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Answer:

Step-by-step explanation:MATHEMATICAL GOALS

This lesson unit is intended to help assess how well students are able to interpret and use scale

drawings to plan a garden layout. This involves using proportional reasoning and metric units.

COMMON CORE STATE STANDARDS

This lesson relates to the following Standards for Mathematical Practices in the Common Core State

Standards for Mathematics, with a particular emphasis on Practices 1, 3, 4, 5, and 6:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

8. Look for and express regularity in repeated reasoning.

This lesson gives students the opportunity to apply their knowledge of the following Standards for

Mathematical Content in the Common Core State Standards for Mathematics:

7.G: Draw, construct, and describe geometrical figures and describe the relationships between

them.

Solve real-life and mathematical problems involving angle measure, area, surface area,

and volume.

7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and

equations.

7.RP: Analyze proportional relationships and use them to solve real-world and mathematical

problems.

INTRODUCTION

This lesson unit is structured in the following way:

• Before the lesson, students work individually on a task designed to reveal their current levels of

understanding. You review their responses and create questions to help them improve their work.

• At the start of the lesson, students reflect on their individual responses, before producing a

collaborative improved solution to the task. Then, in the same small groups students analyze

sample responses. They then discuss as a whole-class the methods they have seen and used.

• In a follow-up lesson, students reflect on their work. If time allows, an extension task is available.

MATERIALS REQUIRED

• Each student will need a copy of Design a Garden and Garden Plan, some blank paper, a miniwhiteboard, pen, and eraser, and the How Did You Work? questionnaire. The Garden Plan should

be copied at exactly 100% scale so the measurements are accurate. If this is not possible,

photocopy the rules on S-3, one rule per student, which should then match the Garden Plan

measurements. It will be useful to have spare copies of the Garden Plan.

• Each small group of students will need a new copy of the Garden Plan, the Assistants’ Methods, a

glue stick, felt-tipped pen, and a sheet of poster paper. For the optional extension Mandy’s Second

Email will be needed. Provide short rules, meter rules, string, protractors, scissors, glue, card,

plain paper, graph paper, and colored pencils for students who choose to use them.

TIME NEEDED

20 minutes before the lesson, a 110-minute lesson (or two 60-minute lessons), and 10 minutes in a

follow-up lesson. Actual timings will depend on the needs of your students.

Answer:

15 and 17

Step-by-step explanation:

x/5=3

x= 15   15/5 is 3

x/2=8.5

x=17   17/2 is 8.5

Answer:

$1.25

Step-by-step explanation:

step 1:

2.32 x 32

answer:

74.24

step 2:

114.24 - 74.24

answer:

40

step 3:

40 divided by 32

FINAL answer:

40 divided by 32 = x

x =

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

the original cost was $1.25! :D

Answer:

48 in^2

Step-by-step explanation:

To find the area of a triangle is (1/2)*base*height, so (1/2)*4in*24in = 2in*24in = 48 in^2.

Answer:

48 in2

Step-by-step explanation:

when finding area we use the equation A= 1/2bh

b meaning base and h meaning height

so for this we would use A= 1/2(24)(4)

multiply them both to get A=1/2(96)

and then take half of 96 to get 48

so the answer is 48in 2

Answer:

69

Step-by-step explanation:

All of the angles in the triangle will add together to be 180 degrees. So to find angle M, you add the two angles that you have together (79 + 32) to get 111. You then subtract 111 from 180 to get angle M (69).

Mark brainiest pls :)

Answer:

IT's -3.6 & 14.4 so D is the correct answer

Step-by-step explanation:

x= -3.6 y= 14.4

HOW I SOLVED IT

-3.6 x 3 = -10.8    2 x 14.4 = 28.8 - 10.8 = 18  so correct since it must equal to 18

-2/3 x -3.6 =2.4  + 12 = 14.4 so correct since y = 14.4

Brainilest would be appreciated :)

Answer:

12/40

Step-by-step explanation:

match the denominators so have 6/30 be multiplies with 40/40 and 12/40 multiplied with 30/30

6/30(40/40) = 240/1200

12/40(30/30) = 360/1200

As we can see, 360/1200 is bigger than 240/1200, therefore 12/40 is bigger

Answer: [tex]\frac{12}{40}[/tex]

Step-by-step explanation:

Hey there!

-If we were to simplify [tex]\frac{6}{30}[/tex] we would be able to simplify it to [tex]\frac{1}{5}[/tex].

-Multiply [tex]\frac{6}{30}[/tex] by 100 and you get 20 .

-Now compare that with [tex]\frac{3}{10}[/tex] which is [tex]\frac{12}{40}[/tex] simplified.

-Multiply [tex]\frac{12}{40}[/tex] by 100 and you get 30.

-We can now tell that [tex]\frac{12}{40}[/tex] is greater than [tex]\frac{6}{30}[/tex].

~I hope I helped :)~

Answer:

12

Step-by-step explanation:

24/2 = 12

Answer:

12

Step-by-step explanation:

Answer

The following is a picture of the number with a point on -2

Answer:

The value of x of the solution to the system of equations

Hence, option (C) is true.

