Please help thank you
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1) in 1992, the average was credit card debt for an
american family was $3275. in 2006, the
average credit card debt for a family was $8900.
find the average rate of change of credit card
debt with respect to time.
a) 390.80
yr
b) 401.79
yr
c) 412.68
yr
d) 423.575
yr
e) 434.46
yr

There are 62 medium-sized bowls and 88 small-sized bowls on the counter.

Calculate the total volume of the bowls on the counter, which is 764 oz.

Calculate the volume of one medium-sized bowl, which is 6 oz.

Calculate the total volume of the medium-sized bowls which would be 62 x 6 = 372 oz.

Calculate the volume of one small-sized bowl, which is 4 oz.

Calculate the total volume of the small-sized bowls which would be 764 - 372 = 392 oz.

Calculate the number of small-sized bowls which would be 392/4 = 88.

Calculate the number of medium-sized bowls which would be 372/6 = 62.

Therefore, there are 62 medium sized bowls and 88 small sized bowls on the counter.

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Answer:

(x - 8) (x + 4)

Step-by-step explanation:

x^2-4x-32

Consider the form x^2+bx+c. Find a pair of integers whose product is c

and whose sum is b. In this case, whose product is −32 and whose sum is −4.

-8,4

Write the factored form using these integers and we get the answer

(x - 8) (x + 4)

For the function 4^x=(1/8)^(x+5), the value of x, using exponents' properties is obtained as option 2: x = -3.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given function is - 4^x=(1/8)^(x+5)

This function can be solved using the properties of exponents.

The first property of exponents is - (a^m)^n = a^(m·n)

The second property of exponents is - 1/(a^n) = a^-n

Simplify the left hand side of the function -

4^x = (2²)^x

Using the first property of exponents -

(2²)^x = 2^(2x)

Simplify the right hand side of the function -

(1/8)^(x+5) = (1/2^3)^(x+5)

Using the second property of exponents -

(1/2^3)^(x+5) = (2^-3)^(x+5)

Using the first property of exponents -

(2^-3)^(x+5) = 2^(-3x - 15)

The function then becomes -

2^(2x) = 2^(-3x - 15)

Since, the base is same they cancel out.

2x = -3x - 15

2x + 3x = -15

5x = -15

x = -3

Therefore, the value of x is obtained as x = -3.

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To solve the equation add 3 to both sides using addition property of equality.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

x - 3 = 12

You should follow the given steps -

Action : Add 3 to both sides.

Property : Addition property of equality

Therefore, to solve the equation add 3 to both sides using addition property of equality.

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Answer:

36

Step-by-step explanation:

7/6 u=42

7u =42×6

u=252/7

u=36

The table represents a function. X y 0 6 2 8 4 10 6 12 complete the statement by selecting from the drop-down menu. The rate of change in the function y = x + 4 is  equal to the rate of change of the function represented in the table.

Consider the function shown in the table.

The table's coordinates are as follows:

(0,6) (2,8) (4,10) and (6,12) (6,12)

Take into account the first two coordinates (0, 6) and (2,8)

x₁=0, y₁=6, x₂=2, y₂=8

Linear equation is provided by (y-y₁) =m(x-x₁)

Where 'm' is the slope (rate of change), the following formula is used:

m = y₂ - y₁

      x₂ - x₁

So,

m = 8 - 6 = 1

      2 - 0

So, the line's equation is:

(y-6)= 1 (x-0) (x-0)

y-6=x

y=x+6

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

Now,

We will calculate the slope for the function y=x+4

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

The rate of change in the function y=x+4 is therefore equal to the rate of change of the function shown in the table.

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The equation can be described as a quadratic equation.

A quadratic equation is a second-order polynomial equation in a single variable x or any algebraic equation of highest degree. The standard form of the quadratic equation in variable is ax^2 + bx + c = 0 with a ≠ 0, where a and b are coefficients and constant. Since a quadratic equation is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

In this case, we have given that:

y = t + 2

So, y – 2 = t

Now, substitute the value of t in the equation:

x = t^1/2

x = (y – 2) ^1/2

And, by squaring both sides we will get:

x^2 = y – 2

y = x^2 + 2

Hence, this is an example of quadratic equation.

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Answer:

D. Quadratic

Step-by-step explanation:

Took the test and it was the right answer. I'll put in answers for other questions in case you have them.

Don't worry you've got it, I believe in you :)

Using the division method it is obtained that Moses is left with 2 dog treats after feeding the 4 dogs with 3 dog treats each.

What is division?

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Number of dogs Moses volunteers with, x = 4

Number of dog treats Moses have, y = 14

Number of dog treats Moses gives to each dog = a

So, to find the value for a use the division method -

a = y/x

a = 14/4

a = 3(2/4)

Where, 3 is the quotient and 2 is the remainder.

Therefore, Moses gives each dog 3 treat and have 2 treats left.

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On solving the provided question, we can say option a) 5x+4 is the simplified form of the equation.

Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.

Given:

=>(−3x − 12) + (16 + 8x)

=> -3x-12+16+8x

=> 5x+4

So 5x+4 is the simplified form of the equation

Therefore option a) 5x+4 is the simplified form of the equation

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[tex]\frac{sqrt{5} }{3}[/tex]

Step-by-step explanation:

Its root 5 over 3

Answer:

--------------------------------------

If m° is one of the angles of a right triangle, the complementary angle is (90 - m)°.

We know that sine of the angle is same as the cosine of the complementary angle. It means:

Therefore the value of cos (90 - m)° is 2/3.

The function that could represent Laura's charges is given by -

y = 5x + 12

Given is that bryan is starting a tutoring company that charges $10 as an initial fee and 7.50 dollars per hour of tutoring. Laura is starting her own company and she wants to charge less for the initial fee, but more per hour.

The function representing the amount charged by Brayan is -

{B} = 10 + 7.5x

Amount charged by Bryan per hour is -

$7.5

Amount charged by Bryan as an initial fee -

$10

The function which charge less for the initial fee, but more per hour is -

y = 5x + 12

Therefore, the function that could represent the amount charged by Laura is given by -

y = 5x + 12

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Answer:

29,

Step-by-step explanation:

Answer:

y=2.50(x)+20

Step-by-step explanation:

Answer:

y=2.50x+20

Step-by-step explanation:

dont forget the x

Answer: 185 minutes

c is the correct option

Step-by-step explanation:

let x = number of minutes

0.46x = 85.10

x = 85.10/0.46 = 185 minutes

Answer:

185 minutes

Step-by-step explanation:

See the attached worksheet.  Note that there are no inequalites mentued in the problem.  That eliminates options 1 and 4.  Option 2 is set up correctly, except that the units are incorrect.  The unit for 0.46 is $/min, not just $.  The final unit should be minutes, not $.

Option 3 has the correct equation, and units.  Note how the word problem can be translated to an equation.  Start with setting up an equation, before mentally trying to answer the question.  An guess at the answer might be helpful, but work with the equation to insure the details are included.  A correct equation will allow proper unit cancellation, which will help verify that the answer is correct.  In this case we wanted an answer with just minutes.  Dividing $ by $/min reduces to only minutes  ($/$/min = min).

========

Making an estimate first is a good safeguard against mistakes.  We can mentally round up $0.46 to 50 cents/minute.  If the total bill is almost $90, we'd expect an answer around 180 minutes ((90/0.5).  We got 185, so we can feel comfortable that the problem was done correctly and quickly move on.

The total cost of one bandana is $0.60.

The theory used in this question is the multiplication principle, which states that when multiplying a number by a factor, the product will be equal to the number multiplied by the factor. In this case, the number is 0.5 yards of fabric, and the factor is 2, so the product is $1.20.

Step 1: Calculate the cost of 0.5 yards of fabric.

Step 2: Multiply the cost of 0.5 yards of fabric by 2, since you need 0.5 yards of fabric to make a banana.

Step 3: The total cost of one bandana is the cost of 0.5 yards of fabric multiplied by 2, which is $1.20.

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The weight of the bag of pinto beans she bought is; 2.4 lbs

Algebraic word problems are defined as questions that require translating sentences to equations, after which we then solve those equations.

Now, we are told that;

Amount paid by Alicia for a bag of pinto = $1.32

Cost of beans = $0.55 per lb

Now, the weight of the bag of pinto beans that Alicia bought will be;

Weight = Amount paid/cost per lb

Weight = 1.32/0.55

Weight = 2.4 lbs

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Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

On solving the provided question, we can say that by permutation, 90  different 8-topping pizzas are possible

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

here,

by permutation

[tex]^{10}P_8[/tex] = 10!/2/1 = 10 X 9 / 1 = 90 ways

90  different 8-topping pizzas are possible

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Answer: Roots=-2, 0, 5

y-int=(0,0)

Step-by-step explanation:

Two tiles will be left over. Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

50 quare tiles divided by 4 rows = 12.5 quare tiles

12.5 quare tiles per row x 4 rows = 50 quare tiles

50 quare tiles used - 50 quare tiles = 0 quare tiles

Remaining tiles = 0 quare tiles

50 quare tiles - 0 quare tiles = 50 quare tiles

Left over tiles = 2 quare tiles

Jenny has 50 square tiles which she arranges into a rectangular array of four rows. To work out how many square tiles are left over, first divide 50 by 4. This gives us 12.5 tiles per row, however this is not possible so we need to round this number down to 12. Multiplying 12 by 4 gives us 48 tiles used in the rectangular array. Subtracting the 48 tiles used from the 50 tiles that Jenny had originally gives us a result of 2 square tiles left over. In conclusion, Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

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A quadratic inequality is an inequality that can be written in the form of "ax² + bx + c < or > 0" where a, b and c are real numbers and x is a variable.

