Which expressions are equivalent to -56Z +28?

The equation of the line parallel to the line is y = -4x + 10

The equation of the line perpendicular to the line is y = 1/4x +3/2

Using the point (1, 6) and (2, 2) on the line to get the slop:

Slope = 2-6/2-1

Slope = -4/1

Slope = -4

The equation is written in point slope form as y-y0 = m(x-x0)

Substitute a point and the given slope for the equation parallel to the line

y - 2 = -4(x-2)

y - 2 = -4x + 8

y+4x = 10

Hence the equation of the line parallel to the line is y = -4x + 10

The needed slope for the perpendicular line is 1/4.

Substitute a point and the given slope for the equation parallel to the line

y - 2 = 1/4(x-2)

4(y - 2) = x - 2

4y - 8 =x -2

4y = x + 6

y = 1/4x + 3/2

Hence the line perpendicular to the line is y = 1/4x + 3/2

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The following question may be like this:

write an equation of the line that passes through the given points and is perpendicular to the given line.

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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After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-4, -5) and (2, -4). Therefore, option C is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(5, -4) and N(4, 2).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(5, -4) →M'(-4, -5)

N(4, 2) →N'(2, -4)

Therefore, option C is the correct answer.

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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 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:

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: ∠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°.

Answer:

20

Step-by-step explanation:

10$ by lisa

10$ by joe

so, 20$ money did lisa and joe put towards the gift

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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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 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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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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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.

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 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?

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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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 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 symmetries of a rectangle and those of a rhombus are not the same, as the rectangle has two additional symmetries.

A rhombus is a quadrilateral with all sides of equivalent length, and it has the accompanying symmetries:

Identity symmetry: The rhombus stays unaltered when reflected about its center.

Rotational symmetry: The rhombus stays unaltered when pivoted 180 degrees about its center.

Reflective symmetry: The rhombus stays unaltered when reflected about its two diagonals.

These symmetries structure a gathering under the operation of the organization of symmetries. A gathering is a bunch of components with a twofold operation (for this situation, the creation of symmetries) that fulfills the cooperative, identity and converse properties.

The arrangement of symmetries of a rhombus fulfills these properties, making it a group.

The Cayley table for the symmetries of a rhombus is as per the following:

E R1 R2 R3

R1 E R3 R2

R2 R3 E R1

R3 R2 R1 E

Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one diagonal, and R3 addresses the symmetry about the other diagonal.

Then again, the symmetries of a rectangle are:

Identity symmetry: The rectangle stays unaltered when reflected about its center.

Rotational symmetry: The rectangle stays unaltered when pivoted 180 degrees about its center.

Reflective symmetry: The rectangle stays unaltered when reflected about its two vertical and two horizontal axis.

The Cayley table for the symmetries of a rectangle is as per the following:

E R1 R2 R3 R4

R1 E R3 R2 R4

R2 R3 E R1 R4

R3 R2 R1 E R4

R4 R4 R4 R4 E

Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one vertical axis, R3 addresses the symmetry around one horizontal axis and R4 addresses the symmetry about the two diagonals.

We can see that the arrangement of symmetries of a rectangle and those of a rhombus are not something similar.

The rectangle has two additional symmetries, the symmetry around one vertical and one horizontal axis, which are not present in the rhombus.

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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: 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

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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On soloing the provided question, we can say that an equation from the graphs for the function. 3x + 13.5y = 4.5 and x+1.5y = 2

Mathematicians use graphs to logically represent or chart facts or values. Typically, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, or vertices, and edges. The nodes, also known as vertices, should be joined with glue. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 4, and 2.5. (3.5). (4.5). Graphical depictions of exponential growth in statistical charts (bar charts, pie charts, line charts, etc.). triangle-shaped logarithmic graph.

an equation for the function.

3x + 13.5y = 4.5

and x+1.5y = 2

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395 gallons will contain 1,495.075 L of water.

A gallon is a unit of liquid measure equal to eight pints. It is approximately 4.546 litres in the United Kingdom.

It is about 3.785 litres in the United States.

To convert litres to gallons, for example, a quart is somewhat less than a litre and 4 litres is slightly more than 1 gallon. 1 litre equals 0.264 gallon (a little more than a quart), and 4 litres equals 1.06 gallon.

One US gallon is approximately 3.79 litres;

one imperial gallon is approximately 4.55 litres.

The dry gallon in the United States is roughly 4.41 litres. As a result, one gallon, regardless of kind, is always larger than one litre.

One gallon contains 3.785 L of water,

Hence 395 gallons will contain 3.785395 3.785×395 Liters of water,

ie, 3.785395 = 1,495.075 L of water.

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Answer:

  2.6 km

Step-by-step explanation:

You want the total distance from Tracey's house to John's house to school, and back again, when the distance from Tracey's to John's is 0.5 km, and the distance from John's to school is 0.8 km.

The total distance will be the sum of the parts:

Total distance = (0.5 +0.8 +0.8 +0.5) km = 2(0.5 +0.8) km = 2(1.3 km)

  = 2.6 km

Tracey rode 2.6 km altogether.

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! :)

Refer to the image attached.

Answer:

Okay so 6,0 3,1 4,1 and 0,2

Step-by-step explanation:

    So take 3,1 you would go over 3 on the x axes and up 1 on the y axes

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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