Helen wrote the following facts to try to show that division by 0 results in 0. Explain her error.

To find the scale factor  the ratio of one length to the other is determined.

The scale factor is a measurement for comparing figures with similar appearances but differing scales or metrics.

Consider two squares that appear to be similar yet have different length of side.

The scale factor describes how much a figure has grown or shrunk in comparison to its original size.

Scale Factor is determined by dividing the new figure dimensions with the original figure.

For scale up the formula is Dimensions of the bigger figure / Dimensions of the smaller one.

On a graph

On each figure, find two corresponding sides.

To find the scale factor  the ratio of one length to the other is determined.

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200 percent i am pretty sure

That is very false and true! because 3 6 9 12 15 18 21 it skips in and out like a pattern!

[tex]1m=100cm\to1cm=\dfrac{1}{100}m\\\\1dam=10m\\\\\text{therefore}\\\\\dfrac{2}{5}cm=\dfrac{2}{5}\cdot\dfrac{1}{100}m=\dfrac{1}{250}m\\\\\dfrac{1}{3}dam=\dfrac{1}{3}\cdot10m=\dfrac{10}{3}m\\\\\dfrac{2}{5}cm\times\dfrac{1}{3}dam=\dfrac{1}{250}m\times\dfrac{10}{3}m=\dfrac{1}{75}m^2[/tex]

Answer,

The top right one.

Explanation,

7 to the 2nd power = 49

The model is showing 49 cubes

In conclusion, that's how I got the answer.

Hope this helps :-)

Answer:  The correct option is

(D) [tex]n<2p+7k-4.[/tex]

Step-by-step explanation:  We are given to solve the following inequality for the unknown variable n :

[tex]21k-3n+9p>3p+12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given inequality for n, we must take terms involving n on the left side and other terms on the right side of the inequality.

From inequality (i), we have

[tex]21k-3n+9p>3p+12\\\\\Rightarrow -3n>3p+12-21k-9p\\\\\Rightarrow -3n>-6p-21k+12\\\\\Rightarrow 3n<6p+21k-12~~~~~~~~~~~~~~~~~[\textup{since }a>b~~\Rightarrow -a<-b]\\\\\Rightarrow n<\dfrac{6p+21k-12}{3}\\\\\Rightarrow n<2p+7k-4.[/tex]

Thus, the required solution for n is [tex]n<2p+7k-4.[/tex]

Option (D) is CORRECT.

Final answer:

The probability of selecting a blue marble from a jar with 10 blue marbles among a total of 100 marbles is 0.10 or 10%.

Explanation:

The probability of randomly selecting a blue marble from a jar containing 100 marbles with 10 blue marbles, 79 green marbles, 6 red marbles, and 5 yellow marbles is calculated using the formula:

Probability (P) = Number of favorable outcomes / Total number of outcomes

Here, the favorable outcomes are the blue marbles, and the total number of outcomes is the total number of marbles in the jar.

P(blue marble) = 10 blue marbles / 100 total marbles = 0.10 or 10%

This means there is a 10% chance of selecting a blue marble. This probability calculation assumes each marble has an equal chance of being selected.

take the number of blocks and multiply it by the stories

hope this helps :)

Answer:

18 inches tall.

Step-by-step explanation:

The width of an image of a book shown on a website = 1.5 inches

and length of the book shown on the website = 3 inches

The actual width of the book = 9 inches

Scale of the book image = [tex]\frac{9}{1.5}[/tex]

   1 inches  = 6 inches

The actual length of the book = 3 × 6

                                                  = 18 inches.

The actual book is 9 inches wide and 18 inches tall.

The actual height of the book, given the image size can be found to be 18 inches.

The image of the book is shown on the computer monitor at 1.5 inches wide, while the actual book is 9 inches wide.

To find the scale of the image on the computer monitor, divide the width of the image on the monitor by the actual width of the book:

= 1.5 inches / 9 inches

= 1/6

So, the scale of the image on the computer monitor is 1/6.

This means that every inch on the monitor represents 6 inches of the actual book.

Now, to find the actual height of the book, you can use the scale and the height of the image on the monitor:

= 3 inches * 6

= 18 inches

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Answer:

a)   Here x represent number of ride tickets

z represent admission fees. = $20

y represent total cost.

Step-by-step explanation:

a)   Here x represent number of ride tickets

     z represent admission fees.

      y represent total cost.

b) Given that,

$0.75 per ticket for the rides.

Number of tickets (x) = 18

Total spent (y) = $33.50

Total cost = (number of tickets)*(price per ticket) + admission fees

y =0.75x + a

We can  calculate the cost for anyone who only pays for festival admission and rides.

c)

Put y = 33.50

x = 18

33.50 = 0.75*18 + a

33.50 = 13.5 + a

Solve for a,

Subtract 13.50  both the side

33.50 - 13.50 = 13.50-13.50 + a

20 = a

So, admission cost (a) = $20

Okay so slope intercept form is y=mx+b so you move the numbers around and ill just do the work here:

10x-7y=-8

-10x to both sides

-7y=-10x-8

divide by -7

y=10/7x + 8/7

To change the standard linear equation 10x - 7y = -8 into slope-intercept form, you subtract 10x from both sides to isolate y and then divide every term by -7, resulting in the equation y = (10/7)x + 8/7.

To convert the given standard form linear equation, 10x - 7y = -8, into slope-intercept form, which is typically denoted as y = mx + b where m is the slope and b is the y-intercept, follow these steps:

So, the slope-intercept form of 10x - 7y = -8 is y = (10/7)x + 8/7.

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The area of a rectangle is its length x width.

The perimeter of a rectangle is its length + length + width + width.

Let's have l stand for length and w for width.  A will stand for area and P for perimeter.  This gives us:

399 = l x w

80 = 2l + 2w  We can divide both sides of this equation by 2 to get 40 = l + w.

Now we need to find two numbers whose sum is 40 and product is 399.

Fitting some random numbers in gives us the numbers 19 and 21 for the length and width.

EXPLANATION

The reason is that

[tex]i^2=-1[/tex]

If we multiply [tex]a+bi[/tex] by its conjugate [tex]a-bi[/tex]

We obtain;

[tex](a+bi)(a-bi)[/tex]

This is difference of two squares so we obtain;

[tex](a+bi)(a-bi)=a^2-(bi)^2[/tex]

This further gives us,

[tex](a+bi)(a-bi)=a^2-b^2i^2[/tex]

Since the [tex]i^2=-1[/tex], we substite to get;

[tex](a+bi)(a-bi)=a^2-b^2(-1)[/tex]

The [tex]i[/tex] is now eliminated and we get,

[tex](a+bi)(a-bi)=a^2+b^2[/tex]

Multiplying a complex number by its conjugate eliminates the imaginary part because [tex]\(i^2\)[/tex] equals -1, simplifying to a real number.

Multiplying a complex number [tex]\(a + bi\)[/tex] by its conjugate[tex]\(a - bi\)[/tex] eliminates the imaginary part because of the difference of squares. Let's break it down:

Step 1:

Write the complex number and its conjugate.

[tex]\(a + bi\) and \(a - bi\).[/tex]

Step 2:

Multiply using the distributive property.

[tex]\((a + bi)(a - bi)\).[/tex]

Step 3:

Apply the FOIL method (First, Outer, Inner, Last).

[tex]\((a \times a) + (a \times -bi) + (bi \times a) + (bi \times -bi)\).[/tex]

Step 4:

Simplify the product.

[tex]\(a^2 - abi + abi - (bi)^2\).[/tex]

Step 5:

Notice that the cross terms [tex]\(abi\)[/tex] and [tex]\(-abi\)[/tex] cancel each other out.

[tex]\(a^2 - (bi)^2\).[/tex]

Step 6:

Recall that [tex]\(i^2 = -1\), so \((bi)^2 = -b^2\).[/tex]

[tex]\(a^2 - (-b^2)\).[/tex]

Step 7:

Simplify further to obtain the final expression.

[tex]\(a^2 + b^2\).[/tex]

The resulting expression, [tex]\(a^2 + b^2\),[/tex] is real and has no imaginary component, hence eliminating the [tex]\(i\).[/tex] This process is fundamental in simplifying expressions involving complex numbers.

Answer: OPTION C.

Step-by-step explanation:

1. By defintion the scale factor of the area is [tex]k^{2}[/tex] and this is:

[tex]k^{2}=\frac{A_1}{A_2}=\frac{320}{80}=4[/tex]

2. Then, the scale factor for the sides is:

[tex]k=\sqrt{4}=2[/tex]

3. Now, you must multiply the length and the width of the original rectangle by 2 to obtain the new dimensions. Thefore, you obtain:

[tex]l=10in*2=20in\\w=8in*2=16in[/tex]

Therefore, the answer is the option C.

Answer:

THE ANSWER ISSS OPTION C

Step-by-step explanation:

I GOT IT RIGHT ON EDMENTUM HOPE THIS HELPS YOU OUT ALOT ;0

Answer: The height of the whiteboard is 4 feet and the length of the white board is 8 feet long

Step-by-step explanation:

The height of the whiteboard is 4 feet and since the length on the white board is double the height it would be 8 feet long.

4+4=8

8+8=16

16+8=24

The dimensions of the whiteboard are 4 ft by 8 ft.

To solve this problem, we can use algebra. Let's assume that the height of the whiteboard is x. Since the length is twice the height, the length is 2x. The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

In this case, we are given that the perimeter is 24 ft, so we can write the equation as 24 = 2(2x) + 2x. Solving this equation, we get 24 = 6x. Dividing both sides by 6, we find that x = 4.

Therefore, the height of the whiteboard is 4 ft and the length is 2 * 4 = 8 ft.

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Given that Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale.

Part A:

Let the number of litres of cranberry juice be x, then the total number of liters of the punch is given by x/0.8

Thus, x + 2 = x/0.8

0.8x + 1.6 = x

0.2x = 1.6

Therefore, the equation with one variable that can be used to find the total number of liters of canbelly juice and ginger ale in the punch is: 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.

Part B.

Given from part A that the number of liters of canberry juice in the punch is given by 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.

Therefore, the number of liters of canberry juice in the punch is x = 1.6 / 0.2 = 8 liters of canberry juice.

Answer:

Given that Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale.

Part A:

Let the number of liters of cranberry juice be represented by = x

Then the total number of liters of the punch is given by [tex]\frac{x}{0.8}[/tex]

Now we have [tex]x+2= \frac{x}{0.8}[/tex]  (ginger ale is also added)

Solving this, we get

[tex]0.8x+1.6= x[/tex]

[tex]0.2x= 1.6[/tex]

Further solving we get x = 2

So, the required equation with one variable is : [tex]0.2x=1.6[/tex]

Part B.

From part A we have-

[tex]0.2x=1.6[/tex]

We will find x now, that is liters of cranberry added.

We have x = [tex]\frac{1.6}{0.2}[/tex] = 8

Hence, there is 8 liters of cranberry juice in the punch.

Answer:The number of sweatshirts to sell in order to break even is 40

Step-by-step explanation:

Let x be the number of sweatshirts. We are looking for break even, which means profit is 0 here.

And softball team purchased a box for 240$ and for printing it costs 12$ per shirt.

So total cost of sweatshirts = 240+12x

And selling price is 18$ per shirt.

Hence selling price for x shirts = 18x.

Now we need to graph y=18x and y=240+12x first and then look for intersection to find the break even.

From the graph attached,  we can see that both lines are intersecting at x=40.

Hence number of sweatshirts to sell in order to break even is 40.

