Suzie bought an antique jewelry box for $34.50. It originally cost $8.75 when it was made. Its value has increased $0.75 a year since it was made and it is now 83 years old. If Suzie were to sell it for what it is worth, how much money would she make? (Please show steps)

Answer:

4

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.

The exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].

Given that in the triangle [tex]\Delta LMN[/tex] marked with angles:
[tex]\angle MLN = \angle1\\\angle LMN = \angle2\\\angle LNM = \angle3[/tex]

And in the triangle, MN  is extended to some point marked with angle [tex]\angle 4[/tex].

To find angle is an exterior angle of the triangle by using the definition of exterior angle:

Definition of exterior angle:

The exterior angle of the triangle is formed by extending one of its sides.

In the triangle, MN  is extended to some point marked with angle [tex]\angle 4[/tex].

By using the definition implies:

exterior angle  = [tex]\angle 4[/tex]

Therefore, the exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].

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Answer:

23

Step-by-step explanation:

Let his current age = x

Now if you add 46 to that, you will get x + 46.

x + 46

At which point he will be 3 times as old as he is now

x + 46 = 3x            Subtract x from both sides.

x-x + 46 = 3x-x      Combine

46 = 2x                  Divide by 2

46/2=2x/2             Do the division

23 = x

He is 23 right now

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It might be a little easier to see if you represent the situation a little more literally.

3x - 46 = x            The answer comes to the same thing. You might think about which way you want to do it.

Answer: 1. 3 can be made  2. i believe it is only one way to put three books on a shelf 3. 3 i believe, its been awhile since i studied this

Step-by-step explanation:

Subtract 121 from both sides:

[tex]25x^2=-121[/tex]

Divide both sides by 25:

[tex]x^2 = -\dfrac{121}{25}[/tex]

The solutions would be

[tex]x = \pm\sqrt{-\dfrac{121}{25}}[/tex]

This expression cannot be evaluated using real numbers, because the square root of negative numbers are not allowed. If we're using complex numbers, the solutions are

[tex]x = \pm\sqrt{-\dfrac{121}{25}} = \pm\dfrac{11i}{5}[/tex]

Answer:

See below.

Step-by-step explanation:

That is a one-to-one function.

Answer: One-to-One function.

Step-by-step explanation:

A One-to-One function (also written as 1-1) is that function for which every element of the Range corresponds to one and only one element of the Domain.

 Given a Set A (Domain of a function) and a Set B (Range of the function), if [tex]If\ f(a) = f (b),\ then\ a = b[/tex] and it is a One-to-One function.

Given the graph of a function, you can determine if it is a One-to-One function if it passes the Horizontal Line Test.

The conclusion is:  A function in which each y-value has only one corresponding x-value is called a One-to-One function.

Answer:

A.

[tex]a_n=9+(n-1)\cdot 5[/tex].

Step-by-step explanation:

The common difference is 5. The y values are going up by 5. So this is an arithmetic sequence since we have a common difference.

The explicit form for arithmetic sequence is:

[tex]a_n=a_1+(n-1) \cdot d[/tex] where d represents the commom difference and [tex]a_1[/tex] is the first term.

Here the first term is [tex]a_1=9[/tex] and we already determined the value for d which is 5.

Inputing these values for first term and common difference give:

[tex]a_n=9+(n-1)\cdot 5[/tex].

Answer:

the answer is A

Step-by-step explanation:

Answer:

(x+5)(x-1)(x+1)

Step-by-step explanation:

Let's attempt factoring by grouping:

So what this means we first want to group the first two terms together and second two terms together, like so:

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

Now we factor what we can from each pair:

x^2(x+5)+1(-x-5)

Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:

x^2(x+5)-1(x+5)

You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:

(x+5)(x^2-1)

You can actually factor this more because x^2-1 is a difference of squares.

The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).

So the factored form of x^2-1 is (x-1)(x+1).

So the complete factored form of our expression we had initially is

(x+5)(x-1)(x+1).

Answer:

[tex]\large\boxed{x^3+5x^2-x-5=(x+5)(x-1)(x+1)}[/tex]

Step-by-step explanation:

[tex]x^3+5x^2-x-5\qquad\text{distributive}\\\\=x^2(x+5)-1(x+5)\\\\=(x+5)(x^2-1)\\\\=(x+5)(x^2-1^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+5)(x-1)(x+1)[/tex]

Answer:

[tex]\large\boxed{m=\dfrac{y-b}{x}}[/tex]

Step-by-step explanation:

[tex]y=mx+b\to mx+b=y\qquad\text{subtract}\ b\ \text{from both sides}\\\\mx+b-b=y-b\\\\mx=y-b\qquad\text{divide both sides by}\ x\neq0\\\\\dfrac{mx}{x}=\dfrac{y-b}{x}\\\\m=\dfrac{y-b}{x}[/tex]

Answer: [tex]m=\frac{y-b}{x}[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Then, to solve for the slope "m", you can follow these steps:

- You need to subtract "b" from both sides of the equation:

[tex]y-b=mx+b-b\\\\y-b=mx[/tex]

- Finally, you can divide both sides of the equation by "x". Then:

[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]

Answer:

[tex]f(x)=a(x-h)^2+k[/tex]

Vertex form.

