Mathematics High School

Jennifer is 30 years old. She has $1200 in a checking account, $8000 in a savings account, $6000 in stock investments, $12,000 in a retirement account, and owns a car worth $8000. What is the total value of her liquid assets?

A. $20,000
B. $15,200
C. $23,200
D $25,200

APEX

Answers

Answer 1

Answer:

B.15,200

Step-by-step explanation:


Related Questions

I need consumer math help!!!!!
1. A house is used as for a loan (1point)
a)an asset
b)security
c)insurance
d)collateral
2.Most credit cards are debt. (1point)
a)unsecured
b)secured
c)collateral
d)relaized
3.You have a balance of $1,678.00 on a credit card with a 15.75% APR. How much intrest is accured if you pay nothing on the principal after 3 months?
a)$22.02
b)$66.07
c)$264.29
d)$88.10
4.you carry a balance of $2,065.00 on a credit card at a 17.25% APR for 5 months. How much is your total payment by the fifth month? (1point)
a)$2,094.68
b)$2,213.42
c)$2,421.21,

Answers

1. d) collateral

2. a) unsecured

3. The interest will be ((1 +.1575/12)^3 -1)*1678 ≈ 66.94. The 2nd selection is the best choice here: b) $66.07

4. The balance will be (1 +.1725/12)^5*2065 ≈ 2217.75. The 2nd selection is the best choice here: b) $2213.42

_____
The answer choices offered in your problems cannot be reproduced without incorrectly rounding interest values used in intermediate calculations.
Answer:        

1.D) collateral

2.A.) Most credit cards are unsecured debt

3.B.)$66.07

4.B.) 2,213.42

4/4 100%  

                                                 

HOPE I HELP I HAVE A NICE DAY

What is the measure of angle B in the triangle?

m∠B= [???]


A triangle labeled ABC with angle A: 120, angle B: x [unknown] and angle C as ( x+16).
What is the value of X (aka angle B.)

Answers

To figure this out, set up this equation:
180 = 120 + x + x + 16

Simplify: 180 = 136 + 2x
Subtract: 44 = 2x
Divide: x = 22

Answer: x (Angle B) = 22

Hope this helps!! :)

A nontoxic furniture polish can be made by combining vinegar and olive oil. the amount of oil should be five times the amount of vinegar. how much of each ingredient is needed in order to make 39 oz of furniture​ polish?

Answers

It would contain 6.5 oz of vinegar and 32.5 oz of oil.

Let V be the amount of vinegar and L be the amount of oil.

Since the amount of oil is 5 times the amount of vinegar, L = 5V.  We know that together they form 39 oz; therefore
V + 5V = 39
6V = 39

Divide both sides by 6:
6V/6 = 39/6
V = 6.5

L = 5V = 5(6.5) = 32.5

Final answer:

To make 39 oz of non-toxic furniture polish with the ratio of olive oil being five times the amount of vinegar, 6.5 oz of vinegar and 32.5 oz of olive oil are needed.

Explanation:

We know the oil to vinegar ratio is 5:1.

Let x be the amount of vinegar: We can use any variable to represent the unknown amount.

Set up the equation: Since the total volume is 39 oz and the ratio is 5:1, we have the equation: x (vinegar) + 5x (olive oil) = 39 oz.

Combine like terms: 6x = 39 oz.

Solve for x (vinegar): x = 39 oz / 6 = 6.50 oz.

Calculate the olive oil amount: Olive oil = 5 ×  vinegar = 5 × 6.50 oz = 32.50 oz.

Therefore, you'll need 6.50 oz of vinegar and 32.50 oz of olive oil to make 39 oz of furniture polish.

Remember to always test the polish on a small inconspicuous area of the furniture before applying it to the entire surface. And, for best results, use a clean, soft cloth to apply the polish and buff it to a shine.

A box measures 6inches by 2inches by 3 inches find the volume of the box in cubic feet enter as a fraction ?

