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Which are the best definitions for theorem, conjecture, and axiom?

A statement that is assumed to be true without proof is a(n)
. A statement that has been shown to be true by vigorous application of logic is a(n)
. A(n)
is a statement that is believed to be true but hasn't been proven.

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Explanation:

The car is initially worth 44000 pounds.

It loses 25% of its value after the first year, but keeps the remaining 75% of it.

75% of 44000 = 0.75*44000 = 33000

The car is worth 33000 pounds at the end of year 1. This is effectively the "starting" value when we change the rate of depreciation.

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The new percentage of the depreciation rate is x%

The car loses x% of its value each year

But it keeps the remaining (100-x)% of the value from year to year. Refer to the previous section.

x% = x/100

(100-x)% = (100-x)/100 = 100/100 - x/100 = 1 - 0.01x

The 1 - 0.01x is the value of b in the exponential equation y = a*b^t

The value of 'a' is the "starting" value of 33000 pounds.

The t represents the number of years after that first year (so that means we have t+1 years total).

The equation we have is

y = a*b^t

y = 33000(1 - 0.01x)^t

The teacher mentions "after 3 years" which means we'll have t+1 = 3 solve to t = 2 which is what we'll plug in along with  y = 25555

Let's solve for x.

y = 33000(1 - 0.01x)^t

25555 = 33000(1 - 0.01x)^2

25555/33000 = (1 - 0.01x)^2

0.77439393939393 = (1 - 0.01x)^2

(1 - 0.01x)^2 = 0.77439393939393

1 - 0.01x = sqrt(0.77439393939393)

1 - 0.01x = 0.87999655646709

-0.01x = 0.87999655646709-1

-0.01x = -0.1200034435329

x = -0.1200034435329/(-0.01)

x = 12.00034435329

Due to rounding error, it appears that it should be x = 12 since your teacher mentions x is an integer.

Also, 12.00034435329 is pretty close to 12.

If it decays at 12% per year, then the car keeps the remaining 88% since 100-12 = 88

Therefore 0.88 is the base of the exponential, it's the value of b.

Computing 33000(0.88)^2 gets us 25,555.2 which isn't too far from the goal of 25,555 pounds.

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

We found the exponential decay equation to be

y = 33000(0.88)^t

where t is the number of years after that first year. We have t+1 years total.

Your teacher asks how much the car will be worth after 4 years, so we'll plug in t = 3 because it's the solution to t+1 = 4.

In other words, we're working 3 years after that first year is up, so 3+1 = 4 total years.

Plug in t = 3 to find the following

y = 33000(0.88)^t

y = 33000(0.88)^3

y = 22,488.576

Rounding to the nearest pence gets us 22,489.58 which is the value of the car after 4 years. You can verify this with a spreadsheet table as I have shown in the diagram below. The highlighted rows mention values on your screenshot.

I'll round to the nearest pound since the other car values mentioned were whole numbers rather than decimal ones.

The 22489.58 rounds to 22490

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

For the final part, we'll need logarithms to solve the equation. Logarithms are useful to isolate the exponent.

We'll plug in y = 14520 and solve for t

y = 33000(0.88)^t

14520 = 33000(0.88)^t

14520/33000 = (0.88)^t

0.44 = (0.88)^t

Log[ 0.88^t ] = Log[ 0.44 ]

t*Log[ 0.88 ] = Log[ 0.44 ]

t = Log[ 0.44 ]/Log[ 0.88 ]

t = 6.42227097958021

This rounds up to t = 7

Round up instead of down because we want to clear the hurdle of passing the 14520 marker.

Recall once again that t is the number of years after the first year.

So t = 7 represents t+1 = 7+1 = 8 years in total that have passed by. Therefore, after 8 years is when the car's value is below 14520 pounds. Refer to the table diagram below.

Using the concepts of the mean and of the mean absolute deviation, the correct option is given as follows:

Last month, the amount of rain that fell each day varied less than the month before.

In this problem, we have that:

Due to the lower mean absolute deviation combined with the higher mean, the amount varied less than the month before, hence the last option is correct.

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The image of the given triangle after transformation that has the rule (x,y)→(x,−y) is graphed below .

In the question

the triangle is given ,

From the figure , we can see that the coordinates of the triangle are

(2,7) , (4,-3) , (-5,-2)

let us name the coordinates of the triangle as A(2,7) , B(4,-3) , C(-5,-2) .

applying the transformation , that has rule (x,y)→(x,−y)

Using this rule to find the new coordinates of the triangle A'B'C' .

when A= (2,7)

A' = (2,-7)

When B = (4,-3)

B' = (4,-(-3))

B' = (4,3)

When C = (-5,-2)

C' = (-5,-(-2))

C' = (-5,2)

So the coordinates of the triangle  A'B'C' is A' = (2,-7) , B' = (4,3) , C' = (-5,2) .

the image triangle A'B'C' is shown below

Therefore , The image of the given triangle after transformation of the rule (x,y)→(x,−y) is graphed below .

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Since both angles are the same, x has a value of 11

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The given parameters are

m∠PQS=(3x−3)° and m∠RQS=(x+19)°.

From the question, the measures of both angles are the same

This means that

m∠PQS=(3x−3)° = m∠RQS=(x+19)°.

So, we have the following equation

3x − 3 = x + 19

Collect the like terms in the equation

So, we have the following equation

3x - x = 3 + 19

Evaluate the like terms in the equation

So, we have the following equation

2x = 22

Divide both sides by 2

So, we have the following equation

x = 11

Hence, the value of x in the angles is 11

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Possible question

m∠PQS and m∠RQS are congruent angles

m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.

Answer:

211/4 is bigger number cause if you look at it right 52 4/9 is smaller than 211/4

The constant of proportionality in cups of water to minute is 80 cups/min

Here we have the proportional relation:

y = k*x

Where y is the number of cups and x the time in seconds, then:

y/x = k

Replacing the values we know:

y = 8 cups.

x = 6 seconds.

We can get the value of k, the constant of proportionality, but first, let's write the time in minutes.

x = 6 seconds

remember that 1 min = 60 sec, then:

6 sec = (6/60) min = 0.1 min

So the constant of proportionality is:

k = 8cups/0.1 min = 80 cups/min

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Answer:

Step-by-step explanation:

Equation of line in slope intercept form: y = mx +c

Pick any two points from the table and find the slope.

 (-2 , 9) ; (-1,7)

  [tex]\sf \boxed{\bf Slope= \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

              [tex]\sf = \dfrac{7-9}{-1-[-2]}\\\\=\dfrac{-2}{-1+2}\\\\=\dfrac{-2}{1}\\\\=-2[/tex]

y = -2x + c

Substitute (-2,9) in the above equation and find the y-intercept 'c'.

      9 = -2*(-2) +c

      9 = 4 + c

 9 - 4 = c

        c = 5

Equation of line:

  y =-2x + 5

The solution for the system of linear inequalities is y <-3 and x < 10.5

Linear inequalities are inequalities that have constant average rates of change.

A system of linear inequalities is a collection of at least two linear inequalities

In this case, the system of inequalities is given as

2x - 3y < 12

y < -3

Substitute y < -3  in 2x - 3y < 12

2x - 3(3) < 12

Evaluate the like terms

2x - 9 < 12

This gives

2x < 21

Divide by 2

x < 10.5

Hence, the solution is y <-3 and x < 10.5

See attachment for the graph where the green line represents y <-3 and the other represents 2x - 3y < 12

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What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%

annual interest, compounded monthly?

Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=$120,000

t=12 years

r=14%=14/100=0.14

n=12

substitute in the given formula

Solve for P

Answer:

Logarithmic functions are the inverses of exponential functions. The logarithmic function y=log(x)  is called the logarithmic function with base a .

When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.

It is shifted 2 units vertical.(2 units down).

or

First, multiply the x by -3 and shift it 9 units to the right. Then, shift the function 1 unit down.

hope this was helpful

The total price that Bryce got charged to his credit card is $120.54  .

In the question ,

it is given that the

price for Shorts = $14.00

price for Soccer Ball = $25.00

price for Shin guard = $10.00

price for Cleats = $60.00

the total price for all the items = 14+25+10+60 = $109  

Given that the sales tax is 6% of the total price .

So , the sales tax = 6% of 109 = 0.06×109 = $6.54

According to the question

total price = price + sales tax + shipping cost

= 109 + 6.54 + 5

= 120.54

Therefore , the total price that Bryce got charged to his credit card is $120.54  , the correct option is (D) $120.54   .

The given question is incomplete , the complete question is

Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary. Shorts=$14.00 ,Soccer ball=$25.00 ,Shin guards=$10.00 ,Cleats=$60.00 .

(A) $104.94

(B) $109.94

(C) $115.54

(D) $120.54

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The relation of the function as a product are found for the long division as:  (n-2)×(6n - 16) + 0 = 6n² - 4n - 16

The following describes the relationship between such four parts:

Divisor x Quotient + Remainder = Dividend

From the given pictures write the value of each part;

Dividend  = 6n² - 4n - 16

Divisor = (n-2)

Quotient = 6n - 16

Remainder = 0

Thus, the relation becomes;

(n-2)×(6n - 16) + 0 = 6n² - 4n - 16

Thus, the relation of the function as a product are found for the long division.

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It was 1.5 times the length of Noah's bike ride as Mai’s bike ride.

The problem we dealing with is related to mixed numbers which are referred to as mixed numbers and could be the whole number, and a proper division spoke together. It for the most part speaks to a number between any two whole numbers.

Since we are providing mai's rate which is  6 3/4  miles and Noah's  rate of 4 1/2 miles, So in  order to find the time the length of Noah's ride is compared to Mal's, we just need to divide the given rates by each other

=> 6 3/4 divided by 4 1/2,  

=> 27/4 divided by 9/2, (The result is an improper fractions)

=> 27/4 X 2/9

=>3/2

=> 1.5

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The rules of Perfect Square Trinomial are, an expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].

Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial. A perfect square is a number that is obtained by multiplying a number by itself. Binomials are algebraic expressions consisting of just two terms that are either separated by a positive (+) or a negative (-) sign. Similarly, trinomials are algebraic expressions consisting of three terms. When a binomial consisting of a variable and a constant is multiplied by itself, it results in a perfect square trinomial having three terms. The terms of a perfect square trinomial are separated by either a positive or a negative sign.

A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression. It is of the form [tex]ax^{2} +bx+c[/tex]. Here a, b, and c are real numbers and a ≠ 0. For example, let us take a binomial (x+4) and multiply it to (x+4). The result obtained is [tex]x^{2} +8x+16[/tex]. A perfect square trinomial can be decomposed into two binomials and the binomials when multiplied with each other gives the perfect square trinomial.

Therefore,

An expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].

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Answer: 41, 54, 6.1

Step-by-step explanation:

By the law of Cosines,

[tex]b^2=4^2 +5^2 -2(4)(5)\cos 85^{\circ}\\\\b=\sqrt{4^2 +5^2 -2(4)(5)\cos 85^{\circ}} \\\\ =\sqrt{41-40 \cos 85^{\circ}}\\\\\approx 6.1[/tex]

By the law of sines,

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}=\frac{\sin B}{b}\\\\\frac{\sin A}{4}=\frac{\sin C}{5}=\frac{\sin 85^{\circ}}{\sqrt{41-40 \cos (85^{\circ})}}\\\\\implies \sin A=\frac{4\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle A \approx 41^{\circ}\\\\\implies \sin C=\frac{5\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle C \approx 54^{\circ}[/tex]

Property justifies the given statement 7(mn)= (7m)n is :

Associative property of multiplication.

As given in the question,

Given statement :

7(mn) = (7m)n

Property justifies the given statement 7(mn)= (7m)n is :

Therefore, property justifies the given statement 7(mn)= (7m)n is :

Associative property of multiplication.

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With the help of the ratio, we can conclude that Allie needs 42.72 ounces of chocolate chips for her new recipe.

So, first, we will take the ratio of a new recipe to the old recipe:

Now, the chocolate chips she needs for the new recipe:

Therefore, with the help of the ratio, we can conclude that Allie needs 42.72 ounces of chocolate chips for her new recipe.

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Answer: we need the immage

Step-by-step explanation:

The percentage of decrease for the chemistry experiment is 25%.

The. percentage is defined as the number representing any number with respect to 100.

In this case, at the begining, the experiment was 4 millimeters and the end had an experiment of 3 millimeters.

The decrease in the percentage will be:

= Change in value /Original value × 100

= (4 - 3)/4 × 100

= 1/4 × 100

= 25%

The percentage is 25%.

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Medical insurance Jessica pays biweekly is $196.58 or 197 dollars.

Dental insurance Jessica pays biweekly is $22.3125 or 22 dollars.

Janice:

Medical insurance costs $6,740 annually

Dental costs $630

Solution:

Jessica:

70% of medical insurance = 70/100*6,740

= 674 * 7

=  $4,718/annum.

85% of dental insurance = 85/100 * 630

= 63 * 8.5

=  $535.5/annum

Medical insurance Jessica pays per month = 4,718/12 = $393.16

Medical insurance Jessica pays biweekly = 393.16/2 = $196.58 or $197

Dental insurance Jessica pays per month = 535.5/12= $44.625

Dental insurance Jessica pays biweekly = 44.625/2 = $22.3125 or $22.

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The line which is parallel to the given line is 2x- y= 0 or y= 2x.

The given line y= 7+ 2x

this is written in the form y= mx +c where if we compare these two equations we get m= 2

Now consider a point which passes through the origin (0,0)

Thus y-y₁= m(x-x₁)

y- 0 = 2 ( x- 0)

y= 2x or 2x- y= 0

Thus, the line which is parallel to the given line is 2x- y= 0.

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The 10.78 watt–hour battery with a voltage rating of 3.85 V gives;

(a) The average current delivered in 3 hours is approximately 0.93 A

(b) The average power delivered at 0.93–A is approximately 3.593 watts

(c) The ampere hour rating of the battery is 2.8 Ah

Power is the rate at which energy is given out or expended.

Required;

(a) The amount of average current that can be delivered in 3 hours

Solution;

The power in the battery is given by the equation;

P = I²•R = I•V

10.78 watt–hour = 10.78 J/s × 60 × 60 s = 38,808 J

In 3 hours, the energy per second, which is the power is given by the equation;

P = 38,808 J/(3×60×60 s) ≈ 3.593 watts

I = P/V

Therefore;

I = 3.593 watts/(3.85 V) ≈ 0.93 A

(b) The average power delivered is given by the equation;

P = Energy/Time

Therefore;

(c) An equation that can be used to find the ampere hour, Ah is as follows;

Ah = Watt hour ÷ Voltage

The ampere hour rating of the battery is therefore;

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Answer:

A

Step-by-step explanation:

[tex]m=2/5 \implies 10(2/5)=4 \\ \\ m=1/2 \implies 10(1/2)=5 \\ \\ m=1 \implies 10(1)=10 \\ \\ m=2 \implies 10(2)=20[/tex]

Of these, only 4 is a perfect square.

Using the angle theorems, the measure of angle 6, m ∠6, is 54°

From the question, we are to determine the measure of angle 6

From the given diagram, we can write that

(13x + 9)° = m ∠5 (Corresponding angles theorem)

and

m ∠5 + (5x + 9)° = 180° (Linear pair theorem)

Thus,

(13x + 9)°  + (5x + 9)° = 180°

Now, we will solve for x

13x + 9 + 5x + 9 = 180

18x + 18 = 180

Subtract 18 from both sides of the equation

18x + 18 - 18 = 180 - 18

18x = 162

x = 162/18

x = 9

Now, to determine the measure of angle 6

m ∠6 = (5x + 9)° (Vertical angles theorem)

Substitute the value of x

m ∠6 = (5(9) + 9)°

m ∠6 = (45 + 9)°

m ∠6 = 54°

Hence, measure of ∠6 is 54°

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The coordinates is (-4,5) and the quadrant is ii

A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane created by the intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line. An area of two dimensions made up of two number lines is known as a coordinate plane. It is created when a point termed the origin, where the X-axis and Y-axis cross, is reached. You may find points by using the numbers on a coordinate grid. Graphing points, lines, and many other things may all be done using a coordinate plane. It serves as a map and provides exact driving instructions.

The coordinates is (-4,5) and the quadrant is ii

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Step-by-step explanation:

X<-3 Inequality form , [XIX <-3]