An equation in standard form with an x-intercept of 5 and a y-intercept of -4 is,
⇒ 5x + 4y = 20
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The x - intercept = 4 ,
So, ( 4,0) is a point on the line.
And, The y - intercept = 5,
So, ( 0, 5) is a point on the line.
Now, Slope of the line passing through the point (4, 0) and (0, 5) is,
⇒ m = (5 - 0) / (0 - 4)
⇒ m = - 5/4
So, The slope intercept form of an equation is,
⇒ y = mx + b
Where, m = slope and b = y- intercept.
Hence, We get;
⇒ y = - 5/4x + 5
We know that;
An equation in standard form is,
⇒ Ax + By = C
So, We get;
⇒ y = - 5/4x + 5
⇒ 4y = - 5x + 20
⇒ 5x + 4y = 20
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enter in the missing numbers to create equivalent ratios i need helpppppp i don’t understand
Answer:
[tex]8....on \: the \: first \: box \: and \\ 64......on \: the \: second \: box[/tex]
Step-by-step explanation:
Greetings!!!
so first let's see how it comes by changing it into ratios
[tex] \frac{1}{4} ....the \: first \\ \frac{2}{8} cancel(simplify) = \frac{1}{4}...the \: second [/tex]
Thus, following the same order
[tex] \frac{8}{32} simplify = \frac{1}{4} \\ \frac{16}{64} simplify = \frac{1}{4} [/tex]
so we get the same ratios.
If any questions tag it on the comments.
Hope it helps!!!
Solve the system of equations by graphing
Because the first equation is already solved for y we can substitute 3x−5 for y in the second equation and solve for x:
y=x−3 becomes:
3x−5=x−3
3x−5+5−x=x−3+5−x
3x−x−5+5=x−x−3+5
3x−1x−0=0+2
2x=2
2x/2=2/2
2x/2=1
x=1
Substitute
1 for x in the first equation and calculate y:
y=3x−5 becomes:
y=(3×1)−5
y=3−5
y=−2
The solution is x=1 and y=−2 or (1, -2)
What is graphical representation?Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.To learn more about anomalies refer to:
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Select the correct answer. The product of two numbers, x and x + 3 , is 550. Which equation could be solved to find the value of the smaller number, x? A. x 2 + 3 = 550 B. 3 x + 3 = 550 C. x 2 + 3 x = 550 D.
The product of two numbers, x and x + 3 , is 550, then x²+3x = 550: Option C
What is a quadratic equation?You should be aware that a quadratic equation is an equation whose highest power of its variable is two. A quadratic equation in the form x can be written as ax²+bx+c = 0 where a, b and c are positive or negative integers
The given expression is
The product of two numbers, x and x + 3 , is 550
this implies x(x+3) = 550
Opening the brackets to get
x²+3x = 550
This in conclusion means that the best option is x²+3x = 550
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Can someone help me with this ? Please
Value of gof(-1) is 2. The solution has been obtained by applying the multiplication operation on the given functions.
What are operations on functions?
Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.
Suppose there are two functions f(x) and g(x). The notations are as follows:
For Addition: (f+g)(x) = f(x) + g(x)For Subtraction: (f-g)(x) = f(x) - g(x)For Multiplication: (f×g)(x) = f(x) × g(x)For Division: (f/g)(x) = (f(x))/(g(x))Now, gof= g(f) = 3-f
We are given f = 2+x
So, f(-1) = 2+(-1) = 1
Now, substituting the value of f(-1) in g(f) , we get
gof(-1)= 3-1=2
Hence, the value of gof(-1) is 2.
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Implicit Differentiation Homework Date Period Problems 1 - 8, Find Dy/Dx By Implicit Differentiation. 1. 8x^2 + Y^2 = 10
The solution to the implicit differentiation problem is dy/dx = -16x/2y.
To solve this problem, we must use implicit differentiation. This means that we must differentiate both sides of the equation with respect to the independent variable, x. We can do this by taking the derivative of both sides of the equation.
The derivative of 8x^2 is 16x and the derivative of y^2 is 2y dy/dx.
Therefore, the equation becomes: 16x + 2y dy/dx = 0
We can then solve for dy/dx by dividing both sides by 2y, which gives us dy/dx = -16x/2y.
Therefore, the solution to the implicit differentiation problem is dy/dx = -16x/2y.
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A candy store sells Nerds in two different sizes. Which is the best buy?
