Help me with simplified expressions of a side length of a triangle, please!

Answer:

  (c)  (-∞, -2) ∪ (-2, 1) ∪ (1, ∞)

Step-by-step explanation:

You want the domain of the given piecewise-defined function.

For x < 2, the function is ...

  [tex]g(x)=\dfrac{x^2+2x}{x^2+x-2}-\dfrac{x(x+2)}{(x-1)(x+2)}=\dfrac{x}{x-1}\quad x\ne\{-2,1\}[/tex]

Both of these exclusions are in the region x < 2, so both must be excluded from the domain.

The log function is defined for all values x > -2, so there are no exclusions in this region.

The domain is (-∞, -2) ∪ (-2, 1) ∪ (1, ∞).

The cost of wrapping both boxes is $0.92.

In three-dimensional space, a prism is a polyhedron where two ends are similar.

Given:

Two boxes need to be wrapped in paper (with no overlap).

Both boxes are in the shape of right rectangular prisms.

Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide.

The surface area of the rectangular prism A,

= 2(1.2 × 0.8 + 1 × 0.8 + 1 × 1.2)

= 5.92 square feet.

Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.

The surface area of the rectangular prism A,

= 2(1.6 × 0.5 + 0.5 × 0.8 + 0.8 × 1.6)

= 4.96 square feet.

The wrapping paper costs $6.79 per 80 square feet.

That means,

unit rate = 6.79 / 80 = $0.08 per square feet.

The cost of wrapping both boxes,

= 5.92 x 0.08 + 4.96 x 0.08

= $0.92

Therefore, the cost is $0.92.

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The correct equation that shows how far (s) Johan is from his destination at the end of 6 hours is option C. 600 - (90 X 6) = s

Johan is driving 90 kilometers every hour and he has been driving for 6 hours, so the distance covered by him is 90*6 = 540 kilometers.

The distance he is away from his destination is the total distance to the destination minus the distance he has covered so far.

That is 600 - 540 = 60 kilometers

So, the equation that shows the distance he is from his destination is -

600 - (90 X 6) = s

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Step-by-step explanation:      

         length of the pole : 15 m

        angle inclined by the wire to the  pole from ground :60 deg

        let the length of wire : x

        therefore

                       sin (angle)  = opposite/hypothesis

                       sin 60 = 15/x

                        √3/2 = 15/x

                         x= 2*15/√3

                         x = 30/√3

                         x = 17.320

the length of the wire is :17 m.

The transformation rule that is used to map the figure to the image is;

Shift the figure by 2 units to the right and then reflect the figure about the line y = -1.5

Looking at the figure which is the top triangle, we can see that it is not in line with the image at the bottom and as such, we need to make it to be in vertical alignment by shifting the figure first of all by 2 units to the right.

When the figure is shifted by 2 units to the right, then it will be in alignment with the image at the bottom and as such we can reflect the figure about the line y = -1.5 to achieve the final mapping that is required.

The transformation rule used will be shifting and reflection

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Answer:

First one is 3^16

Second one is 3^10

Third one is 3^2 * 8^2

Forth one is 3^2/8^2

fifth one is 3^8/3^2

Step-by-step explanation:

Answer:

9 + 9n

Step-by-step explanation:

let 'n' = 'a number'

'more than' implies addition

'product' implies multiplication

9 + 9n

Answer: 9+(1)4=9+r

Step-by-step explanation:

Answer: I believe the answer would be y = 3x.

Step-by-step explanation: I like to start by counting the x-values, then the y-values. Since the y-values are increasing by a constant of 3 and the x-values are increasing by 1, that would technically make the equation y = 3x + 0, but you don't need the 0 in this case. So it's just y = 3x. I hope this helps! :)

It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

What is the Quadratic Equation?

A quadratic equation is a type of polynomial equation that has the general form of ax^2 + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero. The degree of the equation is two, hence the name "quadratic".

x+1/6-y can be rewritten in terms of a,b, and c by using the following equation:

ax + by + c = 0

To get x+1/6-y in the values of a,b, and c we can rewrite the equation as follow:

a = 1, b = -1, c = -1/6

So, x+1/6-y can be written as:

1x - 1y - 1/6 = 0

or

ax + by + c = 0 where a=1, b=-1 and c=-1/6

It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

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The correct option is Option 1 - 3520.

A farmer owns 3520 acres in which three full sections, four half-sections, and two quarter-sections are there.

Three of a farmer's sections were full. Let's say a full section is 640, which is

=3 x 640,

= 1,920.

He had four half portions as well. Divide 640 by two to get 320 (640/2), which is

= 4 X 320

= 1,280.

He had three quarter portions as well. Divide 640 by 4 to create a quarter piece (640/4 = 160)

= 2 X 160

= 320.

Now we have to add all these,

Three full sections       = 1920

Four half-sections        = 1280

Two quarter-sections  = 320

= 1,920 + 1,280 + 320

= 3,520.

Therefore the acres a farmer had is 3520.

