Answer:
y-intercept = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the coefficient is the slope (slope = -2/9x)
the constant is the y-intercept (y-intercept=1/3)
this is true for all functions like this
Answer:
The y-intercept is
c) 1/3
Step-by-step explanation:
PLEASE HELP FIND X
1/2 (2x - 4) + 2 = 4(x + 2) - 11
Answer:
x=1
Step-by-step explanation:
Solve the following system of equations using substitution.
y = 2x-2
-4x-y = 26
Solve for x: Solve for y:
The solution to the given system of linear equations is x = -4, y = -10
Solving system of linear equationsFrom the question, we are to solve the given system of linear equations.
The given system of linear equations is
y = 2x - 2 ------------ (1)
-4x - y = 26 ------------ (2)
Substitute equation (1) into equation (2)
-4x - y = 26
-4x - (2x - 2) = 26
- 4x - 2x + 2 = 26
-6x + 2 = 26
-6x = 26 - 2
-6x = 24
x = 24/-6
x = -4
Substitute the value x into equation (1)
y = 2(-4) - 2
y = -8 - 2
y = -10
Hence, the x = -4, and y = -10
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5. Triangle DEF has vertices D(4, -3), E(-2, 1), and F(-9. -6). Find the area of the triangle.
Area of the triangle DEF = 35 square unit.
What is triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given,
Vertices of triangle
D(4, -3), E(-2, 1), and F(-9. -6)
x₁ y₁ x₂ y₂ x₃ y₃
Area of triangle S = 1/2[x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)]
Area of triangle DEF = 1/2[4(1 - -6) + -2(-6 - -3) + -9(-3 - 1)]
= 1/2 [4(7) -2(-3) -9 (-4)]
= 1/2[28 + 6 + 36]
= (1/2) (70)
Area of triangle DEF = 35 square unit
Hence, 35 square unit is the area of triangle DEF.
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Baseball And Calculus
Answer:
Calculus in baseball. In baseball, calculus can be used to optimize the pitcher’s throw to achieve maximum efficiency. Also, calculus can be used to calculate the projectile motion of baseball’s trajectory and to predict if runners can make it to the next base on time given their running speed and the speed of a hit ball.
Step-by-step explanation:
A total of 64 musicians entered a music contest, and of these musicians are guitarists. Some of the guitarists play jazz solos, and the rest play classical solos. The ratio of the number of guitarists playing jazz solos to the total number of guitarists in the contest is 1: 4. How many guitarists play classical solos in the contest
The number of guitarist who plays classical solos in the contest is 30.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Total number of musicians entered in the contest = 64
5/8 of these musicians are guitarists.
Number of guitarists = (5/8) × 64 = 40
Also we have,
Ratio of number of guitarists playing jazz solos to the total number of guitarists = 1 : 4 = 1/4
That is, of the 4 guitarists, 1 is a guitarist playing jazz solos.
Multiplying both numerator and denominator with 10, 1/4 = 10/40
So of the 40 guitarists, 10 number of guitarists play jazz solos.
Number of guitarists who play classical solos = 40 - 10 = 30
Hence 30 guitarists play classical solos.
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Which polynomial has only one zero?p(x) = 2x²-3x+4p(x) = x² - 2x + 1p(x) = 2x + 3p(x) = 5
The number of zeros in a polynomial equation is determined by the number of degrees it has, which is n.
Polynomial
A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division.
Bi-quadratic Polynomial
(Not comparable) Biquadratic (mathematics) x4 + 3x2 + 2 is an example of a polynomial expression that only uses a variable's zeroth, second, and fourth powers. When used in the form x4 4x3 + 3x2 x + 1, it is sometimes extended to any expression containing the biquadrate or fourth power (but not higher powers).
What is a Polynomial Equation?
Polynomial equations are those created by combining variables, exponents, and coefficients. The greater of its possible exponents is referred to as the equation's degree.
Among all possibilities, the linear polynomial p(x) = 2x+3 is a polynomial of degree 1. Consequently, there is just one zero in it.
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How do you find the coordinates of a vertex in factored form?
In order to find the y− intercept of a parabola in factored form, plug in 0 for x and find the corresponding y− value
What is coordinates of a vertex in factored form?The simplest way to obtain a vertex in factored form is to locate the axis of symmetry, substitute that as x, and then solve for y. With the formula x=r+s2, which means that r and s are the zeros, it is possible to determine the axis of symmetry. x is the vertex's x-component, or the axis of symmetry. Using the formula x=-b/2a, find the quadratic's vertex, and then substitute the result for y in the original equation. After that, enter the vertex as a variable in the vertex form equation, y=a(x-h)2+k. (A remains the same, h equals x, and K equals y.)The factored form of a quadratic expression is one in which the quadratic expression is the product of two factors, each of which is a linear expression. By extending it, which entails multiplying out the factors, a factored expression can be restated in standard form.To learn more about coordinates refer to:
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What is the exponential form of 10x10?
The exponential form of 10 * 10 is [tex]10^{2}[/tex] . We get it from the prime factorization.
In order to get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.
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What is the factoring method of X² 6x 16?
The factoring method for the polynomial x²+6x-16 is to find the values that satisfies the equation.
The given polynomial is x²+6x-16.
Now, in order to factorize the polynomial, we have to think of any two number such that by adding them the sum comes out to be 6 and when we multiply them, there product is -16, this is the factoring method for this polynomial.
So, by hidden trial method, we can analyze that there are two numbers 8 and -2.
By adding them, they becomes 6 and on multiplying they become -16.
So, the factorized form of the polynomial will be,
(x-8)(x+2)
Hence, the polynomial was factorized.
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Why 5 Is it possible to construct a triangle with lengths of its sides as 4 cm 3 cm and 7 cm give reason for your answer?
With sides that are 4 cm, 3 cm, and 7 cm long, a triangle cannot be built. Because the sum of the other two sides does not exceed that of the third side.
A triangle is referred to as a three-sided polygon that has three vertices. The connection of the three sides ends to end at a single point forms the angle of the triangle. The sum of these angles adds up to 180 degrees.
The triangle's three sides are specified as being 4 cm, 3 cm, and 7 cm. Add the two sides together and see if the result exceeds the third side to determine whether these sides constitute a triangle.
Here, the sum of two sides 4 cm and 3 cm is calculated as,
A+B = 4+3
=7 cm
This sum is equal to the third side C = 7 cm.
Therefore, [tex]A+B\ngtr C[/tex]. So, the given sides don't form a triangle.
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help so i can get an A?
Simplified form of -5⁷÷ 5² is -5⁵.
The correct option is C.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
Given expression,
-5⁷÷ 5²
Above expression can be written as
-5⁷/5²
= -1(5⁷)/5²
= -1(5⁵.5²)/5²
= -1(5⁵)
= -5⁵
Hence, -5⁵ is the simplified form of expression -5⁷÷ 5².
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Select all equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”
2/3÷?=1
?⋅2/3=1
1÷2/3=?
1⋅2/3=?
?÷2/3=1
What is the area of the triangle having sides 3 cm 4 cm and 5 cm?
The area of a triangle with sides 3 cm, 4 cm, and 5 cm is 6 cm² using Heron's formula.
Step 1: First, calculate the semi-perimeter of the triangle by adding the three sides of the triangle together and dividing by 2. In this case, the semi-perimeter would be (3 + 4 + 5) / 2 = 6 cm.
Step 2: Next, use the semi-perimeter and the three side lengths of the triangle to calculate the area. The formula for Heron's formula is:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter, and a, b, and c are the three sides of the triangle.
So, plug in the values,
Area = √(6(6-3)(6-4)(6-5))
Area = √(632×1)
Area = √(36)
Area = 6 cm²
Therefore, the area of the triangle is 6 cm²
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2
Solving Systems of Linear and Quadratic Equations: Mastery Test
Select the correct responses in the table.
The relationship between two numbers is described below, where x represents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the
first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
All rights reserved.
Equations
y² +16=x
x² = y +16
1-4y=7x
(2x)² = y + 16
7y-1 = 4x
4y-1 =7x
Reset
(1,15)
(2,-12)
(4,-7)
Next
Solutions
(5,9)
(8,48)
(9,3)
The equations that form the system that models this situation are:
B. x² = y + 16
F. 4y - 1 = 7x
The solution of the system of equations is: A. (5, 9).
How to determine the equations that form the system that models this situation?In this scenario, the relationship between two numbers, where x represents the first number and y represents the second number is given by the following word description:
"The square of the first number is equal to the sum of the second number and 16."
"The difference of 4 times the second number and 1 is equal to the first number multiplied by 7."
Next, we would translate the word problem into an algebraic equation:
x² = y + 16 .......equation 1.
4y - 1 = 7x .......equation 2.
Next, we would use an online graphing calculator to plot the given system of equations in order to determine its solution.
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Anna earns $8 an
hour baby-sitting and $6 an hour working in the garden. Last month, she worked 15 hours baby-sitting and 8 hours in the garden. How much more money does she need to buy a robot which costs $199?
Answer: $31
8(15)+6(8)=168
she needs 31 more to reach 199
what are the x-intercepts of this graph?
- To meet your sales quota at work, you need to average $125 per day. So far you have sold $150,
$175, $90, and $155. How much do you need to sell on the last day to meet your quota for this
week?
Hence he need to sell $55 on the last day to meet his quota for this
week.
What is average ?
average can be defined as the ratio of the sum of observations and total number of observations.
Given,
To meet your sales quota at work, you need to average $125 per day.
So far he sold $150, $175, $90, and $155.
so ,
let last day he need to sell be x .
average = 150+175+90+155+x/ 5
125 = 570+x / 5
625 = 570 + x
x = 55
Hence he need to sell $55 on the last day to meet your quota for this
week.
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Mr. Taylor and Mrs. Miller’s classes have been having a fundraising competition. they’ve both kept track of how much money they’ve raised in dollars versus the time in days. while mr. taylor’s class chose to graph their data, mrs. millers class chose to present it in a table. both classes have found that their fundraising over time has been proportional, where the daily increase in money raised is consistent. please explain why you chose this answer i will mark you brainliest
What is equation easy?
A mathematical equation can be defined in a variety of ways.
Equation that is linear.A quadratic equation.Cubic Formula.Define the term equation?A mathematical equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Equation that is linear.
There could be multiple variables in a linear equation. If a variable's highest power is always 1, an equation is said to be linear. A one-degree equation is another name for it.A quadratic equation.
A second-order equation is this one. At least one of the variables in quadratic equations needs to be raised to exponent 2.Cubic Formula.
Third-order equation.There should be at least one variable raised to exponent 3 in cubic equations.To know more about the equation, here
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What are the roots of the equation 25x^2+60x+37=0 25x ^2 +60x+37=0 in simplest a+bia+bi form?
The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The equation is given below.
25x² + 60x + 37 = 0
The roots of the equation is given as,
x = [- 60 ± √{(60)² - 4 × 25 × 37}] / (2 × 25)
x = [- 60 ± √(-100)] / 50
x = [- 60 ± 100i] / 50
x = - 6/5 ± 100 i
x = - 6/5 + 100i, - 6/5 - 100i
The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.
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Which of the following is a zero of the polynomial x³ 3x² 3x?A - 1B - 2C 1D 2
A polynomial is a kind of algebraic expression in which the exponents of all variables should be a whole number.
The Power of the variables in any polynomial has to be a non-negative integer. A polynomial consists of constants and variables, but we cannot perform division operations by a variable in polynomials.
The example of polynomial is: 3x^2 + 5.
given the equation is x^3+3^2+3x.=0
(x³-x) +(3x²-3) =0
= x (x²-1) +3(x²-1)
= (x²-1) (x+3) = 0
(a² + b²) = (a+b) (a-b)
(x²-1) = (x+1) (x-1)
⇒(x+1) (x-1) (x+3) =0
x =- 3, -1, 1
So, the required zeros are -3, -1,1.
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Which of the following is a solution of the equation x+ 2y 7?a) x=3 y=5b) x=3 y=-5c) x=3,y=2d) x=0.y=7
(3,2) is the required solution of an equation and This is a straight line and has infinite number of solutions.
the solution is explained as :
y=2
x=7−2(2) =3
Hence, (5,1) is one of the solution of the given equation.
A straight line is an infinite length of an line that does not have any curves on it. A straight line in which it can be formed between two given points and also but both the ends extend to infinity. A straight line is formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them and the line that ends are extended to infinity.
In the given representation shown below, a straight line between two points A and B is shown. A straight line AB is represented by:
←→
A B
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question below
Graph the line y=-4(x+1)+2y=−4(x+1)+2 using the given table of values and following the instructions below.
The required graph is attached below.
what is the Cartesian co-ordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The points (0,-2) (-1,2) Also the given equation is
y=-4x-4+2
y=-4x-2
Thus this is linear graph with y intercept at -2 and using the equation we plot the two points from Table 2.
Hence, The points are plotted.
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-3y = -2x - 1
y = x - 1
i need a solution please help
Answer:
x=4, y=3. (4, 3).
Step-by-step explanation:
-3y=-2x-1
y=x-1
--------------
-3(x-1)=-2x-1
-3x+3=-2x-1
-3x-(-2x)+3=-1
-3x+2x=-1-3
-x=-4
x=4
y=4-1=3
Nicholas collected 66 pounds of shells. If he wanted to split the shells equally amongst 7 friends, how much should he give each friend? Between what two whole numbers does your answer lie?
Answer:
9 and 10
Step-by-step explanation:
66 divided by 7 would be 9.4 which lies between 9 and 10.
The band wanted to do a fundraiser to raise money for the competition trip to Disney land they had an initial amount of money in their booster club account and each band member was expected to raise the same amount the equation 300x + 750 = 23,250 represents the total amount of money in the account after they were done fundraising if z represent the number of students in the band what does 750 likely represent
The value 750 in equation 300x + 750 = 23,250 represents the initial amount in the club account.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Initial amount in the club account = m
Amount raised by each member = n
All members raised the same amount.
Number of members = x
The total amount raised by all the members = p
nx + m = p
This is similar to the equation 300x + 750 = 23,250
So,
n = 300
m = 750
p = 23,250
Now,
m = 750 is the initial amount in the club account.
Thus,
750 represents the initial amount in the club account.
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Angela ran for 45 mins, her pace was 9 mph. How far did she run (in miles)?
A hot-air balloon ha a 14
14
-foot diameter that i being deflated at a rate of 0. 25
0. 25
feet per minute. How many minute,
x
, will it take before the balloon ha hrunk to a diameter of 8
8
feet?
Total 24 minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet.
In the given question, we have to find how many minute, x, will it take before the balloon has shrunk to a diameter of 8 feet.
From the given question, a hot-air balloon has a 14-foot diameter.
Hot-air balloon is being deflated at a rate of 0.25 feet per minute.
So the slope will be = -0.25, the negative sign is there because hot-air balloon is being deflated.
Let the amount of air left in the hot-air balloon at time n minutes is A(n) feet diameter.
The initial value of A(n) is 14-foot diameter.
Thus when n = 0, the value A(n) will be 14.
So, we can write the relation as
A(n) = -0.25n + 14
We need to find the amount left after x minute. So n = x.
The balloon has shrunk to a diameter of 8 feet. So A(n) = 8 feet
Now the equation is
8 = -0.25x + 14
Subtract 14 on both side, we get
-0.25x = -6
Divide by -0.25 on both side, we get
x = 24
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The complete question is:
A hot-air balloon has a 14-foot diameter that is being deflated at a rate of 0.25 feet per minute. How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
Moussa practices the piano 840 minutes in 4 weeks. Assuming he practices the same amount every week, how many minutes would he practice in 1 weeks?
Answer:
210 minutes a week
Step-by-step explanation:
840 minutes/4 weeks
Are complex numbers the same as real numbers?
Although every complex number is a real number, not all complex numbers are real numbers.
What connection exists between real numbers and complex numbers?On the number line, the real numbers can be plotted.The number line cannot be used to plot the complex numbers.The symbol designates it.Complex numbers make up all real numbers.Real numbers are not all complex numbers.Although every complex number is a real number, not all complex numbers are real numbers. The symbol Z C Z in mathbb C ZC denotes the collection of all complex numbers.If a number can be expressed as a+bi using the real integers a, b, it is complicated. So, certainly, a complex number can be both real and totally fictitious.To learn more about real numbers refer to:
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