The correct answer is:
D) The amount a person pays for gas compared with the number of gallons purchased
Explanation:
A constant rate of change means that for every x, y increases the same amount.
In the situation "The amount a person pays for gas compared with the number of gallons purchased ," the independent quantity, or x-value, is the number of gallons, and the dependent quantity, or y-value, is the amount paid. Since gas has a set price per gallon, for every gallon purchased, the total amount paid goes up the same amount. This means it has a constant rate of change.
Brady Seitz’s charge account statement showed a previous balance of $1,247.55, a finance charge of $4.72, and new purchases of $112.50. What is the new balance? A. $1,364.77 B. $1,987.00 C. $987.66 D. None of the above.
Factor completely: 12a3b + 8a2b2 - 20ab3 ...?
What is nine tenths as a percentage?
Write two mixed numbers between 3 and 4 that have the product between 9 and 12???
PLZ HELP!!!
Answer:
The product of two mixed fraction lies between 9 and 12.
Step-by-step explanation:
We are given the following information in the question:
Two mixed fractions between 3 and 4.
[tex]3\displaystyle\frac{1}{6} = \frac{19}{6} = 3.17\\\\3\displaystyle\frac{1}{2} = \frac{7}{2} = 3.5\\\\[/tex]
Product of the mixed fraction:
[tex]3\displaystyle\frac{1}{6}\times 3\frac{1}{2} = \frac{19}{6}\times \frac{7}{2}\\\\= \frac{133}{12} = 11\frac{1}{12} = 11.084[/tex]
Hence, the value of the product of two mixed fraction lies between 9 and 12.
a building with a height of 14 m casts a shadow that is 16m long while a taller building casts a 24 meter long shadow. what is the height of the taller building
Eight scores have an average of six. Scores of 15 and x increase the average to 7. Find x
Final answer:
To find the value of x, multiply the original average of 6 by the original number of scores (8) to find the initial total. Then, use the new average of 7 to find the new total when the two scores (15 and x) are added. Solve for x to find that it equals 7.
Explanation:
The question asks to find the value of x such that when two new scores, 15 and x, are added to a set of eight scores with an average of six, the new average for all ten scores is seven.
To solve this, first calculate the total sum of the original scores by multiplying the average by the number of scores: 6 × 8 = 48. Adding the two new scores, the equation to find the new total sum is 48 + 15 + x = 7 × 10 (since there are now ten scores). Simplify this to get 63 + x = 70, therefore x equals 7.
If Sawyer makes $15 an hour, which equation represents his earnings?
W = 15h
W = 15/h
W = h/15
W = 15 + h
Multiply, expressing the product in scientific notation. (9.16X10−3)(5.5X1016)
To multiply numbers in scientific notation, multiply the coefficients and add the exponents.
Explanation:To multiply numbers in scientific notation, we multiply the coefficients and add the exponents.
In this case, we have (9.16 × 10-3) multiplied by (5.5 × 1016).
The product of the coefficients is 9.16 × 5.5 = 50.38.
The sum of the exponents is -3 + 16 = 13.
Therefore, the product in scientific notation is 5.038 × 1013.
I'm bad at word problems. Natasha had 7/8 gallon of paint. her brother ivan took 1/4 gallon to paint his model boat. natasha needs at least 1/2 gallon to paint her bookshelf. did ivan leave her enough paint? ...?
what is the relationship between area and square units
Using the completing-the-square method, find the vertex of the function f(x) =- 3x2 + 6x − 2 and indicate whether it is a minimum or a maximum and at what point.
To find the vertex of the quadratic function using the completing-the-square method, rearrange the equation in vertex form, complete the square, and simplify. The vertex of the given function is located at (1, 1) and represents a maximum point.