14 oz. for $4.20 OR 18 oz. for $5.04
Answer: 18oz
Step-by-step explanation:
Amelia is making a hair bow that requires
one yard of ribbon. The ribbon that she
needs is sold by the meter. Will one meter
of ribbon be enough to make the bow?
Explain.
Yes, one meter of ribbon will be enough to make the bow because one meter is equal to 1.094 yards.
How to determine if one meter of ribbon be enough to make the bow?One meter is equal to 1.094 yards. So, one meter is longer than one yard.
Since Amelia needs one yard of ribbon to make the bow, and she can only find ribbon sold by the meter, which is longer than a yard, one meter of ribbon will be enough to make the bow.
Thus, She can purchase one meter of ribbon to make the bow.
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1. Bennet is getting in shape for football season. He runs 400 yards 3 times a day for 5 days. How many feet did he run in 5 days?
2. The Russel family is keeping track of the milk they drink each week:
- The first week they drank 2 gallons, 1 quart and 1 cup of milk
- the second week they drank 3 gallons of milk
which week did they drink more milk?
Find the coordiantes of the vertices for the figure after the given transformation
Dilation of 2.
Answer:
[tex]I'(-2,-4), J'(-4,4), K'(4,4)[/tex]
Step-by-step explanation:
Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].
how many radians are there in 3 circles
Answer:
There are 6
Step-by-step explanation:
There are two within each circle.
Answer: 18.84 radians
Step-by-step explanation:
f(x)= 2x^2+3x-5
f(f(2))
Answer:
[tex]f(f(2))=184[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+3x-5\\f(2)=2(2)^2+3(2)-5=2(4)+6-5=8+1=9\\f(f(2))=f(9)=2(9)^2+3(9)-5=2(81)+27-5=162+22=184[/tex]
Solve for d. You can choose to show your work below or solve on paper.
Answer:
-4/5
Step-by-step explanation:
Just simply use your knowledge to eliminate the d
How do you identify the base and exponent in an exponential notation?
We can identify the base and its exponent as the exponent indicates the number of times the base is used as a factor in an exponential notation.
What is Exponent ?An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively. Remember that every number multiplied by one is equal to itself.
Exponents are a technique of expressing extremely large numbers in terms of powers. The number of times a number has been multiplied by itself is the exponent, so to speak. For instance, the result of multiplying the number 6 by itself four times is 6 6 6 6. This can be expressed as 6⁴. Here, the exponent and base are 4 and 6, respectively.
An exponential number takes the shape of a, where an is multiplied by itself n times. The simple example is 8=23=222. In exponential notation, A is referred to as the base, whereas n is referred to as the power, exponent, or index. In scientific notation, 10, which is a specific illustration of exponential numbers, is typically always used as the base number.
Exponential notation make it easy to express powers succinctly. The exponent displays the base's multiplicative power. It can be written as 2 2 2 2=25 for the integer 32 because 2 is the "base" and 5 is the "exponent." The correct translation of this phrase is "two to the fifth power."
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Compared to lat yer, the population of Boom Town ha increaed by 25%. The population i now 6,000. What wa the population lat year
Compare to last year the population of the Boom town increased by 25% which is equal to 6000 then population of the last year is 4800.
As given in the question,
Present year population of the Boom town is equal to 6000
Let us consider 'y' be the population of Boom town last year.
Percentage of increase in population = 25%
Equation formed for the given condition is :
y + 25%y = 6000
⇒ y + (25/100)y = 6000
⇒ (100 + 25 / 100 )y = 6000
⇒ y = ( 600,000 / 125 )
⇒ y = 4,800 population of Boom town last.
Therefore, last year population of the Boom town is equal to 4,800.
The above question is incomplete, the complete question is:
Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?
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What circles are drawn on the score sheet at the end of a set?
In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
Following are the circles that are drawn at the end of a set on the NCAA women's volleyball scorecard:
who has the first opportunity to serve:
Based on our existing knowledge of how NCAA Women's Volleyball functions, we can see that each period is divided into sets and that there is a scorecard where each team's points are given. In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
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In 2006, the U.S. Population (or persons) per square mile of land area was 85. In 2014, the persons per square mile was 89.48.
a. Write an equation describing the relationship between year and persons per square mile. Use ordered pairs of the form (years past 2006, persons per square mile)
b. Use equation on question 7 to predict the persons per square mile in 2023. Round to the nearest whole person.
In 2006 we have 93.3 people per sq mile .
