The initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.
The initial value, b = $3.50 is the skate rental fee
The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink based on the query we have;
The roller skating rink's fees are comprised of a skate rental fee and an hourly rate.
Skating for two hours will cost you a total of $9.50.
Five hours of skating will cost you $18.50 in total.
Skating's overall cost and its duration in hours are related in a linear fashion.Let 'x' be the number of hours spent skating, and 'y' denote the overall cost;
The equation has the form y = mx + b.
Where;
m = The linear relationship's rate of change
b = The starting point (y-intercept)
X = 2 and Y = 9.50
Consequently, we can write;
9.50 = 2·m + b..(1) (1)
X = 5 and Y = 18.50
Consequently, we can write;
18.50 = 5·m + b..(2) (2)
Equation (1) minus equation (2) results in;
18.50 - 9.50 = 5·m - 2·m + b - b = 3·m
9.0 = 3 × m
∴ m = 9.0/3 = 3.0
m = 3.0 is the rate of change.
Likewise, we have;
We obtain from equation (1);
9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b
9.50 = 6.0 + b
∴ b = 9.50 - 6.0 = 3.50
The starting point is 3.50.
As a result, the initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.
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Find the Gradient of a line
Answer:
4/
Step-by-step explanation:
gradient=y2-y1/x2-x1
-2-2/-5-2=
-4/-7
=4/
what is the following product? Assume x>0 3root x^2 times 4 root x ^3
The product of radicals is C) x[tex]\sqrt[12]{x^5}[/tex]
What is product of radical form?
The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. It indicates that we should multiply the radicals when they are placed next to one another in this manner. Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.
Here the given form is
=> [tex]\sqrt[3]{x^2} \sqrt[4]{x^3}[/tex]
Now use [tex]\sqrt[n]{a}= \sqrt[mn]{a^m}[/tex] to expand the expression then
=> [tex]\sqrt[12]{x^8} .\sqrt[12]{x^9}[/tex]
Now the product of roots with the same index is equal to the root of the product then
=> [tex]\sqrt[12]{x^8x^9}[/tex]
=> [tex]\sqrt[12]{x^{17}}[/tex]
=> x[tex]\sqrt[12]{x^5}[/tex]
Hence the correct option is C) x[tex]\sqrt[12]{x^5}[/tex]
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A relation i plotted a a linear function on the coordinate plane tarting at point C at (0, −1)and ending at point D at (2, −11). What i the rate of change for the linear function and what i it initial value?
Select from the drop-down menu to correctly complete the tatement. The rate of change i Chooe. And the initial value i Chooe.
The rate of change for the linear is -5 and the initial value is -1
A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. We'll go into great detail about what a linear function is in this article, along with its table, graph, formulas, traits, and examples.
The rate of change refers to the slope of the linear function, because the slope is actually a ration between the two variables. So, to find the slope, we use its definition:
m = [tex]y^{2}[/tex]-[tex]y^{1}[/tex]/[tex]x^{2}[/tex]-[tex]x^{1}[/tex]
Now we replace the given points, being C the first point and D the second point:
m= -11-(-1)/2-0= -5
Therefore, the rate of change is -5, where the negative sign refers to a decreasing change, it's a decreasing linear function. In addition, the initial values is where the independent variable is zero, which is given in the point C (0;-1), so the initial condition is y = -1
Therefore ,The rate of change for the linear is -5 and the initial value is -1
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The scale of the picture is 1 in.: 3 cm. Find the actual length of the Thermos.
The scale of the picture is 1 in,: 3 cm, and the length of the Thermos in the picture is 4 inches, which indicates that the actual length of the Thermos is 12 centimeters
What is a scale factor in a drawing?A scale factor is a number by which the dimensions of an actual or original image are multiplied to obtain the dimensions of the image.
The dimensions of the image are proportionately smaller or larger than the actual dimensions of the image.
The scale of the drawing is 1 inch is equivalent to 3 centimeters
Therefore, each inch of theThermos flask in the drawing is equivalent to 3 centimeter length of the actual Thermos flask.
The dimensions of the thermos flask in the drawing = 4 inches
Therefore;
Length of the thermos flask in the diagram ÷ Actual length of the thermos flask = 1 in./3 cm
Actual length = Image length × 3 cm/1 in.
Actual length = 4 inches × 3 cm/(1 inch) = 12 cm
The actual length of the thermos flask is 12 centimeters
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Select the correct answer. Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial.
f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
Given f(x) and g(x) two polynomial functions in the standard form of the polynomial,
According to Closure Property, when something is closed, the output will be the same as the input.
The polynomials f(x) and g(x) can be seen in the image.
On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.
Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.
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Complete question:
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test
After answering the provided question, we can conclude that The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.
What exactly is a scatter plot?"Scatter plots are graphs that show the relationship between two variables in a data set. Data points are represented by a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are also known as scatter graphs or scatter diagrams."
The y-intercept of the line of fit is approximately 80 based on the scatter plot and line of fit.
The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.
It should be noted that this prediction is based on the linear relationship observed in the sample data and may not be applicable to the entire population. This prediction also assumes that all other factors influencing test performance (such as natural ability, prior knowledge, and test-taking skills) are constant, which may not be the case in real-world situations.
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Answer:
60; a student who studies for 0 hours is predicted to earn 60% on the test
Step-by-step explanation:
Question 2 of 10
Use the substitution method to solve the given system of equations.
3x-2y=8
y=3/2x-5/4
A. (0, -5/4)
B. (11/2,7)
C. Infinitely many solutions
D. No solution
Answer: No solution
Step-by-step explanation:
Since we are given what y is, we can plug in y into the first equation.
[tex]3x-2(\frac{3}{2} x-\frac{5}{4} )=8[/tex] [distribute]
[tex]3x-3x+\frac{5}{2} =8[/tex] [subtract]
[tex]\frac{5}{2}\neq8[/tex]
Since this is false, then the only option is that we have no solution.
Quadrilateral CDEF is inscribed in Circle T F Engle DEF is 3X +7 and angle DCF is 2X +8 what is the value of X?
Since Quadrilateral CDEF is inscribed in Circle A, the value of x is equal to: B. 33.
How to calculate the value of x?Since Quadrilateral CDEF is inscribed in Circle A, we can reasonably infer and logically deduce that line segment DF is the chord of Circle A. Mathematically, an equation which can be used to solve for the value of x in this circle is given by:
m∠DEF + m∠DCF = 180°
Substituting the given parameters into the formula above, we have the following;
(3x + 7)° + (2x + 8)° = 180°
3x + 2x + 8 + 7 = 180°
5x + 15 = 180°
5x = 180° - 15
5x = 165
x = 165/5
x = 33.
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2.5s+r+3c+5 slove this question
Answer: 3c + r + 2.5s + 5
Step-by-step explanation:
Im not gonna explain it thats too much.
How many lb is 1.4 pounds
Answer:1.4
Step-by-step explanation: Because lbs are the same thing as pounds
Two tudent calculated the area of a polygon in the coordinate plane uing different trategie. Explain the two method
Of the two methods for area calculation, the preferred method is the second method because the objects around the polygon are smaller, and easier to calculate their area.
There are several ways to calculate the area of a polygon. Two of them were carried out by the two students in the problem:
Dividing irregular polygons into smaller and more regular shapes. Then determine the area of each shape and add them up to get the area of the polygon.Draw a regular shape such as a rectangle around the polygon. Then divide it into smaller regular shapes (without including the initial polygon) and add up the areas of each. The area of the polygon is the area of the rectangle minus the sum of those smaller areas.Of the two methods for the area of a polygon calculation, the preferred method is the second method because the objects around the polygon are smaller and easier to calculate their area.
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NEED HELP ASAP - Algebra 2
Select 3 functions below and determine how many and what type of zeros the functions could have.
1. f(x) = -2x^7 - 8x^2 + 10
2. g(x) = 8x^6 - 9x^2 - 6x^5
3. h(x) = -4x^2 - 3x - 1
4. k(x) = x^4 + 10x^3 - 6x^2 - 7
5. p(x) = -6x^9 - 3x^4 - 10x - 9
6. q(x) = -x^10 + x^8 - 7x
The number of zeros and nature of zeros for the functions,
g(x) = 8x⁶ - 9x² - 6x⁵ ⇒ 6 Roots and 4 real & 2 imaginary roots
h(x) = -4x² - 3x - 1 ⇒ 2 Roots and both are imaginary
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Functions,
g(x) = 8x⁶ - 9x² - 6x⁵
h(x) = -4x² - 3x - 1
Number of roots and nature of roots = ?
First take,
g(x) = 8x⁶ - 9x² - 6x⁵
8x⁶ - 9x² - 6x⁵ = 0
x² = 0
its two of the zeros are 0, 0
After plotting graph for the given function
It can be say that,
It is intersecting x axis at 3 places
So it will have total 6 roots, 4 real roots and two imaginary roots
h(x) = -4x² - 3x - 1
D = b² - 4ac
= 9 - 4 × -4 × -1
= 9 - 16
D = -7
D is negative so it will have 2 roots and nature will be imaginary
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7. Find the value of x. (AB = 8) (show work pls)
Answer:
Step-by-step explanation:
when GDK goes up GD goes down
Which static characteristics are desirable?
When it comes to static characteristics, there are many desirable attributes that can make a product or service stand out from the competition.
Quality and reliability are essential and desirable, as these are the main factors customers will consider when making a purchasing decision.
Durability is also important, as it ensures that a product will continue to perform to its highest standards over time.
Additionally, value for money is key, as customers want to be sure that they are getting a product or service that is worth the cost.
Furthermore, flexibility is highly desirable, as customers often need the ability to customize products or services according to their specific needs.
Finally, a good customer service experience is an essential static characteristic, as a positive customer experience can increase customer satisfaction and loyalty.
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If y₁=2x-1 construct for x = -5 to 7- a table
Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometers and Rs. y per km for every kilometer travelled thereafter. How much should Ratnam pay the agency for a journey of 50 kilometers?
A. x + 10 y B. 50( x + y ) C. 40 x + y D. 50 x y
The total fee that Ratnam should pay the agency for a journey of 50 kilometers, using a linear equation, is A. x + 10y.
How is the total car hire fee determined?The total fee is a function of summing the fixed charge for the first 40 kilometers and the variable charge for additional kilometers traveled.
In this situation, the variable charge per km represents the slope or the unit rate while the fixed charge for 40 kilometers represents the constant in a linear equation.
Flat charge up to 40 kilometers = Rs. x
Variable charge per kilometer after 40 km = Rs. y
Total distance traveled = 50 kilometers
Total fee paid = Rs. x + (50 - 40)y
= x + 10y
Thus, the correct fee that Ratnam should pay is represented by Option A.
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How do you change Vertex to factored?.
Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.
What is quadratic equation?
Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.
Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Therefore, Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.
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Suppoe p(x) = 2x^2 − 5x 10 and p(x)/x-n ha a remainder of 7. Which one of the following tatement are true?
The statement that is true is that when p(x) is divided by x-n, the remainder is 7.
This statement can be confirmed by solving the equation
p(x)/x-n = q(x) + 7, where q(x) is the quotient. Solving this equation yields the result that q(x) = 2x - 5. This means that when p(x) is divided by x-n, the remainder is 7 and the quotient is 2x - 5.
This statement can also be verified by using synthetic division. By using synthetic division with 2x2 - 5x + 10 as the dividend and x - n as the divisor, the remainder after the division is 7. This confirms that when p(x) is divided by x-n, the remainder is 7.
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if someone could show me how to do this that would be great, i appreciate it!
Discovering an antiderivative of a function is the process of integration.
What is integration?Adding or adding up the components to get the whole is a process known as integration. Reducing the functions into their component elements is a reverse differentiation procedure. Utilizing a broad scale, this method is utilised to find the sum.
A function's antiderivative is discovered by integration. It is the definite integration if a function can be integrated and if the integral of that function across the domain is finite with the given bounds. When d/dx(F(x) = f(x), dx = F(x) + C. Indefinite integrals are what these are.
As opposed to differentiation, integration is the opposite. In other words, the integral of 2 can be 2x + 3, 2x + 5, 2x, etc. Because of this, we must include a constant when integrating. The integral of 2 is therefore 2x + c, where c is a constant.
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Please help !!
Write equations for the vertical and horizontal lines passing through the point (-3, -9).
vertical line:
horizontal line:
Answer:
vertical line x = -3
horizontal line y = -9
Step-by-step explanation:
what is the answer for this????
The inequality which represents the possible additional amounts Dan will spend is; c ≤ 17.
Which inequality represents the possible additional amounts Dan will spend?As evident in the task content; the possible additional amounts Dan will spend is to be determined from the information given in the task content.
Since it is stated that Dan can spend at most $32 in which case, he has spent $15 already.
Let c be the additional amount Dan would spend.
Therefore the inequality which represents the situation is;
c + 15 ≤ 32
Ultimately, the solution set which represents the possible additional amounts he will spend is;
c ≤ 17.
