simplify the expressions by combining in terms

1) 5h - 4j + 2k

The second coordinate in a two-dimensional coordinate system is the y-coordinate, which indicates the vertical distance from the origin point (0, 0).

Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.

The y-coordinate can be either positive, negative, or zero. The y-coordinate is also referred to as the “ordinate” or the “vertical coordinate”. The second coordinate is usually written as the number located at the top of the y-axis on a graph.

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Yes, an exponential function can have 1 as a base.

An exponential function is a function of the form f(x) = a^x, where a is the base and x is the exponent. The base can be any real number, including 1.

When the base is 1, the exponential function is defined as f(x) = 1^x = 1 for any value of x. This function is a constant function that always equals 1.

It is important to note that when the base of an exponential function is less than 0, the domain of the function is all real numbers except for certain values of x.

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Based on the definition of supplementary angles, the measures of the angles are:

Angle x = 122.5°

Angle y = 57.5°

When two angles gives a sum of 180 degrees when they are added together, then the two angles are referred to as supplementary angles.

For example, if angle x and angle y are supplementary angles, it means that:

Measure of angle x + measure of angle y = 180 degrees.'

Given the following:

The measure of angle x = x degrees

The measure of angle y = x - 65 degrees.

Therefore, we have:

x + x - 65 = 180

2x - 65 = 180

2x = 180 + 65

2x = 245

2x/2 = 245/2

x = 122.5

Thus:

Measure of angle x = 122.5°

Measure of angle y = 180 - 122.5 = 57.5°

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Answer:

A

Step-by-step explanation:

Answer:

m<A is 126 degrees

Step-by-step explanation:

Assuming that the whole entire quadrilateral is 360 degrees, I can say that part A is 126 degrees.

The Poisson probability law states that the probability of at least two changes every day is 0.0263. Thus, 0.0263% of changes happen twice or more each day.

The mathematical method it explains for calculating probability calculates all the probabilities of something occurring in the setting of specific random events. A probability's proximity to the value or, alternatively, its distance from zero can make one less confidence in the outcome. The confidence level is based on how close the probability value is, which is calculated using a number range from 0 and 1.

Here,

calculation

The probability distribution function for X is the average number of times the event happens over a specific period of time.

In this experiment, the frequency, or x, at which an event occurs is counted.

The likelihood of the event happening throughout each period is equal.

The number of occurrences in one period is independent of the number in other intervals.

the first step is to set the discrete random variable X to the number of website content updates.

Let's say that there are on average x content changes every day.

The Poisson probability law states that the probability of at least two changes every day is 0.0263.

Consequently, 0.0263% of changes that occur twice or more

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The volume of top solid is 1570cm³, the volume of bottom solid is 157cm³and the total volume of toy is 1727cm³.

Solids or three-dimensional shapes are defined as any shape or figure with three dimensions or more. Solid geometry is the study of the characteristics, volume, and surface area of three-dimensional shapes.

The toy can be divided into two solids :

The top solid is a cone and the bottom solid is a cylinder.

The total volume of the toy can be found by adding the volumes of the cone and cylinder.

Volume of cone

Length of the cone l= 13cm

The radius of the base of the cone r = 5cm

Height of cone h =  = 12cm

Volume of cone =  =  = 1570 cm³

Volume of cylinder

Radius r = 5cm

Height h = 2cm

Volume of cylinder =  = 157cm³

Therefore the total volume of toy =  1570 + 157 = 1727 cm³

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Answer:

please name the chapter

The number of months that the manufacturer should offer is given as follows:

51.7 months.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 60, \sigma = 5.2[/tex]

The z-score associated with the 5.6th percentile is given as follows:

z = -1.59.

Hence the amount of time is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.59 = \frac{X - 60}{5.2}[/tex]

X - 60 = -1.59 x 5.2

X = 51.7 months.

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Answer: I believe the y-intercept would be -5

Step-by-step explanation: If you recall, we find the slope using y=mx+b, with M being your slope and B being your y-intercept! I hope that was helpful!

