Identify the function as a translation, compression, stretch, or reflection of the parent function, ƒ(x) = x^4.
ƒ(x) = (x − 2)^4 + 1

A. translation
B. compression
C. stretch
D. reflection

The sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let us assume: 3 consecutive integers are x, x+1 , x+2.

on adding these three numbers we get,

x + x+1 + x+2 = 3x + 3

which can be further reduced to the form 3(x+1).

If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.

1+2+3=6

2+3+4=9

3+4+5=12

4+5+6=15

5+6+7=18

Thus , the sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.

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The linear equation of the given line on the graph is y = -1/2 + 5

A linear equation is an algebraic equation of the form y=mx+b.

where m is the slope and b is the y-intercept.

We have a graph.

We can see that the graph has two points:

(0, 5) = (a, b) and (4, 3) = (c, d)

The slope m is given by:

m = (d - b) / (c - a)

m = -2 / 4

m = -1/2 ,b = y-intercept

The y-intercept is at y = 5

b = 5

The linear equation is: y = mx + b

y = (-1/2) + 5

y = -1.2 + 5

Thus the linear equation of the given line on the graph is

y = -1/2 + 5

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Answer:

[tex]x\textdegree = 120\textdegree[/tex]

Step-by-step explanation:

Because alternate exterior angles (of a transversal that intersects parallel lines) are congruent, the bottom left interior angle of the triangle is 55º.

Using this information, we can solve for the bottom right interior angle of the triangle (denoted θ) by setting the sum of the measures of the triangle's interior angles to 180º.

[tex]55\textdegree + 65\textdegree + \theta = 180\textdegree[/tex]

↓ subtract 55º and 65º from both sides

[tex]\theta = (180-55-65)\textdegree[/tex]

↓ simplify

[tex]\theta = 60\textdegree[/tex]

Now that we have the measure of the triangle's bottom right interior angle, we can solve for xº because an interior angle of a triangle and its corresponding exterior angle are supplementary (their angle measures add to 180º).

[tex]\theta + x\textdegree = 180\textdegree[/tex]

↓ plug in the solved value for θ

[tex]60\textdegree + x\textdegree = 180\textdegree[/tex]

↓ subtract 60º from both sides

[tex]x\textdegree = (180 - 60)\textdegree[/tex]

↓ simplify

[tex]x\textdegree = 120\textdegree[/tex]

For a triangle to be equilateral all its angle should be same which is 60° but for them to be congruent their sides should also be same in measure.

Therefore two equilateral triangles are not always congruent with one another as because there can be difference in the measure of their sides.

The sum of angles of a triangle is 180 degree  which is the sum of angles of the triangle's three angles.

There are three types of triangles based on different aspects .

Based on the lengths of their sides, triangles can be classified as

As in an equilateral triangle all of the sides are of the same length. and all the angle measure will be 60 degrees. An equilateral triangle is also known as an equiangular triangle since its angles are all the same.

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The required values are x = 12 and y = -3 solution to the given system of equations.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The system of equations is given as:

2x + 7y = 3 ....(i)

x = -4y    ....(ii)

Substitute the value of x = -4y in the equation (i), and solve for y

2( -4y) + 7y = 3

-8y + 7y = 3-y = 3

y = -3

Substitute the value of y = -3 in equation (ii), and solve for x

x = -4(-3)

x = 12

Thus, the solutions are x = 12 and y = -3.

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Answer:

Step-by-step explanation:

Example:

If you have the inequality 3<(x/9)+7

Begin with subtraction by subtracting 7 from both sides, rather than beginning with the parentheses x/9.

Do all processes to both sides of the inequality until you have solved for x.

Example: As mentioned in the previous step, you would begin by subtracting 7 from both sides.

So 3<(x/9)+7 becomes, -4<x/9

Now you would multiply both sides by 9 because the fraction x/9 is the same as x divided by 9, and the opposite of division is of course multiplication.

This process leaves you with the solution, -36<x, so x is greater than -36.

Remember that if your problem requires you to multiply or divide by a negative number, then you need to flip the inequality sign when you do so.

For example: If instead of multiplying by 9 in the previous problem you had to multiply by -9, you would get 36>x rather than 36<x.

The median of this set of scores 19,5/12,10 and 14 is 12.

To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.

In this case, the scores are 5/12, 10, 14, and 19.

After arranging the scores in numerical order, we have 5/12, 10, 14, and 19.

There are four scores in this set, so the median is the average of the two middle scores, which are 10 and 14.

The median of the set is: (10 + 14) / 2 = 12.

The median of this set of scores is 12.

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Answer: No triangle lengths have to add all three length together to equal 180 like 60 60 60 or 90 80 10

Step-by-step explanation:

Answer:

There are an infinte amount of whole numbers

Step-by-step explanation:

7 examples are, 0, 3, 7 , 8 ,9 14, 39

The equation of variation for the given situation is y = 5x.