Step-by-step explanation:

Given the system of equations

[tex]\begin{bmatrix}x=2y-4\\ 7x+5y=-66\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}x-2y=-4\\ 7x+5y=-66\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}x-2y=-4\mathrm{\:by\:}7\:\mathrm{:}\:\quad \:7x-14y=-28[/tex]

[tex]\begin{bmatrix}7x-14y=-28\\ 7x+5y=-66\end{bmatrix}[/tex]

subtracting  7x-14y=-28 from 7x+5y=-66

[tex]7x+5y=-66[/tex]

[tex]-[/tex]

[tex]\underline{7x-14y=-28}[/tex]

[tex]19y=-38[/tex]

so the equations become

[tex]\begin{bmatrix}7x-14y=-28\\ 19y=-38\end{bmatrix}[/tex]

solve 19y = -38

[tex]19y=-38[/tex]

Divide both sides by 19

[tex]\frac{19y}{19}=\frac{-38}{19}[/tex]

[tex]y=-2[/tex]

[tex]\mathrm{For\:}7x-14y=-28\mathrm{\:plug\:in\:}y=-2[/tex]

[tex]7x-14\left(-2\right)=-28[/tex]

[tex]7x+28=-28[/tex]

[tex]7x=-56[/tex]

Divide both sides by 7

[tex]\frac{7x}{7}=\frac{-56}{7}[/tex]

[tex]x=-8[/tex]

Therefore, the value of x of the solution to the system of equations

Hence, option (C) is true.

Answer:

1/8 1/4 1/2

Step-by-step explanation:

i hope it will help you

Step-by-step explanation:

1\8 1\4 1 \2

Answer:

5/2

Step-by-step explanation:

To find slope, just look directly at what is connected to the X. Don’t worry about anything else

Answer:

240 days

Step-by-step explanation:

Create an equation where x represents the total number of days

Use the information that 40 days is 1/6 of the total:

40 = 1/6x

Now, solve for x:

40 = 1/6x

Multiply both sides by 6, since it is the reciprocal of 1/6

40 = 1/6x

240 = x

So, the total number of days he has to record data is 240 days.

Answer:

-2

Step-by-step explanation:

Y-int is the point that touches the y-axis (the verticle line)

look at the point where it touches the y-axis

it is negative and it is 2. so it would be (0,-2) or -2

Answer:

180-(35+28)->180-63=117 and 180-117=63 then 63+36=99 and 180-99=81 so x=99°

2(3^2)−(3)(2)−3(2^2)+9

2(3^2)−(3)(2)−3(2^2)+9

= 9

Answer:

117

Step-by-step explanation:

(0.9)(130)

=117

Answer:

117

Step-by-step explanation:

Step 1:

[tex]\frac{x}{130} = \frac{90}{100}[/tex]           Equation

Step 2:

100x = 11700      Multiply

Step 3:

x = 11700 ÷ 100       Divide

Answer:

117

Hope This Helps :)

Answer:

24 correct questions

Step-by-step explanation:

Answer:

12q -1/2

Step-by-step explanation:

Answer:

12q -1/2

Step-by-step explanation:

Step-by-step explanation:

please see it my steps to work this problem

Answer:

108 deg

Step-by-step explanation:

Since sides DB and CD are congruent, then opposite angles are congruent.

m<C = m<B = 36

m<B + m<C + m<D = 180

36 + 36 + m<D = 180

m<D = 108

The value of h(-1) for the given funciton  h(x) = 3x + 4 will be 1.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given the function  h(x) = 3x + 4

If we want to calculate the value of the function at a certain point then we need to keep that point in the function.

So,

Value of function at = -1 will be

h (-1) = 3(-1) + 4

h(-1) = 1

Hence "  The value of h(-1) for the given funciton  h(x) = 3x + 4 will be 1".

For more about the function,

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Answer:

A. [tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]

Step-by-step explanation:

Required

Determine which system of equation satisfy (-4,2)

To do this, we simply substitute -4 for x and 2 for y in the given functions.

A.

[tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]

[tex]3x + 13y = 14[/tex]

[tex]3(-4) + 13(2) = 14[/tex]

[tex]-12 + 26 = 14[/tex]

[tex]14 = 14[/tex]

[tex]6x + 11y = -2[/tex]

[tex]6(-4) + 11(2) = -2[/tex]

[tex]-24 + 22 = -2[/tex]

[tex]-2 = -2[/tex]

The above shows that the given linear combination has a solution of (-4,2).

Hence, this option answers the question and there is no need to check other options

Answer: the answer is A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D is also equivalent

-8,-6,-4

-10,-6,0

these are the possible test points for your three intervals

Answer:

4≤x≤8

Step-by-step explanation:

Answer:

There needs to be 300 liters of Drink A and 270 liters of Drink B

Step-by-step explanation:

Let a = the amount of Drink A and b = the amount of Drink B

Multiplying a number by 0.2 is the same as calculating 20% of it and same goes with 15% and 0.15. This makes our equation for the amount of fruit juice:

0.2a + 0.15b = 100.5

We know what the difference between a and b will be 30 liters so:

a - b = 30

Now we have our system of equations

To cancel out a, we can multiply the first equation by -5 so we will now have:

-a - 0.75b = -502.5

a - b = 30

Adding these two equations together, we get:

-1.75b = -472.5

Both sides are negative, so we can take the negative signs away.

1.75b = 472.5

Now divide both sides by 1.75

b = 270

Plugging 270 into b, we have:

a - b = 30

a - 270 = 30

Add 270 to both sides

a = 300

There needs to be 300 liters of Drink A and 270 liters of Drink B

The system of linear equations which could be used to find the amount in litres of drinks A and B are :

Let :

Amount of drink A = a

Amount of drink B = b

Percentage of real fruit juice for drink A = 20%

Percentage of real fruit juice for drink B = 15%

Total litres made = 100.5

(Amount of drink A × percentage) + (Amount of drink B × percentage) = Total litres

The difference between the amount of drink A and B made :

Drink A is 30 liters more than B :

The system of equations required to determine the amount of drink A and B made are :

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Answer:

Step-by-step explanation:

a. 3n+2s+2h+1x=42.50

b. 90.3

Answer:

1.2

Step-by-step explanation:

X×5=0.75

X=(6, 5)

x=1.2

Answer:

no

Step-by-step explanation:

5+x=8+0.75x

x=12