Explanation:To find the vertex of the function f(x) = -3x^2 + 6x - 2 using the completing-the-square method, follow these steps:
Start by rearranging the equation in the form f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Factor out the coefficient of x^2. In this case, factor out -3: f(x) = -3(x^2 - 2x) - 2.Complete the square by adding and subtracting the square of half the coefficient of x. In this case, add and subtract (2/2)^2 = 1: f(x) = -3(x^2 - 2x + 1 - 1) - 2.Simplify: f(x) = -3((x - 1)^2 - 1) - 2.Expand and simplify: f(x) = -3(x - 1)^2 + 3 - 2.Final vertex form: f(x) = -3(x - 1)^2 + 1.The vertex of the function is at the point (1, 1). Since the coefficient of x^2 is negative, the vertex represents a maximum point. Therefore, the vertex is a maximum point located at (1, 1).
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What's the difference between an ABSOLUTE extrema and a RELATIVE extrema? ...?
Final answer:
Absolute extrema refer to the highest or lowest points on the entire domain of a function, while relative extrema are high or low points within a specific region. Calculus techniques such as finding derivatives are used to identify these points.
Explanation:
The concepts of absolute extrema and relative extrema are important in the context of mathematics, specifically in calculus and the study of functions. An absolute extrema (or global extrema) refers to the highest or lowest point over the entire domain of a function. Relative extrema (or local extrema), on the other hand, are points where the function takes on a maximum or minimum value within a particular region or interval, but not necessarily the highest or lowest over the entire function. More formally, an absolute maximum is the largest function value and an absolute minimum is the smallest function value in the entire domain; relative maximums and minimums may not be the absolute highest or lowest, but are higher or lower than points immediately around them. To find extrema, calculus students typically use techniques involving derivatives to identify where function values change from increasing to decreasing or vice versa.
For example, let's consider the function f(x) = x^2 on the interval [-1,1]. The absolute extrema of this function would be the global maximum and minimum values, which occur at x = -1 and x = 1, respectively. The relative extrema of this function would be the local maximum and minimum values, which occur at x = 0.
In the Diagram, rectangle ABCD is split in half by like AC. What is the value of tan X?
A. 3/4
B. 4/5
C. 3/5
D. 5/4
E. 4/3
The answer is E)4/3
That is because tangent X = a/b
Since this is a rectangle, the parallel sides are equal.
In this case, a=4, B=3, and C=5.
So, tanX = 4/3
Hope this helps!
For what value(s) of r is 5r-6=7+5r?
How many solutions are there to the equation below?
16(x + 2) - 8 = 16x + 24
A.
Infinitely many
B.
1
C.
0
Answer:
There are infinitely many solution.
Step-by-step explanation:
Given : 16(x + 2) - 8 = 16x + 24.
To find : How many solutions are there to the equation below.
Solution : We have given
16(x + 2) - 8 = 16x + 24.
On distributing 16 over ( x +2) .
16 x + 32 - 8 = 16x + 24 .
16 x + 24 = 16x + 24.
We can see left hand side is equal to right hand sides .
Therefore, There are infinitely many solution.
Bianca has 25¢ she has some nickles an. d pennies how many different combonation of nickles and pennies could bianca have?
Find the roots of the polynomial equation.
2x3 + 2x2 – 19x + 20 = 0
Answer:
1. a, -3,-1,1,3
2. a, 3+i/2, 3-i/2, -4
3. d, 6- sqrt 6
4. a, x3-8x2-11x+148=0
5. d, there are either 2 or 0 positive roots and one negative
Step-by-step explanation:
I did the quick check.
Final answer:
The roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0 are complex.
Explanation:
To find the roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0, we can use the factoring method or the quadratic formula. Let's use the quadratic formula. The formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 2, and c = 20. Plugging the values into the quadratic formula, we get:
x = (-2 ± √(2² - 4(2)(20))) / (2(2))
x = (-2 ± √(4 - 160)) / 4
x = (-2 ± √(-156)) / 4
Since we cannot take the square root of a negative number in the real number system, the roots of the given equation are complex, which means there are no real solutions.
. Store E offers a book that Karen wants for 20% off its regular price of $15.00. Store F sells the same book for $15, before a $3.00 mail-in rebate. Where should Karen purchase the book? Explain your reasoning.
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
Answer with explanation:
Cost of a Pencil = $ 0.25
Cost of a Eraser = $ 0.50
⇒Total Amount Spent on Pencil and Eraser < 3.
⇒Cost of x Pencil +Cost of y Eraser < 3
⇒ 0.25 x + 0.50 y < 3
[tex]\Rightarrow \frac{25 x}{100}+\frac{50y}{100}< 3\\\\\Rightarrow 2 5 x +50 y < 300\\\\\Rightarrow x +2 y < 12\\\\\Rightarrow \frac{x}{12}+\frac{2y}{12}<1\\\\\Rightarrow \frac{x}{12}+\frac{y}{6}<1[/tex]
⇒Put, x=0 and y=0,to know which side of the graph you have to shade.
0+0< 12⇒0< 12
Shade that part under line, which contains origin.
The sum of three consecutive even integers is 36. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
Which equation can be used to find the first integer?
3x = 2x + 6
2x + 6 = 36
3x + 6 = 36
3x + 36 = 2x + 6
Answer:
C. [tex]3x+6=36[/tex]
Step-by-step explanation:
Let x represent the first integer, [tex]x+2[/tex] represent the second integer, and [tex]x+4[/tex] represent the third integer.
The sum of these integers would be [tex]x+x+2+x+4[/tex].
We have been given that the sum of three consecutive even integers is 36. We can represent this information in an equation as:
[tex]x+x+2+x+4=36[/tex]
Combine like terms:
[tex]3x+6=36[/tex]
Therefore, the equation [tex]3x+6=36[/tex] can be used find the first integer.
Rich bought 5 cupcakes and one pie. He knows his total bill and knows the pie was $6.89, but he wants to find the price of the cupcakes. How can he determine the price of each cupcake?
To determine the price of each cupcake, subtract the price of the pie from the total bill and then divide the result by the number of cupcakes. Each cupcake costs $1.62.
Explanation:To determine the price of each cupcake, Rich can subtract the price of the pie from the total bill and then divide the result by the number of cupcakes:
Let's say the total bill is $15.00.Subtract the price of the pie ($6.89) from the total bill: $15.00 - $6.89 = $8.11.Divide the remaining amount by the number of cupcakes (5): $8.11 ÷ 5 = $1.62.Therefore, each cupcake costs $1.62.
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Could a reflection followed by a rotation ever be described as a single rotation?
Write some multiples of 5 and 8. Use the least common multiple to simplify 120\160
What is the value of f(0)
For the given function f(x) = 10x + 20, substituting 0 for x yields f(0) = 20. Graphically, this corresponds to the point (0, 20) on the function's line, illustrating that the output is 20 when the input is 0.
Find the value of f(0) for the function f(x) = 10x + 20:
1: Understand the function:
We are given that f(x) is defined as 10x + 20. This means that for any input value (x), the function outputs the result of multiplying x by 10 and adding 20.
2: Substitute x with 0:
We are asked to find the value of f(0). This means we need to plug in 0 for x in the function equation.
f(0) = 10 * 0 + 20
3: Simplify the expression:
Multiplying 10 by 0 gives us 0. Therefore, the equation becomes:
f(0) = 0 + 20
4: Evaluate the expression:
Adding 0 and 20 gives us:
f(0) = 20
Therefore, the value of f(0) is 20.
This means that when you input 0 into the function f(x) = 10x + 20, the function outputs 20.
To visualize this geometrically, you can imagine the function as a straight line on a coordinate plane. The point (0, 20) would lie on this line, indicating that the function output is 20 when the input is 0.
Complete question:
What is the value of f(0)?
If f(x) = 10x + 20
The value of ( f(0) ) is 5. To calculate it, we substitute ( x = 0 ) into the expression [tex]\( 3x^{2x} + 5 \)[/tex]ero number raised to the power of 0 is 1, the simplified result is [tex]\( f(0) = 3 \cdot 1 + 5 = 8 \).[/tex]
Explanation:The expression for ( f(x) ) is given as [tex]\( 3x^{2x} + 5 \)[/tex] , we substitute ( x = 0 ) into the expression:
[tex]\[ f(0) = 3 \cdot 0^{2 \cdot 0} + 5 \][/tex]
Since any non-zero number raised to the power of 0 is 1, the term [tex]\( 0^{2 \cdot 0} \)[/tex]re,
[tex]\[ f(0) = 3 \cdot 1 + 5 \][/tex]
Simplifying further,
f(0) = 3 + 5
Combining like terms,
f(0) = 8
So, the final answer is ( f(0) = 8 ).
In summary, when evaluating ( f(0) ), we substitute 0 for ( x ) in the given expression. The calculation involves raising 0 to the power of 0, which results in 1. The remaining terms are simplified to arrive at the final answer of 8. This process follows the principles of algebraic substitution and simplification, providing a clear understanding of how the value of ( f(0) ) is determined.
Complete Question:
Consider the function f(x) with the following expression: ( f(x) = [tex]3x^2[/tex]x + 5 ). Calculate the value of f(0).
Christopher is a graphic designer who creates business websites. It takes him 2.4 hours to complete one website page. He finds out about a new software program that will cut his time in half for completing one page, but it will take him 15 hours to learn the new program.
Which equation can be used to find the number of website pages, x, that Christopher needs to create so that his time spent using the new program will be the same as his current time?
Answer:
1. 2.4x=1.2x+15
2. 13
Step-by-step explanation:
.002 times 900000 scientific notation
What is the explicit rule for this geometric sequence?
4,4/5,4/25,4/125,…
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period?
The domain is all real numbers 0 through 9.
The domain is all integers 0 through 9.
The domain is all positive real numbers.
The domain is all positive integers.
Answer:
The domain is all real integers 0 through 9.
I've done the test, hope this helps
What is the solution of the system? use the substitution method. {y−2x=816 4x=2y the only solution is (24, 0) . the only solution is (1, 10) . there is no solution. there are an infinite number of solutions.?
Final answer:
The system of equations given has no solution because substitution leads to a contradiction, indicating that the lines are parallel and do not intersect.
Explanation:
To solve the given system using the substitution method, we start with the two equations:
y − 2x = 8164x = 2yFrom the second equation, we can express y in terms of x by dividing by 2:
y = 2x
Now, we substitute this expression for y into the first equation:
2x − 2x = 816
This simplifies to:
0 = 816
This is a contradiction since 0 cannot equal 816. Therefore, there is no solution to the system of equations. This means that the two lines represented by these equations are parallel and never intersect.
By decreasing each side of a rectangle by 1 unit, the area decreased from 60 square feet to 44 square feet. Find the perfect decrease in area. ...?
Answer:
Decrease in area would be 26.67%
Step-by-step explanation:
By decreasing each side of a rectangle by 1 unit area of the rectangle decreases from 60 square feet to 44 square feet.
So decrease in area = 60 - 44 = 16 square feet.
Percentage decrease in the area will be = [tex]\frac{\text{Decrease in area}}{\text{Area before decrease}}\times 100[/tex]
= [tex]\frac{16}{60}\times 100[/tex]
= [tex]\frac{160}{6}[/tex]
= 26.67%
Decrease in area would be 26.67%
The perfect decrease in area of the rectangle when each side is decreased by 1 unit, resulting in a decrease from 60 square feet to 44 square feet, is 16 square feet.
The question asks to calculate the perfect decrease in area of a rectangle when each side is decreased by 1 unit, resulting in a change in area from 60 square feet to 44 square feet. To solve for this, let's assign variables to the original dimensions of the rectangle. Let the length be L and the width be W.
The original area A1 is given by L imes W = 60. After reducing each dimension by 1, the new length and width are L - 1 and W - 1, respectively, so the new area A2 is (L - 1) imes (W - 1) = 44. The perfect decrease in area is the difference between the original and new areas, which is 60 - 44 = 16 square feet.