In mathematics, a direct proportion is a comparison of two integers where the ratio of the two numbers equals a constant value. According to the concept of proportion, two ratios are in proportion when they are equal.

If a varies directly to b then the relation between them can represent as

=> a ∝ b  

=> a = kb      [ where 'k' is proportionality constant]

Here we have

y varies directly as x, this can be shown as

=> y ∝ x  

=> y = kx ---- (1)     [ Where 'k' is proportionality constant ]

Given that y = 0.1 and x = 0.5

Substitute the above  values in (1)

=> 0.1 = k(0.5)

=> k = 0.5/ 0.1

=> k = 5  

(1) => y = 5x  

Therefore,

The equation of variation for the given situation is y = 5x.

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Answer:

1.5

Step-by-step explanation:

Answer: Answer is

Step-by-step explanation:

I don't know how to explain it but I went over it with my teacher and it is

Yes, a 5 year old can typically count to 100.

Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.

Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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Answer: 7/ -8

Step-by-step explanation:

The slope is rise/run

Our two points are (10,9) ( 2,16)

We see that y increased by 7, and the x decrease by 8

So the slope is 7/ -8

Option (A) cos 47° is equal to sin 43°.

What is cos in trigonometry ?

The cos meaning in trigonometry defines the cosine of an angle. This angle is an acute angle in a right angled triangle, which is considered to find the ratios. Thus, cosine of an angle, in a right-triangle, is equal to the ratio of adjacent side of that angle and hypotenuse of the triangle.

What is sin in trigonometry ?

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.

Have given,

cos 47°,

We know that cos x = sin (90 - x),

Thus cos 47° = sin (90 - 47)

cos 47° = sin 43°

Therefore, cos 47° is equal to sin 43°.

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cos 47°,

We know that cos x = sin (90 - x),

Thus cos 47° = sin (90 - 47)

cos 47° = sin 43°

Therefore, cos 47° is equal to sin 43°.

It offers a rich and meaningful environment for the application of spatial and mathematical concepts due to this it is necessary to learn the  concepts of measurement.

Linking the various branches of mathematics together requires measurement. For instance, it offers a rich and meaningful framework for the application of math abilities and spatial concepts. Links between mathematics and other academic areas are also provided via measurement.

It makes comparison easier since we no longer need to locate several items to serve as the reference; instead, we may compare multiple objects by only comparing the numbers of a single established unit.

It offers a rich and meaningful environment for the application of spatial and mathematical concepts due to this it is necessary to learn the  concepts of measurement.

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Using system of linear equations, Amelia spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges

System of linear equations is the set of two or more linear equations involving the same variables. A linear equation can be defined as the equations of the first order, whereby the highest power of the variable in the equation is one.

To solve this problem, we have to write a system of linear equation;

Let;

We can represent the problem with two set of equations as;

x + y = 120 ...eq(i)

x = 3y + 10 ...eq(ii)

From equation 1

x + y = 120

x = 120 - y ..eq(iii)

Put eq(iii) into eq(ii)

120 - y  = 3y + 10

collect like terms

120 - 10 = 3y + y

110  = 4y

y = 110 / 4

y = 27.5 minutes

Put y = 27.5 in equ(i)

x + 27.5 = 120

x = 120 - 27.5

x = 92.5 minutes

She spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges.

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Answer:

3

Step-by-step explanation:

The lower bound of f-g is 41.31 .

The upper bound of f-g is  41.49 .

Given,

A number 'f' rounded to 1 decimal point is Number = 49.2

A number 'g' rounded to 1 decimal point is  Number = 7.8

Now,

The range of f rounded to 1 decimal point is [49.15 , 49.24].

The range of g rounded to 1 decimal point  is [7.75 , 7.84].

So,

Lower bound of f-g = 49.15 - 7.84

Lower bound of f-g = 41.31

Next,

Upper bound of f-g = 49.24 - 7.75

Upper bound of f-g = 41.49

Therefore the lower bound of f - g is 41.31 and upper bound of f - g is 41.49.

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Answer:

Eighth half-hour

Step-by-step explanation:

Given pattern:

Calculate the differences between the number of bows used:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]

Therefore, the pattern for the bows used is:

If the pattern continues:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]

Create a table with the given and found data, and add a cumulative total column:

[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]

If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.

The mean and standard deviation are 50.292 and 10.362 respectively.

The mean is the average of all available data value. And standard deviation is the measure of how far each data value apart from the mean value.

We are given, 7% of item are under 35 and 89% of item are under 63.

Let, M refers to mean, and SD refers to standard deviation.

