What is the numerator of the simplified sum?

StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction

Triangle 1's x value is 8 and LN's length is 14 units. Triangle 2's x value is 8 and IH's length is 11 units. Triangle 3's x value is 9 and CB's length is 23 units. Triangle 4's x value is 11 and its IH length is 11 units.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.

Here,

Since these are similar triangle,

ME=EN

MN=ME+EN

MN=2ME

this will be same for all the triangles,

1. 2x-9/2x-2=1/2

2(2x-9)=2x-2

4x-18=2x-2

2x=16

x=8

LN=2x-2

LN=14 units

2. 2x-5/x+14=1/2

2(2x-5)=x+14

4x-10=x+14

3x=24

x=8

IH=2x-5

=11 units

3. (x+14)/(x+19)=1/2

2(x+14)=x+19

2x+28=x+19

x=9

CB=x+14

CB=23 units

4. 2x-11/x+11=1/2

2(2x-11)=x+11

4x-22=x+11

3x=33

x=11

IH=2x-11

IH=11 units

In triangle 1, The value of x is 8 and length of LN is 14 units. In triangle 2, The value of x is 8 and length of IH is 11 units. In triangle 3, The value of x is 9 and length of CB is 23 units. In triangle 4, The value of x is 11 and length of IH is 11 units.

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Answer:

y-10=   1/2(x-2) --- point slope form

Step-by-step explanation:

Point slope form is:

y- y1=m(x-x1)

y1= 10

m= y2-y1/x2-x1

y2= 6

x2= -10

x1= -2

Using point slope form and defining the variables using the given coordinates, the equation can be written.

Answer:

y-6 = -1/3(x-10)

Step-by-step explanation:

Let's use point slope form! The form of this is y-y1 = m(x-x1) where m is the slope.We have points to use, so let's find the slope.

The slope is rise over run, so we take the difference in y and divide it by the difference in x. This gives us [tex](10-6)/(-2-10)[/tex], which simplifies to -1/3. Now we plug in a point, say (-2, 10) for x1 and y1, and -1/3 for the slope, which gives us y-6 = -1/3(x-10)

Another way you could approach this is to plug in both the points to solve for m. Plug in both the y-values(10, 6) for y and y1 and both the x-values(-2, -10) for x and x1.

This gives us [tex]10-6 = m(-2-10)[/tex], which simplifies to [tex]4 = -12m[/tex]. Dividing both sides by -12 gives m = -1/3, which is the slope. Whichever way makes most sense works!

I hope this helps!

Step-by-step explanation:

remember :

when multiplying terms with the same base, we add the exponents.

when dividing terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator.

when putting exponent on exponent, we multiply the exponents.

a negative exponent means 1/...

e.g. 6^-4 = 1/6⁴

1/6^-4 = 1 / 1/6⁴ = 6⁴

so,

1.

(3^-4 × 3²)/3 = 3^-2 × 3^-1 = 3^-3 = 1/3³ = 1/27 =

= 0.037037037...

2.

(4²)^-1 × 4² = 4^-2 × 4² = 4⁰ = 1

3.

(2^-4 / 2^-2)^-1 = (2^-4 × 2²)^-1 = (2^-2)^-1 = 2² = 4

4.

(3^-3)² / (3²)^-1 = 3^-6 / 3^-2 = 3^-6 × 3² = 3^-4 =

= 1/3⁴ = 1/81 = 0.012345679...

Answer:

It would have saved 445$

Explanation: because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 280$ and the he saved 175$ on the fifth week because 7/8 of 200 is 175 so 280+175 is 445

Step-by-step explanation:

It should be noted that 23.4 is 8.1 percent of 288.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

23.4 is what percent of 288 will be calculated thus:

= 23.4 / 288 × 100

= 8.1%

The percentage is 8.1%.

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Answer:

11

Step-by-step explanation:

11*11 = 121

The probability of at most one team making a Type II error is 0.3651.

1. The probability of a Type II error for a single team is 0.2 (since the power of the test is 0.8).

2. The probability of all 10 teams making a Type II error is 0.2^10. This is because the probability of each individual team making a Type II error is 0.2 and the probability of all 10 teams making a Type II error is the product of the individual probabilities (0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 = 0.2^10).

3. The probability of at least one team making a Type II error is 1 - 0.2^10. This is because the probability of at least one team making a Type II error is the complement of the probability of all 10 teams making a Type II error (1 - 0.2^10).