Answers

------------------------------------------------
Convert 6 inches to feet:
------------------------------------------------
6 inches = 6 ÷ 12 = 1/2feet

------------------------------------------------
Convert 2 inches to feet:
------------------------------------------------
2 inches = 2 ÷ 12 = 1/6 feet

------------------------------------------------
Convert 3 inches to feet:
------------------------------------------------
3  inches = 3 ÷ 12 = 1/4 feet

------------------------------------------------
Find Volume:
------------------------------------------------
Volume = 1/2 x 1/6 x 1/4 = 1/48 ft³

------------------------------------------------
Answer: 1/48 ft³
------------------------------------------------


Convert the equation to the standard form for a hyperbola 4x^2-25y^2-8x+50y-121=0

Answers

we have that
4x²-25y²-8x+50y-121=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation
(4x²-8x)+(-25y²+50y)=121

Factor the leading coefficient of each expression
4(x²-2x)-25(y²-2y)=121

Complete the square twice. Remember to balance the equation by adding the same constants to each side.
4(x²-2x+1)²-25(y²-2y+1)²=121+4-25

Rewrite as perfect squares
4(x-1)²-25(y-1)²=100

Divide both sides by the constant term to place the equation in standard form
(4/100)(x-1)²-(25/100)(y-1)²=100/100
(1/25)(x-1)²-(1/4)(y-1)²=1

[(x-1)²]/25-[(y-1)²]/4=1

the answer is
[(x-1)²]/25-[(y-1)²]/4=1


This table shows the weekly rainfall, in inches, for two cities for ten weeks.

City A 0.2 0 1.5 1.3 2.5 3 0.4 0.3 0.2 1
City B 0 0 0.4 0.2 0.3 1 1 1 0.1 0.1
Which conclusion can be drawn from the data?


During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

The range between the maximum and minimum values for City B is greater than the range between the maximum and minimum values for City A.

For the ten weeks, City A received less rainfall, on average, than City B

The median for City A is less than the median for City B. pls help me

Answers

To determine the correct answer, you will need to find the ranges, means, medians, and mode of City B.  You can compare the answers then to answer the question.  Please see the attached picture for the necessary information.

The correct choice is the first statement about the mode for City B.

Answer:  A.  During the 10 wk period, the rainfall amount recorded most often for City B was 1 in

Step-by-step explanation: k12 test unit 5.10

Given: Quadrilateral ABCD is inscribed in circle O.
Prove: m∠A + m∠C = 180°

Drag an expression or phrase to each box to complete the proof.

Statements → Reasons
1. ___________ → Given
2. mBCD = 2(m∠A) → ________
3. mDAB = 2(m∠C) → Inscribed Angle Theorem
4. _________ → The sum of arcs that make a circle is 360°.
5. 2(m∠A) + 2(m∠C) = 360° → _________
6. m∠A + m∠C = 180° → Division Property of Equality

Answer Choices:
Substitution Property
Inscribed Angle Theorem
Central Angle Theorem
mBCD + mDAB = 360°
mBCD = mDAB
Quadrilateral ABCD is inscribed in circle O.


I'm guessing:
1. Quadrilateral ABCD is inscribed in circle O.
4. mBCD + mDAB = 360°
5. Inscribed Angle Theorem

I'm not sure about 5 or 2.

Thanks.

Answers

1. Quadrilateral ABCD is inscribed in circle O
A quadrilateral is a four sided figure, in this case ABCD is a cyclic quadrilateral such that all its vertices touches the circumference of the circle.
A cyclic quadrilateral is a four sided figure with all its vertices touching the circumference of a circle.

2. mBCD = 2 (m∠A) = Inscribed Angle Theorem
An inscribed angle is an angle with its vertex on the circle, formed by two intersecting chords. 
Such that Inscribed angle = 1/2 Intercepted Arc
In this case the inscribed angle is m∠A and the intercepted arc is MBCD
Therefore; m∠A = 1/2 mBCD

4. The sum of arcs that make up a circle is 360
Therefore; mBCD + mDAB = 360°
The circles is made up of arc BCD and arc DAB, therefore the sum angle of the arcs is equivalent to 360°

5. 2(m∠A + 2(m∠C) = 360; this is substitution property
From step 4 we stated that mBCD +mDAB = 360
but from the inscribed angle theorem;
mBCD= 2 (m∠A) and mDAB = 2(m∠C)
Therefore; substituting in the equation in step 4 we get;
2(m∠A) + 2(m∠C) = 360

Answer:

I took the test :) have a great day!

Step-by-step explanation:

How many positive integers less than 1000 are divisible by exactly one of 7 and 11?

Answers

994/7(number of multiples of 7 smaller than 1000) + 990(number of multiples of 11 smaller than 1000) - 924/(lcm of 7 and 11) (number of multiples of 77 smaller than 1000) = 142+90-12
                   = 220

hope i helped :)

a. The figure at the right shows a long rectangular strip of paper, one corner of which has been folded over to meet the opposite edge, thereby creating a 30-degree angle. Given the width of the strip is 12 inches, find the length of the crease.
b. Instead of a 30-degree angle, suppose that the angle has an unspecified size t. Use trigonometry to find the length of the crease, expressed in terms of t.
c. Find the approximate value of t that makes the crease as short as it can be. Restrict your attention to values of t that are less than 45 degrees. Explain your method.

Answers

A. We want to know the length of the crease. Let x represent that length. In the picture below, that is segment AD. If t represent m∠EAD, then ED = CD = x*sin(t). Of course DF = 12 -ED.

m∠CDF = m∠CAE = 2t

Putting these relationships together, we have
.. DF/CD = cos(2t) = (12-x*sin(t))/(x*sin(t))
Solving for x, we get
.. x*sin(t)*cos(2t) = 12 -x*sin(t)
.. x*sin(t)*(1 +cos(2t)) = 12
.. x = 12/(sin(t)*(1 +cos(2t))
.. x = 6/(sin(t)*cos(t)^2)
For t = 30°, x = 6/(3/8) = 16

For a 30° angle, the length of the crease in 16 inches.


B. From above,
.. crease length = (6 inches)/(sin(t)*cos(t)^2)


C. Using a graphing calculator, we can find the angle that makes the crease length a minimum. See the second figure. It is about 35.264°.

___
An exact solution using derivatives gives arcsin(1/√3) ≈ 35.264390°.

What is the sum or difference?

1. 2x^4 - 8x^4

(A). -6x^8
(B). -6x^4
(C). -16x^4
(D). -16x^8

What is the sum or difference?

2. 6y^5 - 9y^5

(A). -3y^10
(B). 15y^5
(C). -54y^5
(D). -3y^5

3. Write the Polynomial in standard form. Then name the Polynomial based on its degree and number of terms.

6 - 12x + 13x^2 - 4x^2

(A). 9x^2 - 12x; quadratic binomial
(B). 9x^2 - 12x + 6; quadratic trinomial
(C). -3x^2 + 6; quadratic binomial
(D). 9x^2 - 12x - 6; cubic trinomial

4. A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. The biologist modeled the populations, in ten of thousands, with the following polynomials where x is time, in years.

Common guppies: 3.1x^2 + 6x + 0.3
Endler's guppies: 4.2x^2 - 5.2x + 1

What polynomial models the total number of common and Endler's guppies?

(A). 7.3x^2 + 0.8x + 0.7
(B). 7.3x^2 - 0.8x + 1.3
(C). 7.3x^2 + 0.8x + 1.3
(D). 7.3x^2 + 0.8x - 1.3

5. A family is building a circular fountain in the backyard. The yard is rectangular and measures 14x by 19x and the fountain is going to be circular with a radius of 6x. Once the fountain is built, what will be the area of the remaining yard?

(A). 230πx^2
(B). 230x^2
(C). 266x^2 - 6πx^2
(D). 2x^2(133 - 18π)

6. A sports team is building a new stadium on a rectangular lot of land. If the lot measures 6x by 10x and the sports field will be 1x by 4x, how much of the lot will be left over to build bleachers on?

(A). 56x^2
(B). 64x^2
(C). 30x^2
(D). 60x^2

Can someone please help!! This is lesson 9, Unit 3, Polynomials and Factoring!!

Answers

1. Ans: Option (B) [tex]-6x^4[/tex]

Explanation:
Given: [tex]2x^4 - 8x^4[/tex]
Take the common out:
=> [tex]x^4(2 - 8)[/tex]

Hence: => [tex][tex]-6x^4[/tex][/tex] (Option B)

2. Ans: Option (D) [tex]-3y^5[/tex]

Explanation:
Given: [tex]6y^5 - 9y^5[/tex]
Take the common term(s) out:
=> [tex]y^5(6-9)[/tex]

Hence: => [tex]-3y^5[/tex] (Option D)

3. Ans: Option (B) [tex]9x^2 - 12x + 6[/tex] quadratic trinomial 

Explanation:
Given: [tex]6 - 12x + 13x^2 - 4x^2[/tex]

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> [tex]13x^2 - 4x^2 - 12x + 6[/tex]
=> [tex]9x^2 - 12x + 6[/tex] (Option B)

