 = x
y = 2
Step-by-step explanation:
2 ( x + 5 ) = 3x + 1
2x +10 = 3x + 1
10 = 1x + 1
- 1 -1
9 = 1x
9 = x
3y - 4 = 6 - 2y
5y -4 =6
5y = 10
y = 2
3 (n + 2) = 9 ( 6-n)
3n + 6 = 54 -9n
3n +9n = 54 - 6
12n =54 -6
12n =48
n = 4
the admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. on a certain day, 351 people entered the park, and the admission fees collected totaled 1014 dollars. how many children and how many adults were admitted?
There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.
Given that,
The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.
We have to find how many people and kids were allowed inside.
We know that,
We get equations as,
1.5x+4y=351 ----->equation(1)
The other equation is
x+y=1014 ----->equation(2)
Take the equation(2)
x+y=1014
y=1014-x
Substitute y=1014-x in equation(1)
1.5x+4y=351
1.5x+4(1014-x)=351
1.5x+2056-4x=351
1.5x-4x=351-2056
-2.5x=-1705
2.5x=1705
x=1705/2.5
x=682
Substitute x=682 in equation(2)
y=1014-x
y=1014-682
y=332
Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.
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Show that 10^logx = x ?
A logarithmic function is defined by f(x) = [tex]log_a[/tex]x(r) y = [tex]log_a[/tex]x, where a > 0 and y = [tex]log_a[/tex]x. It is the inverse of the exponential function [tex]a^{y}[/tex] = x.
During the 16th century, Scottish mathematician, scientist, and astronomer John Napier discovered logarithms. The technique is widely used in astronomical and scientific calculations involving huge numbers. As an inverse of exponential functions, logarithmic functions are closely related to exponential functions. By transforming [tex]a^{x}[/tex] = N into [tex]log_a[/tex] N = x, the exponential function is transformed into a logarithmic function.
Let's say that y=[tex]10^{\log x}[/tex]
see this, 100=[tex]10^2[/tex],
then [tex]log _{10}[/tex] 100 = 2
therefore, [tex]log _{10}[/tex] y=[tex]\log _{10}[/tex] xy = x
[tex]10^{\log x}[/tex] = x
Hence, proved.
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From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop. What is the distance between John's friend and the building?
The distance between John's friend and the building is 14.9 metres.
How to find the distance between the building and John's friend?From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop.
Therefore, the distance of John's friend from the building can be calculated as follows:
This situation forms a right angle triangle.
Hence, using trigonometric ratios,
tan 50 = opposite / adjacent
tan 50 = 16 + 1.8 / x
tan 50° = 17.8 / x
cross multiply
x tan 50° = 17.8
x = 17.8 / tan 50
x = 17.8 / 1.19175359259
x = 14.9359734675
x = 14.9 metres
Therefore,
distance of John's friend to the building = 14.9m
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ABC has vertices at A(-7,8). B (7,0), and C(-5, -8) Show that point A is equidistant from the endpoints of segment BC. [3 points]
The distances between the points are given as follows:
AB: square root of 260.AC: square root of 260.As these two distances are equal, point A is equidistant from the endpoints of segment BC.
How to obtain the distance between two points?The distance between points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance of point A to the endpoint B is calculated as follows:
[tex]D = \sqrt{(7 - (-7))^2 + (0 - 8)^2} = \sqrt{260}[/tex]
The distance of point A to the endpoint C is calculated as follows:
[tex]D = \sqrt{(-5 - (-7))^2 + (-8 - 8)^2} = \sqrt{260}[/tex]
As the distance from point A to point B is equals to the distance from point A to point C, the point A is equidistant from the endpoints of segment BC.
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Which of the following describes the nature of the solutions of the quadratic
equation-2x^2-x-1=0?
A. One real, rational solution
B. Two real, rational solutions
C. Two real, irrational solutions
D. Two complex conjugate solutions
Answer:
D
Step-by-step explanation:
To find the solutions, let's calculate the determinant:
Δ = (-1)²-4(-2)(-1) = 1-8 = -7
the solution is: (1 ±√-7)/(-4)
√-7 indicates there are two complex solutions
Given the image below, find the maximum value for x.
The maximum value of x in the figure given is of:
x = 33º.
How to obtain the maximum value of x?The maximum value of x is obtained when the segment traced represents a bisection of the angle at the vertex of the quadrilateral.
A bisection is defined as a segment that splits an angle measure into two equal measures.
The angle measures for this problem are given as follows, from the image:
2x + 5.71º.Then the maximum value of x is obtained when these two measures are equal, as follows:
2x + 5 = 71
2x = 71 - 5
2x = 66
x = 66/2
x = 33º.
(the bisection concepts means that the larger angle, which would be of 2 x 71 = 142º, would be split into two angles with an equal measure of 71º).
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PLS ANSWER ASAP
40 POINTS
The function g(x) = √x + 4 is the result of a vertical translation 4 units up of the function f(x) = √x. (Right choice: B)
What kind of transformation should be used to obtain the image of a function?
In this problem we find the definition of a function f(x) and its image g(x). Both f(x) and g(x) are radical functions and we need to determine the transformation rule to obtain the latter function. By direct inspection, g(x) is the result of applying a vertical translation, whose definition is shown below:
g(x) = f(x) + k
Where:
f(x) - Original function.g(x) - Resulting function.k - Translation step.Please notice that k indicates a translation in the +y direction. k > 0 indicantes a vertical shift k units up.
Then, g(x) is the result of a vertical translation (4 units up) on f(x).
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for a standard normal distribution, what is the probability that z is greater than 1.75? a) 0.0401 b) 0.0459 c) 0.4599 d) 0.9599
For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.
A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.
Using a standard normal table the area to the right of z = 1.75 is given by
P(z > 1.75) = .0401
Therefore, the correct option is a.
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Explain what the symbol Z 0.05 represents and state its value: (choose one of the following answers..) a. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65. b. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value is Z0.05 =1.65. c. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =2.58. d. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value is Z0.05 =2.58.
Option 'a' is the correct answer.
Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65.
In a normal distribution, data points are referred to as x, whereas in a z-distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations a given number (x) is from the mean:
If your x value is higher than the mean, your z score will be positive.If your z score is negative, it indicates that your x value is below the meanYour x value is the same as the mean if your z score is zero.Every z score has a corresponding p-value that indicates the likelihood that all values below or above that z score will occur.
Find more on Z-scores at :brainly.com/question/24213960
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