4. The probability of at most one team making a Type II error is 1 - (1 - 0.2^10). This is because the probability of at most one team making a Type II error is the complement of the probability of at least one team making a Type II error (1 - (1 - 0.2^10)).

5. The probability of at most one team making a Type II error is 0.3651.

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if h(x) = 2x² - 5x + 7

h(-3) = 2(-3)² - 5(-3) + 7

= 18 + 15 + 7

= 40

Answer:

y=1/2x-2

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

The length of the rectangle is found as 7 feet.

For the stated question;

Let the length and the width of the rectangle be 'L' and 'B'.

Then, width is given as;

W = L-2

Area = 35 square feet

A = LW = 35

Put the value of W

L(L-2) = 35

L² -2L - 35 = 0

L² -2L - 35 =0

(L-7)(L+5) = 0

L > 0 so, L=7 is solution

Thus, the length of the rectangle is found as 7 feet.

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The correct question is-

A rectangle is drawn so that the width is 2 feet shorter than the length. the area of the rectangle is 35 square feet. find the length of the rectangle.

Answer:

The machine requires at least 9 hours and 45 minutes to complete the hole on schedule.

Step-by-step explanation:

To find this, you can use the formula provided in the previous response:

(required depth - current depth) / digging rate = hours of digging

Plugging in the values from the problem, you get:

(12.5 feet - 4.75 feet) / (3/5 feet per hour) = (7.75 feet) / (3/5 feet per hour)

This simplifies to:

(7.75 feet) / (3/5 feet per hour) = 15.5 hours

Then, to convert this number of hours to hours and minutes, you can divide by the number of minutes in an hour (60 minutes) and round up to the nearest whole number for the number of hours. The remainder will be the number of minutes:

15.5 hours / 60 minutes/hour = 0.258333... hours

Rounding up to the nearest whole number, you get:

0.258333... hours = 1 hour

The remainder is:

15.5 hours - 1 hour = 14.5 hours

14.5 hours / 60 minutes/hour = 0.241666... hours

Rounding up to the nearest whole number, you get:

0.241666... hours = 0 hours

The remainder is:

14.5 hours - 0 hours = 14.5 hours

14.5 hours / 60 minutes/hour = 0.241666... hours

Rounding up to the nearest whole number, you get:

0.241666... hours = 0 hours

The remainder is:

14.5 hours - 0 hours = 14.5 hours

14.5 hours * 60 minutes/hour = 870 minutes

Therefore, the machine requires at least 9 hours and 45 minutes to complete the hole on schedule.

Answer: the first one

Step-by-step explanation:

...

Answer:

Here,

Given:

Area of a square- 264 sq. cm

To find:

1. The length ( side)

2.Perimeter.

Solution :

Now,

Let the side of the square be x cm.

according to the formula for finding the area of a square:

Area= side× side

264= x× x

264= x^2

√264= x

16.2481= x

16.25= x

hence,

Length= side= 16.25 cm.

Now,

Perimeter of a square:

= 4× side

= 4× 16.25

= 65

Hence,

perimeter of the square= 65 cm

Step-by-step explanation:

I hope I helped you

John has the greater total change in the amount of detergent in their bottle.

Given that, Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L. She fills the cap 314 times in all.

Now, the volume of bottle =314×0.26

= 81.64

≈ 82 L

Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L. He fills his cap 256 times in all.

Here, the volume of bottle =256×0.21

= 53.76

≈ 54 L

Hence, John has the greater total change in the amount of detergent in their bottle.

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The function that has a graph that is parallel to the graph of 2x-y=6 is y = 2x - 8

From the question, we have the following parameters that can be used in our computation:

2x - y = 6

Subtract 2x from both sides of the equation

So, we have the following representation

-y = -2x + 6

Multiply both sides of the equation by -1

y = 2x - 6

Also, from the question;

We have the following points

The point is given as

Point = (3, -2) i.e.  (x, y) = (3, -2)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

The slopes of parallel lines have the same values

This means that the slope of the other line is 2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = 2

(x₁, y₁) = (3, -2)

So, we have

y = 2(x - 3) - 2

Open the brackets

y = 2x - 6 - 2

Evaluate the like terms

y = 2x - 8

Hence, the line has an equation of y = 2x - 8

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Step-by-step explanation:

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

Answer:

y ≥ 2x + 4

hope this may help!

The required answer choice is vertical translation 2 units up and vertical translation 4 units down.

What is translation?

In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the same size as the original shape, and thus the shapes are congruent. They were simply shifted in one or more directions. There is no change in the shape because it is simply moved from one location to another.

