Geometric Transformations

In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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Answer:

-------------------------------

Total hours worked is x + y.

Earning from the part time job is 24x, from the internship is 12y.

Inequality for the number of hours:

Inequality for the earning:

This can be simplified by dividing all terms by 12:

Answer:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

Step-by-step explanation:

Part-time job

Internship

The student needs to work less than 15 hours a week:

[tex]\implies x+y < 15[/tex]

The student needs to earn at least $240 a week:

[tex]\implies 24x+12y \geq 240[/tex]

Therefore, the system of inequalities is:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

The second inequality can be simplified by dividing each term by 12:

[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]

[tex]\implies 2x+y \geq 20[/tex]

Therefore, a second system of inequalities is:

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

To solve the system of equalities, graph both inequalities and shade the overlapping region.  

Any (x, y) point in the overlapping region is a solution to the system of inequalities.

The standard form of the expression is [tex]0.000286 \times 10^a[/tex].

What is a standard form?

A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.

The given expression is

              [tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]

Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].

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The algebraic expression for "The room capacity does not exceed 250" is D. c≤250

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

It should be noted that "the room capacity does not exceed 250" simply means it should be less than or equal to 250. This will be c≤250.

In conclusion, the correct option is D.

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The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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Answer:

Step-by-step explanation:

You want to know the measure of angle 1 given that angle 2 is four times angle 1, and their sum is 95°.

The angle sum theorem tells you the whole is equal to the sum of the parts.

  ∠1 +∠2 = ∠WXZ

Using the given information, we can write ...

  ∠1 + (4×∠1) = 95°

  5×∠1 = 95° . . . . . . . . collect terms

  ∠1 = 19° . . . . . . . . . divide by 5

Then angle 2 is ...

  ∠2 = 4×∠1 = 4×19°

  ∠2 = 76°

6/7

Step-by-step explanation:

1 - x = 1/7

- x = 1/7 - 1

- x = 1/7 - 7/7

- x = -6/7

x = -(-6/7)

x = 6/7

thus,

1 - 6/7 = 1/7

First, state the null and alternate hypothesis for the hypothesis test

H0:p=0.52

Ha:p≠0.52

z=pˆ−p/√p(1−p)/n

z= pˆ−p divided by the square root of p(1−p) divided by the sample (n)

z= 0.49^-0.52/ √0.52 ( 1- 0.52) / 340 = -2.24

z=-2.24

When using rejection regions, we reject the null hypothesis, H0, if:

z<−zα for a left-tailed test

z>zα for a right-tailed test

|z|>zα/2 for a two-tailed test

Thus the decision rule is: Reject the null hypothesis, H0, if |z|>2.33.

Since the absolute value of the z test statistic, 2.24, is less than the critical value, 2.33, we fail to reject the null hypothesis.

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A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

If the age is expressed as a ratio, such as p:q, then qx and px are taken into account as the age. If you assume that you are x years old now, then n times that number is (xn) years. If you're assuming that x is the current age, then 1/n of that number will equal (x/n) years.

calculation

Let's say there is an age difference of x and y,

in which case the answer to question 28 should be 2.03 years:

(x-y)*60/100.

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

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The volume of the rectangular block in this problem is given as follows:

1300 cm³.

The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:

V = length x width x height.

The dimensions for this block are given as follows:

However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:

Hence the volume of the rectangular block can be calculated as follows:

V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.

(total volume subtracted by the removed volume from the empty space at the middle).

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The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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Answer: B

Step-by-step explanation:

vertical angles are =

Answer: B

Step-by-step explanation:

Answer: The answer is D. 2 | 0.25

Step-by-step explanation:

I don't really have a good explanation, but I hope it helps!

Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.

Answer:

24

Step-by-step explanation:

True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.

When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.

                   While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.

When there is no association in a correlational analysis, what happens?

The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.

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Answer:18 1/8

Step-by-step explanation:

5x3=15

5x5/8=25/8=3 1/8

15+3 1/8=18 1/8

The glide reflection that maps ABC to A'B'C' is given as follows:

The glide reflection is a combination of a reflection with a translation.

The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.

The midpoint of segment A'B' is given as follows:

The slope of this segment is given as follows:

m = (-6 - (-2))/(6 - 4) = -1.

Then the slope of the reflection line is of:

m = 1.

(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).

Then:

y = x + b.

When x = 5, y = -4, then the intercept b is calculated as follows:

-4 = 5 + b

b = -9.

Thus the reflection line is of:

y = x - 9.

Then the translation is given subtracting the coordinates of one of the vertices, as follows:

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The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.

What is a sphere?

The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.

Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.

The radius of a sphere is the half of its diameter.

The radius of the bottom ball is 3/2 feet =1.5 feet

The radius of the middle ball is 2/2 feet = 1 feet.

The radius of the top ball is 1/2 feet = 0.5 feet.

The volume of a sphere is 4/3 × ∏r³.

The volume of  bottom ball is  4/3 × ∏ × (1.5)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (1)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (0.5)³  cubic foot.

The total amount of snow is

4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³

=  4/3 × ∏ [1.5³  +1³  + 0.5³ ]

=  4/3 × ∏× 4.5

= 18.84

≈ 19 cubic foot

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Answer:

4th one

Step-by-step explanation:

Hope that helps.

In 3 hour  Mr. Reed can presents 15 presentations.  The division equation and a multiplication equation are 3 ÷ 1/5 =15 and 3 × 5 = 15 respectively.

What is an equation of division?

Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety. The division operator and the numbers that are being divided will both be on one side. The other side displays the result of the division.

The 3 large rectangles represent the 3 hours.

Each presentation is 1/5 hour so each rectangle is divided into 5 equal sections.

From the model you can write the division equation: 3 ÷ 1/5 =15

You can also write the multiplication equation: 3 × 5 = 15

Both equations show 15 projects are presented in 2 hours.

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Answer: C

Step-by-step explanation:

It should be 5 x 3, considering that rows come before the columns.

Proof of ray BC is the angle bisector of angle ABA' is given.

Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.

A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.

Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.

Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.

Therefore, <A'B'C' = <ABC

by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.

Therefore, the ray BC is the angle, bisector of angle ABA'.

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The true statements about the image of the parallelogram are,

The corresponding sides have different lengths.

The parallelograms are congruent.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A parallelogram in a coordinate plane is translated, rotated, and then reflected.

In the case of translation, rotation and reflection would only change its coordinate points, and the preimage and image will be congruent.

The coordinate points of the vertices would only change if given.

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Answer:

None of these

Step-by-step explanation:

[tex]\frac{1}{4}+\frac{1}{2} \cdot \frac{4}{7}=\frac{1}{4}+\frac{4}{14}=\frac{1}{4}+\frac{2}{7}=\frac{7+8}{28}=\frac{15}{28}[/tex]

Answer:

Option 3:  the function that goes through the point (3, 5) is f(x-5)-1

Step-by-step explanation:

To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).

For option 1, f(x-5)+1, we have:

f(3-5)+1 = f(-2)+1 = 6+1 = 7

For option 2, f(x+5)-1, we have:

f(3+5)-1 = f(8)-1 = ?

For option 3, f(x-5)-1, we have:

f(3-5)-1 = f(-2)-1 = 6-1 = 5

For option 4, f(x+5)+1, we have:

f(3+5)+1 = f(8)+1 = ?