The required value of k will the system of linear equations has infinite number of solutions is -9.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:We know that
2x+3y13=0. ..........(1)
6x−ky−39=0 ..........(2)
Because there are infinity many solutions to linear equations.
[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]
⇒ 2/6 = -3/k = -13/-39
-3/k = 1/3
k = -9
Thus,required value of k is -9.
To know more about Linear equation visit:
brainly.com/question/11897796
#SPJ4
Write a function rule for the given situation. Do not use spaces in your answers and use x and y as your variables.
(help me out pls )
The situation can be modeled with the linear function:
f(x) = $30*x + $100
Evaluating that, we can see that after two years you will pay $820.
How to write a function rule for the situation?Here we know that you buy a gym membership for $100 plus $30 per month.
So, the cost after x months can be modeled by the linear function:
f(x) = $30*x + $100
Where x is the number of months and f(x) is the amount of money that you pay after x months.
We want to find how much you will pay after 2 years, there are 24 months in two years, then we will get:
f(24) = $30*24 + $100 = $820
Learn more about linear functions:
https://brainly.com/question/4025726
#SPJ1
michael is examining a data set and trying to determine which category he can transform into a dummy variable. of the four variables, employee number, pay rate, hire date, and sex, which is the best fit to use a dummy variable?
Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.
The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.
Read more about variables:
brainly.com/question/15158734
#SPJ4
What is another name for the addition method to solve a system of equations in two variables?
The elimination method is another name for the addition method to solve a system of equations in two variables.
What is The elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.
What are some instances of elimination methods?
Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Each side of an equation can be increased by the same amount.
You can therefore add x + y to the left side of the first equation and add 8 to the right side of the equation if your system is x - 6 = 6 and x + y = 8.
Learn more about The elimination method
brainly.com/question/30287548
#SPJ4
The cost of 5 sixty minute cassette tapes and 9 ninety minute tapes is $71.40. The cost of 8 sixty minute tapes and 7 ninety minute tapes is $74.65. Find the cost of each type of tape.
The cost of a sixty minute tape is $11.40 and the cost of a ninety minute tape is $1.60.
What is the step by step explanation?This is a system of equations problem. We can start by setting up the equations using the information given. Let x be the cost of a sixty minute tape and y be the cost of a ninety minute tape.From the first piece of information:5 x + 9 y = 71.40From the second piece of information:8 x + 7 y = 74.65To solve for x and y, we can use the method of substitution, where we solve one equation for one variable and substitute that expression into the other equation.5 x + 9 y = 71.408 x + 7 y = 74.65Solve the first equation for x:x = (71.40 - 9 y)/5Substitute this expression into the second equation:8((71.40 - 9 y)/5) + 7 y = 74.65Solving for y:y = $1.60Now we can substitute this value of y into the first equation to find the value of x:5 x + 9(1.60) = 71.405 x = 71.40 - 14.405 x = 57x = $11.40So, the cost of a sixty minute tape is $11.40 and the cost of a ninety minute tape is $1.60.To learn more about systems of equation refer:
brainly.com/question/13729904
#SPJ1
A recipe to make green paint calls for 4 cups yellow and 5 cups blue paint. If I used 100 cups of blue paint, how much yellow paint would I need ?
Answer:
Step-by-step explanation: 500
Consider the quadratic equation $ax^2 + bx + c = 0$ with $a, b, c$ integers from $-4$ to $4$ and $a not equal to 0$.
The solutions to this equation are in the form [tex]\frac{P+=\sqrt{D}}{Q}[/tex] where $D$ is square free.
Determine the largest possible value of $D$.
The largest possible value of D is 6.4.
What is the largest possible value of D?
The largest possible value of D is calculated by applying the following formula as shown below.
The largest possible value of D is obtained when the situation occurs;
b will be positive or negative a is positive and c is negativea is negative and c is positivelet b = 3
a = 4
c = - 2
D = √ ( b² - 4ac )
D = √ ( 3² - ( 4 x 4 x - 2 )
D = √ ( 9 + 32 )
D = √ ( 41 )
D = 6.4
Learn more about discriminant here: https://brainly.com/question/2507588
#SPJ1
4
If f(x)=x-4 and g(x) = -2x² + 3, which polynomial is equivalent to g(f(x))?
A -2x² + 16x - 29
C-2x² - 1
B -2x²-16x +35
D -2x³ +8x² + 3x - 12
Answer: A. -2x² + 16x -29
Step-by-step explanation:
f(x) = x-4
g(x) = -2x² + 3
g(f(x)) = -2( x² + 16 -8x) + 3
= -2x² - 32 + 16x + 3
= -2x² + 16x -29
Pls help this one question is worth 25 points !!!
3. (05. 04 MC)Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches. The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches. Part A: Using the formula for circumference, solve for the value of pi for each circle. Part B: Use the formula for area and solve for the value of pi for each circle. Part C: What observation can you make about the value of pi for circles A and B?
Part A: The value of π for circle A using the circumference is 3.14 and the value of π for circle B using the circumference is 3.14.
Part B: The value of π for circle A using the area is 3.14 and the value of π for circle B using the area is 3.14.
Part C: You can notice that pi's value remains constant in both circles, proving that it is a constant.
Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches.
The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle.
Circumference formula of circle = 2πr
The diameter of circle A d = 7 inches
The radius of circle A r = 7/2 inches
The circumference of circle of A = 21. 98 inches
Now putting the values in the formula
2π×[tex]\frac{7}{2}[/tex] = 21. 98 inches
7π = 21. 98 inches
Divide by 7 on both side, we get
π = 3.14
The value of π for circle A is 3.14.
The diameter of circle B d = 6 inches
The radius of circle B r = 6/2 inches = 3 inches
The circumference of circle of B = 18.84 inches
Now putting the values in the formula
2π×3= 18.84 inches
6π = 18.84 inches
Divide by 6 on both side, we get
π = 3.14
The value of π for circle B is 3.14.
Part B: Use the formula for area and solve for the value of pi for each circle.
The area of circle = [tex]\pi r^2[/tex]
The radius of circle A r = 7/2 inches = 3.5 inches
The area of circle A = 38.465 square inches
Now putting the value
[tex]\pi (3.5)^2[/tex] = 38.465
π × 12.25 = 38.465
Divide by 12.25 on both side, we get
π = 3.14
The value of π for circle A is 3.14.
The radius of circle B r = 3 inches
The area of circle B = 28.26 square inches
Now putting the value
[tex]\pi (3)^2[/tex] = 28.26
π × 9 = 28.26
Divide by 9 on both side, we get
π = 3.14
The value of π for circle B is 3.14.
Part C: We have to explain what observation you can make about the value of pi for circles A and B.
You can notice that pi's value remains constant in both circles, proving that it is a constant.
To learn more about circumference and area of circle link is here
brainly.com/question/16125353
#SPJ4
Which math statement compares the decimal numbers 0.34 and 0.8 correctly?
Answer:
0.34 < 0.8
Step-by-step explanation:
On compares the decimal numbers 0.34 and 0.8 the correct math statement is 0.34 < 0.8.
To compare the decimal numbers 0.34 and 0.8 correctly, we need to determine which one is greater or if they are equal. One way to do this is by aligning the decimals and comparing the digits from left to right.
0.34 and 0.8 have a different number of decimal places. To make the comparison easier, we can add a trailing zero to 0.34:
0.34 ( or 0.340 ) and 0.8
Now, we can compare them:
0.340 < 0.8
So, the correct math statement is: 0.34 < 0.8.
To know more about decimal numbers click here :
https://brainly.com/question/123818
#SPJ2
At Andy's Market, the price of a box of brand-name cereal is 1.5 1.51, point, 5 times the price of a box of generic cereal. If the price of a box of brand-name cereal is $ 3.60 $3.60dollar sign, 3, point, 60, which of the following can be used to determine � xx, the price of a box of generic cereal in dollars? Choose 1 answer: Choose 1 answer: (Choice A) A � 1.5 = 3.6 1.5 x =3.6start fraction, x, divided by, 1, point, 5, end fraction, equals, 3, point, 6 (Choice B) B 1.5 � = 3.6 1.5x=3.61, point, 5, x, equals, 3, point, 6 (Choice C) C 3.6 � = 1.5 3.6x=1.53, point, 6, x, equals, 1, point, 5 (Choice D) D � + 1.5 = 3.6 x+1.5=3.6
C 3.6 = 1.5 3.6x=1.53, point, 6, x, equals, 1, point,5.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It is composed of two expressions, one on each side of an equals sign, and can be used to solve for unknown values. Equations can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to solve a wide variety of mathematical problems.