4. Ans: Option (C) [tex]7.3x^2 + 0.8x + 1.3[/tex]

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: [tex]3.1x^2 +6.0x + 0.3[/tex]
Endler's guppies:   [tex]4.2x^2 - 5.2x + 1.0 [/tex]
(add both)
-----------------------------------------------------------------
Total number:          [tex]7.3x^2 +0.8x + 1.3[/tex]
-----------------------------------------------------------------
Hence the ans is Option(C) [tex]7.3x^2 + 0.8x + 1.3[/tex]

5. Ans: Option (D) [tex]2x^2(133 - 18 \pi )[/tex]

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = [tex]266x^2[/tex]

Now the area of the circular fountain:
Area of the Circular Fountain = [tex] \pi r^2[/tex]
Since, r=6x
Therefore,
Area of the Circular Fountain = [tex] \pi (6x)^2 = 36 \pi x^2[/tex]

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = [tex]266x^2[/tex] - [tex]36 \pi x^2[/tex]
=> Final area of the Yard = [tex]2x^2(133 - 18 \pi)[/tex] (Option D)

6. Ans: Option (A) [tex]56x^2[/tex]

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = [tex]60x^2[/tex]

Now the area of the stadium:
Area of the stadium = 1x * 4x = [tex]4x^2[/tex]

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= [tex]60x^2[/tex] - [tex]4x^2[/tex]
=> Final area of the lot = [tex]56x^2[/tex] (Option A)

-i

Answer:1. B


Step-by-step explanation:


PLZ HELP!!!!!! The assessment for this lesson is to participate in a discussion about composite figures. You will be able to participate in the discussion throughout the unit. You are required to complete the following: 1) Respond to the discussion topic. 2) Respond to your two of your classmates’ ideas as well. Discussion Topic: What is an example of a composite figure in your home or community? How would you decompose it to find the area? Can you think of another reason that it would be helpful to decompose these figures in addition to making it easier to find the area of the figure? Before participating in the discussion, please review the discussion guidelines and grading rubric used to evaluate your participation.

Answers

Answer: Kitchen cabinets can be an example of a 3D composite figure.

Imagine the sets of regular kitchen cabinets going around the walls, refrigerators and sinks in your kitchen. They are generally all connected together in one piece. 

However, there are also all individual pieces. To find the total volume of the cabinets, you should break them all down into the individual single prisms.

You could also look at it as an area problem on the wall. How much total space are the cabinets taking up.

PLEASE HELP ASAP!! BRAINLIEST TO RIGHT/BEST ANSWER

Answers

12x^4 / 8

Answer is B

How to solve: \frac{1}{y^{\frac{2}{5}}} ?

Answers

well, there's nothing to solve per se, however assuming you meant "rationalizing the denominator", which means namely to "get rid of that pesky radical at the bottom", then

[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------[/tex]

[tex]\bf \cfrac{1}{y^{\frac{2}{5}}}\implies \cfrac{1}{\sqrt[5]{y^2}} \quad \stackrel{rationalizing~it}{\implies }\quad \cfrac{1}{\sqrt[5]{y^2}}\cdot \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^3}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^2}\cdot \sqrt[5]{y^3}} \\\\\\ \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^2y^3}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^{2+3}}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^5}}\implies \cfrac{\sqrt[5]{y^3}}{y}[/tex]

The difference of two numbers is 3 and their quotinet is 2 what are the 2 numbers

Answers

The two numbers are 6 and 3

I rly need help pls help me

Answers

x = 11/cos24° 
   = 11/0.9135
   = 12.0  to the nearest tenth. 

One card is drawn from a well shuffled deck of 52 cards find the probability of getting a red 10

Answers

The probability of getting a red card is 1/2 and the probability of getting a 10 is 4/52. To find the probability of getting both a red card and a 10, multiply the two.

(1/2)(4/52) = 4/104
4/104 = 1/26

Therefore, the probability is 1/26

Elliot has deposited $723 in a savings account that earns interest at a rate of 2.9% compounded twice a year. What will the account balance be in 23 years? (2 points)
Select one:
a. $826.02
b. $743.97
c. $1,401.95
d. $2,096.70

Answers

A=P(1+r/n)^(nt) where n= number of times compounded yearly, t= time and p= principle

A=723(1+.029/2)^(2*23)

A=$1,401.95   So C

Simplify the expression square root -1/(3+8i)-(2+5i)
a. 3+i/10.
b.-3+i.
c.3-I/10.
d.-3-i/10

Answers

None of the offered choices is correct, either for the problem stated or for a modification of it that gets closer to the answer choices.
.. -1/((3 +8i) -(2 +5i)) = (-1 +3i)/10

When solving negative one over five(x − 25) = 7, what is the correct sequence of operations?

A. Multiply each side by negative one over five, add 25 to each side
B.Multiply each side by 5, subtract 25 from each side
C.Multiply each side by negative one over five, subtract 25 from each side
D.Multiply each side by −5, add 25 to each side

Answers

C.Multiply each side by negative one over five, subtract 25 from each side
Answer:

Option: D is the correct answer.

D.Multiply each side by −5, add 25 to each side

Step-by-step explanation:

We are given an algebraic expression in terms of variable x as follows:

   [tex]\dfrac{-1}{5}(x-25)=7[/tex]

Now, firstly we will multiply both side of the equation by -5 to get:

[tex]\dfrac{-1}{5}\times (-5)(x-25)=7\times -5\\\\i.e.\\\\x-25=-35[/tex]

Now we add both side of the equation by 25 to get:

[tex]x-25+25=-35+25\\\\i.e.\\\\x+0=-10\\\\i.e.\\\\x=-10[/tex]

What’s the answer ???

(ONLY ANSWER IF YOU KNOW)

Answers

The correct answer is:  [B]:  " IV, II, I, III " .
______________________________________________________

Using the image, explain which angles are angles of elevation and which are angles of depression. Name all the angles that apply.

Answers

Angles of depression are measured below the horizontal.
Angles 1 and 3 are angles of depression.

Angles of elevation are measured above the horizontal.
Angles 2 and 4 are angles of elevation.
Elevation - 1, 3
Depression - 2, 4 

A convex, 11 sided polygon can have at most how many obtuse interior angles?

Answers

I think it would depend on the way the shape is made. If it's just a regular hendecagon, then it would have at most 11 obtuse interior angles.

Answer:

11

Step-by-step explanation:

Medal
The table below shows the distance y, in miles, traveled by a toy car in x minutes:

Time (x)
(minutes)
10 20 30 40

Distance (y)
(miles)
4 8 12 15

Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance traveled by the toy car.
[Choose the value of correlation coefficient from 1, 0.99, 0.5, 0.02]

Part B: What is the value of the slope of the graph of distance versus time between 10 minutes and 30 minutes, and what does the slope represent?

Answers

A) The data form an almost linear correlation making their most likeable correlation coefficient 0.99. Thus the greater the time elapsed the greater the distance traveled, example of positive correlation. B) Value of slope for the given time interval is deltaY/deltaX = (12-4)/(30-10) = 8/20 = 0.4. The slope represents the velocity with which the toy car moves, i.e. 0.4miles/min.

How do you solve this?

Answers

You have correctly found a=2, b=5, c=3.
You know a > 0, so the parabola will open up.
If the parabola opens up, the vertex is a minimum.

Use the formula for the axis of symmetry.
.. x = -b/(2a) = -5/(2*2) = -5/4
.. f(-5/4) = 2(-5/4)^2 +5(-5/4) +3 = -1/8
The vertex is (-5/4, -1/8).

Use the formula for the discriminant.
.. b^2 -4ac = 5^2 -4*2*3 = 25 -24 = 1
This is positive and a perfect square, so there are 2 real roots. They are (1) rational and unequal.

Use the quadratic formula to tell you the roots.
.. x = -b/(2a) ±(√discriminant)/(2a)
.. = -5/4 ±√1/(2*2)
.. = -5/4 ±1/4
.. = {-3/2, -1}

1. London Heathrow airport sees on average 191,200 passengers a day. How many passengers is this per minute?

Answers

191200 / 24 hours in a day = 7966.67 people per hour

60 minutes in 1 hour

7966.67 / 60 = 132.78 people per minute  round to 133 people

Three dice are going to be rolled. What is the probability that the first die rolled is a 1, the second die rolled is a 2, and the third die rolled is a 3? (If necessary, round to the nearest tenth)

Answers

Answer: The probability is 0.46%.

The chance of each given event happening is 1/6 because there are 6 different number on the dice and only 1 number is chose.

Therefore to find the combined probability, we have to multiply all the individual probabilities.

(1/6) x (1/6) x (1/6)

Or

(1/6)^3

The answer is about 0.46%,

Probability of getting first die rolled is a 1, second die rolled is a 2 and third die rolled is a 3 is equals to 0.46% (nearest tenth).

What is probability?

" Probability is a mathematical expression which represents the ratio of number of favourable outcomes to the total number of outcomes."

Formula used

Probability = [tex]\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]

According to the question,

Possible outcomes on each die = { 1, 2, 3, 4, 5, 6}

Substitute the value in the formula as per the given condition we get,

Probability that the first die rolled is a 1 =  ( 1 / 6)

Probability that the second die rolled is a 2 =  ( 1 / 6)

Probability that the third die rolled is a 3 =  ( 1 / 6)

Required Probability = (1 / 6) × (1 / 6) ×(1 / 6)

                                  =  ( 1 / 216)

                                  = 0.0046

                                  = 0.46% (nearest tenth)

Hence, required probability  (nearest tenth) = 0.46%

Learn more about probability here

https://brainly.com/question/11234923

#SPJ2

Based on the graph below, what is the solution of the equation f(x) = g(x)? graph of function f of x equals negative x plus 0.5 and graph of function g of x equals x squared plus 3 multiplied by x minus 4

Answers

we have that
f(x)=-x+0.5
g(x)=x²+3x-4
f(x)=g(x)------------> -x+0.5=x²+3x-4-------------> x²+3x-4+x-0.5=0

x²+3x-4+x-0.5=0---------------> x²+4x-4.5=0

using a graph tool

see the attached figure

the solution are the points (-4.915,0) and (0.915,0)

A four sided sandbox has exactly two right angles side lengths 5ft and two side lengths 6ft what shape best describes the shape of the sandbox

Answers

The sandbox is most likely in the shape of a kite. As it has only two right angles, it cannot be a square or other form of rectangle. It also cannot be a parallelogram, which has no right angles, nor is it a rhombus- all four sides are not of the same length.

A kite, however, has two pairs of equal-length sides that are adjacent to each other. It also has two sets of equal-measure angles, one of which can be 90° if it is a cyclic kite.

The sandbox has two right angles and two side lengths of 5ft and two side lengths of 6ft. This shape is consistent with a rectangle. Therefore, the shape of the sandbox is best described as a rectangle.

The sandbox described possesses two right angles and two pairs of opposite sides with equal lengths. Specifically, it has two sides of 5ft and two sides of 6ft. These characteristics are indicative of a rectangle.

Rectangles are quadrilaterals with four right angles, meaning each corner of the shape forms a 90-degree angle. Additionally, opposite sides of a rectangle are equal in length, which is evident in this sandbox with its 5ft and 6ft sides. The presence of two right angles further reinforces the shape's rectilinear nature.

Moreover, rectangles have parallel opposite sides, which allows for uniformity in the sandbox's shape. This geometric feature is crucial for ensuring a consistent and stable structure.

By definition, squares are also rectangles, but not all rectangles are squares. Given that the sides of the sandbox are not all of equal length (i.e., not a square), it is more appropriate to classify it as a rectangle.

Therefore, considering the sandbox's right angles, equal opposite sides, and parallel sides, it aligns most closely with the characteristics of a rectangle.

2) two florist purchased flower bouquets and vases at the same store. The first florist bought 2 flower bouquets and two vases for a total of $12.50. The second florist bought 8 flower bouquets and 2 vases for a total of 29.00

Let b represent the cost of one flower bouquet and v represent the cost of one vase. Write and solve a system of equations to find the price of each type of arrangement. SHOW ALL WORK!

Answers

Let
b---------> the cost of one flower bouquet
v-------->  the cost of one vase.

we know that
2b+2v=12.50-----> Multiplied by -1------------->-2b-2v=-12.50
8b+2v=29---------------------------------------------> 8b+2v=29
           I add the two equations                    ------------------------
                                                                        6b=16.50
b=2.75
2*2.75+2*v=12.50---------------> v=(12.50-5.5)/2---------> v=3.5

the answer is
the cost of one flower bouquet is $2.75
the cost of one vase is $3.5

The steps used by Taylor to solve the equation 3(x - 2) = 6(2x + 1) + 6 are shown below:

3(x - 2) = 6(2x + 1) + 6
x - 2 = 2(2x + 1) + 2
x - 2 = 4x + 2 + 2
x - 2 = 4x + 4
-3x - 2 = 4
-3x = 6
x = -2

Which properties did Taylor use to solve
the equation? Choose all that apply.

A. Distributive property

B. Commutative property

C. Inverse Operation Property

D. Associative property of multiplication

E. The sum of a number and its additive inverse is 0.

F. The product of a number and its multiplicative inverse is 1.

Answers

Both A and C are used within this problem. Distributing happens in the first and second step. Also, Inverse operations are used in nearly every step that is solving. 
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