what similarity statement can you write relating the three triangle in the diagram?​

Answer: 30 is the maximum possible value of y

We'll need the slope formula which is

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\[/tex]

We subtract the y values together, and divide that over the difference in the x values when subtracted in the same order.

Let's find the slope of line DE

[tex]D = (x_1,y_1) = (6,1) \text{ and } E = (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 1}{2 - 6}\\\\m = \frac{2}{-4}\\\\m = -\frac{1}{2}\\\\[/tex]

The slope of line DE is -1/2.

Next, compute the slope of line EF

[tex]E = (x_1,y_1) = (2,3) \text{ and } F = (x_2,y_2) = (-1,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{-1 - 2}\\\\m = \frac{-6}{-3}\\\\m = 2\\\\[/tex]

The slope of line EF is 2.

Lastly, compute the slope of line FD

[tex]F = (x_1,y_1) = (-1,-3) \text{ and } D = (x_2,y_2) = (6,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-3)}{6 - (-1)}\\\\m = \frac{1 + 3}{6 + 1}\\\\m = \frac{4}{7}\\\\[/tex]

The slope of line FD is 4/7.

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

To recap everything so far, we found the following:

The product of the first two slopes gets us (-1/2)*(2) = -1 showing that DE is perpendicular to EF.

Perpendicular slopes multiply to -1 as long as neither line is vertical nor horizontal.

Since DE is perpendicular to EF, this proves we have a 90 degree angle at point E.

Therefore triangle DEF is a right triangle.

The step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomials.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

The polynomial that Omar is dealing with is:

[tex]3x^3 - 15x^2 -4x + 20[/tex]

We see that 3 times 5 = 15 and 4 times 5 = 20, so trying in that way:

[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5)[/tex]

Taking out a negative factor from second term would make the binomials same, after which we can take that common out, as shown below:

[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5) \\3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) -4(x-5) \\3x^3 - 15x^2 -4x + 20 = (x-5)(3x^2-4)[/tex]

It successfully got factored, thus not a polynomial.

Thus,the step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.

Learn more about prime polynomials here:

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Answer: Omar should factor out a negative from one of the groups so the binomials will be the same.

Step-by-step explanation: Answer on edge

200 times 40000 is 8000000.

       200

x 40000

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

8000000

Answer: 8,000,000

Step 1: Multiply by smaller parts.

2 x 4 = 8

Step 2: Add all the zeros.

8,000,000

Answer = 8,000,000

Hope this helps!

Answer:

x = 9/5 = 1 4/5

Step-by-step explanation:

5x - 6 = 3

    +6   +6

(add positive 6 to the negative 6 = - 6 + 6 = 0, and to the answer = 3 = 3 + 6 = 9)

5x = 9

÷5   ÷5

x = 9/5 (improper fraction)

= 1 4/5 (mixed numeral)

Hello.

First, let's add 6 to both sides:

[tex]\tt{5x-6+6=3+6}[/tex]

[tex]\tt{5x=9}[/tex]

The next step is to divide both sides by 5:

[tex]\tt{x=\displaystyle\frac{9}{5}[/tex] (Improper fraction)

[tex]\tt{x=\displaystyle1\frac{4}{5}[/tex] (Mixed number)

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

Answer:

12$

Step-by-step explanation:

he worked from 1:45-4:45 wich means he worked 3 hours,then 3 hours *4$ =12$

Answer:

12 dollars

Step-by-step explanation:

Hello!
To solve this question, we understand that:
- the rate at which he earns money is 4 dollars an hour.

-if we find how many hours elapsed between 1:45pm-4:45pm, it is three hours which means he has worked for three hours
(4:45pm-1:45pm=3:00 hours)

Knowing this equation, we must figure out how much he earns during this time frame, 3 hours.

Since we know that the rate is 4 dollars an hour and he has worked 3 hours, let's multiply 4 times 3 (or add 4 three times 4+4+4) to get 12 dollars he has worked during this time.

Answer:

Ans of a = 18x

Ans of b = 3.111

1 cm..............2 km               = scale of the map

2,85 cm....... n km              = to be calculated

n x 1 = 2 x 2,85

n = 5,7 km

Step-by-step explanation:

1cm rep 2km

2.85x2

=5.7

=5.7km

Answer:

[tex]\frac{13}{12}a\\[/tex]

Step-by-step explanation:

[tex]\frac{a}{3} + \frac{3a}{4}= \frac{13}{12}a[/tex]

Answer:

the answer is 13a/12 simplified

Answer:

He needs to read 14 pages on Thursday to finish the book

Answer:

A factor of 0.2

Step-by-step explanation:

If we multiply 2.5 by 0.2, we get 0.5, the width of the smaller rectangle.

Answer:

22.5 weeks

Step-by-step explanation:

Answer:

14 ft.

Step-by-step explanation:

First, we will assign variables to each value. If height is h, and base is b, then

1/2bh = 112 and h=b+2.

We will use substitution in this system of equations. first, we will isolate the b in bh/2=112. To do this we will multiply both sides by 2 to isolate the variables, so bh=224. Then, to isolate just one variable, in this case, b, we will divide 224 by h, getting us b=224/h.