The -2 indicates that you need to translate 2 units up, and the -4 indicates that you need to translate 4 units down.

As a result, the answer is vertical translation 2 units up and vertical translation 4 units down.

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Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Slope can be determined by using two points (x1, y1) and (x2, y2) and putting them in rise-over-run format (rise-over-run is equal to slope)

in this case we can use (3, 2) as (x1, y1) and (0, 0) as (x2, y2)

Rise-over-run format is: [tex]\frac{y2 - y1}{x2 - x1}[/tex]

so substitute our number in and you get: [tex]\frac{2-0}{3-0}[/tex]

solve to get: [tex]\frac{2}{3}[/tex]

this is your slope

If the side lengths of triangle are 2 cm, 8 cm, and x cm then the measure of x can be 9 , the correct option is (b) .

In the question ,

it is given that ,

the side lengths of the triangle are 2 cm, 8 cm, and x cm .

we know that the sum of two sides of triangle is greater than the third side ,

So , x < 8 + 2 ,

x < 10 ,

and the difference of two sides of triangle is less than the third side ,

So , 8 - 2 < x

6 < x .

So , the side length x can be ,  6 < x < 10 .

the options that suits the condition is (b) 9 .

Therefore , the correct option is (b) .

The given question is incomplete , the complete question is

A triangle has side lengths of 2 cm, 8 cm, and x cm. Which measure could be the value of x in centimeters?

(a) 6

(b) 9

(c) 10

(d) 12

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Answer:

Step-by-step explanation:

Step 1 Find the slope

1-3/3-(-3)

-2/6=1/3

m=-1/3

Use the point slope formula

y-1=-1/3(x-3)

y=-1/3x+2

Answer: a

Step-by-step explanation:

Answer:

  C.  x² -8x +16 = 20

Step-by-step explanation:

You want the next step in completing the square after you get x² -8x = 4.

The constant in a perfect square monic trinomial is the square of half the coefficient of the linear term.

The coefficient of x is -8. Half that is -4, and its square is (-4)² = 16. This will be the value added to the equation in the second step.

  x² -8x +16 = 4 +16

  x² -8x +16 = 20

__

Additional comment

A monic polynomial has a leading coefficient of 1. We generally work with monic quadratics when completing the square. We do this by factoring the leading coefficient out of the variable terms.

The two points A and B that will be added to produce the complex number -3 + 4i are; -1 + 2i and -2 + 2i.

A complex number is defined as one that has both a real and an imaginary component, whereby both of them are preceded by the letter i which denotes the square root of -1.

Complex numbers are written in the general form; x + iy

Where;

x is the real part.

iy is the imaginary part.

From the graph attached, we can deduce that the two points that were added to obtain the result of -3 + 4i are;

A = -1 + 2i

B = -2 + 2i

Now, let us confirm the sum of the two points A & B;

A + B

= -1 + 2i + -2 + 2i

⇒ -3 + 4i

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Answer: If you are looking for Area, use the formula A=length x width

If you are looking for Perimeter, use the formula P= 2(length x width)

Step-by-step explanation:

So, the Area would be A=12x9 = 108 meters squared (you're multiplying 12 meters and 9 meters, which squares the unit)

and the Perimeter would be P= 2(12x9) = 216 meters

Answer:x>1

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

part of a low is anything lower than 1oo

twice of 1/8 = 2/8 = 1/4

Answer:

25%

Step-by-step explanation:

"twice" means two times.

"twice the value of 1/8" is

2 × 1/8

(to multiply a whole number times a fraction, multiply the big number × the top number)

2 × 1/ 8 is 2/8

2/8 is 1/4.

1/4 = .25 = 25%

Since the answer is a percent, change 1/4 to a decimal, .25, change the decimal to a percent.

Or you could change 1/4 to 25/100. Percent means "per hundred" 25/100 is 25%.

Answer:

2i[tex]\sqrt{6[/tex]

Step-by-step explanation:

So, for right now, ignore the negative. Consider the factors of 24. Both 6 and 4 multiply to 24. This means that [tex]\sqrt{24} = \sqrt{6}[/tex] x [tex]\sqrt{4}[/tex]. [tex]\sqrt{4}[/tex] can simplfy down to just 2. Now let's remember the negative. When taking a negative square root, you need to add an 'I' to the number you take out of the root. So right now you have 2i. Then [tex]\sqrt{6}[/tex] does not have any additional square roots to take out. So your final answer is 2i[tex]\sqrt{6[/tex].

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