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the velocity time graph for a cycle is shown. work out the total distance travelled on the cycle. work out the acceleration in the last 8 seconds. Need the answer before 6th of Feb 2023.
Part A - The cycle has a total distance travelled of 130 meters.
Part B - The cycle has an acceleration of 0 meters per square second at t = 8 seconds.
How to apply kinematics from a graph
In this question we find the case of a graph between time (t), in seconds, and velocity (v), in meters per second, from which we need to determine the total distance travelled (s), in meters, on the cycle and the acceleration (a), in meters per square second, at a given time.
Part A - The total distance travelled is the area below the curve, defined as the sum of the areas of two triangles and rectangle, thus:
s = 0.5 · (6 s) · (10 m / s) + (6 s) · (10 m / s) + 0.5 · (8 s) · (10 m / s)
s = 30 m + 60 m + 40 m
s = 130 m
The total distance traveled by the cycle is 130 meters.
Part B - The acceleration at a given time t is the slope of the curve at point (t, v). In this case, we find that slope can be found by secant line formula:
a = [v(12) - v(6)] / (12 - 6)
a = (0 - 0) / (12 - 6)
a = 0 m / s²
The acceleration of the cycle at t = 8 seconds is equal to 0 meters per square second.
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how to simplify radical trinomial
The method of simplification of the radical trinomial is described below.
How to simplify radical trinomial?Particularly those polynomials that are persistent under the influence of the perpendicular group are referred to as radical polynomials. A rated subalgebra of the circle of all polynomials is the circle of radical polynomials.
Utilize the Product Property to condense a radical phrase.
Locate the radicand's greatest factor which is also a perfect exponent of the index. Use that factor to recreate the radicand as the combination of two components.Rewrite the radical as the result of two radicals by applying the product rule.Reduce the ideal power to its most basic form.More about the radical trinomial link is given below.
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The sales tax rate in Georgia is 7%.
Find the tax paid for a video game with a list price of $59.99.
What is the total cost of the video game?
Responses
Answer:
Tax paid on video game: $4.20
Total price of game w/tax: $64.19
Step-by-step explanation:
7% of 59.99 = 4.20
59.99+4.20=64.19
GIVING 10
POINTS FOR CORRECT ANSWER!
Answer:
Step-by-step explanation: Since both the numerator and the denominator have a minus (-), they even each other out and the minus signs can be removed. Then we are left with this:
13
23
Now that both the dividend and divisor are positive numbers, we can simply divide 13 by 23 as follows:
13 ÷ 23 = 0.565217391304348
Which means that this is the answer to "What is negative 13 divided by negative 23?":
(-13) ÷ (-23) = 0.565217391304348
Answer:
t = -299
Step-by-step explanation:
[tex]\frac{t}{-13} = 23\\\\ t = 23 * -13\\\\t = -299\\\\Check:\\-\frac{-299}{-13} = 23[/tex]
Sam has $2,500 in his bank account and withdraws $45 each week. Write the function that models this situation. Let W=weeks and B=bank balance.
The answer is 2500 - 45W = B
2500 is the total amount
45 is taken out a week, so let w be the variable
B is the total bank balance
So 2500 - 45W = B
I hope this was able to help you :D
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Answer:
Solutions 1 and 2.
Step-by-step explanation:
determine the closest correlation coefficient (R-value) for this data
The closest correlation coefficient of the scatterplot is 0.8
How to determine the closest correlation coefficient of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Because the points appear to be on a straight line, but they are not on a straight line, the r value will most likely be between 0.7 and 0.9
The closest value to this is 0.8
Hence, the r value is 0.8
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Which two equations relate the measure of ∠4, to the measures of ∠1, ∠2, and/or ∠3.
Answer:
A and C
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle so first option,
A. m∠4 = m∠1 + m∠2
is correct.
m∠3 and m∠4 are supplementary angles because they make a straight line and their sum is equal 180°, so third option,
C. m∠4 = 180 - m∠3
is also correct.
Find sine, where is the angle shown.
Give an exact value, not a decimal approximation.
8
17
8
The value of sinθ is 15/17.
What are the trigonometric functions?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here, we have
Given:
Cosθ = 8/17
We apply here trignometric functions.
Sinθ = √1 - cos²θ
Sinθ = √1 - (8/17)²
Sinθ = √(289 - 64)289
Sinθ = √225/289
Sinθ = 15/17
Hence, the value of Sinθ is 15/17.
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