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
In order to determine the equation for this relationship, we need to first find the slope between these two values. There are two ways to do this:
1. Create a graph
*Create a graph with the x-axis representing the years past 2000 (so 2000 would be 0 and 2003 would be 3 and so on)
*Use the fact that slope=rise/run to get slope=2.7/3 (because we rise 87-84.3=2.7 and run 3 (from 2000 to 2003), and 2.7/3=27/30=9/10
*Plug this and the point (0, 84.3) into the formula y=mx+b to find the y-intercept of your equation
--> 84.3=(9/10)(0)+b --> b=84.3
So, your equation can be written now as y=(9/10)x+84.3
[Note: To check, if you plug in 3 you should get 87, and you do, so it works!]
2. Use the slope formula
Alternatively, you could have did slope=(y2-y1)/(x2-x1)=(87-84.3)/(3-0)=2.7/3=9/10
The process here would be the same as above
b) Here, just plug 10 into the equation above (since 10 is the number of years 2010 is after 2000, or 2010-2000=10). Doing this we get:
y=(9/10)(10)+84.3=9+84.3=93.3
So, in 2006 we have 93.3 people per sq mile
Therefore, In 2006 we have 93.3 people per sq mile .
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Use the function f(x) = 4x2 − 7x − 15 to answer the questions.
Part A: Completely factor f(x).
Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Part C: Describe the end behavior of the graph of f(x). Explain.
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
a) The factored function is given as follows: f(x) = 4(x + 1.25)(x - 3).
b) The x-intercepts are given as follows: x = -1.25 and x = 3.
c) The end behavior is given as follows: Due to the positive leading coefficient, the function increases to left and right.
d) The graph of the function is given by the image presented at the end of the answer.
How to graph the function?The quadratic function for this problem is defined as follows:
f(x) = 4x² - 7x - 15.
The coefficients are given as follows:
a = 4, b = -7, c = -15.
Inserting these coefficients into a quadratic function calculator, the roots, which are the x-intercepts, are given as follows:
x = -1.25 and x = 3.
Considering the leading coefficient of 4 and the linear factors of the function, the factored function is given as follows:
f(x) = 4(x + 1.25)(x - 3).
The x-coordinate of the vertex is given as follows:
x = -b/2a = 7/8.
Hence the coordinates of the vertex are:
(7/8, f(7/8)).
Then the graph is made considering:
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8x to the third power -9x
The value of the expression is 512x³-9x²
How to find the value of the expression?You should be aware that an expression is a mathematical statement that is not an equation but have variables. It is also an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
The given expression is
8x to the third power -9x
This is expressed as follows
(8x)³-9x²
In this expression, every term inside the bracket is raised to the third power
⇒8³ * x³ - 9 *x
= 512*x - 9x²
= 512x³-9x²
In conclusion, the value of the expression is 512x³-9x²
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What is a 30% residual?
A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.
What is residual?In statistical or machine learning models, the differences between actual and expected data values are referred to as residuals.
They act as a diagnostic instrument for assessing the caliber of a model. They are also known as errors.
The primary column, Inflation, of the table below provides details on US inflation for each month of 2017. Forecasts from a model that seeks to predict the rate of inflation are shown in the Predicted column.
Following are the calculations for the residuals: Residual is equal to predicted inflation.
The Residual column contains them.
The model predicted 1.8% for the data for January 2017, while the actual inflation rate was only 0.5%, leaving a residual of -1.3%.
Hence, A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.
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Probability of being a senior or white
The probability of being a senior citizen and white is: (0.63)(0.3) = 0.189.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.
Given that the probability of identifying white is 0.63.
Then the probability of not white is:
1 - 0.63 = 0.37
Given that the probability of being a senior citizen is 0.3.
Then the probability of not a senior citizen is:
1-0.3 = 0.7
Hence, the probability of being a senior citizen and white is:
(0.63)(0.3) = 0.189
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A touchdown in football count for 6 point. If n tand for the number of touchdown, which equation repreent how many point n touchdown are worth
A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]
Given that,
A touchdown in football count for 6 point.
If n and for the number of touchdown,
We are given that a touchdown in football counts for 6 points.
We have to find an equation which represents number of points in n touchdown.
In order to find the number of points in n touchdown we will multiply 6 with n.
Number of points in one touchdown y = 6
Number of points in n touchdown y = [tex]6*n[/tex]
Number of points in n touchdown y = [tex]6n[/tex]
Therefore,
A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]
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15% of $9 is… can someone please help with the solution
Answer:
$1.35
Step-by-step explanation:
15% of $9
= [tex]\frac{15}{100}[/tex] × $9
= 0.15 × $9
= $1.35
if you can solve this that would be great
Answer:
I wish you luck
Step-by-step explanation:
What are the 4 properties of subtraction?