Answer:

4x/7 = product of 4 times x divided by 7

2x-5 = five subtracted by two times the product of x

2(x+5) = two times the product of x and 5

4x+7 = the product of 4 times x and 7

3/x-2 = the last one (too lazy to type lol)

Hope this helps! :)

Where the above rectangle has the given dimensions, this means that:

m∠1 = 49°

m∠2 = 41°

m∠3 = 41°

∠ADC = 90°

AB = 7.5

BD = 10

CE = 5

The following are the qualities of a rectangle:

1) Since the diagonals cut one other in half, it means that ΔCEB, ΔAED are congruent isosceles triangles. It also means that ΔAEB and ΔDEC are congruent isosceles triangles.

This means that ∠BCE = ∠CEB

Where ∠AEB = 98°

∠ABE = (180-98)/2

= 41°

Thus, m∠1 = 90- 41°

m∠1= 49°

2 and 3) Given that ΔAEB and ΔDEC are congruent isosceles triangles, and ∠AEB and ∠DEC are opposite angles (which are congruent), that means

∠AEB and ∠DEC = 98°

Thus,

m∠2 and m∠3 =  (180-98)/2 that is

m∠2 and m∠3 = 41° respectively.

4) ∠ADC = 90° (Property of a rectangle)

5) Given an angle and the hypotenuse, we can find AB. Using the law of sines that is:

AB = AC * Sin ∠DAC

Note that ∠DAC ≅ ∠1

Note that AC = 10 (properties of a Rectangle)

Thus

AB = 10 * Sin 49°

AB = 10 * 0.75470958022
AB = 7.5470958022

AB [tex]\approx[/tex] 7.5

6) BD = 10 [Qualities of a Rectangle]
7 ) CE = 5  [Qualities of a Rectangle]

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The y intercept equation will be [tex]y=-2x+3[/tex] .A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

When a straight line is described by the equation "y = mx + b," the slope is the number "m" multiplied on the x, and the y-intercept is "b." (that is, the point where the line crosses the vertical y-axis).

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Answer: $36

Step-by-step explanation:

Bill is $40, the 25% off coupon is used, and the 20% tip is left.

Step 1: Find 25% of 40

is/40=25/100 ------> 40(25)/100=10

Step 2: Find the new bill price after discount

40-10=30

Step 3: Find the 20% tip of 30

is/30=20/100 ---------> 30(20)/100=6

Step 4: Add the tip with the restaurant bill

30+6=$36

Answer:

[tex]I'(-2,-4), J'(-4,4), K'(4,4)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

So on solving the provided question, we can say that in this triangle,

angle B = 90, AC = 13; AB = x 10

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

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here, in this triangle,

angle B = 90

AC = 13

so by Pythagoras theorm

AB = x 10

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The figure is a regular polygon then the value of x is 21.

What is a regular polygon?

A regular polygon is a polygon that has all sides equal and each side subtends an equal interior angle at the center.

The sum of the interior angles of a polygon is

sum = 180° (n - 2)

n is the number of sides

Here n = 12, then

sum = 180° × 10 = 1800°

So the angle subtended by one side at the center is given as follows

Each of the 12 interior angles = 1800° ÷ 12 = 150

Then,

7x + 3 = 150

7x = 147

x = 21

Hence, If the figure is a regular polygon the value of x is 21.

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Therefore , the solution of the given problem of equation comes out to be 0.24(d−c) is the required equation.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

$d dollar purchase price

Selling price = $c

25% commission rate

The difference between the selling price and the purchasing price is the profit.

=Buy price - Selling price =d - C

The commission is the result of the profit and the commission rate.

=> Profit = Commission rate * Profit

=> 24% * (d- c)

=>0.24×(d−c)

=> 0.24(d−c)

​

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Answer:

Pleae see the attached graph.

Step-by-step explanation:

The values of x are graphed for their respective valid regions, as defined in the question.

8.269 feet is the horizontal distance between the wall and the ladder's base.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to the physical length in physics or to an estimate based on other factors in ordinary language (e.g. "two counties over").

The term is frequently used metaphorically to refer to a measurement of the difference between two common pieces (such as statistical distance between probabilistic or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by the distance between people in a social network).

So, using a right-angled triangle's trigonometry:

(x  = required distance)

cos 74 = x / 30      

x = 30 cos 74

x = 8.269 ft

Therefore, 8.269 feet is the horizontal distance between the wall and the ladder's base.

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Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is  36,54 and 90.

