Carolina's charges can be represented by the linear equation y = 8 + 6x, where x represents hours worked and y represents the total fee charged for the service.
Explanation:The subject this question pertains to is Mathematics, specifically linear equations. Carolina's job can be modelled by a linear equation, where the independent variable is the number of hours worked and the dependent variable is the total fee charged.
In this case, Carolina charges an initial flat fee plus $6 per hour worked. Her total charge for a 4-hour job is $32, which means her initial fee can be deduced by subtracting four times her per-hour fee from the total fee, that is $32 - 4*$6 = $32 - $24 = $8. Therefore, the linear equation that models Carolina's job is y = 8 + 6x, where x is the number of hours worked and y is the total fee charged.
This is similar to the linear equation that represents Svetlana's tutoring job in Example 12.4, where each tutoring session earns her a one-time fee of $25 plus $15 per hour of tutoring, modeled by the equation y = 25 + 15x.
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when the solutions to each of the two equations below are graphed in the xy coordinate plane, the graphs of the solutions intersect at two places. Write the y-coordinate of the points of intersection in the boxes below in order from smallest to largest. y=2x and y=x^2-3
Answer:
Step-by-step explanation:
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
⇒ -3,
⇒ 0.59,
⇒ 3.41
The explicit rule for a sequence is an=9(−5)n−1 .
What is recursive rule for the sequence?
an=5−(an−1),a1=9
an=−9(an−1),a1=5
an=9−(an−1),a1=5
an=−5(an−1),a1=9
Answer:
Option 4th is correct.
[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Step-by-step explanation
The explicit sequence of the geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex] ....[1]
where,
r is the common ratio
n is the number of terms
[tex]a_1[/tex] is the first term
As per the statement:
The explicit rule for a sequence is:
[tex]a_n=9(-5)^{n-1}[/tex]
On comparing [1] we have;
[tex]a_1 = 9[/tex] and r= -5
Recursive formula for the geometric sequence is given by:
[tex]a_n = r \cdot a_{n-1}[/tex] for [tex]n\geq 2[/tex]
Substitute the given values we have;
[tex]a_n = -5 \cdot a_{n-1}[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
What is the ratio of CDs & DVDs
Simplify these algebraic expressions: 12x + 3 − 4x + 7, 8 − 7x − 13 + 2x, −3x − 18 + 5x − 2
The simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
What is an expression?A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.
To simplify each expression, we combine like terms:
Expression 1:
12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)
12x + 3 − 4x + 7 = 8x + 10
Expression 2:
8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5
Expression 3:
−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.
Therefore, the simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
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Warren wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if warren has 500 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a.let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). write an function for the area a of the enclosure in terms of w . (hint first write two equations with w and l and
a. solve for l in one equation and substitute for l in the other). a ( w ) = 1/2w
b.what width w would maximize the area? w = ft
c.what is the maximum area? a = square feet
Let's solve this step by step.
a. We begin by establishing the relationship between the width (w) and the length (l) using the total amount of fencing available (500 feet). Since one side of the pen is against the barn, we only need to fence the other three sides. Thus, the total amount of fencing used will be for two widths and one length, or \(2w + l\).
Setting up the equation for total fencing, we get:
\[2w + l = 500\]
Now, to express \(l\) in terms of \(w\), we solve for \(l\):
\[l = 500 - 2w\]
Next, we can write the function for the area \(A\) of the enclosure in terms of \(w\). Since area is \(width \times length\), we substitute our expression for \(l\):
\[A(w) = w \cdot l\]
\[A(w) = w \cdot (500 - 2w)\]
\[A(w) = 500w - 2w^2\]
This is the function that expresses \(A\) in terms of \(w\).
b. To find the width \(w\) that maximizes the area, we take the derivative of \(A(w)\) with respect to \(w\) and set it equal to zero to find the critical points.
\[A'(w) = \frac{d}{dw}(500w - 2w^2)\]
\[A'(w) = 500 - 4w\]
Setting \(A'(w)\) equal to zero and solving for \(w\):
\[500 - 4w = 0\]
\[-4w = -500\]
\[w = \frac{500}{4}\]
\[w = 125\]
The width that maximizes the area of the enclosure is 125 feet.
c. Now let’s find the maximum area by substituting \(w = 125\) back into the area function \(A(w)\):
\[A(125) = 500 \cdot 125 - 2 \cdot 125^2\]
\[A(125) = 62500 - 2 \cdot 15625\]
\[A(125) = 62500 - 31250\]
\[A(125) = 31250\]
The maximum area that Warren can enclose is 31,250 square feet.
every day Josie bakery bakes muffins and bagels. the ratio of m7ffins to bagels is always the same. the table shows data about what Josie bakery bakes 3 days of the week. How many bagels did Josie bakery bakes on wednesday
Find the product by using the FOIL method
(11z-5y)(3z+2y)
Plz help!
Jim runs a food cart and during a business outdoor Festival he sold $8470 worth of food he sells hot dogs for $2.50 and steak sandwiches for $10 if he sold a total of 985 items that they how many of each item did he sell?
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm
Answer:
11.1 cm, 4.9 cm
Suppose a population of 175 crayfish doubles in size every month. the function f(x) = 175(2x) gives the population after x months. how many crayfish will there be after 1 year?
You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.
The balance after 2 years when the interest is compounded daily is
$1,725.39.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given:
P= $1500
R= 7%
T = 2 years
Now, using
A = P[tex](1 + r/n)^{nt[/tex]
A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]
A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]
A = $1,725.39
Hence, the balance is $1,725.39.
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Censorship was established in the Bill of Rights. True or false! First answer will be marked brainliest!
Answer:
make the other brainliest but its false
Step-by-step explanation:
What is the measure of angle x, help
A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ? Enter your answer, in simplest form, in the boxes. :
-7(3x+5) use Distributive property to solve
What would be the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang? (Correct answer will get reward)
The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.
To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).
Therefore, to fit a 40-cm chopstick along the diagonal:
Let d = 40 cm.
Use the equation s√2 = 40 cm to find s, the side of the square.
s = 40 cm / √2.
s ≈ 28.284 cm when rounded to three decimal places.
So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.
PLEASE HELP ME ON THIS QUESTION
THX
~BRAINLIEST AVAILABLE TO CORRECT ANSWER
Three times a number added four times the number equals 84 find the number
Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter. If Philip and his friends want to split the cost of gas evenly, how much should they each pay?
Solve 2x^3-5x^2-11x-4=0
Find the area of a triangle with a base length of 3 units and a height of 4 units.
what effect does the value of the coefficient of x^2 have on the graph?
Ben bought a desk for $249.99. The sales tax rate was 6.25%. How much did Ben pay for the desk? Round your answer to the nearest cent. (1 point)
$15.62
$187.49
$265.61
$406.23
Just tell me if its A,B,C, or D.
The Price for Desk after tax is $265.614.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Ben bought a desk for $249.99.
Tax rate = 6.25%
So, the price for desk after tax
= 249.99 + 249.99 x 6.25%
= 249.99 + 249.99 x 0.0625
= 249.99 +15.62
= $265.614
Hence, the Price for Desk after tax is $265.614.
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The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
Can someone help me please, how to add this? Thank you!
Describe the graph of a system of linear equations that has infinite solutions.
HELP!!...................
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg and the hypotenuse 2 cm more than the shorter leg. how long should the sides of the triangle be?
using these complex zeros (1,1,-1/2,2+i,2-i) factor f(x)=-2x^5 +11x^4 -22x^3 +14x^2 +4x -5