The equation to solve for the price of a box of generic cereal is 3.6/1.5 = x, where x is the price of the box of generic cereal. By dividing 3.6 by 1.5, the price of a box of generic cereal is determined to be $2.40.
To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1
5m3 + 3m² – 2m
5m3 + 3m? – 2m
8m3 - 4m2 + 3m
What is the perimeter of the triangle?
Help ASAP!!!!!
The perimeter of the triangle is given by an expression 18m³ + 2m² - m
Consider the following diagram.
In this question we have been given a triangle.
The sides of the triangles are represented by a mathematical expressions
(5m³ + 3m² - 2m), (8m³ - 4m² + 3m) and (5m³ + 3m² - 2m)
From given expression we can observe that, there are two sides with expression 5m³ + 3m² - 2m.
This means, the triangle must be an isosceles triangle.
We know that the formula for the perimeter of isosceles triangle.
P = 2a + b
where, a = side and b = base of isosceles triangle
Using above formula the perimeter of given triangle would be,
P = 2(5m³ + 3m² - 2m) + (8m³ - 4m² + 3m)
P = (10m³ + 6m² - 4m) + (8m³ - 4m² + 3m)
P = (10 + 8)m³ + (6 - 4)m² + (-4 + 3)m .....(combine like terms)
P = 18m³ + 2m² - m
Learn more about an expression here:
https://brainly.com/question/30091997
#SPJ4
Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?
The expression [tex]\sqrt[3]{8^{x} }[/tex] is equivalent to, [tex]8^{x/3}[/tex], So Option C is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression, [tex]\sqrt[3]{8^{x} }[/tex]
equivalent expression = ?
⇒ [tex]\sqrt[3]{8^{x} }[/tex]
⇒ [tex]\sqrt[3][/tex]cube root can be written as 1/3 power of 8
So, expression will convert like this,
⇒ [tex]8^{x/3}[/tex]
Hence, the equivalent expression is [tex]8^{x/3}[/tex]
To know more about Expressions check:
brainly.com/question/16804733
#SPJ1
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS
The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle,
prove that the triangles are congruent using SSS or SAS?
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.
To learn more about triangles refers to:
https://brainly.com/question/1058720
#SPJ1
.
What are the coordinates of the midpoint of the line segment joining the point A (4,-2) and B (10,-6)?
Answer: (7, -4)
Step-by-step explanation: To find the midpoint of a line segment, We take the average of the X-coordinates and the Y-coordinates of the two endpoints.
Given points A(4,-2) and B(10,-6), the midpoint can be found using the following steps.
1. Take the average of the X-coordinates: (4+10)/2=7.
2 Take the average of the Y-coordinates: (-2 + -6)/2=-4.
So the midpoint of the line segment joining A and B is (7,-4).
A system of equestions is given for the following scenario Solve using substitution and fill in the blanks Brittany wants to buy a charm braceletSpringdale Fine Jewelry charges $11 per charm, plus 42 for the braceletChu Jewelers, in contrast charges per charm and 84 for the braceletBrittany wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shopHow many charms would that be? What would the total cost of the bracelet be? Springdale Fine Jewelry y = 11c + 42 Chu Jewells y = 8c + 84
Answer:
Step-by-step explanation:
is this college
What is the range of the function shown in the graph below?
Based on the graph, it looks like the only y-value not used by the graph is –6.
So, the range would be (-infty, -6) U (-6, infty).
FIND THE SLOPE BETWEEN THE FOLLOWING POINTS!!!
15 POINTS
The slope between the points (-6, 6) and (-6, -1) is -infinity.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect with the change in the independent variable.
Therefore, the slope is define as rise over run.
Hence let's find the slope between the points (-6, 6) and (-6, -1)
Therefore,
slope = y₂ - y₁ / x₂ - x₁
x₁ = -6
x₂ = -6
y₁ = 6
y₂ = -1
Therefore,
slope = -1 - 6 / -6 + 6
slope = -7 / 0
slope = - infinity
learn more on slope here:https://brainly.com/question/15166299
#SPJ1
the diagonal of a particular square is 5 inches. the diameter of a particular circle is also 5 inches. by how many square inches is the area of the circle greater than the area of the square? express your answer as a decimal to the nearest tenth.
7.13 square inches is the area of the circle greater than the area of the square
area of a circle is pir^2 = pi*2.5^2
side of the square by Pythagoras
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
5^2 = 2x^2
x^2 = 12.5 = area of the square
area of circle = pi * 6.25 = 19.63
difference in areas = 19.63 - 12.5 = 7.13 sq ins
Know more about area of a circle
https://brainly.com/question/14068861
#SPJ4
What is the constant of proportionality in the equation y=7xy=7xy, equals, 7, x?.
The constant of proportionality is the number that is multiplied by the variable in the equation. In the equation y=7x, the constant of proportionality is 7.
Step 1: Identify the equation: y=7x
Step 2: Determine what the constant of proportionality is: The constant of proportionality is 7.
Step 3: Calculate the value of the constant of proportionality: The constant of proportionality is 7.
The constant of proportionality is a number that is multiplied by the variable in an equation. For example, in the equation y=7x, the constant of proportionality is 7. This means that for every unit increase in x, y will increase by 7. To calculate the constant of proportionality, simply identify the equation and determine what number is multiplied by the variable. In this case, the number is 7. Consequently, 7 is the constant of proportionality. The constant of proportionality is an important concept in mathematics and is used to calculate the relationship between variables in equations. Knowing the constant of proportionality can help make equations easier to solve and understand.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
How do you solve a 30 60 90 triangle given only the hypotenuse?
Yes, it is possible to solve 30 60 90 triangles if only a hypotenuse is given. The 30, 60, and 90 are special right triangles.
30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse
In this type of triangle, the hypotenuse is double of height.
Let's assume the hypotenuse given = [tex]x[/tex]
therefore, height = [tex]\frac{x}{2}[/tex]
and the base is [tex]\sqrt{3}[/tex] times the height
so, base = [tex]\frac{x}{2}\sqrt{3}[/tex]
Points to be noted:
the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.
Learn more about 30 60 90 triangles here:
https://brainly.com/question/11751274
#SPJ4
Jordan's pet grooming business has a monthly cost function of C = $15p + $1520. His Revenue is given by the function R = $55p, where C is the total cost per month, R is the total revenue he receives each month and p is the number of pets he grooms in a month. How many pets must he groom each month to break even?
For Jordan's pet grooming business to break even, he must groom 38 pets each month.
What is the break-even point?The break-even point describes a sales situation where the total costs equal the total revenue.
At the break-even point, there is no profit or loss.
Cost function: C = $15p + $1520
Revenue function: R = $55p
The total cost per month = C
The total revenue each month = R
The number of pets Jordan grooms monthly = p
To break even, C must be equal to R:
$15p + $1520 = $55p
15p + 1520 = 55p
-40p = 1,520
p = 38
Check:
Total costs = $15p + $1520
= $15(38) + $1520
= $570 + $1520
= $2,090
Total revenue = $55p
= $55(38)
= $2,090
Thus, grooming 38 pets each month, the total costs and revenue are equal to $2,090, respectively.
Learn more about the break-even point at https://brainly.com/question/21137380
#SPJ1
A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw that graph for the relation between the market price and the discount.
Hence find (1) the marked price when a customer gets a discount of Rs3250(from graph)
(2)the discount when the market price is rs2500
The marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The relation between the market price and the discount is
y=0.5x
Which is the required relationship between the Marked Price and the Discount.
We have to find the marked price when a customer gets a discount of 3250
As discount is 3250
In the graph is represent the point F ( 3250, 0)
If we draw a line parallel to Y axis and passing through the point F( 3250, 0) then it intersects the line y = 2x at B( 3250 , 6500)
Accordingly we get the point A ( 3250, 6500)
Hence the Marked Price = 6500
Manually it can be checked
As discount is 3250
x = 3250
So y = 2 × 3250 = 6500
(2) We have to find the discount when the marked price is 2500
As marked price is 2500
In graph it represent the point C( 0, 2500)
If we draw a line parallel to X axis and passing through the point C( 0, 2500) then it intersects the line y = 2x at B( 1250 , 2500)
Accordingly we get the point B( 1250 , 2500)
Hence the discount = 1250
Manually it can be checked
As marked price is 2500
y = 2500
So x = 2500 ÷ 2 = 1250
Hence, the marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Find the intercept on the x and y axes 3y=2/3x+4
Answer: The x-intercept is when y is equal to 0, so we can find it by setting y to 0 and solving for x:
0 = 2/3x + 4
3x = -4
x = -4/3
So the x-intercept is (-4/3, 0)
The y-intercept is when x is equal to 0, so we can find it by setting x to 0 and solving for y:
3y = 2/3 * 0 + 4
3y = 4
y = 4/3
So the y-intercept is (0, 4/3)
Step-by-step explanation:
Geomatry: Sin Cos and Tan: Find the value of X. (pls)
Answer:
16 degrees, I believe
Step-by-step explanation:
You would use an inverse sine, if I'm not mistaken. You have the O (opposite) and the H (hypotenuse). With that you can do SOH - or sine. But since you want the angle, you do an inverse. So you do the inverse sine of O over H, or the inverse sine of 5/18. It gives you 16.128 degrees or so.
question 1 a clinic surveys a group of male and female patients about their experience with physical therapy. the survey does not include people with disabilities. is the survey data biased?
Yes, the survey data is biased.
The survey data is biased because the sample group lacks inclusivity.
Bias is a statistical word that means a systematic deviation from the actual value. It is a sampling method that may show some serious problems for the researcher as a less increase cannot reduce in sample size.
In a biased sample, one or more parts of the population are favored over others, whereas in an unbiased sample, each member of the population has an equal chance of being selected. We also saw that a representative sample is a subset of the population that reflects the characteristics of the larger group.
Read more about bias:
https://brainly.com/question/24491228
#SPJ4
What is the slope 0 /- 2?
The slope 0/(-2) means, the line is coincident or parallel to the x-axis
We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.
The slope of the line describes the steepness of a line.
Also, if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ
m = tan θ
Here we have been given a slope 0/(-2)
As we know 0/(-2) = 0
So, the slope is 0.
Let m = 0
From definition of slope of line,
m = tan θ
0 = tan θ
θ = arctan(0)
θ = (nπ) where n = 0, 1, 2, . . .
This means, the slope 0/(-2) means for every two units of horizontal distance crosses there is no change of vertical distance.
Learn more about the slope here:
brainly.com/question/16180119
#SPJ4
Please answer fast I will mark brainliest
Answer: bro what question is it
melanie is driving on a long road trip. She currently has 10 gallons of gas in her car. each hour that she drives, her car uses up 1.5 gallons of gas. How much gas would be in the tank after driving for 6 hours? how much would be left after t hours
Answer:
1 gallon
Step-by-step explanation:
using 1.5 gallons per hour for 6 hours equals their product, which is 9
so if there was originally 10 gallons, after driving 6 hours, there would be 1 gallon remaining
solve each equation
20x-3/15=8
Answer:
20x-3/15=8
We move all terms to the left:
20x-3/15-(8)=0
determiningTheFunctionDomain
20x-8-3/15=0
We multiply all the terms by the denominator
20x*15-3-8*15=0
We add all the numbers together, and all the variables
20x*15-123=0
Wy multiply elements
300x-123=0
We move all terms containing x to the left, all other terms to the right
300x=123
x=123/300
x=41/100
Answer:
x = 0.41
Step-by-step explanation:
20x-3/15=8
20x - 1/5 = 8
20x - 1/5 = 40/5
20x = 41/5
20x = 8.2
x = 0.41
How do you find f (- 1 on a graph?
To find f(-1) on a graph, you need to locate the point (-1, y) and then read off the value of y.
Begin by locating the point (-1, 0) on the graph. This point is located at the far left side of the x-axis. Then, draw a line from this point to the line representing the function. This line will intersect the line of the function at a point which is the coordinates (-1, y).
Now, read off the value of y at this point. This is the value of f(-1). To double-check your answer, make sure that the coordinates of the point you have located are (-1, y). If they are, then the value of y is the value of f(-1).
For more questions like Graph click the link below:
https://brainly.com/question/74883
#SPJ4