A triangle is a three-sided polygon in geometry that has three edges and three vertices. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. Angle sum property of a triangle is the name of this property.

Here,

Using the angle sum property of triangle,

90+4x-16+3x+15=180.( Since its a right angle triangle)

7x+89=180

7x=91

x=13

Therefore, ∠G=4X-16=36 and ∠H=3x+15=54.

Hence, the measure of each angle is triangle is 36,54 and 90.

Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is  36,54 and 90.

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The coordinates of the point on the line is (1/2, -27/10)

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

Point A is at (-4,-6) and point C is at (11,5).

Also, we have the ratio of AB to AC to be 3 : 7 i.e. 3/10

The partition involves dividing the line into subsegments

This means that

(x, y) = (-4,-6) and  (11,5).

m : n = 3 : 7

The coordinates of the partition are calculated as:

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

Point = 1/(3 + 7) * (3 * 11 + 7 * -4, 3 * 5 + 7 * -6)

Evaluate the products

So, we have the following representation

Point = 1/10* (5, -27)

Evaluate the quotients

Point = (1/2, -27/10)

Hence, the coordinate of the partition is (x,y) = (1/2, -27/10)

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The coordinates of M´ would be : (4, 1) after reflection across the line y = x.

The coordinates of J'' would be : (3, -1) after counterclockwise about the origin.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The quadrilateral JKLM is shown in the given figure.

As per the given graph, we can see that

The coordinates of M would be : (4, 1)

Suppose quadrilateral J´K´L´M´ is a reflection of JKLM in the line y = x.

Then the coordinates of M´ would be : (4, 1)

The coordinates of J would be : (1, 3)

Suppose quadrilateral J''K''L''M'' is a rotation of JKLM 90° counterclockwise about the origin.

Under a counterclockwise rotation about the origin of  90 degrees

A coordinate ( x, y ) → ( y, - x ),

The coordinate J is (1, 3) and is translated using the rule

Then simply plug in the values of x and y which are x = 1 and y = 3

Thus (1, 3) → (3, -1)

Thus, the coordinates of J'' would be : (3, -1)

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Answer:

10

Step-by-step explanation:

using the distance formula

The maximum number of air hockey games that can be played out of the $100 game card at Dave & Buster's is 50.

With a $100 game card, the maximum amount of times to play air hockey is found thus;

After 2 rounds of ski-ball at the cost of $2 per game = $4

After 3 rounds of Dance Dance Revolution at the cost of  $2.50 per game = $7.50

If air hockey costs $1.75 per game, then;

$4 + $7.50 = $11.50

$100 - $11.50 = $88.50

Therefore $88.50/$1.75 = 50.5 approximately 50 times.

It will take 50 times to use up the rest of the $88.50 left from the $100 game card if air hockey costs $1.75.

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Answer: We can write a system of equations to model this scenario using the information given.

Let x represent the number of children who played minigolf that day, and let y represent the number of adults who played minigolf that day.

The first equation represents the total number of customers, which is the sum of the number of children and the number of adults.

x + y = 320

The second equation represents the total amount of money earned, which is the product of the number of children playing and the cost per child's game plus the product of the number of adults playing and the cost per adult's game.

7x + 10y = 2900

So the system of equations that models this scenario is:

x + y = 320

7x + 10y = 2900

We can use this system of equations to find the number of children and adults who played minigolf that day, given the total number of customers and total amount of money earned. By solving this system of equations we can find the values for x and y.

Step-by-step explanation:

Answer: It is True

Step-by-step explanation:

The increase in thermal energy allows molecules to decrease their density and escape the liquid state to become gas molecules.

Due to its superior fit when drawn through the points, the regression line is occasionally referred to as the "line of best fit." It is a line that reduces the difference between the actual and anticipated scores.

What does regression line mean?

An estimated linear relationship between two variables, which is known as the real but unobserved linear relationship, is shown by a regression line.

                      A given value for the explanatory variable is used to predict (or estimate) the value of the response variable using the equation of the regression line.

What does the term "regression line" mean?

Regress, which is derived from the Latin verb "regressus" (to go back), is the root of the word "regression" (to something). Regression, in this sense, is a method that enables "going back" from muddled, difficult-to-interpret data to a more understandable and valuable model.

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Answer:

pro

Step-by-step explanation: