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2 months ago

Hello!

Whole numbers are closed under addition and multiplication

Integers are closed under addition, subtraction, and multiplication

natural numbers are positive whole integers so they are also closed under addition

The answers are A, B and D

Hope this helps!

Whole numbers are closed under addition and multiplication

Integers are closed under addition, subtraction, and multiplication

natural numbers are positive whole integers so they are also closed under addition

The answers are A, B and D

Hope this helps!

Question

A group of friends share 3 1/2 slices of cakes each friend gets half a slice of cake how many friends shared the slices of cake ? Each whole slice of cake can be divided into _____( 3 halves,1 half,2 halves) so 3 1/2 slices of cake is a total of _____ ( 4 halves,7 halves,9 halves) because each friend gets half a life of cake there are _____ (9,7,4) friends

Solution 1

Each whole slice of **cake **can be divided into ___2__( 3 **halves**,1 half,2 halves) so 3 1/2 slices of **cake **is a total of ___7__ ( 4 halves,7 halves,9 halves) because each **friend **gets half a life of cake there are __7___ (9,7,4) **friends**

There is a **fraction**, containing **numerator**(upper value) and **denominator**(lower value).

When the **numerator **is less than the **denominator**, the **fraction **is called proper **fraction**, otherwise it is called **improper fraction**.

A **proper fraction **is also called fraction which is less than 1.

And an **improper fraction **is â‰¥ 1

A **mixed fraction **contains a **sum **of whole number and a proper fraction.

One example of **mixed fraction **is

Â

It can be taken as

Since it is given that there are in total **slices **of **cakes**, we can **convert **it to **normal fraction **as

This shows the **amount **of slices of **cakes**. Â It means there were 7 half slices of cake.

Since each **friend **took half slice, and all of **slices **was consumed, thus, there must be 7 friends in the group.

Thus,

The completed **statement **is

Each whole slice of **cake **can be divided into ___2 halves__( 3 **halves**,1 half,2 halves) so 3 1/2 slices of **cake **is a total of ___7__ ( 4 halves,7 halves,9 halves) because each **friend **gets half a life of cake there are __7___ (9,7,4) **friends**

Learn more about **fractions **here:

Solution 2

**Answer:**

Each whole slice of cake can be divided into** 2 halves **so slices of cake is a total of **7 halves** because each friend gets half a life of cake there are** 7.**

**Step-by-step explanation:**

**Given : **A group of friends share Â slices of cakes each friend gets half a slice of cake.

**To find : **How many friends shared the slices of cake ? Â Â

**Solution : **

**According to question,**

**i.e.** it divided into 2 halves.

**i.e.** total slices are 7 halves.

Each friend gets half a life of cake

**i.e. **there are 7 friends.

**Rounding all the statements together,**

Each whole slice of cake can be divided into** 2 halves **so slices of cake is a total of **7 halves** because each friend gets half a life of cake there are** 7.**

Question

A pine tree measured 40 1/2 feet tall. Over the next 7 1/2 years,it grew to a height of 57 feet. During the 7 1/2 years, what was the average yearly growth rate of the height of the tree?

Solution 1

Question

A coin is tossed 100 times resulting in 46 heads and 54 tails. The same coin is tossed 1000 times resulting in 495 heads and 505 tails. What is the theoretical probability of getting heads with this coin?

Solution 1

Theoretically the chance of flipping a coin is still 50%. However, the likelihood based on a data set such as this is 49.18%. You can get this by adding the numbers together and dividing by the total number of times flipped.Â

Question

What is the difference of the two polynomials?
(9x2 + 8x) â€“ (2x2 + 3x)

Solution 1

Answer:

(9xÂ² + 8x) - (2xÂ² + 3x)

= 7xÂ² + 5x

Step-by-step explanation:

(9xÂ² + 8x) - (2xÂ² + 3x)

open the bracket

= 9xÂ² + 8x - 2xÂ² - 3x

collect like terms

= 9xÂ² - 2xÂ² + 8x - 3x

= 7xÂ² + 5x

Solution 2

(9x^2+8x)-(2x^2+3x)

9x^2+8x-2x^2-3x

7x^2+5x

9x^2+8x-2x^2-3x

7x^2+5x

Question

Can you discuss the differences between circumference and area of a circle ?

Solution 1

The circumference (C) of any circle is the perimeter around it; it is circles' one dimensional measurement (i.e. in, ft, cm, mi, etc.). As a circle grows, increasing the

circle's size, the distance around it (circumference) increases proportionately with

the radius. Thus this length can be found by multiplying the radius Ã— 2 (or diameter Ã— 1) Ã— a constant known as pi. Pi, an infinitely long decimal that begins 3.1416, was calculated by working backwards from the length of a circle, divided by 2Ã—radius. No matter the size of any circle, they discovered that the distance will always vary 3.1416... Ã— twice the radius (or diameter). An example is a circle of radius 40 cm: C = 2piÃ—r = 80pi cm, or 251.33 cm.

The area (A) of a circle, however, covers much more matter; it is the two dimensional measure of any circle (i.e. sq.in., sq.ft, sq.cm, etc.). Area also varies according the constant pi Ã— the radius, BUT it increases much more than the radius once; it varies by the radius Ã— radius (radius squared) Ã— the value pi. Using the same circle example of radius 40cm: A = piÃ—r^2,

A = (40Ã—40)pi = 1600pi = 5,026.55 cm^2.

So you can see that the [2-dimensional] area of this circle is 20 times the [1-dimensional] circumference

circle's size, the distance around it (circumference) increases proportionately with

the radius. Thus this length can be found by multiplying the radius Ã— 2 (or diameter Ã— 1) Ã— a constant known as pi. Pi, an infinitely long decimal that begins 3.1416, was calculated by working backwards from the length of a circle, divided by 2Ã—radius. No matter the size of any circle, they discovered that the distance will always vary 3.1416... Ã— twice the radius (or diameter). An example is a circle of radius 40 cm: C = 2piÃ—r = 80pi cm, or 251.33 cm.

The area (A) of a circle, however, covers much more matter; it is the two dimensional measure of any circle (i.e. sq.in., sq.ft, sq.cm, etc.). Area also varies according the constant pi Ã— the radius, BUT it increases much more than the radius once; it varies by the radius Ã— radius (radius squared) Ã— the value pi. Using the same circle example of radius 40cm: A = piÃ—r^2,

A = (40Ã—40)pi = 1600pi = 5,026.55 cm^2.

So you can see that the [2-dimensional] area of this circle is 20 times the [1-dimensional] circumference

Solution 2

TheÂ circumferenceÂ of aÂ circleÂ is the length around theÂ circleÂ which is equal to 360Â°. Pi is the number needed to find theÂ circumferenceÂ of theÂ circle. In circlesÂ theÂ AREAÂ is equal to 3.14xRadias^2

Question

Î”DEFÂ rotates 90Â° clockwise about point A to create Î”DÂ 'EÂ 'F. Therefore, which equation must be true? mâˆ DEF = mâˆ DÂ 'FÂ 'EÂ '

Solution 1

The equation that is given does not have to be true, because the letters are not in the same order. Therefore, we are not comparing the corresponding pairs of angles. They may or may not be congruent.

When a shape is rotated, the corresponding pairs of angles are congruent.

When a shape is rotated, the corresponding pairs of angles are congruent.

Solution 2

As Rotation does not bring any changes in the shape and size of a geometrical figure.

So, the two triangles , Î”DEFâ†’â†’Called Pre image

when rotated through an angle of 90Â°, will be congruent to

, Î”D'E'F'â†’â†’â†’Called Image.

â†’So, when two triangles are congruent , their corresponding parts will be equal ,that is congruent.

1. âˆ FD Eâ‰…âˆ F' D'E'

2.âˆ DEFâ‰…âˆ D'E'F'

3.âˆ E FDâ‰…âˆ E'F'D'

4. EDâ‰…E'D'

5. F E=F'E'

6. Â FD=F'D'

All six possibilities are true when, Î”DEF rotates 90Â° clockwise about point A to create Î”D 'E 'F.

Question

Choose all questions that are true A. 4+9=6+7
B. 12-8=1+3
C. 15-8=5+3
D. 9-2=16-9
E. 6+5=18-9

Solution 1

I believe the correct answers are A, B, and D

Question

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 â€“ 7x + 4 has. Which best describes the discriminant and the number of zeros? The equation has one zero because the discriminant is 1. The equation has one zero because the discriminant is a perfect square. The equation has two zeros because the discriminant is greater than 0. The equation has no zeros because the discriminant is not a perfect square.

Solution 1

For the discriminant is

there are 3 basic cases of what happens for different discriminants

1. if the discriminant is less than 0, then there are no real zeroes

2. if the discriminant is 0, then it has 1 zero

3. if the discriminant is greater than 0, it has 2 zeroes

so given

a=3,b=-7,c=4

thus the discriminant is

the discriminant is 1. 1 is positive, thus the equation has 2 zeroes because the discriminant is greater than 0

the answer is the equation has two zeroes because the discriminant is greater than 0

there are 3 basic cases of what happens for different discriminants

1. if the discriminant is less than 0, then there are no real zeroes

2. if the discriminant is 0, then it has 1 zero

3. if the discriminant is greater than 0, it has 2 zeroes

so given

a=3,b=-7,c=4

thus the discriminant is

the discriminant is 1. 1 is positive, thus the equation has 2 zeroes because the discriminant is greater than 0

the answer is the equation has two zeroes because the discriminant is greater than 0

Solution 2

The equation has two zeros because the discriminant is greater than 0

An equation always has two zeroes unless the discriminant is 0 or negative.Â

An equation always has two zeroes unless the discriminant is 0 or negative.Â

Question

PLEASE HELP, ASAP! Deborah is planting a rectangular garden. The garden is 15.25 feet long and 12.5 feet wide.
The formula for the area of a rectangle is A=bh.
What is the area of the garden?
Enter your answer as a decimal in the box.

Solution 1

**Answer: **

**Step-by-step explanation:**

Given: Â Deborah is planting a rectangular garden.

The breadth of the garden (b)= 12.5 feet

The length of the garden (h)= 15.25

**The formula for the area of a rectangle is given by :-**

**Therefore, the area of the garden = **

Solution 2

27.75 hope it helps!

Question

How to simplify 4(2a)+7(-4b)+(3Ã—cÃ—5)

Solution 1

â†’Â **Solutions**

â‡’Â**SimplifyÂ **4(2a)+7(âˆ’4b)+3c(5)â‡’Â 8a+âˆ’28b+15c

**Answer **

Â â‡’Â 8aâˆ’28b+15c

â‡’Â

Â â‡’Â 8aâˆ’28b+15c

Solution 2

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