Answer:

(x-9)(x-3) which is the same as (x-3)(x-9)

Step-by-step explanation:

Think of ways to factor the last number 27. One way is 1*27 = 27. Another way is 3*9 = 27 and so on. Now think to yourself "which factor of 27 add to -12?". You'll need to consider negative factors. It turns out that

-3 plus -9 = -12

-3 times -9 = 27

Therefore the two values we care about are -9 and -3. So x^2-12+27 factors to (x-3)(x-9). The order of the factors does not matter. So we can write the answer as (x-9)(x-3) just fine.

Pretty sure it's c because when you want to stretch something, you multiply and divide if compressing

Answer:

The weight of the parcel is approximately 6 kilograms.

Step-by-step explanation:

The weight of the parcel is  12 lbs and 8 oz.

1 lb = 16 oz

So,  8 oz = [tex]\frac{1}{2}lb = 0.5[/tex] lb.

That means,  12 lbs and 8 oz = (12 + 0.5) lbs = 12.5 lbs

Now, 1 lb = 454 g

So,  12.5 lbs = (12.5 × 454) g = 5675 g

As,  1 kilogram = 1000 g

That means, 1 g = 0.001 kilogram

So,  5675 g [tex]= (5675 \times0.001) kilograms= 5.675 \approx 6[/tex] kilograms. (Rounded to the nearest whole kilogram)

Thus, the weight of the parcel is approximately 6 kilograms.

Answer:

(-1)^2 = +1

Step-by-step explanation:

(-1)(-1) is equivalent to (-1)^2, and vice versa.  Recall that when two negative numbers are mult. together, the product is positive.  Thus, (-1)^2 = +1.

Based on the definition of the square of a negative number, the result of (-1)² is: 1.

The square of a number represented as "x" can be found by multiplying "x" by itself, expressed as x², where "x" represents the number being squared.

When you square a number, you multiply it by itself. In this case, you are squaring -1.

Calculation:

(-1)² = (-1) * (-1) = 1

So, (-1)² is equal to 1. The negative sign is squared along with the number, resulting in a positive value.

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Answer:

8 months.

Step-by-step explanation:

We have been given that Carrie borrows $960 interest-free to pay for a car repair. She will repay $120 monthly until the loan is paid off.

To find the number of months, it will take to pay off the loan, we will divide total amount of loan by monthly payment.

[tex]\text{Months to pay off the loan}=\frac{960}{120}[/tex]

[tex]\text{Months to pay off the loan}=8[/tex]

Therefore, it will take Carrie 8 months to pay off the loan.

Hii!

__________________________________________________________

Answer:

4(x+3)

Step-by-step explanation:

In this example, both terms, 4x and 12, have something in common. In math, this is known as the greatest common factor (g.c.f.)

The g.c.f. of 4 and 12 is 4, so that's what I'm going to divide both 4x and 12 by.

Upon doing so, we obtain

x+3

Put parentheses around x+3. You'll see why soon.

(x+3)

Now we put 4 outside the parentheses.

4(x+3)

See, the parentheses indicate that we multiply 4 times both x and 3.

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Hope that this helped! Best wishes

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The factored expression of 4x + 12 is 4(x + 3), applying the highest common factor (HCF) method.

To solve the expression 4x +12, we want to factor it, which means we need to find the highest common factor (HCF) of the terms 4x and 12. In this case, the HCF is 4. Once we identify the HCF, we divide each term of the expression by the HCF, which reduces the expression to simpler terms. For our expression:

4x + 12 = 4(x + 3)

This means the factored form of the expression 4x +12 is 4(x + 3).

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-2(x+14)+1=15

distribute

-2x - 14 + 1 = 15

add 14 to each side

-2x + 1 = 29

subtract one from each side

-2x = 28

divided by -2

x = -14

-2(x+14)+1=5

First, distribute -2 into x and 14.

-2x-28+1=5

Combine like terms.

-2x-27=5

Add 27 to both sides.

-2x=32

Divide both sides by -2.

x=-16

Your answer is -16.

I hope this helps :)

answer is 3/4 because that is 24/32 reduced

Answer: the solution is x<-3 or x>-3

Step-by-step explanation:

i cant tell what is says so ill just give you the formulas

perimiter = Length x 2 + Width x 2

Area = Length x Width.