Answer:
y=-4x+21
Step-by-step explanation:
1. Draw these points on a graph.
2. Point A is (4,5) and Point B is (7,-7).
3. You find the slope (gradient) by the Change in Height/ Change in Horizontal distance.
4. Now put that slope and one point into the "Point-Slope Formula"
5. Simplify Algebraically.
Answer:
y = - 4x + 21
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5 ) and (x₂, y₂ ) = (7, - 7 )
m = [tex]\frac{-7-5}{7-4}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 , then
y = - 4x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 5 )
5 = - 16 + c ⇒ c = 5 + 16 = 21
y = - 4x + 21 ← equation of line
Describe the power function f(x)=x^5. What does it look like? Where does it cross the x- and y-axis?
f(x) = x⁵ – 8x⁴ + 16x³ at x = 4, does not cross the x-axis. at x = 0, crosses the x-axis. This relates to the x-axis end behavior of a graph of a function.
What is meant by Function?A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.A function, which generates one output from a single input, is an illustration of a rule. The photographer is Alex Federspiel.Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.An input is connected to an output by a function. It resembles a device with an input and an output.Let's now find the roots of this function;
f(x) = x⁵ - 8x⁴ + 16x³
Let's factorize it first to get;
f(x) = x³(x² – 8x + 16)(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).
Thus; f(x) = x³ (x – 4)(x - 4)
C) Since we have found the factorized form to be;
f(x) = x³ (x – 4)(x - 4)
The roots are at f(x) = 0;
The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0
This indicates that x=0 and x=4 are f(xroots. )'s x = 4
As a result, the graph will touch the x-axis but not the repeated root of 4, which indicates that the graph has a repeated root.
D) The graph will cross at x = 0 because it is a root and does not cross at x = 4.
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Carter A charges $15 per person and $100 to set up tables. Carter B charges $20 per person and $50 to set up tables. Graph a system of equations. For what number of guests will the cost of Carter A be the same as the cost of Carter B? What is the cost for that number of guests?
PLEASE HELP AS SOON AS YOU SEE THIS!!!
Answer:
x=10 guests and $250
Step-by-step explanation:
Cater A=15x+100
Cater B=20x+50
2x+50=15x+100
5x=50
x=10
At the store, I bought
coffee that costs $9.86,
creamer for $2.15, and
sugar that was $1.99. If I
used my employee
discount and got 15% off,
what was my total bill?
Answer:
$11.90
Step-by-step explanation:
.85(9.86 + 2.15 + 1.99)
.85(14)
11.90
If we take off 15% from 100%, that leaves 85%. 85% as a decimal is .85
Answer:
$11.90 total bill after discount.
Step-by-step explanation:
the original amount is $14.00 with 15% discount it will come down to $11.90. Your discount was $2.10.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,
⇒ x²+ (y - 6)² = 36
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Now, We know that;
The standard form for finding the equation of a circle is expressed as;
⇒(x - a)² + (y - b)² = r²
where; (a, b) is the center of the circle and r is the radius of the circle.
Here, we have;
⇒ Diameter = 12 units
⇒ Radius = 12/2 = 6 units
Since, The center lies on the y-axis,
Hence, the center will be at (0, 6).
Substituting into the formula, we will have;
⇒ (x - 0) + (y - 6)² = 6²
⇒ x² + (y - 6)² = 36
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4. The ratio of students who made
the honor roll to the total number
of students is 1:50. If there are
500 students in total, how many
made the honor roll?
Answer: 10 made the honor roll
Step-by-step explanation:
Can you form a triangle using lengths 3/4 and 7?
It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.
In the given question, we have to check that it is possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 3 and 4
3 + 4 = 7
7 = 7
Now we add 3 and 7
3 + 7 > 4
10 > 4
Now we add 4 and 7
7 + 4 > 3
11 > 3
It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.
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The complete question is:
Can you form a triangle using lengths 3cm 4 cm and 7 cm?
missy flipped a coin 50 times. she flipped heads 26 times and tails 24 times. what is the experimental probability that the next flip will be tails
50%
because a coin only has 2 sides, resulting with a 50/50 chance of either option
I know that the sequence models the value of a car that originally cost $26,500 but loses 10% of its value each year. What do you know?Common ratio or difference : Explicit equation : Recursive equation :
Recursive equation :
A equation for one term that depends on another. If we want to generalize this sequence, we can achieve this by first defining the first term and then describing how the subsequent terms relate to one another. Recursive representation of a sequence occurs when the connection between its succeeding terms is described.Thus,
For the given question;
Common ratio or difference : 90% or 0.9.
first term = $26,500.