The solutions to a quadratic inequality are the values of x that make the inequality true. To solve a quadratic inequality, we first set the expression equal to zero and then find the roots (also known as the zeroes or solutions) of the equation. We then use these roots to divide the number line into three regions: the region where the expression is less than zero, the region where the expression is greater than zero, and the region where the expression is equal to zero.

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Answer: To solve this problem, we can use the law of cosines. The law of cosines is a useful tool for solving problems involving distances and angles between points in two-dimensional space. We can use the law of cosines to find the distance between the starting and ending point of the hike, and the bearing to get back to camp.

The law of cosines states that:

c^2 = a^2 + b^2 - 2ab * cos C

where c is the distance between the two points, a and b are the distances of the two legs of the hike, and C is the angle between them.

Using the given information, we can set a as the distance traveled at 3.5 miles per hour for 2 hours, which is 3.5 * 2 = 7 miles,

b as the distance traveled at 3.5 miles per hour for 4 hours which is 3.5 * 4 = 14 miles,

C as the angle between the two legs of the hike which is (72 + 23) = 95 degrees.

Now we can substitute this values into the law of cosines formula:

c^2 = 7^2 + 14^2 - 2(7)(14) * cos 95

Solving this equation will give us the square of the distance between the starting and ending point of the hike. To find the actual distance, we'll have to take the square root of that.

The distance directly back to camp is √(196 - 98*(√2/2)) = √(196 - 98*(√2/2)) ≈ 8.14 miles

To find the bearing to head back to camp, we must know that the bearing of a line is defined as the angle between the line and the North direction, measured clockwise.

We can use the bearing of N72°W and S23°W to find the back bearing to camp.

The back bearing is (180 + 72 + 23) = 275 degrees. The hikers should take a bearing of 275 degrees to head back to camp.

Step-by-step explanation:

Tao rode his bike for 4 miles.

What are the speed, distance, and time?

Speed, distance, and time are related concepts in physics, and the relationship between them is often represented by the equation:

Speed = Distance/Time

To find out how many miles Tao rode his bike, you can use the formula:

distance = speed x time

In this case, the speed is 12 mph (miles per hour) and the time is 20 minutes. To convert the time to hours, you need to divide 20 minutes by 60 minutes (1 hour) which gives us 0.33 hours.

So,

distance = 12 mph x 0.33 hours = 4 miles

Hence, Tao rode his bike for 4 miles.

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Answer:

Below

Step-by-step explanation:

For the Quadratic Equation   - 16t^2+ 60t + 80

   the max value will occur at   t = - b/2a =  -60 / (2 * -16) = 1.875 s

     use this value f t in the equation to find max height = 136.25 ft

The value of m∠5 = m∠4 + 10° or  m∠3 + 20°.

The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. The measure of each exterior angle of a polygon is equal to the sum of the interior angles of the polygon divided by the number of sides of the polygon.

Solution:

The given value of m∠4 = m∠3+ 10°

The value of m∠5 is increase in 10° of m∠4

The answer is m∠5 = m∠4 + 10°.

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When 12 is subtracted from a number, the result is 5. What is the number?

Answer:

? - 12 = 5

? = 17

Step-by-step explanation:

You can just do:

12 + 5

= 17

Now you can see that it fits:

17 - 12 = 5

You're welcome

5=-7/2x+12

-7=-7/2x

x=2

−5.25  > −6.

There are two of them.

These two numbers need to be compared.

A number's square root is never greater than the number itself.

According to the question, we have -

A = −5.25

B =  −6.

Clearly, A > B

Hence,−5.25  > −6.

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In this quadrilateral, Dilation A will have largest scale factor.  Dilation B is smallest and will have smallest scale factor. Now for the given scale factors: 3/4 > 1/2 > 1/4

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

in this quadrilateral

Dilation A will have largest scale factor.

Dilation B is smallest and will have smallest scale factor.

Now for the given scale factors:

3/4 > 1/2 > 1/4

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The system of equations 2x + y = 40 and x - 2y = -20 has a solution of x = 12 and y = 16. We can solve this system by using the method of substitution or elimination.

One way to solve the system is to use the method of substitution. We can first solve one of the equations for one of the variables and substitute that expression into the other equation.

For example, we can solve the first equation for y by isolating y on one side: y = 40 - 2x. Then we can substitute that expression into the second equation and solve for x:

x - 2(40 - 2x) = -20

x - 80 + 4x = -20

5x = 60

x = 12

Then we can substitute x = 12 into the first equation, or either equation to find the value of y:

2(12) + y = 40

y = 16

So the solution to the system of equations is x = 12 and y = 16.

Another way to solve the system of equations is to use the method of elimination. This involves adding or subtracting the equations to eliminate one of the variables. For example, we can add the equations and get:

3x - y = 20

Then we can solve for x or y and substitute it back into either of the equation to find the other variable.

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The complete question is:

What is the solution to this system of equations 2x + y = 40 and x - 2y = -20?

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