A recent college graduate has a $2,400 balance on a credit card that charges 13.5% interest, compounded monthly. What monthly payment must be made to pay this balance in two years?

$116.46
$102.25
$114.66
$113.50

A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation

Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.

The system of equations that represents the constraints in this situation is:

x + y = 82 (total number of jars collected)

16x + 28y = 1876 (total amount of peanut butter collected in ounces)

b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank

we need to solve the system of equations from part (a). One way to do this is to use elimination:

Multiplying the first equation by 16, we get:

16x + 16y = 1312

Subtracting this equation from the second equation, we get:

12y = 564

Dividing both sides by 12, we get:

y = 47

Substituting this value of y into the first equation, we get:

x + 47 = 82

Subtracting 47 from both sides, we get:

x = 35

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The set of ordered pairs which represents a function among the given answer choices is; {(1, 2), (-6, 2), (3,9), (5,3)}.

By definition, a function is a special kind of relation in which case, each input value is assigned not more than one output value.

On this note, by evaluation of the given sets of ordered pairs; the set {(1, 2), (-6, 2), (3,9), (5,3)} represents the relation which is a function.

Ultimately, the answer choice which represents a set of ordered pairs that represents a function is; {(1, 2), (-6, 2), (3,9), (5,3)}.

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The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

y = 2

Step-by-step explanation:

substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula

y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)

 = 5 + [tex]\sqrt{1}[/tex] - 4

 = 5 + 1 - 4

 = 6 - 4

 = 2

Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

6a7

Step-by-step explanation:

To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.

Answer: 6a7

Step-by-step explanation: Got this right b4.

The percentage of saline solution in brand B is 3%.

Let x be Percentage of saline solution in brand B

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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The order of steps of constructing an inscribed circle of a triangle:

Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.

Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.

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The approach employed in this specific instance is a non-probability sampling technique labeled as convenience sampling.

It involves selecting the participants based on convenience or, in other words, selecting those who are readily available to take part in the study. Hence the school district has decided to dispatch the survey to all parents whose children have access to the online questionnaire.

The selected sample principally arises from considerations of the ease with which it can be attained, thus making convenience rather than randomness the dominant factor informing the selection process.

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A school district sends an online survey to all parents of students in the district asking for feedback on props educational changes on recent tax cuts

What is the sampling method used here

The cost of one hour of television each day is $1.

We have,

The average electricity bill reduced to $130 to $40.

Number of days in month= 30 days

So, the cost of one hour of television is

= (130- 40) /30

= 90 /30

= $30

Thus, the cost of one hour of television is $ 30.

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We raise the fraction to the power of 4/3.

To evaluate the expression:

\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},

we can simplify each term within the parentheses before multiplying them together.

Let's simplify each term step by step:

\left( \frac{16}{9} \right)^{2/3}:

To simplify this term, we raise the fraction to the power of 2/3.

\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}

\left( \frac{4}{3} \right)^{4/3}:

Similarly, we raise the fraction to the power of 4/3.

\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}

\left( \frac{9}{16} \right)^{2/3}:

We raise the fraction to the power of 2/3.

\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}

\left( \frac{3}{4} \right)^{4/3}:

We raise the fraction to the power of 4/3.

\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256

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Figure C shows only a line segment highlighted in red.

Figure C has four line segments connected to form a square, with the bottom line segment colored red.

The other three line segments in the figure are not colored, and only the bottom line segment is highlighted in red.

This means that only a line segment is shown in red, which is what the question is asking for.

Hence, figure C shows only a line segment highlighted in red.

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To find the variability in the distribution of the means, we need to calculate a measure of spread, such as the standard deviation. We can use the dot plot to estimate the standard deviation of the distribution.

From the dot plot, we see that the range of the means is from 0 to 150 bags of dog food sold per day. The midpoint of this range is 75, which we can use as an estimate of the population median. We can estimate the standard deviation by calculating the distance between the median and the quartiles.

From the dot plot, we can see that the lower quartile (Q1) is around 60, and the upper quartile (Q3) is around 110. Therefore, the interquartile range (IQR) is:

IQR = Q3 - Q1 = 110 - 60 = 50

We can use the IQR to estimate the standard deviation by assuming that the distribution is approximately normal and using the empirical rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Since the IQR is about half of the range, we can estimate the standard deviation as:

SD ≈ IQR / 1.35 ≈ 50 / 1.35 ≈ 37

Therefore, an appropriate estimate of the standard deviation of the distribution of means is 37, rounded to the nearest whole number.

Interpretation: The variability in the distribution of means is relatively large, with a standard deviation of approximately 37 bags of dog food sold per day. This means that the mean number of bags sold per day can vary by as much as 37 bags from one sample to another.

The x and y values in the triangle are:

x = 58°

y = 26°

Trigonometry deals with the relationship between the ratios of the sides of a triangle with its angles.