As per given data, P(x<35) = 35%

P(z<Z1) = 0.07

hence, Z-score= Z1 = -1.4758 [obtained from Z table]

we know that the z-score = (observed value - mean)/ standard deviation

                      Z1 = (x - M)/ SD

       - 1.4758 = (35 - M)/ SD

-1.4758SD = 35 -M ......... equation 1

as per the 2nd condition in the given data

89% of items are under 63

so, X= 63, P(X<63)

hence, the z-score = 1.2265 [ obtained from Z table]

Z2= 1.2265= (X- mean)/ SD

1.2265SD = 63 - M.......equation 2

Solving equation 1 and 2, we get standard deviation = 10.362

                                   Mean value = 50.292

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The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

What is Inequalities of equations ?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things.
p ≠ q means that p is not equal to qp &lt; q means that p is less than qp &gt; q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to q
Different kinds of inequality exist. Important inequities include the following: the inequalities of polynomials
Inequalities in absolute values
Logic-based disparities
Calls made by Hazar = 2370
Calls recieved by Hazar = 1645Let the number of Calls by Huzan be x.
And the number of calls recieved by Huzan be y.
Then the inequalities arex&lt; 2370 and y&gt; 1645
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

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The median of 1,2,3,4,5 is 3.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

Here we have to find the median of 1,2,3,4,5.

Here we can see that there are 5 numbers given

so, n= 5  which is an odd number so we will use the formula for finding the median in the case of the odd number of data.

So, M = 5+1/2 = 3

Thus the median is the 3rd term which is 3.

Therefore, the median of 1,2,3,4,5 is 3.

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The two column proof is written as follows

Statement                              Reason                            

h || g                                        given

j || g                                         given

< 2  ≅  < 1                               Alternate angle theorem

< 1  ≅  < 3                               Corresponding angle theorem

< 1  ≅  < 3                               Transitive property

According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."

hence if < 2  ≅  < 1 and < 1  ≅  < 3,  then < 1  ≅  < 3  

According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.

Two angles are said to be congruent when they are equal to each

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The solution to the system of equations is (4,3). Option C

Generally, To solve this system of equations by graphing, you can start by graphing each equation separately on the same set of axes.

For the first equation, Y = x - 1, you can start by plotting a few points to get a feel for the graph.

, if x = 0, then Y = -1.

If x = 1, then Y = 0.

If x = 2, then Y = 1.

You can continue plotting points like this to get a better idea of what the graph looks like.

For the second equation, y = 1/2x + 1, you can do the same thing. For example,

if x = 0,

then y = 1.

If x = 1,

then y = 1.5.

If x = 2,

then y = 2.

Again, you can plot a few more points to get a better sense of the graph.

Once you have graphed both equations, you can look for the point where the two graphs intersect.

This point will be the solution to the system of equations. In this case, the solution is (4,3), so the correct answer is C.

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The first step in solving the inequality is -12 + 20x ≥ -6x + 9

An inequality can be defined as a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Given the inequality

–4(3 – 5x)≥ –6x + 9

Solving the inequality

⇒-12 + 20x ≥ -6x + 9

Keeping all x on one side it can be written ,

⇒20x + 6x ≥ 12 + 9

Adding both sides,

⇒26 x ≥ 21

divide both sides by 26,

⇒x ≥ 0.80

So, the first step in solving the inequality is -12 + 20x ≥ -6x + 9

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The correct question is :

What is the correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

The z-score 30 points below the mean is -3

The normal distribution of scores has a standard deviation(σ) of 10

Below the mean is (X-μ)=-30

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Z=(X-μ)/σ

Z=-30/10

Z=-3

Therefore, the z-score is -3.

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Using vector calculation and analyzing directions, The answer is 20 miles west from the starting point.

An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

The process of adding two or more vectors together to create a vector sum is known as vector addition.

20 miles to north and 40 miles left .

Using triangle law of vector addition, Distance from point at the location = [tex]\sqrt{20^2 + 40^2}[/tex]

=[tex]20\sqrt 5[/tex] miles.

Now turns left walks 20miles , Using triangle law of vector addition,

distance from point at the location = [tex]\sqrt{(20\sqrt 5)^2 - 20^2}[/tex]

=40 miles from location.

This location is horizontally same from the start point.

So he turns left and walks 20miles again.

distance from point= 40-20

=20 miles west of start point.

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Answer:

In given right angled triangle,

h=30 cm,p=18 cm,b=?

By Pythagoras theorem,

h²=p²+b²

or,b²=h²-p²

or,b²=(30)²-(18)²

or,b²=900-324

or,b=√576

or,b=24 cm

hence, the length of missing side is 24 cm

The equation of the line in intercept form will be x / 1.6 + y / 2 = 1. Then the graph of the line is drawn below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is negative 5/4 and the y-intercept of the line is 2. Then the equation of the line is given as,

y = -(5/4)x + 2

Convert the equations into intercept form. Then we have

y = -(5/4)x + 2

4y = -5x + 8

5x + 4y = 8

x / 1.6 + y / 2 = 1

The condition of the line in the capture structure will be x/1.6 + y/2 = 1. Then, at that point, the diagram of the line is drawn underneath.

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