A car loses its 15% of its current value every year. What is the value of a car that was bought for $20,000 in two years?

[tex]\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} f(1)&\\ f(2)&\\ f(3)&7\\ f(4)&7r\\ f(5)&7rr\\ &252\\ \cline{1-2} \end{array}\qquad \qquad 7rr=252\implies 7r^2=252\implies r^2=\cfrac{252}{7} \\\\\\ r^2=36\implies r=\sqrt{36}\implies r=6 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} f(1)&\stackrel{\frac{7}{6}\div 6}{\cfrac{7}{36}}\\ &\\ f(2)&\stackrel{7\div 6}{\cfrac{7}{6}}\\ &\\ f(3)&7\\ f(4)&42\\ f(5)&252\\ f(6)&1512\\ \cline{1-2} \end{array}[/tex]

notice, once we know what the common factor "r" is, from the 3rd term we can simply multiply it by "r" to get the next term, and divide the 3rd term by "r" in order to get the previous term, namely the 2nd term, and then divide the 2nd by "r" to get the 1st one.

Answer: if the iguana is five feet it would be 60 inches

The store will have 29 pizzas.

This is because:

D is the correct answer

Answer:

Step-by-step explanation:

(look at the picture)

We have opposite and adjacent. Therefore we must use the tangent:

[tex]\tangent=\dfrac{opposite}{adjacent}[/tex]

[tex]adjacent=500\\opposite=x\\\tan10^o\approx0.1763[/tex]

Substitute:

[tex]\dfrac{x}{500}\approx0.1763[/tex]       multiply both sides by 500

[tex]x\approx88.15\to x\approx88.2[/tex]

Answer:

w = 93°

Step-by-step explanation:

The angle with measure 142° forms a straight angle with the third angle in the triangle and are supplementary, thus

third angle = 180° - 142° = 38°

The sum of the 3 angles in the triangle = 180°

w = 180° - (38 + 49)° = 180° - 87° = 93°

Answer:

Difference

Step-by-step explanation:

Remember that the therms of any subtraction problem are minuend, subtrahend, and difference.

- The minuend is the number from which you subtract something. For example, in the subtraction problem 4 -3 = 1, 4 is the minuend (you are subtracting 3 form it).

- The subtrahend is the number you subtract (from the minuend). For example, in 4 - 3 = 1, 3 is the subtrahend (you are subtracting 3 from the minuend 4).

- The difference is the result of subtracting the subtrahend form the minuend, in other words, the result of the subtraction problem. For example, in 4 - 3 = 1, 1 is the difference (the result)

We can conclude that the result of a subtraction problem is called the difference.

. In mathematics, the answer to a subtraction problem is called the difference.

For example, when you subtract 3 from 5, you perform the following calculation:

5 - 3 = 2

Here, 2 is the difference. Similarly, if you subtract -6 from 2, you change the sign of the number being subtracted and then add:

2 - (-6) = 2 + 6 = 8

The answer, 8, is the difference as well.

The concept of difference holds true for both scalar and vector quantities. For both types, the difference is the result of the subtraction operation.

Answer:

Option A. Ahmed wins the chess game

Step-by-step explanation:

we know that

The probability of Ahmed winning the chess games is 45%

45%=045/100=0.45

The probability of Ahmen winning the checkers games is 0.36

Compare the probability

0.45> 0.36

so

Is more likely that  Ahmed wins the chess game

Answer:

A

Step-by-step explanation:

Answer:

1) The probability of getting an even number when rolling a six-sided number cube is 0.5. Choice A

2) 80%. Choice C

Step-by-step explanation:

1)

We are required to determine the probability of getting an even number when rolling a six-sided number cube. The six-sided number cube has the following numbers written on its faces;

1, 2, 3, 4, 5, 6

The numbers; 2, 4, and 6 are even

The probability of getting an even number;

= ( number of faces with even numbers)/ (total number of faces)

= 3/6

0.5

2)

We are required to determine the probability of choosing a letter that is not a vowel after placing the letters for the word smart in a bag.