To find the x and y values in the triangle, check the attached image for labeling.

In the image:

Triangle ABC is isosceles. Thus,

t = 61° (base angles of isosceles triangles are equal)

x + t + 61 = 180  (sum of angles in a triangle is 180°)

x + 61 + 61 = 180

x = 180 - 61 - 61

x = 58°

x + v = 180 (sum of angles on a straight line is 180°)

58 + v = 180

v = 180 - 58

v = 122°

In triangle ACD:

32 + v + y = 180  (sum of angles in a triangle is 180°)

32 + 122 + y = 180

y = 180 - 32 - 122

y = 26°

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The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.

First, we can factor out a common factor of z:

z(20z² - 11z - 3) = 0

Now we need to factor the quadratic expression in the parentheses.

We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:

z(20z² - 11z - 3) = 0

z(4z - 3)(5z + 1) = 0

Setting each of the factored terms equal to zero, we have:

z = 0, 3/4, -1/5

Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.

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A table representing the transactions based on the question prompt is given below:

Date Transaction Type Check No. Description Debit (-) Credit (+) Balance

10/01 Starting Balance - - - - $1,863.90

10/03 Check 621 Telephone Company $71.10 - $1,792.80

10/07 Check 622 Banner Reality (Rent) $500.00 - $1,292.80

10/08 Check 623 Electric Company $51.12 - $1,241.68

10/10 Check 624 Cathy Santoro (Piano) $25.00 - $1,216.68

10/15 Deposit - Paycheck - $650.00 $1,866.68

10/16 Check 625 Don's Day Camp $200.00 - $1,666.68

10/18 Check 626 Ed's Sporting Goods $90.00 - $1,576.68

10/21 Check 627 Maple Place Garage $49.00 - $1,527.68

11/15 Deposit - Paycheck - $400.00 $1,927.68

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The solution to the given expression by using distributive law is 114

The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.

From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.

Let the two integers be 10 and 9.

So, we can have can express this by using the addition distributive law: A(B+ C)

Mathematically, we have:

= 6(10 + 9)

= 6(19)

= 114

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10 times will the smaller gear turn.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).

Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.

So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.

Therefore, the smaller gear will turn 10 times.

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The equivalent radian to 300 degree is 5π/3.

The given angle measures 300 degree.

We know that, formula used to convert degrees is Radians = Degrees × π / 180

Here, Radians = 300×π/180

= 30 ×π/18

= 10π/6

= 5π/3

Therefore, the equivalent radian to 300 degree is 5π/3.

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Answer:

142ft^2

Step-by-step explanation:

I hope this picture helps, but if you have any questions about the steps let me know

The Subtraction property of equality justifies the conclusion based on the given information.

The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. In simple words, we can say that when a number is subtracted from one side of an equation, the same number must be subtracted from the other side of the equality.

if a = b

then;

a-c = b-c

We have:

If x + 5 = 15

By subtraction property of equality:

Subtract 5 from both sides we have;

x = 10

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The new mean annual wage is; $ 43,149.82.

Given that the initial mean weekly wage is $ 2.117.

The growth rate is 4.75%.

We need to find a new annual wage.

Consider the equation, A be the new annual wage.

Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.

The number of weeks in a year = 52 weeks.

Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.

A = 2.117 x 52(1 + 0.0475)

A = 43,149.82

The new mean annual wage is; $ 43,149.82.

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a.) The value of each angle when 5 is substituted for X would be ;

Y = 55°

Y = 55°W = 75°

Y = 55°W = 75°Z = 45°

b). Chelsea is wrong in her calculation because the total internal angle of a triangle should be 180° and not 175°.

For angle Y;

11x = 11(5) = 55°

For angle W;

15x = 15(5) = 75°

For angle Z;

(8x+5) = 8(5) +5

= 45°

The total angles = 55+75+45 = 175°

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Answer: 1/5

Step-by-step explanation:

In this case, you multiple the exponents together because you are raising a power to a power:

25^(-3/2 * 1/3)

25^(-3/6)

25^(-1/2)

Next, when the power is negative, we can get rid of it by changing the whole number to its reciprocal (divide the number by one):

1/(25^(1/2))

Now, when an exponent is a fraction, the numerator is what the base is raised to and the denominator is what the base is rooted to:

1/(sqrt(25))

Now, simplify:

1/5

Applying the triangle sum theorem, the value of x in the image given is:

x = 33°;   x = 45°

Recall that according to the triangle sum theorem, all three interior angles of a triangle is equal to 180 degrees.

a. x + 21 + (180 - 54) = 180 [triangle sum theorem]

x + 147 = 180

x = 180 - 147

x = 33°

b. (180 - 102) + x + 57 = 180 [triangle sum theorem]

x + 135 = 180

x = 180 - 135

x = 45°

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