Answer:
x = 6
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 25 when y = 100 , then
100 = 25k ( divide both sides by 25 )
4 = k
y = 4x ← equation of variation
When y = 24 , then
24 = 4x ( divide both sides by 4 )
6 = x
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.
Learn more about Ratios here :
https://brainly.com/question/1504221
#SPJ1
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
Solve for r (PLEASE HELP DUE TODAY)
14.3 = pi (r²) (1.4)
In the equation, r will have the value 1.79.
What is an Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. The sign shows the relationship of equality between the expression written on the left side with the expression written on the right side.
14.3 = pi (r²) (1.4)
(r²) = 14.3/pi(1.4)
where pi = 3.142
(r²) = 14.3/3.142(1.4)
(r²) = 14.3/4.3988
(r²) = 3.212
r = √3.212
r = 1.79
Learn more about equations here:https://brainly.com/question/2972832
#SPJ1
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.
Read more on equations and numbers here: https://brainly.com/question/8435632
#SPJ1
What is the solution to the equation 6y –2(y + 1) = 3(y – 2) 6? a. y = –10 b. y = –2 c. y = 2 d. y = 6
The solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.
What is algebraic equation ?
An algebraic equation is a mathematical statement that asserts the equality of two expressions, each of which is made up of numbers and/or variables. The expressions are separated by an equal sign (=). The goal of solving an algebraic equation is to find the value(s) of the variable(s) that make the equation a true statement.
To find the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6, we must first simplify both sides of the equation by following the order of operations (PEMDAS). First, we simplify the right side of the equation: 3(y - 2) 6 = 3y - 6 * 6 = 3y - 36. Next, we simplify the left side of the equation: 6y - 2(y + 1) = 6y - 2y - 2 = 4y - 2.
Now we have the equation: 4y - 2 = 3y - 36
Next, we can add 2 to both sides of the equation and get: 4y = 3y - 34
Finally we subtract 3y from both sides of the equation and get: y = -34
Therefore, the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.
To learn more about algebraic equation visit : brainly.com/question/953809
#SPJ4
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.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ1
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.
Know more about Polynomial Equation
https://brainly.com/question/1600696
#SPJ4
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
Learn more about triangle at
https://brainly.com/question/29003298
#SPJ4
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 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.
To learn more about Exponential form please visit:
https://brainly.com/question/26588173
#SPJ4
What is the slope of =- 10?
The slope of -10 as calculated from the data given is found out to be as 0.
Let's say y = -1= ,
Now, we know that the formula to calculate slope is y = mx+ b y .
This is known as slope-intercept form and can be written as ,
y = m x + b,
m = slope and b b= y-intercept.
y = mx +b y
y = m x + b
Therefore , by looking at this formula we can say that the value of m is 0 .
So , the slope is found out to be 0.
The slope is defined as the change in y coordinate with respect to the change in x coordinate of that line.
To learn more about slope
brainly.com/question/3605446
#SPJ4
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.
More about the roots of the equation link is given below.
https://brainly.com/question/12029673
#SPJ1
what is the answer to two plus two. Please help
Answer:
the answer is 4
2+2=4 bc 1+1 is 2 ×2 and that is 4 your welcome
what are the x-intercepts of this graph?
A t-shirt company needs to restock their inventory by ordering 562 shirts. The company only has room for 951 shirts in their stock room. Model the number of shirts the company can order, using a compound inequality.
x ≥ 562 and x ≤ 951
x ≤ 562 and x ≥ 951
x ≤ 562 and x ≤ 951
x ≥ 562 and x ≥ 951
PLEASE HELP FIND X
1/2 (2x - 4) + 2 = 4(x + 2) - 11
Answer:
x=1
Step-by-step explanation:
Due today.. ixl assignments. I have to pick the equation, then solve it.
The graph shows the number of possible passengers for a given number of roller coaster cars that leave the platform. Complete parts a and b.
the slope of the line is 8 and equation line is y = 8x.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
slope m = 24-16 / 3-2
m = 8/1 = 8
y = 8x
Hence the slope of the line is 8 and equation line is y = 8x.
Learn more about Slope, by the following link
https://brainly.com/question/3493733
#SPJ1
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
To learn more about writing the equation link is here
brainly.com/question/13386239
#SPJ4
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?
Need help on question b
The algebraic expression in question b can be simplified to give (x² - 5x)/5.
Simplifying Algebraic expressionSimplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.
2x²(x - 5)/10x = 2x × x(x - 5)/ 2x × 5
2x is a common factor to both the numerator and denominator, hence can cancel out
2x²(x - 5)/10x = x(x - 5)/5
opening bracket we have;
2x²(x - 5)/10x = (x² - 5x)/5
Therefore, (x² - 5x)/5 is the result after simplifying the algebraic expression 2x²(x - 5)/10x
Learn more about algebra here:https://brainly.com/question/11875858
#SPJ1
H divided by 5 equal 18
Answer: 90
Step-by-step explanation: I multiplied 18 by 5
Answer:
H=90
Step-by-step explanation:
if H÷5=18, then reverse it. so 18×5=90
Determine if this statement is always, sometimes, or never true.
If a ≥ 0, then |a| = -a
never
sometimes
always
The statement "If a ≥ 0, then |a| = -a" is always false.
What is the absolute value?
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
The absolute value of a real number, denoted by |a|, is the non-negative value of a without regard to its sign.
Therefore, if a is greater than or equal to zero, the absolute value of a is equal to itself.
On the other hand, -a is the negative of a, which is only the case when a is less than zero.
Hence, |a| can never equal to -a when a ≥ 0, because the absolute value is always non-negative, while -a is always negative.
To learn more about the absolute value visit,
https://brainly.com/question/24368848
#SPJ1
The sentence "If a 0, then |a| = -a" is untrue at all times. 4 is equal to 4 in absolute terms. The formal notation for a number's absolute value is |x|.
What is the absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value. The non-negative value of a, indicated by the symbol |a|, is the absolute value of a real number, regardless of its sign. It follows that if an is higher than or equal to zero, its absolute value is also zero.
However, -a is the opposite of a, and is only true when an is less than zero. This means that when an is greater than 0, |a| can never equal -a because the absolute value is always non-negative whereas -a is always negative. Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
To learn more about Absolute value refer to :
https://brainly.com/question/24368848
#SPJ1
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.
Learn more about coordinate system here:
https://brainly.com/question/29762404
#SPJ1
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.
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:
https://brainly.com/question/20935031
#SPJ4
i need help with this
Answer:
lo l oh my gosh hi i havent seen u in so many years
Step-by-step explanation:
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
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
Learn more on Solving system of linear equations here: https://brainly.com/question/13729904
#SPJ1
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.
To know more about Polynomials, visit,
https://brainly.com/question/2833285
#SPJ4
-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