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The following question may be like this:

A farmer owns three full sections, four half-sections, and two quarter-sections. How many acres is this?

Refer to the image attached.

The dimensions of the base would be: base: 12 cm ; height : 8 cm

The correct answer is an option (D)

We know that the formula for the volume of a pyramid is:

V = 1/3 × B × h

where B is the base area of the pyramid

h is the height of the pyramid

The shape of the box is a triangular pyramid.

Each box contains 240 cubic centimeters of confetti.

this means, the volume of the box is V = 240 cubic centimeters

Using above formula of the volume of a pyramid,

V = 1/3 × B × h

here V = 240 cubic centimeters and h = 15 centimeters

240 = 1/3 × B × 15

240 = B × 5

B = 240/5

B = 48 square centimeters

The dimensions of the base must be such that the area of the base would be  48 square centimeters.

Here, a pyramid has triangular base.

Using the formula for the area of triangle,

B = 1/2 × base of triangle × height of triangle

48 = 1/2 × base of triangle × height of triangle

base of triangle × height of triangle = 96

for the dimensions Base, 12 cm; height, 8 cm

12 × 8 = 96

Thus, the dimension of the base: base of triangle = 12 cm and the height of triangle = 8 cm

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Answer: ∠1= 53°

∠3, ∠6, ∠7 are all 127°

∠4,∠5,∠8 are all 53°

Step-by-step explanation: 127° and ∠1 are supplementary angles meaning they add up to 180° You subtract 127° from 180° to get 53°.

∠3 and 127°are vertical which makes them equal and both 127°.

∠4 is vertical to ∠1 which makes them equal and both 53°.

∠5 is corresponding to ∠1 so they are equal and both 53°.

∠6 is corresponding to 127° so they are equal and both 127°.

∠7 is vertical to ∠6 so they are equal and both 127°.

∠8 is vertical to ∠5 so they are equal and both 53°.

If the new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams , then the equation best models the situation here is (b) 4(x+9) = 76 .

the number of sensor in the boxes is = 4 ;

let the weight of each of sensors be = x ;

So , in new design the weight of each sensor is increased by 9 grams ,

the new weight of sensor becomes = x + 9  ;

the new weight of 4 sensors will be = 4(x + 9) ;

the total weight of new package is = 76 grams ;

So , the equation representing the situation is (b) 4(x+9) = 76  .

The given question is incomplete , the complete question is

A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally ?

Which equation best models the situation here ?

(a) 4x + 9 = 76

(b) 4(x+9) = 76

(c) 4(9x) = 76

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Answer:

A and B

Step-by-step explanation:

A:  Has a positive slope which will be a positive rate of change

B:  Will have a positive if you turn it into 7 + 3x instead of subtracting

The answer for the given senary expressions is 35₆.

What are senary numbers?

A senary numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.

Now,

To find 2434₆/42₆

2434\(_6\) to base 10

2 \(\times\) 6\(^3\) + 4 \(\times\) 6\(^2\) + 3 \(\times\) 6\(^1\) + 4 \(\times\) 6\(^0\)

2 \(\times\) 216 + 4 \(\times\) 36 + 3 \(\times\) 6 + 4 \(\times\) 1

432 + 144 + 18 + 4 = 598

And: 42\(_6\) to base 10

4 \(\times\) 6\(^1\) + 2 \(\times\) 6\(^0\)

4 \(\times\) 6 + 2 \(\times\) 1

24 + 2 = 26

Then divide 598 by 26

= 23

Then convert 23\(_{10}\) to base 6

i.e. 35₆

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The Standard form of y= 4/9x - 3 is 4x - 9y = 27.

What is standard form of an equation?

The general form of a linear equation, commonly referred to as the standard form, is written as Ax + By = C.

Given equation : y= 4/9x - 3

Taking LCM on both sides

we get, 9y = 4x - 27

Since the standard form of a linear equation is Ax + By = C.

So, we can write it as 4x - 9y = 27

        where A= 4, B = -9 and C= 27.

Hence, the standard form of y= 4/9x - 3 is 4x - 9y = 27.

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The final cost for the tile was $208 − $52 = $156.

208/8 = x/2

8x = 416

x = 416/8

x = 52

The price for the two unopened cases was $52.

Thus, The final cost for the tile was $208 − $52 = $156.

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By finding the intercept between the graphs of the equations, we can see that the solution is (-1, 3)

Here we have a system of linear equations:

3x - y = -6

y = x + 4

To solve the system of equations graphically, w ejust need to graph both equations on the same coordinate axis and find the point where the lines do intercept.

The graph of the system of equations can be seen on the image at the end.

There you can see that the lines intercept at the point (-1, 3), so that is the solution of the system of equations.

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Answer: d=12

Step-by-step explanation:

4(65)+ 4d=308

multiply 65 by 4

260+4d=308

move the constant to the right

4d=308-260

calculate

4d=48

divide both sides

d=12

Each bottle of juice costs $ 1.05 that Sophia bought snacks for her team's practice.

j - The cost of each bottle of juice .

The cost of popcorn - $1.98

The cost of juice 10 * j = 10 j

The total cost = $12.48

So , 1.98 + 10 j = 12.48

10 j = 10.5

j = 1.05

The whole expense a company incurs to produce a specific level of production. On the other hand, the total cost represents the cost of all fixed and variable expenses combined. It displays as TC (total cost). The sum of the two yields the Total Cost (TC). The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost is calculated as follows: (Average Fixed Cost x Average Variable Cost) x Units Produced.

Together, fixed and variable costs make up the overall cost.

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The quantity is a variable is the lowest overnight temperature

In math the term variable is defined as variable is an alphabet which is used to represent the unknown number and this one represents the value.

Here we have know that it rained 0. 5 inches on Tuesday and 0. 2 inches on Wednesday.

And the climate was warmer on Thursday than it was on Friday.

Where the humidity was 15% for 3 days of the week and thus the lowest temperature overnight was 68∘F.

Here we have identified that the temperature is continually falling and it will lead the lowest temperature overnight.

Then the correct option is (c).

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.0175)(6) \implies I = 525[/tex]

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The value of the Population Variance is 25.

Given:

The standard deviation of a population is 5

The mean of a population is 50

The size  of a population is 10

[tex]Variance = (Standard \ deviation)^{2}[/tex]

[tex]Variance = 5^{2}[/tex]

σ = 25.

So, The value of the Population Variance is 25.

Population variance is a metric for gauging how dispersed a set of data points is. It calculates the typical squared deviation from the mean. Therefore, the variance will be smaller if all of the data points are close to the mean than it will be if the data points are dispersed widely.

We are aware that the population variance describes the distribution of data points within a population by averaging the squared distances between each data point and the mean.

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The water depths can be modeled by a sinusoidal function. So the value of period is 18 hours, amplitude is 14.5, maximum is 24, equation of the midline is 10, and minimum is -4.

The tide at an Eastern seaport is at its maximum at 3 a.m.

High tide is 24 ft deep.

Low tide occurs at 9 a.m. with a depth of 4 ft.

We have to determine the period.

Period = time between two consecutive high tides

Period = 2 × Time between high and low tide

Time between 3 a.m. and 9 a.m. is 6 hours.

Period = 2 × 6

Period = 18 hours

We have to determine the Amplitude.

Amplitude = (High - Low)/2

Amplitude = (24 - (-5))/2

Amplitude = (24 + 5)/2

Amplitude = 29/2

Amplitude = 14.5

We have to determine the Maximum.

The maximum tide is 24.

We have to determine the Equation of the midline.

Equation of the midline = (max + min)/2

Equation of the midline = {24 + (-4)}/2

Equation of the midline = (24 - 4)/2

Equation of the midline = 20/2

Equation of the midline = 10

We have to determine the minimum.

The minimum tide is -4.

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The complete question is:

The tide at an Eastern seaport is at its maximum at 3 a.m. High tide is 24 ft deep. Low tide occurs at 9 a.m. with a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight

Find the following and make sure to show work for the midline and amplitude:

period=

Amplitude=

Maximum=

Equation of the midline:

minimum:

The numbers that Austin could choose from are: 80, 100 which have 4, 5, and 10 as their multiples

The numbers between 61 and 107 are:

62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106

we will observe that only 70, 80, 90 and 100 have 10 and 5 as their multiple, amongst which, only 80 and 100 have 4 as their multiple.

Therefore, Austin must choose only the two numbers 80 and 100 which have 4, 5, and 10 as their multiples.

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Greg would need to visit his parents at least 18 times each year to attain gold status. To calculate this, we need to take the minimum flight miles required for gold status (16200) and subtract 900 miles, the round-trip flight distance to visit his parents.

where the value comes from the calculation of 15300 miles. Then, we divide 15300 miles by 900 miles, the round-trip flight distance to visit his parents, and get the answer of 18. Therefore, Greg needs to visit his parents at least 18 times each year to reach gold status.   To be eligible for gold status, one must fly a certain amount of miles within a year.

For the airline company that Greg is using, the minimum flight miles required for gold status is 16200. Since Greg is taking a 900-mile round-trip flight to visit his parents, he needs to make up the difference in order to reach the minimum required flight miles. Thus, he needs to visit his parents at least 18 times each year to ensure that he meets the required flight miles for gold status.

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The example of adjacent angles that are complementary and those that are non-complementary are given as attached.

When two adjacent angles have a similar vertex and side, they might be complementary or supplementary angles.

If the total of neighboring angles equals 90 degrees, then they are complementary. If the total of neighboring angles equals 180 degrees, they are complementary to one another.

Non-adjacent Complementary Angles: Two angles that are not next to each other are non-adjacent complementary angles. AOB and XOY are non-adjacent angles since they share neither a vertex nor an arm. They also add up to 90°. As a result, these two angles are non-adjacent complimentary.

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