Thus, Recursive equation : f(n) = f(n - 1) + 9
Explicit equation :
Based on the term number, a formula for just any term.We explicitly represent a series when we have a formula that allows us to find any term as in sequence without considering any other terms.Thus,
Explicit equation : f(n) = 26,500 + (n - 1)(0.9).
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Please help me with my classwork
Answer:(b)7m^4
Step-by-step explanation:
56m^8/8m^4
is can be said as
(7m^4 )(8m^4)/8m^4
8m^4 from both numerator and as well as denominator cancels so the final answer is 7m^4(7 m to the power 4)
What is the relationship between cardiac output and intensity of exercise?
There is a linear relationship between exercise intensity and cardiac output. Therefore, when one rises, the other rises as well.
Cardiac output quantifies the volume of blood that your heart can pump in a minute. The phrase "exercise intensity" refers to how hard your body is working throughout a workout. These two are directly related to one another in some way.
The increase in cardiac output is linearly associated with exercise intensity up until the point of exhaustion. This happens as a direct result of the interaction between the heart rate and stroke volume reactions to the intensity of activity. Therefore, cardiac output will increase as exercise intensity does.
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X- 2.6 =5. Help me plsss
Answer: x=7.6
Step-by-step explanation:
x-2.6=5
Step 1: Move 2.6 to another side of the equation with addition
X-2.6+2.6=5+2.6
X=7.6
Check your answer!
7.6-2.6=5 Correct!
Answer:
x = 7.6
Step-by-step explanation:
x - 2.6 = 5
x = 5 + 2.6
x = 7.6
--------------------------
check7.6 - 2.6 = 5
5 = 5
the answer is goodTell whether each equation has no solution, one solution, or infinitely
many solutions.
a. 1+3x = 3x + 1
b. 4x + 1 = 3x + 2
c. 5x + 1 = 5x - 2
d. -3(x+1)=-3x+3
Conving is not permitted.
LESSON 11
Answer:
see below
Step-by-step explanation:
a. 1+3x = 3x + 1 --> infinite, it's the same thing
b. 4x + 1 = 3x + 2 --> x=1 one solution
c. 5x + 1 = 5x - 2 --> no solution. it's not possible
d. -3(x+1)=-3x+3 --> x=-1, one solution
What is the degree of 2x² 5x² 7?
The degree of 2x² 5x² 7 is 4.
The degree of a polynomial is the highest power of the variable in a given polynomial. In this case, the highest power of the variable is 4, making the degree of the polynomial 4.
We can calculate the degree by using the formula Degree = Max (exponent of x).
In this case, the exponent of x is 2 and 5 respectively, making the degree of the polynomial 4.
Therefore, the degree of the polynomial 2x² 5x² 7 is 4.
To calculate this, we can use the following formula:
Degree = Max (exponent of x)
For the given polynomial 2x² 5x² 7, we can calculate the degree as follows:
Max (2, 5) = 5
Therefore, the degree of the polynomial 2x² 5x² 7 is 5.
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Griffen's house is 40 feet by 20 feet. He is building an attached deck that is x feet long and 13 as wide as it is long. Use the drop-down menus below to complete statements using words and symbols to describe the total area in square feet of the house and deck. CLEARCHECK Using Words The total area of the house and deck is given by the sum: + . Using Symbols The total area of the house and deck is given by the sum: ft² + ft².
Answer:
Using Words: The total area of the house and deck is given by the sum: 40x20 + x(13x) .
Using Symbols: The total area of the house and deck is given by the sum: 800 + 13x^2 ft².
Step-by-step explanation:
1. When you hear the word MONEY what's the first thing that comes to mind?
Answer:
I think of bills/notes.
Step-by-step explanation:
Money is the mode or medium of exchange for goods and services.
What is currency?Currency is a type of money that is used as a medium of exchange in a specific country or region. It is a standardized unit of value that is accepted as payment for goods and services within the jurisdiction where it is used. Currency can take the form of physical banknotes and coins, or digital representations of money that can be used for online transactions.
Here,
Money is medium of exchange or a unit of account that is used to purchase goods and services. It is a tangible or intangible asset that represents value and is accepted by individuals, businesses, and governments in exchange for goods or services. Money is a fundamental component of modern economies, and its importance cannot be overstated.
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I need help with classifying this triangle!!
Answer:
Should be right and scalene
I need help with the problem on the photo. It’s in French so angines who can read French please tell me the answer.
Answer:
Step-by-step explanation:
Karine De Marchand is 54 years
How do I make a table of values?
The relationship between data items is displayed using tables of values. In science class, you might utilize a table of values. Some methods are explained.
Write the method to prepare a table?Tables of values are used by scientists and researchers to record their data, which is then examined for patterns. Then, they can use this pattern to make predictions.
A table of values might be used, for instance, by an arceologist tracking earthquake activity.Movement underground in relation to a fault line's location. Then, she could estimate the movement's perceived distance using the table.Some steps to prepare the table are-
A linear equation can be converted into a table of values by solving for y while substituting values for x.Simplify the equation after substituting each pair of x- and y-values to see if it accurately represents the data in the value table. If every statement you receive is accurate,The data are represented by the equation.To know more about the table, here
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Which ordered pair is in the solution set of the following system of inequalities
y≤ 3x+1
x-y>1
Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).
An explanation of inequalityAn inequality in mathematics is a relationship between two concepts or variables that isn't comparable. Therefore, inequality follows imbalance. When two integers are not equal, there is an inequality in mathematics. Egality and inequality are different. When two values aren't genuinely equal, the not equal basic is usually used to indicate this (). The values, whether tiny or huge, are contrasted using a variety of inequalities. By alternating the two characteristics until the constants integers become the only thing left, it is possible to solve many straightforward inequalities. However, a few things promote inequality: Negative values are halved or added to either side.
Here,
Given :
y≤ 3x+1
x-y>1
To find the value of x and y :
y≤ 3x+1
put the value of y
=> x - 3x -1 > 1
=> -2x -1>1
=>-2x > 2
=> -x>1
=>x >-1
x =1
Thus,
y≤ 3(1)+1
=> y ≤ 4
Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).
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What is obtuse triangle Class 7?
A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle.
What is obtuse in math?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. Isosceles (two equal sides and two equal angles) or scalene are two possible types of obtuse triangles (no equal sides or angles). This indicates that every angle is less than 90 degrees. A triangle with two angles that are less than 90 degrees and one angle that is 90 degrees (acute angles). A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.To learn more about obtuse refer to:
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How do you find 3 dimensional space?
Three-dimensional space is a geometric concept that involves three values, known as coordinates, to determine the position of an object. These three coordinates are known as length, width, and height. It can also be referred to as x, y, and z coordinates.
1. Understand the concept of three-dimensional (3D) space. Three-dimensional space is a geometric concept that involves three values, known as coordinates, to determine the position of an object.
2. Identify the three coordinates. These three coordinates are known as length, width, and height. They can also be referred to as x, y, and z coordinates.
3. Determine the coordinates of a specific point. To find the exact coordinates of a point in 3D space, you must determine the length, width, and height of that point.
4. Use the coordinates to calculate the distance between two points. To calculate the distance between two points in 3D space, you must use the Pythagorean Theorem to determine the length of the hypotenuse.
5. Visualize the 3D space. To better understand 3D space, you can use tools such as 3D modeling software to create a virtual representation of the space.
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Consider this system of equations 2/3 x + 3/5 y =12 (equation A) 5/2y - 3x = 6 (equations B)
The values of x and y that are solutions to the system of simultaneous equations are; y = 573/25 and x = 17.1
How to solve the system of linear equations?We are given the simultaneous equations;
²/₃x + ³/₅y = 12 -----(eq A)
⁵/₂y - 3x = 6 ------(eq B)
Multiply eq A by 9 and eq B by 2 to get;
6x + ²⁷/₅y = 108 -----(eq C)
5y - 6x = 12 ------(eq D)
Add eq C to eq D to get;
5y + ²⁷/₅y = 120
Multiply through by 5 to get;
25y + 27 = 600
25y = 600 - 27
25y = 573
y = 573/25
Thus;
5(573/25) - 6x = 12
6x = 5(573/25) - 12
6x = 102.6
x = 17.1
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From a 200-foot observation tower on the beach, a man sights a whale in difficulty. The angle of depression of the whale is 7 degrees. How far is the whale from the shoreline?
Whale is 1628.87 feet far from the shoreline.
What is angle of depression?The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
Given,
Height of the tower = 200 feet
Angle of depression = 7°
Distance of whale from the shore line = x = AB = ?
In the figure
tan 7° = BC/AB = 200/AB
0.1228 = 200/AB
AB = 1628.87 feet = x
Distance of whale from the shoreline = 1628.87 feet.
Hence, Whale and shoreline are 1628.87 feet far from each other.
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Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC
Answer:
121
Step-by-step explanation:
3x + 94 + x + 36 + 2x - 4 = 180
6x + 126 = 180
6x = 54
x = 9
m<AOC = 3x + 94
m<AOC = 3(9) + 94
m<AOC = 121
if f(x)=x^3+x^2 and g(x)=x^4+x^2+x, what is the value of f(x)-g(x) when x=1
hello need this due in 3 minutes have a good one
The line of the best fit for the data points plotted in the scatter plot is y = 0.67x + 4.05
How to determine the line of the best fit for the data points plotted in the scatter plot?From the question, we have the following parameters that can be used in our computation:
The graph
Using the line of the best fit, we have"
(x, y) = (0, 4) and (7, 9)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 4
Using the points, we have
9 = 7m + 4
This gives
m = 0.71
So, we have
y = 0.71x + 4
The closest to this is
y = 0.67x + 4.05
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What is a 2 step equation?
A two-step equation is an algebraic issue that can be resolved in two steps.
Define the term 2 step equation?An algebraic problem that can be solved in two steps is known as a two-step equation.Once you've figured it out, you'll know what the variable's value is that makes the equation true.Two-step equations typically take the form ax b = c, where a, b, and c are real numbers.
For instance, 2 - 3x = 7 is an illustration of a two-step equation.
Use the following steps to solve 2-step equations:
so that there is only one term left, add or subtract the same amount from both sides of the equation.Use the same number to multiply or divide both sides of the equation.When the variable (letter) is placed by itself on one side of the equals sign, the equation is considered to be solved.To know more about the 2 step equation, here
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Answer:
Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps.
Step-by-step explanation:
Example 1: Solve the two step equation (x/6) - 7 = 11
Solution: To solve the given two step equation, we will follow the steps discussed above in the article.
Step 1: Add 7 to both sides of the given two step equation
(x/6) - 7 + 7 = 11 + 7
= (x/6) = 18
Step 2: Multiply both sides of the equation by 6.
6 × x/6 = 6 × 18
= x = 108
Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.
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does the following graph go with the equation given?
1. f(x)3x^2+6x-24
2. What is the y-intercept of this graph?
3. What is the location of the vertex of this graph?
The equation does not represent the graph
The y-intercept is (0, -16)The location of the vertex of this graph is (-1, -18)How to determine if the equation represents the graphThe equation is given as
f(x) =3x² + 6x - 24
Calculate f(0) and f(1)
f(0) =3(0)² + 6(0) - 24 = -24
f(1) =3(1)² + 6(1) - 24 = -15
On the graph, we have
f(0) = -16
This means that the equation is not the graph
The y-interceptThis is when x = 0
So, we hav
f(0) = -16
How to determine the vertex of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The vertex of a graph is the minimum or the maximum of a graph
In this case, it is a minimum and the minimum is located at (-1, -18)
Hence , the vertex is (-1, -18)
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What is the exponential form of 3 4?
The given statement "number 3 to exponent 4" in exponential form is be written as 3⁴ , and the value of this expression is 81 .
The Exponential expression represented as "xⁿ" is read as the number x multiplied by itself "n" number of times .
we have to write "3 to exponent of 4" in exponential form ,
So , the exponential form is 3⁴ , it means that the number 3 is multiplied itself four times ;
the value of this expression is calculated as :
⇒ [tex]3^{4} = 3\times 3\times 3\times 3[/tex]
⇒ [tex]9\times 9[/tex]
⇒ 81 .
Therefore , the exponential form of "3 to the exponent of 4 " is 3⁴ .
The given question is incomplete , the complete question is
What is the exponential form of 3 to the exponent 4 ?
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There is 50 people with their probabilities that pick a season of the year
Someone picking spring: 18/50: 36%
Someone picking summer 16/50: 32%
Someone picking fall 4/50: 8%
Someone picking winter: 12/50: 24%
What is the probability that two people in a row have chosen fall?
Out of 50 people, there are 50C5 = 50!/(5!*45!) ways to select 5 of them.
A probability simple definition is what?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
How many of those methods involve picking a particular person (you)? If you are selected, there are only 4 more options left out of the remaining 49. There are thus 49C4 = 49!/(5!*44!) ways to select both you and the other 4 individuals.
Therefore, (49C4)/(50C5) = 1/10 is the probability.
The probability that you are one of the five individuals chosen from 50 is 5/50, or 1/10, as a second check.
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