The non-vowels in the word smart are; s, m, r, and t. There are 4 non-vowels out of a total of 5 letters. The required probability is thus;

(4/5)*100 = 80%

Answer:

73

292

173

Step-by-step explanation:

x = first number

4x = second number

100 + x = third number

x + 4x + 100 + x = 538

6x + 100 = 538

6x + 100 - 100 = 538 - 100

6x = 438

6x/6 = 438/6

x = 73

Check:

73 + 4(73) + 100 + 73 = 538

73 + 292 + 173 = 538

538 = 538

Answer:

The numbers are 73, 173 and 292.

Step-by-step explanation:

If the numbers are x, y and z we have:

y = 4x

z = x + 100

x + y + z = 538

Substituting for y in the last equation:

x + 4x + z = 538

5x + z = 538.............(1)

From the second equation:

z - x = 100................(2)

Equation (1) - (2) gives:

6x = 438

x = 73

Therefore y = 4x) = 4(73) = 292

and z = x + 100 = 73 + 100 = 173.

Answer:

1). Option C

2). Option A

Step-by-step explanation:

The given vertices of polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8) and E(6, 6)

After reflection new polygon formed MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8) and Q(-6, 6).

By comparing the vertices we find the x-coordinates of polygon ABCDE have been changed to MNOPQ by negative notation only.Y- coordinates are same.

Therefore, polygon ABCDE has been reflected across the y-axis.

Option C. is the answer.

If polygon MNOPQ is translated 3 units right and 5 units down then the new vertices of congruent polygon VWXYZ will be

M(-2, 8) = [(-2 - 3), (8 + 5)] = (-5, 13)

N(-4, 12) = [(-4 - 3), (12 + 5)] = (-7, 17)

O(-10, 12) = [(-10 - 3),(12 + 5)] = (-13, 17)

P(-8, 8) = [(-8 - 3), (8 + 5)] = (-11, 13)

Q(-6, 6) = [(-6 -3),(6 + 5)] = (-9, 11)

Therefore, Option A. is the correct option.

Answer:

16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2

Step-by-step explanation:

is it 9 times square root of 16 cubed, or is it really 9th root? I think it's

9th root of 16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2

The answer is:

The second option,

[tex]SU=13.02=13[/tex]

We are working with a right triangle, it means that we can use the following trigonometric property:

[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}[/tex]

Which applied to our problem, will be:

[tex]Tan(\alpha)=\frac{TU}{SU}[/tex]

We are given:

m∠S, equal to 21°

The side TU (opposite) equal to 5 units.

So, substituting and calculating we have:

[tex]SU=\frac{TU}{Tan(\alpha)}[/tex]

[tex]SU=\frac{5units}{Tan(21\°)}[/tex]

[tex]SU=13.02=13[/tex]

Hence, the answer is the second option

[tex]SU=13.02=13[/tex]

Have a nice day!

Answer:

13.0

Step-by-step explanation:

The given angle is m<S=21.

The given side length UT=5 units.

This side length is opposite to the given angle.

Since we want to find SU, the adjacent side; we use the tangent ratio to obtain;

[tex]\tan 21\degree=\frac{opposite}{adjacent}[/tex]

[tex]\tan 21\degree=\frac{5}{SU}[/tex]

This implies that;

[tex]SU=\frac{5}{\tan 21\degree}[/tex]

Therefore SU=13.025

The nearest tenth

SU=13.0

Answer:

BF = 30

Step-by-step explanation:

Since B and F are midpoints then BF is parallel to CE and half it's size

BF = 0.5 × CE = 0.5 × 60 = 30

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=6.5\\ s=5.7 \end{cases}\implies 5.7=\cfrac{\theta \pi (6.5)}{180}\implies 1026=6.5\pi \theta \\\\\\ \cfrac{1026}{6.5\pi }=\theta \implies \stackrel{\textit{rounded up, using }\pi =3.14}{50.27=\theta }[/tex]

The measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]

where

θ is the angle, that arc creates at the centre of the circle in degree.

As we know that the length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\pi r \times \dfrac{\theta}{360^o}[/tex]

Given the length of the arc is 5.7 cm, while the radius of the circle is 6.5cm, therefore, the angle made by the arc at the centre of the circle is,

[tex]5.7 = 2\pi (6.5) \times \dfrac{\theta}{360^o}\\\\[/tex]

θ = 50.27°

Hence, the measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.

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Answer:

16 ft²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 8 and h = 4, thus

A = [tex]\frac{1}{2}[/tex] × 8 × 4 = 16 ft²

The values of x and y, when the smaller triangle has an area of 10 cm² are x = 4cm and y = 5cm.

In the given triangle, the area can be expressed as [tex]\( \frac{1}{2} \times x \times y \)[/tex], where x and y represent the base and height of the triangle, respectively. Since the area is given as 10 cm², the equation becomes [tex]\( \frac{1}{2} \times x \times y = 10 \)[/tex].

To find x and y, we can rearrange the equation:

[tex]\[ x \times y = \frac{10 \times 2}{1} \][/tex]

[tex]\[ x \times y = 20 \][/tex]

Now, we need to find two numbers whose product is 20. The pair x = 4 and y = 5 satisfies this condition, as 4 × 5 = 20. Therefore, the values of x and y that satisfy the given area are x = 4cm and y = 5cm.

In conclusion, the solution x = 4cm and y = 5cm satisfies the given area condition. This is determined by substituting these values into the area formula, resulting in an area of 10 cm².

Answer:

The answer is C

Step-by-step explanation:

I just took the exact same test and got a 100% on it, I had previously answered this question when echo2155 rudely claimed that I didn't show any work, most people just answer the question and don't show work because most people just want the answer not the work for it. IF YOU AGREE WITH ME GIVE A THANKS AND 5-STARS, AND COMMENT "BOO echo2155!"

Thank you all who do this!

Answer:

an = 600,000 (1.15)^(n-1)

Step-by-step explanation:

So the first year, a₁ = 600,000.  The next year, a₂ = 690,000.  So:

r = a₂ / a₁

r = 690,000 / 600,000

r = 1.15

So an = 600,000 (1.15)^(n-1).

Your answer is correct!

Answer:

1/9

Step-by-step explanation:

(1/3)^2 = 1/3 x 1/3 =1/9

plus I checked the answer after I got it wrong so...

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

This is a case of enlargement of a figure of scale factor [tex]\frac{1}{3}[/tex].

In any enlargement, [tex]Area(F')=k^2 Area(F)[/tex], where the transformation maps F onto F'.

In this case, let F be polygon XXX and let F' be polygon YYY. Hence,

[tex]Area(YYY) = k^2 Area (XXX)[/tex]

[tex]Area(YYY) = (\frac{1}{3})^2 Area(XXX)[/tex]

[tex]Area(YYY) = \frac{1}{9} Area(XXX)[/tex]

Therefore, the area of polygon YYY is [tex]\frac{1}{9}[/tex] of the area of polygon XXX.

The area of a right triangle with side lengths 7 and 7 is [tex]\frac{bh}{2} = \frac{7*7}{2} = \frac{49}{2} = 24.5[/tex]

Answer: ≈ 13.98 in2

Step-by-step explanation:

A segment of a circle is a region bounded by an arc and its chord.

To determine the area of the segment, begin by finding the area of the sector defined by the central angle.

A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.

The formula for the sector area is A = πr2 (m∘/360∘).

It is given in the figure that central angle MNO is a right angle. So, m∠MNO = 90∘. It is also given that r = 7 in.

Substitute the given values into the formula and simplify.

A = π(7)2 (90∘/360∘) = 49/4π in2

Find the area of △MNO.

Since the radii in a circle are congruent, NO = NM = 7.                                  To find the area of △MNO, use the formula for the area of a triangle, A = 1/2bh.

Substitute 7 for b and 7 for h, then simplify.

A = 1/2 (7) (7) = 24.5 in2

The area of the segment is the difference between the two areas, the area of the sector and the area of the triangle.

A = 49/4π − 24.5 ≈ 13.98 in2

Therefore, the area of segment MNO is ≈ 13.98 in2.

Answer:

The simplest form is 2(3x - 7)/x(x³ + 4)

Step-by-step explanation:

* Lets revise how can divide fraction by fraction

- To simplify (a/b)/(c/d), change it to (a/b) ÷ (c/d)

∵ a/b ÷ c/d

- To solve it change the division sign to multiplication sign and

 reciprocal the fraction after the sign

∴ a/b × d/c = ad/bc

* Now lets solve the problem

∵ [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{2}}{2}+\frac{2}{x}}[/tex]

- Lets take the denominator and simplify by make it a single

 fraction, let the denominator of it 2x and change

 the numerator

∴ [tex]\frac{x^{2}}{2}+\frac{2}{x}=\frac{x(x^{2})+2(2)}{(2)(x)}=\frac{x^{3}+4}{2x}[/tex]

∴ The fraction = [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}[/tex]

* Now lets change it by (up ÷ down)

∴ [tex]\frac{3x-7}{x^{2}}[/tex] ÷ [tex]\frac{x^{3}+4}{2x}[/tex]

- Change the division sign to multiplication sign and reciprocal

 the fraction after the sign

∴ [tex]\frac{3x-7}{x^{2}}[/tex] × [tex]\frac{2x}{x^{3}+4}[/tex]

∴ [tex]\frac{(2x)(3x-7)}{(x^{2})(x^{3}+4)}[/tex]

- We can simplify x up with x down

∴ [tex]\frac{2(3x-7)}{x(x^{3}+4)}[/tex]

* The simplest form is 2(3x - 7)/x(x³ + 4)

To find the change in the temperature, solve for the equation below.

[tex]x - 13 = -4[/tex]

We now know that the temperature changed by 9 degrees.

[tex]x = 9[/tex]

So, we are looking for the answer which indicates that the temperature changed by 9 degrees.

[tex]-4 + 13 = 9[/tex]

The equation that would be used to show the difference in temperature from Saturday to Sunday is -4 + 13 = 9.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The temperature Saturday is -13°, and on Sunday it is -4°.

The change in the temperature, solve the equation below.

x - 13 = -4

Now, we know that the temperature changed by 9 degrees.

x = 9

The answer indicates that the temperature changed by 9 degrees.

-4 + 13 =9

The equation that would be used to show the difference in temperature from Saturday to Sunday is -4 + 13 = 9.

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Answer:

374.1

Step-by-step explanation:

Area of Hexagon = [tex]\frac{3\sqrt{3} }{2} * a^{2}[/tex]

The ' a ' is the side length.

So now we just plug in the values

[tex]\frac{3\sqrt{3} }{2} *12^{2}[/tex] = 374.12

Answer:

Expand the polynomial using the FOIL method.

− 8 x^ 2- 26 x − 15

Answer:

I believe the answer is B

Step-by-step explanation:

Answer:

the answer is B  

Step-by-step explanation:

Probability=number of favorable outcomes/ number of all possible outcomes

P(1st green and 2nd blue) = 2/6 x 3/6 = 1/6

Answer:

10 pounds

Step-by-step explanation:

You forgot the inequality sing, but since Antoine can't spend more than $18.20, I am positive that the sign is [tex]\leq[/tex] (Antony can spend $18.20 or less than $18.20).

Therefore, our inequality is: [tex]1.30x+5.20\leq 18.20[/tex]

where [tex]x[/tex] is the pounds of oranges

Let's solve step-by-step to find how many pounds of oranges he can buy

Step 1. Subtract 5.20 fro both sides of the inequality

[tex]1.30x+5.20-5.20\leq 18.20-5.20[/tex]

[tex]1.30x\leq 13[/tex]

Step 2. Divide both sides of the inequality by 1.30

[tex]\frac{1.30x}{1.30} \leq \frac{13}{1.30}[/tex]

[tex]x\leq 10[/tex]

We can conclude that Antony can buy 10 pounds of oranges.

Answer:

23.32 degrees

Step-by-step explanation:

We set up a large right triangle that has 2 triangles within it.  The large triangle is a right triangle.  The height of it is the height of the tower, the base angle is 62, the hypotenuse is 95, and the base measure is y.  The other triangle has the same height which is the height of the tower, the angle is what we are looking for, and the base measure is 150 feet beyond y, so its measure is y + 150.  We have enough information to find the height of the tower, so let's do that first.  Going back to the first smaller triangle.  

[tex]sin62=\frac{x}{95}[/tex] so the height of the tower is 83.88 feet.  Now we need to solve for y.  Using that same triangle and the tangent ratio, we find that [tex]tan62=\frac{83.88}{y}[/tex].  Now let's do the same thing for the other triangle with the unknown angle.

[tex]tan\beta =\frac{83.88}{y+150}[/tex]

Solve both of these for y.  The first one solved for y:

[tex]y=\frac{83.88}{tan62}[/tex]

The second one solved for y will simplify to:

[tex]y=\frac{83.88-150tan\beta }{tan\beta }[/tex]

Now that these are both solved for y, and y = y, we can set them equal to each other by the transitive property of equality:

[tex]\frac{83.88-150tan\beta }{tan\beta }=\frac{83.88}{tan62}[/tex]

Cross multiply to get this big long messy looking thing:

[tex]tan62(83.88-150tan\beta )=83.88tan\beta[/tex]

Distribute through the parenthesis to get

[tex]83.88tan62-[(tan62)(150tan\beta)]=83.88tan\beta[/tex]

Get the unknown angles on the same side so it can be factored out:

[tex]83.88tan62=83.88tan\beta +[(tan62)(150tan\beta )][/tex]

And then factoring it out gives you:

[tex]83.88tan62=tan\beta(83.88+150tan62)[/tex]

Divide to get

[tex]tan\beta =\frac{83.88tan62}{83.88+150tan62}[/tex]

Do this on your calculator in degree mode to give you an angle measure of 23.32°.  I know this is really hard to follow without being able to draw the pics for you like I do in my classroom, but hopefully you can follow my description and draw your own triangles and follow from that!

An angle of elevation is formed by two reference lines; the horizontal line and the line from the reference point to the point in view

The angle of elevation from the point on the ground where Joey is standing to the top of the tower is approximately 23.318°

Reason:

Given parameter;

Length of the wire = 95 ft.

Angle formed by the wire and the ground = 62°

Location Joey is standing behind the wire, L = 150 feet

Required:

The angle of elevation from the ground at the point where Joey is standing to the top of the tower

Solution:

The height of the tower, h = 95 × sin(62°) ≈ 83.88 feet

Distance of the tower to the point the wire touches the ground, d, is given as follows;

d = 95 × sin(62°) ≈ 44.6 ft.

The distance of of Joey from the base of the tower, D = L + d

D = 150 ft. + 44.6 ft. = 194.6 ft.

Distance of Joey from the base of the tower, D = 194.6 ft.

Let θ represent the angle of elevation from the point on the ground where Joey is standing to the top of the tower, we have;

[tex]tan(\theta ) = \dfrac{h}{D}[/tex]

Therefore;

Which gives;

The angle of elevation from the point on the ground where Joey is standing to the top of the tower, θ ≈ 23.318°

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the awnser should be -x^2 +2

Answer:

y = -x^2+2

Step-by-step explanation:

shift down y=x^2 for 2 units then it becomes y = x^2-2

reflect across x-axis then it becomes y = -(x^2-2) which is y = -x^2+2