There are various properties of subtraction , out of which four of them are ,
Commutative propertyAssociative property Identity propertyDistributive propertySubtraction means to reduce one number or quantity from another. It is one of the most common mathematical operations which are present as well as it is represented by the symbol , " - " .
The associative property does not apply to subtraction which are performed between whole-number. The order of subtraction is significant.
The distributive property helps to simplify the difficult algebraic expression. As a result, the distributive property favors multiplication over subtraction. The property states that subtracting any number from the same number results in the number 0.
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Which equation has infinitely many solutions?
• A 3x - 2 - 2 - 3х
B. x+3x+6=6+4x
C 2x+7x-5=-9x+5
D 4x-5x+3= -5x + 4x -3
Answer: i think its A
Answer:
B. x+3x+6=6+4xStep-by-step explanation:
B)
x+3x+6=6+4xx+3x+6-6=6+4x-6x+3x=4x4x=4xSince both sides are equal, there are infinitely many solutions.
-Hope this helps!
What is 2 with an exponent of 1?
The 2 with an exponent of 1 is represented as 2¹ and the value of 2 with an exponent of 1 is 2 .
When the number "a" is multiplied by itself "n" number of times , then it can be represented in Exponential Form as "aⁿ " , the number "a" is called the base and the number "n" is called the exponent or power .
we have to find the value of 2 with an exponent of 1 ;
So , it is represented as ⇒ 2¹ ;
and the value of this exponential expression is ⇒ 2 .
Therefore , the value of 2 with an exponent of 1 is 2 .
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How do you dilate a linear equation?
Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation. How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r. Every time, k will have a value larger than 0.
What is the rule to dilate?A transformation in geometry is an action that shifts, rotates, or modifies an existing shape to produce a brand-new shape.
Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation.
How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r.
A two-scale factor dilation has been applied to Image A in relation to its origin. It is important to note that every coordinate point in the dilation picture is twofold that of the preimage.
The notation shown below can be used to represent a dilation with a scale factor close to the origin:
Dk (x , y ) = (kx, ky)
there will always be a number greater than 0 in the equation.
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Use the drawing tools to graph the solution to this system of inequalities
y> 2x + 4
x+y≤6
A collection of two or more inequalities in one or more variables is known as a system of inequalities.
What does it mean to solve a system of inequalities?Two or more inequalities in one or more variables make up a system of inequalities. When a problem calls for a variety of answers and those answers are constrained by multiple factors, systems of inequalities are used.
The intersection region of every solution in the system of inequalities is the system's solution.
Comparable to solving a system of linear equations, solving a system of linear inequalities involves locating the point (or points) of intersection, however this is not the case with inequalities. Instead, the area that fulfils each linear inequality will make up the solution set.
An inequality system's graph shows how the inequalities are resolved.
The system of inequality needs to be fixed by [tex]$y > \frac{2}{3}$ \\ and $x \leq \frac{16}{3}$[/tex]
Following is a description of the inequality system:
[tex]$y > 2 x+4$$x+y \leq 6$[/tex]
The charts for these are in the attached.
[tex]$y > 2 x+4$ and $x+y \leq 6$[/tex]
The graph shows us:
[tex]$y > \frac{2}{3}$$x \leq \frac{16}{3}$[/tex]
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A ferris wheel can accommodate 40 people in 20 minutes. How many people could ride the ferris wheel in 5 hours? What was that rate per hour?
Answer:
600 people
Step-by-step explanation:
40 people in 20 minutes => 120 people per hour. 5 hours, so 5 x 120 = 600 people.
Drag and drop the angle measures below.
122
142
38
44
58
84
96
Type here to search
122%
/R
14101
960
EE
43
96
P
hp
122
Q
The measures of the angle are a = 84°, b = 84°, c = 96°, d = 58°, e = 38° and f = 142°
How to determine the angle measures?
Angle geometry is a branch of mathematics that deals with the properties and relationships of angles in geometric figures.
Check the attached image for labeling
d = 180 - 122 = 58° (sum of angles on a straight line)
c = 96° (vertically opposite angles are equal)
a = 180 - 96 = 84° (sum of angles on a straight line)
b = a (vertically opposite angles are equal)
b = 84°
e = 180 - b -d (sum of angles in a triangle)
e = 180 - 84 - 58 = 38°
f = 180 - e (sum of angles on a straight line)
f = 180 - 38 = 142°
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