Step-by-step explanation:

You are talking about the vertex form for a parabola.

[tex]f(x)=a(x-h)^2+k[/tex] tells us:

A) The vertex is (h,k).

B) Open up (if a is positive) or open down (if a is negative)

C) a also tells us how much it is vertically stretched or compressed.

Answer:

Answer choice 4

Step-by-step explanation:

Since alternate interior angles create congruent angles, angle 5 and 3 are congruent as well as 4 and 2, and since the only option that has these statements is answer choice 4, it is the correct answer.

Answer:

it is d

Step-by-step explanation:

Answer:

The answer is B. 2374

Answer:

B. 2374

Step-by-step explanation:

Division by 5: If a number ends in 0 or 5 it is divisible by 5.

A. 5000 is divisible by 5.

D. 2505 is divisible by 5.

Division by 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

B. 2374

Add the digits of 2374: 2 + 3 + 7 + 4 = 16. 16 is not divisible by 3, so 2374 is not divisible by 3. It is also not divisible by 5 since it does not end in 0 or 5.

C. 1203

Add the digits of 1203: 1 + 2 + 0 + 3 = 6. Since 6 is divisible by 3, 1203 is divisible by 3.

Answer: B. 2374

Answer:(a+b)^2+(ab+a+b)2

Step-by-step explanation:

You break it up into two part, based on the exponents.

(a^2+b^2)+(2ab+2a+2b)

Now you can factor out from each...

(a+b)^2+(ab+a+b)2

Answer: (x+y+2)(x+y)

Step-by-step explanation:

Using square roots and factorising

Answer:

26 m

Step-by-step explanation:

Perimeter = 92 m

Length = 8 m more than width

Width: 20 m

Therefore,

The width of the rectangular lot is 19 m and the length is 27 m.

The subject of this question is the calculation of the length of a rectangular lot. The perimeter of a rectangle is the sum of all its sides, given by the formula 2*(length + width). From the question, we know that the perimeter is 92 m, and the length is 8 m more than the width. Suppose 'w' is the width. Thus the length is 'w + 8' m.

So, we can set up the equation 2*(w + w + 8) = 92. Solving this equation will give us the value for the width (w) and consequently, the length by adding 8 to it.

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Answer:

D:  (9, 23)

Step-by-step explanation:

Substitute the given value, 9, for x in y = 3x - 4.  We get:

y = 3(9) - 4, or y = 23.  Thus, the solution is (9, 23) (Answer D)

D. (9, 23) is the required ordered pair.

Substitution method is a mathematical method in which we have to pick one variable from one equation and substitute it to another equation.

Given equations are,

y = 3x - 4  .....(1)  &  x = 9   .....(2)

By using substitution method,

We have to put the value of x of (2) in (1),

i.e. we have to put x = 9 in (1),

∴ y = (3×9) - 4

     = 27 - 4

     = 23

So, the required ordered pair is (9, 23)

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Step-by-step explanation:

[tex]\dfrac{a}{b}\cdot(-1)=-\dfrac{a}{b}[/tex]

On the number line, fractions a/b and -a/b lie on the opposite sides of the number 0, at the same distance (look at the picture).

Answer:

-1 9/18 and then -32/40 and then 1 8/20

Step-by-step explanation:

The largest negatives is the least , then the second to least and then non-negative should be the greatest or the last

Answer:

If you can draw one straight line through a polygon and cross more than two sides, the polygon is concave - A.

Answer:

B. y + 2 = ½(x + 3)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

Look at the picture.

Use the long division.

Answer:

9. 75°

10. 60°

Step-by-step explanation:

Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.

Question 9

Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is  76/2 = 38

Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:

X + W + V = 180

? + 67 + 38 = 180

? + 105 = 180

? = 180 - 105 = 75°

Question 10

Using the theorem we can say that Angle B is HALF of ARC XYZ.

So,

2*Angle B = Arc XY + Arc YZ

2*102 = Arc XY + 124

204 = Arc XY + 124

Arc XY = 204 - 124 = 80°

Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus

Arc BX + Arc XY = 70 *2

Arc BX + Arc XY = 140

Arc BX + 80 = 140

Arc BX = 140 - 80 = 60°

Answer: Option D

Step-by-step explanation:

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = f (x + h) = (x + h) ^ 4[/tex]

Then it is fulfilled that:

If [tex]h> 0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the left

If [tex]h <0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the right

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = -f(x) = -x ^ 4[/tex]

Then it is fulfilled that:

The graph of [tex]g(x)[/tex] is equal to the graph of [tex]f(x)[/tex] reflected on the x axis

In this case we have to:

[tex]g(x) = -(x + 3)^4[/tex] and [tex]f(x) = x^4[/tex]

Therefore [tex]h=3>0[/tex] and [tex]g(x) = -f(x)[/tex]

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.

Answer:

Perimeter= 36mm

Area= 81mm

Step-by-step explanation:

Answer:

(x+2) + x + (x+4) = 2(1/2) + 2(x+3)

Step-by-step explanation:

They are equal to each other and the rectangle has 2x more perimeter

The triangle would be divided in half from that rectangle.

Sorry If this is confusing I am not very good at explaining things.

Answer:

i

Step-by-step explanation:

The square root of -1 is i which is an imaginary number

Answer:

n = 2 + 2√3 and n = 2 - 2√3

Step-by-step explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.

Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.

By applying the quadratic formula, we find that the roots are:

      - (-4) ± √12

n = ------------------

              2

or n = 2 + 2√3 and n = 2 - 2√3

Answer:

3.732 or 0.268 to the nearest thousandth.

Exact values are 2 + √12/2  or 2 - √12/2.

Step-by-step explanation:

Let the original number be x, then:

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2

x =  (4 + sqrt12)/ 2  , (4 - sqrt12) / 2

= 3.732, 0.268.

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (2, 6).

Substitute:

[tex]y-6=-5(x-2)[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Convert:

[tex]y-6=-5(x-2)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y-6=-5x+(-5)(-2)[/tex]

[tex]y-6=-5x+10[/tex]            add 6 to both sides

[tex]y=-5x+16[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y=-5x+16[/tex]            add 5x to both sides

[tex]5x+y=16[/tex]

Answer:

b^2-4ac, the value of the discriminant is 4

Step-by-step explanation:

The part b^2-4ac called the discriminant will tell you how many solutions a particular equation has, after plugging in the values you can tell how many solutions and what type of solutions that equation has by looking at whether the result is positive and a perfect square, positive, zero, or negative.  If the result is a positive perfect square, there will be two rational solutions; if the result is positive there will be two real zeros; if the result is zero, there is one real zero; if the result is negative, there will be two complex conjugates or imaginary terms.

To find the value of the discriminant plug in the values of the equation.

6^2-4(4)(2)=4

The value of the discriminant in this particular equation is a perfect square, that means that there are two rational solutions.  Put simply, this equation is factorable.

4x^2 + 6x + 2 = 0

(x+1)(4x+2)=0

x=-1 or -1/2

Answer:

The above explanation was correct.

To make it clear, just type 4 as the answer

Answer:

Equation:

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

[tex]( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )[/tex]

Plug in the points to get:

[tex]( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )[/tex]

[tex]( \frac{ -2}{2}, \frac{ 2}{2} )[/tex]

[tex]( - 1, 1)[/tex]

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

[tex]r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

[tex]r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} } [/tex]

[tex]r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} } [/tex]

[tex]r = \sqrt{ 36+ 1 } = \sqrt{37} [/tex]

The equation of the circle is given by:

[tex](x-h)^2 + (y-k)^2 = {r}^{2} [/tex]

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

[tex](x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2} [/tex]

[tex](x + 1)^2 + (y - 1)^2 = 37[/tex]

We expand to get:

[tex] {x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

[tex]{x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0[/tex]

[tex]{x}^{2} +2x - 35= 0[/tex]

[tex](x - 5)(x + 7) = 0[/tex]

[tex]x = 5 \: or \: x = - 7[/tex]

The point (5,0) and (-7,0) lies on the circle.

When x=0

[tex]{0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0[/tex]

[tex] {y}^{2} - 2y - 35= 0[/tex]

[tex](y - 7)(y + 5) = 0[/tex]

[tex]y = 7 \: or \: y = - 5[/tex]

The point (0,-5) and (0,7) lie on this circle.

Answer:

y = - 6x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 6x + 2 ← is in this form with slope m = - 6

• Parallel lines have equal slopes, hence

y = - 6x + c ← is the partial equation of the parallel line.

To find c substitute (- 1, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = - 6x - 4 ← equation of parallel line

Answer:

0.089: eighty-nine thousandths, 3.71: three and 71 hundredths, 0.3: three tenths, 13.701: thirteen and 701 thousandths, 5.005: five and five thousandths

Step-by-step explanation:

The first place back is the tenths place (0.0), the second is the hundredths place (0.00), the third place is the thousandths (0.000).