Simplify.
21. 5t(2)(3)
24. 9(8n)
22. 7(a-b+5)
25. 3k+ 6k-12
23. 9y+ 15y-10y
26. 2t + 5m+7t-4m

The limit of the function [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)] when x tends to 1 is - 3 / 2.

In this problem we must determine the limit of a function, that is, the value to which the function goes when x tends to 1. This can be done by means of limit properties for polynomial and trigonometric limits.

First, write the limit:

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)]

Second, use limit properties and algebra properties:

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 + 3 - 3 · x] / (2 · x - 2)]

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3] / (2 · x - 2)] + [tex]\lim_{x \to 1}[/tex] [(3 - 3 · x) / (2 · x - 2)]

(3 / 2) · [tex]\lim_{x \to 1}[/tex] [[1 - cos (1 - x)] / (1 - x)] + (3 / 2) · [tex]\lim_{x \to 1}[/tex] [(1 - x) / (x - 1)]

Third, use polynomial and trigonometric limits:

(3 / 2) · 0 + (3 / 2) · (- 1)

Fourth, simplify the result:

- 3 / 2

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Answer:

C) 21

Explanation:

The middle column represents the tens place, while the column on the left is the ones place. Range is the difference between the highest number and the lowest number.

The lowest number for road A is 29, the 2 from the middle column and 9 from the left. The largest number is 50, the 5 from the middle column and 0 from the left column.

50 - 29 = 21

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:

  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.

Answer:

2x+y=-4

Step-by-step explanation:

y-2=-2(x+3) is in point-slope form.

Ax+By=C is standard form.

We have to bring x and y to the same side of the equation.

First, let's distribute.

y-2=-2(x)-2(3)

y-2=-2x-6

Next, we will add 2 to both sides to get rid of the -2 on the left side of the equation.

y=-2x-6+2

Then, we will add 2x to both sides to get rid of the -2x on the right side of the equation.

2x+y=-6+2

Now x and y are on the same side of the equation. We just need to simplify the right side.

2x+y=-4

This is the answer in standard form.

Answer:

2x + y = -4

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y-2=-2(x+3)[/tex]

To write the given equation in standard form, collect the terms with variables on the one side of the equation (ensuring the term in x is positive), and collect the constants on the other side of the equation.

Distribute the right side of the equation:

[tex]\implies y-2=-2 \cdot x+(-2) \cdot 3[/tex]

[tex]\implies y-2=-2x-6[/tex]

Add 2x to both sides of the equation:

[tex]\implies y-2+2x=-2x-6+2x[/tex]

[tex]\implies y-2+2x=-6[/tex]

Add 2 to both sides of the equation:

[tex]\implies y-2+2x+2=-6+2[/tex]

[tex]\implies y+2x=-4[/tex]

Rearrange the left side to standard form:

[tex]\implies 2x+y=-4[/tex]

The values of x and y after solving the equations by using elimination method are :- 3 and 1

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method

In the above equations

Multiplying equation 1 with 2 and adding it to equation 2 we get

X= 3

Y=1

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Answer:

11

Step-by-step explanation:

11*11 = 121

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

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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After solving the equation the greatest rate is y=x. therefore, the correct option is D

What does rate in math mean?

In mathematics, the term 'rate' usually refers to a ratio or a comparison between two different values. It is defined as the amount of one quantity with respect to another, and is most commonly expressed as a fraction, with one value being the numerator and the other being the denominator. For example, "the rate of increase" is a comparison between the amount of increase in an item over time, such as the rate of inflation over a period of time. Additionally, the term 'rate' can also be used to describe a rate of change, such as the rate of growth of a population. In this case, the rate of change describes how quickly the population is changing over time.

Given that:

For rate we have to differentiate all the function first

A) y = 3/4x + 1

dy/dx = 3/4

B) y = -x

dy/dx = -1

C) y = 1/2x +2

dy/dx = 1/2

D) y = x

dy/dx = 1

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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

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:

y=1/2x-2

Step-by-step explanation:

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:

the percentage of change is 300%

Step-by-step explanation:

30 times 300% equals 90 more dollars which equals $120

Answer: the first one

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:

11.8 m

Step-by-step explanation:

this makes up a right triangle so we can use the Pythagorean theorem

a^2+b^2=c^2

a- height/leg a

b- length/ leg b

c- hypotheneus

since we are tying to find b we can isolate b^2 on one side of the equation

a^2+b^2=c^2

-a^2.       -a^2

b^2=c^2-a^2

And now we can plug in values

b^2=36^2-34^2

b^2=1296-1156

b^2=140

Square root both sides

b=11.8

Hopes this helps please mark brainliest

Answer: a

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

Answer:

y ≥ 2x + 4

hope this may help!

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.

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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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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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:

Step-by-step explanation:

the adjacent angles are congruent

angle 1 = 51°

the sum of the angles is 360°

51 · 2 + 2 · angle (2) = 360

102 + 2angle(2) = 360

2angle (2) = 360 - 102

2 angle (2) = 258

angle (2) = 258/2

angle (2) = 129°

angle (3) = 129°

A 31.2 foot ladder is required to access an electrical box that is 28 feet up.

Which ratios in trigonometry are there?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

A right-angled triangle is formed by the ladder, the distance from the wall to the ladder's base, and the distance from the ground to the electrical box.

The link between the sides and angles of a right-angled triangle is demonstrated through trigonometric ratios.

If x stands for the ladder's length, then:

28 feet/x for sin(64).

28 feet/sin x = (64)

x = 31.2 ft

Therefore, a 31.2-foot ladder is required to reach an electrical box that is 28 feet up.

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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

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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