Then, we will substitute b for this value in h+2=b, leaving us with h+2=224/h

Then isolate the variable. h will equal either -14 or 16. Because this is a geometric shape, the value of its sides cannot be negative, so it has a height of 16.

Then, plug this into the second equation. If the height is 2 ft more than the base, then the base will be 14 ft.

Answer:

$11.70

Step-by-step explanation:

X= starting amount ($200)

R= interest rate (6%)

Y= years (6)

simple interest= [tex]X(1+ r^{y} )[/tex]

compounded interest= [tex]X(1+r)^{y}[/tex]

Answer:

± i [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the result that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-2}[/tex]

= ± [tex]\sqrt{2(-1)}[/tex]

= ± [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]

= ± [tex]\sqrt{2}[/tex] × i

= ± i [tex]\sqrt{2}[/tex]

Answer:

Reflections, rotations, and translations produce an image that is congruent to the pre-image. Sequences of those transformations produce congruent images.

Answer:

A

Step-by-step explanation:

The answer is circle because if you slice a cone parallel to the base, the cross section is circle

A Right Cone is sliced parallel to its base the resulting shape is Circle.

A cone is a" three dimensional shape consisting one circular shape and once continuous curved surface tapering to a point".

According to the question,

A right cone is slice parallel to its base.

In order to find the resulting shape. When a right cone is sliced parallel to its base it results Circle.

Hence, right Cone is sliced parallel to its base the resulting shape is Circle.

Learn more about Cone here

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[tex] = \frac{7}{8} \div \frac{1}{4} [/tex]

[tex] = \frac{7}{8} \times \frac{4}{1} [/tex]

[tex] = \frac{(7 \times 8)}{4} [/tex]

[tex] = \frac{56}{4} [/tex]

[tex] = \frac{56 \div 4}{4 \div 4} [/tex]

[tex] = \frac{14}{1} [/tex]

[tex] = 14[/tex]

Therefore :-

[tex] \frac{7}{8} \div \frac{1}{4} = 14[/tex]

Answer:

7/8 quart

Step-by-step explanation:

Answer:

He should have divided by 4, not 6....

Step-by-step explanation:

Just did the lesson

Abdul have done error by dividing with 6 instead of 5, So Abdul should have divided by 5, not 6 is correct option.

The area of Rectangle is length times of width.

According to the information provided, the initial dimensions of the pool are a rectangle with length 24 feet and width 15 feet.

The corresponding dimensions in the drawing are a rectangle with length 4 feet and width 3.75 feet.

Therefore, the scale factor for the length is:

24/4 = 6

And the scale factor for the width is:

15 feet / 3.75 feet = 4

Abdul wants to fit the pool into a smaller space, so he needs to find the corresponding dimensions of the pool in the drawing that has a length of 20 feet.

To maintain the same scale, he needs to apply the same scale factor to the new length.

Thus, the new length in the drawing is:

20/6 = 3.33 feet

Similarly, he needs to apply the same scale factor to the new width to maintain the same scale.

Thus, the new width in the drawing is:

18.75/4 = 4.69 feet

Now, let's check Abdul's work:

24/6×6/20=4/3

Left side is not equal to right side.

Abdul should have divided by 5, not 6.

Hence, Abdul have done error by dividing with 6 instead of 5, So Abdul should have divided by 5, not 6 is correct option.

To learn more on Rectangles click:

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They paid sales tax on a customer which cost $196.00​ is 75 %.

We have given that,

At a store, 3 cents on every dollar spent is charged as sales tax.

A sales tax is a tax paid to a governing body for the sales of certain goods and services

0.3 multiplied by $196.00

0.3 *196=58.8

$58.8 as sales tax.

Adding that to the $196 dollars

$58.8+$196=$254.80

Therefore total sum and amount of

=$254.80

Therefore, they paid sales tax on a customer which cost $196.00​ is 75%.

To learn more about the sale tax visit:

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Answer:

1

Step-by-step explanation:

You can find slope by the formula

y2-y1 over x2-x1

In this case, 6-5 over -3-(-3) or -3=3

This is equal to 1 over 0 which is 1

Answer:

$110

Step-by-step explanation:

divide 330 by 3

$115 i think..........................

Answer:

32

Step-by-step explanation:

negative times negative = positive

Answer:

You didn't add any options but here is a couple that could work.

3m - 9 + 4

3m - 5

Hope that helps and have a great day!

Answer:

b

Step-by-step explanation:

The solution of the considered system of equation is represented by: Option C: (1,3) and (4,0)

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

For the considered case, the system of equations given to us is:

[tex]y = x^2 - 6x + 8\\y = -x + 4[/tex]

Plotting both's graph and finding the common points on both's graph, we get the common points as:

(1,3) and (4,0)

These points satisfy both the equations simultaneously.

Therefore, the solution of the considered system of equation is represented by: Option C: (1,3) and (4,0)

Learn more about solutions to a system of equations here:

https://brainly.com/question/2825832

Answer:

c is correct

Step-by-step explanation: